The inverse of material properties of functionally graded pipes using the dispersion of guided waves and an artificial neural network

Using guided circumferential wave dispersion characteristics, an inverse method based on artificial neural network (ANN) is presented to determine the material properties of functionally graded material (FGM) pipes. The group velocities of lowest modes at six lower frequencies are used as the inputs of the ANN model. The distribution function of the volume fraction of the FGM pipe is fitted to a polynomial, then the outputs of the ANN are the coefficients of the fitting polynomial. The Legendre polynomial method is employed as the forward solver to calculate the dispersion curves for the FGM pipe. Levenberg–Marquardt algorithm is used as numerical optimization to speed up the training process of the ANN model.