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CN110985897B - A Pipeline Leak Location Method Based on Frequency Domain Transient Wave Model and MUSIC-Like Algorithm - Google Patents

A Pipeline Leak Location Method Based on Frequency Domain Transient Wave Model and MUSIC-Like Algorithm Download PDF

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CN110985897B
CN110985897B CN201911401119.9A CN201911401119A CN110985897B CN 110985897 B CN110985897 B CN 110985897B CN 201911401119 A CN201911401119 A CN 201911401119A CN 110985897 B CN110985897 B CN 110985897B
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李娟�
吴莹
卢长刚
刘颖
叶心
左英泽
吕伟力
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F17STORING OR DISTRIBUTING GASES OR LIQUIDS
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Abstract

本发明公开了一种基于频域瞬态波模型和MUSIC‑Like算法的管道泄漏定位方法,包括:步骤一、设置多个用于检测管道泄漏位置的振动频率,并且确定估计管道实际泄漏位置的向量G(xL);步骤二、基于MUSIC‑Like算法,确定管道泄漏定位优化的目标函数,并且根据所述目标函数计算得到最优权向量;其中,所述目标函数为:

Figure DDA0002347502640000011
式中,w表示最优权向量,wH表示w的共轭转置,GH(xL)表示向量G(xL)的共轭转置,λ表示拉格朗日乘子,c表示任意常数,β表示控制参数,RCM表示相关矩阵;步骤三、建立确定管道泄漏位置的空间功率谱函数P(xL),并且根据所述空间功率谱函数P(xL)的峰值位置确定泄漏位置。

Figure 201911401119

The invention discloses a method for locating pipeline leakage based on a frequency domain transient wave model and MUSIC-Like algorithm. Vector G (x L ); Step 2, based on the MUSIC-Like algorithm, determine the objective function of pipeline leak location optimization, and calculate and obtain the optimal weight vector according to the objective function; Wherein, the objective function is:

Figure DDA0002347502640000011
In the formula, w represents the optimal weight vector, w H represents the conjugate transpose of w, GH (x L ) represents the conjugate transpose of the vector G(x L ), λ represents the Lagrange multiplier, and c represents Arbitrary constant, β represents a control parameter, R CM represents a correlation matrix; Step 3, establish a spatial power spectrum function P(x L ) for determining the leakage position of the pipeline, and determine according to the peak position of the spatial power spectrum function P(x L ) leak location.

Figure 201911401119

Description

一种基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位 方法A Pipeline Leak Location Based on Frequency Domain Transient Wave Model and MUSIC-Like Algorithm method

技术领域technical field

本发明属于管道泄漏检测技术领域,特别涉及一种基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法。The invention belongs to the technical field of pipeline leak detection, in particular to a pipeline leak location method based on a frequency domain transient wave model and a MUSIC-Like algorithm.

背景技术Background technique

管道在工业中发挥了重要作用,为石油,水和天然气的运输提供便捷、经济的运输方式。研究发现,管道是最安全的运输方式,但这并不意味着这种运输就是无风险的,因此确保管道基础设施的完整性和可靠性已成为一项关键要求。在供水系统中,考虑的主要威胁是管道泄漏,发生的泄漏无论大小,它们可以产生相当大的影响,这些影响超过了包括停工和维护费用在内的成本,损害了公民安全,甚至造成环境损害。因此,迫切需要一种切实可行的方法来准确定位泄漏点,以减少水资源的浪费,最大限度地降低泄漏的不利影响。Pipelines play an important role in industry, providing a convenient and economical means of transporting oil, water and natural gas. Research has found that pipelines are the safest mode of transport, but that doesn’t mean it’s risk-free, so ensuring the integrity and reliability of pipeline infrastructure has become a key requirement. In water systems, the main threat considered is pipeline leaks. No matter how large or small they occur, they can have a considerable impact that outweighs costs including downtime and maintenance costs, compromises citizen safety, and even causes environmental damage. . Therefore, there is an urgent need for a practical method to pinpoint the leak point to reduce the waste of water resources and minimize the adverse effects of the leak.

关于泄漏检测和定位的研究已经进行了数十年,并且已经开发了多种可用的商业泄漏检测技术,从简单的物理检查到声学技术,如振动信号,负压波,声波等。过去十年中,基于瞬态分析的检测技术在泄漏检测和定位方面引起了极大的关注。基于瞬态的泄漏检测方法的工作原理如下:在充液管道中引入的液压波,并在特定位置处测量泄漏管道的瞬态压力响应,通过识别采集压力信号特征识别泄漏位置。Research on leak detection and localization has been going on for decades, and a variety of commercially available leak detection techniques have been developed, ranging from simple physical inspections to acoustic techniques such as vibration signals, negative pressure waves, acoustic waves, and more. In the past decade, detection techniques based on transient analysis have attracted great attention in leak detection and localization. The working principle of the transient-based leak detection method is as follows: the hydraulic wave is introduced in the liquid-filled pipeline, and the transient pressure response of the leaking pipeline is measured at a specific location, and the leak location is identified by identifying the characteristics of the collected pressure signal.

具体而言,管道或系统物理结构的任何变化(例如堵塞、泄漏、粗糙度过渡、收缩或膨胀)都会在入射瞬态信号上产生波反射,从而以某种方式改变系统的流量和压力响应。在特定位置处测量的流体管道中的压力响应信号会随着其在整个系统的传播和反射过程中与物理系统的相互作用而发生变化,因此,它包含有关系统属性和状态的有用信息。该原理构成了一系列基于瞬态的缺陷检测方法(TBDM)的基础。TBDMs可以分为四类。第一种方法是基于逆瞬态的方法(ITM),它试图校准测量数据和模拟数据之间的目标函数;第二种方法是基于频率响应的方法(FRM),它利用频率响应的变化来检测泄漏,因为泄漏的存在会使管道的频率响应总是在变化;第三,基于瞬态阻尼的方法(TDM)利用压力衰减特征来识别泄漏。最后,基于瞬态反射的方法(TRM)通过研究压力曲线的某些特殊特征定位泄漏。Specifically, any change in the physical structure of a pipe or system (such as blockages, leaks, roughness transitions, contractions, or expansions) can create wave reflections on the incident transient signal that alter the flow and pressure responses of the system in some way. The pressure response signal in a fluid conduit measured at a specific location changes as it interacts with the physical system during propagation and reflection throughout the system, and as such, it contains useful information about the properties and state of the system. This principle forms the basis of a family of transient-based defect detection methods (TBDM). TBDMs can be divided into four categories. The first method is the inverse transient-based method (ITM), which attempts to calibrate the objective function between the measured and simulated data; the second method is the frequency-response-based method (FRM), which uses changes in the frequency response to Detect leaks, because the presence of leaks will always change the frequency response of the pipeline; third, transient damping-based methods (TDM) use pressure decay characteristics to identify leaks. Finally, transient reflection-based methods (TRM) locate leaks by studying some special features of the pressure curve.

如前文献所示,目前基于流体瞬态的缺陷检测方法的实现方案对于信噪比(SNR)较高或存在单泄漏的简单管道系统是可靠的,但是在现实生活中,管道环境包含许多噪声源,例如湍流,机械设备,动态流量控制,交通或许多其他活动。王洵等人提出了一种基于频谱的方法,可以基于一维搜索来定位泄漏。然而,这种方法并不能识别出两个紧密的泄漏。因此,期望有一种能够检测出在高水平噪声情况下的管道泄漏和定位紧密泄漏情况的基于瞬态的泄漏检测方法。As shown in previous literature, current implementations of fluid transient-based defect detection methods are reliable for simple piping systems with high signal-to-noise ratio (SNR) or a single leak, but in real life, the piping environment contains a lot of noise sources such as turbulence, mechanical equipment, dynamic flow control, traffic or many other activities. Wang Xun et al. proposed a spectrum-based method that can locate leaks based on a one-dimensional search. However, this method does not identify two close leaks. Therefore, a transient-based leak detection method that can detect pipeline leaks and locate tight leaks under high levels of noise is desired.

MUSIC-Like方法是一种信号处理方法,适用于嘈杂的环境和未知参数估计问题。它已成功用于许多阵列信号处理应用中:定位信号源;MUSIC-Like方法也已应用在恶劣水下环境中的声源定位问题;Borijindargoon将MUSIC-Like算法应用于电阻抗断层扫描中的源定位。The MUSIC-Like method is a signal processing method suitable for noisy environments and unknown parameter estimation problems. It has been successfully used in many array signal processing applications: locating signal sources; the MUSIC-Like method has also been applied to the problem of sound source localization in harsh underwater environments; Borijindargoon applies the MUSIC-Like algorithm to sources in electrical impedance tomography position.

发明内容SUMMARY OF THE INVENTION

本发明的目的是提供一种基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,其能够在高噪声环境下提供精确的泄漏定位估计;在多点泄漏情况下,能够识别并定位出距离小于最小探测半波长的两点泄漏。The purpose of the present invention is to provide a pipeline leak location method based on the frequency domain transient wave model and the MUSIC-Like algorithm, which can provide accurate leak location estimation in a high-noise environment; in the case of multi-point leaks, it can identify and Locate two leaks with a distance less than the minimum detectable half wavelength.

本发明提供的技术方案为:The technical scheme provided by the present invention is:

一种基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,包括如下步骤:A method for locating pipeline leakage based on a frequency domain transient wave model and MUSIC-Like algorithm, comprising the following steps:

步骤一、设置多个用于检测管道泄漏位置的振动频率,并且确定估计管道实际泄漏位置的向量G(xL);其中:Step 1. Set a plurality of vibration frequencies for detecting the leakage position of the pipeline, and determine the vector G(x L ) for estimating the actual leakage position of the pipeline; wherein:

G(xL)=(G(ω1,xL,x1),...,G(ωJ,xL,x1),...,G(ω1,xL,xM),...,G(ωJ,xL,xM))TG(x L )=(G(ω 1 ,x L ,x 1 ),...,G(ω J ,x L ,x 1 ),...,G(ω 1 ,x L ,x M ) ,...,G(ω J ,x L ,x M )) T ;

式中,ω1……ωJ分别表示用于检测管道泄漏位置的振动频率,ω1是管道的共振频率,ω2……ωJ均是ω1的倍数,J为设置的用于检测管道泄漏位置的振动频率的数量;xL表示管道泄漏位置坐标;x1……xM分别表示管道上安装的压力传感器的位置坐标,M为压力传感器的数量;G(ωJ,xL,xM)表示泄漏位置的函数;In the formula, ω 1 ... ω J respectively represent the vibration frequency used to detect the leakage position of the pipeline, ω 1 is the resonance frequency of the pipeline, ω 2 ... ω J are multiples of ω 1 , and J is the set for detecting the pipeline. The number of vibration frequencies at the leak location; x L represents the location coordinates of the pipeline leakage; x 1 ...... x M represent the location coordinates of the pressure sensors installed on the pipeline, M is the number of pressure sensors; G(ω J , x L , x M ) represents a function of leak location;

步骤二、基于MUSIC-Like算法,确定管道泄漏定位优化的目标函数,并且根据所述目标函数计算得到最优权向量;Step 2: Determine the objective function of pipeline leak location optimization based on the MUSIC-Like algorithm, and calculate and obtain the optimal weight vector according to the objective function;

其中,所述目标函数为:Wherein, the objective function is:

Figure BDA0002347502620000031
Figure BDA0002347502620000031

式中,w表示最优权向量,wH表示w的共轭转置,GH(xL)表示向量G(xL)的共轭转置,λ表示拉格朗日乘子,c表示任意常数,β表示控制参数,RCM表示相关矩阵;In the formula, w represents the optimal weight vector, w H represents the conjugate transpose of w, GH (x L ) represents the conjugate transpose of the vector G(x L ), λ represents the Lagrange multiplier, and c represents Arbitrary constant, β represents the control parameter, R CM represents the correlation matrix;

步骤三、建立确定管道泄漏位置的空间功率谱函数P(xL),并且根据所述空间功率谱函数P(xL)的峰值位置确定泄漏位置;其中:Step 3: Establish a spatial power spectral function P(x L ) for determining the leakage position of the pipeline, and determine the leakage position according to the peak position of the spatial power spectral function P(x L ); wherein:

Figure BDA0002347502620000032
Figure BDA0002347502620000032

优选的是,所述泄漏位置的函数为:Preferably, the function of the leak location is:

Figure BDA0002347502620000033
Figure BDA0002347502620000033

其中,

Figure BDA0002347502620000034
a表示波速,ω表示管道振动频率,i表示虚数单位;g表示重力加速度,A表示管道横截面积,R表示摩擦阻力,zL表示泄漏处的管道高度,Z表示特性阻抗,h(xU)表示管道的上游端由于流通设置快速变化引起的压头变化,
Figure BDA0002347502620000038
表示管道泄漏位置的稳态压头,q(xU)表示管道的上游端流量。in,
Figure BDA0002347502620000034
a represents the wave speed, ω represents the vibration frequency of the pipeline, i represents the imaginary unit; g represents the acceleration of gravity, A represents the cross-sectional area of the pipeline, R represents the frictional resistance, z L represents the height of the pipeline at the leak, Z represents the characteristic impedance, h(x U ) represents the head change at the upstream end of the pipe due to rapid changes in the flow setting,
Figure BDA0002347502620000038
represents the steady-state head at the leak location of the pipeline, and q(x U ) represents the flow at the upstream end of the pipeline.

优选的是,所述上游端流量为:Preferably, the upstream flow is:

Figure BDA0002347502620000035
Figure BDA0002347502620000035

式中,

Figure BDA0002347502620000036
表示安装在上游端的压力传感器处的压头,
Figure BDA0002347502620000037
表示安装在上游端的压力传感器的位置坐标,xU表示管道上游端的位置坐标。In the formula,
Figure BDA0002347502620000036
represents the head at the pressure sensor installed on the upstream end,
Figure BDA0002347502620000037
Indicates the position coordinates of the pressure sensor installed at the upstream end, and x U denotes the position coordinates of the upstream end of the pipeline.

优选的是,所述相关矩阵为:Preferably, the correlation matrix is:

Figure BDA0002347502620000041
Figure BDA0002347502620000041

其中,Δh=(Δh11,...,ΔhJ1,...,Δh1M,...,ΔhjM)T;Δhn表示对Δh进行N次测量的测量值,n=1,2,…,N;

Figure BDA0002347502620000048
表示Δhn的共轭转置,ΔhjM表示在第j个振动频率ωj下第M个压力传感器处的由于管道泄漏引起的压头差。Among them, Δh=(Δh 11 ,...,Δh J1 ,...,Δh 1M ,..., Δh jM ) T ; ..., N;
Figure BDA0002347502620000048
represents the conjugate transpose of Δh n , and Δh jM represents the head difference due to pipeline leakage at the M-th pressure sensor at the j-th vibration frequency ω j .

优选的是,ΔhjM=h(ωj,xM)-hNLj,xM);Preferably, Δh jM =h(ω j ,x M )-h NLj ,x M );

式中,h(ωj,xM)表示管道泄漏时在第j个振动频率ωj下第M个压力传感器处的压头,hNLj,xM)表示管道不存在泄漏时在第j个振动频率ωj下第M个压力传感器处的压头。In the formula, h(ω j , x M ) represents the pressure head at the M-th pressure sensor at the j-th vibration frequency ω j when the pipeline leaks, and h NLj , x M ) represents when the pipeline does not leak at The pressure head at the Mth pressure sensor at the jth vibration frequency ωj.

优选的是,h(xM)通过如下传递矩阵计算得到:Preferably, h(x M ) is calculated by the following transfer matrix:

Figure BDA0002347502620000042
Figure BDA0002347502620000042

其中,

Figure BDA0002347502620000043
in,
Figure BDA0002347502620000043

Figure BDA0002347502620000044
Figure BDA0002347502620000044

式中,h(xU)表示管道的上游端流量的压头,q(xM)表示第M个压力传感器处的流量,

Figure BDA0002347502620000045
表示管道泄漏位置稳态流量。In the formula, h(x U ) represents the head of the flow at the upstream end of the pipeline, q(x M ) represents the flow at the M-th pressure sensor,
Figure BDA0002347502620000045
Indicates the steady state flow at the leak location of the pipeline.

优选的是,所述管道泄漏位置稳态流量为:Preferably, the steady-state flow rate at the leakage position of the pipeline is:

Figure BDA0002347502620000046
Figure BDA0002347502620000046

式中,zL表示泄漏处管道的高度,sL表示集总泄漏参数,g表示重力加速度,

Figure BDA0002347502620000047
表示管道泄漏位置稳态压头。In the formula, z L is the height of the pipeline at the leak, s L is the lumped leakage parameter, g is the gravitational acceleration,
Figure BDA0002347502620000047
Indicates the steady state pressure head at the leak location of the pipeline.

优选的是,所述集总泄漏参数为:Preferably, the lumped leakage parameter is:

sL=CdALs L =C d A L ;

式中,Cd表示泄漏的流量系数,AL表示泄漏孔的流通面积。In the formula, C d represents the flow coefficient of leakage, and AL represents the flow area of the leakage hole.

优选的是,所述控制参数为:Preferably, the control parameters are:

Figure BDA0002347502620000051
Figure BDA0002347502620000051

其中,L=JM,ξL为相关矩阵RCM最小的特征值,ξL-1为相关矩阵RCM第二最小特征值。Wherein, L=JM, ξ L is the smallest eigenvalue of the correlation matrix R CM , and ξ L-1 is the second smallest eigenvalue of the correlation matrix R CM .

本发明的有益效果是:The beneficial effects of the present invention are:

本发明提供的基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,能够在高噪声环境下提供精确的泄漏定位估计;在多点泄漏情况下,能够识别并定位出距离小于最小探测半波长的两点泄漏。The pipeline leak location method based on the frequency domain transient wave model and the MUSIC-Like algorithm provided by the present invention can provide accurate leak location estimation in a high-noise environment; in the case of multi-point leaks, it can identify and locate the distance less than the minimum distance. Detects two point leaks at half wavelength.

附图说明Description of drawings

图1为本发明所述的管道系统示意图。FIG. 1 is a schematic diagram of the pipeline system according to the present invention.

图2为本发明所述的SNR为0dB的MFP算法定位单泄漏的示意图。FIG. 2 is a schematic diagram of locating a single leak by the MFP algorithm with an SNR of 0 dB according to the present invention.

图3为本发明所述的SNR为0dB的Capon’s BF算法定位单泄漏的示意图。FIG. 3 is a schematic diagram of the Capon's BF algorithm with an SNR of 0 dB for locating a single leak according to the present invention.

图4为本发明所述的SNR为0dB的MUSIC算法定位单泄漏的示意图。FIG. 4 is a schematic diagram of locating a single leak with the MUSIC algorithm with an SNR of 0 dB according to the present invention.

图5为本发明所述的SNR为0dB的MUSIC-Like算法定位单泄漏的示意图。FIG. 5 is a schematic diagram of locating a single leak with the MUSIC-Like algorithm with an SNR of 0 dB according to the present invention.

图6为本发明所述的SNR为-40dB的MFP算法定位单泄漏的示意图。FIG. 6 is a schematic diagram of locating a single leak by the MFP algorithm with SNR of -40dB according to the present invention.

图7为本发明所述的SNR为-40dB的Capon’s BF算法定位单泄漏的示意图。Fig. 7 is a schematic diagram of the Capon's BF algorithm with an SNR of -40dB for locating a single leak according to the present invention.

图8为本发明所述的SNR为-40dB的MUSIC算法定位单泄漏的示意图。FIG. 8 is a schematic diagram of locating a single leak with the MUSIC algorithm with an SNR of -40dB according to the present invention.

图9为本发明所述的SNR为-40dB的MUSIC-Like算法定位单泄漏的示意图FIG. 9 is a schematic diagram of the MUSIC-Like algorithm with an SNR of -40dB locating a single leak according to the present invention

图10为本发明所述的泄漏数量错误的MUSIC算法定位单泄漏的示意图。FIG. 10 is a schematic diagram of locating a single leak according to the MUSIC algorithm with the wrong number of leaks according to the present invention.

图11为本发明所述的MUSIC-Like算法定位单泄漏的示意图。FIG. 11 is a schematic diagram of the MUSIC-Like algorithm for locating a single leak according to the present invention.

图12为本发明所述的泄漏位置在600m和1200m的MFP算法定位双泄漏的示意图。FIG. 12 is a schematic diagram of the MFP algorithm for locating double leaks according to the present invention with leak positions at 600m and 1200m.

图13为本发明所述的泄漏位置在600m和1200m的Capon’s BF算法定位双泄漏的示意图。Fig. 13 is a schematic diagram of locating double leaks by Capon's BF algorithm with leak positions at 600m and 1200m according to the present invention.

图14为本发明所述的泄漏位置在600m和1200m的MUSIC算法定位单双泄漏的示意图。FIG. 14 is a schematic diagram of the MUSIC algorithm for locating single and double leaks according to the present invention with leak positions at 600m and 1200m.

图15为本发明所述的泄漏位置在600m和1200m的MUSIC-Like算法定位双泄漏的示意图。FIG. 15 is a schematic diagram of the MUSIC-Like algorithm for locating double leaks according to the present invention with leak positions at 600m and 1200m.

图16为本发明所述的泄漏位置在300m和1200m的MFP算法定位双泄漏的示意图。FIG. 16 is a schematic diagram of the MFP algorithm for locating double leaks according to the present invention with leak positions at 300m and 1200m.

图17为本发明所述的泄漏位置在300m和1200m的Capon’s BF算法定位双泄漏的示意图。Fig. 17 is a schematic diagram of locating double leaks by Capon's BF algorithm with leak positions at 300m and 1200m according to the present invention.

图18为本发明所述的泄漏位置在300m和1200m的MUSIC算法定位单双泄漏的示意图。FIG. 18 is a schematic diagram of the MUSIC algorithm for locating single and double leaks according to the present invention with leak positions at 300m and 1200m.

图19为本发明所述的泄漏位置在300m和1200m的MUSIC-Like算法定位双泄漏的示意图。FIG. 19 is a schematic diagram of the MUSIC-Like algorithm for locating double leaks according to the present invention with leak positions at 300m and 1200m.

图20为本发明所述的SNR为-10dB的MFP算法定位近泄漏的示意图。FIG. 20 is a schematic diagram of the MFP algorithm with SNR of -10dB according to the present invention for locating near leakage.

图21为本发明所述的SNR为-10dB的Capon’s BF算法定位近泄漏的示意图。Fig. 21 is a schematic diagram of the Capon's BF algorithm with SNR of -10dB according to the present invention for locating near leaks.

图22为本发明所述的SNR为-10dB的MUSIC算法定位近泄漏的示意图。FIG. 22 is a schematic diagram of the MUSIC algorithm with an SNR of -10dB according to the present invention for locating near leaks.

图23为本发明所述的SNR为-10dB的MUSIC-Like算法定位近泄漏的示意图。FIG. 23 is a schematic diagram of the MUSIC-Like algorithm with an SNR of -10dB according to the present invention for locating a near leak.

图24为本发明所述的SNR为0dB的MFP算法定位近泄漏的示意图。FIG. 24 is a schematic diagram of the MFP algorithm with an SNR of 0 dB according to the present invention for locating near leakage.

图25为本发明所述的SNR为0dB的Capon’s BF算法定位近泄漏的示意图。Fig. 25 is a schematic diagram of the Capon's BF algorithm with an SNR of 0 dB according to the present invention for locating near leaks.

图26为本发明所述的SNR为0dB的MUSIC算法定位近泄漏的示意图。FIG. 26 is a schematic diagram of the MUSIC algorithm with an SNR of 0 dB according to the present invention for locating near leakage.

图27为本发明所述的SNR为0dB的MUSIC-Like算法定位近泄漏的示意图。FIG. 27 is a schematic diagram of the MUSIC-Like algorithm with an SNR of 0 dB according to the present invention for locating near leaks.

图28为本发明所述的SNR为-20dB的MFP算法定位近泄漏的示意图。FIG. 28 is a schematic diagram of the MFP algorithm with SNR of -20dB according to the present invention for locating near leakage.

图29为本发明所述的SNR为-20dB的Capon’s BF算法定位近泄漏的示意图。Fig. 29 is a schematic diagram of the Capon's BF algorithm with SNR of -20dB according to the present invention for locating near leaks.

图30为本发明所述的SNR为-20dB的MUSIC算法定位近泄漏的示意图。FIG. 30 is a schematic diagram of the MUSIC algorithm with SNR of -20dB according to the present invention locating near leakage.

图31为本发明所述的SNR为-20dB的MUSIC-Like算法定位近泄漏的示意图。FIG. 31 is a schematic diagram of the MUSIC-Like algorithm with SNR of -20dB according to the present invention for locating near leaks.

具体实施方式Detailed ways

下面结合附图对本发明做进一步的详细说明,以令本领域技术人员参照说明书文字能够据以实施。The present invention will be further described in detail below with reference to the accompanying drawings, so that those skilled in the art can implement it with reference to the description.

一、管道的瞬态波传播模型描述1. Description of the transient wave propagation model of the pipeline

对于管道的瞬态波传播模型说明如下,如图1所示,为该模型所考虑的管道系统配置。一条水平单管道由两个水库限定,两个水库的坐标分别为x=xU=0(上游端)和x=xD=l(下游端)。将压力传感器位于阀门上游处,其坐标由x=xM表示。令xL(xL<xM)为泄漏的位置,

Figure BDA0002347502620000071
Figure BDA0002347502620000072
分别为泄漏处稳态流量和压头。泄漏稳态流量与集总泄漏参数有关:
Figure BDA0002347502620000073
其中,g是重力加速度,zL表示泄漏处管道的高度。集总泄漏参数sL=CdAL代表泄漏大小,其中,Cd是泄漏的流量系数,AL是泄漏孔的流通面积。The transient wave propagation model for the pipeline is described below, as shown in Figure 1, for the pipeline system configuration considered for this model. A single horizontal pipeline is defined by two reservoirs whose coordinates are x= xU =0 (upstream end) and x= xD =l (downstream end). The pressure sensor is located upstream of the valve, and its coordinates are denoted by x= xM . Let x L (x L <x M ) be the location of the leak,
Figure BDA0002347502620000071
and
Figure BDA0002347502620000072
are the steady-state flow and head at the leak, respectively. The leakage steady state flow is related to the lumped leakage parameter:
Figure BDA0002347502620000073
where g is the acceleration due to gravity and z L is the height of the pipe at the leak. The lumped leakage parameter s L =C d AL represents the size of the leakage, where C d is the flow coefficient of the leakage, and AL is the flow area of the leakage hole.

在时域中,管道状态满足动量方程和连续性方程:In the time domain, the pipeline states satisfy the momentum and continuity equations:

Figure BDA0002347502620000074
Figure BDA0002347502620000074

Figure BDA0002347502620000075
Figure BDA0002347502620000075

式中,q和h分别表示由于流通设置的快速变化(如阀门操作)而引起的流量和压头的波动,a为波速,g为重力加速度,A为管道横截面积,R为摩擦阻力项,x∈[xU,xL)∪(xL,xD]为距离上游节点的距离,t为时间变量。In the formula, q and h respectively represent the fluctuation of flow and pressure head caused by the rapid change of the flow setting (such as valve operation), a is the wave speed, g is the acceleration of gravity, A is the cross-sectional area of the pipe, and R is the friction resistance term , x∈[x U ,x L )∪(x L ,x D ] is the distance from the upstream node, and t is the time variable.

对等式(1)和(2)进行关于t的傅立叶变换,在频域中给出q和hTaking the Fourier transform of equations (1) and (2) with respect to t gives q and h in the frequency domain

Figure BDA0002347502620000076
Figure BDA0002347502620000076

Figure BDA0002347502620000077
Figure BDA0002347502620000077

其中,ω是振动频率(角频率),利用在x=xU处的边界条件和在泄漏处满足的条件解方程组(3)和(4),则xM处的状态量可通过传递矩阵法计算出:where ω is the vibration frequency (angular frequency), and the equations (3) and (4) are solved using the boundary conditions at x=x U and the conditions satisfied at the leakage, then the state quantity at x M can be obtained through the transfer matrix method calculates:

Figure BDA0002347502620000081
Figure BDA0002347502620000081

在等式(5)中,In equation (5),

Figure BDA0002347502620000082
Figure BDA0002347502620000082

是场矩阵,上角标NL表示没有泄漏;is the field matrix, and the superscript NL indicates that there is no leakage;

Figure BDA0002347502620000083
Figure BDA0002347502620000083

是传播函数;is the propagation function;

Z=μa2/(iωgA) (8)Z=μa 2 /(iωgA) (8)

是特性阻抗。is the characteristic impedance.

等式(5)右侧的传递矩阵可以进一步简化为一个线性形式:The transfer matrix on the right-hand side of equation (5) can be further simplified to a linear form:

Figure BDA0002347502620000084
Figure BDA0002347502620000084

其中,in,

Figure BDA0002347502620000085
Figure BDA0002347502620000085

为与泄漏位置xL有关但与泄漏大小sL无关的矩阵。is a matrix related to the leak location x L but independent of the leak size s L.

假设给定振动频率ωj(j=1,2,…,J),传感器x=xM处的水头测量值遵循公式(9)中的理论表达式再加上噪声项:Assuming a given vibration frequency ω j (j = 1, 2,..., J), the head measurement at sensor x = x M follows the theoretical expression in equation (9) plus a noise term:

h(ωj,xM)=hNLj,xM)+sLG(ωj,xL,xM)+nj (11)h(ω j ,x M )=h NLj ,x M )+s L G(ω j ,x L ,x M )+n j (11)

其中,in,

hNLj,xM)=-Zsinh(μxM)q(xU)+cosh(μxM)h(xU) (12)h NLj ,x M )=-Zsinh(μx M )q(x U )+cosh(μx M )h(x U ) (12)

Figure BDA0002347502620000091
Figure BDA0002347502620000091

nj服从均值为0和方差为σ2的加性独立高斯随机噪声。n j obeys additive independent Gaussian random noise with mean 0 and variance σ 2 .

在本发明的实验中,上游节点h(xU))和q(xU)的边界条件是已知的。上游端直接与水库相连,因此有h(xU)=0,q(xU)可以通过在上游端附近放置一个压力传感器获得,假设xU和xM 0之间不存在泄漏,则有,In the experiments of the present invention, the boundary conditions of the upstream nodes h(x U )) and q(x U ) are known. The upstream end is directly connected to the reservoir, so h(x U )=0, q(x U ) can be obtained by placing a pressure sensor near the upstream end, assuming that there is no leakage between x U and x M 0 , then there are,

Figure BDA0002347502620000092
Figure BDA0002347502620000092

Have

Figure BDA0002347502620000093
Figure BDA0002347502620000093

这项工作的目的是利用J个频率的压力差来估计xL(泄漏位置)。The purpose of this work is to use the pressure difference at J frequencies to estimate x L (leak location).

令Δhj=h(ωj,xM)-hNLj,xM)表示由于泄漏引起的压头差,则相应的压头差遵循如下线性模型,Let Δh j =h(ω j ,x M )-h NLj ,x M ) denote the head difference due to leakage, then the corresponding head difference follows the following linear model,

Δh=sLG(xL)+n (16)Δh=s L G(x L )+n (16)

在上式中,G(xL)是一个JM维向量,In the above formula, G(x L ) is a JM-dimensional vector,

G(xL)=(G(ω1,xL,x1),...,G(ωJ,xL,x1),...,G(ω1,xL,xM),...,G(ωJ,xL,xM))T(17)G(x L )=(G(ω 1 ,x L ,x 1 ),...,G(ω J ,x L ,x 1 ),...,G(ω 1 ,x L ,x M ) ,...,G(ω J ,x L ,x M )) T (17)

Δh=(Δh11,...,ΔhJ1,...,Δh1M,...,ΔhJM)T (18)Δh=(Δh 11 ,...,Δh J1 ,...,Δh 1M ,...,Δh JM ) T (18)

n=(n11,...,nJ1,...,n1M,...,nJM)T (19)n=(n 11 ,...,n J1 ,...,n 1M ,...,n JM ) T (19)

是随机噪声矢量。其中,数据Δh用于定位泄漏。is a random noise vector. Among them, the data Δh is used to locate the leak.

二、建立MUSIC-Like泄漏检测算法模型2. Establish the MUSIC-Like leak detection algorithm model

使用波束成形框架下的MUSIC-Like方法解决管道泄漏定位问题。所提出的优化问题可以定义为:Using the MUSIC-Like method under the beamforming framework to solve the pipeline leak localization problem. The proposed optimization problem can be defined as:

Figure BDA0002347502620000094
Figure BDA0002347502620000094

Figure BDA0002347502620000095
Figure BDA0002347502620000095

其中,权向量w是优化问题的解,RCM是相关矩阵的估计,G(xL))是需要调整以估计实际泄漏位置的函数,β是控制参数,对约束条件进行了一定的松弛,c是任意常数,它的值对优化过程的结果并不重要。在二次等式中在权矢量上使用L2范数来约束与目标函数相关的期望信号功率

Figure BDA0002347502620000101
以保证有意义的结果。where, the weight vector w is the solution of the optimization problem, R CM is the estimation of the correlation matrix, G(x L )) is the function that needs to be adjusted to estimate the actual leak location, β is the control parameter, which relaxes the constraints to a certain extent, c is an arbitrary constant whose value is not important to the outcome of the optimization process. Use the L2 norm on the weight vector in the quadratic equation to constrain the desired signal power relative to the objective function
Figure BDA0002347502620000101
to ensure meaningful results.

对Δh进行N次测量,用Δhn,n=1,2,…,N表示,相关矩阵可以表示为:N times of measurements are made on Δh, denoted by Δh n , n=1,2,...,N, and the correlation matrix can be expressed as:

Figure BDA0002347502620000102
Figure BDA0002347502620000102

利用拉格朗日乘子法处理,λ表示拉格朗日乘子,目标函数可以构造为:Using the Lagrange multiplier method, λ represents the Lagrange multiplier, and the objective function can be constructed as:

Figure BDA0002347502620000103
Figure BDA0002347502620000103

将式(22)对w进行求导,并令其等于零,解向量w是矩阵束{RCM,(G(xL)GH(xL)+βI)}的广义特征向量。Taking equation (22) with respect to w and making it equal to zero, the solution vector w is the generalized eigenvector of the matrix bundle {R CM ,(G(x L ) GH (x L )+βI)}.

RCMw=λ(G(xL)GH(xL)+βΙ)w (23)R CM w=λ(G(x L ) GH (x L )+βΙ)w (23)

上式等价于The above formula is equivalent to

(G(xL)GH(xL)+βΙ)-1RCMw=λw (24)(G(x L ) GH (x L )+βΙ) -1 R CM w=λw (24)

由上式可得,最优权向量w是矩阵(G(xL)GH(xL)+βI)-1RCM的最小特征值λmin对应的特征向量。根据以下公式给出的空间功率谱的峰值确定泄漏位置,It can be obtained from the above formula that the optimal weight vector w is the eigenvector corresponding to the minimum eigenvalue λ min of the matrix (G(x L ) GH (x L )+βI) -1 R CM . The leak location is determined from the peak of the spatial power spectrum given by,

Figure BDA0002347502620000104
Figure BDA0002347502620000104

β值是相关矩阵特征值的函数,其表达式为:The beta value is a function of the eigenvalues of the correlation matrix, and its expression is:

Figure BDA0002347502620000105
Figure BDA0002347502620000105

其中,L=JM,ξL为相关矩阵RCM最小的特征值,ξL-1为相关矩阵RCM第二最小特征值。Wherein, L=JM, ξ L is the smallest eigenvalue of the correlation matrix R CM , and ξ L-1 is the second smallest eigenvalue of the correlation matrix R CM .

三、通过对比验证实验对本发明的有效性进行进一步说明3. The effectiveness of the present invention will be further explained by comparison and verification experiments

在这一部分中,提供了大量的仿真结果来验证所提算法的有效性。将MUSIC-Like方法与其他泄漏定位方法分别在单点泄露和多点泄漏两种情况进行比较。In this section, extensive simulation results are provided to verify the effectiveness of the proposed algorithm. The MUSIC-Like method is compared with other leak localization methods in single-point leak and multi-point leak, respectively.

a)数值设置a) Numerical setting

采用的管道系统的设置如图1所示。阀门位于单管道的下游端,并且在下游端附近有两个压力传感器。通过快速关闭和打开阀门产生脉冲波,给出边界条件h(xU)=0和q(xD)=1。在正向问题中,利用式(9)中的传递矩阵法完成了瞬态波在频域的传播模拟。根据式(15),使用x=xM 0=50m处的另一个压力传感器来估计q(xU)。主要参数见表1。The setup of the piping system used is shown in Figure 1. The valve is located on the downstream end of the single pipe, and there are two pressure sensors near the downstream end. A pulse wave is generated by rapidly closing and opening the valve, giving boundary conditions h(x U )=0 and q(x D )=1. In the forward problem, the propagation simulation of the transient wave in the frequency domain is completed by using the transfer matrix method in equation (9). According to equation (15), q(x U ) is estimated using another pressure sensor at x=x M 0 =50m. The main parameters are shown in Table 1.

表1管道实验参数Table 1 Pipeline experimental parameters

Figure BDA0002347502620000111
Figure BDA0002347502620000111

此处,均值为零的高斯白噪声被添加到所有压力传感器。噪声等级用信噪比表示(以分贝为单位),定义为:Here, Gaussian white noise with mean zero is added to all pressure sensors. Noise levels are expressed in terms of the signal-to-noise ratio (in decibels), defined as:

Figure BDA0002347502620000112
Figure BDA0002347502620000112

其中,

Figure BDA0002347502620000113
表示平均水头压力差,σ表示高斯白噪声的标准差。in,
Figure BDA0002347502620000113
is the mean head pressure difference, and σ is the standard deviation of Gaussian white noise.

b)单点泄漏b) Single point leak

考虑单个泄漏情况。假定泄漏位置xL=800m,泄漏大小sL=1.0×10-4m2。模拟了瞬态波传播,在xM 1=2,000m和xM 2=1,800m处得到的测量值构成了测量水头。用于泄漏检测的频率ω=κωth,κ=1,2,…,31,其中,ωth=aπ/2l。M=2代表压力传感器的数量,相关矩阵RCM的样本大小为620,即N=620。利用这些参数,应用MUSIC-Like算法,并与MFP、Capon波束形成(BF)和MUSIC三种算法进行比较,在这种情况下,空间功率谱函数在实际泄漏位置达到最大值。当信噪比相对较高时,即SNR=0dB,结果如图2-5所示(图中点划线和星号分别表示泄漏位置和传感器位置)。根据图2所示的泄漏定位结果,不同于MFP方法有着较宽的主瓣、并且在1600m处附近存在很高旁瓣,其他三种方法Capon’s BF、MUSIC和MUSIC-Like成功地实现了窄峰并移除了所有旁瓣。尽管这四种方法都能准确地估计泄漏,但较高旁瓣的存在会影响泄漏位置的准确性,因为较高旁瓣被误认为泄漏,尤其是在泄漏数量未知的情况下。SNR=-40dB的情况,如图6-9所示(图中点划线和星号分别表示泄漏位置和传感器位置),可以观察到,随着噪声水平的提高,各种算法的性能都会下降,这体现在四种算法都返回一个带有旁瓣的结果,但仍然可以大致定位泄漏。MUSIC和MUSIC-Like方法在抑制旁瓣和波动方面优于其他方法。值得注意的是,MUSIC算法需要预先估计泄漏的数量,而MUSIC-Like方法不需要估计泄漏的数量。使用MUSIC算法得到的以上结果的前提是正确估计出了泄漏数量,然而,在低信噪比环境下,很难准确地估计泄漏数量,这样会导致算法性能下降。如图10-11所示(图中点划线和星号分别表示泄漏位置和传感器位置),实际泄漏数量为1,估计泄漏数量为3。MUSIC方法具有比MUSIC-Like更明显的峰。综上所述,MUSIC-Like方法更适合于低SNR的情况,且定位性能与泄漏数量无关。Consider a single leak situation. It is assumed that the leak position x L =800 m and the leak size s L =1.0×10 −4 m 2 . Transient wave propagation was simulated and the measurements taken at x M 1 =2,000m and x M 2 =1,800m constitute the measured head. Frequency for leak detection ω=κω th , κ=1, 2, . . . , 31, where ω th =aπ/2l. M=2 represents the number of pressure sensors, and the sample size of the correlation matrix R CM is 620, ie N=620. Using these parameters, the MUSIC-Like algorithm is applied and compared with three algorithms, MFP, Capon beamforming (BF), and MUSIC, in which the spatial power spectral function reaches a maximum value at the actual leak location. When the signal-to-noise ratio is relatively high, that is, SNR=0dB, the results are shown in Figure 2-5 (the dot-dash line and asterisk in the figure represent the leak location and the sensor location, respectively). According to the leak localization results shown in Fig. 2, unlike the MFP method which has a wide main lobe and a high side lobe around 1600m, the other three methods, Capon's BF, MUSIC and MUSIC-Like, successfully achieve narrow peaks and removed all side lobes. Although all four methods can accurately estimate leakage, the presence of higher sidelobes can affect the accuracy of leak location because higher sidelobes are mistaken for leakage, especially when the amount of leakage is unknown. For the case of SNR=-40dB, as shown in Figure 6-9 (the dot-dash line and asterisk in the figure represent the leak location and the sensor location, respectively), it can be observed that with the increase of the noise level, the performance of various algorithms will decrease , which is reflected in the fact that all four algorithms return a result with sidelobes, but can still roughly locate the leak. The MUSIC and MUSIC-Like methods outperform other methods in suppressing sidelobes and fluctuations. It is worth noting that the MUSIC algorithm needs to estimate the number of leaks in advance, while the MUSIC-Like method does not need to estimate the number of leaks. The premise of the above results obtained by using the MUSIC algorithm is that the number of leaks is correctly estimated. However, in a low signal-to-noise ratio environment, it is difficult to accurately estimate the number of leaks, which will lead to a decrease in the performance of the algorithm. As shown in Figure 10-11 (the dot-dash line and asterisk in the figure represent the leak location and sensor location, respectively), the actual leak number is 1, and the estimated leak number is 3. The MUSIC method has more pronounced peaks than MUSIC-Like. To sum up, the MUSIC-Like method is more suitable for low SNR situations, and the localization performance is independent of the number of leaks.

c)多点泄漏c) Multiple leaks

考虑两点泄漏的情况,即xL 1=600m,xL 2=1,200m,sL 1=1.0×10-4m2,sL 2=1.2×10-4m2。传感器的放置与单个泄漏情况相同。假定所有频率下噪声的信噪比为0dB,样本大小N=10JM=620。结果如图12-15所示(图中点划线和星号分别表示泄漏位置和传感器位置),很明显的看出,每个图中每个实际泄漏附近都有一个局部极大值,也就是说,这四种方法都能准确地定位两个泄漏。然而,所有的算法都有旁瓣,特别是MFP方法有相对较宽的主瓣和一些旁瓣,尤其在1800m左右有一个非常高的旁瓣,高旁瓣的存在会干扰泄漏定位,因为它们可能被错误地识别为泄漏,特别是在泄漏数量未知的情况下。MUSIC-Like算法和其他两种算法在抑制旁瓣方面的能力几乎相同。这三种方法的性能都优于MFP方法。Consider the case of two-point leakage, ie x L 1 =600m, x L 2 =1,200m, s L 1 =1.0×10 −4 m 2 , s L 2 =1.2×10 −4 m 2 . The placement of the sensors is the same as for a single leak. It is assumed that the signal-to-noise ratio of noise at all frequencies is 0 dB, and the sample size is N=10JM=620. The results are shown in Figure 12-15 (the dot-dash line and asterisk in the figure represent the leak location and the sensor location, respectively). It is obvious that there is a local maximum near each actual leak in each figure, and That said, all four methods can pinpoint both leaks. However, all algorithms have side lobes, especially the MFP method has a relatively wide main lobe and some side lobes, especially a very high side lobe around 1800m, the presence of high side lobes can interfere with leak localization because they May be incorrectly identified as a leak, especially if the number of leaks is unknown. The MUSIC-Like algorithm and the other two algorithms are almost identical in their ability to suppress side lobes. All three methods outperform the MFP method.

如图16-19所示(图中点划线和星号分别表示泄漏位置和传感器位置),为其他泄漏位置的功率谱。两个泄漏位于xL 1=300m和xL 2=1,200m处,泄漏大小sL 1=1.0×10-4m2和sL 2=1.2×10-4m2。SNR设置为0dB。可以看出,在每个实际泄漏位置都存在局部最大值,但在其他位置可能有较高的波瓣,这将影响泄漏位置的确定。从以上结果可以得出,两点泄漏的定位精度与泄漏位置有关。另外,MUSIC-Like、MUSIC和Capon’s BF比MFP具有更好的抗干扰能力。As shown in Figure 16-19 (the dot-dash line and asterisk in the figure represent the leakage position and sensor position, respectively), it is the power spectrum of other leakage positions. Two leaks are located at x L 1 =300 m and x L 2 =1,200 m, with leak sizes s L 1 =1.0×10 −4 m 2 and s L 2 =1.2×10 −4 m 2 . SNR is set to 0dB. It can be seen that there are local maxima at each actual leak location, but there may be higher lobes at other locations, which will affect the leak location determination. From the above results, it can be concluded that the location accuracy of the two-point leak is related to the location of the leak. In addition, MUSIC-Like, MUSIC and Capon's BF have better anti-interference ability than MFP.

下面,考虑两个近泄漏的情况,其中xL 1=1,000m和xL 2=1,020m,泄漏大小为sL 1=1.0×10-4m2和sL 2=1.2×10-4m2。用于泄漏定位的其他模拟条件与前面的情况相同。定位结果如图19-22所示,在这种条件下,最短探测波长为λmin=2πa/(31ωth)=258m,两个泄漏之间的距离(20m)小于最短探测波长(129m)的一半。。如图20-23所示(图中点划线和星号分别表示泄漏位置和传感器位置),使用MFP,Capon’s BF和MUSIC这三种方法时,两个泄漏之间只有一个最大值,这意味着无法分别识别这两个泄漏,这使得在不知道实际泄漏数量的情况下,很容易错误地将两个近泄漏的情况判断成仅有一个泄漏的情况。然而,MUSIC-Like方法返回的结果是,尽管两个峰没有完全分开,但可以找到两个局部最大值来确定泄漏位置,从而避免了泄漏的遗漏。SNR=0dB的情况如图24-27所示(图中点划线和星号分别表示泄漏位置和传感器位置),泄漏位置xL 1=1,000m,xL 2=1,040m,SNR=-20dB如图28-31所示(图中点划线和星号分别表示泄漏位置和传感器位置)。MUSIC-Like方法仍然可以确定存在两个近泄漏,而其他三个方法仅具有一个局部最大值,即只能判断出仅有一个泄漏。In the following, two near leak cases are considered, where x L 1 = 1,000 m and x L 2 = 1,020 m, with leak sizes s L 1 = 1.0×10 −4 m 2 and s L 2 = 1.2×10 −4 m 2 . Other simulation conditions for leak localization are the same as in the previous case. The positioning results are shown in Figure 19-22. Under this condition, the shortest detection wavelength is λmin = 2πa/(31ω th ) = 258m, and the distance between the two leaks (20m) is less than that of the shortest detection wavelength (129m). half. . As shown in Figure 20-23 (the dot-dash line and asterisk in the figure indicate the leak location and sensor location, respectively), when using the three methods of MFP, Capon's BF and MUSIC, there is only one maximum value between the two leaks, which means The inability to identify the two leaks separately makes it easy to erroneously judge two near leaks as only one leak without knowing the actual number of leaks. However, the result returned by the MUSIC-Like method is that, although the two peaks are not completely separated, two local maxima can be found to locate the leak, thus avoiding the omission of the leak. The case of SNR=0dB is shown in Fig. 24-27 (the dot-dash line and the asterisk in the figure indicate the leak position and the sensor position, respectively), the leak position x L 1 =1,000m, x L 2 =1,040m, SNR=-20dB As shown in Figure 28-31 (the dot-dash line and asterisk in the figure indicate the leak location and the sensor location, respectively). The MUSIC-Like method can still determine that there are two near leaks, while the other three methods have only one local maximum, that is, only one leak can be judged.

用均方根误差(RMSE)来评价MUSIC-Like方法的定位性能,如表2所示。RMSE计算公式为The root mean square error (RMSE) is used to evaluate the localization performance of the MUSIC-Like method, as shown in Table 2. The formula for calculating RMSE is

Figure BDA0002347502620000131
Figure BDA0002347502620000131

其中,实验次数K=100,xL表示实际泄漏位置,

Figure BDA0002347502620000132
代表第i次实验的估计值。通过比较表2和表3,发现随着信噪比的增加,该算法的定位性能有所提高。如每个表所示,可知估计误差随着样本量N的增加而减少。结果表明,在两个近泄漏的情况下,MUSIC-Like方法的性能优于其他三种方法。Among them, the number of experiments K=100, x L represents the actual leakage position,
Figure BDA0002347502620000132
represents the estimated value of the ith experiment. By comparing Table 2 and Table 3, it is found that the localization performance of the algorithm improves with the increase of the signal-to-noise ratio. As shown in each table, it can be seen that the estimation error decreases as the sample size N increases. The results show that the MUSIC-Like method outperforms the other three methods in the two near leakage cases.

表2参数情况为xL=1,000m and 1,020m,SNR=-10dB的均方误差RMSE(m).The parameters in Table 2 are x L = 1,000m and 1,020m, SNR = -10dB mean square error RMSE (m).

Figure BDA0002347502620000141
Figure BDA0002347502620000141

表3参数情况为xL=1,000m and 1,020m,SNR=-10dB的均方误差RMSE(m).The parameters in Table 3 are x L = 1,000m and 1,020m, SNR = -10dB mean square error RMSE (m).

Figure BDA0002347502620000142
Figure BDA0002347502620000142

本发明利用流体瞬态压力波检测管道泄漏的问题,通过动量方程和连续性方程推导的传递场矩阵法,建立了充水管道的瞬态波模型。基于单泄漏模型,将MUSIC-Like算法应用到管道泄漏检测中,并与MFP,Capon’s BF和MUSIC三种方法进行比较。仿真结果表明,四种方法均能准确定位单个泄漏。当泄漏个数正确估计时,MUSIC方法在嘈杂环境中具有最佳的抑制旁瓣和波动的能力,其次是MUSIC-Like、Capon's BF和MFP。否则,MUSIC-Like会比MUSIC稍好一些,并且MUSIC-Like算法能够避免泄漏数量的估计。同时,将MUSIC-Like应用到两个近泄漏的情况。当压力差的样本数量足够大时,本发明提供的基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法可以识别出两个泄漏,并粗略地确定泄漏位置且定位误差在可接受范围,但其他三种方法只能将此情况确定为只有一个泄漏的情况。因此,本发明中提供的基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法对于泄漏检测和定位具有高精度。The invention utilizes the fluid transient pressure wave to detect the leakage of the pipeline, and establishes the transient wave model of the water-filled pipeline through the transfer field matrix method derived from the momentum equation and the continuity equation. Based on the single leak model, the MUSIC-Like algorithm is applied to pipeline leak detection and compared with three methods: MFP, Capon's BF and MUSIC. Simulation results show that all four methods can accurately locate a single leak. When the number of leaks is correctly estimated, the MUSIC method has the best ability to suppress side lobes and fluctuations in noisy environments, followed by MUSIC-Like, Capon's BF and MFP. Otherwise, MUSIC-Like is slightly better than MUSIC, and the MUSIC-Like algorithm is able to avoid the estimation of the number of leaks. At the same time, MUSIC-Like was applied to two near-leak situations. When the number of samples of pressure difference is large enough, the pipeline leak location method based on the frequency domain transient wave model and the MUSIC-Like algorithm provided by the present invention can identify two leaks, and roughly determine the location of the leak with an acceptable location error range, but the other three methods can only identify this case as one with only one leak. Therefore, the pipeline leak location method based on the frequency domain transient wave model and the MUSIC-Like algorithm provided in the present invention has high precision for leak detection and location.

尽管本发明的实施方案已公开如上,但其并不仅仅限于说明书和实施方式中所列运用,它完全可以被适用于各种适合本发明的领域,对于熟悉本领域的人员而言,可容易地实现另外的修改,因此在不背离权利要求及等同范围所限定的一般概念下,本发明并不限于特定的细节和这里示出与描述的图例。Although the embodiment of the present invention has been disclosed as above, it is not limited to the application listed in the description and the embodiment, and it can be applied to various fields suitable for the present invention. For those skilled in the art, it can be easily Therefore, the invention is not limited to the specific details and illustrations shown and described herein without departing from the general concept defined by the appended claims and the scope of equivalents.

Claims (9)

1.一种基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,其特征在于,包括如下步骤:1. a pipeline leakage localization method based on frequency domain transient wave model and MUSIC-Like algorithm, is characterized in that, comprises the steps: 步骤一、设置多个用于检测管道泄漏位置的振动频率,并且确定估计管道实际泄漏位置的向量G(xL);其中:Step 1. Set a plurality of vibration frequencies for detecting the leakage position of the pipeline, and determine the vector G(x L ) for estimating the actual leakage position of the pipeline; wherein: G(xL)=(G(ω1,xL,x1),...,G(ωJ,xL,x1),...,G(ω1,xL,xM),...,G(ωJ,xL,xM))TG(x L )=(G(ω 1 ,x L ,x 1 ),...,G(ω J ,x L ,x 1 ),...,G(ω 1 ,x L ,x M ) ,...,G(ω J ,x L ,x M )) T ; 式中,ω1……ωJ分别表示用于检测管道泄漏位置的振动频率,J为设置的用于检测管道泄漏位置的振动频率的数量;xL表示管道泄漏位置坐标;x1……xM分别表示管道上安装的压力传感器的位置坐标,M为压力传感器的数量;G(ωJ,xL,xM)表示泄漏位置的函数;In the formula, ω 1 ...... ω J respectively represent the vibration frequencies used to detect the leakage position of the pipeline, J is the number of vibration frequencies set for detecting the leakage position of the pipeline; x L represents the coordinates of the leakage position of the pipeline; x 1 ...... x M respectively represents the position coordinates of the pressure sensors installed on the pipeline, M is the number of pressure sensors; G(ω J , x L , x M ) represents the function of the leakage position; 步骤二、基于MUSIC-Like算法,确定管道泄漏定位优化的目标函数,并且根据所述目标函数计算得到最优权向量;Step 2: Determine the objective function of pipeline leak location optimization based on the MUSIC-Like algorithm, and calculate and obtain the optimal weight vector according to the objective function; 其中,所述目标函数为:Wherein, the objective function is:
Figure FDA0002705921580000011
Figure FDA0002705921580000011
式中,w表示最优权向量,wH表示w的共轭转置,GH(xL)表示向量G(xL)的共轭转置,λ表示拉格朗日乘子,c表示任意常数,β表示控制参数,RCM表示相关矩阵;In the formula, w represents the optimal weight vector, w H represents the conjugate transpose of w, GH (x L ) represents the conjugate transpose of the vector G(x L ), λ represents the Lagrange multiplier, and c represents Arbitrary constant, β represents the control parameter, R CM represents the correlation matrix; 步骤三、建立确定管道泄漏位置的空间功率谱函数P(xL),并且根据所述空间功率谱函数P(xL)的峰值位置确定泄漏位置;其中:Step 3: Establish a spatial power spectral function P(x L ) for determining the leakage position of the pipeline, and determine the leakage position according to the peak position of the spatial power spectral function P(x L ); wherein:
Figure FDA0002705921580000012
Figure FDA0002705921580000012
2.根据权利要求1所述的基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,其特征在于,所述泄漏位置的函数为:2. the pipeline leakage localization method based on frequency domain transient wave model and MUSIC-Like algorithm according to claim 1, is characterized in that, the function of described leakage position is:
Figure FDA0002705921580000013
Figure FDA0002705921580000013
其中,
Figure FDA0002705921580000014
a表示波速,ω表示管道振动频率,i表示虚数单位;g表示重力加速度,A表示管道横截面积,R表示摩擦阻力,zL表示泄漏处的管道高度,Z表示特性阻抗,h(xU)表示管道的上游端由于流通设置快速变化引起的压头变化,
Figure FDA0002705921580000021
表示管道泄漏位置的稳态压头,q(xU)表示管道的上游端流量。
in,
Figure FDA0002705921580000014
a represents the wave speed, ω represents the vibration frequency of the pipeline, i represents the imaginary unit; g represents the acceleration of gravity, A represents the cross-sectional area of the pipeline, R represents the frictional resistance, z L represents the height of the pipeline at the leak, Z represents the characteristic impedance, h(x U ) represents the head change at the upstream end of the pipe due to rapid changes in the flow setting,
Figure FDA0002705921580000021
represents the steady-state head at the leak location of the pipeline, and q(x U ) represents the flow at the upstream end of the pipeline.
3.根据权利要求2所述的基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,其特征在于,所述上游端流量为:3. the pipeline leak location method based on frequency domain transient wave model and MUSIC-Like algorithm according to claim 2, is characterized in that, described upstream flow is:
Figure FDA0002705921580000022
Figure FDA0002705921580000022
式中,
Figure FDA0002705921580000023
表示安装在上游端的压力传感器处的压头,
Figure FDA0002705921580000024
表示安装在上游端的压力传感器的位置坐标,xU表示管道上游端的位置坐标。
In the formula,
Figure FDA0002705921580000023
represents the head at the pressure sensor installed on the upstream end,
Figure FDA0002705921580000024
Indicates the position coordinates of the pressure sensor installed at the upstream end, and x U denotes the position coordinates of the upstream end of the pipeline.
4.根据权利要求2或3所述的基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,其特征在于,所述相关矩阵为:4. the pipeline leak location method based on frequency domain transient wave model and MUSIC-Like algorithm according to claim 2 or 3, is characterized in that, described correlation matrix is:
Figure FDA0002705921580000025
Figure FDA0002705921580000025
其中,Δh=(Δh11,...,ΔhJ1,...,Δh1M,...,ΔhjM)T;Δhn表示对Δh进行N次测量的测量值,n=1,2,…,N;
Figure FDA0002705921580000026
表示Δhn的共轭转置,ΔhjM表示在第j个振动频率ωj下第M个压力传感器处的由于管道泄漏引起的压头差。
Among them, Δh=(Δh 11 ,...,Δh J1 ,...,Δh 1M ,..., Δh jM ) T ; ..., N;
Figure FDA0002705921580000026
represents the conjugate transpose of Δh n , and Δh jM represents the head difference due to pipeline leakage at the M-th pressure sensor at the j-th vibration frequency ω j .
5.根据权利要求4所述的基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,其特征在于,ΔhjM=h(ωj,xM)-hNLj,xM);5. the pipeline leakage localization method based on frequency domain transient wave model and MUSIC-Like algorithm according to claim 4, is characterized in that, Δh jM =h(ω j ,x M )-h NLj ,x M ); 式中,h(ωj,xM)表示管道泄漏时在第j个振动频率ωj下第M个压力传感器处的压头,hNLj,xM)表示管道不存在泄漏时在第j个振动频率ωj下第M个压力传感器处的压头。In the formula, h(ω j , x M ) represents the pressure head at the M-th pressure sensor at the j-th vibration frequency ω j when the pipeline leaks, and h NLj , x M ) represents when the pipeline does not leak at The pressure head at the Mth pressure sensor at the jth vibration frequency ωj. 6.根据权利要求5所述的基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,其特征在于,h(xM)通过如下传递矩阵计算得到:6. the pipeline leak location method based on frequency domain transient wave model and MUSIC-Like algorithm according to claim 5, is characterized in that, h(x M ) is obtained by following transfer matrix calculation:
Figure FDA0002705921580000027
Figure FDA0002705921580000027
其中,
Figure FDA0002705921580000031
in,
Figure FDA0002705921580000031
Figure FDA0002705921580000032
Figure FDA0002705921580000032
式中,h(xU)表示管道的上游端流量的压头,q(xM)表示第M个压力传感器处的流量,
Figure FDA0002705921580000033
表示管道泄漏位置稳态流量。
In the formula, h(x U ) represents the head of the flow at the upstream end of the pipeline, q(x M ) represents the flow at the M-th pressure sensor,
Figure FDA0002705921580000033
Indicates the steady state flow at the leak location of the pipeline.
7.根据权利要求6所述的基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,其特征在于,所述管道泄漏位置稳态流量为:7. the pipeline leakage localization method based on frequency domain transient wave model and MUSIC-Like algorithm according to claim 6, is characterized in that, described pipeline leakage position steady-state flow rate is:
Figure FDA0002705921580000034
Figure FDA0002705921580000034
式中,zL表示泄漏处管道的高度,sL表示集总泄漏参数,g表示重力加速度,
Figure FDA0002705921580000035
表示管道泄漏位置稳态压头。
In the formula, z L is the height of the pipeline at the leak, s L is the lumped leakage parameter, g is the gravitational acceleration,
Figure FDA0002705921580000035
Indicates the steady state pressure head at the leak location of the pipeline.
8.根据权利要求7所述的基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,其特征在于,所述集总泄漏参数为:8. the pipeline leakage localization method based on frequency domain transient wave model and MUSIC-Like algorithm according to claim 7, is characterized in that, described lumped leakage parameter is: sL=CdALs L =C d A L ; 式中,Cd表示泄漏的流量系数,AL表示泄漏孔的流通面积。In the formula, C d represents the flow coefficient of leakage, and AL represents the flow area of the leakage hole. 9.根据权利要求1所述的基于频域瞬态波模型和MUSIC-Like算法的管道泄漏定位方法,其特征在于,所述控制参数为:9. the pipeline leakage localization method based on frequency domain transient wave model and MUSIC-Like algorithm according to claim 1, is characterized in that, described control parameter is:
Figure FDA0002705921580000036
Figure FDA0002705921580000036
其中,L=JM,ξL为相关矩阵RCM最小的特征值,ξL-1为相关矩阵RCM第二最小特征值。Wherein, L=JM, ξ L is the smallest eigenvalue of the correlation matrix R CM , and ξ L-1 is the second smallest eigenvalue of the correlation matrix R CM .
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