基于多线性支持向量机的样本点正确分类与复杂失效方程稳步模拟

为克服一般响应面方法重构复杂隐式失效方程所需样本数量较多、精度较差的不足,提出了一种基于多线性支持向量机的结构失效方程模拟方法。该方法的显著特点是应用了样本点正确分类技术,因而其求解精度随着样本点数量的增多而稳步趋近于真实失效方程。其主要求解过程为,(1)结合均匀设计方法,生成均匀的紧邻极限状态曲面的失效和可靠样本点。(2)依据样本点向量模和样本点向量间夹角余弦值将总体空间划分成多个子空间,确保每个子空间内的样本点能由一个线性支持向量机完全分开。(3)采用一种基于扩充样本点对的迭代算法不断更新样本点集合,从而逐步修正模拟的多个线性失效方程。算例分析表明,无论失效方程为强非线性函数还是多个失效模式组成的分段函数,该方法的计算精度与效率均较为稳定。这为具有复杂失效方程结构的可靠度分析提供了有益参考。

Stable fitting of complex failure functions and correct classifying of sample points based on multiple linear support vector machines

To overcome the shortcomings of the current response surface methods,which are less accurate and need a large number of samples to rebuild a complex implicit failure function,a new fitting method of structural failure function is proposed based on multiple linear support vector machines.One of the main features of this method is the application of correct classifying techniques of sample points.Thus,its solution can approximate the real failure function steadily as the number of samples increases.Its main solving steps are:(1) use the uniform design method to generate reliable and failure samples,which are close to the real limit state surface;(2) divide the total space into multiple subspaces based on vector modules and angles of sample points to ensure that the sample points in each space can be classified correctly by a linear support vector machine;(3) establish an iterative algorithm based on additional sample pairs to update sample sets continuously to modify the obtained multiple linear support vector machines.Numerical examples show that this method has a better accuracy and efficiency,no matter the failure function is a highly nonlinear one or a piecewise one due to its multiple failure modes.This method provides a useful basis for the reliability analysis of structure with a complex failure function.