Reliability updating with equality information
This addresses a specific bottleneck in structural reliability analysis for engineers, offering a more flexible approach but is incremental as it builds on existing methods.
The paper tackled the problem of updating reliability estimates for engineering systems when information is given as exact equalities, which previously required approximations. The result is a method that transforms equality information into inequality form, enabling the use of any structural reliability method, including simulation-based ones, as demonstrated in three numerical examples.
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.