基于贝叶斯支持向量回归机的自适应可靠度分析方法

Adaptive algorithm based on Bayesian support vector regression for structural reliability analysis

进行复杂结构可靠度分析时,由于涉及隐式功能函数和耗时的数值计算,减少结构模型的调用次数在提高分析效率方面显得尤为重要。为此,本文基于贝叶斯支持向量回归机,提出了一种高效的自适应可靠度分析方法。该方法利用贝叶斯支持向量机提供的概率估计信息(均值和方差)构建学习函数,同时通过引入样本间的距离测度防止选取与现有样本过于临近的冗余点,进而能快速有效地选取极限状态曲面附近具有代表性的样本点,以提高代理模型的构建速度和预测精度。此外,在学习过程中引入了有效抽样域策略,有针对性地选取对失效概率估计误差贡献大的点,从而进一步提升结构可靠度分析的计算效率。最后,通过数值算例验证了本文方法对结构可靠度分析的适用性和有效性。

The reliability analysis of complex structures usually involves an implicit performance function and time-demanding simulation model, hence the reduction of the number of functional calls is of critical importance to improve computational efficiency.In this regard, an adaptive algorithm based on Bayesian support vector regression(ABSVR) is proposed for efficient reliability analysis.To improve the overall performance of ABSVR,a new learning function is devised using the probabilistic information provided by the Bayesian SVR model.Besides, a distance constraint term is added into the learning function to avoid the clustering of samples, so that the selection of informative sample points can be achieved more efficiently.Moreover, an effective sampling region scheme is introduced in the learning process to filter out samples with weak probability density, through which only samples with large contributions to the failure probability are retained.Several numerical examples are employed to illustrate the accuracy and efficiency of the proposed method.