Frequency division method for AE source characterization

Abstract

This paper describes a new algorithm based on a frequency‐division method by which a solution to the inverse source problem of acoustic emission can be obtained. The algorithm is applicable to cases in which the acoustic emission signal can be expressed as a bilinear equation involving weighted Green’s functions or its spatial derivatives, convolved with a common source–time function. Through division of the detected signals in the frequency domain, the common source–time function is eliminated and the ratios of the weighting constants can be recovered by solving a set of linear equations. Using these recovered ratios, the source–time function can be found from the signal at any receiver point. Application of this algorithm is made to process the signals simulating the formation of a microcrack in an elastic plate modeled with a second‐order moment tensor. Dynamic information about the source is recovered by processing the signals at two receiver points. If four receivers are used, the second‐order tensor can be recovered at each frequency of the recorded signals. Additional information about the source can be extracted by diagonalizing and rotating the recovered moment tensor. The effect of noise on the inversion scheme is also considered.