The Non-gradient-based Reliability Method in Equivalent Linear Systems for Nonlinear Random Vibration

Abstract

A conventional approach for nonlinear random vibration analysis is using equivalent linearization method. Tail-Equivalent Linearization Method (TELM) is one the best proposed methods in the recent decade for determination of equivalent linear model. In TELM, the design point is obtained using first-order reliability method. In the current research, a non-gradient-based method is applied for determination of the design point. One of the main advantages of this method is non-application of limit-state function gradient for calculation of the design point. In the implemented method, n arbitrary points in n-dimension standard normal space are selected and limit-state function in these points is estimated. Then, these points converge to the design point using a convergent algorithm. Since many random variables are produced in TELM for discretization of seismic excitation, iterative algorithms for determination of design point numerical instability would be encountered. By modification of step length for each iteration and application of a magnification coefficient for each step, an appropriate non-gradient method is proposed for analysis of the problems with many random variables. The efficiency of this method was investigated by solving numerical examples. Moreover, the convergence of this method for finding the design point was presented. It was also indicated that results obtained using this method are in good agreement with results obtained by gradient methods.