An improved weighted response surface method based on vector projection sampling

Abstract

Structural reliability theory stems from the nature of randomness, fuzziness, characteristic and some other uncertainties in the process of engineering structural design, construction and employment. With the rapid development of science technology and industry, many departments have realized the importance of structural reliability problem and its potential economic benefits. Solving the problem of structural reliability has quickly become an important issue in the field of academic research. Because of the complexity of the structure and the harsh working environment which lead to a complex structural reliability problem, the traditional quality analysis method can’t explain the failure problems in practical engineering. How to solve the problem of large-scale complex structural reliability, improve the accuracy and efficiency of reliability analysis method, and further obtain great economic benefits, have become one of the most important exploration areas for the enterprises and scholars at home and abroad. The response surface method, which can replace the implicit limit state function by small amount of computation arises at this time. Through a series of deterministic response surface method, it uses polynomial function to approximate implicit limit state function. By reasonably selecting sites and iteration strategy, it ensures that the polynomial function on the failure probability can converge to the failure probability of the implicit limit state function. Response surface method, with high efficiency of clarity and precision, strong operability, combined with finite element advantage, is a reliability method widely used at present. In the process of the implementation of the response surface method, it uses three key steps of selecting the response surface function forms, obtaining sample points by the experiment design and using the regression fitting model, which has direct impact on the degree of the response surface method approximating limit state function and determines the performance of the response surface method. This is a problem that the response surface method must solve. It is the paper’s original intention to conduct the research work based on the response surface method of structural reliability optimization, improving the above three steps and the efficiency of engineering structure .The paper aims at the implicit limit state function problem, studying the structural reliability analysis of the weighted response surface method, combining the advantage of obtaining better sites by vector projection method and increases weighted coefficient by weighted response surface method. The improved weighted response surface method based on vector projection sampling is proposed. It uses the vector of the gradient projection method to get new design point and sample points, giving the actual limit state function of sample points more weights to construct the quadratic response surface function, updating the iterative response surface function, and solves the problem of the structural reliability of the implicit limit state function. Example analysis shows the characteristics of the proposed method, a steady design point can be found, and the calculation of stability has been improved considerably. The classical response surface method is optimized and reduces the defects that the calculation results are seriously affected by the interpolation coefficient. To some extent, it improves the calculation accuracy and can get relatively better results. Improved weighted response surface method based on vector projection sampling combines the advantages of obtaining test sample points by vector projection and weighted regression method, which is effective, feasible and can operate directly. It extends the application field of the response surface method to some degree and gets better approximate fitting limit state function at design point. It has better stability and robustness and provides new approach and ideas to solve the implicit limit state function.