隐式极限状态方程可靠性分析的加权响应面法

针对隐式极限状态方程的可靠性分析，提出加权回归响应面法，该方法采用线性响应面来拟合隐式极限状态方程。所提方法的策略可以归结为三点，一是选取极限状态函数绝对值更小的实验抽样点；二是根据每个实验抽样点的极限状态函数绝对值的大小，构造每个点在回归分析中的权数，增强极限状态函数绝对值小的实验抽样点对响应面函数确定的作用，削弱极限状态函数绝对值大的实验抽样点对响应面函数确定的作用；三是采用与传统响应面法一样的向设计点收敛的迭代方法。这三点策略保证了所得到的线性响应面函数能够在设计点附近更好地拟合真实隐式极限状态函数值为零的表面，从而达到高精度计算隐式极限状态方程可靠度指标的目的，算例结果充分显示所提方法的优越性。文中所提方法与组合响应面法结合，可以发展成为非线性高变异性隐式极限状态方程失效概率计算的高精度方法。

RESPONSE SURFACE METHOD FOR RELIABILITY ANALYSIS OF IMPLICIT LIMIT STATE EQUATION BASED ON WEIGHTED REGRESSION

A response surface method on the basis of weighted regression is proposed for reliability analysis of implicit limit state equation,in which a linear response surface function(RSF) is used to fit the actual implicit limit state.The strategy of the method can be summed up as three.(1)The sampling points are selected at those experimental points with smaller absolute value of actual limit state(AVALS).(2) In regression analysis,the weight factor for each point is calculated based on its AVALS.By the weighted regression,the effect of those sampling points with smaller AVALS on determination of RSF is augmented,and the effect of those sampling points with bigger AVALS is weakened.(3) Analogous as the traditional response surface method,the iteration strategy converging at design point is employed in the method.The above three strategies ensure the linear RSF can fit the actual implicit limit state equation better in the vicinity of the design point.Therefore highly precise evaluation of reliability index can be obtained.The examples are illustrated the advantage of this method.Further more,through the combination of the multiple linear response surfaces,the present method can be developed as a precise reliability evaluation method for the implicit limit state equation with high non-linearity in limit state and high coefficients of variability in basic variables.