Study On Optimization Algorithm For Alternative Solutions In Finite Element Model Updating

Most of the existing studies about finite element model updating concentrate on the finding one single solution.The main process can be illustrated as two phases.Firstly,use the error between real structural response and finite element model response to establish the objection function.Secondly,minimize the objection function by applying different algorithms.Traditional routine is finding a solo global minimum value.However,due to different and unknown reasons such as incomplete and noise in accelerate single testing,error in model identification,and different ways used to establish the objections function,some local minimum values can be better represent the real conditions.In these cases,offering a global minimum and some different local minimums will increase the chance to find the real structure.However,traditional optimize algorithms aim to find one single solution,and cannot directly be used to find different alternatives.To solve this problem and offer some options to the authority,this paper proposed three different algorithms.All the three algorithms can be used to find several alternatives and they all be verified by numerical examples.Firstly,some conditions are analyzed which may lead to alternative solutions.This paper points out that reasons such as incomplete and noise in accelerate single testing,error in model identification,and different ways used to establish the objections function may result in this problem.That means the global minimum may not be better to some global minima to present the real structure.Thus,offering some different solutions seems more reasonable.This paper proposes three evolutionary algorithms that are able to identify both global and local minima.The first algorithm based on artificial bee colony,but adds two operators.The first operator is confined the searching area,which ensured the possibility to find different solutions.The second operator is adding the process of candidate bee selection,which used to find different minima.Multiple peeks functions and single peek function were used to verify the proposed method.The result shows that comparing to stand artificial bee colony algorithm,neighbor searching based artificial bee colony algorithm can be efficiently identity all the local minima.The first algorithm based on steady-state genetic algorithms.Steady-state genetic algorithms use one angle to distinguish whether two solutions belong to the same peek area or different peek areas.However if those two minima deposit in line,it may missing some minimum.Thus,this paper suggests use two angles to determine minima,which can theoretically avoid missing condition.In addition,to insure the efficiency,genetic algorithm was replaced by particle swarm optimization algorithm.The separate community strategy was used to insure the diversity of particles,which can increase the possibility to identify different minima.The proposed algorithm was used in a finite element model updating.The result verified proposed algorithm's available.Finally,this paper combines Steady-state genetic algorithms and gradient descent algorithm to improve the accuracy of Steady-state genetic algorithms.Steady-state genetic algorithms have a better performance in identifying alternative minima,but with a low accuracy.The gradient descent algorithm has a better searching accuracy,but it too sensitive to initial position.Using the advantage of those two algorithms can insure the diversity and accuracy of the final result.The proposed methodology is validated with two numerical examples.The first example shows the capabilities of the technique with a mathematical function.A model updating problem using the American Society of Civil Engineering Structural Health Monitoring Benchmark structure is used for the second numerical example.