基于序贯层次Kriging模型的微型飞行器机身结构设计优化

在基于仿真模型的工程设计优化中，采用高精度、高成本的分析模型会导致计算量大，采用低精度、低成本的分析模型会导致设计优化结果的可信度低，难以满足实际工程的要求。为了有效平衡高精度与低成本之间的矛盾关系，通过建立序贯层次Kriging模型融合高/低精度数据，采用大量低成本、低精度的样本点反映高精度分析模型的变化趋势，并采用少量高成本、高精度的样本点对低精度分析模型进行校正，以实现对优化目标的高精度预测。为了避免层次Kriging模型误差对优化结果的影响，将层次Kriging模型与遗传算法相结合，根据6σ设计准则计算每一代最优解的预测区间，具有较大预测区间的当前最优解即为新的高精度样本点。同时，在优化过程中序贯更新层次Kriging模型，提高最优解附近的层次Kriging模型的预测精度，从而保证设计结果的可靠性。将所提出的方法应用于微型飞行器机身结构的设计优化中，以验证该方法的有效性和优越性。采用具有不同单元数的网格模型分别作为低精度分析模型和高精度分析模型，利用最优拉丁超立方设计分别选取60个低精度样本点和20个高精度样本点建立初始层次Kriging模型，采用本文方法求解并与直接采用高精度仿真模型求解的结果进行比较。结果表明，所提出的方法能够有效利用高/低精度样本点处的信息，建立高精度的层次Kriging模型；本文方法仅需要少量的计算成本就能求得近似最优解，有效提高了设计效率，为类似的结构设计优化问题提供了参考。

Design optimization of micro-aerial vehicle fuselage structure based on sequential hierarchical Kriging model

In simulation model based engineering design optimization, adopting high-fidelity and high-cost analysis model may cause unaffordable computational cost while adopting low-fidelity and low-cost analysis model may lead to optimization results with low reliability, which is difficult to meet the needs of engineering. In order to balance the contradiction between high accuracy and low cost,a sequential hierarchical Kriging model was established to fuse high/low fidelity data. In the proposed approach, many low-cost and low-fidelity sample points were used to indicate the changing trends of the high-fidelity analysis model, and a small number of high-cost and high-fidelity sample points were used to calibrate the low fidelity analysis model, so as to achieve high-fidelity prediction of the optimization objectives. To avoid the influence of hierarchical Kriging model errors on the optimization results, the hierarchical Kriging model was combined with the genetic algorithm to calculate the prediction interval of each generation of optimal solution according to 6σ criteria. The current optimal solution with a large prediction interval would be selected as a new high fidelity sample point. At the same time, sequentially updating the hierarchical Kriging model in the optimization process could improve the prediction accuracy of the hierarchical Kriging model near the optimal solution, so as to ensure the reliability of design results. The proposed approach was applied to the design optimization of a micro-aerial vehicle fuselage structure to verify its effectiveness and superiority. The grid models with different number of elements were selected as the low-fidelity analysis model and high-fidelity analysis model, respectively. Sixty low-fidelity sample points and twenty high-fidelity sample points were selected by optimal Latin hypercube design (OLHD) to construct the initial hierarchical Kriging model. The design optimization problem was solved by the proposed approach, and the solution results were compared with the results solved by the high-fidelity simulation model. The results showed that the proposed approach could effectively utilize the information of high/low fidelity data to construct hierarchical Kriging model with high accuracy and only a small amount of computational cost was required to obtain the approximate optimal solution. The proposed approach can effectively improve the design efficiency and provide a reference for similar structure design optimization problems.