Hidden biases and insufficient uncertainties in residual stress measurements, and clever ways to beat them

“Ignorance is not probabilistic [1].” So how can we put true uncertainty bars on measurements when we don't know all the biases? This talk presents two recent but very different examples tackling this vexing issue for residual stress measurements.

First, incremental slitting and hole drilling require an inverse solution that suffers from a bias-variance tradeoff. Frustratingly, the significant bias is mathematically unknowable. Beghini and Grossi recently proposed an ingenious method: start with a low-bias inverse solution but plagued by high variance, then spatially average it to obtain accurate uncertainties without reduced variance (noise). We show this approach works even better than expected and then discuss the implications of spatially averaging stress measurements.

Second, neutron diffraction measurements often show insufficient uncertainties when based solely on peak-fit statistics. Fortunately, neutron measurements have a little-used physical constraint that can be exploited to test whether uncertainties are adequate. Strain measurements at different orientations must obey the strain transformation equation. In measurements on an additive friction-stir deposition component, we show that peak-fit uncertainties had to be approximately doubled to achieve agreement across strains measured at 36 orientations. We discuss how to apply this justified approach to get true uncertainties in practice using a minimal number of additional orientations.

Because residual stress measurements are used to make life-critical structural integrity assessments, applying large enough uncertainties to our measurements is essential.

1. Yakov Ben-Haim on Info-Gap theory.