A Model-Based Bayesian Framework for Pipeline Leakage Enumeration and Location Estimation

Juan Li,Ying Wu,Changgang Lu,Wenjun Zheng

doi:10.1007/s11269-021-02955-8

Abstract

With the development of cities, the water resources loss and environmental pollution caused by pipeline leakage need to be solved urgently. In this paper, a probabilistic method of model-based Bayesian analysis is designed to solve the multi-leakage detection problem of reservoir pipeline valve system. Bayesian inference selects the model best suited to the measured data. This process estimates the number of leaks and then extracts the leak locations from a model that measures data preferences. In this paper, according to the characteristics of water head in pipeline, the Likelihood function of water head for Bayesian evidence calculation is given. It solves the problem that the location ability of recent research methods is limited by leakage location. The number and locations of leakages can be determined simultaneously. Different experimental Settings and scenarios are given to verify the effectiveness of the proposed method. For three leaks that do not contain tight leaks, the RMSE of each leak is 2.3068 m, and in the case of tight leaks, the average RMSE of each leak is 3.5011 m. The results demonstrating that this model-based Bayesian analysis is an accurate tool for leakage enumeration and location estimation.

Highlights

With the rapid development of economy, pipeline transportation is playing an increasingly important role in the national economy, national defense industrial and people’s daily life
This paper presents different experimental setups and scenarios to demonstrate the availability of the proposed method, demonstrating that this model-based Bayesian analysis is an accurate tool for leakage enumeration and location estimation
Natural gas, and water pipelines have become the lifeblood of national economic development (Li et al 2019)

Summary

Introduction

With the rapid development of economy, pipeline transportation is playing an increasingly important role in the national economy, national defense industrial and people’s daily life. Transient-based technology utilizes the hydraulics of transient flow and measured pressure response at specified location(s) to detect leaks in the pipeline (Wang and Ghidaoui, 2018) The reason that such methods are expected to work is that the pressure response signal in fluid conduits measured at a specific location is changed by its interaction with the physical system as it propagates and reflects throughout the system as a whole. Inspired by the above research, the paper presents a transient model-based Bayesian analysis for pipeline leak localization using nested sampling, which is a method that can infer the number of leaks and their locations through probabilistic analysis. By rewriting Eq (2), the head measurement at x = xm (m = 1,..., M) near the downstream for a given angular frequency ωj (j = 1,2,...,J) is assumed to follow the theoretical expression from Eq (2) plus a noise term (Wang et al 2018): Fig. 1 Setup of the considered pipeline system. Assuming there is no leak between xU and xM0 and using the pressure head measurement h(xM0) at xM0 and applying the boundary h(xU) at xU, the discharge q(xU) at xU can be solved via q

Parameter Estimation

Model Selection

Nested Sampling Algorithm Theory

Numerical Setup

Three-Leak Example

Conclusions