Dynamic Model Updating Using Particle Swarm Optimization Method

Introduction 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 [3-5]. 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 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 …