Research On Key Technologies Of Variable-Fidelity Approximation-Based Design Optimization

Computer simuations have gradually developed into an indispensable and important techonology in the design optimization of modern complex engineering products. Along with the rapid development of computer technique, finite element size of simulation and analysis models becomes smaller and smaller, and the finite elements’ amount becomes larger and larger. Thus, the simulation accuracy is greatly improved, however, the computational expense is exponentially increased meanwhile, which becomes a great challenge to the engineering practice of complex product design optimization. In this case, the approximation methods come into being. By simply replace the simulation analysis models in design optimization, approximation models reduce the consumption of computing resources greatly and effectively. The variable fidelity approximation model, which was fristly proposed in the late20th century, can ceate accurate approximation models with a small sample size, and shows great potential.The variable fidelity approximation based design optimization, take full advantages of analysis models of different fidelity level, becoming an effective way to solve the important problem of how to improve the computational efficiency as greatly as possible and at the same time ensure an accurate optimization results. Variable fidelity approximation model can replace complex, implicit or unknown function relations, arid it is a foundation of the whole optimization process. Before creating variable fidelity approximations, how to effectively configure the sample points of high and low fidelity analysis models is an important issue, as the sample configuration has a bearing on the cost and accuracy of the final variable fidelity approximation. The optimization strategy is related to different roles of high and low fidelity analysis models. It can improve the optimization accuracy, and at the meantime reduce the computing cost. Therefore, experimental design for variable fidelity approximation, creation of variable fidelity approximation model and optimization strategy constitutes the core and key contents of variable fidelity approximation based design optimization method. In this thesis, further researches about these key contents are carried out.For experimental design of variable fidelity approximation, the translational propagation based nested Latin hypercube design is proposed. Simple nested design can be copied and translated into the entire design space to form a nested Latin hypercube design. The whole process requires no additional optimization, which can help the engineering product designers to get an experimental scheme efficiently and build a variable fidelity approximation with good performance. Next, output mapping based global variable fidelity approximation modeling method, PKI-LSSVR, is proposed. Characteristics and applications of PKI-LSSVR and other global variable fidelity approximations are compared and summarized. PKI-LSSVR takes the LF outputs as prior knowledge, and directly establish a mapping relationship between HF and LF models responses. At the same time, CPSO is adopted to estimate the hyperparameters in PKI-LSSVR to improve its generalization capbility. Different from the commonly used scaling methods, PKI-LSSVR adopts the idea of ouput mapping, to establish a direct relationship between the high and low fidelity responses, which is a new thought in model fusion. Considering sample quality factors, including different sample size and sample noises, a comprehensive comparision among PKI-LSSVR and other commonly used global variable fidelity approximations is conducted, in terms of predictive accuracy, computational efficiency and robustness. Their respective characteristics and applications are summerized, to provide a guidance or reference for engineering product designers when choosing a proper approximation model.And then, a sequential optimization strategy based on Parameterized Lower Confidence Bounding (PLCB) is proposed, which controls an effective updating of approximation models through the PLCB infilling criterion. This strategy can guide a optimization procedure to the global optimum effectively, which can get a more accurate solutions with a smaller computative cost, and eliminates the shortcomings of TR-AMMO strategy, such as not making full use of the sample points and easily falling into the local optimum etc..After that, in order to solve computational complexity problem in multidisciplinary design optimization, this thesis presents an integrated optimization of the variable fidelity approximation based design optimization and multidisciplinary design optimization, by appling the research theories and achievements mentioned above into the multidisciplinary design optimization field and proposing a variable fidelity based Analytical Target Cascading (ATC) method. The analysis module in ATC is replaced by variable fidelity approximation model constructed by nested Latin hypercube design and PKI-LSSVR. At the same time, the design optimization module in ATC applies the PLCB based sequential optimization strategy to control the updating of approximation in analysis module, reducing the computational complexity in ATC. Then, through an application of the parameter design optimization in small waterplane area twin hull form, the new method proposed in this thesis is verified. Results show that the proposed methods can reduce the computational complexity greatly in engineering product design optimization.