Development a Mathematical Model of Acoustic Signals for the Implementation of a Universal Leak Detection Method

Abstract

A universal mathematical model of a noise signal in pipeline systems from the point of its origin to the observation point was presented. Due to the indicator function introduced into it, the model makes it possible to use different types of components and perform appropriate actions depending on the task, and the indicator function in some cases will be zero. The developed model advantage consists in that it is universal for the leak detection methods which use two signal receivers regardless of their physical nature. This model was implemented in the study on an example of a method of acoustic leakage detection, which uses the inter-correlation function. A block diagram of an acoustic system for detecting leakage location, its main blocks, and their parameters were presented. To test the working capacity of the mathematical model, a computer measuring experiment was conducted in the MATLAB software system. The algorithm of the computer experiment with indicator function was presented and the results of detecting leakage location according to the corresponding sample were given. A universal formula for calculating coordinates of the fluid leakage location both along the axis of the pipeline and the pipeline circumference was presented. This formula features accounting of the distance from the transducer to the possible leakage location and the sample number. This formula serves a universal model of the noise signal and confirms the results of the computer experiment. As a result of the experiment, dependences of the values of the fluid leakage location on the sample number and the distance to the receiver of the acoustic noise signal were obtained. To test the model adequacy, a diagram of influential factors was constructed in a form of Ishikawa diagram. The diagram shows the cause-and-effect relationships that affect the computer experiment built on the proposed mathematical model of acoustic signals to implement the universal method of leak detection. Adequacy of the proposed universal model was verified and confirmed by statistical methods. The results obtained can be used in technical diagnostics of pipelines and for reducing costs of repair and restoration of technological systems by identifying breakdown sites.