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A spatial-processing algorithm of acoustic-emission signals for leak detection in one-way access pipelines is considered. Basic formulas are determined, and results from numerical calculations are reported.

A spatial-processing algorithm of acoustic-emission signals for leak detection in one-way access pipelines is considered. Basic formulas are determined, and results from numerical calculations are reported.One of the methods for checking impermeability of linear pipeline portions is the acoustic-emission technique based on detection of leakage-induced acoustic radiation by sensors placed on a pipeline surface [1]. Investigations carried out in [2] have shown that analysis and processing of acoustic-emission signals are expedient when being performed in the frequency range 10-50 kHz, since equipment misoperation is prevented and the detection of all leaks with a consumption of >8 liters per hour is ensured. According to [3,4], in the indicated range, the pipeline appears to be a multimode heterogeneous layered waveguide formed by the transported liquid, the pipeline wall, and the ground. The number of modes excited in the pipe, their group velocities, and their energy mode distribution depend on many factors which cannot be evaluated and taken into account in a general case. Due to this, the problem of exact leakage localization in the given frequency range using existing methods becomes appreciably more difficult. At the same time, the multimode nature of signal propagation allows actualization of one-way access localization algorithms, which can be useful for leak detection in difficultly accessible pipeline portions lying at great depths. The principle of these algorithms is based on determination of the delay time of signals transferred by different modes. In this study, we propose to use a horizontal antenna array, which performs spatial processing of acoustic-emission signals by means of cospectral-density phase analysis. The main computational relationships are determined, and the results of numerical calculations are presented.Let us consider a receiving antenna consisting of four sensors (Fig. 1). Let the distance between sensors 1 and 3 equal b , and the distance between sensors 1 and 2 and sensors 3 and 4 equal d . Let us assume that sensors have uniform gain-frequency characteristics equal to unity in a wide frequency range. Let the seal failure at point z lead to the appearance of accidental stationary ergodic signal x ( t ), which is deformed by noise during its propagation through the pipeline. Let us assume that signal x ( t ) is frequency bounded by white noise with a maximum in the range 10-50 kHz (the maximum of the leak acoustic-emission spectrum [2]). The acoustic signal propagation path is nonuniform for the multimode waveguide and can be represented as a set of several uniform acoustical paths with individual unit-impulse responses. Since the absorption coefficient increases by increasing the order of a normal wave, we assume that, far from the leak, an acoustic field is formed by a finite number of normal waves with close magnitudes of phase velocities. Thus, a signal recorded by the l th antenna sensor can be expressed in the form of a convolution sum Here, indices i and l indicate the pip...