面向低精度分析模型不可分层级的多保真度近似建模方法研究

Research on multi-fidelity surrogate modeling method for non-hierarchical low-fidelity analysis model problem

  • 摘要:
    目的 鉴于多保真度代理模型能够有效降低产品设计中的建模成本,为放宽多保真度近似建模技术对于分析模型层级关系的预设条件,拓展其实际工程应用场景,针对低精度分析模型不可分层级情形,提出基于方差量化的多保真度近似建模方法。
    方法 基于各组不可分层级低精度数据,分别构建Kriging代理模型,根据其预测方差值量化每组低精度数据的不确定性,并对每组低精度数据进行评估加权以组合构建趋势函数,同时引入改进层次Kriging模型来融合高/低精度数据,使得趋势函数的修正系数能够根据设计空间形貌特征变化进行取值。通过典型数值算例对所提方法进行测试,同时使用该方法开展MI50-超材料隔振器的性能预报。
    结果 数值算例结果表明所提方法的预测精度比同类方法提高85%以上。隔振器的性能预报结果表明该方法预测精度相比同类方法提高60%以上。
    结论 所提方法在放宽低精度分析模型之间层级要求的同时,能够充分挖掘低精度数据的有用信息,实现高精度分析模型和不可分层级低精度分析模型的有效融合。

     

    Abstract:
    Objective Multi-fidelity surrogate (MFS) modeling technology can reduce simulation costs in the design process of engineering products. In order to relax the hierarchical relationship between low-fidelity (LF) analysis models and broaden the engineering application of MFS, this paper proposes an MFS modelling method based on variance-weighted sum (VWS-MFS) for the fusion of multiple non-hierarchical LF data.
    Method The proposed method builds LF surrogate models using Kriging technology. By quantifying the uncertainty of the LF surrogate models with variance, the non-hierarchical LF data is weighted to construct a trend function. In addition, the improved hierarchical Kriging (IHK) model is introduced to fuse the high-fidelity (HF) and LF data, enabling the correction coefficient of the trend function to change throughout the design space. The proposed method is then tested on nine typical examples and applied to the performance prediction of a vibration isolator.
    Results According to the experimental results, the proposed method shows higher prediction accuracy than similar methods by more than 85%, and its vibration isolator performance prediction is significantly improved by more than 60% compared with the static prediction method.
    Conclusion The proposed method integrates the HF analysis model and multiple non-hierarchical LF analysis models. While the hierarchical relationship between LF analysis models is relaxed, the information of LF data is mined to the maximum extent.

     

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