Error and uncertainty quantification and sensitivity analysis in mechanics computational models
Multiple sources of errors and uncertainty arise in mechanics computational models and contribute to the error and uncertainty in the final model prediction. This research develops a systematic error quantification methodology for computational models. Some types of errors are deterministic, and some are stochastic. Appropriate procedures are developed to either correct the model prediction for deterministic errors or to account for the stochastic errors through sampling. First, input error, discretization error in FEA, surrogate model error, and output measurement error are considered. Next, uncertainty quantification error which arises due to the use of sampling-based methods is also investigated. Model form error is estimated based on the comparison of corrected model prediction against physical observations, and after accounting for solution approximation errors, uncertainty quantification errors, and experimental errors (input and output). Both local and global sensitivity measures are investigated to estimate and rank the contribution of each source of error to the uncertainty in the final result. Two numerical examples are used to demonstrate the proposed methodology, by considering mechanical stress analysis and fatigue crack growth analysis.