Linear Model and Regularization for Transient Wave-Based Pipeline-Condition Assessment

Condition assessment or defect detection of a pipeline is a difficult inverse problem. This paper proposes a general linear model framework that can approximately describe a wide range of pipeline condition assessment and defect detection problems. More specifically, the system response is governed by a linear function of a pipe property at discrete locations along a pipe, such that the pipe property can be reconstructed via a least-squares fit to the measured response. Real pipe systems in general involve a large number of uncertain pipe characteristics, limited data, and a very high level of noise, such that the inverse problem is ill-posed. The well-known Tikhonov regularization scheme is employed on the linear model to provide a general solution for the ill-posed inverse problem. The optimal regularization parameter, which is crucial and problem-dependent such that no universal approach always generates satisfactory results, are decided via the generalized cross validation (GCV) and L-curve approaches. The proposed general linear model and inverse problem methodologies are illustrated via two application examples: time-domain impulse response function extraction using least-squares deconvolution and leakage detection based on a frequency-domain linearized model. In both examples, numerical and experimental results demonstrate the significance of the regularization parameter and the merits of the GCV and L-curve methods in the pipeline condition assessment problems.