Research On Nested Design Of Experiment In Variable-Fidelity Approximation Optimization

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, along with the simulation accuracy greatly improved, the computational expense is exponentially increased, which becomes a great challenge to the engineering practice of complex product design optimization. How to reduce the computational cost and improve the computational efficiency as far as possible and ensure an accurate optimization results at the same time, become an important practical problem. That's where the variable fidelity approximation based design optimization resulting from. Variable fidelity approximation based design optimization realizes an effective simulation and efficiency optimization of the design space through fusing the HF and LF analysis models.Before the model of variable fidelity approximation is built, it's important to make research on nested design of experiment. The nested design of experiment makes essential influence one the accuracy of the model of variable fidelity approximation. This paper carries out further research into three core and key techniques of variable fidelity approximation: the low fidelity experiment, the high fidelity experiment and the variable fidelity approximation modeling method.Firstly, the improved successive local enumeration algorithm is proposed to build the low fidelity experiment. The iterated search is used to improve successive local enumeration algorithm, which can help the sampling points get good space-filling prosperity and build a variable fidelity approximation with good performance. Thus, the engineering product designers can get an experimental scheme efficiently and build a variable fidelity approximation with good performance.Secondly, the high fidelity experiment based on the improved harmony search algorithm is proposed. In the maximum diversity problem, we add the minimum projection distance as a constraint to prevent sample points gathered at the edge of the sample space. Then, an innovative way is used to improve the harmony search, and applied to solve the MDP issues. Some numerical examples are demonstrated to improved harmony search algorithm. The results show that the improved nested experimental design can quickly and easily produce high-quality sample point.Next, the hybrid variable fidelity approximation modeling method is proposed based on RBF(radial basis function) and kriging. In this paper. In the proposed hybrid VF approach, information from both HF and LF models are employed. The LF model is ?rst approximated by RBF, and then this RBF LF approximation is pulled to the HF by the linear tuning model to gain a base surrogate. After that, this tuned RBF base is modi?ed by a kriging-based linear correction function. The proposed hybrid VF approach use the information of both HF and LF models at the same time, takes advantage of the c of different models.Finally, the above research results are applied in the pressure vessel problem, to solve the computational complexity of the optimization problem: Firstly, using the nested Latin Hypercube design nested to produce HF and LF sample points, then the proposed hybrid VF modeling approach based on Kriging and RBF is used to build the model. The results show that the proposed method can greatly reduce the computational complexity in engineering product design, improve the accuracy of the approximation models and minimize the computational cost.