Research On Methods Of Metamodel-based Design Optimization Based On Accurate Metamodeling And On-line Sampling

With the rapid development of computer technology,the experimental design optimization method based on computer simulation has been widely used in the field of engineering product design.However,with increasing demands on product performance,the accuracy of the simulation model becomes higher and higher and the involved simulation time cost increases in a exponential way,thus seriously hindering the application of simulation-based design optimization in engineering practice.In order to improve the design efficiency,scholars put forward the metamodel-based design optimization method(MBDO).It can use the metamodeling techniques to replace the complex and time-consuming computer simulation analysis,and then obtain the optimal design through the corresponding reasonable sampling and optimizing strategies.The design optimization process thus can greatly reduce the computational cost involved in the simulation-aided design.In engineering,the MBDO method has shown a good application prospect.Metamodel-based design optimization methods can be broadly divided into two categories: one is the design optimization based on building an accurate metamodel;and the other is design optimization based on the optima-oriented sampling methods.The constructed accurate metamodel in the methods of type one can be also used for prediction analysis.Although the metamodel-based design optimization method s has been widely used in engineering,how to establish the metamodel more efficiciently and utilize the online sampling strategies more rationally to improve the design optimization efficiency and thus reduce the design cost is still the hot research topic.This research mainly analyzes the shortcomings of methods involving current multi-fidelity metamodeling,metamodeling for high dimensional problems and optimization based on-line sampling in solving design optimization problems,and then put forward the corresponding optimization strategies to further improve the optimization efficiency of MBDO in engineering design.The specific contents are described as follows:(1)The current research status of MBDO is introduced.The deficiency of existing research is discussed,and the corresponding solutions and research framework are put forward.(2)A RBF-based multi-fidelity metamodeling method is proposed.Different from the traditional multi-fidelity metamodels,the proposed metamodel consists of a linear sum of radial basis functions corresponding to each sample point,thus making it sufficiently use the information provided by both the high and low fidelity samples.The weights of the radial basis functions can be obtained from least square estimation,which need only one-matrix calculation.The proposed metamodel has the advantages of simple structure,convenient calculation,metamodeling by using more than two-fidelity samples,and so on.In addition,a sequential sampling method based on cross validation error and voronoi partition is extended for multi-fidelity metamodeling,which further improves the metamodeling efficiency of the proposed metamodel.(3)The multi-fidelity metamodeling method for high dimensional problems is proposed.With the dimension of design problems increasing,the traditional metamodel or multi-fidelity metamodel can hardly use limited samples to obtain an accurate metamodel because of their mathematical structures.Therefore,in terms of how to utilize the multi-fidelity samples to construct an accurate approximated model for a high dimensio nal problem under the structure of HDMR,a double-stage metamodeling strategy is proposed.It first uses the multi-fidelity samples and multi-fidelity metamodeling tools to build a multi-fidelity metamodel and uses it to transform the low-fidelity data into the high-fidelity data.Then the single-fidelity metamodeling tools combing the high-fidelity samples with transformed high-fidelity samples can be used to build an approximated component function of HDMR.Finally,by using the similar double-stage metamodeling strategies for all the component functions in the HDMR structure,the approximated model for a high dimensional problem is obtained and it can be used for the design optimization.Because of the use of low-fidelity sample points,the metamodeling efficiency for high dimensional problems is greatly improved.(4)An adaptive metamodeling method based on ensemble of multiple metamodels is proposed for high dimensional problems.I n the aspect of approximating for high dimensional problems,the current high dimensional model representation(HDMR)always combines the traditional single metamodel,while it is difficult to know in advance which metamodel is suitable for an unknown problem.Therefore,these HDMR models have the instability problem in the metamodeling process.In this paper,the ensemble metamodel is used in the HDMR construction.The ensemble metamodel uses multiple metamodels and thus can improve the metamodeling stability and guarantee the accuracy of the built metamodel.In addition,due to the fact that many parameters of ensemble under the structure of HDMR could be inconvenient for the post prediction or optimization process,an enhanced RBF model based on ensemble is proposed.The metamodel has both the metamodeling stability of ensemble and all the advantages belonging to RBF,such as explicit expression,simple structure and gradient model.Besides,in order to improve the metamodeling efficiency of the proposed method,this paper proposes an efficient sequential sampling method based on the gradient information provided by the enhanced RBF model and voronoi partition.(5)A multi-point sampling method based on kriging is proposed for global optimization.Although the off-line optimization method based on building an accurate metamodel can be well applied in the engineering design problems,its metamodeling process and optimization process are totally separately.It usually has a high demand for the metamodel's accuracy and use a large amount of sample points in the design optimization process,thus making the design cost is very high.Therefore,the on-line optimization method based on the optima-oriented sampling methods has been gradually a research hotpot in engineering design optimization.This kind of method can adaptively adjust the sampling direction according to the optima information provided by the current samples,thus making it very efficient in the design optimization process.In terms of the disadvantages of the on-line optimization method of mode-pursuing sampling method(MPS)that its speed factor is difficult to be controlled and its global convergence is poor,the paper prosposes to combine the expected improvement(EI)function of kriging with the MPS sampling mechanism in the optimizing process in order to improve optimizing efficiency of MPS.And according to the space change determined by the number of random points which meet the EI constraints,the corresponding speed control factor and the local search strategies are put forward,thus greatly improving the efficiency of the method for global optimization.(6)An accelerated surrogate-assisted particle swarm optimization method is proposed for high dimensional problems.Because of the low accuracy and low efficiency of the traditional MBDO methods in solving the high dimensional design optimization problems,the paper proposes an efficient updating strategy of the particle swarm for global optimization of high diemensioanl problems.It is obtained through using the global search ability of particle swarm optimization algorithm for high dimensional problems and reasonably use the predicting ability of surrogates.Through building the global surrogate in the whole design space and the local surrogate around the best history particle to direct the movement of the swarm particles,the proposed method can converge in a fast speed and with a high accuracy for high dimensional design optimization problems.Besides,in terms of the fact that the method could have the unstable optimizing process in handling the complex high dimensional and multimodal optimization problems,two strategies biased to global search are put forward.In addition,an improved accelerated surrogate-assisted particle swarm optimizing algorithm is proposed to adapt to engineering practice.It can update an inconstant number of particle points in each iteration.To sum up,the proposed accelerated surrogate-assisted particle swarm optimization method has a good application prospect in global optimization of high dimensional problems.(7)The research results and main innovation points of this paper are summarized,and the future research directions are given.