Chaos control of form iterative algorithm in structural reliability analysis

The HL-RF algorithm of First Order ReliabilityMethod (FORM) in structural reliability analysis is an iterativealgorithm for reliability index with a wide application. However, itsometimes suffers from convergent failure such as periodic oscillation,bifurcation and chaosfor some nonlinear limit state functions. The convergent failure of FORM iscontrolled by using chaos control principle in the present paper. Theinherent relationship of various kinds of methods for global and local chaosfeedback control is clarified. It is shown that the stability transformationmethod and adaptive adjustment method are global chaos feedbackcontrol method, and the adaptive adjustment method can be viewed as aspecial case of the stability transformation method. The parameter adjustmenthybrid method is only a different form of the relaxed Newton method, bothof which are local chaos feedback control methods. Thecorresponding relationship between the formulations of chaos feedbackcontrol and iterative schemes for convergence control in engineeringmechanics is explored. Furthermore, the effectiveness and limitations ofthese measures for convergence control of iterative algorithms arediscussed.An effective, simple and general chaos feedback control methodcombining the stability transformation and relaxed Newton method isproposed, which is applied to control the periodic oscillation, bifurcationand chaos of FORM iterative algorithm for reliability analysis.