Surrogate-enhanced stochastic search algorithms to identify implicitly defined functions for reliability analysis

• Two methods are proposed to locate and trace an implicit limit state function.
• Global tracing places samples along the function in sparsely sampled locations.
• Local tracing propagates tracing points from existing points along the function.
• Adaptive stochastic search algorithms use a continually evolving surrogate model.
• Surrogate models of any form can be fit to these points for reliability.

The paper proposes two adaptive stochastic search algorithms to locate and trace an implicitly defined function with samples that are used to construct a surrogate model for reliability analysis. Both methods begin by propagating a series of surrogate-informed stochastic processes toward the implicit performance function. Having located the function, the first method conducts a “global” tracing of the function while the second traces the function by propagating samples locally. A key feature of both proposed algorithms is that the surrogate model evolves continuously with the sample selection and is used to inform the selection of new samples such that it converges rapidly to an accurate representation of the limit surface. In the present implementation, an artificial neural network surrogate model is employed but the method can, in principle, be applied with any surrogate model form. Performance of the algorithms is illustrated through problems with highly nonlinear limit state functions and high dimensional non-Gaussian random variables.