The Compressed Sampling Response Surface Method To Simulating Optimization Of Complex Product

Compared with the traditional global optimization method, response surface optimizationmethod needs fewer times of simulation and has the high efficiency of optimization; thereforeit is widely applied to engineering design. However, the simulation model of complex productsuch as plane, automobile, high-end CNC machine tools, is often a multidisciplinary andnonlinear characteristic which leads to much more changeable and complex response surfaces;therefore the response surface method still need a lot of simulation computations, furthermorethe results of optimization are non-ideal.Compressive sampling theory points out that when the signal with compressiblecharacteristics, a small amount of sampling data of related observations in low dimensionalspace can achieve precise and stable reconstructions of higher dimensional signal. Therefore,this article puts forward a kind of response surface method based on compressive sampling.The main contents are as follows:1) Response surface sparse expression. By comparing the natural distributioncharacteristics of the existing response surface model with the orthogonal sparserepresentation of image signal processing, in order to reduce the number of sampling pointsand improve the efficiency of simulation optimization, the article puts forward the sparserepresentation methods of Legendre orthogonal polynomial.2) Response surface compressive sampling. On the basis of sparse Legendre orthogonalpolynomial expression, in order to realize the stable response surface reconstruction, superLatin cube compressive sampling method is proposed, through iteration to determine theobservation matrix which meet the minimal correlation criterion,.3) The1norm response surface algorithm of unknown sparse degree. According to thecomplexity and unknown sparse degree of simulation optimization response surface, adaptivesparse degree1norm algorithm to reconstruct response surface is proposed, which makesfull use of the1norm characteristic that solves the convex optimization problem withsparse, and can reconstruct the response surface precisely. 4) The response surface simulation optimization method based on compressive sampling.On the precise reconstructing response, accurate and stable subdivision matrix method is usedto get the optimal design point. Numerical experiments show that when the response surfacecan be compressed, the method needs fewer simulations and optimization results are moreprecise and stable.Finally, the method and algorithm in this paper are realized in Matlab, and apply to theICF indirectly driven radiation symmetry analysis. Compared with hybrid adaptive responsesurface method, experimental result shows that the simulation calculation times of theresponse surface simulation optimization method based on compressive sampling is reduced,and the optimization results more accurate and stable.