A Response Surface Structure Reliability Analysis Method Based On Multi-layer Extreme Learning Machine

With the rapid development of civil engineering industry,the actual engineering structure has become large-scale and complex.There are more and more uncertain factors arising in complex structures,and the security issue is more pronounced,which poses new challenges on structural reliability analysis and methods.Traditional structural reliability methods such as: the first-order second-moment method(FORM),second-order second-moment method(SORM),Monte Carlo method(MCS),and etc,due to their respective limitations,are difficult to meet the accuracy and efficiency requirements to solve structural reliability analysis problems.Response surface method is widely used to reduce the amount of calculation of structural reliability analysis in engineering,which approximates the original limit state function with some explicit analytic expressions.The accuracy of response surface function depends on the choice of function type and the locations of sample points.In view of the characteristics of multi-layer extreme learning machine with fast deep learning ability and capturing high dimensional information,this paper proposes structural reliability analysis methods based on multi-layer extreme learning machine,using multi-layer extreme learning machine to approximate the original limit state function,and carrying out structural reliability analysis.The main research content is as follows:Firstly,a second-order moment structure reliability method based on multi-layer extreme learning machine is given.This method uses a multi-layer limit learning machine to reconstruct the original limit state function,performs structural reliability analysis based on the reconstructed multi-layer limit learning machine with the second-order moment method with a finite step size,which is compared with that based on the single hidden layer.Dropout and targeted dropout technologies are incorporated into the reconstruction procedure to overcome the overfitting.The analysis and discussion of numerical examples proves the feasibility and effectiveness of the method.Sencondly,Monte Carlo method for structure reliability analysis based onmulti-layer extreme learning machine is presented.This method uses random sequences or Halton pseudo-random sequences to generate training sample points and train a multi-layer limit learning machine to reconstruct the original limit state function.Dropout or targeted dropout technologies are also discussed in the multi-layer limit learning machine.And then Monte Carlo method is employed to calculate structural reliability.Compared with the traditional Monte Carlo method,the proposed method yields better accuracy and efficiency.Thirdly,Monte Carlo method for structure reliability analysis based on multi-layer extreme learning machine with the samples generated by particle swarm optimization algorithm.By this means,some sample points distributed as close as possible to the design point or extreme points are obtained as the training set for the reconstruction function and the number of samples are reduced.The multi-layer extreme learning machine is then built and Monte Carlo simulation provides the answer of the structural reliability analysis.Some reliability analysis problems solved by the proposed method are demonstrated with good accuracy and efficiency.