The Key Of Research And Application Of Metamodel-based Optimization

Metamodel-based optimization is one of the most popular and hopeful methods which can solve large scale engineering problems. According to its efficiency, the metamodel-based optimization method is widely applied for engineering optimization problems. Many large scale engineering problems can be done well if the metamodel-based optimization runs efficiently and stable. With the development of in-depth research, the scale and complexity of engineering problems are increasingly improved correspondingly. Although several kinds of metamodeling techniques have been approached, it is still difficult to solve practical engineering problems by current developed metamodeling technologies, especially for large-scale nonlinear problems. The major bottleneck of current developed metamodeling techniques is that how to construct accurate metamodel efficiently and how to balance the relationship between the accuracy and efficiency.The metamodel-based optimization frame is composed of three phases: design of experiment (DOE), construction of metamodel and optimization. Due to the complexity and variety of practical engineering problems, it is impossible to develop a general metamodel method. Therefore, existing metamodeling techniques commonly possess special characteristics for different kinds of engineering problems. According to features of an engineering problem, the feasible way is to propose a type-specific strategy.According to the metamodel-based optimization, the key factors are the accuracy and efficiency of metamodels. As long as a reliable and accurate metamodel is constructed, the corresponding optimum solution should be easy to achieve. Thus, the emphases of this thesis are DOE, metamodeling technique and time-based metamodeling strategy.The major innovative suggestions are summarized as follows Intelligent DOEAccording to the technique of the popular off-line design of experiment, two on-line DOE are suggested. The on-line sampling strategies are not purely DOEs based on statistical theories; these kinds of strategies are learning procedure essentially. The on-line sampling strategies use responses derived from evaluations to generate new samples automatically. Thus, this kind of online sampling strategy is so-called intelligent DOE. One intelligent DOE is particle swarm optimization (PSO)-based intelligent sampling strategy (PSOIS). This scheme is based on the modified PSO method; the other one is to use the boundary and best neighbor samples to generate new samples and so called BBNS (Boundary and best neighbor sampling) strategy. The BBNS cannot only generate new samples automatically but also correct the initial boundary constraints according to responses of evaluations. Furthermore, in order to improve the efficiency of the proposed intelligent sampling strategies, the parallel intelligent sampling strategy is also built. To assess the performance of the proposed strategies, comparisons between the proposed strategies and popular off-line methods are performed. The test results demonstrate that the proposed intelligent sampling strategies can control the initial design space and optimize the quality of the sample, such that the accuracy of the follow-up metamodel should be evaluated accordingly.Probability-based least square support regression techniqueIn this study, a least square support vector regression-based (LS-SVR) metamodeling technique is proposed. Compared with widely used metamodeling techniques, such as Kriging, RBF, etc., the notable difference of the LS-SVR is to construct metamodel by considering the empirical risk minimization (ERM) and structure risk minimization (SRM). It means that the ERM-based metamodeling techniques try to use a complex model to approximate finite samples and the robustness property of metamodel might be lost. In order to overcome this defect, a probability-based LS-SVR (PLS-SVR) metamodeling is implemented. The advantage of the suggested method is to use probability-based weight function to filter noise and outliers. Therefore, the PLS-SVR can obtain more robust estimates for regression compared with the LS-SVR. According to the results of benchmark tests, the PLS-SVR is shown to be promising for highly nonlinear problems. However, the proposed scheme might lead to long computational time due to neural network (NN)-based training procedure. To improve the efficiency and accuracy of the optimization and make the suggested approach feasible in practice, the proposed intelligent sampling strategy is integrated to generate training samples in PLS-SVR.Response-based space mapping methodSpace mapping (SM)-based optimization is a self-contained method and developed rapidly recently. Severe differences between the coarse and fine models and non-uniqueness of the parameter extraction procedure may cause the space mapping algorithm to be trapped in local minima and time consuming. According to this bottleneck, response-based space mapping (RBSM) method is proposed in this study. The distinctive feature of the RBSM is to construct space projection of response space instead of design space. A high dimensional problem can be transferred to lower dimensional problem and the parameter extraction procedure is also avoided. Thus, the RBSM is easy to converge compared with popular SM methods. Additionally, to improve the efficiency of the proposed algorithm, the intelligent sampling is also integrated. The mathematical nonlinear test function demonstrates that the convergence and accuracy of the proposed algorithm are easy to achieve. Application of the proposed metamodeling techniques to sheet forming optimizationDeformation mechanism of sheet forming procedure is very complicated, which contains geometry, contact, and material nonlinearity. In this study, the proposed intelligent DOE methods, metamodeling techniques and RBSM strategies are integrated to build a sheet forming optimization system. To verify the feasibility of proposed system, the proposed system is applied to optimize the real-world engineering problems. Compared with other popular metamodeling techniques, such as Kriging, RBF, sequential 2nd PR, the efficiency and accuracy of the built system are well improved.Time-based metamodeling techniqueA time-based metamodeling technique is suggested for vehicle crashworthiness design. The characteristics of the proposed method are the construction of a time-based objective function and the establishment of a metamodel by the PLS-SVR. Compared with other popular metamodel-based optimization methods, the design space of time-based strategy is extended to time space. Therefore, more time features and information can be extracted by considering time-dependent effect. Because the objective function is based on the time history, the design variables is more convenient to control the objective function in entire simulation procedure and the optimization result is also more useful and feasible in practice. To validate performance of the suggested method, cylinder impacting and full vehicle frontal collision are optimized by the time-based strategy. The results demonstrate the capability and potential of this approach in solving the crashworthiness design of vehicles.