This paper proposes the use of particle swarm optimization method (PSO) for finite element (FE) model updating. The PSO method is compared to the existing methods that use simulated annealing (SA) or genetic algorithms (GA) for FE model for model updating. The proposed method is tested on an unsymmetrical H-shaped structure. It is observed that the proposed method gives updated natural frequencies the most accurate and followed by those given by an updated model that was obtained using the GA and a full FE model. It is also observed that the proposed method gives updated mode shapes that are best correlated to the measured ones, followed by those given by an updated model that was obtained using the SA and a full FE model. Furthermore, it is observed that the PSO achieves this accuracy at a computational speed that is faster than that by the GA and a full FE model which is faster than the SA and a full FE model.
Finite Element (FE) model updating entails tuning the model so that it can better reflect the measured data from the physical structure being modeled [1]. One fundamental characteristic of an FE model is that it can never be a true reflection of the physical structure but will forever be an approximation. In other words, FE updating fundamentally implies that we are identifying a better approximation of the physical structure than the original model. The aim of this paper is to introduce updating of finite element models using Response Surface Method (PSO) [2]. Thus far, the PSO method has not been used to solve the FE updating problem [1]. This new approach is compared with a method that uses simulated annealing (SA) or genetic algorithms together with a full FE model for updating. FE updating methods have been implemented using different types of optimization methods such as genetic algorithm (GA) and conjugate gradient method [3][4][5]. Levin and Lieven [5] proposed the use of simulated annealing (SA) and genetic algorithms (GA) for FE updating.
PSO is an approximate optimization method that looks at various design variables and their responses and identify the combination of design variables that give the best response. In this paper, the best response is defined as the one that gives the minimum distance between the measured data and the data predicted by the FE model. PSO attempts to replace implicit functions of the original design optimization problem with an approximation model, which traditionally are polynomials and are less expensive to evaluate. This makes PSO very useful to FE model updating because optimizing the FE to match measured data is a computationally expensive exercise. Furthermore, the calculation of the gradients that are essential when traditional optimization methods, such as conjugate Associate Professor Copyright © 2004 by Tshilidzi Marwala. gradient methods, are used is computationally expensive and often encounters numerical problems such as ill-conditioning. PSO tends to be immune to such problems when used for FE model updating. This is largely because PSO solves a crude approximation of the FE model rather than the full FE model which is of high dimensional order. In this paper we use the multi-layer perceptron (MLP) [6] to approximate the response equation. The PSO is particularly useful for optimizing systems that are evolving as a function of time, a situation that is prevalent in model-based fault diagnostics in the manufacturing sector. To date, PSO has been used extensively to optimize complex models and processes [7,8].
In summary, the PSO is used because of the following reasons: (1) the relative ease of implementation that includes low computational time when compared to other methods; (2) the suitability of the approach to the manufacturing sector where model-based methods are often used to monitor structures that evolve as a function of time.
Finite element model updating has been used widely to detect damage in structures [9]. When implementing FE updating methods for damage identification, it is assumed that the FE model is a true dynamic representation of the structure. This means that changing any physical parameter of an element in the FE model is equivalent to introducing damage in that region. There are two approaches used in FE updating: direct methods and iterative methods [1]. Direct methods, which use the modal properties, are computationally efficient to implement and reproduce the measured modal data exactly. Furthermore, they do not take into account the physical parameters that are updated. Consequently, even though the FE model is able to predict measured quantities, the updated model is limited in the following ways: it may lack the connectivity of nodes -connectivity of nodes is a phenomenon that occurs naturally in finite element modeling because of the physical reality that the structure is connected; the updated matrices are populated instead of banded -the fact that structural elements are only connected to their neighbors ensures that the mass and stiffness matrices are diagonally dominated with few couplings between elements that are far apart; and there is a possible loss of symmetry of the systems matrices. Iterative procedures use changes in physical parameters to update FE models and produce models that are physically realistic. In this paper, iterative methods that use modal properties for FE updating are implemented in the context of the PSO. In this paper, FE models are updated so that the measured natural frequencies match the natural frequencies predicted by the FE model. The mode shapes are then used to cross-validate the accuracy of the model. The proposed PSO updating method is tested on an unsymmetrical H-structure.
In this paper, modal properties, i.e. natural frequencies and mode shapes, are used as a basis of FE model updating. For this reason these parameters are described in this section. Modal properties are related
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