3-D defect profile reconstruction from magnetic flux leakage signatures using wavelet basis function neural networks

The most popular technique for inspecting natural gas pipelines involves the use of magnetic flux leakage (MFL) methods. The measured MFL signal is interpreted to obtain information concerning the structural integrity of the pipe. Defect characterization involves the task of calculating the shape and size of defects based on the information contained in the signal. An accurate estimate of the defect profile allows assessment of the safe operating pressure of the pipe. Artificial neural networks (ANNs) have been employed for characterizing defects in the past. However, conventional neural networks such as radial basis function neural networks are not always suitable for the following reasons: (1) It is difficult to quantify and measure the confidence level associated with the profile estimates. (2) They do not provide adequate control over output accuracy and network complexity trade-off. (3) Optimal center selection schemes typically use an optimization technique such as least-mean-square (LMS) algorithm---a tedious and computationally intensive procedure. These disadvantages can be overcome by employing a wavelet basis function (WBF) neural network. Such networks allow multiple scales of approximation. For the specific application on hand, Gaussian radial basis functions and Mexican hat wavelet frames are used as scaling functions and wavelets respectively. The proposed basis function centers are calculated using a dyadic expansion scheme and the k-means clustering algorithm.; The validity of the proposed approach is demonstrated by predicting defect profiles from simulation data as well as experimental magnetic flux leakage signals. The results demonstrate that wavelet basis function neural networks can successfully map MFL signatures to three-dimensional defect profiles. The center selection scheme requires minimal effort compared to conventional methods. Also, the accuracy of the output can be controlled by varying the number of network resolutions. It is also shown that the use of a priori information such as estimates of the geometric parameters of the defect helps improve characterization results.