Research And Optimization Application Of The Adaptive Surrogate Model

The surrogate model can solve the black-box problem and greatly reduce the huge computational burden caused by complex analysis,so it has been widely used.The adaptive surrogate model is the mainstream research direction of the surrogate model technology.Its main idea is to build an adaptive surrogate model with fewer sample points to solve the problems of black-box optimization and structural reliability analysis.The adaptive surrogate model technology simplifies the calculation of engineering problems and improves the efficiency of the algorithm.But it still needs to be further improved in sampling strategy,algorithm optimization and performance function fitting.This thesis studies the application of adaptive surrogate model in different directions,mainly includes:（1）For the model fitting problem with complex nonlinear relationship and high dimension,in order to reduce the number of samples in the sequence sampling based on adaptive surrogate model,an adaptive infilling strategy for Kriging model based on the combination of sensitivity and correlation function analysis is proposed.Firstly,the strategy uses the low difference sequence to take the sample points,constructs the initial model,and analyzes the sensitivity of each parameter.According to the sensitivity index,the parameter interval is divided,a new key sampling space is constructed as the key interval,and several candidate points that can express the characteristics of the approximate model are added in it.The method proposed in this paper is verified by the test function,and compared with the maximum minimum distance algorithm（MDA）.The results show that the method proposed in this paper can improve the model accuracy and calculation efficiency faster when meeting the accuracy requirements.（2）The organic combination of the adaptive surrogate model and intelligent optimization algorithm can improve the efficiency of model fitting and algorithm optimization at the same time.Based on the idea of the adaptive surrogate model,in order to improve the fitting accuracy and optimization efficiency of the model to local and global regions,an efficient global optimization algorithm based on local search and global optimization is proposed.Firstly,the algorithm constructs the expected function in the local region and optimizes it to get the update point.Secondly,the update point is added to the global region to improve the global accuracy,and then the differential evolution algorithm is used for global optimization.The results show that the algorithm can quickly converge to the accuracy requirements of the model and find the optimal value efficiently in the face of complex problems with more local extremum and too large variable space.The algorithm is applied to the fluid analysis and optimization of the impeller,which effectively reduces the pressure value of the impeller under load.（3）Based on the Kriging’s reliability analysis method,an adaptive active learning function of improved learning function U is proposed to reduce the modeling complexity of surrogate model and eliminate the random uncertainty of random variables on reliability analysis results.The AK-UPDIF algorithm composed of the learning function and the Monte Carlo sampling can accurately construct the limit state of the performance function with a small number of sample points and effectively evaluate the failure probability.At the same time,considering the misjudgment of prediction sample symbols,a convergence criterion with good robustness and suitable for a variety of learning functions is proposed.Four examples are used to verify the AK-UPDIF algorithm and the new convergence criterion,which improves the efficiency and accuracy of reliability analysis.