Beating the “Unknowable” Bias in Residual Stress Inverse Solutions

Although it is not always recognized, almost all residual stress measurement methods require an inverse solution to analyze the data, and inverse solutions suffer from a bias-variance tradeoff. The bias is mathematically “unknowable” and often at least the same magnitude as the variance. Since the bias is unknown, just the variance is often reported as the total uncertainty but significantly underestimates the true, total uncertainty. Beghini and Grossi recently proposed an ingenious method to manipulate a low-bias high-variance inverse solution to get an accurate uncertainty without noisy results. In this work, their method is checked on the incremental slitting method using some synthetic data so that the bias and variance are known. The result is also compared to an older, well-cited heuristic method for estimating the true uncertainty. Finally, the Beghini-Grossi method is applied to several examples of real data to see if the achievable regularization (smoothing) is sufficient. This talk will close with the first ever presentation of a very broad hypothesis on the typical magnitude of true uncertainty relative to what gets reported. This hypothesis applies broadly to much of experimental mechanics and experimental physics.