结构二次二阶矩可靠度指标的回归分析预测算法

REGRESSION ANALYSIS-PREDICTION ALGORITHM FOR STRUCTURAL SECOND-ORDER SECOND-MONMENT RELIABILITY INDEX EVALUATION

针对具有强非线性结构功能函数的可靠度指标计算问题,通过数值抽样及回归分析方法对改进的功能函数二阶展开形式进行了系统研究,揭示了二次二阶矩可靠度指标βSORM与一次二阶矩可靠度指标βFORM之间的关系规律。根据上述规律结合线抽样Monte Carlo法,建立了基于回归分析预测算法的可靠度分析方法。该方法通过对若干基本抽样点的回归分析,确定了βSORM与βFORM之间一般关系规律的具体表达式,从而实现了强非线性可靠度问题的高精度求解。研究表明:所建立的方法能够有效改善传统二阶可靠度算法计算过程繁琐、求解效率低下的问题;在求解精度、适用范围及算法稳定性等方面具有优势;且计算直观简便,易于为一般设计人员掌握,更适合于实际工程应用。

Aiming at the reliability index calculation of a strong nonlinear structural performance function, the numerical sampling and regression analysis methods are introduced to analyze the second-order expansion of a modified performance function. Thereby the form of general law between SOSM reliability index flSORM and FOSM reliability index flFORM is obtained. On the basis of a regression analysis-prediction algorithm, a new reliability analysis method is presented according to the general law above and the application of a line sampling Monte Carlo method. Through the regression analysis of certain sampling points, the proposed algorithm can establish the specific expression of a general law between flSORM and flFORr~. And the high precision solution of a strong nonlinear performance function reliability index can be achieved. The study results show that a cumbersome calculation and an inefficient iteration can be alleviated effectively by the present algorithm. The advantages of the present method in accuracy, application scope and calculation stability are obvious. Because of its convenience and intuition, the present algorithm is easy to be mastered by general designers and applied to an actual engineering analysis.