结构可靠性优化的多输出高斯过程代理模型

对于具有多失效模式的结构,基于可靠性的结构优化计算成本是比较昂贵的。本文利用多输出高斯过程MOGP(Multiple Output Gaussian Process)代理模型以降低计算成本,首先利用Bucher方法生成初始样本,然后结合均匀训练样本和学习函数对MOGP代理模型进行构建。学习函数可在大范围内筛选出较为满意的训练样本,能够确保MOGP代理模型具有较好的全局精度,在整个优化过程中不再重新构建MOGP代理模型。利用协方差矩阵,MOGP代理模型能够考虑各失效模式的相关性,对多输入多输出系统具有良好的预测性能。数值算例表明,本文方法具有较好的计算结果,且计算效率较高,尤其是设计变量数目与失效模式数目较多时效率提升明显。

Multi-Output Gaussian process surrogate model for structural reliability optimization

The calculation cost of Reliability-Based Design Optimization is relatively expensive for structures with multiple failure modes.Therefore,this paper uses a Multi-Output Gaussian Process (MOGP) surrogate model to reduce the calculation cost.In this study,first of all,the Bucher''s method is used to generate initial samples,and then uniform training samples and a learning function are both used to build the MOGP surrogate model.The learning function can obtain satisfactory training samples in a large range,which can ensure that the MOGP surrogate model has better global accuracy,so that there is no need for MOGP surrogate model to be rebuilt in the whole optimization process.The MOGP surrogate model can consider the correlation of each failure mode by using the covariance matrix,thus it has a good prediction for the multi-input and multi-output system.Numerical examples show that the proposed method has satisfactory results and high calculation efficiency,especially when the numbers of design variables and failure modes are large.