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A dual-sensor-based method to recognize pipeline leakage and interference signals
Journal of Loss Prevention in the Process Industries 38 (2015) 79e86
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Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
A dual-sensor-based method to recognize pipeline leakage and interference signals Lin Weiguo a, Wang Xiaodong a, Wu Haiyan a, *, Mu Changli b, Wang Fenwei c a
College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, PR China Beijing Ray Applied Research Centre, Beijing 100012, PR China c Stae Key Laboratory of NBC Protection for Civilian, Beijing 102205, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 April 2015 Received in revised form 11 July 2015 Accepted 20 August 2015 Available online 1 September 2015
During the detection of pipeline leakages, false alarms of leak detection could be markedly reduced if the interference signals resulting from pressure regulating, pump regulating or valve movements could be accurately distinguished. A digital recognition method for interference signals and leakage signals based on a dual-sensor system is proposed in this paper. It is demonstrated that the direction of the signal can be recognized by a cross-correlation calculation between two signals from the dual-sensor, one of which undergoes forward linear interpolation and backward linear interpolation. Based on this theory, the interference signal and the leak signal can be discriminated exactly, and the distance between the two sensors in the dual-sensor system can be considerably reduced without needing to increase the sampling frequency. The monotonicity of the cross-correlation function is demonstrated, and a fast discrimination algorithm based on a binary extreme search method, which decreases the computational load and maintains global optimization, is also proposed. A pre-processing method of the actual signal is proposed to decrease the identity requirement for the two sensors in a dual-sensor system. In the experiment based on artificial signals, the proposed discrimination algorithm could achieve accurate recognition of the abnormal signal, and as such, the theory and application of pipeline leak detection based on dualsensor systems are extended. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Dual-sensor structure Leak detection Signal interpolation Cross-correlation Abnormal signal recognition
1. Introduction Pipelines are the most important equipment in the transportation of oil, gas and dangerous chemicals. The major contributors to pipeline leakages are erosion, mechanical failures, construction defects, natural disasters and other unknown causes. Consequently, leakages lead to heavy financial losses and can even cause fatalities, as well as environmental pollution (Weiguo and Zhishou, 2006). Currently, considerable research has been conducted into leak detection, including methods such as the Acoustic Method (Weiguo and Zhishou, 2006), the Negative Pressure Wave Method (Souza de Joode et al., 2011), the Optical Method (Kasai et al., 2011), and the Mass/Volume Balance (Doorhy, 2011). In the Acoustic Method, continuous mode operation is feasible. Acoustic methods can also help in determining the location of the leak and estimating its size, and they can be used on new as well as on
* Corresponding author. E-mail address: [email protected] (W. Haiyan). http://dx.doi.org/10.1016/j.jlp.2015.08.002 0950-4230/© 2015 Elsevier Ltd. All rights reserved.
existing pipelines (Murvay and Silea, 2012; Kim and Lee, 2009; Hayashi et al., 1996). Thus, this technique is widely used. However, in the acoustic method, the detection of pipeline leakage will be influenced by interference signals generated from pressure regulating, pump regulating or valve movements due to their similar time and frequency domain response. False alarms happen when different interferences acting at different monitoring points upstream and downstream are detected in the same time period. False alarms can also occur due to location error. The highly accurate discrimination of interference signals, therefore, can reduce false alarms and increase the reliability of the acoustic leak detection method. In general, the following three types of methods can be used to distinguish interference signals: 1) discriminations could be realized by characteristic values of the normal signal, interference signal and leakage signal (Singh and Rama Rao, 2011; Prashanth Reddy et al., 2011); 2) discriminations between interference and leakage signals can be completed through location function (Lingya et al., 2011; Cuiwei et al., 2015); and 3) the interference signal coming from the operating point can be filtered through
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dual-acoustic sensors installed at both ends (Loth et al., 2003; Shijiu et al., 1997).The last approach is based on judgments of transmission directions of the signals, which applies dual-sensor structure with a time delay of the hardware circuit. Interference happens frequently, and this discrimination method aims at determining the signal propagation direction, which can lessen the computational burden and increase the calculation speed, may have greater accuracy than the first two methods. However, the time delay between two sensors based on the hardware circuit is fixed. Nevertheless, if acoustic velocity varies along with the changes of pressure and temperature of the medium in the pipeline (Hamilton and David, 1997), the delay time cannot be adjusted adaptively. Moreover, to attain accurate discrimination about the transmission directions of the signals, it asks for consistency in the sensitivity, responding characteristic and signal gain of the two sensors installed at the same end, and it also demands a large installation distance between the two sensors, along with high signal sampling frequency. These conditional requirements limit the application of dual-sensor structure in the field of pipeline leak detection. To solve these problems, a digital discrimination method of leakage signal and interference based on the dual-sensor structure is proposed in this paper, which applies the signal interpolation method to process abnormal signals from one of the two sensors settled in the same end. One of the signals is linearly interpolated by linear interpolation method, and cross-correlation is performed between the interpolated signal and another signal from the dualsensor. The peak value of the cross-correlation coefficient is proportional to the signal similarity. Based on this, the direction of the signal can be judged by the cross-correlation calculation between the interpolated signal and the original signal from another sensor, and then the discrimination of the leakage signal and the interference is realized. Pre-processing methods to limit inaccuracy from differences in the two sensors are used prior to the crosscorrelation calculation, and the requirement of high consistency between the two sensors at the same end can be avoided as a result. Thanks to the high-frequency interpolated signal realized by signal interpolation, the distance installation of the dual-sensor is decreased. At the same time, there is no need for an increase in sampling frequency. Considering that the timeline will be affected by the huge computational requirements of the method, the monotonicity of the cross-correlation function is discussed in this paper. The dichotomy method is used for finding the maximum cross-correlation, and the signal direction can be determined rapidly. Furthermore, timeliness of the system is improved. This paper presents a theory to distinguish the interference signal based on a dual-sensor structure. Moreover, a solution in practice is proposed, and its effectiveness is proved. 2. Principle of the leak detection method based on dualsensor structure Generally, leak signals come from the pipe section between upstream and downstream monitoring points, while interference signals caused by actions of the pump, regulator and valve come
from outside the two monitoring points. Thus, the interference signals can be distinguished if the direction of abnormal signals is confirmed. Based on this, abnormal signals from outside the monitored pipe section can be excluded when the direction of the signal is distinguished through the signal collection and crosscorrelation of two sensors in the dual-sensor system, and then following the leak diagnosis and determination of the leak location, the leakage alarm is activated. The architecture of the pipeline leak detection system based on the dual-sensor structure is shown in Fig. 1. As shown in Fig. 1, there are two sets of dual-sensor system installed separately in each end of the pipeline (upstream station and downstream station), and one set of dual-sensor system including two sensors. The signals of the sensors are processed in the central processing unit transferred by the network. Thus, the processing unit has four signals in every processing period. Because of the same working principle at each of the two ends, the upstream station is selected as the object of analysis in the following sections, and the principle is similar to that of the downstream station. XL(k) and XR(k),k ¼ 1,2,…N present the signals of the left sensor and the right sensor installed separately in the upstream station. The cross-correlation can be obtained in
rðXL ðkÞ; XR ðk þ tÞÞ ¼
N X
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ,v u N N X uX XL ðkÞXR ðk þ tÞ t X 2L ðkÞ X 2R ðk þ tÞ
k¼1
k¼1
k¼1
(1) where the time shift factor t2Z. The nature of the cross-correlation coefficient shows that if the waveforms of XL and XR are consistent, r(t) ranging from the extreme 1. r(t) is closer to 1 when the waveforms of XL and XR are more consistent. In the upstream station, the time difference between the interference signals arriving at the left and right sensors can be calculated by
Dt ¼ D=V < 0
(2)
where D is the distance between the two sensors in the starting station, and V is the sound velocity in the pipe. Furthermore, the cross correlation coefficient r(t) peaks when
t ¼ intðDt=TÞ < 0
(3)
where T is the sampling time. The abnormal acoustic signal arrives first at the left sensor, where it is confirmed to be an interference signal. If t > 0, the abnormal acoustic signal arrives at the right sensor first, and it may be a leak signal. If t ¼ 0, the direction cannot be deduced, and the method fails. The same method can also be used at the downstream station. If the abnormal signal is thought to have comes from the right sensor in the upstream station while it is thought to have come from the left sensor in the downstream station, then the abnormal signal can be confirmed as a leak signal. According to the derivation above, Dt T 1 is required for the
Fig. 1. Architecture of the dual-sensor pipeline leakage detection system.
L. Weiguo et al. / Journal of Loss Prevention in the Process Industries 38 (2015) 79e86
accurate detection of signal direction. So
~ RB ðk; nÞ ¼ FðX
D VT f V=D
(4)
81
M n n jw þ e FðwÞ M M
(9)
where F(w) is the Fourier transformation of XR(k). At the same time, is needed. f is the sampling frequency. It can be concluded that the distance between the two sensors installed at the same end should be longer than 8 m, when V ¼ 400 m/s and T ¼ 20 ms. Similarly, if the installation distance is 1 m, T should be less than 2.5 ms or f should be more than 4 KHz. Therefore, the strict requirements for installation distance limit the actual application of the dual-sensor method. To solve this problem, a signal interpolating method is proposed. This is based on the realization of the high-frequency approximation of the original signal, which provides a theory and a practical foundation for the interference signal discrimination method using the cross-correlation calculation. 3. Interference in the signal detection method of the dualsensor system 3.1. Signal interpolation method Signal interpolation helps to obtain a high sampling frequency of the signal sequence from the low-frequency signal. Taking the difference between the current signal and the time before and after into consideration, the linear interpolation method based on numerical calculation principles is used for one of the sensor signals. Similarly, take the upstream station as an example. Using Newton's interpolation method for equidistant pitch, forward and backward linear interpolation on the right sensor signal for M points:
~ RF ðk; nÞ ¼ XR ðkÞ þ n ðXR ðkÞ XR ðk 1ÞÞ X M ~ ðk; nÞ ¼ X ðkÞ þ n ðX ðk þ 1Þ X ðkÞÞ X RB R R M R
(5)
where M expresses the number of interpolation points; k ¼ 1,2,…N is the number of actual sample points; N is length of actual sampling data;n ¼ 1,2,…M 1 is the number of interpolation points; ~ RF is the signal obtained from forward interpolation and X ~ RB is X obtained from backward interpolation. Discussions in Section 2 tell us that higher sampling frequency leads to a decrease in the installation distance requirement. The frequency of the interpolated signal is f ¼ M/T, then based on the discussion in Section 2 (Eq. (4)), a constraint should be satisfied for M, that is:
M intðTV=D）
~ ð1; 1Þ X RF ~¼4 X « ~ RF ðN; 1Þ X
/ /
~ ð1; M 1Þ X RF « ~ RF ðN; M 1Þ X
~ ð1; 1Þ X RB
/
(10)
FðXRB ðk; DtÞÞ ¼ ejwDt FðwÞ
(11)
Eq. (10) is the Fourier transformation of the forward motion of the original signal, and Eq. (11) is the Fourier transformation of the backward motion of the original signal. Contrast of Eqs. (8)e(11) leads to the following conclusions: Conclusion 1. The interpolated signal sequence from the linear interpolation method has differences in the amplitude as well as the phase angle with the original signal, but the phase change direction from the two sampling point is consistent with the original. Eq. (8) and Eq. (10) separately denote the forward interpolation and the forward motion, the angle change is expressed as ejw and ejwDt, which differ in their values but have the same change direction (they are all negative). The contrast between Eq. (9) and Eq. (11) has the same results. From the analysis in Section 2, when the cross-correlation coefficient r(t) peaks, the sign of the time shift coefficient t is the key parameter with which to judge the direction of the signal, and the interference can be distinguished from abnormal signals. Although, there are difference in the processed signal obtained from linear interpolation, the sign of t is unchanged, so the interpolated signal sequence in Eq. (7) can be used for the cross-correlation calculation and to obtain the accurate sign of t, which can subsequently be used for the judgment of interference signals. The following conclusion is based on the analysis in Section 2: Conclusion 2. Taking the column vectors ~ R ðk; nÞ; k ¼ 1; 2; …N; n ¼ 1; 2; …2M 2 from the matrix obtained X from Eq. (7) instead of XR, based on Eq. (1), the cross-correlation with XL can be presented by Eq. (12):
rn ¼
~ RB ðN; 1Þ X
/
M þ n n jw e FðwÞ M M
N X
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ,v u N N X uX ~ R ðk; nÞ t ~ 2 ðk; nÞ XL ðkÞX X 2L ðkÞ X R
k¼1
k¼1
(8)
(12)
k¼1
And the vector of the cross-correlation coefficient is obtained by:
3 ~ ð1; M 1Þ X RB 52Rð2M2ÞN « ~ X RB ðN; M 1Þ
Every row in the matrix is an interpolated signal sequence. The result of the Fourier transformation on Eq. (5) is obtained by:
~ RF ðk; nÞ ¼ FðX
FðXRF ðk; DtÞÞ ¼ ejwDt FðwÞ
(6)
The matrix of the interpolated signal obtained from the linear interpolation can be presented as:
2
the Fourier transformation of the original signal as a time shift Dt ¼ can be calculated by: int ðMnÞT M
rLR ¼ ½r1 ; …rM1 ; rM ; …r2M2
(7)
(13)
MAXr is the maximum of rLR, and the location number of MAXr is presented by nmax. Then, the abnormal signal can be judged as an interference signal coming from the pipeline if nmax < M, on the contrary, if nmax M the signal can be concluded as coming from
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the right part of the pipe. It should be noted that the algorithm principle applies well also to the dual-sensor installed at the end station. Through the linear interpolation algorithm, the installation distance between the two sensors is reduced for M times; as a result, this limitation faced by the dual-sensor system is removed. 3.2. The monotonicity of the cross-correlation function It should be noted that the calculation burden of the method increases greatly with the increasing data length (N) and number of insertion points (M). Consequently, it is difficult to ensure timeliness of the system in real applications. Therefore, the monotonicity of the cross-correlation function, which is the theory underlying the orientation algorithm, is discussed in this section. Taking the interpolated signal derived from Eq. (5) into consideration, the phase shift of the forward interpolation of the data can be expressed as:
M þ 1 cosw FRF ðwÞ ¼ arctan sinw n
(14)
It is easy to know that FRF(w) monotonically increases or decreases with the change of n, and it is the same in backward interpolation. Through data processing, the effect of the signal amplitude in the cross-correlation calculation can be eliminated, and then the phase variation is left as the only parameter of the cross-correlation parameter. Therefore, the cross-correlation coefficient increases with the decrease in the phase difference and reaches its maximum when the phase difference is minimal. Therefore, the following conclusion can be derived: Conclusion 3. The function curve formed by the cross-correlation coefficient rn is a monotonic function in two fields n3[1,M 1] and n3[M,2M 2]. Based on conclusion 3, a dichotomy method was designed to obtain fast orientation algorithms for abnormal signals. Because the cross-correlation function is a subsection of a single peak function, the local optimum of the dichotomy method can be avoided by using a subsection design. Therefore, the accuracy of the fast algorithm is ensured. The realization method is explained in the next section. 3.3. Fast orientation algorithm for abnormal signals based on the dual-sensor system Pipeline leak detection is generally performed once per minute, and for the purpose of integrity of the leak signal, 1-min historical data and 1-min real-time data are usually combined to form a full frame of data for leakage diagnosis. Taking the case of the 20-ms sampling period, one frame of data has 6000 points, that is N ¼ 6000. As such, the calculation burden is huge, and this has a great impact on the real-time performance of the system. The monotony of the cross-correlation function has been proved in the above section. Based on that, a dichotomy method is proposed to obtain a fast calculation result in the orientation algorithm for the abnormal signal. It should be noted that the calculations of the forward interpolation and the backward interpolation are separated. The flow chart of the dichotomy method is expressed in Fig. 2. The value of peak of the cross-correlation between XL and the forward and backward interpolated sequences of XR can be calculated separately. The position of the larger value indicates the direction of the abnormal signal. Based on the demonstration in Section 3.2, the optimal result obtained from the upper algorithm is
Fig. 2. The flow chart of the dichotomy method.
global. At the same time, the calculation burden can be decreased greatly. 3.4. Simulation experiment A simulation experiment was designed to testify the method proposed above. Assume that the output signal of the two sensors, respectively are:
XL ¼ Að1 þ sinð2pnf =fs þ 41 Þ=2 XR ¼ Að1 þ sinð2pnf =fs þ 42 Þ=2
(15)
where fs ¼ 50 Hz; A ¼ 3300 mV; n ¼ 1……N; N ¼ 100; f ¼ 1 Hz; 41 ¼ 0.1235 rad;42 ¼ 0.1297 rad; and 4142 ¼ 0.0063 rad, meaning that the time difference between the two signals is approximately 1 ms.The resulting signal is shown in Fig. 3, and the corresponding amplified phase difference is shown below Fig. 3. The crosscorrelation coefficients with M ¼ 100 are calculated using the method proposed in Section 3.2. The cross-correlation of XL with XRF and XRB, gives the curve of the cross-correlation coefficients shown in Fig. 4. From the figure, the maximum position of the function nmax ¼ 95 < M so the abnormal signal is the interference signal comes from upstream. Furthermore, let 4142 ¼ 0.0063 rad, and then do the same experiment. If the derived maximum position as shown in Fig. 4, which is equal to 104 and larger than M, then the abnormal signal comes from downstream. It can be observed that the crosscorrelation based on linear interpolation can give an accurate result of the phase difference. Thus, the accuracy of the method is verified. 4. Pre-processing of dual-sensor signals Based on the above results, the differences between two sensors
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Fig. 3. Two analog signal waveforms.
Fig. 4. The curve of the cross-correlation coefficients.
Fig. 5. The experimental device.
in the same end, including sensitivity, response characteristics and signal amplitude, influence the signals and will lead to failure of accurate results. Unfortunately, two sensors used in actual leakage detection are generally different. The method is used in a laboratory pipeline system, which is expressed in Fig. 5. The output of an acoustic signal transmitter is a 4e20 mA current signal. The sensitivity of the left and right sensors is 15248pC/105pa and 15440pC/105pa, respectively. Meanwhile, the installation distance between the two sensors is approximately 146 cm; both sampling periods are 20 ms, leading to a data length of 6000 points. The 12bit A/D converter AD7352 with the sample and hold function helps to achieve synchronous sampling. The transport medium is water. Assuming acoustic propagation velocity is 1480 m/s, the analog leakage signal reception time difference between the two sensors is approximately 1.0 ms. Assuming that the two sensors are settled at the upstream station, and the interference signal comes from left pipeline, then the leak signal comes from the right pipeline. To test the accuracy of the method, the fast algorithm is used to orient 5 artificial interference signals from the left sensor and 5 artificial leak signals from the right sensor. Fig. 6 shows one pair of artificial leak signals of the dual-sensor.
Fig. 6. The artificial leak signal of the dual-sensor settled in the upstream station.
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signals are then obtained and have the same mean values. The bipolar signals are shown in Fig. 7(b). The abnormal signal is selected by the method introduced by (Yuanhua et al., 2013). Between 20% and 80% of the abnormal signal peak is smoother and is not influenced by noise. Thus, these parts of the signal are retained for the calculation, and the amplitude of the boundary points is extended to substitute for the other part of signal. The criterion of boundary point selection is shown in Eq. (16):
W ¼ maxfWL ; WR g H ¼ minfHL ; HR g
Fig. 7. Processed signals. (a) signal processed by the wavelet de-noising method and (b) the bipolar signal.
Fig. 6 shows that there are many differences in the signals of the two sensors. The pre-processing method is designed in this section to decrease the identity requirement between the two sensors in a traditional dual-sensor system, while at the same time avoid the failures in judgment that may be generated by these differences. The wavelet de-noising method is introduced, and Fig. 7(a) shows the processed signal with the DB9 wavelet and a decomposition scale of 3. Fig. 7(a) shows that the difference in magnification of the two sensor signal will lead to different amplitudes and that different benchmarks of the V/I conversion circuit (corresponding to 12 mA output) will lead to different mean values. From Fig. 7(a), there is noise in the signals, and because of different response characteristic of the two sensors, the output signal shows different time domain responses during the recovery process after sudden change. Meanwhile, the skipping part of the signal is smoother and is not affected by noise. To avoid the influence of noise and difference in the two sensors (transmitters), the hopping part of the signal is selected as an object signal for interpolation and cross-correlation calculation. In this paper, the output signal skips up at the time of the leak, so the up transmission part is selected. Two signals are normalized, and their mean values are subtracted. The two bipolar
(16)
where WL and WR are 20% of the abnormal signal peak of the left and right signals separately, and HL and HR are 80% of the abnormal signal peak of left and right signals separately. The processed signals are shown in Fig. 8. Up to this point, pre-processing has been conducted to avoid the influence of noise and differences in sensors (transmitters) in the calculation results by the selection of the up transmission part of signal. There is the cross-correlation calculation to follow. The curve of the cross-correlation coefficient is shown in Fig. 9 with M ¼ 100.
Fig. 8. Pre-processed signals.
Fig. 9. Cross-correlation curve.
L. Weiguo et al. / Journal of Loss Prevention in the Process Industries 38 (2015) 79e86
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Fig. 10. Algorithmflowchart.
Fig. 12. Stop pumping signal and cross-correlation curve. (a) stop pumping signal and (b) cross-correlation curve.
Fig. 11. Simulation of the interference signal and cross-correlation curve. (a) simulation of the interference signal and (b) cross-correlation curve.
From Fig. 9, the maximum of the curve lies in the 143th sampling point, which is bigger than M, so the abnormal signal comes from the right pipeline. To summarize, the flowchart of the abnormal signal recognition algorithm is shown in Fig. 10.
5. Further experiments When the abnormal signal comes from left pipeline, the sampling signals and cross-correlation curve is shown in Fig. 11. From
Fig. 11, the peak of the cross-correlation curve is in the 40th point, which is smaller than M, while the signal comes from the left pipeline. The method was used in 8 additional experiments to testify its accuracy. The results of the signal orientation are shown in Table 1, where L stands for the signal first arriving at the left sensor (interference signal comes from the station), and R stands for the abnormal signal first arriving at the right sensor (leak signal). With regards to the cross-correlation calculation number, the number of forward and backward interpolations is shown in for positions corresponding with two sides of þ. Except those signals simulated by opening and closing the valve, the stop pumping signal is used to test the method. Fig. 12 shows the output signal of the sensor and the cross-correlation curve. From Fig. 12, the peak of the cross-correlation curve stands on the 28th points, which is smaller than M. Thus, the abnormal signal can be concluded as being the interference signal that comes from the left pipeline. From Fig. 5, the pump is installed upstream of the left sensor, and the result of the signal orientation is accurate. Comparison between Fig. 12(a) and Fig. 6 shows that the time domain characteristic of stop pumping and the close valve is obviously different, and the method proposed here can obtain accurate results in every situation. Experiments tested the validity of the method. From Table 1, the peak position changes in different experiments (the peak position of the cross-correlation curve), but if the distance between two sensors is fixed, the peak position will remain essentially
Table 1 The experimental results of the signal for the orientation experiment. Number
Signal origin
Cross-correlation calculation number
Position of maximum
Guiding result
1 2 3 4 5 6 7 8
Leak signal Leak signal Leak signal Leak signal Interference Interference Interference Interference
9 þ 11 11 þ 13 12 þ 14 13 þ 14 9 þ 12 12 þ 14 9 þ 12 11 þ 13
130 151 133 152 70 49 68 46
R R R R L L L L
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unchanged, which is different in our experiments. The reason is that the peak position may be associated with the speed of opening the valve and the pressure of the pipeline. Different speeds of opening the valve will yield different time domain characteristics of the abnormal signal. This is because the cross-correlation is calculated between the linear interpolated signal sequence and the other output signal, which is different with the real high-frequency signal. Thus, the peak position in different experiments is different, which can testify to the accuracy of conclusion 1, that is the linear interpolated signal sequence is different with real high-frequency signals in amplitude and phase but can obtain an accurate calculation of signal orientation. The calculation number of the crosscorrelation calculation shows that the fast orientation algorithm greatly decreases the calculation burden. Therefore, the theory and method discussed in this paper is evidently feasible and highly efficient. 6. Conclusions A digital discrimination algorithm combining numeric computation theory and the cross-correlation method for identifying abnormal signals is proposed in this paper, and the viability of the theory was first explained. Compared with a dual-sensor method based on hardware circuit delay, the proposed algorithm conquered the limitation of installation distance without needing high sampling frequency. The characteristic of the cross-correlation function between the interpolated signal of one sensor and the signal of another sensor is shown to be unimodal, and the theory underlying the fast orientation algorithm has been supplied. The dichotomy method is introduced to decrease the computational burden and increase the real-time performance. The simulation experiment indicates the validity of this method. Furthermore, a pre-processing method for the signal is proposed to solve the problem of variance between two sensors installed at the same end by aligning the two signals for the cross-correlation calculation, which helps to improve the accuracy of algorithm in practice. This method can be used for but is not limited to leakage discrimination in a pipeline, and there are many other failure detection fields and high-precision measurement fields that require similar resolution.
Acknowledgments The authors gratefully acknowledge the support from the State Key Laboratory of NBC Protection for Civilians (SKLNBC2014-10); the National Natural Science Foundation of China (61403017); and the Fundamental Research Funds for the Central Universities (YS0104).
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Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
A dual-sensor-based method to recognize pipeline leakage and interference signals Lin Weiguo a, Wang Xiaodong a, Wu Haiyan a, *, Mu Changli b, Wang Fenwei c a
College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, PR China Beijing Ray Applied Research Centre, Beijing 100012, PR China c Stae Key Laboratory of NBC Protection for Civilian, Beijing 102205, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 April 2015 Received in revised form 11 July 2015 Accepted 20 August 2015 Available online 1 September 2015
During the detection of pipeline leakages, false alarms of leak detection could be markedly reduced if the interference signals resulting from pressure regulating, pump regulating or valve movements could be accurately distinguished. A digital recognition method for interference signals and leakage signals based on a dual-sensor system is proposed in this paper. It is demonstrated that the direction of the signal can be recognized by a cross-correlation calculation between two signals from the dual-sensor, one of which undergoes forward linear interpolation and backward linear interpolation. Based on this theory, the interference signal and the leak signal can be discriminated exactly, and the distance between the two sensors in the dual-sensor system can be considerably reduced without needing to increase the sampling frequency. The monotonicity of the cross-correlation function is demonstrated, and a fast discrimination algorithm based on a binary extreme search method, which decreases the computational load and maintains global optimization, is also proposed. A pre-processing method of the actual signal is proposed to decrease the identity requirement for the two sensors in a dual-sensor system. In the experiment based on artificial signals, the proposed discrimination algorithm could achieve accurate recognition of the abnormal signal, and as such, the theory and application of pipeline leak detection based on dualsensor systems are extended. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Dual-sensor structure Leak detection Signal interpolation Cross-correlation Abnormal signal recognition
1. Introduction Pipelines are the most important equipment in the transportation of oil, gas and dangerous chemicals. The major contributors to pipeline leakages are erosion, mechanical failures, construction defects, natural disasters and other unknown causes. Consequently, leakages lead to heavy financial losses and can even cause fatalities, as well as environmental pollution (Weiguo and Zhishou, 2006). Currently, considerable research has been conducted into leak detection, including methods such as the Acoustic Method (Weiguo and Zhishou, 2006), the Negative Pressure Wave Method (Souza de Joode et al., 2011), the Optical Method (Kasai et al., 2011), and the Mass/Volume Balance (Doorhy, 2011). In the Acoustic Method, continuous mode operation is feasible. Acoustic methods can also help in determining the location of the leak and estimating its size, and they can be used on new as well as on
* Corresponding author. E-mail address: [email protected] (W. Haiyan). http://dx.doi.org/10.1016/j.jlp.2015.08.002 0950-4230/© 2015 Elsevier Ltd. All rights reserved.
existing pipelines (Murvay and Silea, 2012; Kim and Lee, 2009; Hayashi et al., 1996). Thus, this technique is widely used. However, in the acoustic method, the detection of pipeline leakage will be influenced by interference signals generated from pressure regulating, pump regulating or valve movements due to their similar time and frequency domain response. False alarms happen when different interferences acting at different monitoring points upstream and downstream are detected in the same time period. False alarms can also occur due to location error. The highly accurate discrimination of interference signals, therefore, can reduce false alarms and increase the reliability of the acoustic leak detection method. In general, the following three types of methods can be used to distinguish interference signals: 1) discriminations could be realized by characteristic values of the normal signal, interference signal and leakage signal (Singh and Rama Rao, 2011; Prashanth Reddy et al., 2011); 2) discriminations between interference and leakage signals can be completed through location function (Lingya et al., 2011; Cuiwei et al., 2015); and 3) the interference signal coming from the operating point can be filtered through
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dual-acoustic sensors installed at both ends (Loth et al., 2003; Shijiu et al., 1997).The last approach is based on judgments of transmission directions of the signals, which applies dual-sensor structure with a time delay of the hardware circuit. Interference happens frequently, and this discrimination method aims at determining the signal propagation direction, which can lessen the computational burden and increase the calculation speed, may have greater accuracy than the first two methods. However, the time delay between two sensors based on the hardware circuit is fixed. Nevertheless, if acoustic velocity varies along with the changes of pressure and temperature of the medium in the pipeline (Hamilton and David, 1997), the delay time cannot be adjusted adaptively. Moreover, to attain accurate discrimination about the transmission directions of the signals, it asks for consistency in the sensitivity, responding characteristic and signal gain of the two sensors installed at the same end, and it also demands a large installation distance between the two sensors, along with high signal sampling frequency. These conditional requirements limit the application of dual-sensor structure in the field of pipeline leak detection. To solve these problems, a digital discrimination method of leakage signal and interference based on the dual-sensor structure is proposed in this paper, which applies the signal interpolation method to process abnormal signals from one of the two sensors settled in the same end. One of the signals is linearly interpolated by linear interpolation method, and cross-correlation is performed between the interpolated signal and another signal from the dualsensor. The peak value of the cross-correlation coefficient is proportional to the signal similarity. Based on this, the direction of the signal can be judged by the cross-correlation calculation between the interpolated signal and the original signal from another sensor, and then the discrimination of the leakage signal and the interference is realized. Pre-processing methods to limit inaccuracy from differences in the two sensors are used prior to the crosscorrelation calculation, and the requirement of high consistency between the two sensors at the same end can be avoided as a result. Thanks to the high-frequency interpolated signal realized by signal interpolation, the distance installation of the dual-sensor is decreased. At the same time, there is no need for an increase in sampling frequency. Considering that the timeline will be affected by the huge computational requirements of the method, the monotonicity of the cross-correlation function is discussed in this paper. The dichotomy method is used for finding the maximum cross-correlation, and the signal direction can be determined rapidly. Furthermore, timeliness of the system is improved. This paper presents a theory to distinguish the interference signal based on a dual-sensor structure. Moreover, a solution in practice is proposed, and its effectiveness is proved. 2. Principle of the leak detection method based on dualsensor structure Generally, leak signals come from the pipe section between upstream and downstream monitoring points, while interference signals caused by actions of the pump, regulator and valve come
from outside the two monitoring points. Thus, the interference signals can be distinguished if the direction of abnormal signals is confirmed. Based on this, abnormal signals from outside the monitored pipe section can be excluded when the direction of the signal is distinguished through the signal collection and crosscorrelation of two sensors in the dual-sensor system, and then following the leak diagnosis and determination of the leak location, the leakage alarm is activated. The architecture of the pipeline leak detection system based on the dual-sensor structure is shown in Fig. 1. As shown in Fig. 1, there are two sets of dual-sensor system installed separately in each end of the pipeline (upstream station and downstream station), and one set of dual-sensor system including two sensors. The signals of the sensors are processed in the central processing unit transferred by the network. Thus, the processing unit has four signals in every processing period. Because of the same working principle at each of the two ends, the upstream station is selected as the object of analysis in the following sections, and the principle is similar to that of the downstream station. XL(k) and XR(k),k ¼ 1,2,…N present the signals of the left sensor and the right sensor installed separately in the upstream station. The cross-correlation can be obtained in
rðXL ðkÞ; XR ðk þ tÞÞ ¼
N X
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ,v u N N X uX XL ðkÞXR ðk þ tÞ t X 2L ðkÞ X 2R ðk þ tÞ
k¼1
k¼1
k¼1
(1) where the time shift factor t2Z. The nature of the cross-correlation coefficient shows that if the waveforms of XL and XR are consistent, r(t) ranging from the extreme 1. r(t) is closer to 1 when the waveforms of XL and XR are more consistent. In the upstream station, the time difference between the interference signals arriving at the left and right sensors can be calculated by
Dt ¼ D=V < 0
(2)
where D is the distance between the two sensors in the starting station, and V is the sound velocity in the pipe. Furthermore, the cross correlation coefficient r(t) peaks when
t ¼ intðDt=TÞ < 0
(3)
where T is the sampling time. The abnormal acoustic signal arrives first at the left sensor, where it is confirmed to be an interference signal. If t > 0, the abnormal acoustic signal arrives at the right sensor first, and it may be a leak signal. If t ¼ 0, the direction cannot be deduced, and the method fails. The same method can also be used at the downstream station. If the abnormal signal is thought to have comes from the right sensor in the upstream station while it is thought to have come from the left sensor in the downstream station, then the abnormal signal can be confirmed as a leak signal. According to the derivation above, Dt T 1 is required for the
Fig. 1. Architecture of the dual-sensor pipeline leakage detection system.
L. Weiguo et al. / Journal of Loss Prevention in the Process Industries 38 (2015) 79e86
accurate detection of signal direction. So
~ RB ðk; nÞ ¼ FðX
D VT f V=D
(4)
81
M n n jw þ e FðwÞ M M
(9)
where F(w) is the Fourier transformation of XR(k). At the same time, is needed. f is the sampling frequency. It can be concluded that the distance between the two sensors installed at the same end should be longer than 8 m, when V ¼ 400 m/s and T ¼ 20 ms. Similarly, if the installation distance is 1 m, T should be less than 2.5 ms or f should be more than 4 KHz. Therefore, the strict requirements for installation distance limit the actual application of the dual-sensor method. To solve this problem, a signal interpolating method is proposed. This is based on the realization of the high-frequency approximation of the original signal, which provides a theory and a practical foundation for the interference signal discrimination method using the cross-correlation calculation. 3. Interference in the signal detection method of the dualsensor system 3.1. Signal interpolation method Signal interpolation helps to obtain a high sampling frequency of the signal sequence from the low-frequency signal. Taking the difference between the current signal and the time before and after into consideration, the linear interpolation method based on numerical calculation principles is used for one of the sensor signals. Similarly, take the upstream station as an example. Using Newton's interpolation method for equidistant pitch, forward and backward linear interpolation on the right sensor signal for M points:
~ RF ðk; nÞ ¼ XR ðkÞ þ n ðXR ðkÞ XR ðk 1ÞÞ X M ~ ðk; nÞ ¼ X ðkÞ þ n ðX ðk þ 1Þ X ðkÞÞ X RB R R M R
(5)
where M expresses the number of interpolation points; k ¼ 1,2,…N is the number of actual sample points; N is length of actual sampling data;n ¼ 1,2,…M 1 is the number of interpolation points; ~ RF is the signal obtained from forward interpolation and X ~ RB is X obtained from backward interpolation. Discussions in Section 2 tell us that higher sampling frequency leads to a decrease in the installation distance requirement. The frequency of the interpolated signal is f ¼ M/T, then based on the discussion in Section 2 (Eq. (4)), a constraint should be satisfied for M, that is:
M intðTV=D）
~ ð1; 1Þ X RF ~¼4 X « ~ RF ðN; 1Þ X
/ /
~ ð1; M 1Þ X RF « ~ RF ðN; M 1Þ X
~ ð1; 1Þ X RB
/
(10)
FðXRB ðk; DtÞÞ ¼ ejwDt FðwÞ
(11)
Eq. (10) is the Fourier transformation of the forward motion of the original signal, and Eq. (11) is the Fourier transformation of the backward motion of the original signal. Contrast of Eqs. (8)e(11) leads to the following conclusions: Conclusion 1. The interpolated signal sequence from the linear interpolation method has differences in the amplitude as well as the phase angle with the original signal, but the phase change direction from the two sampling point is consistent with the original. Eq. (8) and Eq. (10) separately denote the forward interpolation and the forward motion, the angle change is expressed as ejw and ejwDt, which differ in their values but have the same change direction (they are all negative). The contrast between Eq. (9) and Eq. (11) has the same results. From the analysis in Section 2, when the cross-correlation coefficient r(t) peaks, the sign of the time shift coefficient t is the key parameter with which to judge the direction of the signal, and the interference can be distinguished from abnormal signals. Although, there are difference in the processed signal obtained from linear interpolation, the sign of t is unchanged, so the interpolated signal sequence in Eq. (7) can be used for the cross-correlation calculation and to obtain the accurate sign of t, which can subsequently be used for the judgment of interference signals. The following conclusion is based on the analysis in Section 2: Conclusion 2. Taking the column vectors ~ R ðk; nÞ; k ¼ 1; 2; …N; n ¼ 1; 2; …2M 2 from the matrix obtained X from Eq. (7) instead of XR, based on Eq. (1), the cross-correlation with XL can be presented by Eq. (12):
rn ¼
~ RB ðN; 1Þ X
/
M þ n n jw e FðwÞ M M
N X
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ,v u N N X uX ~ R ðk; nÞ t ~ 2 ðk; nÞ XL ðkÞX X 2L ðkÞ X R
k¼1
k¼1
(8)
(12)
k¼1
And the vector of the cross-correlation coefficient is obtained by:
3 ~ ð1; M 1Þ X RB 52Rð2M2ÞN « ~ X RB ðN; M 1Þ
Every row in the matrix is an interpolated signal sequence. The result of the Fourier transformation on Eq. (5) is obtained by:
~ RF ðk; nÞ ¼ FðX
FðXRF ðk; DtÞÞ ¼ ejwDt FðwÞ
(6)
The matrix of the interpolated signal obtained from the linear interpolation can be presented as:
2
the Fourier transformation of the original signal as a time shift Dt ¼ can be calculated by: int ðMnÞT M
rLR ¼ ½r1 ; …rM1 ; rM ; …r2M2
(7)
(13)
MAXr is the maximum of rLR, and the location number of MAXr is presented by nmax. Then, the abnormal signal can be judged as an interference signal coming from the pipeline if nmax < M, on the contrary, if nmax M the signal can be concluded as coming from
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the right part of the pipe. It should be noted that the algorithm principle applies well also to the dual-sensor installed at the end station. Through the linear interpolation algorithm, the installation distance between the two sensors is reduced for M times; as a result, this limitation faced by the dual-sensor system is removed. 3.2. The monotonicity of the cross-correlation function It should be noted that the calculation burden of the method increases greatly with the increasing data length (N) and number of insertion points (M). Consequently, it is difficult to ensure timeliness of the system in real applications. Therefore, the monotonicity of the cross-correlation function, which is the theory underlying the orientation algorithm, is discussed in this section. Taking the interpolated signal derived from Eq. (5) into consideration, the phase shift of the forward interpolation of the data can be expressed as:
M þ 1 cosw FRF ðwÞ ¼ arctan sinw n
(14)
It is easy to know that FRF(w) monotonically increases or decreases with the change of n, and it is the same in backward interpolation. Through data processing, the effect of the signal amplitude in the cross-correlation calculation can be eliminated, and then the phase variation is left as the only parameter of the cross-correlation parameter. Therefore, the cross-correlation coefficient increases with the decrease in the phase difference and reaches its maximum when the phase difference is minimal. Therefore, the following conclusion can be derived: Conclusion 3. The function curve formed by the cross-correlation coefficient rn is a monotonic function in two fields n3[1,M 1] and n3[M,2M 2]. Based on conclusion 3, a dichotomy method was designed to obtain fast orientation algorithms for abnormal signals. Because the cross-correlation function is a subsection of a single peak function, the local optimum of the dichotomy method can be avoided by using a subsection design. Therefore, the accuracy of the fast algorithm is ensured. The realization method is explained in the next section. 3.3. Fast orientation algorithm for abnormal signals based on the dual-sensor system Pipeline leak detection is generally performed once per minute, and for the purpose of integrity of the leak signal, 1-min historical data and 1-min real-time data are usually combined to form a full frame of data for leakage diagnosis. Taking the case of the 20-ms sampling period, one frame of data has 6000 points, that is N ¼ 6000. As such, the calculation burden is huge, and this has a great impact on the real-time performance of the system. The monotony of the cross-correlation function has been proved in the above section. Based on that, a dichotomy method is proposed to obtain a fast calculation result in the orientation algorithm for the abnormal signal. It should be noted that the calculations of the forward interpolation and the backward interpolation are separated. The flow chart of the dichotomy method is expressed in Fig. 2. The value of peak of the cross-correlation between XL and the forward and backward interpolated sequences of XR can be calculated separately. The position of the larger value indicates the direction of the abnormal signal. Based on the demonstration in Section 3.2, the optimal result obtained from the upper algorithm is
Fig. 2. The flow chart of the dichotomy method.
global. At the same time, the calculation burden can be decreased greatly. 3.4. Simulation experiment A simulation experiment was designed to testify the method proposed above. Assume that the output signal of the two sensors, respectively are:
XL ¼ Að1 þ sinð2pnf =fs þ 41 Þ=2 XR ¼ Að1 þ sinð2pnf =fs þ 42 Þ=2
(15)
where fs ¼ 50 Hz; A ¼ 3300 mV; n ¼ 1……N; N ¼ 100; f ¼ 1 Hz; 41 ¼ 0.1235 rad;42 ¼ 0.1297 rad; and 4142 ¼ 0.0063 rad, meaning that the time difference between the two signals is approximately 1 ms.The resulting signal is shown in Fig. 3, and the corresponding amplified phase difference is shown below Fig. 3. The crosscorrelation coefficients with M ¼ 100 are calculated using the method proposed in Section 3.2. The cross-correlation of XL with XRF and XRB, gives the curve of the cross-correlation coefficients shown in Fig. 4. From the figure, the maximum position of the function nmax ¼ 95 < M so the abnormal signal is the interference signal comes from upstream. Furthermore, let 4142 ¼ 0.0063 rad, and then do the same experiment. If the derived maximum position as shown in Fig. 4, which is equal to 104 and larger than M, then the abnormal signal comes from downstream. It can be observed that the crosscorrelation based on linear interpolation can give an accurate result of the phase difference. Thus, the accuracy of the method is verified. 4. Pre-processing of dual-sensor signals Based on the above results, the differences between two sensors
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Fig. 3. Two analog signal waveforms.
Fig. 4. The curve of the cross-correlation coefficients.
Fig. 5. The experimental device.
in the same end, including sensitivity, response characteristics and signal amplitude, influence the signals and will lead to failure of accurate results. Unfortunately, two sensors used in actual leakage detection are generally different. The method is used in a laboratory pipeline system, which is expressed in Fig. 5. The output of an acoustic signal transmitter is a 4e20 mA current signal. The sensitivity of the left and right sensors is 15248pC/105pa and 15440pC/105pa, respectively. Meanwhile, the installation distance between the two sensors is approximately 146 cm; both sampling periods are 20 ms, leading to a data length of 6000 points. The 12bit A/D converter AD7352 with the sample and hold function helps to achieve synchronous sampling. The transport medium is water. Assuming acoustic propagation velocity is 1480 m/s, the analog leakage signal reception time difference between the two sensors is approximately 1.0 ms. Assuming that the two sensors are settled at the upstream station, and the interference signal comes from left pipeline, then the leak signal comes from the right pipeline. To test the accuracy of the method, the fast algorithm is used to orient 5 artificial interference signals from the left sensor and 5 artificial leak signals from the right sensor. Fig. 6 shows one pair of artificial leak signals of the dual-sensor.
Fig. 6. The artificial leak signal of the dual-sensor settled in the upstream station.
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signals are then obtained and have the same mean values. The bipolar signals are shown in Fig. 7(b). The abnormal signal is selected by the method introduced by (Yuanhua et al., 2013). Between 20% and 80% of the abnormal signal peak is smoother and is not influenced by noise. Thus, these parts of the signal are retained for the calculation, and the amplitude of the boundary points is extended to substitute for the other part of signal. The criterion of boundary point selection is shown in Eq. (16):
W ¼ maxfWL ; WR g H ¼ minfHL ; HR g
Fig. 7. Processed signals. (a) signal processed by the wavelet de-noising method and (b) the bipolar signal.
Fig. 6 shows that there are many differences in the signals of the two sensors. The pre-processing method is designed in this section to decrease the identity requirement between the two sensors in a traditional dual-sensor system, while at the same time avoid the failures in judgment that may be generated by these differences. The wavelet de-noising method is introduced, and Fig. 7(a) shows the processed signal with the DB9 wavelet and a decomposition scale of 3. Fig. 7(a) shows that the difference in magnification of the two sensor signal will lead to different amplitudes and that different benchmarks of the V/I conversion circuit (corresponding to 12 mA output) will lead to different mean values. From Fig. 7(a), there is noise in the signals, and because of different response characteristic of the two sensors, the output signal shows different time domain responses during the recovery process after sudden change. Meanwhile, the skipping part of the signal is smoother and is not affected by noise. To avoid the influence of noise and difference in the two sensors (transmitters), the hopping part of the signal is selected as an object signal for interpolation and cross-correlation calculation. In this paper, the output signal skips up at the time of the leak, so the up transmission part is selected. Two signals are normalized, and their mean values are subtracted. The two bipolar
(16)
where WL and WR are 20% of the abnormal signal peak of the left and right signals separately, and HL and HR are 80% of the abnormal signal peak of left and right signals separately. The processed signals are shown in Fig. 8. Up to this point, pre-processing has been conducted to avoid the influence of noise and differences in sensors (transmitters) in the calculation results by the selection of the up transmission part of signal. There is the cross-correlation calculation to follow. The curve of the cross-correlation coefficient is shown in Fig. 9 with M ¼ 100.
Fig. 8. Pre-processed signals.
Fig. 9. Cross-correlation curve.
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Fig. 10. Algorithmflowchart.
Fig. 12. Stop pumping signal and cross-correlation curve. (a) stop pumping signal and (b) cross-correlation curve.
Fig. 11. Simulation of the interference signal and cross-correlation curve. (a) simulation of the interference signal and (b) cross-correlation curve.
From Fig. 9, the maximum of the curve lies in the 143th sampling point, which is bigger than M, so the abnormal signal comes from the right pipeline. To summarize, the flowchart of the abnormal signal recognition algorithm is shown in Fig. 10.
5. Further experiments When the abnormal signal comes from left pipeline, the sampling signals and cross-correlation curve is shown in Fig. 11. From
Fig. 11, the peak of the cross-correlation curve is in the 40th point, which is smaller than M, while the signal comes from the left pipeline. The method was used in 8 additional experiments to testify its accuracy. The results of the signal orientation are shown in Table 1, where L stands for the signal first arriving at the left sensor (interference signal comes from the station), and R stands for the abnormal signal first arriving at the right sensor (leak signal). With regards to the cross-correlation calculation number, the number of forward and backward interpolations is shown in for positions corresponding with two sides of þ. Except those signals simulated by opening and closing the valve, the stop pumping signal is used to test the method. Fig. 12 shows the output signal of the sensor and the cross-correlation curve. From Fig. 12, the peak of the cross-correlation curve stands on the 28th points, which is smaller than M. Thus, the abnormal signal can be concluded as being the interference signal that comes from the left pipeline. From Fig. 5, the pump is installed upstream of the left sensor, and the result of the signal orientation is accurate. Comparison between Fig. 12(a) and Fig. 6 shows that the time domain characteristic of stop pumping and the close valve is obviously different, and the method proposed here can obtain accurate results in every situation. Experiments tested the validity of the method. From Table 1, the peak position changes in different experiments (the peak position of the cross-correlation curve), but if the distance between two sensors is fixed, the peak position will remain essentially
Table 1 The experimental results of the signal for the orientation experiment. Number
Signal origin
Cross-correlation calculation number
Position of maximum
Guiding result
1 2 3 4 5 6 7 8
Leak signal Leak signal Leak signal Leak signal Interference Interference Interference Interference
9 þ 11 11 þ 13 12 þ 14 13 þ 14 9 þ 12 12 þ 14 9 þ 12 11 þ 13
130 151 133 152 70 49 68 46
R R R R L L L L
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unchanged, which is different in our experiments. The reason is that the peak position may be associated with the speed of opening the valve and the pressure of the pipeline. Different speeds of opening the valve will yield different time domain characteristics of the abnormal signal. This is because the cross-correlation is calculated between the linear interpolated signal sequence and the other output signal, which is different with the real high-frequency signal. Thus, the peak position in different experiments is different, which can testify to the accuracy of conclusion 1, that is the linear interpolated signal sequence is different with real high-frequency signals in amplitude and phase but can obtain an accurate calculation of signal orientation. The calculation number of the crosscorrelation calculation shows that the fast orientation algorithm greatly decreases the calculation burden. Therefore, the theory and method discussed in this paper is evidently feasible and highly efficient. 6. Conclusions A digital discrimination algorithm combining numeric computation theory and the cross-correlation method for identifying abnormal signals is proposed in this paper, and the viability of the theory was first explained. Compared with a dual-sensor method based on hardware circuit delay, the proposed algorithm conquered the limitation of installation distance without needing high sampling frequency. The characteristic of the cross-correlation function between the interpolated signal of one sensor and the signal of another sensor is shown to be unimodal, and the theory underlying the fast orientation algorithm has been supplied. The dichotomy method is introduced to decrease the computational burden and increase the real-time performance. The simulation experiment indicates the validity of this method. Furthermore, a pre-processing method for the signal is proposed to solve the problem of variance between two sensors installed at the same end by aligning the two signals for the cross-correlation calculation, which helps to improve the accuracy of algorithm in practice. This method can be used for but is not limited to leakage discrimination in a pipeline, and there are many other failure detection fields and high-precision measurement fields that require similar resolution.
Acknowledgments The authors gratefully acknowledge the support from the State Key Laboratory of NBC Protection for Civilians (SKLNBC2014-10); the National Natural Science Foundation of China (61403017); and the Fundamental Research Funds for the Central Universities (YS0104).
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