Research On Variable-Fidelity Approximation Modeling Method Based On Self-Organizing Maps

The simulation analysis of physical models has become a necessary method in engineering application. However, the computation cost becomes extremely expensive with the higher requirement for simulation accuracy, metamodels are commonly used to replace these expensive simulations to reduce the computational expenses. Particularly, the variable-fidelity approximation model can ensure higher accuracy while reducing the computational cost by combining the information of fidelity simulation with varying degrees. Using a small number of high-fidelity simulative models to ensure high approximation precision and a large number of low-fidelity simulative models to control the computing cost. Therefore, this model shows enormous potential in engineering applications.However,the current variable-fidelity approximation modeling methods based on the Taylor expansion which has relatively high approximation accuracy only within the local scope. In addition, the existing variable-fidelity approximation modeling methods are one-stage without using the obtained sample point information to guide the modeling process,while the sequential modeling can get better fitting accuracy with the same scale samples. Therefore, this paper focus on the variable-fidelity approximation modeling methods which has good approximation accuracy within the global scope, as well as the sequential modeling based on variable-fidelity approximation model. The specific contents are as follows:Firstly, this paper conducts research on the variable-fidelity approximation modeling method which has relatively high approximation accuracy in the global scope,proposes a new variable-fidelity modeling method named AS-Kriging which based on the additive scaling of Kriging. In the end, mathematical examples have demonstrated that the AS-Kriging method has a good approximation accuracy within the global scope.Secondly,in view of the shortcoming that the current sequential modeling method is mainly based on single-fidelity approximation model,this paper introduces the sequential modeling to the field of variable-fidelity approximation model,reducing design space by the method named self-organizing map and then generating sample points in the reduced key scope by the method of maximum distance.The feasibility and efficiency of the new method mentioned-above in mathematical and engineering examples are demonstrated by comparing it with the sequential modeling method based on the maximum estimated error criterion.Finally, the sequential optimization strategy based on variable-fidelity approximation model is studied and the statistical lower bound method is improved to prevent the optimization results from becoming locally optimal by adding two samples in each iterative process, that is, generating sample points to improve the overall accuracy of the approximate model by the design space reduction method named SOM, and then adding the optimal solution of the current approximate model to improve the local accuracy. In the end, the feasibility of the proposed method is verified by some mathematical examples.