Inverse analysis of low frequency electromagnetic signals for sizing local wall thinning using a multivariate probabilistic model

Local wall thinning is a common form of degradation in carbon steel pipes, and a low frequency electromagnetic method is proposed in this study to inspect such wall thinning defects. In addition, an appropriate method needs to be developed to solve the inverse problem, which is to estimate defect size based on the inspection signal. Resolving the inverse problem of nondestructive inspection usually involves a machine learning algorithm and training data should be large and realistic to enable the algorithm to produce an accurate and reliable estimate of defect size. However, the acquisition of such training data is sometimes time-consuming and costly. Therefore, this study aims to estimate the size of local wall thinning based on the inspection signal by developing a new method to generate training data for a machine learning algorithm. With the aid of signals obtained from numerical simulation, a multivariate probabilistic model is proposed to infer a joint distribution over features extracted from measured multi-frequency signals from the low frequency electromagnetic inspection method. The joint distribution is subsequently leveraged to quickly generate sufficient training data for a Gaussian process regression algorithm that uses the signal features as the input to estimate defect size. The multivariate probabilistic model is proved able to reasonably characterize the joint distribution over the features. Moreover, the trained algorithm has been validated by experimental data and it is confirmed it can be used to estimate the residual thickness of a pipe wall with errors within tolerance and high reliability even when the lift-off is changed.