Variability estimation in a non-linear crack growth simulation model with controlled parameters using Designed Experiments testing

TL;DR

This paper compares the effectiveness of Propagation of Errors, Monte Carlo, and Tolerance Design methods in estimating variability in complex nonlinear crack growth simulations, highlighting the efficiency of the TD method.

Contribution

It demonstrates that the Tolerance Design method provides accurate variability estimates with fewer trials compared to traditional Monte Carlo and Propagation of Errors methods.

Findings

PE method is suboptimal for input coefficient of variance above 5%

TD method performs well with moderately sized designed experiments

Results help in designing physical tests by estimating variability efficiently

Abstract

Variability in multiple independent input parameters makes it difficult to estimate the resultant variability in the system's overall response. The Propagation of Errors and Monte-Carlo techniques are two major methods to predict the variability of a system. However, in the former method, the formalism can lead to an inaccurate estimate for systems that have parameters varying over a wide range. For the latter, the results give a direct estimate of the variance of the response, but for complex systems with many parameters, the number of trials necessary to yield an accurate estimate can be very large to the point the technique becomes impractical. In this study, the effectiveness of the Tolerance Design method to estimate variability in complex systems is studied. We use a linear elastic 3 point bending beam model and a nonlinear extended finite elements crack growth model to test and compare the PE and MC methods with the TD method. Results from an MC estimate, using 10,000 trials, serve as a reference to validate the result in both cases. We find that the PE method works suboptimal for a coefficient of variance above 5% in the input variables. In addition, we find that the TD method works very well with moderately sized trials of designed experiment for both models. Our results demonstrate how the variability estimation methods perform in the deterministic domain of numerical simulations and can assist in designing physical tests by providing a guideline performance measure.