Modification of Variance-Based Sensitivity Indices for Stochastic Evaluation of Monitoring Measures

Abstract

In complex engineering models, various uncertain parameters affect the computational results. Most of them can only be estimated or assumed quite generally. In such a context, measurements are interesting to determine the most decisive parameters accurately. While measurements can reduce parameters’ variance, structural monitoring might improve general assumptions on distributions and their characteristics. The decision on variables being measured often relies on experts’ practical experience. This paper introduces a method to stochastically estimate the potential benefits of measurements by modified sensitivity indices. They extend the established variance-based sensitivity indices originally suggested by Sobol’. They do not quantify the importance of a variable but the importance of its variance reduction. The numerical computation is presented and exemplified on a reference structure, a 50-year-old pre-stressed concrete bridge in Germany, where the prediction of the fatigue lifetime of the pre-stressing steel is of concern. Sensitivity evaluation yields six important parameters (e.g., shape of the S–N curve, temperature loads, creep, and shrinkage). However, taking into account individual monitoring measures and suited measurements identified by the modified sensitivity indices, creep and shrinkage, temperature loads, and the residual pre-strain of the tendons turn out to be most efficient. They grant the highest gains of accuracy with respect to the lifetime prediction.

Keywords

• sensitivity analysis
• probability
• probabilistic methods
• Monte Carlo
• monitoring
• lifetime prediction