Leakage location on water-cooling wall in power plant boiler based on acoustic array and a spherical interpolation algorithm

Accepted Manuscript Leakage location on water-cooling wall in power plant boiler based on acoustic array and a spherical interpolation algorithm Shiping Zhang, Guoqing Shen, Liansuo An PII: DOI: Reference:

S1359-4311(18)35165-2 https://doi.org/10.1016/j.applthermaleng.2019.02.073 ATE 13367

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

21 August 2018 23 January 2019 15 February 2019

Please cite this article as: S. Zhang, G. Shen, L. An, Leakage location on water-cooling wall in power plant boiler based on acoustic array and a spherical interpolation algorithm, Applied Thermal Engineering (2019), doi: https:// doi.org/10.1016/j.applthermaleng.2019.02.073

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Leakage location on water-cooling wall in power plant boiler based on acoustic array and a spherical interpolation algorithm Shiping Zhang*, Guoqing Shen, Liansuo An School of Energy, Power and Mechanical Engineering, North China Electric Power University, No.2 Beinong Road, Huilongguan, Changping, 102206 Beijing, China *Corresponding author. Tel.: +86 010 61772961; *Fax: +86 010 61772961. *E-mail address: [email protected]

ABSTRACT. In a coal-fired power plant, locating the leak area during boiler hot-state operation has practical engineering value, has apart from its significance in proper shutdown procedures, repair-time reduction, and reduction of financial losses. In this study, we adopted a three-dimensional space location algorithm based on acoustic array to determine the location of water-cooling wall tube leaks in real time. We used a spherical interpolation algorithm to solve the location problem and adopted a time delay estimation based on SWITCH function to obtain the time of arrival. An acoustic location test platform was constructed for studying location accuracy in different location condition. Finally, a field study was performed to verify the spherical interpolation algorithm’s feasibility and practicability in a boiler. Results show that the proposed three-dimensional, eight-element array can locate the leak area during boiler hot-state operation. Keywords: coal-fired power plant; three-dimensional space location algorithm; acoustic array; time delay of arrival; spherical interpolation

1.

Introduction A boiler is one of the most important parts of a thermal equipment in a thermal power plant, and is responsible for

transforming thermal energy into mechanical energy [1]. Because of the high combustion temperature and harsh combustion environment in a boiler, the bursting of a pressure tube has become the most common and the most dangerous accident that

can occur in a boiler, which can seriously affect the safety and economical operation of a thermal power plant [2-4]. Predicting the bursting of a boiler at an early stage, by, for example, diagnosing and locating small leaks in the pipes before they produce catastrophic bursting, can assist in scheduling the shutdown time of a power plant in advance, which reduces maintenance and labour costs [5,6]. Identifying leakage can prevent tube explosions, and one of the many technologies used for leakage identification is acoustic detection technology [7, 8]. Current acoustic detection technology works by deploying microphones in different locations in the boiler and using real-time monitoring to determine whether the noise signal in the boiler contains the acoustic signal generated from a pipeline leak [9, 10]. If the signal is deemed to contain leakage signal, an alarm is generated at the monitoring point closest to the leakage. The leak is located over a broad region in boiler [11, 12]. However, identifying the exact location of a tiny leakage hole within such a space takes a substantial amount of labour and time. In other words, identifying the precise location of the leakage source is the biggest technical challenge for implementing acoustic detection technology in the pressure tubes of power plant boilers. In other words, identifying the precise location of the leakage source is the biggest technical challenge in implementing the acoustic detection technology in the pressure tubes of power-plant boilers. The reverberation within a closed system of the boiler and a strong background noise can both severely affect the detection of the leakage signal, which results in false alarms, failed alarms, and inaccurate location of the leakage source. In this article, we used an acoustic array and a spherical interpolation algorithm based on the delay of arrival (TDOA) to determine the location of water-cooling wall tube leaks in real time. Location algorithm and time delay estimation are the keys to solving this problem. Around the above problems, an acoustic location test platform was constructed and a field study was performed to verify its feasibility and practicability in a boiler. 2.

Method

2.1 Three-Dimensional Space Location Algorithm 2.1.1 Time Difference of Arrival (TDOA) Location Method Using a three-dimensional signal array makes it possible to determine the position of the leak wherever it is in the

entire space [13]. Figure 1 shows the spatial geometry of the four-element topology used for locating the leak. In this figure, point S represents the leakage signal source and M 1, M2, M3, and M4 represent the four microphones. Assuming that the coordinate of the leakage signal source S is (x,y,z) and denoting the arrival time difference from the leakage source S to microphones Mi and Mj as τij, and the difference in the distance between the microphones M i and Mj as dij, respectively, the location of the leakage source in the boiler pressure tube should then satisfy the following hyperbolic equation: (1) Using a spherical interpolation algorithm [14,15], a hyperbolic equation system can be established based on the time delay associated with multiple acoustic sensors. This equation system can be solved under the minimum mean-square-error criterion. 2.1.2 Spherical Interpolation Algorithm A microphone, whose coordinate is defined as the reference point coordinate, is defined reference microphone. Now, assume that the microphone array consists of N+1 microphones located at microphone is located at located at

,

is the origin of the coordinate system, and the leakage signal source is

. Now, consider Ri and Rs to be the distance from the microphone and leakage signal noise to the

origin, respectively, as given by the following: (2) (3) The distance from the leakage source to the ith microphone is given by the following: (4) The difference in the distance between the ith and jth microphones is expressed as follows: (5) Setting

, i=0,1,2,…,N, the reference

, we obtain the following: (6)

Substituting Eq. (6) into Eq. (4) and taking the square on both sides yields the following:

(7) Expanding and re-organizing the equation yields the following: (8) In the actual measurement performed in the power-plant boiler,

is estimated by the time delay, which may deviate from the

actual value. Therefore, the right-hand side of the above equation does not equal zero: ε

(9)

There are a total of N time delays for microphones 1 to N compared with the reference microphone 0. Therefore, N equations can be obtained based on Eq. (9), which can be written in the matrix form as follows:

ε

(10)

where

δ

,

,

(11)

If Rs is a fixed parameter, then Eq. (10) is linear in rs. Similarly, if rs is a fixed parameter, then Eq. (10) is linear in Rs. For a given Rs, one can derive the minimum mean-square error of Eq. (1) at

, where

.

Then, Rs can be obtained by substituting the expression of rs in Eq. (10). Finally, by substituting the expression of in

and applying the linear minimum average method, it is possible to derive the leakage signal

source

.

The measurement accuracy for the time delay of the jet noise generated during the leakage process will directly affect the location accuracy. If the time delay is inaccurate, then the algorithm may not converge, or a false location may be generated irrespective of how much improvement was made to the algorithm. The operation of the boiler in a large power plant is accompanied by a considerable amount of combustion noise. In addition, the reflection of the leakage signal from the boiler wall or pipe surface in the closed space inside the boiler can produce strong reverberations that severely affect the accuracy of the estimation. In the subsequent sections, we introduce and discuss an improved generalized cross-correlation

time-delay estimation method. 2.2 Time-delay Estimation Algorithm Suppose that the distance between two sensors is L. Without any reverberation interference, the signals received by the two microphones are found as follows [16]: (12) (13) where

is the leakage signal,

and

are the background noises in the boiler,

required for the leakage signal to propagate to the microphones, and

and

and

are the times

are the acoustic attenuation coefficients.

The cross-correlation function between the leakage signals received by the two microphones

and

is

given by the following: (14) We denote α

. Based on the Wiener-Khinchin theorem, the inverse Fourier transform of the cross-power

spectrum function is a cross-correlation function. In this case, Eq. (14) can be transformed into the following: ∞ ∞

∞ ∞

(15)

To improve the noise resistance and accuracy of the time-delay algorithm, a prefiltering process can be implemented for functions and

and

. In this way, the signals collected by the microphone will first be transformed into

through filters H1 and H2 and then used for calculating the cross-correlation function. After filtering

and

through H1 and H2, the cross-power spectrum between the new functions

and

can be expressed as follows: (16) Therefore, the generalized cross-correlation function follows: ∞ ∞

where

ω (17) .

between

and

can be expressed as

There are two widely used weighting functions for the generalized correlation function: the maximum likelihood (ML) window, which has a strong resistance to noise, and the phase-transform (PHAT) window, which exhibits a stronger resistance to reverberation. Among these two choices, the ML window has the best anti-noise performance and therefore is better suited for a low reverberation and low-signal-to-noise-ratio environment. In contrast, the PHAT window is more frequently used in a high-signal-to-noise-ratio and medium-reverberation environment. The ML weighting function is given by the following: (18) In this equation,

represents the Fourier transform of the leakage signal received by the microphone, and represents the power spectrum of the background noise in the boiler received by the microphone.

The PHAT weighting function is given by the following: (19) When the boiler is in operation in a power plant, strong background noise will be generated from combustion. Meanwhile, the large closed space inside the boiler chamber will also induce a strong reverberation. Therefore, the time-delay algorithm used in the generalized correlation function must be improved by incorporating the ML algorithm under the reverberation condition. A SWITCH function is designed to allow switching between the PHAT and ML window functions to accommodate frequency points with high and low signal-to-noise ratios when estimating the generalized correlation time delay: (20) where

is a threshold value that is determined by sound pressure levels of the leakage acoustic signal and the

background noise, based on experience. 2.3 Experimental location platform To ensure the availability of the method developed in this paper, an acoustic location test platform was constructed. The experimental platform consisted of a

(

) acoustic array, as shown in Figure 2. The distance was

measured using a laser rangefinder (Fluke 414D, Fluke Corp., USA). Microphones (model MPA201, BSWA Technology

Co., Beijing, China) were used to construct the microphone array. Microphone M0 was set as the origin in the coordinate system, and the coordinates of the rest of the microphones, designated M1 to M12 from bottom to top, are shown in Figure 2. S1–S5 were set as the leakage points and their coordinates are also shown in Figure 2. It was hard and dangerous to generate jet noise of high-pressure steam. Therefore, the leakage signal was produced using a speaker developed by the Power Station Acoustics Laboratory at North China University. The data were collected using a PCI4472 card (NI Instruments Co., USA). The power amplifier (ASZ-MTC300) used in the test was also developed by the Power Station Acoustics Laboratory at North China University. The steam has a very high pressure and temperature in boiler tube. It is very difficult to use steam source, and the current conditions is impossible to do experiments. By the computer simulation, we’ve discovered that the leakage noise is a white Gaussian noise, and the frequencies are predominantly cantered between 1000 to 3000 Hz, which vary slightly with the size of the leakage aperture. Relevant contents will be studied in subsequent research papers. Therefore, the noise signal source was simulated using Gaussian white noise, which is similar to the leakage noise. This Gaussian white noise was generated using MATLAB and LabVIEW. The noise had a frequency range of 1000–3000 Hz. The subsequent sections show how the position of the leakage source was systematically determined. 3.

Results and Discussion

3.1 Location error The average absolute error of a single axis can be calculated as follows: (21) where

is the initial coordinate of the leak source determined from the location algorithm,

is the actual

location of the leakage point, and N is the number of measurements. The root-mean-square error is given as (22) 3.2 Experimental study using experimental location platform 3.2.1.

Influence of conventional microphone arrangement on location accuracy

To reduce the effects of reverberation and noise, experiments were performed in an open environment with a free

sound field and no reverberation. The experimental environment was also quiet and free from strong noise. Figure 3 shows the experimental photograph of the acoustic arrayin an open environment. First, we explored the feasibility of the location algorithm and the influence of different array arrangements on the location accuracy. Microphones M0, M2, M6, and M12 constituted a three-dimensional four-element array. S1–S5 were used as the leakage signal sources. For each experiment, the data were measured and collected 20 times. Using this type of arrangement, a highly accurate time delay could be obtained in the open environment. As shown in the results, the three-dimensional (3D), four-element array could accurately locate the leakage point in an open environment. Next, we studied the impact of changing the coordinates for the three-dimensional four-element array on the location accuracy. In the previous experiment, the first 3D four-element array was constructed of microphones M0, M2, M6, and M12. In the subsequent tests, 3D four-element arrays II–V were constructed using microphones M0, M1, M5, and M11; microphones M0, M3, M8, and M10; microphones M0, M4, M7, and M10; and microphones M0, M2, M7, and M10, respectively. These microphone arrays were used to locate the five different leakage signal sources. Figure 4 shows the distance-measurement errors. It can be clearly seen from the results that changing the arrangement of the 3D four-element arrays (i.e., the coordinates of the different microphone units) had a negligible impact on the location accuracy. The MAE and RMSE values associated with each testing result were also found to be insensitive to the change in the microphone arrangement. The above findings suggest that in an open, quiet environment, 3D four-element arrays can yield an accurate location for the leakage source. Next, we explored the effect of increasing the number of microphones on the location accuracy. 3.2.2.

Effect of microphone quantity on location accuracy

Three-dimensional five-, six-, seven-, and eight-element arrays were constructed from microphones M 0, M2, M6, M8, and M11; microphones M0, M2, M6, M8, M10, and M12; microphones M0, M2, M6, M7, M8, M10, and M12; and microphones M0, M2, M3, M6, M7, M8, M10, and M12, respectively. These arrays were used in the experiments together with the four-element arrays previously outlined. The same sound sources, S1–S5, were used as the leakage sources. For each experimental group, the data were collected 20 times. Figure 5 summarizes the measurement error in our study.

It can be clearly seen that the measurement MAE and RMSE values decrease with increasing number of microphones. The decreasing trend became flattened when using seven- or eight-element microphone arrays. Considering the real situation when performing on-site measurements in the boiler, an eight-element array was selected for the leak detection system. 3.2.3.

Effect of environmental conditions on measurements

A hot, operating boiler in a power plant will generate noises with a high sound-pressure level. Because the power-plant boiler chamber is a closed environment, the spatial sound field will also significantly affect the measurement. In the subsequent tests, all of these factors were considered in the leak detection experiments using the eight-element microphone array under different working conditions. The same leakage sources (S1, S2, S3, S4, and S5) were used in the experiments. The working conditions simulated in our experiment included the following: I, leakage location in an open, noise-free environment; II, leakage location in an open environment with boiler combustion noise; III, leakage location in a closed environment without noise; IV, leakage location in a closed environment with combustion noise; and V, leakage location in a closed environment with combustion noise exhibiting an increased sound-pressure level. A cold boiler chamber model was constructed to perform experiments simulating working conditions III, IV, and V. The external and inner structures of the apparatus are shown in Figure 6. The length, width and height of the boiler model were 5 m, 4 m, and 3 m, and the inner surface of the model was iron sheet (see Figure 6b). The combustion background noise inside a boiler was recorded using an acoustic temperature measurement system. Our analysis showed that the boiler background noise was white noise following a Gaussian distribution. The main frequency and sound-pressure level were approximately 500 Hz and 120 dB, respectively. Figure 7 shows the MAE and RMSE values associated with the five working conditions. It can clearly be seen that under working condition I (open environment), the coordinates of the five leakage points can be accurately obtained with minimum measurement error. Under working condition II, where the boiler combustion background noise was introduced to the experiment, the location accuracy was found to be dependent on the accuracy of the time-delay estimation. By implementing the SWITCH algorithm, an accurate time delay could be obtained during the experiments. Therefore, while the working condition was slightly harsher than that in case I, a relatively accurate location of the leakage could still be

achieved. Under working condition III, the microphone array was moved into the experimental boiler chamber without adding any combustion noise. In this closed environment, the sound field now became diffusive, where the major interference was the reverberation. In this case, it was found that the SWITCH algorithm could still yield accurate measurements of the time delay and leakage location. The location error was found to be greater than that under working condition I, but smaller than that under working condition II. Under working condition IV, the combustion background noise was again introduced into the experiments. The time delay calculated by the SWITCH algorithm was now affected by both the strong background noise and the reverberation, which resulted in higher errors in the time delay and location of the leakage compared to the previous three cases. Under working condition V, the sound-pressure level of the leakage source was increased, which led to better accuracy for the time delay calculated using the SWITCH algorithm. Therefore, the location error was considerably reduced, and accurate leakage coordinates could be obtained during the experiments. 3.3 Experimental field study in a boiler It is often difficult to find an opportunity to perform a field study in a boiler, because maintaining the stable operation of a boiler under a hot condition is critical for running an entire power plant. Moreover, it is challenging to perform on-site leakage location experiments in an operating hot boiler. However, our research team has also been working on the acoustic monitoring of the temperature field inside a boiler chamber in a power plant. We have already installed multiple acoustic thermometers in several boilers, and these acoustic thermometers comprise both acoustic emission and receiving components. Therefore, the acoustic receivers embedded in these acoustic thermal measurement systems could be used to form the detection array, while the acoustic generator could be used to simulate the leakage sound. In this case, a hot-state field study on leakage location could be performed to verify the feasibility of the proposed method. The boiler used in our experiment was a 660-MW domestic coal-fired supercritical boiler designed and manufactured by Shanghai Boiler Works Co., Ltd. The boiler has a single chamber, a single re-heating cycle in the chamber center, and a corner tangential firing pattern. Black coal was used in the combustion for the boiler. The acoustic thermal measurement systems were installed in two layers. The heights of the installation sites on the bottom and top layers measured in the standard boiler elevation system were 39.4 and 48.0 m, respectively. Figure 8 shows the distribution of the measurement points. The bottom and top

measurement planes are defined as planes i and ii, respectively. Fifteen acoustic measurement points were installed on each layer, which included five acoustic emission points and seven acoustic receiving points. Defining the acoustic receiver near the center of the front wall on plane i as the origin o(0,0,0) of the detection array coordinate system, an eight-element location array was then constructed from eight acoustic receivers selected from the two measurement planes. Two acoustic emitters on plane ii were selected to simulate the leakage signal, which were labelled leakage sources SI and SII. The coordinates for all the measurement points and leakage sources were measured using a Fluke 414D laser rangefinder, as shown in the coordinate map in Figure 8. When performing the hot-state experiment, Gaussian white noises similar to the leakage noise were generated from leakage signal sources SI and SII. The frequency of the simulated noise was set between 1000 and 3000 Hz. During the experiment, the load of the boiler was maintained at 580 MW. No additional task, such as soot-blowing, was performed during the experiment. Each leakage source was measured 20 times, and the errors in the measurement coordinates were still represented by the MAE and RMSE values. The measurement results are summarized in Table 1. As shown in these results, the location error became larger in the real boiler compared to that obtained with the experimental platform. This was primarily due to the larger size of the boiler chamber used in the field study. When the boiler chamber was under combustion, the measurement of the duration of the acoustic transmission could be affected by many additional factors in a more complex way. Therefore, the location error was mainly induced by the measurement error in the duration of the acoustic wave transmission. When the boiler was running in a hot state, a large amount of flying ash became attached to the surface of the water cooling wall in the boiler chamber. This phenomenon resulted in the weaker reflection of acoustic waves in the space, where the sound field more closely resembled a free sound field. Therefore, in the hot-state operating environment, a relatively accurate estimation of the leakage acoustic wave time delay could still be obtained from the SWITCH algorithm, which further yielded an accurate location for the leakage source. To visualize the location performance more intuitively, the mean absolute distance was introduced in the study to quantify the distance between the coordinates obtained from the acoustic location and the real coordinates of the leakage source. This value is defined as follows:

(39) where

represents the coordinate of the leak calculated from the ith iteration of the location algorithm,

is the actual coordinate of the leakage source, and N is the number of measurements. Analyzing the measurement results, it was found that the mean absolute distances for leakage sources SI and SII were 0.947 and 0.990 m, respectively. In other words, the leakage locations identified by the proposed algorithm were within 1 m of the actual locations. Figure 9 shows the location result. SI and SII are labelled leakage sources and SI′ and SII′ are location sources. Considering the extremely large size of the boiler chamber, this level of accuracy satisfied the basic requirement for practical applications. 4.

Conclusions In this study we have addresses the challenging issue of thermal power-unit safe operation during a water-wall leak

accident. Acoustic location technology based on the time difference of arrival was used to accurately locate the furnace tube leak. The spherical interpolation algorithm accurately located the leak and the SWITCH algorithm derived a more precise time-delay estimation under different conditions. The proposed 3D, eight-element array was shown to locate the leak area during the boiler hot-state operation and has practical engineering value, which also has significant meaning in proper shutdown procedures, repair-time reduction, and a reduction in financial losses. Acknowledgments This research was supported by the Beijing Excellent Talents Training Program (2016000020124G080). We are grateful to the anonymous reviewers whose constructive suggestions have improved the quality of this paper.

References [1] M.C. Barma, R. Saidur, S.M.A. Rahman, A. Allouhi, B.A. Akash, Sadiq M. Sait, A review on boilers energy use, energy savings, and emissions reductions, Renewable and Sustainable Energy Reviews. 79 (2017) 970-983, https://doi.org/10.1016/j.rser.2017.05.187. [2] S.W. Liu, W.Z. Wang, C.J. Liu, Failure analysis of the boiler water-wall tube, Case Studies in Engineering Failure Analysis. 9(2017) 35-39, https://doi.org/10.1016/j.csefa.2017.06.002. [3] A.K. Pramanick, G. Das, S.K. Das, M. Ghosh, Failure investigation of super heater tubes of coal fired power plant, Case Studies in Engineering Failure Analysis. 9(2017) 17-26, https://doi.org/10.1016/j.csefa.2017.06.001. [4] X. H. Yu, B. G. Gong, Q. Gao, Y. C. Zhao, C. Tian, J. Y. Zhang, Investigation of fireside corrosion at water-cooled wall from a coal-fired power plant in China, Applied Thermal Engineering. 127(2017) 1164-1171, https://doi.org/10.1016/j.applthermaleng.2017.08.053. [5] E. SooKim, Fracture analysis of tube boiler for physical explosion accident, Forensic Science International. 278(2017)

[6] [7] [8]

[9]

[10]

[11]

[12]

[13] [14] [15] [16]

e1-e7, https://doi.org/10.1016/j.forsciint.2017.07.036. Z. Yue, Analysis of Coated-after Superheater Pipe Bursting Accident in Utility Boiler, Procedia Engineering. 43(2012) 594-599, https://doi.org/10.1016/j.proeng.2012.08.105. S. P. Zhang, G. Q. Shen, L. S. An, G. S. Li, Ash fouling monitoring based on acoustic pyrometry in boiler furnaces, Applied Thermal Engineering. 84(2015) 74-81, https://doi.org/10.1016/j.applthermaleng.2015.03.019. S. P. Zhang, G. Q. Shen, L. S. An, Y. G. Niu, Online monitoring of the two-dimensional temperature field in a boiler furnace based on acoustic computed tomography, Applied Thermal Engineering. 75(2015) 958-966, https://doi.org/10.1016/j.applthermaleng.2014.10.085. Y. Gao, M.J. Brennan, Y.Y. Liu, F.C.L. Almeida, P.F.Joseph, Improving the shape of the cross-correlation function for leak detection in a plastic water distribution pipe using acoustic signals Applied Acoustics. 127 (2017) 24-33, https://doi.org/10.1016/j.apacoust.2017.05.033. A.H. Muntakim, A.S.Dhar, R. Dey, Interpretation of Acoustic Field Data for Leak Detection in Ductile Iron and Copper Water-Distribution Pipes, Journal of Pipeline Systems Engineering and Practice. 8(2017) 05017001:1-05017001:14, https://doi.org/10.1061/(ASCE)PS.1949-1204.0000257. G. S. Jiang, Y. C. Liu, W. L. Xu, Q. Kong, Acoustic radiation and cold point defect in boiler tube arrays based on phononic crystals theory, Applied Thermal Engineering. 123(2017) 746-752, https://doi.org/10.1016/j.applthermaleng.2017.05.103. N. Modlinski, P. Madejski, T.Janda, K. Szczepanek, A validation of computational fluid dynamics temperature distribution prediction in a pulverized coal boiler with acoustic temperature measurement, Energy. 92(2015) 77-86, https://doi.org/10.1016/j.energy.2015.05.124. J. Park, K. Kotun, Spectral coherence and hyperbolic solutions applied to time difference of arrival localisation, Applied Acoustics. 136(2018) 149-157, https://doi.org/10.1016/j.apacoust.2017.08.026. R. Cavoretto, A. D. Rossi, Spherical interpolation using the partition of unity method: An efficient and flexible algorithm, Applied Mathematics Letters. 25(2012) 1251-1256, https://doi.org/10.1016/j.aml.2011.11.006. M. F. Carfora, Interpolation on spherical geodesic grids: A comparative study, Journal of Computational and Applied Mathematics. 210(2007) 99-105, https://doi.org/10.1016/j.cam.2006.10.068. C. Knapp, G. Carter, The generalized correlation method for estimation of time delay, IEEE Transactions on Acoustics Speech & Signal Processing. 24 (2003) 320-327, http://dx.doi.org/10.1109/TASSP.1976.1162830.

Table 1. Location errors of the 8-element array in the boiler furnace (Unit: m). Leakage source

MAE-x

MAE-y

MAE-z

RMSE

SⅠ

0.455

0.675

0.485

0.935

SⅡ

0.366

0.455

0.799

0.985

Figure 1. Spatial geometry of the four-element topology used for locating the leak.

M0 (0.000, 0.000, 0.000) M1 (1.011, 0.000, 0.000) M2 (1.998, 0.997, 0.000) M3 (1.011, 1.999, 0.000) M4 (0.000, 0.997, 0.000) M5 (1.011, 0.000, 1.010) M6 (1.998, 0.997, 1.010) M7 (1.011, 1.999, 1.010) M8 (0.000, 0.997, 1.010) M9 (1.011, 0.000, 2.011) M10 (1.998, 0.997, 2.011) M11 (1.011, 1.999, 2.011) M12 (0.000, 0.997, 2.011)

S1 (1.981, 0.011, 0.562) S2 (0.011, 1.993, 0.852) S3 (1.981, 1.981, 1.011) S4 (1.992, 0.491, 2.002) S5 (0.551, 1.981, 2.002)

Figure 2. Acoustic array and leak test point distribution map in the experimental platform.

Figure 3. Experimental photograph of the acoustic array in an open environment.

(a) MAE

(b) RMSE

Figure 4. Distance measurement errors of the 3D four-element array in the experimental platform.

(b) RMSE

(a) MAE

Figure 5. Distance measurement errors of different three-dimensional array arrangements in the experimental platform.

(a)

Figure 6. Cold boiler chamber model in the laboratory.

(b)

(a) MAE

(b) RMSE

Figure 7. MAE and RMSE values associated with the five working conditions.

Figure 8. Acoustic array and leak test point distribution map in boiler furnace.

z y o x

Figure 9. Location result in boiler furnace.

HIGHLIGHTS 

An approach to locate water-cooling wall tube leak based on acoustic array was provided.



The paper used a three-dimensional space location algorithm based on spherical interpolation and SWITCH algorithm.



The location precisions in different experimental environments were compared.



The leak location technology was applied to a domestic 660-MW coal-fired boiler.