Uncertainty quantification for damage mechanics models using the bootstrap method

TL;DR

This paper introduces a bootstrap-based method to quantify uncertainty in damage mechanics models, specifically the L"ammer damage evolution model, using cyclic fatigue experimental data with noisy observations.

Contribution

It develops a novel bootstrap approach combined with a resilient optimization algorithm for parameter identification in damage models.

Findings

Quantifies uncertainty in model parameters, damage evolution solutions, and failure time distributions.

Demonstrates the method on multiple datasets with high-performance computing.

Provides confidence bands for damage evolution predictions.

Abstract

We quantify the uncertainty of the L\"ammer model of damage evolution when fitted to (noisy) observations of damage evolution in cyclic fatigue experiments with and without dwell time. We therefore develop a bootstrap method by sampling over blocks of load cycles in the experiments in order to quantify the uncertainty in the material parameters of the L\"ammer damage evolution equation. We first develop a resilient optimization algorithm for parameter identification based on numerical solutions of damage evolution. The uncertainty is quantified on three levels: distribution of parameters of the L\"ammer model, confidence bands for the solutions of damage evolution, and distributions of failure times. The method is tested on several data sets, committing considerable high-performance computing resources to the task.