Sparsity-Based Nondestructive Evaluations of Downhole Casings Technique Using the Uniform Linear Array

Abstract

Borehole pulsed eddy-current (PEC) systems based on uniform linear multicoil arrays (ULMAs) perform efficient nondestructive evaluations (NDEs) of metal casings. However, the limited physical space of the borehole restricts the degrees of freedom (DoFs) of ULMAs to be less than the number of constraints, which leads to the difficulty of compensating for the differences in signals acquired by different receivers with different transmitting-to-receiving distances (TRDs), and thus limits the effectiveness of the ULMA system. To solve this problem, this paper proposes sparse linear constraint minimum variance (S-LCMV) for NDEs of downhole casings employing ULMAs. By transforming and characterizing the original PEC signal, it was observed that the signal power dramatically decreased with increasing Legendre polynomial stage, confirming that the signal was sparsely distributed over the Gauss–Legendre stages. Using this property, the S-LCMV cost function with reduced constraints was constructed to provide enough DoFs to accurately calculate the weight coefficients, thus improving the detection performance. The effectiveness of the proposed method was verified through field experiments on an 8-element ULMA installed in a borehole PEC system for NDEs of oil-well casings. The results demonstrate that the proposed method could improve the weighting effect by reducing the number of constraints by 70% while ensuring the approximation accuracy, which effectively improved the signal-to-noise ratio of the measured signals and reduced the computational cost by about 87.9%.