Uncertainty quantification of quadratically nonlinear local damage size quantification using nonlinear ultrasonics

Abstract

Backscattered and forward scattered harmonic waves from local damage modeled as quadratically nonlinear material in a 1D bar are used to solve a deterministic inverse problem to find the local damage size by Ghodake (2020). Due to highly nonlinear (|sin(x)/x|) nature of the proposed forward problem, the constrained nonlinear deterministic optimization problem was solved using non-gradient-based algorithms. The forward model is a function of input frequencies, linear wave velocity, and local damage size. In practice, slight uncertainty of these parameters gives a completely different solution. To address this problem, uncertainty quantification of the modified forward problem is carried out along with solving the inverse problem using reliability-based design optimization (RBDO) and Bayesian Inverse (BI) approaches. In RBDO studies, Quantile Monte Carlo (QMC) approach gives more reliable and accurate results in comparison with approaches such as reliability index approach (RIA), performance measure approach (PMA), sequential optimization and reliability assessment (SORA), and inverse first-order reliability method (FORM) integrated with optimization methods such as interior-point (IP) and sequential programming (SQP). Multiple models are solved using the BI approach. Support vector machines regression (SVR), polynomial chaos expansions (PCE), and Kriging surrogate models are used along with RBDO and BI to reduce computational time.