﻿ 基于序贯概率的音波泄漏监测方法研究

# 基于序贯概率的音波泄漏监测方法研究 Acoustic Wave Leakage Monitoring Method Based on Sequential Probability

Abstract: In this paper, sequential probability ratio test is applied to acoustic pipeline leakage monitoring system. According to the characteristics of the small leakage, firstly, Kalman filter is used to preprocess the deformation monitoring data; secondly, sequential probability ratio test method is used on the basis of acoustic positioning method to improve the accuracy of leakage judgment through judging boundaries. The experimental results show the validity and applicability of this method.

1. 引言

2. 音波检漏系统原理介绍

3. 基于序贯概率的音波泄漏监测方法

$\begin{array}{l}{x}_{t+1}={x}_{t}+{\omega }_{t}\\ {z}_{t}={x}_{t}+{v}_{t}\\ {e}_{t}={z}_{t}-{x}_{t}\end{array}$ (1)

$P\left({e}_{t}\right)=\frac{1}{\sqrt{2\pi {S}_{t}}}\mathrm{exp}\left(-{e}_{t}^{2}{S}_{t}^{-1}/2\right)$ (2)

${P}_{0m}=\frac{1}{{\left(\sigma \sqrt{2\pi }\right)}^{m}}\mathrm{exp}\left(-\frac{1}{2{\sigma }^{2}}\underset{i=1}{\overset{m}{\sum }}{\left({x}_{i}-{\mu }_{0}\right)}^{2}\right)$ (3)

${P}_{1m}=\frac{1}{{\left(\sigma \sqrt{2\pi }\right)}^{m}}\mathrm{exp}\left(-\frac{1}{2{\sigma }^{2}}\underset{i=1}{\overset{m}{\sum }}{\left({x}_{i}-{\mu }_{0}-\Delta \mu \right)}^{2}\right)$ (4)

$\frac{{P}_{1m}}{{P}_{0m}}\le \frac{\beta }{1-\alpha }$ (5)

$\frac{{P}_{1m}}{{P}_{0m}}>\frac{1-\beta }{\alpha }$ (6)

$\frac{\beta }{1-\alpha }<\frac{{P}_{1m}}{{P}_{0m}}<\frac{1-\beta }{\alpha }$ (7)

$\mathrm{ln}\frac{\beta }{1-\alpha }<\lambda \left(n\right)<\mathrm{ln}\frac{1-\beta }{\alpha }$ (8)

$\lambda \left(n+1\right)=\lambda \left(n\right)+\frac{\Delta \mu }{{\sigma }^{2}}\left({x}_{n+1}-{\mu }_{0}-\frac{\Delta \mu }{2}\right)$ (9)

$X=\frac{L+a\Delta t}{2}$ (10)

4. 实验说明及分析

4.1. 实验数据来源说明

Figure 1. Station yard system construction drawing

4.2. 实验说明及分析

Figure 2. Upstream sound wave

Figure 3. Downstream sound wave

Figure 4. Kalman filtering of upstream data

Figure 5. Kalman filtering of downstream data

Figure 6. Residual sequence of upstream data (asymptotic Gaussian distribution)

Figure 7. Residual sequence of downstream data (asymptotic Gaussian distribution)

Figure 8. Sequential probability ratio test parameters of upstream acoustic wave data

Figure 9. Sequential probability ratio test parameters of downstream acoustic wave data

5. 结论

NOTES

*通讯作者。

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