Simulation Optimization Method Based On Sparse Response Surface For Complex Products And Application Research

The simulation-based product design method has become an indispensable design tool for complex product development processes because it can greatly reduce the physical prototype and reduce the test cost.As the composition and control of the system become more and more complex,the product simulation model is getting larger and larger,and the solution time is increasing.The performance optimization is relatively inefficient because the simulation process needs to be frequently called.Based on design of computer experiments and surface approximation,the response surface method can effectively reduce the number of simulation model calls,and has been widely used in complex product performance simulation optimization.However,there are still many design sampling points required for the construction of the existing response surface,which limited the optimization efficiency.To this end,a complex product simulation optimization method based on sparse response surface is proposed,and the following aspects are studied:Because of the sparse characteristics of response values distribution on one type of basis function(such as the Legendre orthogonal polynomial fuction),a quasi-sparse response surface construction algorithm based on Elastic net regression is proposed.The l1 norm sparse convex is employed to optimize the selection of the base atoms strongly correlated with the residual of the response values and sparsely represent the response surface of complex product.Further,when the number of sampling point is too small and the base atom selection is insufficient,the P2 norm regularization is used to supplement the base atoms associated with the residual of the response values while the sparsity is appropriated reduced,and the characterization ability is improved.Meanwhile,in order to obtain a strong generalized solution as the target,the l2 norm factor is selected by cross validation,and the Elastic net regression is translated to be LASSO(Least Absolute Shrinkage and Selection Operator)regression problem and solved,then the quasi-sparse response surface with strong generalization ability is stably constructed.The response surfaces of complex product simulation model may contain composite features.It is difficult to be sufficiently sparsely represented by a single sparse base,which more sampling points are required to complete the accurate reconstruction of the response surface.To this end,a construction algorithm sparese response surface with combined bases based on CG-FOCUSS(Conjugate Gradient FOCal Underdetermined System Solver)is proposed,in which,the commonly used basis functions with different expression characteristics are grouped into a combined base dictionary to high sparsely represent the response surface.Based on lp(p=1/2)norm optimization,the the CG-FOCUSS is used to efficiently obtain the conbined base atom representation coefficients from the combined base dictionary.Meanwhile,the cross-validation method is employed to provide good initial values of the iteration and obtain a high accuracy response surface.Based on the combined basis,the high sparse and accuratation reconstruction of the response surface is realized under a small sampling number,which provides supportment for efficient simulation optimization of complex productsAn optimization algorithm with GPU(Graphic Processing Unit)parallel processing based on branch and bound is proposed for sparse response surface.In which,the subset of the space to be searched is mapped to different GPU threads,and the second response surface based on Chebyshev basis function is constructed in each thread,and the compact subset bound is obtained through the interval operation,thereby the ootpimization space is large-scale reduced.The branch and bound process is repeated based on dichotomy until the subset fineness requirement is reached,and the fine subset of optimal design points are efficiently obtained.The remaining less subsets are mapped to different GPU threads again,and sequential quadratic programming algorithm is used to quickly obtain the optimized design points of each subset.The global optimization design points and multiple reference local optimization design points are obtained by comaring all optimal of each subset,which can support the efficient and rapid optimization design decisions for complex products.Finally,based on the proposed theoretical research algorithm,combined with the National Natural Science Foundation of China named "Response Surface Simulation and Optimization Method Based on Non-adaptive Compressed Sampling for Complex product"(project number:51375185),the prototype system "response surface simulation and optimization for complex products " is developed and applied to the optimization design of a fire-fighting vehicle boom hydraulic system and control system,the pressure fluctuation of the balance valve during the joint action process of boom is reduced from 13Mpa to 1Mpa,which solves the problem of jitter in the movement of the vehicle boom.