A novel multiple linearization method for reliability analysis based on evidence theory

Evidence theory has been applied in structural reliability assessment to address epistemic uncertainties, given its capability to deal with imprecise, incomplete and even contradictory information. An important challenge in structural reliability assessment based on the framework of evidence theory is its expensive computational cost in multidimensional problems. In this work, a modified multiple linearization method is proposed to identify a set of hyperplane approximations to the limit state function. It provides a clear guidance for the hyperplanes by evaluating curvature magnitude of the original limit state at the most probable point along each axis in the rotated standard normal space, and shows good stability and satisfactory accuracy in nonlinear reliability analysis based on evidence theory. The belief measure and plausibility measure of the structure are assessed by the hyperplanes through the intersection or union of the failure domains. In the meantime, the classification and division of focal elements in failure set, safety set and uncertain set will be made through the segment edge of the failure and safety domain to reduce the computation burden. Finally, four mathematical examples and engineering cases are explored to illustrate the methodology and show its benefits.