Reliability updating with equality information

TL;DR

This paper introduces a method to convert equality information into inequality form, allowing the use of standard reliability methods for updating system reliability estimates with equality data.

Contribution

It presents a novel transformation technique that enables the application of existing structural reliability methods to equality information, expanding their practical utility.

Findings

Transformation of equality to inequality information facilitates reliability updating.

The method is applicable with any SRM, including simulation-based approaches.

Demonstrated effectiveness through three numerical examples, including fatigue reliability.

Abstract

In many instances, information on engineering systems can be obtained through measurements, monitoring or direct observations of system performances and can be used to update the system reliability estimate. In structural reliability analysis, such information is expressed either by inequalities (e.g. for the observation that no defect is present) or by equalities (e.g. for quantitative measurements of system characteristics). When information Z is of the equality type, the a-priori probability of Z is zero and most structural reliability methods (SRM) are not directly applicable to the computation of the updated reliability. Hitherto, the computation of the reliability of engineering systems conditional on equality information was performed through first- and second order approximations. In this paper, it is shown how equality information can be transformed into inequality information, which enables reliability updating by solving a standard structural system reliability problem. This approach enables the use of any SRM, including those based on simulation, for reliability updating with equality information. It is demonstrated on three numerical examples, including an application to fatigue reliability.