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.