Rock mechanics modeling based on soft granulation theory

1. INTROUDC TION In the r ecent y ears, deve lopin g new ind irect ana l ysis method s has opened new horizons in rock engineeri ng solut ions. T endenc y to the micro-vi ew of the natural even ts in the rock based systems, upon the h igh speed P C technology ; behind larg e- scale investi gations, has allocated new challenges in this track. T ransition from a general (overall) view in to the detailed descrip tions, can be interpreted as rela tions (inter-extra relations) of the commuted “information packages”, got from accumulations of data, exp erience, no velt y and ot her effecti ve agent s. Such const ruction o f the “whol e” from “par t” (gra nules) is the current behavio r of human cognition. Among the basi c concept s which underli e human cogniti on there are three rema rkabl e sides, whic h are: granulation, org aniza tion, and causation. Granulation involv es decomposition of whole i nto part s; organi zati on inv olves in te gratio n of parts in to whole; and cau sation relates to association of caus es with effects [1]. Under this vi ew from t he discrit ization (mesh in g, block ing, latticing …) of the interior or b oundary of a field to the solving steps (thinking ) of the pr oblem are the perspectives of gran ulation. W e called first level of gr anulati on as “hard gr anulat ion” , and second level as “ soft granulat ion”. To better unde rstand of th e meaning o f hard and sof t granula tion, we r eproduce the gener al rock engineerin g desi gn fl owchart i n fi gure1 [2] . Lev el1 can be suppose d as a hard gra nulation whe re level2 is related with soft granulati on. Clearly, in soft gr anulati on; we are appro aching to the real hu man co gnition, whereas in hard p acki n g the machine computations are distinguished . Let us, c onsi der th e la st c las s in lev e l2 ( in c ateg ory D) : internet based sy stem. Interesti ngly, this ca t egory shows h ow the discrimina ted pro jects, unde r the virtua l world, e mploy the distributed informa tion gra nules. P lainly, the contributions of a ny pr ojects and the su b-sets of gra nules in construction of this Rock mechanics modeling based on soft granulation theory H. Owladeghaffari Dept . M inin g &Met all urgi cal Engi ne eri ng, Ami rk abi r Univ ers ity of Tech nol ogy, Te hran, Ir an ABSTRACT: This paper describes application of information granula tion theory , on the design of rock eng ineering flowcharts. F irstly , an over all fl owchar t, based on information granulation theory has been highlighted. Informa tion granulation theory , in cris p (non-fuzzy ) or fuzzy format, can take into account engineeri ng experiences (especially in fuzzy s hape-in complete i nform ation or su perfluou s), or en gineering jud gments, in each s tep of designi ng procedure, while the suitable instrume nts modeling ar e employ ed. In this manner and to exte nsion of soft modeling instruments, using three combinations of Self O rganizing M ap (SO M), Neur o-Fuz zy Inference Sy stem (NFIS) , and Roug h Set Theory (RS T) crisp and fuzzy granules, from m onitored data sets are obtained. The main unde rlined core of our algorit hms are bal ancin g of cris p(rough or non-fuzzy) granules and sub fu zzy granul es, with in non fuzzy informat ion (initial granulation) upon the “open- close iterations”. Using different criteria on balancing best granules (information pock ets), are obtained. Validations of our propose d methods, on the data set of in-situ permeability in rock m asses in Shiva shan dam, Iran have been high l ighted. general networ k are affect ed fr om the s everal parameter s, conc luded in “gra nulation level” fact or. I n this paper, we interest to tack in to account soft granul ati on i n rock s ystem. Upo n th is, b y focusi n g in two categori es C-1 and C-2, in fi gure1, we develo p different sof t granulation methods ba sed on intel ligent s ystems an d approx imate reasonin g method s. Added to this, the bridg ing betwee n hard and soft granulat ion is abstracted. The mo st main distinguished fa cets of the soft gr an ul es ar e: s et t he or y, i n terval anal ysis, fuzzy set, rough set. Ea ch of these t heories considers part of uncerta inty of informa tion (data , wor ds, pictur es...). Due to associat ion of uncertaint y and vaguen ess with th e m oni tore d da ta set , pa rt icu larly , resu lted from t he i n-sit u tes ts (su ch l ugeon test ), accoun tin g relevant approaches such probability, Fuzzy Set Theor y (FST) and Ro ugh S et Theor y (RST) t o knowledge acquisition, extraction of rules and prediction of unknown ca ses, more tha n the past have been d istinguished. Z adeh has emphasize d the role of FS T in geosciences will be increased during future years [3]. The RST intr oduced by Paw lak has ofte n proved to be an excellent mathem atical tool for th e anal y sis of a vague descr iption of object [4 ], [5] . The adje ctive vague, r eferrin g to t he qual it y of infor mati on, means incon sistency, or ambig uity which follows from information granulation. T he roug h set philosophy is based on the assumption that with ever y object of the universe, i s associated a certain amoun t of information, expre ssed by means of some attribut es used for object d escriptio n. The indiscernibilit y relation (si milarity), which is a mathematical basis of the rough set theor y, induces a partition of the universe in to blo cks of indiscerni ble objects, called elem entar y sets, wh ich can be used to build know ledge about a real or abstrac t world. Precise condition r ules c an be extracted from a discernib ilit y matrix. Applicatio n of RST i n di fferent fi elds o f the appl ied s cienc es has been re ported [6], [ 7], b ut dev elopin g of su ch system (based on app ro ximate anal ysis) in rock engineeri ng hav e not been outs tandi ng, relati vely. Figu re 2 s hows a gen eral proc edure, in whi ch t h e IGT acco mpanies b y a predefined proje ct based rock engineering design. Af ter determination of constraint s and the as sociated roc k engin eerin g considerations, the initial granulation of information as well as numerical (d ata base) or in linguis tic formats is accomplis hed. Impr ove ment of model in g instrum ents based upon I Gs, whether in independent or affili ated shape wit h hard computi ng me thods (suc h fuzzy finite elem ent, fu zzy b oundary element, stochastic finite element…) are new challenges in the current discussion. In this stu dy, unde r “modeling instrume nts” box, we propose three algorithms; namely successive elicitation of crisp (non-fuzzy ), fuzzy and roug h gra nulations: S el f O rga niz ing Ne uro-F uzzy In fe renc e Sy ste m (Ran dom and Reg ular neuron grow th), in an abbreviated manner: SO NFIS-R, SO NFIS -AR; and S el f Org an iz ing Roug h Set T h eory (S ORST) . Fig.1. one of the last general flowcharts to rock engineering desig n [2] In figure 3, we have concluded a summa ry of cur rent overa ll gran ulation in a rock project th at leads to the formati on of fu zzy gran ules on th e attributes (properties) of joints. Figure4 show ho w one usually employs g r anulation procedure to permeability anal ysis in a dam site, insti nctively. The re st of paper h as been org anized as section 2: preliminaries on some soft granulation methods, i.e. SOM, NFIS, an d RST in next section, we propose three main algorithms and part 4 covers a pract ical instance, describ es how the soft granul es ensue a relatively complete analysis on the permeabil ity of Shivashan dam site, in Iran. 2. PRE LIMINAR IES 2.1. Self Organizing feature Map ( SOM) Ko honen’s SOM algorithm has been well reno wned as an ide al candidate fo r classifying in put data in an unsu pervised le arnin g wa y [8]. Koh one n sel f- orga nizing networks (K ohonen feature maps or topolo gy-preservi ng ma ps) are co mpeti tion-based network paradig m for data c lustering . The le arning proc edure of Kohonen feature maps is similar to the competitive learning networ ks. The main idea behind competitive learning is sim ple; the winner takes all. The competitive transfer function returns neural o utputs of 0 for all ne urons except f or the winn er which re ceives t he hi ghest net in put wit h output 1. SOM c hanges all weight ve ctors o f neuron s in the near vicinity of the winner neuron towar ds the input vector . Due to this proper ty SOM, are use d to reduce the dimensiona lit y of comp lex data ( data clustering). Competitive layers will automatically learn to classify input vectors, th e classes that the competitive layer finds are depend only on the distances be t ween in put vectors [ 8]. Fi g.2. A gene ral m eth odol og y for b ack a nal ysis bas ed on I GT 2.2. Neuro-fuzzy inference system ( NFIS) There ar e different solut ions of fuzz y inferen ce systems. Two well-known fuzzy modeling methods are the Tsu kamoto fu zzy model an d T akagi – Sugeno– Kang (TSK) model. In the presen t work, only the TSK model has be en cons idered. The TSK fuzz y inference s ystems can be easil y implanted in the form of a so called Neuro-fuzzy network str ucture .in this study , we have emp loyed an adapti ve ne uro-fuzz y in ference s ystem [9 ]. Fig.3 . Cur rent overall gran ulati on in a rock p roj ect Fi g.4 . Gr anulation procedure to p ermeability analysis in a d am site One of the most impo rtant stages o f the Neu ro- fuzzy TSK network generation is th e establishment of the infer ence rules. Often us ed is the so -call ed gr id method, in w hich the rules are defi ned as the combinations of t he membership functions for each input variable. If we split the input variable ra nge into a limited number (say n i for i=1, 2... n ) of membership func t ions, the combin ations of them lead to m any diff erent in feren ce rul es. The probl em is that these co mbinations correspon d in man y cases to the reg ions of no data, and hence a lot of them may be deleted . This problem can be solve d by using the fuzzy self-organization algorithm. This algorithm splits the data space into a specified numbe r of overla pping clusters. Each cl uster may be associated with the specific rule of the center corr esponding to the center of the appr opriate cluster. In this way a ll rules correspond to the reg ions of the space-con t aining major ity of data and the problem o f the emp t y ru les can be avoi ded. The ultimate goal of data clustering is to pa rtition the data into similar subg roups. This is accomplished by employing some similar measures (e.g., the Euclidean distanc e) [9]. In this paper data clusterin g is used to derive member ship f unctions f rom mea sured d ata, wh ich, in turn, determine the numb er of If-Th en rules in th e mod el ( i.e., ru les indic ation) . The method employed in this paper is the subtractive cluster ing method, propose d by Yager as one of the simplest c l ustering method s [10]. 2.3. Roug h Set Theory (RST) The rou gh set theo r y introduced b y Pawl ak [4], [5] has often proved to be an ex cellent mathe matical tool for the an al ysis of a va gue des cript ion of object. The adjective va gue referrin g to the qu alit y of information means inconsistency, or ambiguit y which foll ows from infor m ation granul ati on. An information s y stem is a pair S=< U, A > , w her e U is a nonempty f inite set called the universe and A is a nonempty finite set of attributes. An att ribute a can be regarded as a function from the domain U to some value se t a V . An infor mation sy stem can be repre sented a s an attribute-value tabl e, in w hich rows are labeled by objects of the universe and columns by attributes. With eve r y subset of attribut es B ⊆ A , one can easily associate an equivale nce relation B I on U : {( , ) : , ( ) ( )} B I x y U f or ev er y a B a x a y =∈ ∈ = (1) Then , Ba B a I I ∈ = I . If X U ⊆ ,the sets [ ] {: } xU x X B ∈⊆ and [] {: } B xU x X ϕ ∈≠ I , where [] B x denotes the equival ence class o f the object xU ∈ relative to B I , are called the B-lower and the B-upper approxima tion of X in S and d enoted by B X and B X , respectivel y. Consider 12 n {x , x , ...,x } U = and 12 n {a , a , ..., a } A = in the information sy stem S= U, A pf . By the discernibility matrix M(S) of S is meant an n*n matrix such tha t { } :( ) ( ) ij i j ca A a x a x =∈ ≠ (2) A discern ibilty function s f is a function of m Boolean variables 1 ... m aa correspon din g to attribute 1 ... m aa , respectively , and define d as follows: 1 ( , ..., ) { ( ) : , , , } s m ij ij f aa c i j n j i c ϕ = ∧∨ ≤ ≠ p (3) Where () ij c ∨ is the disjuncti on of all variables with ij ac ∈ .Using such discriminan t matrix the appropriate rules are elici ted. One of the ma in parameter s in the cove ring of the obtained rule is “dependency rul e or strength “. Let; we ha ve a rule in the disjunctive no rmal form (D.N.F), fo r instan ce: 11 ( ... ) ( ... )..... ( ) i nm i P a a b a d decision a ttr ibute ∧∨ ∧ ∧ → 144 4 4 4 244444 3 The depe ndenc y fact or i df is gi ven by: (( ) ) () i Bi i i Ca r d P OS d df Ca r d U = (4 ) W here () ( ) id i Bi X I i P OS d B X ∈ = U ,an d () i B X is the lower approximation of X with resp ect to () i B X . i B is the set of condition attributes( say inputs) occurring in th e rule. () i B i P OS d is th e positive re gion of the d ecision class i d that can be surely described by attribute s i B [6]. The ex isting induction algorithms use one of the followi ng strategies: (a) Gene ration of a mini mal s et of ru les co v ering all objects from a decision table; (b) Gener ation of an e xhaustive set of r ules consisting of all possible rules for a dec ision table; (c) Generation of a set of ` strong' d ecision rule s, even p artly discri minant, cove ring relatively many objects each but not necessaril y all ob jects fro m the deci sion table [ 11]. In this study we have develop ed RST in MatLab7 , and on this added toolbox other appro priate alg o rithms have been prepared. 3. PROPOSED A LGORIT HMS In the w hole of our algori thms, we use four basic axioms upon t he balan cing of the successive granule s: Step ( 1): dividing the monitored data into gro ups of training and testing data Step (2) : first granulation (crisp) by SOM or other cris p gran ulati on methods Step (2-1 ): selecting the level of granularity randomly or de pend on t he obtaine d error from the NFIS or RST (regu lar neuron growth) Step (2-2): co nstr uction of the gran ules (cr isp ). Step (3): se cond granulation (fuzzy or ro ugh IGs) by NFIS or RST Step (3 -1): crisp granules as a new data. Step (3-2) : selecting th e level of granularit y; (Error level, nu mber of rules, streng th threshold ...) Step (3-3): checking the suitabili ty. (C lose- open itera tion: referring to the real da ta and reinspect closed world) Step ( 3-4): c onstruct ion of fuzzy/rough granules. Step (4): extraction of kn owledg e rules Selection of initial crisp g ranules can be supp osed as “C lose World Ass ump tion (C WA)” .Bu t in man y application s, the as sumpti on of co mpl ete informa tion is not feasible, a nd only cannot be used. In such cases, an “Open W orld Assumption (OW A)’, w here info rmatio n not kn own by an agent is assume d to be unknown, is often ac cepted [1 2]. Balancing assumption is satisfied b y the close-open iterations: this process is a guideline to balancing of crisp an d sub fu zzy/r ou gh granules b y s ome rando m/regular selection of initia l gra nules or other optimal str uctures a nd increme n t of su pporting ru les (fuzzy partitions or inc rea sing of lower /uppe r approximat ions ), gradually. The overall schemat ic of Self Orga nizin g Neuro- Fuzzy Infer ence Sy stem -Random and Reg ular neuron gro wth-: S ONFIS-R , SON FIS-AR; has been sho wn in fi gure5. In fi rst regul ar granulation , we use a linear relati on is gi ven b y: 1 ; tt t t t NN E α βγ + =+ ∆ ∆ = + (5) Wh e r e 12 1 2 ;. t Nn n n n M i n =× − = is nu mber of neurons in SOM; t E is the obtained e rror (measured error) from secon d granulation on the test da ta and coefficien ts must be d etermined, d epend on the u sed data set. O bviously , one can em ploy like manipu lation in the rule (seco nd granulation) generat ion pa rt, i.e., nu mber of rules . Determi nati on of gr anu lat ion le vel is co ntrol led with three m ain param eters: range of neuron growth, num ber of r ules and er ror level. T he main benefit of this algorithm is to looking for best structu re and rules for two known intelli gent system, whi le in independent situations each of them has s ome appropriate problems su ch: finding of spur ious pattern s for the large data se ts, extra- time tra ining of NFIS or SOM. Fi g.5 . Self Org anizing Neuro- Fuzzy I nferenc e Sy stem (SO NFIS ) In second algo rithm, apart fro m empl oying hard computin g m ethods (har d granules), RST instead of NF IS has been proposed ( figure 6 ). Applying of SOM as a preprocessing step and discretization to ol is second process. Categ ori zation of a ttributes (inputs/ou tput s) is transferring of t he attribut e space to the symbolic appropriate attributes. In fact for continuo us valued at tributes, the feature space ne eds to be d isc re tized for de finin g i ndis ce rn ibilty relations and eq uivalen ce classes. We discretize each feature in to some levels b y SOM, for examp le “low, med ium, and hi gh” for attr ibut e “a ” . Finer discretization may lead t o better accu racy to rec ognizing of test data but imposes the higher cost of a comput ati onal l oad. Ho wever, to look for b est scale d condition a nd decision attr ibutes, we h ave develop ed other SORST system, upon the adaptive scaling of attrib utes (S ORST-AS), gradu ally [ 13]. Because of the ge nerate d rul es by a rough set a re coarse and ther efore n eed t o be fine-tu ned, here, we have used t he preprocess ing step on data set to crisp granula tion by SOM (close wor ld assumption). In fact, with re ferri ng to the instinct o f the huma n, we unders tand th at human being want to states th e events in the best simple w ords, sentences, rules, func tions and so forth. Undou btedly, suc h granules while satisfies the mentioned axiom that describe the distingu ished initial st ructure(s) of events or immature data sets. Second SOM, as well as clo se world assumption, gets suc h dominant structu res on the r eal data. In othe r word , condensa tion of re al world and conc entratio n on th is space i s associated with ap prox imate anal ysis, such ro ugh or fuz zy facets. Fig.6 . Bridg ing of hard co mputa tions an d Self Organi zi ng Rough Set The or y -R andom ne uron g r owth & adaptiv e strength factor (SORST-R) Before bal ancin g step between SOM and R ST, we use a checkpoint ba sed on granulation le vel, or possible best emerged granules, is assessed b y setting of threshold dependen cy fac tor. In figure 5, we haven’ t given up the real wo rld (as here hard granul es pa rt) an d da shed arrow keeps on l ink age with upper level if and only if SORST-R cou ldn’t gratify the pre-define d c onstraints. N ext part of th is study show how thes e algori thms comp lete not1-1 mapping levels. 4. PRACT ICAL EXA MP LE In this part of our study , we p ursue a p ractical example , which c overs a c omprehensive data set from lugeon te st in S hivashan dam. 4.1. Permeability assessment in Shiva shan dam site-Iran Shiv ashan hyd roelect ric earth d am is lo cated 45 km north of Sard asht city in northw estern of Iran. Ge olog ica l inve stig atio n fo r th e site selec ti on of the Shivashan hydroelec tric power plant wa s made with in an area of ab ou t 3 sq uare kilom eter. The widt h of the V-s haped v alle y with si milarl y sl opi ng flanks, at th e elevat ion of 1185m and 1 310m with respect to sea l evel are 38m and 467m , respectively. At the site area, the rock type indicates generally signs of metamorphism s, which are formed b y low temperature metamorph ic rocks, overlai n b y quaternar y alluvial deposi t s. The bed rocks cons is t of two t ypes of lo w temp erature meta morphic ro cks, namely, slates and ph yll ites. Indeed, sl ate is the brea dline between metam orphic and se dimentary rocks also known as a weakl y metamorphosed ro ck. F igure 7 shows overall view of dam site. Tota ll y, 20 bor eholes ha v e been drilled an d conseq uentl y abou t 789 objec ts wer e resulted. W ater Pr essure Test ( WP T ) has used for determ ination of this a rea’s permeability. WPT is an effective method f or wide ly determ ination of roc k mass permea bility. The Lugeon unit is not stat ed as a ratio of perme ability, but to ge t a sense of pr oportion, it might be relat ed such tha t: 1Lugeon =1.3*1 0-5 cm/s. In practice, usuall y , the Lugeon test is utilized before grouti ng t o det ermin e qua ntit ativel y the volum e of water t ake per unit of time [13]. A general pattern from five chief attributes of th e bo re ho le s, na mely : Z =elev atio n of the te st, L: length of the test ed section, RQD and Type of the W eathering Rock T y pe ( T. W.R ) - se e table 1- h as been sh own i n fi gure 3. Fig. 7. Overall view of axial position at Shi vashan dam To eva luate the permeability due to the lug eon values we follow two situ ations: 1) util izing of SONFIS and S ORST on th e five chi ef attributes(f igure8); 2) direc t application of RST and NF IS on the local coor dinates of dam site (as cond itional attribu tes) an d lugeon va lues (as decision p art) to dep ict 3D Iso-surface s of lugeon variat ions dia grams . Analysis of first situation is started off by settin g number of close -open iteratio n and max imum numbe r of rules equal to 10 a nd 4 in SONF IS-R, respectivel y. The error measure cri terion in SONFIS is Root Mean S quare Error (RMSE ), give n as below: *2 1 () m ii i tt RMSE m = − = ∑ ; Where i t is outp ut of SONFIS and * i t is real answer; m is th e number of test data (test ob jects). In the rest of pape r, let m=93 an d number of training data set =600 . Figures 9, 10 indicate t he results of the afo resaid system (so, perfor mance of selected SON FIS-R o n the test data). Two indicated positions i n figure 10 st at e mini mum R M SE o ver sa me ru les , a re n ear t o each other. In such case, we have two opportunities: selection of SONF IS wit h min number of rules ( n. r ) or involved m in object s. Figure 10 sho w second occasion. With augmenti n g of close-open i terations SONFIS-R or ran ge of n.r , our system emerges mo re n ear min R MS E, not def iantly lowe st va lue (fig ure 10-a , c ). B y empl oyin g of (5) in SON FIS-AR, and α =1.0 1; β =.001 an d γ =.5 ; the gener al patt ern of R MSE vs. neuro n gro wth ( in first lay er of a lgorithm) can be obs erved (fi gur e11). Wit h ne glectin g of so me details, the same trend of error fluctuation is distinguisha ble (highlighted by colored window s). It is worth noting that by α =.8 and n.r=2 ; SON FIS- AR reveals a general ch aos for m (fi gure 12). Th e main reason of this can be fol lowed in the first la yer proper t y : regulation of ne urons in S OM may ge t in to the “dead st ation” an d rando m se lectio n of weights in such layer. Other reason is about the range of error vacillatio n. In fact in this case o ur system has a high se nility to the error, and then to the neur on grow th. In this case, we c an determine two new balance measures: durability of neurons and distribution o f points in a neuron-er ror space. First measure gets lesser than 20 neu rons while in second measur e system after 100 iterations fall s in the “balan ce hole” with nearly 50 neuron s size. Figure 13 shows our mean a bout structur e detection. Under SO NFIS -R (fi gure10-c) figur e 13-a, d ecla res three major clusters in lu geo n-T .W.R . W it h more neuro ns in SOM, we can ac quire like patterns but may lose the supposed balancing criteria. T his proves the bal ance meas ure ev en if get min RM SE but losses the data distrib utions or major structures. In employ ing of part of seco nd algorith m (figure6), we use- -for in this case- only exact rules i.e., one decision cla ss in right hand of an if-then rule. F igure 14 and 15 depi ct the scalin g process b y 1-D SO M (3 neur ons) and th e performance of SO RST-R over 7 random se lection of SOM structure, respec tively . The a pplied error measure is: 2 1 () m rea l cla s si f i ed ii i dd MSE m = − = ∑ ; Fig. 8. Real data se t -Z,L ,RQ D,T.W.R& lugeon- in matrix pl ot form (a s traini ng data set to S ONFI S&SORS T ) Table1 . The revele d codes of Ty pe of We atheri ng Roc k (TWR) , MW: Med ium Wea t hering , SW: S li ght ly Weatheri ng, CW: Clay Weathering, HW: Hig h Weather i ng ; Typ e of weather i ng Ascr ibed c ode Fres h-MW 1.5 SW-MW 2 Fresh-SW .5 Fres h 0 MW 3 CW 2.5 SW 1 HW-MW 3. 5 HW 4 It must be noticed that for unreco gnizable objects in test data (elicited by rules) a fix value such 4 is ascribed. So fo r measure part when an y object is not identified, 1 is attributed. This is main reason of such sw ing of MSE in reduc ed data set 6 (fig ure 15- b). Clearly, in data set 7 S ORST gains a lowest erro r (2 6 neurons in SOM ). The extrude d rules in the optimum case can be purchased in t able 2. We have e xplained a pplication of S ORST in ba ck anal ysis in other st ud y [14] . Fig.9. (a&b) S ONFI S-R re sults wi th maxim um numbe r of rules is 4 and close-open it erations is 10; c) Answer of s el ect ed SON FIS -R on th e t est da t a Now, we investi gate dir ect appli cation o f RST and NFIS on the local coordinate s of dam site (a s conditional a ttributes) an d lugeon values (as decision part) to d epict 3 D Iso-surfaces o f lugeon varia tions diagr ams. Fig.10. (a &b) SONFIS-R results with maximum numb er of rules 4 and c lose-open iterations 20 ;(c ,d SONFIS-R with 5 to 8 rules n umber varia tion and 10 close- open itera tions &e) Answer of se lec ted SONFI S-R b ased on n.r= 5, on the test data Figure 17 shows the varia tion of the luge on data in Z*= {1} t o {5 } whi ch has b een acqu ired b y servi n g five condition attributes in RST (figure 16; the symbol ic val ues b y 1-D SOM -5 n euron s). Th e categ ories 1 to 5 state: very low, low, medium , hi g h, and ve r y high, respectiv el y. Numbe r 6 (more than 5) characterizes ambi guity and unknown cases. Fig.1 1.SON FIS-A R: n eur on growt h & error fluctu ations vs. iter atio n; 1.01 α = a) nu mber of rules ( n.r ) =2; b) n. r =3and c) n.r =4 Fig. 12. SON FIS-AR : neuron grow th & error fluc tuation s vs . iter atio n; .8 α = - number of rules =2-a) RM SE-iteration; b) neur on gr owt h-it erati on c ) RMS E- n eur on fluct uatio n: congestion of p oints can be used as a “balance hole Fi g13. Matri x plot of cris p granu l es by 7*9 gr i d topol ogy SOM after 5 00 epoc hs on the traini ng data set Fig. 14. Resul ts of tr ansfer ring attribu te (Z , L, RQ D, T.W. R, and lugeon ) in three categories (vertical a xes) by 1-D SOM Fig.15. SORST- R result s on the lug eon data se t: a) stre ngth fac tor; b) error measu re vari atio ns al ong st rength fact or updat ing and c) 3-D column perspe ctive of error measu re- neu ron c hange s Table2 . Rules on N=2 6 selec ted among 696 ob jects ; by SORS T -R To clarif y of per meabilit y changes, in con sequ ent part of rules, the lower value on the symbolic lugeon values w hich have relativel y similar ca tegory ,f or exam ple 1,2,3 or 2,3 or 3,4,5, h ave been conside r ed. With serving NF IS on such attributes( X, Y, Z& lugeon- without sca ling), permeability variations in figures 18 h as been portra yed. In this step, three M Fs (Gaussian just as like SO NFIS) for inpu t param eters ha ve bee n utilized. In Consequent o f comparis on betw een the results of RST and NFIS, one ma y interprets the variations in z= {2} is the sup erpositi on of sub leve l s, involved z=1160 to 1200 by NFIS, appr oximately. So, the compatibility of the results, derived from RST and NFIS can be prob ed b y comparis on of fi gurs17 &1 8. The forecasted domains -dar k colors- in figur e17, b y RST, have been co incided by same reg ions in figure 18, closel y. It must be not iced that t he RST model hasn’t covered the high permeabilit y zones, because of emp lo ying con servative way in e stimation of decision part whe reas the NFIS has ex posed such possible territories. The r ate of lugeon variations, or density of perm eable p arts, distingu ishes the zones with capability of possible spring or hole. Such cavities in the dam struc tures discussed as “karst s”, which are the main characteristi cs of the li mestone deposits (fi gure 20). To find out th e correlation b etween effecti ve param eters an d procuring of v alid patter ns of the rock mass- in the da m site- one ma y employ the similar process of NF IS or RST to e st imate altera tions of RQD and T.W .R (figure 1 9 using 3 MF s in NFIS). The contrary outputs in som e zones with general contextual associated rules about RQD and lugeon, implicate to the relativel y complex st ru ct ur es ab o ar d th e ro ck mas s . Apart from a few deta ils, comparison of result s indicates three overall zones in the rock m ass: in first zone the theor etic rules (such r everse rel ate 1 (z = 2) => (Dec = 1); 2 (l in {2, 3}) & (rqd = 2) => (D ec = 1) ; 3 (z = 3) & (l = 2) & (rqd = 1) => (Dec = 3) ; 4 (l = 2) & (twr = 3 ) => (Dec = 3) ; 5 (z = 3) & (l = 1) => (Dec = 1) OR (Dec = 3); 6 (l in {1, 2}) & (twr = 2) => (D ec = 2); 7 (rqd = 2) & ( twr = 3) => (Dec = 2) OR (De c = 3); 8 (z = 1) & (rqd = 1) => (Dec = 2); c) between RQD& lugeon) are satisfied, but in other zones, the said rule is disre garded. Fi g 16. Res ult s of t ransfer ring a t tri but es(X, Y, Z an d l uge on) in fi ve categories by 1-D SOM To fin ding out of th e backg round on the se ma jor zones, we refer t o the clustered data set b y 2D SOM with 7*9 weights in competitive layer (figure 10-c), on the first set of the attributes. The clustered and gra phic al e stima tio n di sc los e su itab le c oor dina tion , rela t ively . Fo r exam ple in fig ure 13-b, w e have hig hlig hted three dis tin ctiv e pa tter ns am ong lug eon and Z, RQD, TW R. One of the main reas ons of being such patterns in the investigated rock mass is in the defi nition of RQD. I n measureme nt of RQD, the direction of joints has not bee n considered, so that the rock masses with appropriate joints may foll ow hi gh RQD. Fi g 17. Lugeo n va riat io ns grap hs in z= {1} to z= {5}; accomplished by RST and five scaling of attributes. Number 6 charac terize s ambigu ity and unknow n cases Fig. 18 . A cross s ect ion pe rs pecti ve of l uge on change s obtai ned by NFIS Fig .1 9. RQD var iati ons in Z = 116 0 t o Z= 1200; by NFIS Fig. 20. The r ate of luge on varia tions-poss ible sp ring s (negative) and cavities (positive values); on the NFIS predic tions (diverg ence of l ugeon value s) 5. CONC L USION The roles of uncertaint y and va gue information in geomechnaics anal ysis are undeniable features. Y Z X Indeed , with de veloping of new approaches in information the ory and com putational intelligence , as well as, soft co mputing approaches, it is necessar y to co nsider t hese approaches to better under stand of natural eve nts in r ock mass. Under this view a nd granulation theory , we proposed two main algorithms, to complete soft granul es construc tion in not 1- 1 mapping level: Self Org anizing Neuro-F uzzy Infe renc e System (Random and Regular ne uron g rowth-SONF IS-R, SONFIS-AR- and Self O rganizing Rough Se t Theor y (SORST). So, we used our systems to ana ly sis of pe rmeab ility in a dam site, Ir an. ACKNO WLEDG MENT The au t hors wo uld like to appre ciate from P rof. Witold Pedrycz- De pa rtment of Electrical and Computer Engineering , University of Alberta , Canada- fo r his en coura gements and assurances along wr iting this pa per. REF ERE NCES [1] Zadeh, L. A. 199 7. 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Bac k Analysis based on SOM- RST s ystem. Accepted in the 10th Inter nationa l Sy mposium on L andslide s and E nginee ring a nd Engineered Slopes, Xi’an, China.