Survey of prognostics methods for condition-based maintenance in engineering systems

Surv ey of prognostics metho ds for condition-based main tenance in engineering systems Ehsan T aheri 1, ∗ , Ily a Kolmanovsky 2 Dep artment of A er osp ac e Engine ering, University of Michigan, Ann A rb or, MI 48105, USA Oleg Gusikhin 3 F or d R ese ar ch & A dvanc e d Engine ering Abstract It is not surprising that the idea of eﬃcien t maintenance algorithms (originally motiv ated b y strict emission regulations, and no w driv en b y safety issues, logistics and customer satisfaction) has culminated in the so- called condition-based main tenance program. Condition-based program/monitoring consists of t wo ma jor tasks, i.e., diagnostics and pr o gnostics eac h of whic h has provided the imp etus and tec hnical challenges to the scien tists and engineers in v arious ﬁelds of engineering. Prognostics deals with the prediction of the remaining useful life, future condition, or probability of reliable op eration of an equipmen t based on the acquired condition monitoring data. This approach to mo dern maintenance practice promises to reduce the do wntime, spares in ven tory , maintenance costs, and safety hazards. Giv en the signiﬁcance of prognostics capabilities and the maturit y of condition monitoring technology , there ha ve b een an increasing n umber of publications on machinery prognostics in the past few years. These publications cov er a wide range of issues imp ortan t to prognostics. F ortunately , improv emen t in computational resources technology has come to the aid of engineers b y presen ting more pow erful on b oard computational resources to mak e some aspects of these new problems tractable. In addition, it is possible to ev en leverage connected v ehicle information through cloud-computing. Our goal is to pro vide a rep ort on the state of the art and to summarize some of the recent adv ances in prognostics with the emphasis on mo dels, algorithms and tec hnologies used for data pro cessing and decision making. Keywor ds: Prognostics and health managemen t (PHM), Condition-based maintenance (CBM), Remaining useful life (R UL), Automotive, Aerospace and Marine engineering ∗ Corresponding author Email addr esses: etaheri@umich.edu (Ehsan T aheri ), ilya@umich.edu (Ily a Kolmano vsky ), ogusikhi@ford.com (Oleg Gusikhin ) 1 Research fellow, Departmen t of Aerospace Engineering, 1320 Beal Aven ue, Ann Arb or, MI 48109, USA 2 Professor, Departmen t of Aerospace Engineering, 1320 Beal Aven ue, Ann Arb or, MI 48109, USA 3 Adv anced Connected Services, F ord Researc h & Advanced Engineering, Dearb orn, MI, 48124, USA Pr eprint submitte d to arXiv De c emb er 6, 2019 Con ten ts 1 In troduction 4 2 Review of CBM, Mo delings and Algorithms 6 2.1 Diagnostics and Prognostics: Key Diﬀerences . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Critical comp onen t iden tiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 F ailure mo des and Prognostic tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Conﬁdence limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Implemen ting prognostic mo dels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3 Prognostic Mo dels And Their Classiﬁcation 12 4 Life exp ectancy mo dels 22 4.1 Sto c hastic mo dels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.1.1 Aggregate reliability functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.1.2 Conditional probability mo dels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.1.3 RUL probability density function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.1.4 Static Bay esian Netw orks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.1.5 Dynamics Bay esian Netw orks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.1.6 Bay esinan estimation with Kalman ﬁlters . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.1.7 Bay esian estimation with particle ﬁlters . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2 Statistical mo dels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.2.1 T rend ev aluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 20 4.2.2 Autoregressive mo dels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2.3 Prop ortional hazards modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.3 Ph ysical mo dels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5 P&HM T ool Selection Metho d 37 5.1 Visualization to ols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6 Performance Metrics for Ev aluating Prognostic Predictions 40 6.1 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 7 Automobile Applications 42 7.1 P eer-to-Peer Collab orativ e V ehicle Health Management . . . . . . . . . . . . . . . . . . . . . 42 7.1.1 System Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 7.1.2 Exp erimen tal Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 7.1.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2 7.1.4 Preliminary p enetration analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 7.2 Automatic transmission: W et-clutch system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 7.3 Alternator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 8 Challenges And Opp ortunities 51 9 Concluding remarks 51 3 1. In tro duction Mec hanical and electrical systems, and in particular, their building blo c ks/comp onen ts, are sub ject to gradual tear and w ear that will ultimately disrupt their proper op eration and make them faulty . Ho wev er, 40 the deterioration pro cedure v aries and depends on certain operating conditions suc h as stress, load and en vironment, etc. Considering the v ast application and reliance of our daily life on machines, maintenance has a signiﬁcan t role in assuring safe and prop er op eration of the existing systems. T raditionally , maintenance activities hav e tak en one of tw o approaches: preven tiv e and corrective [1]. The (time- or dut y-based) preven tiv e maintenance also known as planne d maintenanc e deﬁnes a p eriodic time interv al (or a certain duty), usually based on exp erience (or tests), to replace the component irre- sp ectiv e of its actual health status [2]. F or instance, the most common application of such a strategy , in automotiv e engineering, is the replacement of engine oil. These tasks are sc heduled to o ccur after driving for a certain n umber of months (or miles). Another example is the timing b elt on an automobile, which ma y b e recommended to b e replaced after ﬁve years (or 60,000 miles [3]). Prev entiv e main tenance leads to a costly maintenance strategy given the exp enses asso ciate with the mo dern complex comp onents. In addition, the preven tiv e maintenance do es not provide any information ab out the health status of a component, which is a ma jor defect for safety-critical comp onents, whic h could lead to disasters, for instance, in the ﬁeld of aerospace engineering. On the other hand, the corrective main tenance strategy seeks to replace a comp onen t once it is no longer op erational and is not capable of p erforming its assigned task. This maintenance strategy , which is the most undesirable form of main tenance, has signiﬁcant drawbac ks. It is more lab or intensiv e, do es not eliminate catastrophic failures and causes unnecessary maintenance, which is costly b y itself. In addition, there are costs associated with maintenance lab or and down time as well as the safety concerns and customer satisfaction. Considering a passenger v ehicle, the impact on customer satisfaction is a ma jor driving factor simply b ecause the comp onent failure 60 migh t o ccur miles aw a y from an y repair shop. F or other safety-critical applications (e.g. in the aerospace engineering), the corrective main tenance is a v oided by adopting alternativ es in whic h redundan t comp onen ts are considered since the failure is not tolerated. Collectively , exp enses due to preven tiv e and corrective main tenance constitute a signiﬁcant p ortion of the exp enses of many industrial companies. Bet ween these tw o extreme main tenance strategies lies condition-based main tenance (CBM), wherein main tenance actions are p erformed as needed based on the condition of the equipmen t or comp onen t (see Fig. 1). CBM av oids an y unnecessary maintenance task by sc heduling maintenance actions based on the conditions or observ ation of abnormal b ehaviours of a comp onent. The more eﬀectiv e a CBM program is implemen ted the less maintenance cost will be. Within the aerospace communit y , and aside from the safety issue, this corresponds to lo w ering the do wn time, whic h directly translates in to signiﬁcan t amoun ts of money . With resp ect to the automotive industry , the replacement prices as well as the repair costs when multiplied b y the p opulation of vehicles is quite considerable. A CBM maintenance scheme can directly aﬀect the follo wing asp ects of a system: 1) to improv e the ability in detecting faults, 2) to impro ve the plant safety , 4 Figure 1: Schematic diagram for operational, maintenance and total cost; colored regions denote diﬀeren t main tenance strategies. 3) to b etter maintenance plans and decision making, 4) to reduce the insp ection time and associated lab or costs, 5) to increase the a v ailabilit y of assets. CBM gran ts the abilit y to ev aluate a system’s actual health/damage conditions and pro vides the user with a prediction of failure, which is quite an essential to ol for industrial applications. The costs asso ciated to interruption of a business usually prov e to b e signiﬁcan tly higher than the exp enses due to the repairs to return a business back to service [4]. F or the electrical machines the av erage annual rate of failure is estimated to b e at least 3% and for motors that ha ve to op erate under hostile conditions and en vironment, 80 suc h as mining or pulp and paper industries, the annual failure rate is even greater and could b e as high as 12% [5]. Therefore, it is inevitable to ensure the av ailability of assets if a business is in terested in proﬁtable op eration. This directly translates to an accurate estimation of the remaining useful life (RUL) of a system and its constituen ts or comp onen ts. In other words, accurate RUL estimation can enable failure preven tion in a more controllable manner in that eﬀective main tenance can b e executed in appropriate time to correct imp ending faults. There are tw o main tasks in a successful CBM, i.e., diagnostics and prognostics, whic h will b e discussed in the next section. The ov erall life cycle cost of systems is reducible by implementing prognostics health monitoring (PHM) [6, 7]. On the other hand, developing a CBM is a signiﬁcant technical c hallenge. Presen ting a survey for a ﬁeld as div erse as CBM could be a daunting task. P erhaps the most diﬃcult issue is restricting the scop e of the surv ey to permit a meaningful discussion within a limited amoun t of space. T o ac hieve this goal, we made a conscious decision to fo cus on the most imp ortan t asp ect of the CBM, i.e., prognostics. How ev er, ﬁrst we try to distinguish some of the salient asp ects of diagnostics and its relation to prognostics. W e, then, elab orate on the utmost ob jectives of CBM and highligh t the signiﬁcance of eac h task 5 necessary for realizing any CBM program. A brief discussion of the metho ds, mo dels and other important ma jor steps of a CBM program are presented, whereas the emphasis is to provide the reader with a review that highligh ts and classiﬁes the existing applications of prognostics in engineering areas such as aerospace, marine and automotiv e. W e then discuss a few applications to prognostics of automotiv e engineering. Finally , w e describe some of the c hallenges and opp ortunities that b elong to the ongoing researc h. The authors’ inten t is to provide the researchers in scientiﬁc communit y , with the state-of-the-art in the aforementioned ma jors 100 of engineering o ver the recent few years. 2. Review of CBM, Mo delings and Algorithms In order to b etter understand the sub ject of CBM, it is necessary to distinguish b etw een its tw o main constituen ts, i.e., diagnostics and pr o gnostics . In the following sections w e explain brieﬂy the fundamental diﬀerences b etw een these tw o tasks. W e will also discuss the imp ortance of the conﬁdence limit, which is a ma jor factor in the decision making pro cedure. Classiﬁcation of the mo dels used in prognostics is also pro vided. 2.1. Diagnostics and Pr o gnostics: Key Diﬀer enc es In principle, diagnostics is conducted to inv estigate the ro ot cause of a failure and analyze the nature of a problem, whereas prognostics is related to predicting the future b eha viour as a result of rational study and analysis of av ailable p ertinent data. Diagnostics itself is brok en into three subtasks: 1) fault detection, 2) fault isolation, and 3) fault iden tiﬁcation when it o ccurs [1]. F ault detection is a task to indicate whether something is going wrong in the monitored system; fault isolation deals with a task to lo cate the faulty comp onen t; and the last step, fault identiﬁcation, is a task to determine the nature of the fault when it is detected. In terms of the relationship b et ween diagnostics and prognostics, the former is an in-depth exploration of the failure mo de to iden tify its leading cause after it has o ccurred within a system/comp onent, whereas the latter is the pro cess of generating a rational estimation of the RUL. Therefore, in its simplest form, prognostics is to monitor and detect the initial indications of degradation in a comp onen t, and b e able to consistently make accurate predictions [8]. It is imp ortant to realize that time is a critical v ariable in prognostics and it is more or less trying to answ er the question “when a component will fail?”, distinguishing 120 it from diagnostics, in which time plays a less imp ortant role, and instead the emphasis being placed more on determining the parameters of an already o ccurring fault or failure. A diagnostics system consists of a series of steps eac h of whic h of its o wn imp ortance. These steps include 1) data collection, 2) feature extraction (signal processing), and 3) a knowledge base of faults, which ma y b e deriv ed from expert knowledge, physical mo dels and historical data. Therefore, it is highly reliant on the kno wledge base as the ﬁnal determination of what type of failure has o ccurred, and why it is achiev ed b y comparing the utilizing feature extraction results with the knowledge base. A comprehensiv e review of tec hniques and metho ds used in fault diagnostics in beyond the scop e of this work; ho wev er, the interested 6 readers are referred to some of the excellen t reviews [1, 9, 10, 11]. The prognostics, on the other hand, shares some of the tasks of the diagnostics and requires several other steps. It shares the same tasks of feature extraction and a knowledge base of faults and further conducts p erformance assessment, degradation mo dels, analysis of the degradation patterns and making judicious predictions. Ho wev er, signals such as fault indicators and degradation rates, that the prognostics relies on, b elong to the outputs of the diagnostics, whic h means that these tw o parts are somewhat intert wined. When com bined, p erformance assessment and degradation mo dels can describ e a mac hine’s relative health status and indicate what kind of degradation patterns may exist. The ultimate goal of most prognostic systems is accurate prediction of the R UL of individual systems or comp onents, on the basis of their use and p erformance. This is imp ortan t since it allo ws adv ances scheduling of main tenance activities, proactive allocation of replacement parts and enhances ﬂeet deplo ymen t decision based on the estimated progression of comp onen t life. Prediction algorithms, whic h could b e derived from classic time series theories, statistics or artiﬁcial intelligence technologies, can forecast 140 when machine p erformance will decrease to an unacceptable level as deﬁned b y the failure analysis and health managemen t. Engineering prognostics is used b y industry to reduce business risks due to unexpected failures of equip- men t. It still relies highly on the exp erience and kno wledge gained o ver years and its application is limited to systems for whic h signiﬁcant data base is a v ailable (e.g., rotary machines). On the other hand, the mo dels used in prognostics are application dep enden t, which requires extensive analysis of the results and assump- tions. Appropriate mo del selection for successful practical implementation, requires b oth a mathematical understanding of eac h mo del type, and also an appreciation of how a particular business intends to utilize the mo dels and their outputs. Unfortunately , there is no general prognostic model to ﬁt all business needs and not all of the mo dels are well prov en mathematically . In addition, eﬃcacy of models is dependent up on the a v ailabilit y of required data, skilled p ersonnel and computing infrastructure. Prognostics is a relatively new research area and is not a w ell-developed discipline compared to other areas of CBM. A num ber of literature reviews co vering CBM with emphasis on prognostic components including mo dels and approac hes hav e already b een presen ted in [12, 13, 14, 15, 16, 17, 18, 19, 20]. T able 1 summarizes some of the most imp ortan t review papers to date where AI, SA and ANN stand for Artiﬁcial Intelligence, Signal Analysis and Artiﬁcial Neural Netw orks, resp ectiv ely . In addition, Reference [21] reviews the b eneﬁts and challenges of prognostics and Reference [22] reviews the condition-based main tenance. T able 2 also sho ws highlights typical applications for some of the more common predictive main tenance technologies [23]. Although useful in appreciating the state of the art, w e feel that there is a need for a literature review that incorporated the salient asp ects of a reliable CBM that not only presents a review of mo dels and their 160 merits but also fo cuses on sp eciﬁc practical implementations in sp eciﬁc engineering ﬁelds. Reference [20] adopts a similar strategy while fo cusing on rotary machine systems whereas the application of prognostics for other comp onen ts is gro wing. Knowledge of the prior work is a necessity for future research eﬀorts. T o address this gap, this paper pro vides a review of the ﬁeld of PHM, which fo cuses on the practical applications 7 T able 1: Summary of the existing review pap ers and their fo cus on diﬀerent prognostics methods. Reference Y ear Kno wledge- Exp erience- Data- Mo del- Hybrid Other metho ds based based Driv en based [24] 2003 D D [3] 2005 D [1] 2006 D D AI [25] 2006 D D D [26] 2006 D D [27] 2006 D Reliabilit y , Sto c hastic [28] 2008 D Stress and eﬀects-based [17] 2009 D D D [29] 2011 D D Life Exp ectancy , ANN [21] 2011 D [30] 2014 D D D D D [31] 2014 D D SA, Sto c hastic, ANN [31] 2015 D on v arious comp onen ts in the ﬁelds of engineering such as automotive, aerospace and marine engineering. 2.2. Critic al c omp onent identiﬁc ation Iden tifying critical components is the ﬁrst step in dev eloping a prognostics and health monitoring system. One approac h in identifying the signiﬁcance of components on the o verall p erformance and cost down time of a system is to use a quadrant chart as is shown in Fig. 2 (tak en from [20]). A similar ﬁgure is also sho wn in [32] for the selection of critical comp onen ts. It displays the frequency of failure versus the av erage Figure 2: Component fault F requency-Down time c hart and four quadrants for identifying critical components [20]. 8 T able 2: Common predictiv e tec hnology applications. T ec hnology Pumps Electric Motors Diesel Generators Condensers Hea vy Equipment/Cranes Circuit Break ers V alv es Heat Exc hangers Electrical Systems T ransformers T anks, Piping Vibration Monitoring/Analysis × × × × Lubrican t, F uel Analysis × × × × × W ear P article Analysis × × × × Bearing, T emp erature/Analysis × × × × P erformance Monitoring × × × × × × Ultrasonic Noise Detection × × × × × × × Ultrasonic Flo w × × × × Infrared Thermograph y × × × × × × × × × × Non-destructiv e T esting (Thickness) × × × Visual Insp ection × × × × × × × × × × × Insulation Resistance × × × × × Motor Curren t Signature Analysis × Motor Circuit Analysis × × × P olarization Index × × × Motor Circuit Analysis × × 9 do wntime asso ciated with failure for relev an t components of 890 SW Rob ots. The eﬀectiv eness of the curren t main tenance strategy can b e seen when the data is graphed in this wa y . The horizontal and v ertical lines that divide the graph to four quadrants are user-deﬁned parameters based on their demands on pro duction and/or main tenance. The resulting quadran ts are n umbered 1-4 starting with the upper right and moving coun ter clo ckwise. The ﬁrst quadrant represents those comp onen ts that not only fail more frequen tly , but also result in extensive do wntime. Typically , there should not b e any comp onen ts in this quadrant b ecause suc h issues should hav e been noticed and ﬁxed during the design stage. How ev er, there could be instances in whic h a manufacturing defect in, or contin ued improp er use of, a particular comp onen t could result in rep etitiv e failures and signiﬁcan t down time. The second quadran t still contains comp onen ts with a high frequency of failure, but eac h comp onent causes a short do wntime. The maintenance recommendation for 180 suc h comp onen ts is to ha ve an adequate num ber of spare parts on hand. The third quadrant con tains comp onen ts with a low frequency of failure and low av erage down time p er failure, which means that the curren t main tenance practices are w orking for these comp onents and no c hanges are required. In the fourth quadran t lie the most critical comp onen ts as their failures, though infrequent, cause the most down time p er o ccurrence and could p oten tially incur signiﬁcant costs. The comp onen ts of this last quadrant should b e the fo cus of prognostics. F or instance, as is shown in Fig. 2, the ﬁled of robotics prognostics should fo cus on enco der, motor and gearb o x as critical comp onen ts. The existence of similar data for the other engineering ﬁelds improv es the return of prognostics by developing frameworks for components that pla y a critical role in the ov erall p erformance and cost. The reader is referred to [20] for additional information on this matter. 2.3. F ailur e mo des and Pr o gnostic tasks T o understand the role of mo dels in prognostics, it is imp ortan t to identify the v arious steps in volv ed in obtaining an RUL estimate (whic h is the holy grail of prognostics) and its conﬁdence bounds. Figure. 3 sho ws the pro cess a comp onent undergo es from a healthy state p erformance until its ﬁnal failure. It depicts highly simpliﬁed degradation curv es for three diﬀeren t and indep enden t failure mo des, whic h could represent diﬀeren t t yp es of failure of the same comp onen t. There is a stable zone during whic h the performance of the comp onent is not aﬀected. Ho wev er, the comp onen t is even tually going to degrade and fall into the degradation zone, whic h itself is divided into tw o regions, i.e.,- low and high-degraded regions deﬁned b y their b ounds (levels), resp ectively . The selection of the p erformance levels is a critical task in any prognostics approach. In addition, Fig. 3 shows the spread of the time once a degradation curv e hits a sp eciﬁc level. The conﬁdence (precision) in determining those probabilities is essential in decision making 200 and is discussed in the next section. Note also that there are factors that eﬀect the degradation patterns whic h triggers diﬀeren t failures. The progression of any failure mo de may b e acc elerated due to the changes in the op erating conditions, main tenance actions or even progression of the other failure mo des (e.g, a b earing fault causes high vibration that induces and accelerates mechanical seal degradation). Therefore, an eﬃcien t pro cedure to estimate RUL correctly needs to address the following questions (or know preliminary information ab out them): 1) what is the current degradation rate?, 2) whic h failure mo de (or mo des) has 10 Figure 3: T ypical performance degradation for three diﬀerent failure mo des. (ha ve) b een triggered and contributes to the degradation?, and 3) how muc h is known of the severit y of the degradation? (determines the p osition of the comp onen t of the particular curve). If a systems-oriented approach to prognostic-based decision supp ort is desired, then RUL estimates should b e further supplemented with forecasts describing the impact of predicted failures on op erational and main tenance activities which can b e considered at the business management lev el rather than prognostics task [33, 34]. Based on the collective approac hes, one could conceptualize a diagnostic/prognostic framework that addresses prognostics through three levels with v arying degrees of complexity , i.e., existing failure mo de prognostics, future failure mo de prognostics and p ost-action prognostics [29]. The prognostics mo dels discussed in this review keeps the complexit y to the simplest level, i.e., existing failure mode prognostics. Almost all of the w orks in the literature b elong to this category . 2.4. Conﬁdenc e limits The output of a prognostic algorithm has t wo comp onen ts: 1) an estimate of time to failure, which is also referred to as the RUL and 2) an asso ciated conﬁdence limit [15]. Analysis of the conﬁdence limit is imp ortan t since the prognostics in trinsically deals with estimating an uncertain v ariable parameter, which 220 is eﬀected by several factors including the future op eration of the comp onen t, op erating conditions and errors due to the ﬁdelity of the utilized diagnostics and prognostics mo dels. Conﬁdence limits are even more imp ortan t in prognostic mo delling than for diagnostic prediction. This is due to the fact that in diagnostics the failure and the exten t of damage is known and is an externally veriﬁable quantit y (e.g., actual crac k size) whereas this is not the case in prognostics as it deals with failure. It is highly imp ortant for business 11 decisions to b e made based on the b ounds of the R UL conﬁdence interv al rather than a sp eciﬁc v alue of the comp onen t exp ected life [15]. 2.5. Implementing pr o gnostic mo dels There are certain asp ects that hav e to b e considered b efore implemen ting any prognostics mo del. First of all, most of the prognostics program deal with acc urate prediction of URL of an identiﬁed failure mode. This strategy is retained to k eep the pro cess simple and tractable. In addition, the existence of certain t yp e of data, lev el of complexity of the mo del and the underlying assumptions will make the mo dels b etter suited to certain applications. One could p ose a series of questions to assess the p erformance and suitability of a particular mo del to a particular problem, • Prediction requiremen t: what do es the RUL prediction need to achiev e? • Mo del-process capability: can the mo del describ e the reality? • Resource requiremen ts: are the resources av ailable to undertake the mo delling? • Approac h readiness: is the mo delling approach suﬃciently well prov en to b e relied up on? These four criteria do not include factor that should b e considered before prognostics are undertaken in the ﬁrst place, whic h is b ey ond the scop e of this w ork. A go o d discussion of this topic is presented in [35]. 240 3. Prognostic Mo dels And Their Classiﬁcation With the discussion given on the ov erall task of prognostics and the imp ortance of the RUL estimation w e fo cus on the existing mo dels and their capabilit y in providing the necessary information to practitioners. Curren t prognostic approaches can be categorized in to four ma jor classes: exp erimen tal, data-driven, mo del- based and hybrid. Reviewing the literature it is apparent that pap ers limit their discussions to data-riven or mo del-based approaches and a few of them address the experience-based approach. A detailed classiﬁcation of mo dels into four groups is giv en in [29] sp eciﬁcally designed for RUL prediction. It is further divided into v arying num b er of subgroups (see Fig. 4). The material of this section is mainly taken from [29]. • Kno wledge-based mo dels [36, 37, 38, 36, 39]: these mo dels assess the similarity b et ween an observed situation and a database of previously deﬁned failures and deduce the life exp ectancy from previous ev ents. Sub-categories include exp ert systems and F uzzy systems . • Life exp ectancy mo dels: determine the life exp ectancy of individual machine comp onents with resp ect to the exp ected risk of deterioration under kno wn operating conditions. Sub-categories are separated in to statistic al and sto chastic mo dels. Sto chastic models are further divided into t wo mo dels i.e., aggregate reliability functions and conditional probabilit y methods. Statistical mo dels include trend extrap olation, auto-regressive moving av erage (ARMA) mo del and its v arian ts, and prop ortional hazard mo delling (PHM). 12 Figure 4: Classiﬁcation of mo dels used for URL prediction. • Artiﬁcial Neural Net works: These mo dels compute an estimated output for the RUL of a comp onent, directly or indirectly , from a mathematical represen tation of the comp onent that has b een derived from observ ation data rather than a physical understanding of the failure pro cesses. They are further 260 group ed into mo dels used for direct URL forecasting and parameter estimation for other mo dels. • Ph ysical mo dels: These mo dels compute an estimated output for the R UL of a comp onen t from a mathematical representation of the ph ysical b eha vior of the degradation pro cess. T yp es of physical mo dels tend to b e application (failure mo de) speciﬁc and are therefore not classiﬁed further. It is a diﬃcult task to strictly categorize a mo del into the presented classes, particularly due to the fact that more recently the mo dels in the literature are a com bination of tw o or more classical mo delling approaches. Mo del selection requires that the main adv an tages and disadv antages of eac h model type b e w ell understo od. F or a list of generic adv an tages and disadv an tages of the introduced mo dels refer to [29]. A brief description of each mo del is given in T able 3 to familiarize the reader with their basic adv an tages and disadv an tages. The adv antages and disadv antages are mostly asso ciated with the simplicity of the metho d (either mo del and/or its of implementation), capability to provide conﬁdence limit, reliance on the amount and accuracy of data, av ailability of to ols and softw ares, capabilit y to incorp orate new data, ability to mo del previously unan ticipated faults, capability to manage incomplete data sets, b eing able to mo del m ultiv ariate dynamic mo dels and their lev el of computational eﬃcacy . T able 4 summarizes considerations for using or a voiding a particular type of mo del. These tw o tables serve as an initial guideline for selecting a particular mo del to 13 b e used in the later stages of a prognostic framework. In the next sections we brieﬂy discuss the underlying principles of eac h mo del. T able 3: Adv an tages and disadv antages of prognostic mo delling options. Model Adv antages Disadv antages Knowledge based Expert systems • Simple (alb eit time consuming) to develop • Easy to understand • Relies entirely on knowledge of sub ject matter exp erts • Significant num ber of rules required • Significant management overhead to keep knowledge base up to date • Precise inputs required • No confidence limits supplied • Not feasible to provide exact RUL output F uzzy systems • F ew er rules required than for expert systems • Inputs can b e imprecise, noisy or incomplete • confidence limits can b e provided on the output with some types of models Domain exp erts required to develop rules 14 T able 3 (contin ued). Model Adv antages Disadv antages Stochastic Aggregate reliability functions • Simple and well understo od by reliability engineering communit y • Numerous software options av ailable • Theoretically can b e p erformed at all equipment hierarch y levels, especially whin a small number of failure mo des dominate • Confidence limits are av ailable for RUL predictions • Accuracy and precision increases as RUL decreases resulting in the ability to set useful warning limits • F ailures must be statistically independent and identically distributed • In most cases will require a statistically significant sample size p ertaining to each failure mode for reliable RUL predictions • W arnings prior to actual failure are not readily av ailable RUL PDF • Simple and easy adaptation of basic reliability approaches • Only requires that time at which failure has not o ccurred is monitored (i.e, no condition monitoring data) • Theoretically can b e p erformed at all equipment hierarch y levels, especially when a small number of failure mo des dominate • Confidence limits are av ailable for RUL predictions • Accuracy and precision increases as RUL decreases resulting in the ability to set useful warning limits • Av ailable accuracy and precision is dep enden t on forecasting interv al • In most cases will require a statistically significant sample size p ertaining to each failure mode for reliable RUL predictions • Assumes that hazard is a function of op erating time rather than external risk factors 15 T able 3 (contin ued). Model Adv antages Disadv antages Stochastic Static Bayesian Netw orks • Can readily manage incomplete data sets • Allow/force user to learn about causal relationships • Captures and integrates exp ert knowledge • Algorithms av ailable to avoid the ov er fitting of data • Computer software av ailable for modelling • Confidence limits are intrinsically provided • Cannot mo del previously unanticipated faults and/or ro ot causes • Computational difficulty of exploring a previously unknown netw ork • A Bayesian network is only as useful as the prior knowledge is reliable • Results may be sensitive to selection of prior distribution • Modelling experts required in addition to domain exp erts Marko v, Semi-Marko v models • W ell established approach and able to mo del numerous system designs and failure scenarios • Can readily manage incomplete data sets • Reasonably large volume of data required for training • Assumes a single monotonic, non temporal failure degradation pattern (i.e., different stages of failure cannot b e accounted for) • Cannot mo del previously unanticipated faults and/or ro ot causes • More complex semi-Markov models are required if failures or failur progression times are not exponentially distributed • Not appropriate for repairable systems that are only partially restored 16 T able 3 (contin ued). Model Adv antages Disadv antages Stochastic Hidden Markov, Semi-Marko v models • Can mo del different stages of degradation so failure trend do es not need to b e monotonic • Can mo del spatial and temporal data • Specific knowledge of failure mechanism progression is not required • Can readily manage incomplete data sets • Provide confidence limits as part of their RUL prediction • Large volume of data required for training, prop ortional to the num ber of hidden states • Cannot mo del previously unanticipated faults and/or ro ot causes • More complex Hidden semi-Marko v mo dels are required if failures or failure progression times are not exp onen tially distributed • Computationally intensive, particularly for a large number of hidden states Bay esian techniques with Kalman Filters • Can b e used to model multiv ariate, dynamic pro cesses • Basic KF is computationally efficient, particulary for systems with a large number of states • Can accommo date incomplete and noisy measurements • V arian ts av ailable for non-linear processes • Other advan tages on underlying Bay esian technique • Process and measurement noise must be Gaussian • Some varian ts diverge easily • V arian ts for non-linear systems are more computationally intensiv e than basic Kalman filters • Measurement data required • Other disadvan tages dep end on underlying Bayesian technique 17 T able 3 (contin ued). Model Adv antages Disadv antages Stochastic Bay esian techniques with Particle Filters • Can b es used to model multiv ariate, dynamic processes • Noise do es not need to b e either linear of Gaussian • More accurate than Kalman filter varian ts for non-linear systems • Other advan tages dep end on underlying Bayesian technique • A large number of samples (or resampling) are required to avoid degeneracy problem • Can b e more computationally intensiv e than basic Kalman filters • Measurement data required • Other disadvan tages dep end on the underlying Bayesian technique Statistical T rend extrapolation • Simplest technique to apply and explain • Easy to set alarms • Adv anced software tools not required • F ew failures have a well-defined monotonic, single-parameter trend • Interpretabilit y is affected by process/measurement noise and v ariations in operating conditions • Av ailability of confidence limits dependent on amount of data at the different states of failure developmen t ARMA Mo dels & v ariants • Adv anced ARMA related techniques av ailable for non-stationary data • Historical failure data is not required • Usually computationally efficient and therefore can be performed in real time • An understanding of detailed failure mechanisms not required • Provide accurate and reliable short term predictions of RUL • Basic ARMA mo dels assume stationarity of the pro cess and noise • Does not integrate prior or exp ert knowledge • sensitive to noise and initial conditions • significant data required for model developmen t and v alidation • Long-term predictions of RUL are less reliable 18 T able 3 (contin ued). Model Adv antages Disadv antages Statistical PHM • COTS software av ailable • Accounts for age dep endent and indep enden t hazards • Models are simple to develop Confidence limits can b e calculated • All relevan t cov ariates must be included in the mo del • Mixing different types of cov ariates in one mo del may be problematic • Strict (alb eit implied) assumptions regarding nature of underlying pro cess • Historical data required p ertaining to individual failure mo des • Multi-collinearity , monotonicity and large cov ariate values that can cause a failure of the mo del parameter estimation pro cess • Parameter selection often manual and time consuming and the selection of parametric estimation technique is not straightforw ard • T raditional PHM equation assumes cov ariates describe a stationary process. Dynamic PHM is more inv olved • Can only b e used to develop models for failures that have b een exp erienced previously and for which associate cov ariate data is av ailable • T oo easy to develop a mo del that may be statistically adequate but do es not represent any actual failure phenomenon (i.e. physically meaningless) 19 T able 3 (contin ued). Model Adv antages Disadv antages Artiﬁcial Neural Netw orks F or F orecasting with ANNs • Complex multi-dimensional, non-linear systems can b e modelled • Physical understanding of the system b ehaviour not required • ANN varian ts facilitate the use of any type of input data • Computer software is av ailable for mo delling • Requires a significant amount of data for training data that needs to b e representativ e of true data range and its variabilit y • Determining the most appropriate model is largely trial and error and therefore can b e time consuming • Most networks cannot provide confidence limits on the output • Pre-processing is required to limit the num ber of data inputs and reduce model complexity • All published research is relatively recent • Outputs need to mapp ed to a physical representation Parameter Estimation with ANNs • As for RUL F orecasting with ANNs • Useful for incorp orating with physics of failure mo dels • Confidence limits av ailable from underlying mo del (for which parameters are b eing estimated) • Less data required for estimating parameters as mo dels tend to b e failure sp ecific • Determining the most appropriate model is largely trial and error and therefore can b e time consuming Physical mo dels Physical Models • Provide most accurate and precise estimates of all modelling options • Confidence limits provided • Outputs can b e easily understoo d • Detailed and complete knowledge of system b eha viour required • The accuracy and robustness are sub ject to the experimental conditions under which models were developed 20 T able 4: When to consider/av oid using particular models. Model When to consider When to avoid Knowledge based Expert systems • W ell-understood, stable, narrow problem area • human experts are av ailable to develop the knowledge base; and operating conditions are stable and predictable; and simple precise queries to define p otential faults is imp ossible; and only an approximate RUL estimate is required • No human experts are av ailable to define comprehensive set of rules; or fault maintenance are not well understoo d; or op erating conditions are highly variable; or highly accurate or precise RUL estimates are required F uzzy systems • One or more variables are contin uous; and a mathematical model is not av ailable or not feasible to implement; and data contains high levels of noise or uncertaint y; and difficult to define exact queries that identify specific faults No human experts are av ailable to define fuzzy rules; or input data is discrete and limited to a small number of options Stochastic Aggregate reliability functions • Sample size is statistically significant and representativ e of individual sample; and • Small set of dominant failure modes; and • PDF is not exp onen tial; and Reliability growth is not occurring; and • RUL prediction is predominantly used for overall maintenance management rather than tracking of a sp ecific asset (e.g., when redundancy is av ailable) so gradual escalation of warning levels are not required • Only a small number of failures can b e attributed to individual failure mo des; or • Significant num ber of p ossible failure mo des that cannot be easily differentiated, or historically have not been; or • Hazard rate is constant; or • Past operating conditions are not representativ e of current environmen t or usage; or • The sp ecific asset is critical to plant safety or operations and warning is required prior to failure 21 T able 4 (contin ued). Model When to consider When to avoid Stochastic RUL PDF • Sample size is statistically significant and representativ e of individual sample; and Small set of dominant failure mo des; and • PDF is not exp onen tial; and • Reliability growth is not o ccurring • Condition monitoring data is not av ailable; and • Operating age can be track ed to confirm absence of failure; and • Only final estimates need to b e particularly accurate and precise • Only a small number of failures can b e attributed to individual failure mo des; or • Significant num ber of p ossible failure mo des that cannot be easily differentiated, or historically have not been; or • Hazard rate is constant; or • Past operating conditions are not representativ e of current environmen t or usage; or • F ailure is hidden and no failure finding is b eing undertaken; or • High-level of accuracy and precision is required a long time into the future 4. Life exp ectancy mo dels The basic idea in dev eloping the life expectancy mo dels is to determine the RUL of a comp onen t with resp ect to the exp ected risk of deterioration. It is also assumed that the op erating conditions are known. 280 4.1. Sto chastic mo dels Sto c hastic mo dels provide reliabilit y-related information, suc h as Mean Time to F ailure (MTTF) as probabilities of failure with resp ect to time. Sto c hastic b ehaviour is at the heart of these metho ds and they are based on the assumption that the times to failure of identical components can be represented b y statistically iden tical and independent random v ariables and thus b e described by a probabilit y density function. One main driving factor of these models is the existence of data, which in the case of sparse failures leads to ov erly pessimistic estimates. It is sho wn that the accuracy of the estimate of MTTF can be impro v ed b y utilizing censored (suspended data) (times at whic h failure has not o ccurred or there is no evidence of failure) [40]. The ability to use censored data is imp ortan t since most of the exp erimen tal data is attained through accelerated tests using exp erimen tal rigs or bench tests and most of the time the accelerated tests are terminated after a certain p erio d of time and consequently results in censoring. Using censored data is not necessarily helpful esp ecially in small data sets in which censoring might o ccur early in life and this can in tro duce other errors [41]. In the simplest form of application, RUL is equated to the time remaining b efore a critical n umber of failures (e.g., 5%) are exp ected to o ccur. 22 T able 4 (contin ued). Model Adv antages Disadv antages Stochastic Static Bayesian Netw orks • Incomplete, multiv ariate data av ailable; and • Root cause of failure known; and • process and plant configuration is relatively static or network is confirmed up to date; and • Modelling experts are av ailable • Root causes of failure unknown; or • Expert plant and mo delling knowledge unav ailable; or • T raining data is unav ailable Marko v, Semi-Marko v models • Simple to develop and implement; • Incomplete, multiv ariate data av ailable; and Ro ot causes of failure known; and • Process and plant configuration is relatively static or network is confirmed up to date; and • Relatively accurate and precise RUL estimate is required • Repairable system; or • T emporal measurement data as model inputs; or • Sufficient data related to failure mode is not av ailable for training; or • F ailure being modelled has more than one discrete stage (e.g., crack initiation, growth , final failure, etc) Hidden Markov, Semi-Marko v models • Repairable systems; and • Root causes of failure known; and • F ailure being modelled has more than one discrete stage • T emporal data to b e used as model inputs • Relatively accurate and precise RUL required • Sufficient data related to failure mode is not av ailable for training; or • Suitable hardware for computation is not av ailable Bay esian techniques with Kalman Filters • Multiv ariate p osterior distribution; and • Additive; and • Condition monitoring data is av ailable; and • Relatively accurate and precise RUL estimate required • Multiplicative noise; or • Single variable p osterior distribution; or • Cov ariate data is not av ailable for the failures of interest 23 T able 4 (contin ued). Model Adv antages Disadv antages Stochastic Bay esian techniques with Particle Filters • Multi-v ariate or non-standard p osterior distribution • Non-linear, non-Gaussian noise; and • Relatively accurate and precise RUL estimate required • Typical deterministic posterior distribution; or • Linear, Gaussian; or • Multiplicative noise; or • Single variable p osterior distribution; or • Cov ariate data is not av ailable for the failures of interest Statistical T rend extrapolation • Single defined failure mo de associated with a single monitored (or calculated) parameter that can b e described with a monotonic trend; and op erating conditions are stable or do not affect monitored parameter; and • Measurements are repeatable, reliable and not highly sensitive to measurement processes (e.g., online sensors) • Incipient failure cannot b e related to a simple measurable input; or • V arying operating conditions that affect the measured parameter but are not related to failure; or • T rend is not monotonic; or • Data highly dep endent on measurement process; or Data is sub ject to high levels of pro cess or measurement noise; or • Reliable confidence limits are required on the extrap olated RUL estimate ARMA Mo dels & v ariants • Hazard rate is a linear relationship of cov ariates and noise; and • Short-term predictions required; and • Hazard rate is independent of age (i.e., exp onential distribution); and • Measurement data is av ailable for mo delling and application but historical failure data is not • Hazard rate is not a linear relationship of cov ariate and noise; or • When historical or exp ert data is av ailable in addition to measurement data; or • Long-term predictions are required; or • Sufficiently large volume of data is not av ailable for mo del construction and v alidation 24 T able 4 (contin ued). Model Adv antages Disadv antages Statistical PHM • Times to failure are independent and identically distributed; • Cov ariate hav e a multiplicativ e effect on the baseline hazard rate; and • A number of cov ariates are av ailable and required to describe change in risk; and • Process represented by cov ariates is stationary (unless using Dynamic PHM); and • Associated cov ariate data is av ailable for the failure modes being modelled; and • Only the final RUL estimate and confidence limit is required (not an estimate of a precursor to failure) • F ailures hav e not occurred previously or have no associated cov ariate data • Hazard rate is not multiplicative; or • F ailures cannot b e segregated into individual (or dominating) failure modes; or • Cov ariates related to the failure mo des being mo delled cannot be measured; or • Process represented by the cov ariates is non-stationary; or • If a precursor to failure is to be predicted rather than final failure itself 4.1.1. A ggr e gate r eliability functions This is the standard approach widely accepted and used in industry , esp ecially in certain problems for whic h reliable and considerable amount of data is av ailable. Detailed information on applying statistical distributions to mo delling and failure data can b e found in v arious publications [41, 42, 43, 44, 45, 46, 47]. The ov erall task consists of determining a probability density function and its related hazard function for a p opulation of comp onents and analyzing the time to failure (TTF). Ob viously , the density function is 300 the representativ e of the whole p opulation and not a single fault progression. In the simplest theoretical appro ximation, a fault progression curve typically follows an exp onential curve and pro vides information ab out the exp ected time of failures. There are v arious mathematical relations to approximate the proba- bilit y distributions that best mo del the failure data (e.g., Exp onential, Gaussian, Normal, Lognormal and W eibull functions). Gaussian distribution is the most famous and commonly used distribution in reliability engineering due to its ability to describ e many diﬀerent failure types. The classical w ell-known bathtub curv e (see Fig 7 in [29]) is most commonly describ ed as a piece-wise function made up of three W eibull distributions, each of whic h describ es a diﬀerent set of dominating failure modes, i.e., early (infan t failures), random failures and w ear-out failures. F or more complex systems there exists another mo del for reliability estimation assuming that load and material strength distributions are known. This mo del is kno wn as Overstress Reliability in tegral [44]. F ailure data can b e ﬁtted to a W eibull distribution using a v ariet y of parameter estimation metho ds, such as least squares, moments and maxim um likelihoo d. These mo dels make the most famous distributions and are 25 T able 4 (contin ued) Model Adv antages Disadv antages Artiﬁcial Neural Netw orks F or F orecasting with ANNs • Large amount of noisy , numerical, temporal data; and • Physical, statistical or deterministic mo del is not known or impractical to apply; and • An exact optional answer for RUL is required • Data is complex or symbolic; or • Justification or physical extrap olation not required; or • T emporal inputs are not av ailable; or • Minimal data is av ailable for training Parameter Estimation with ANNs • An RUL model (typically a physical model) is av ailable but contains unko wn parameters; and • Large amount of noisy , numerical temp oral data; and • An exact optimal answer for RUL is required • Data is complex or symbolic; or • Minimal data is av ailable for training Physical mo dels Physical Models • F ailure modes are well understoo d and defined; and • A physical model for each failure mo de is av ailable; and • Operating conditions can be monitored and statistically represented; and • Process/condition data is av ailable; and • High-accuracy and precision required in RUL prediction • A physical model is not av ailable 26 usually incorporated in commercially av ailable softw ares. All of these mo dels still dep end on reliable large sample sets of failure data p oin ts, which hav e to b e collected and stored during extensive (time consuming) tests or under real en vironmental conditions. In addition, any situation where the failure distribution is exp onen tial, reliabilit y analysis on its own is insuﬃcient for estimating RUL. This is due to the fact that the hazard rate of an exp onen tial distribution is constant ov er the life of a comp onen t and is indep enden t of its service life. On the other hand, what makes the reliability-based mo delling approaches app ealing is that distribu- 320 tions are usually deriv ed from observ ed statistical data and are mathematically easy to construct. The required data can often be extracte d relatively easily from a company’s existing computerized maintenance managemen t systems. In addition, they pro vide conﬁdence limits for the results, which is an essential infor- mation for decision making. Consequently , analysis of the results is also relatively straightforw ard and can b e p erformed by reliability engineers and av oids exp ertise on the sub ject under study . F rom a theoretical standp oin t, the reliability analysis can b e extended to include larger systems b y combining the failure data appropriately . In practice how ev er, it is not advised to aggregate to o many failure mo des together since the failure distributions of a system b ehav es similar to that of an exponential distribution, which is problematic as discussed earlier. More adv anced prognostic mo dels are required for estimating RUL of systems. 4.1.2. Conditional pr ob ability mo dels A num ber of sto c hastic mo dels try to use conditional reliability functions in conjunction with the Bay es’ theorem. In essence, a conditional reliability function is used to describ e the current state of the comp onen t. The future b ehaviour/status of the comp onen t is estimated based on the recursive up date of the conditional function through direct or indirect utilization of Bay es’ theorem (thereb y they could also b e referred to as Bay esian mo dels). Kno wing the curren t state of the asset, once a conditional reliability function is determined, the RUL function is deﬁned as the conditional exp ected time to failure (whic h ma y or ma y not b e time dep enden t) [48, 49, 50, 51]. Mo delling v arian ts diﬀer in the calculation pro cedure of the conditional probabilit y function as well as the kind of information used to deﬁne the current state. 4.1.3. RUL pr ob ability density function The RUL probability density function is probably the simplest Bay esian approach which is an extension 340 of traditional aggregate reliability analysis. It requires the probability densit y function of the relev an t failure mo de. Information is then obtained to lo cate a sp eciﬁc item on this general distribution (e.g., an age at whic h the item has not failed). This p opulation grows in size as the new data is app ended and similarly the distribution is amended to consider this information using Bay es’ theorem [52]. The pro cess rep eated eac h time a new data p oint is av ailable and this pro cess is called Bay esian ‘up dating’. There are v arious names to the resulting distribution, i.e., the predictiv e density function or the remaining R UL PDF. It is also p ossible to deriv e a credibility interv al (equiv alent to a conﬁdence in terv al) [43, 53]. It is also possible to mak e impro ved predictions for the new state (i.e., the condition probabilit y , or posterior function) b y incorporating 27 more adv anced state estimation techniques suc h as Kalman ﬁltering, particle ﬁltering metho ds. The rational b ehind selection of the most appropriate metho d depends on b oth the system as well as the noise type. In addition, predictions for the next state often in volv e ev aluation of integrals that do not p ossess closed-form solutions. Th us integration approximation metho ds are often required, suc h as regression mo dels [49] or b ootstrapping metho ds [51], to estimate the exp ected v alue and cov ariance of these PDFs. The accuracy and precision of R UL estimation using this technique improv e as the end of life approaches. Besides, it is also relativ ely simple to calculate and use these techniques. 4.1.4. Static Bayesian Networks Ba yesian Net w orks (BN)/Bay esian Belief Net works (BBF) are probabilistic acyclic graphical models that represen t a set of random v ariables and their probabilistic interdependencies. Depending on the t yp e of the information used, these can also b e considered as either kno wledge-based, sto c hastic or hybrid approac hes. There are a num ber of no des, which are connected b y directional arcs that represent a direct causal inﬂuence 360 b et w een no des in a mandatory acyclic pattern. The no des themselv es can take on distinct states or levels and represent random v ariables. The strength of the causal inﬂuences are quantiﬁed using conditional probabilities. Ultimately , each no de has a conditional probabilit y table that deﬁnes probabilities for each state of the no de given the states of its parents [54]. Giv en a netw ork design conﬁguration and no dal conditional probabilities, a BN can b e used to ev aluate the likelihoo d of each p ossible cause b eing the actual cause of an even t. It could also represen t probabilities asso ciated with a particular even t occurring next if time series mo delling is adopted. The output of the BN is in the form of probabilities, which intrinsically con tain information ab out their conﬁdence. This is a ma jor adv an tage. A detailed mathematical description of BN mo delling in reliability and a list of mo delling softw are a v ailable can b e found in [55]. 4.1.5. Dynamics Bayesian Netw orks Dynamics Bay esian netw orks are those in which the directed BN arc ﬂo w forw ard in time and are therefore useful for mo delling time series data [56]. Prognostic URL estimation is inv ariably undertak en using time series forecasting as in [57]. The most common v arian ts used in engineering prognostics include Marko v mo dels, Kalman ﬁlters and Particle ﬁlters. F or a detailed review of Mark ov mo dels see Ref. [29]. 4.1.6. Bayesinan estimation with Kalman ﬁlters Both Kalman and Particle ﬁlters (which is discussed in the next section) are not diﬀerent types of models, but rather diﬀeren t approaches to implementing generic dynamic BNs. Ho wevv er, they are widely used in engineering prognostics and deserv e particular atten tion, which requires a brief ov erview of the underlying assumptions, limitations and strengths of these speciﬁc approaches. The complexit y of the dynamics and the type of noise are crucial in assessing the domain of the application of these metho ds. The Kalman ﬁlter 380 is a computationally eﬃcient recursive digital pro cessing tec hnique used to estimate the state of a dynamic system from a series of incomplete and noisy measurement in wa y that minimizes mean squared error. It is 28 the most famous estimation metho d within the control communit y . At any instan t, it is deﬁned by its state estimate and error co v ariance. In ﬁve steps, it estimates unknown states from only current observ ations and the most recent state and these states need not b e directly measurable [58]. Kalman ﬁltering assumes certain features for the pro cess and measurement noise i.e, Gaussian, white, independent of each other and additiv e. T raditionally , it was also assumed that the dynamic b eing mo delled needed to b e linear, how ev er, it has b een shown that this is not the case if the aforementioned assumptions on noise holds [59, 60]. During the iterative pro cedure, it is necessary to solve a n umber of integrals; but if the linearity assumptions are met, they ha ve exact solutions and it is not necessary to use approximation metho ds. The Kalman ﬁlter requires an appropriate initial quantiﬁcation of the measuremen t noise co v ariance, whic h is relatively easy when observ ations are stationary . How ev er, determining the pro cess noise cov ariance is more c hallenging as it is often not possible to directly observ e the pro cess b eing mo delled. The performance of the ﬁlter impro ves when these parameters are tuned separately to their proper v alues. The ﬁlter will reach steady-state very quic kly if b oth noise cov ariances are constant betw een iterations, i.e., pro cess and observed data are stationary . There are sev eral v ariants of Kalman ﬁlter. F or instance, Extended Kalman ﬁlter (EKF) is a mo diﬁcation of basic Kalman ﬁlter free of the assumption regarding the linearit y of either the underly- ing pro cess or of the relationship b etw een the pro cess and the measurements. Instead, partial deriv ativ es of the pro cess and measurements functions are calculated to linearize the estimation around the current state prediction. Unfortunately , this also transforms the noise, which no linger remains Gaussian, thereby inv al- 400 idating one of the ﬁlter’s original assumptions. This is a fundamental ﬂaw in the EKF model, the eﬀect of whic h is that the state estimator only appro ximates the optimalit y of Ba y es’ rule b y linearization [58]. It also requires a solution (alb eit approximate) for a Jacobian matrix, which is diﬃcult to ﬁnd. Computationally , it is less eﬃcien t and pro cess time increases as all cov ariance and mo del parameters need to b e recalculated in eac h iteration. Most imp ortan tly , there exists the p ossibilit y of ﬁlter divergence. T raditionally , the EKF was the most p opular Kalman v ariant for state estimation of non-linear pro cesses. Ho wev er, due to the issues men tioned, and improv ement is computational resources alternativ es hav e recently b een developed [59, 60]. The Gauss-Hermite quadrature Kalman ﬁlter (GHKF), a modiﬁed version of the GHKF called the unscented Kalman ﬁlter (UKF), and Monte-Carlo Kalamn ﬁlters (MCKF) are all v arian ts of the basic Kalman ﬁlter applied to non-linear pro cesses; they diﬀer in ho w estimates for the Kalman ﬁlter in tegrals are calculated and consequen tly hav e v arying computational eﬃciencies. F or all of the v arian ts, assumptions ab out Gaussian noise are still required [60]. In practice, if the system has a large num b er of states, the UKF is the technique of interest for especially when the non-linear functions are smo oth [60, 61]. Sp eciﬁc examples of applying Kalman ﬁlters to BN for the purp oses of RUL estimation of engineering assets can b e found in [62, 63]. 4.1.7. Bayesian estimation w ith p article ﬁlters P article ﬁlters are the candidate alternatives to Kalman ﬁlters as they are not constrained by linearity or Gaussian noise assumptions. They are particularly useful for situations in which the p osterior distribution is m ultiv ariate or non-standard. The principle diﬀerent b et ween Kalman ﬁlter and Particle ﬁlter (with resp ect 29 to how they calculate the p osterior PDF) is that the former relies on extrap olating from the prior state, whereas the latter uses a sequen tial imp ortance sampling scheme to sim ulate the entire next state in every 420 iteration of the ﬁlter. P article ﬁlter does this by generating a set of random samples (also known as particles) from a theoretical densit y function and then adjusts the asso ciated set of particle weigh ts at eac h iteration. Samples of dynamic noise are also generated with each cycle. It is imp ortant to note that with suﬃcien t samples, P article ﬁlters are more accurate than either the EKF or UKF. In addition, compared to the classical Mon te-Carlo in tegration, they require fewer samples to adequately approximate the distribution, which results in a sup erior computational p erformance. Ho wev er, there are certain problems in real applications. The ﬁrst diﬃculty is that as the n um b er of iterations increases, the ﬁlter can degenerate and the p osterior PDF appro ximation b ecomes zero [60]. One possible method of a v oiding this problem is ob viously to increase the n umber of samples and reduce the num b er of iterations. Unfortunately , this is not alw ays practical due to the increased computation time. Alternatively , a re-sampling step can b e in tro duced to each time interv al that replaces low probability particles with the same num b er of high probability particles. A num b er of diﬀeren t re-sampling metho ds can b e used [64, 65], including the inv erse transformation metho d [60] and the Bo otstrap P article Filter [66, 67, 68, 69]. A detailed discussion on optimal sampling (and re-sampling) is given in [70]. There are also a num ber of Particle ﬁlter approximation techniques that do not in volv e re-sampling. These use Monte-Carlo, GaussHermite or Unscented Kalman ﬁlters to deﬁne an imp ortance densit y functions, from whic h particles are sampled. In the ﬁrst t w o of these methods the importance density is assumed to be Gaussian, based on the mean and cov ariance output of the updated prior density . According to Haug, b oth the GaussHermite and Unscented Particle ﬁlters w ork w ell and are implemen table in real-time, while the Monte-Carlo Particle ﬁlter requires an excessiv ely large num ber of samples and outliers can result in numerical instabilities that preven t conv ergence [60]. Although particle ﬁlters hav e b een used extensiv ely 440 in b oth econometrics and target tra jectory forecasting, there are only a few published example applications related to asset health prognosis [71, 72]. [71] used sequential imp ortance sampling Particle ﬁlters to estimate the time progression of a fatigue crac k, which was mo delled with a combined state dynamic mo del and a measuremen t mo del to predict the posterior probability density function of the stage (the fatigue crac k gro wth) [71]. Similarly , in [72] a combined Bay esian-b eha vioural mo del is used along with Particle ﬁlters for prediction of fatigue crac k growth progression. 4.2. Statistic al mo dels In this section we talk ab out the statistical branch of Fig. 4. Statistical models use previous insp ection results on similar components to estimate b oth initiation and progression of a p ossible failure mode. They are most of the time used in problems when suitable dynamic model is not av ailable as an alternativ e for ANN. The nominal (standard) b eha viour of the comp onen t is used as a reference and prediction of the R UL is ac hieved by comparing the current behaviour to the nominal one. Statistical mo dels are generally categorized among the data-driven metho ds since they utilize temp oral data suc h as condition or pro cess monitoring outputs. 30 4.2.1. T r end evaluation Probably the simplest approac h to RUL prediction is based on trend analysis. It uses the trend of a single monotonic parameter whic h is b elieved to b e related to the remaining life of the comp onen t. The selection of the appropriate “feature parameter”, whic h may represent a single sensor (feature) or a num ber of sensor (features) is critical. This one feature parameter is then plotted as a function of time and is used along with a pre-deﬁned alarm lev el. A warning end-of-life signal will b e triggered when the feature 460 parameter reaches the alarm level. In fact, there could b e several alarm lev els dep ending on the severit y of the health deterioration of the comp onent and its capabilit y to p erform the assigned tasks. F or instance, there could b e alarms for early-w arning and ‘ﬁnal failure’ (denoted by asterisk and red circles in Fig. 3). Standard regression metho ds are used to calculate a candidate trend e.g, p olynomial ﬁt using a least-square metho d. There are situations in whic h there is no data for all parameter levels up to and exceeding the alarm limits and requires trend extrap olation. How ever, in engineering prognosis, often times failure mechanisms c hange with the progress of failure and may alter the trends signiﬁcantly . Therefore, in terp olation is alw ays preferred o ver extrap olation. It is also imp ortant to chose alarm limits with acceptable accuracy (through data records and p ersonnel knowledge). It is obvious that if a somewhat conserv ativ e limit is selected, there is great p ossibilit y of premature replacement, and in contrast, if a high v alue for alarm is used, it is highly probable that the algorithm will miss a failure. With resp ect to the conﬁdence limits, if only in terpolated data is being used, conﬁdence levels on the prognosis can b e calculated based on the v ariance of the underlying trend. Ho wev er, conﬁdence limits cannot b e calculated for extrap olated regions. Implementation of this t yp e of trend ev aluation is simple and easy but indications of imp ending failure are typically noisy and often non-monotonic [15]. T he failure situation gets even more complicated when m ultiple failure mo des exist. Consequen tly , simple thresholds may not result in a reliable RUL prediction, particularly where data needs to b e extrap olated. On the other hand, as the failure is approac hed damage conditions b ecome clearer, whic h results in clearer trends. Note also that parameters most appropriate for predicting RUL ma y not b e the same as those used for detecting the b eginning of a fault mode. F or example, in the early stages of b earing’s failure, Kurtosis (4th statistical momen t) of a b earing’s vibration signal often increases but can 480 then decrease as the b earing approaches its end of life. 4.2.2. Autor e gr essive mo dels F orecasting of time series data are widely achiev ed through using Autoregressiv e moving av erage (ARMA), Autoregressiv e in tegrated moving av erage (ARIMA) and ARMAX models [73]. In all the v arian ts, a linear function of past observ ations (and random errors) is used to calculate the future v alue; a comprehensiv e summary is presented in [74]. The three mentioned autoregressive mo dels are slightly diﬀerent in the linear equation, whic h is used to relate inputs, outputs, and noise. ARMA and ARMAX mo dels should only b e used for stationary data since they can remov e temp oral trends. Note that a time series is deﬁned to b e (w eakly) stationary when its ﬁrst tw o moments, i.e., mean and v ariance, resp ectively , are time-in v arian t 31 under translation [75]. The auto correlation also needs to b e indep enden t of time. Consequen tly , prior to mo delling it is essential to p erform trend tests to ensure the v alidity of the stationarity assumption. ARIMA mo dels, that use the concept of in tegration enforcemen t, are capable of describing systems with lo w frequency disturbances. Autoregressive mo dels are developed in three recursive steps: I. Mo del iden tiﬁcation: Initially , using a set of time series data, v alues for the orders of the autoregressive and moving av erage parts of the ARMA/ARIMA equations are hypothesized, as w ell as the regular- diﬀerence parts for the ARIMA mo del. A suitable criterion of ﬁt is also assumed. I I. Parameter estimation: Using non-linear optimization techniques (e.g., a least-squares metho d), param- eters of the ARMA/ARIMA equations are calculated to minimize the ov erall error betw een the mo del output and observ ed input-output data. I II. Mo del v alidation: A num b er of standard diagnostic chec ks are used to v erify the adequacy of mo dels, 500 utilizing unseen data. According to [76], options include the following: examining standardized resid- uals, auto correlation of residuals, ﬁnal prediction error, Ak aik e information criterion, and Ba y esian Information Criterion (BIC). These three steps are rep eated until a satisfactory mo del is obtained. Once the mo del parameters are ﬁxed, it can be used to forecast future v alues; if the minimum mean squared error is used as the criterion these are simply the conditional exp ectations of the mo del. Ho wev er, note that, typical ARMA models (and v arian ts) are eﬀective for short-term predictions, but less reliable when used for long-term predictions. They are not reliable for the long-term predictions due to dynamic noise, their sensitivity to initial system conditions and an accumulation of systematic errors in the predictor [73]. An extension of the basic ARIMA approac h is prop osed in [76] that uses b ootstrap forecasting for machine life prognostics. This v arian t a voids using previous v alues predicted to forecast future v alues, and instead generates predictions only based on true observ ations. As parameters were updated in realtime, the mo del w as able to adapt to dynamic changes in the op erating process and did not suﬀer from error accumulation. Predictions w ere sup erior to those based on traditional ARIMA models. Another example utilizing ARMA mo delling for prognostic estimation is presen ted in [77]. Although few details are av ailable on the models themselv es, ARMA tec hniques hav e also incorp orated into the prognostic and data fusion softw are developed by the NSF Center for Intelligen t Maintenance System as describ ed in [25] (the system also uses other types of mo delling for residual life estimation including prop ortional hazards and neural net work approac hes). One no vel alternative to ARMA metho ds for prediction of time-series data worth y of mention uses DempsterShafer regression. Application of this tec hnique to mac hinery prognostics is presen ted in [78]. It oﬀers signiﬁcant 520 p oten tial for applications where temp oral trends of prognostic parameters (to b e used for extrap olation) are non-linear and/or chaotic and thus can not b e mo delled using ARMA tec hniques. Reference [79] discusses the application of autoregressiv e to s lo wly degrading systems sub ject to soft failure and condition monitoring at equidistan t, discrete time ep o c hs. 32 4.2.3. Pr op ortional hazar ds mo del ling Prop ortional Hazards Mo delling (PHM) was ﬁrst prop osed in [80] and mo dels the wa y explanatory or concomitan t v ariables, also referred to as co v ariates, aﬀect the life of the equipmen t, and at the same time, is one of the most extensively used mo dels for prognostics. The basic diﬀerence b etw een PHM and the linear regression methods is that the former assumes a multiplicativ e relationship for co v ariates, whereas that latter assumes an additiv e eﬀect on the ov erall hazard rate. PHM mo dels deterioration as the pro duct of a baseline hazard rate, and a p ositiv e function. The multiplicativ e function reﬂects the eﬀect of the op erating en vironment on the baseline hazard and is describ ed b y a v ector of cov ariates and an asso ciated vector of unkno wn regression parameters. R UL can b e deduced from the asso ciated surviv al function [81]. The positive function is usually assumed to b e exp onen tial (primarily for conv enience) although other mathematical functions suc h as logarithmic, inv erse linear, linear or quadratic functions are also common [82, 83]. It is p ossible for the elements of the cov ariate process vector to take p ositiv e v alues implying that the co v ariate is actually impro ving the condition and thus reducing the hazard rate when compared to the baseline. F or instance, increased corrosion inhibits (or concentration reduces) the rate of internal corrosion [82]. F or some mec hanical as well as electrical comp onen ts the seasonal v ariation of temp erature results in p ositiv e and negativ e con tributions. Cov ariates are often referred to as in ternal or external. In the prognostics con text, 540 in ternal cov ariates refer to outputs generated by the comp onen t b eing degraded and thus only exist as long as the degraded comp onen t remains in service. An example of internal cov ariate is the vibration lev el at the inner race b earing frequency that is used to predict b earing failure. In ternal co v ariates can also b e considered ‘resp onse cov ariates’ as they are generated in direct resp onse to the failure pro cess. On the other hand, external co v ariates refer to outputs generated by an indep endent pro cess; they can also b e considered ‘risk factors’ and are usually not aﬀected by repairing or replacing the degraded comp onen t. An example for external cov ariate is sulphur concen trations in crude oil that ma y b e used to indicate increased risk of pro cess pip e corrosion. A more detailed discussion on co v ariates is giv en in [84]. PHM w orks according to a n umber of assumptions: a) Times to failure are indep enden t and iden tically distributed, i.e., p erfect repair. b) Co v ariates ha ve a multiplicativ e eﬀect on the baseline rate. c) Individual co v ariates are indep enden t (i.e., the v alue of the co v ariate function for one item does not inﬂuence the time to failure of other items). d) The eﬀect of the co v ariates is assumed to be time indep endent. e) All inﬂuen tial cov ariates should b e included in the mo del. f ) The ratio of any t wo hazard rates is constant with resp ect to time (thus the resp ectiv e surviv al curves will not in tersect). 33 It is p ossible to use graphical analytical go o dness-of-ﬁt tests to verify whether these assumptions are v alid for the system b eing mo delled [82, 85]. Applying PHM requires the estimation of the parameters of the baseline hazard function and the co v ariate pro cess vector. Initially , the cov ariate v ector w eightings are 560 calculated irresp ectiv e of the form of the baseline hazard function for which the maxim um likelihoo d metho d is the most commonly applied tec hnique, but a v ariety of other approaches hav e also b een used [86, 80, 82, 87, 88]. Higher weigh tings are given to the cov ariates that are go o d indicators of failure, while those with little correlation to failure are assigned muc h smaller weigh tings. The accuracy of the mo delling is improv ed if only relev ant c o v ariates are incorp orated in to the mo del. Consequen tly , a backw ard step wise pro cedure is often implemen ted to exclude the least signiﬁcant cov ariates and re-estimates the mo del parameters; this pro cedure is rep eated until all remaining factors are signiﬁcant. Alternativ ely , new v ariables can b e sequen tially forced into the mo del during the search for signiﬁcant cov ariates. Once cov ariate parameters ha ve b een deﬁned, v ariables of the baseline hazard function can b e estimated using either parametric or non-parametric metho ds. The latter is generally preferred by statisticians as the form can be estimated from the data [86, 80, 82, 89], which is then compared with v arious standard distributions forms to identify the most appropriate mo del. In practice, how ever, the baseline hazard function is often assumed in adv ance to b e a W eibull or exp onential function to facilitate the use of common parametric regression metho ds. Due to the confusing eﬀects of the co v ariates, these pre-assumed forms of the hazard function ma y not b e justiﬁed and ma y not be the b est choice [86]. T o ensure that the baseline hazard function remains ph ysically meaningful it is desired to conﬁgure cov ariates in a manner that they equate zero for the ‘baseline’ op erating state (although this requirement is not a mathematical constrain t). A critique of early attempts to apply prop ortional hazards mo del to problems of engineering reliability w as provided by [86]. A more comprehensiv e review is conducted in [82]. Nev ertheless, the b ody of work on PHM clearly demonstrated the adv an tages of PHM o ver standard regression techniques, including the ability to manage n uisance v ariables 580 (unrelated cov ariates), censored data [89]. Over the past years, these basic techniques ha ve b een reﬁned, extrap olated and expanded, particularly for the purp oses that include optimizing main tenance decisions [90, 91, 92, 93, 94, 95, 96, 97, 82, 98], analysing data obtained from acce lerated life tests [83], and appliction to mo del systems that are sub ject to partial repair [99, 100, 101]. Speciﬁc examples of industry led research include [102, 103, 104, 105]. A v ariation of PHM that do es not assume p erfect repair, known as the Prop ortional Intensit y Mo del, exists and has also been applied by sev eral researc hers [106]. Intuitiv ely , the b est mo dels are exp ected to b e based on a mixture of diagnostic indicators, whic h seems to be problematic due to the lack of published examples. T o ov ercome the problem of insuﬃcient failure data, Ref [107] has applied an exp ert judgement approac h (paired comparison), in conjunction with a small amount of actual failure data to p opulate the PHM parameters [107]. Collectiv ely , this work to date on the application of PHM to asset prognostics has b een conducted using highly selective and w ell-controlled data sets (alb eit some of the data was collected from real op erating plan ts); in each case, only a small num b er of o verlapping failure mo des was modelled. 34 Th us, the ability of PHM to estimate RUL for prognosis of v aried faults in complex systems is uncertain and lik ely to be an ongoing c hallenge. The extension of the PHM to complex repairable systems with a n um b er of sub-systems is a diﬃcult task. A complex system has several components with their associated failure mo des and the assumption that failures are indep enden t and identically distributed is far from truth. In addition, it is hard to ﬁnd a comprehensive set of cov ariates to describ e all failure mo des. How ever, as equipment b ecomes more reliable it is diﬃcult, from a practical standp oin t, to obtain suﬃcient data p ertaining to failures and corresp onding cov ariates to mo del all failures [108]. F urthermore, data aggregation can obscure 600 information ab out comp onen t failures th us making it diﬃcult to pro duce consisten t and applicable histories [85]. All in all, it is suggested to apply PHM at the failure mo de lev el when appropriately reﬁned failure histories and physically relev an t cov ariates are known. This is not a straightforw ard task as it requires more data collection pro cedures in addition to the kno wledge of the ph ysical root causes of failures (i.e., the failure mo de). In addition, asso ciated working age and diagnostic information must b e recorded accurately [97] and in an accessible format. Note that given curren t mo delling limitations, when a subsequen t repair/replacement is made, susp en- sion ev ents need to b e recorded against all other p oten tial failure mo des that are aﬀected by that re- pair/replacemen t, so that w orking ages for these failure modes can be adjusted. (This is only practicable if implemen ted as an autonomous pro cess.) This is done to av oid biases in estimates for the RUL, which may result in underestimations [97]. More information ab out data requirements for PHM is given in [108]. Since the PHM relies on the data of particular failure mo des, it is not capable of estimating RUL of failure mo des, whic h hav e not occurred previously . The traditional PHM approach to non-stationary pro cess (e.g., reliabilit y growth of repairable system) is p erformed by using a stratiﬁed approach [89, 109] in which data is group ed based on v arious failure times in the life cycle for each comp onent. Each step is then mo delled individually , with required failure histories for eac h step [82]. Dynamic PHM is an alternativ e to the traditional PHM where a generalization of the basic PHM equation is used to take in to account time dependent cov ariates [92, 110, 88]. The dynamic mo del is capable of predicting the future developmen t of cov ariate and failure times. In this work, the non- stationarit y w as accommo dated by assuming that the cov ariate vector w as a m ultiv ariate non-homogenous 620 Mark ov pro cess with all but failure state hidden. It w as also assumed that cov ariates were only observ able at certain times (i.e., p erio dic insp ection/monitoring) [88, 92]. Bac kward recursion algorithms and optimal stopping framew ork were then used to determine optimal inspection interv als (based on minimizing exp ected cost) as well as to calculate the exp ected RUL. It was assumed that the system was renewed after replacement. In practice, only a few states are needed to represen t the failure pro cess, suc h as those corresp onding to p eriods of ‘w ear-in’, ‘normal’ and ‘wear-out’. Some publications hav e reported the results of this approach for analyzing real op erating systems [94, 97, 111]. 35 4.3. Physic al mo dels Ph ysical mo dels (also known as physics of failure or b eha vioral mo dels) exploit physical la ws to quantita- tiv ely characterize the b eha viour of a failure mode. Obviously , this requires a thorough/detailed understand- ing of the system b ehavior in resp onse to external loads such as stress, at b oth macroscopic and microscopic lev els. It is based on the fact that it is p ossible to describ e the b eha vior of a comp onen t accurately and analytically . At the heart of the metho d is the estimation of an output for the RUL of a comp onen t by solving a deterministic equation or set of equations derived from extensiv e empirical data. Data includes common scien tiﬁc and engineering knowledge as well as those acquired through speciﬁc lab oratory or ﬁled exp erimen tation. The ph ysical mo del en tails physical prop erties, constant parameters of the equations, cor- rosion rates, etc. In the end, the model is describ ed by using a series of ordinary or partial diﬀerential equations that can then b e solved in most cases with Lagrangian or Hamiltonian dynamics, approximation metho ds applied to partial diﬀerential equations, distributed mo dels [18, 112]. A more comprehensive list of b eha vioral mo dels is provided in [17]. 640 Once a model is developed and veriﬁed, sensor measurements of the actual component are used against outputs of the dev elop ed model to calculate the residuals (i.e., diﬀerences b et ween reality and the mo del); The status of fault is drawn if large residuals are observed while small residuals are attributed to noise and modelling errors under normal operating conditions [24]. A n umber of thresholds could b e deﬁned to iden tify the presence and/or condition of faults. There are several metho ds to calculate the residuals including parameter estimation, state-space metho ds or parit y equations the b eneﬁts of eac h are discussed in [113]. The pro jection of the degradation b eha vior in to the future is used for estimating R UL. One has to deﬁne c haracteristics for a set of features and their asso ciated levels of accuracy in order to construct a ph ysics of failure mo del: a) Iden tify likely initiating failure mo des for which b eha vioral mo dels are required. b) Pro cess b ehavior across p ossible/t ypical op erating ranges. c) Degradation b eha vior under aforemen tioned pro cess conditions. d) Relationship b et w een pro cess measuremen ts and degradation b eha vior(s). e) Pro cess and measurement noise. In practice and for many cases, the abov e parameters are inherently probabilistic random v ariables thus demands the incorp oration of their statistical distributions into the model. This enables the estimation of conﬁdence limits. F or the purp oses of prognostics, failure mechanisms can b e broadly divided in to t wo categories [114]. The ﬁrst t yp e of failure is asso ciated to ov er stress failures and they occur when incurred load exceeds the strength of the material; this kind of stress is not destructiv e, i.e., they ha ve no long-term eﬀect once the load has b een remov ed. Examples include brittle fracture, yielding and buc kling. Once the 660 particular damage reaches the allow ed tolerance, normal op erating loads exceed the remaining strength of 36 the material and an ov er-stress failure is said to ha ve happ ened [46]. The second type of failure is w ear-out failures which are c haracterized by accum ulated damage that do es not disapp ear when the load is remov ed (e.g., fatigue, wear in brak e pads). A physical prognostic mo del for wear-out failure mo des needs to b e able to trac k aggregated damage and its rate of progression under any/all op eration conditions. Consequen tly , if a v ailable and when suﬃciently complete, physics-based models tend to signiﬁcantly outp erform other types of mo dels [24]. Additionally , the outputs of physical mo dels are easy to interpret. Their obvious disadv antage is that the b ehavior of the system must b e deriv able from ﬁrst principles, whic h ma y not alwa ys b e p ossible due to an imp erfect understanding of how the failure mechanisms b eha ve under the range of relev ant op erating conditions. Ev en if the mec hanisms are fully understoo d, assigning the appropriate parameters for all asp ects of the mo del requires a signiﬁcant volume of accurate and reliable m ultiv ariate data that is rarely a v ailable. Condition indicators sp eciﬁc to the failure mo de b eing modelled m ust also b e identiﬁed and contin ually collected. Consequently , physics of failure mo dels tend to b e used in isolated cases, for w ell-understo od faults in simple systems and/or by users with established diagnostic systems and predictive maintenance programs. It seems that crack propagation failure mo des are the most commonly dev elop ed b eha vioral mo dels for prognostics. 5. P&HM T o ol Selection Metho d In this section, a pro cedure is explained to facilitate the selection of the most appropriate metho ds/algorithms for v arious steps inv olv ed in P&HM [20]. The av ailable data is a steppingstone tow ard dev eloping a sys- tematic approach to apply P&HM metho dologies to traditional as well as no vel areas. Prior to examining 680 the possibility of using certain algorithms, it is pivotal and b eneﬁcial to understand the characteristics of the data and possible causality b et w een these characteristics, and the nature of the system in terms of the op erating condition, service intensit y , system dynamics and all other applicable attributes. Achieving an eﬀectiv e metho dology with the appropriate blend of algorithms that results in reliable accuracy is, more or less, dominated by the c haracteristics of the data whether it is in the form of vibration, acoustic emissions, en vironmental parameters, etc. The ma jor tasks in the ﬁeld of PHM are already describ ed and include signal pro cessing, feature extraction and reduction, fault diagnosis, health assessment, p erformance prediction and so on. How ever, within eac h task there exist a multitude of algorithms which ha ve b een developed and b enc hmark ed to pro cess signals, classify them and using the results determine the current health status and estimate the future condition of the comp onen t under study . Practitioners and researchers usually hav e dif- feren t algorithms preferences which is dep enden t up on the application and av ailable infrastructure. T able 3 presen ts a list of the most commonly used algorithms including their applications, strengths and weaknesses in the ﬁeld of P&HM. Algorithm selection is a crucial step for dev eloping an eﬀective P&HM system, which will ultimately aﬀect the results and their conﬁdence limit. One wa y of selecting algorithms is to take a heuristic approach that relies on researchers’ exp erience and exp ertise to meet users’ requirement. How ev er, such an approach is not ideal for situations in which there 37 is a lack of exp ert knowledge (and exp ert p ersonnel), and could b e time-consuming for complex problems or systems. The goal is to achiev e the following targets in the most eﬃcient w ay: 1) to provide quan tiﬁed selection criteria, 2) to enable automatic benchmarking, and 3) to recommend the appropriate to ol(s) for a particular application. It is therefore inevitable to devise a selection sc heme that compares and ranks 700 the suitabilit y of eac h algorithm by considering the application attributes, proﬁciency and requiremen ts of the end user. A feasible solution can b e a numerical comparison based on the ranking of algorithm scores for each category so that the top algorithms can b e selected. A suitable ranking metho d for algorithm selection is Qualit y F unction Deplo ymen t (QFD) [115] and is b est kno wn as a tool for product design, qualit y managemen t, customer need analysis and decision making purposes [116]. In traditional QFD, a House of Qualit y (HOQ) is constructed to combine engineering attributes and customer needs (and their assigned w eights), and transform them into design sp eciﬁcations and con trollable parameters. This provides the quan tiﬁcation step of the aforementioned targets. F or algorithm selection, data c haracteristics, corresponding algorithm suitability and user inputs are integrated to give a ranking of all algorithm candidates in each category . The pro cess of applying QFD for algorithm selection can b e summarized through the following main steps: 1) According to the application and av ailable knowledge of the data, all criteria related to the application should b e selected. 2) The prop erties of each criterion should be iden tiﬁed in order to describe the a v ailable data in a detailed manner. These criteria do not hav e to be binary as long as am biguit y can b e a v oided, so users can classify the lev el of the characteristic with high conﬁdence. F urthermore, a quan tiﬁed description is recommended in this step, for example, low, medium and high stationarit y can b e presen ted by ascending in tegers like 1, 3 and 5. 3) Eligible algorithms for each characteristic are compared in a pair-wise w ay based on algorithm applica- bilit y . Analytical Hierarch y Pro cess (AHP) [117], employ ed in this step, is a decision making to ol, which 720 is able to compare every paired combination of algorithms and pro vide ﬁnal applicabilit y indices for all algorithms for eac h sp eciﬁc c haracteristic. 4) An HOQ can b e established for each one of the algorithm categories to aggregate all the indices from the previous step for all characteristics in order to generate an o verall w eight, based on which a ﬁnal rank of algorithms can b e decided for this category . Therefore, a pro cedure can b e established for the user to execute an eﬀectiv e, systematic P&HM approach with the top ranked algorithms from each category . As an example application, Figure 5 in Ref [20] illustrates the QFD algorithm selection to ol using the gears of a wind turbine. Rotary comp onen ts of a wind turbine system such as rotor blades, bearings, shafts and gears are working under dynamic loads and are more susceptible to failure than other components. The aforemen tioned systematic metho dology can b e referenced to explore and develop fundamen tal techniques 38 to aid in establishing a P&HM system for wind turbines under v arying en vironmental, operational and aging pro cesses. In this case, only vibration data is av ailable, and the applicabilit y of each relev ant algorithm is deﬁned by assigning an imp ortance to diﬀerent characteristics using a scale ranging from 1 to 5 (5 b eing the most imp ortant). The rankings are structured so that in each catalog the algorithm with low est ranking is the most recommended one. The to ol selection for eac h of the other critical comp onen ts can b e p erformed in this fashion. 5.1. Visualization to ols After the selected algorithms hav e digested the data, prognostics information is ready for further utiliza- tion to supp ort the decision making process. One v aluable ob jective of PHM is to enable a supp ort system to conv ey the right information to righ t p erson so that judicious decisions can b e made at the righ t time. 740 Therefore, visualization tools are essential parts of a PHM metho dology . F our frequently used visualization to ols, Degradation Chart, Performance Radar Chart, Problem Map and Risk Radar Chart, can b e designed to presen t prognostics information as shown in b elow Figure taken from [20] for the sake of discussion. Figure 5: F our visualization tools for P&HM [20]. The functionalities of the presen ted visualization to ols are describ ed as follows [118]: • Degradation Chart -If the conﬁdence v alue (0-unacceptable, 1-normal, b et ween 0 and 1-degradation) of a comp onent drops to a lo w lev el, a maintenance practitioner can trac k the historical conﬁdence v alue curv e to ﬁnd the degradation trend. The conﬁdence v alue curv e shows the historical, curren t and predicted conﬁdence v alue of the equipment. An alarm will b e triggered when the conﬁdence v alue drops under a preset threshold. • P erformance Radar Chart -A main tenance practitioner can lo ok at this c hart to get an ov erview of the p erformance status of each component. Eac h axis on the chart corresponds to the conﬁdence v alue of a sp eciﬁc comp onent. • Classiﬁcation and F ault Map -A Classiﬁcation and F ault Map is used to determine the ro ot causes of degradation or failure. This map classiﬁes diﬀerent failure mo des of the monitored comp onen ts by presen ting diﬀerent failure mo des in clusters, each indicated by a diﬀerent color. 39 • Risk Chart -A Risk Chart is a visualization to ol for plant-lev el maintenance information management that displays risk v alues, indicating equipment maintenance priorities. The risk v alue of a machine (determined b y the pro duct of the degradation rate and the v alue of the corresp onding cost function) indicates how imp ortan t the machine is to the maintenance pro cess. The higher the risk v alue, the higher the priorit y given to that piece of equipment for requiring maintenance. 760 6. P erformance Metrics for Ev aluating Prognostic Predictions P erformance criteria on metrics determine the adequacy of a prognostic approach for a given application [119]. Extensive work has b een rep orted to deﬁne the appropriate p erformance metrics for a given appli- cation and health management and conation monitoring approac hes [120, 119, 28, 121]. As the literature sho ws, there are three ma jor p erformance indicators to determine the eﬃciency and eﬀectiveness of PHM applications: prognostic distance, accuracy , and precision. The time b etw een the predicted time of incipient failure and actual comp onent failure is called the prognostic distance. This deﬁnition of prognostic distance has b een derived from the application of canaries [122]. Accuracy means the correctness of the remaining life estimates. The correctness of the prediction of time determines the accuracy of prediction. Precision accoun ts for the uncertaint y estimates in remaining life prediction. The width of the uncertaint y band de- termines the precision of the estimates. A shorter band has higher precision, and a wider band has low er precision. The parameters that are of interest to risk-informed applications include assessment of the relia- bilit y/safety margin for case or scenario b eing evolv ed. Even though extensiv e work has b een p erformed on the developmen t of p erformance metrics, there is need for further research on the developmen t of acceptance criteria for p erformance metrics [123]. 6.1. Applic ations In this section, we present a list of works on the rotary machinery prognostics as w ell as other critical comp onen ts that are widely used in engineering platforms, engines and mechanical systems. T able 5 gives an in tro ductory summary of to ols for common critical comp onents, regarding the comp onents’ issue and p ossible failure mo des, characteristics, common a v ailable data types, common features and algorithms ap- 780 plied for diagnostics and prognostics. Note that the following abbreviations are used for F ourier T ransform (FT), Short Time F requency T ransform (STFT), W av elet T ransform (WT), Empirical Mo de Decomp osition (EMD), Auto-regression (AR), Hilb ert-Huang T ransform (HHT), Neural Netw ork (NN), Hidden Marko v Mo deling (HMM), Supp ort V ector Machine (SVM), Genetic Algorithm (GA), Auto-regressive Moving Av- erage (ARMA), Principal Component Analysis (PCA),Wigner-Ville T ransforms (WVT), Supp ort V ector Regression (SVR). In addition, there are pap ers that discuss the prognostics on v arious comp onen ts/system including bat- teries [216, 217, 218, 219, 220, 221, 222, 223] (prognostics for batteries app ears to b e at a more adv anced stage than prognostics for structures [3]), DC-motor [215, 224, 225], electric motors [226, 227, 228] b oiler 40 T able 5: In tro ductory summarization of to ols of critical comp onents. Item Issue & failure Characteristic Common measures Common features Used mo dels Bearing Outer-race, inner-race, roller, and cage failures Raw data does not contain insightful information; low amplitude; high noise Vibra- tion, oil debris, acoustic emission Vibration characteristic frequency , time domain statistical characteristics, metallic debris shape, size, quantit y , sharp pulses and rate of developmen t of stress-wa ves propagatoin FT [124, 125], STFT [126], WT [127], EMD [128], Bispectrum [129], AR F requency Spectra [130], NN [131, 132, 133], HMM [134, 135], F uzzy logic [136], GA [137], ARMA [138], Sto c hastic Model [139, 140], PCA [141] Gear Manufacturing error, to oth missing, to oth pitting/spall, gear crack, gear fatigue/wear High noise; high dynamics; signal modulated with other factors; gear specs need to be known Vibra- tion, oil debris, acoustic emission Time domain statistical features, vibration signature frequencies, oil debris quantity and chemical analysis FT [142], STFT [143, 144], WT [145, 146], EMD [147, 148, 149], HHT [149, 150, 151], NN [152, 153, 154, 155], F uzzy Logic [156], Neuro-F uzzy Hybrid Mo del [157], Energy Index Analysis [157], Kalman Filter [158, 158, 159], SVM [160], Autoregressive Model [161, 162], Particle Filter [163] Shaft Unbalance, bend, crack, misalignment, rub Vibration signal is relatively clean and harmonic frequency components of rotating sp eed can indicate the defects Vibra- tion Vibration characteristic frequency , time domain statistical characteristics, system mo dal characteristics FT [164], WT [165], WignerVille T ransforms (WVT) [166], EMD [167, 168], Analytical or Numerical Mo dels [169, 170], NN [171, 172, 173], F uzzy Logic [174], Support V ector Regression (SVR) [175], GA [176, 177], ARMA [178, 179] Pump V alv e impact, score, fracture, piston slap, defective bearing and revolving crank, hydraulic problem Pump’s dynamic responses, generated by a wide range of possible impulsive sources, are very complex; nonlinear, time-v arying behavior Vibra- tion, pressure, acoustic emission Vibration characteristic frequency , pressure time domain statistical characteristics, sharp pulses and rate of developmen t of stress-wa ves propagation FT [180], STFT [181, 182, 183], WT [184], Envelop Analysis [185], NN [186, 187, 188], F uzzy Logic [189, 190], Neuro-F uzzy Hybrid Mo del [191], Rough Set [192], PCA [193] 41 T able (contin ued). Item Issue & failure Characteristic Common measures Common features Used mo dels Alternator Stator faults, rotor electrical faults, rotor mechanical faults Currents and voltages are preferred for noninv asiv e and economical testing Stator currents and voltages, magnetic fields and frame vi- brations Specific harmonic components, sideband components FT [194], WT [195, 196, 197], Instantaneous Po wer F ourier T ransform [198], Bispectrum [199, 200], High Resolution Spectral Analysis [201, 202], Exp ert Systems [203, 204], NN [205, 206, 207], HMM [208], F uzzy Logic [209, 210, 211], GA [211], Higher Order Statistics [212], Park’s Current V ector Pattern [213], Petri Net [214], Kalman Filter [215] tub e [229], b earing [230, 134, 231], engine [232], diesel engine [91], wind turbine [233], gearb ox [234, 235], oil [236], h ydraulic system [237], pumps [238, 239], (automatic) transmission [105, 240] and alternator [241]. In addition, there exist considerable literature on the application of prognostics to aerospace engineering systems with a few of them listed here due to their imp ortance for further study [242, 243, 244, 207, 154, 245, 246, 247, 107, 248, 21, 249, 250] 7. Automobile Applications In this section, w e discuss the details of a few relev ant applications of prognostics. There are a few papers that worth attention. F or instance, Ref [251] determines a reliability index for the most failure parts and complex systems of tw o brands of cit y buses for the p erio d of time failures. The analysis co vered damages of the follo wing systems: engine, electrical system, pneumatic system, brak e system, driving system, central heating and air-conditioning and doors. F urthermore, the reliability w as analyzed based on a W eibull model. 800 Ref [252] discusses the maintenance planning for a commercial heavy v ehicle. Reference [95] discusses work completed to improv e the existing oil analysis condition monitoring program b eing undertaken for wheel motors. Oil analysis results from a ﬂeet of 55 haul truc k wheel motors were analyzed along with their resp ectiv e failures and repairs o ver a nine-year p erio d. 7.1. Pe er-to-Pe er Col lab or ative V ehicle He alth Management This section reviews an adv anced vehicle diagnostics and prognostics (D&P) technology initiated by the General Motors company [253]. The proposed framew ork which is called Collab orativ e V ehicle Health 42 Managemen t (CVHM) is dev elop ed to automatically optimize the D&P algorithms on a host v ehicle, using the ﬁeld data collected from p eer vehicles encountered on the road. The ob jective is to improv e the D&P p erformance without incurring costs of human interv en tion. The exp erimen tal results on battery RUL prediction show the eﬀectiv eness of the prop osed framework. This prop osed framework has b een implemented in a small test ﬂeet as a pro of-of-concept prototype. It is known that the failure mo des of vehicles are diverse and v ary from vehicle to v ehicle. As a result, it is very challenging to achiev e accurate and robust D&P p erformance for vehicle systems in the ﬁeld. The traditional approac h to D&P is achiev ed b y introduction of individual faults on b enc h tests, test vehicles or through accelerated ageing tests and b y collecting a large amoun t of data. This requires a signiﬁcant amoun t of algorithm tuning to b e done by the dev elopment engineers. The prop osed CVHM framework is a resp onse to the ab o ve challenge, where ﬁled data from p eer v ehicles are aggregated to automatically optimize the D&P algorithms for the host vehicle. This is an extension of the decade-long evolving research and developmen t in the area of remote v ehicle diagnostics [254, 255, 256, 257, 258, 259], which recently 820 has b een accelerated due to the adv ances made in the wireless communication technology and the need for connected v ehicle prognostics. The necessary ingredients of a CVHM include 1) An on board CVHM arc hitecture that facilitates eﬃcient aggr egation of peer v ehicle data, and host vehicle D&P algorithm adaptation. 2) In telligent data mo delling and statis tical decision making tec hnologies that allo w the extraction of fault signature, failure precursor, trending information, and other kinds of knowledge that enhances the p er- formance of D&P . 3) A heterogeneous wireless communication solution that combines cellular netw ork, and opp ortunistic v ehicle-to-vehicle (V2V) communication to allow the exc hange of large-v olume data betw een v ehicles in a cost-eﬀectiv e wa y . The work in [253] addresses the ﬁrst t wo items abov e, using battery RUL for demonstration. A t ypical v ehicle health management system architecture should address the three main tasks associated with CBM, i.e., data collection, feature extraction and decision making. Figure 6 (tak en from [253]) illustrates a typical arc hitecture. Sensor information regarding particular vehicle subsystem is either directly collected by the VHM ECU that runs D&P algorithms or is transferred from other ECUs through an in-v ehicle comm uni- cation net work. Note that, in real implementations, the VHM ECU may b e implemen ted as a functional mo dule within an ECU, such as a b o dy con trol mo dule (BCM), that executes con trol functions. The D&P mo dule has v arious D&P algorithms for diﬀeren t targeted vehicle comp onen ts or subsystems, such as battery , electrical p ow er generation and storage (EPGS) system, fuel delivery system, etc. The D&P mo dule pro- cesses the sensor information, and generates D&P results, including the detected anomalies, isolated faulty 840 comp onen ts, and the predicted RUL of related comp onen ts. The D&P algorithms are usually developed, calibrated, and tested through a sophisticated vehicle developmen t pro cess. Once the vehicle is released for 43 pro duction, the D&P algorithms and the asso ciated calibration v alues are usually ﬁxed. If ma jor up dates on the onboard algorithms are needed, an ECU reprogramming can b e done after the vehicle is usually called to a dealer service shop. Lately , the technology of remote ECU refresh is maturing, which ma y allo w the ECU reprogramming to b e done remotely through telematics connections. Figure 6: A t ypical VHM system architecture in the state-of-the-art [253]. The CVHM system arc hitecture prop osed in [253] should address the tree main ingredien ts of a realizable CBM system. Figure 7 demonstrates the prop osed CVHM system architecture. The newly added V2X ECU Figure 7: CVHM system architecture prop osed in [253]. 44 pro vides the wireless comm unication interface in order to exchange vehicle health related data b et ween the host vehicle and p eer vehicles. V2X represents v ehicle-to-vehicle or vehicle to infrastructure. The V2X ECU stores the data in an onboard database. The VHM ECU has an algorithm adaptation mo dule and a learning algorithm library , in addition to the regular D&P mo dule. The algorithm adaptation mo dule makes use of appropriate learning algorithms to pro cess the vehicle health related data stored in the onboard database in order to tune and optimize the calibration v alues within the D&P mo dule. The adv an tage of CVHM can be understo o d based on the follo wing example. A battery life prediction algorithm usually implements an ageing mo del that sp eciﬁes how the battery internal resistance grows giv en the num ber of charge-disc harge cycles. There are parameters in the ageing mo del that sp eciﬁes the growth rate of the battery internal resistance, which is critical in battery life prediction. These parameters are t ypically calibrated using accelerated ageing test during the vehicle dev elopment pro cess, and applied to across the b oard to all vehicles. Ho wev er, it is diﬃcult for a pre-calibrated mo del to account for the intrinsic 860 div ersity of usage patterns and environmen t impacts. The fact is that batteries for the same battery/vehicle mo del may hav e diﬀerent life span that ranges from 1 year to 10+ years. A t the same time, with large enough vehicle p opulation, for any given v ehicle, chance is high that there are p eer vehicles with similar usage proﬁles that ha ve been used for longer time, and therefore ha v e gone further ahead in the ageing pro cess. With CVHM, ﬁeld data from these p eer v ehicles can b e used to ﬁne tune the growth rate in the battery ageing mo del, and consequently achiev e higher prediction p erformance. The general framework to develop mo del-based prognostics for RUL prediction inv olves the following steps. First, one or more fault signatures are identiﬁed to characterize target systems state of health (SOH), Z = f ( S O H ). Dep ending on applications, these fault signatures ma y be assessed either directly or indirectly . F or example, in the application of Starting, Light, Ignition (SLI) battery life prediction, multiple fault signatures hav e b een proposed. The second step is to establish the failure criteria for fault signatures with resp ect to sp eciﬁc applications. That is, if Z > Z 0 , a system failure is declared, where Z 0 is a threshold. F or example, one of the main functions for SLI battery is to crank the engine. As battery ages, its SOH deteriorates, and so do es its cranking capabilit y . One of the fault signatures, cranking resistance, increases during the ageing pro cess. When the cranking resistance reaches certain level, the engine can hardly b e started. This is when a battery failure is declared. The failure criteria are highly application speciﬁc, and usually require careful calibration. The third step is to establish a system-ageing mo del that sp eciﬁes ho w the fault signatures ev olve with resp ect to usage. That is, Z = Z ( L ; θ ) , where L is a set of v ariables that c haracterize the usage proﬁle of the target system, and θ is a set of parameters that sp ecify the detailed relationship b etw een the usage and the fault signature evolution. Extensiv e previous researc h has b een conducted, and multiple SLI battery fault signatures hav e b een iden tiﬁed, including minim um cranking voltage, delta V, cranking p o w er, voltage residual, and cranking resistance. F or instance, the cranking resistance increases in an accelerated ageing experiment. In [253], a 45 few static parametric mo dels are adopted, including p olynomial curve ﬁtting. The algorithm dev elopment is based on a 3rd order p olynomial mo del due to its structural simplicity . Each fault signature is mo deled b y the following equation ˆ y ( t ) = p 1 t 3 + p 2 t 2 + p 3 t + p 4 , where ˆ y is predicted fault signature v alue, t is the battery age in terms of service time, and p 1 , p 2 , p 3 and p 4 are mo del parameters. Since b oth SOC and battery temp erature can aﬀect battery fault signature, diﬀerent mo dels hav e to b e learned for diﬀerent SOC and temperatures. The battery R UL is deﬁned as RU L = ar g min t [ ˆ y ( t ) = y 0 ] − t curr ent , where y 0 is a predeﬁned threshold, and t curr ent is the current battery age. The ageing mo del calibrated with accelerated ageing test may not be able to characterize the ageing process in the ﬁeld. In the prop osed CVHM, the ageing mo del is adapted using the data from p eer vehicles that ha ve gone further in the ageing pro cess. Let y H ( t j ) b e the fault signature v alue measured or estimated by the host v ehicle at time instant t i , where j = 1 · · · J and J is the current time index for the host vehicle. Let P H, 1 , P H, 2 , P H, 3 , and P H, 4 b e the ageing mo del parameters main tained by host vehicle, and P P k , 1 , P P k , 2 , P P k , 3 , and P P k , 4 b e the ageing mo del parameters used by p eer vehicle P k , where k = 1 · · · K and K is the num ber of peer vehicles. The mo del adaptation pro cedure is as follows, 1) Estimate host v ehicle fault signature v alues using peer vehicle’s ageing mo del parameters, which yields, ˆ y H,P k ( t j ) = p P k , 1 t 3 j + p P k , 2 t 2 j + p P k , 3 t j + p P k , 4 , where ˆ y H,P k ( t j ) indicates the estimate of host vehicle fault signature using the ageing mo del from p eer v ehicle P k . 2) Calculate the corresp onding estimation error for the ageing mo del from each p eer v ehicle P k as, R H,P k = J X j =1 [ ˆ y H,P k ( t j ) − y H ( t j )] 2 . 3) Pic k N mo dels with the smallest error. Without loss of generality , the corresp onding p eer vehicles can b e represented as P k 1 , P k 2 , · · · , P k N . In the exp eriment presented in this pap er, N is set to 3. 880 4) Calculate the adjusted host vehicle fault signature v alues, ¯ y H ( t j ), by av eraging the fault signature v alues based on the selected p eer vehicle’s ageing mo dels, ¯ y H ( t j ) = 1 N N X n =1 ˆ y H,P k n ( t j ) . 5) Up date the host vehicle ageing mo del, using the adjusted fault signature v alues p H, 1 , · · · , p H, 4 = ar g min p 1 , ··· p 4 J X j =1 [ ˆ y H ( t j ) − ˆ y ( t j )] 2 , where ˆ y ( t j ) = p 1 t 3 j + p 2 t 2 j + p 3 t j + p 4 . 46 The adjusted ageing mo del parameters p H, 1 , · · · , p H, 4 are used for future battery RUL prediction of the host v ehicle. 7.1.1. System Implementation The CVHM arc hitecture prop osed in [253] has been implemen ted in a three-vehicle test ﬂeet for the battery RUL prognosis application. T o reduce the developmen t cycle and cost, the test ﬂeet is constructed in a wa y that one host vehicle implements the full CVHM architecture, and t wo p eer vehicles implement only the V2X mo dule. Each of the t w o p eer v ehicles maintain a database of battery D&P data from m ultiple batteries, which simulates the situation where data from multiple p eer vehicles can b e transferred to the host v ehicle for D&P algorithm adaptation. F or the host vehicle protot yp e implementation, there are three ma jor hardware comp onen ts. The ﬁrst one is a dSpace MicroAutoBox (MAB) that has direct connection with the sensors on the battery . It emplo ys the functions of data acquisition, signal pre-pro cessing, and fault signature generation. During eac h vehicle cranking process, the MAB generates multiple battery-status related parameters, including battery temp erature, SOC, cranking resistance, minimum cranking v oltage, cranking p o wering, delta V, v oltage residual. The third ma jor hardware comp onent is a V2X comm unication laptop (an HP Compaq 6910P with the OS of Linux Ubuntu 10) that communicates with the VHM laptop through TCP/IP based connection. The V2X laptop implemen ts the V2X mo dule that in teracts with peer v ehicles and infrastructure through a wireless communication to exchange data. It maintains a MySQL database server to organize the data as well as manage the retriev al requests from the VHM mo dule. The V2X laptop also serves as the 900 driv er interface mo dule to provide battery health information to the end user. 7.1.2. Exp erimental R esults The CVHM system has b een v alidated using the J B I A g ing 2 008 data set. In this data collection eﬀort, 15 batteries from diﬀerent suppliers were aged from fresh to the end of life through an accelerated ageing pro cess. The battery age v aries from 8 to 16 weeks. During the ageing pro cess, weekly cranking tests w ere conducted on a test vehicle for eac h battery after it was conditioned to 100% state of charge (SOC) and the temp erature of 25C. Battery current, battery voltage, and engine RPM w ere collected during cranking. After data cleaning, there are totally 1710 cranking data ﬁles that ha ve adequate data for 14 batteries. Among these fault signatures, cranking resistance app ears to b e b etter SOH indicators than others, due to its consistency and monotonic correlation with the battery age. Therefore, we selected the cranking resistance as the fault signature in the rest of the exp erimen ts. The accuracy sp eciﬁes the diﬀerence b et ween predicted v alue and the actual v alue. The precision sp eciﬁes the spread of the predicted v alues. 7.1.3. Simulation R esults Figure 8 illustrates the battery RUL prediction results during one particular ignition cycle. At this particular ignition cycle, the host vehicle battery has been in service for 540 da ys, assuming eac h week 47 of accelerated ageing corresp onding to ab out 90 days of real-w orld driving. The cranking resistance has increased from the initial v alue, but is still signiﬁcan tly low er than the end of life threshold indicated by the blac k horizontal line. The initially calibrated ageing mo del, as sho wn by the blue line, predicts the R UL is ab out 250 da ys, since the cranking resistance is predicted to pass the threshold in ab out 250 days. This prediction is very diﬀerent from the actual cranking resistance data that are shown b y the black cycles. A t 920 the same time, the host vehicle has access to the data from p eer vehicles batteries, of whic h the data from nearest neighbors are sho wn b y the green crosses. F ollowing the mo del adjustment pro cedure presented b efore, an up dated battery ageing mo del is obtained, and shown b y the green line. The up dated ageing mo del traces the actual cranking resistance very well, and pro vides a fairly accurate RUL prediction. Figure 8: Comparison of battery RUL prediction with pre-calibrated mo del and adaptive mo del [253]. 7.1.4. Pr eliminary p enetr ation analysis A discussion is presen ted on ho w many peer v ehicles are needed to achiev e sp eciﬁc RUL prediction p erformance. The p erformance of RUL prediction can b e measured by the accuracy and the precision. The relations indicate that under the i.i.d. assumption, the RUL estimation will hav e zero exp ected error, whic h is very desirable. And the error spread of the CVHM-based prediction is reduced by a factor of √ n +1 n from the single vehicle battery RUL prediction, which shows why the CVHM framew ork enhances the prediction p erformance. 48 7.2. Automatic tr ansmission: Wet-clutch system No wada ys, automatic transmissions ha v e become a p opular c hoice in commercial vehicles and been widely used in oﬀ-road/heavy-dut y vehicles. As is obvious from its name, an automatic transmission is a trans- mission that shifts p o w er or speed by itself. The key elemen t that enables automatic p o wershifti ng or sp eed-selection in automatic transmissions is a wet friction clutc h. The p ow er transmission from the engine to the wheels through w et friction clutch is based on the friction o ccurring in lubricated contacting surfaces. A wet friction clutc h (hereafter called wet clutc h) is lubricated b y an automatic transmission ﬂuid (A TF) ha ving a function as a co oling lubricant cleaning the con tacting surfaces and giving smo other p erformance and longer life. F or high-p o w er applications, the clutch is t ypically assembled with multiple friction and 940 separator discs. The friction disc is made of a steel-core-disc with friction material b onded on both sides and the separator disc is made of plain steel. An electromechanical h ydraulic a ctuator is usually used for engaging/disengaging a wet clutch. This actuator consists of some main comp onen ts, suc h as a piston, a return spring which is alwa ys under compression and a hydraulic group consisting of a con trol v alv e, an oil pump, etc. T o engage the clutch, pressurized A TF is con trolled by the v alve to generate a force acting on the piston. A n umber of researchers hav e explored and developed mo del-based prognostics tec hniques for wet clutches. Y ang et al. (see [260, 261]) developed a ph ysics-based prognostics mo del by considering that the degradation o ccurring in a wet clutc h is due to thermal eﬀect alone in the friction materials. T o this end, a dedicated in v asiv e and destructive test, i.e., thermal gravimetric analysis, is required for identifying some parameters for the prognostics mo del. Since the degradation mec hanism o ccurring in the clutc h friction material is not only due to thermal eﬀect but also another ma jor mechanism namely adhesiv e w ear (see [262, 263, 264]), the assumption made within the prognostics metho d in [260, 261] is, therefore, to o ov ersimpliﬁed. Moreov er, this approac h w ould be diﬃcult to implemen t b y the end users when the complete design data of a w et clutc h system are not av ailable. Prognostics algorithms for the A TF (i.e., lubricant) of wet clutc hes hav e b een also dev elop ed and rep orted in the literature. References [265] and [266] dev elop ed an empirical degradation mo del for predicting the lifetime of A TF based on an SAE#2 modiﬁed plate test, in which the energy p er shift and bulk lubrican t temp erature are used as input parameters. The degradation mo del applies only to a sp eciﬁc A TF under certain op erating conditions. F urthermore, Ref [267] developed a prognostics metho dology using extra lubrican t sensor which is immersed in A TF. The sensor provides an electrical signal 960 indicating in real time the chemical condition of the lubrican t to b e monitored. Three parameters, namely 1) total acid num b er (T AN), 2) delta o xidation (OX), and 3) HPDSC induction time (MIN), can b e derived from the sensor readings. An empirical mo del was developed to predict the RUL of A TF based on the three parameters. Because of its robustness, h ybrid prognostics approac h under the Ba yesian framework (e.g., Kalman ﬁltering) has b een attracting a num b er of researc hers now ada ys and b een successfully applied to v arious applications like b earings, batteries, material crack growth, electrolytic capacitors, etc. Demands of low-cost prognostics to ol for automatic transmission clutches (i.e., based on measurement 49 data from sensors t ypically a v ailable) b y industry ha v e increased since the last few years. In [240], a prognos- tics to ol is dev elop ed b y fusing a newly dev elop ed degradation model with the measurable pre-lo ckup feature under the extended Kalman ﬁltering framew ork. As this feature can b e extracted from sensory data t ypically a v ailable in w et clutc h applications, the developed prognostics to ol, hence, does not require extra cost for an y additional sensor. New history data of commercially av ailable w et clutches obtained from accelerated life tests using a fully instrumented SAE#2 test setup hav e b een acquired and pro cessed. The exp erimen tal results show that the prognostics algorithm developed outp erforms the early developed prognostics algo- rithm, which is based on the weigh ted mean slop e metho d (i.e., data-driv en approac h). It is shown that the clutc h remaining useful life estimations with the no vel prognostics algorithm remain in the desired accuracy region of 20% with relatively small uncertaint y interv al in comparison .with the early dev elop ed prognostics algorithm. In this framework, empirical or ph ysics-based degradation models are fused with measurement data (i.e., feature) in order to impro ve the RUL estimation. 7.3. Alternator 980 A v ehicle alternator shares many similarities to A C generators and induction motors, and studies ha ve sho wn that b earing failure is resp onsible for 40% of the failures for induction motors, making it the most common mechanical failure [268]. The alternator is coupled to the engine by either a v-b elt or a serp en tine b elt pulley s ystem and a higher than normal lev el of b elt te nsion can provide greater lateral loads on the b earing and reduce its life. There is also a great deal of researc h in b earing health monitoring and prognostics, whic h is likely not only due to b earings b eing an imp ortant comp onent for rotating machinery , but also due to the b earing geometry , there are sp eciﬁc fault frequencies that are seen in the vibration sp ectrum [269]. A vehicle alternator’s ov erall function is to charge the v ehicle battery as well as pow er the electrical auxiliaries; an alternator that is degraded or failed will ultimately result in the inability to use these additional auxiliaries and an increased p otential for a dead battery and stalled car. Considering the imp ortance of the alternator in the ov erall functioning of the v ehicle and p erhaps in particular for military vehicles for which mission success is dep endent on the use of surveillance equipment or other features that require a properly functioning v ehicle electrical system; knowledge of the health status of the alternator is useful information that can supp ort logistical, tactical and maintenance planning eﬀorts. The vehicle alternator is essen tially a rotating machine that generates a 3-phase alternating current that is rectiﬁed by a set of dio des in order to produce a DC curren t with low ripple con tent; the vehicle alternator s hares many similarities with a generator, and to some degree electrical motors, and in turn some of the common health monitoring and prognostic techniques, as w ell as common failure mo des, for motors and generators are applicable. Considering the similarity b et ween vehicle alternators, electric motors and generators, a general metho dology for assessing the health of rotating electro-mec hanical comp onen ts was 1000 dev elop ed and demonstrated for an automotiv e alternator comp onen t. The approach applies domain sp eciﬁc knowledge, along with pro cessing the data and extracting features from the time domain signal, as w ell as the order sp ectrum, to train machine learning algorithms, such as 50 statistical pattern recognition, logistic regression, or a self-organizing map to assess the health of the v ehicle alternator. F or this particular case study , three comp onents of the alternator w ere monitored, the alternator bearings, stator windings and dio des, with resp ective features from the electrical or vibration signals that are correlated to the degradation of each of those comp onen ts. The pro cessing of the alternator tachometer signal and the vibration and electrical signals into the order sp ectrum provides a wa y to extract relev an t information that is indicativ e of b earing, dio de and stator health. Three health assessmen t algorithms were highlighted for this particular study with b oth the logistic regression metho d and the self-organizing map metho d p erforming quite well with the logistic regression tec hnique ha ving a type I and I I error of 5% [241]. The ov erall framework utilized in this case could b e extended to other applications, and assessing the comp onen t health ov er time is a pre-requisite for prognostics in whic h further w ork could lo ok at developing a remaining useful life prediction tec hnique for v ehicle alternators. 8. Challenges And Opp ortunities This section discusses some of the challenges and diﬃculties asso ciated with developing prognostics mo dels. Atten tion is given to those asp ects that need to be further inv estigated for reliable metho ds to b e used in real-life situations. It is essen tial to dev elop metho ds that could utilize the av ailable data and 1020 accurately incorp orate them into the mo dels. On the other hand, the op erating conditions of mac hines in the real-life is diﬀerent from the exp erimental test done in the lab. The ﬁnal consequent of these op erational complexities can greatly diminish the accuracy of the prognosis output. In most of the literature, it is only tried to predict a sp eciﬁc failure mo de of one individual component without considering the interaction of the other comp onent with the asset under study or with the op erating en vironment. It is imp ortant to lo ok at particular areas in whic h new ideas and impro vemen ts could oﬀer opp ortunities for enhanced prognostics. These include: prop er incorp oration of CM data into reliability; prop er incorporation of incomplete trending data; how the maintenance actions and op erating conditions eﬀect the results; what w ould b e the best non-linear or linear mo del to describ e the actual degradation vs the predicted one; how the failure interactions should be considered; ho w to verify the accuracy of the assumptions. These challenges are discussed more in [17]. 9. Concluding remarks In this pap er, a review of the state-of-the-art mo dels, metho ds and algorithms to engineering prognostics is presented with a fo cus on practical asp ects. The adv antages and weaknesses of the metho ds and models and brieﬂy review ed which is later revisited within the context of prognostics and health management to ol dev elopment. A separate section of the w ork is dev oted to the prominent instances of applications of 51 prognostics to comp onen ts that are highly used in engineering system and a few automobile-related examples are discussed in details. • The remaining useful life estimation mo dels are categorized into 1) data-driven 2) mo del-based ap- proac hes 3) hybrid approaches 1040 • The selection of the b est mo del dep ends on the lev el of accuracy and av ailability of data. • In cases of quic k estimations whic h are less accurate, the data driv en metho d is preferred, while the ph ysics-based approach is applied when the accuracy of estimation is imp ortant. • F or most industry applications, ph ysics-based mo dels might not b e the most practical solution since fault t ype is question is often unique from comp onent to component and is hard to b e iden tiﬁed without in terrupting op eration. Ho wev er, physics-based mo dels ma y b e the most suitable approac h for cost- justiﬁed applications in whic h accuracy outw eighs other factors and ph ysics mo del remain consisten t across systems, suc h as in air vehicles. They also generally require less data than data-driven mo dels. • Data-driv en mo dels may often b e the more av ailable solution in man y practical cases in which it is easier to gather data than to build accurate system physics mo dels. • The mo delling approach selected m ust b e ﬁt for purp ose. All mo dels are sub ject to underlying as- sumptions of implemen tation constraints that restrict their applicability to certain types of problems. Common issues relate to the following: (1) amount,t yp e and quality of data required;(2) eﬀect of pro- cess and measurement noise on data; (3) type of repair (p erfect,imperfect);(4) num ber of failure mo des that can be sim ultaneously or collectiv ely mo delled; and(5) whether or not nov el failure types can b e managed. • Although all mo dels require some understanding of the underlying failure pro cess, some approaches require detailed tec hnical kno wledge of failure mechanisms and data collection pro cesses for mo del implemen tation. Of the mo dels discussed, Neural Net works require minimal understanding ab out the pro cesses go v erning failure to apply , while exp ert and fuzzy systems require a medium amoun t;physical 1060 mo dels require comprehensive knowledge pertaining to all ph ysical mec hanisms and en vironmental factors inﬂuencing equipmen t failure for their successful application. • All mo dels require data for design, parameter deﬁnition and v alidation. The completeness requirement for data sets v aries b et ween mo dels. Organisations need to improv e data quality management pro cesses if they wish utilize prognostic mo delling more widely to supp ort asset decision making. • Data requiremen ts for diagnostics are often diﬀerent to data required for prognostic mo delling. • Not all models supply conﬁdence limits on their predictions,which is necessary to manage the uncer- tain ty in setting priorities, decision making and for practical risk management. Most Neural Netw or kmo dels in particular cannot determine conﬁdence b ounds for an estimate. 52 • Not all mo dels are able to predict R UL with the same lev el of accuracy and precision. Therefore business requiremen ts need to b e clearly articulated and incorp orated into mo del selection pro cesses. • F ew of the curren t approac hes are suitable for imp erfect repair. Exceptions include Duane gro wth(type of aggregate reliability function), prop ortional intensit y mo del(v ariant of PHM)and Hidden/Semi- hidden Mark ov Bay esian mo dels. • Most mo dels are b etter suited for comp onen t failure mo de R UL estimation (i.e., one dominant failure mo de) yet are often applied at a system level due to data av ailability on time constraints. Not sur- prisingly , results on system failure prognostics are mixed. Successful applications of system level RUL estimation are mainly for equipment where one failure mo de(or at most a very small num b er of failure mo des) dominates ov erall system reliabilit y . More examples illustrating the eﬀect of ov erlapping failure mec hanisms are required to verify the suitability of techniques for system-level prognostics. 1080 • F ew case studies are a v ailable that illustrate the application of the prognostic mo dels published in the academic literature to real w orld problems in realistic op erating en vironments (i.e., systems with o verlapping failure modes, sub ject to common mo de failures or undergoing highly v ariable process c hanges). This is an area where signiﬁcantly more work needs to b e published to verify that prognostic mo dels are useful for main stream asset management decision making of routine assets. • Mathematical or computing complexity currently limits curren t use of many approaches to industry practitioners. Although commercially a v ailable soft ware tools eliminate the need for softw are program- mers, dev eloping a meaningful model is often more inv olv ed than the suppliersliterature implies. Where soft ware is not av ailable, users should not underestimate the resources required to de v elop the code to instantiate a mo del. More information provided b y authors of journal articles ab out the lev el of mo delling skill and time exp ended when building the particular mo del presented in a published work w ould b e helpful to industry practitioners to iden tify resource requirements. • Appropriate model selection for successful practical implementation, requires both a mathematical understanding of eac h mo del t yp e, and also an appreciation of how a particular business intends to utilize the mo dels and their outputs. • The ability of PHM to estimate R UL for prognosis of v aried faults in complex systems is uncertain and lik ely to b e an ongoing c hallenge. References References [1] A. K. Jardine, D. Lin, D. 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