Reconstruction of 3D defect profiles from the MFLT signals by using a radial wavelet basis function neural network iterative model

Abstract

To achieve multi-resolution approximation of 3D defect profile reconstruction from magnetic flux leakage (MFL) signals, a radial wavelet basis function neural network iterative model, which contains a forward model and an inverse model based on a parallel radial wavelet basis function neural network (PRWBFNN), is proposed. The forward model in the loop is to determine the MFL signals for a given set of flaw parameters, and the inverse model is used to predict the profile given the measured value of the MFL signals and acts to constrain the solution space. This approach iteratively adjusts the weights of the inverse network to minimise the error between the measured and predicted values of the MFL signals. The reconstruction results of different defects indicate that significant advantages over other neural network-based defect characterisation schemes could be obtained.

Finite-Element Neural Network-Based Solving 3-D Differential Equations in MFL

“…The updated formula of the CG algorithm can be written as follows: (10) where is the learning rate which is a constant in general, and is the search direction at iteration . The initial search direction is negative gradient direction, i.e.,…”

“…In the iteration process, the maximum iteration is 10 , the convergent threshold is 10 , and the learning rate is 2 10 . A defect with 6 mm at width, 6 mm at depth, 6 mm at length is an example.…”

“…The problem would be more acute while 3-D magnetic field is analyzed. Then artificial neural networks such as radial basis function neural networks and wavelet basis function neural networks are considered to solve the forward model [10], [11]. Neural networks are learning machines that can learn any arbitrary functional mapping between input and output.…”