CALIFORNIA STATE UNIVERSITY, NORTHRIDGE. Water Leak Detection and Localization Using Multi-Sensor Data Fusion

Transcription

1 CALIFORNIA STATE UNIVERSITY, NORTHRIDGE Water Leak Detection and Localization Using Multi-Sensor Data Fusion A thesis submitted in partial fulfillment of the requirements For the degree of Master of Science in Electrical Engineering By Fei Yang December 2012

2 The thesis of Fei Yang is approved: Dr. Deborah, van Alphen Date Dr. Xiyi, Hang Date Dr. Xiaojun, Geng, Chair Date California State University, Northridge ii

3 Table of Contents Signature Page List of Tables List of Figures Abstract ii iv v vii Chapter 1: Background Research and Motivation The Necessity of Leak Detection and Localization Review of Current Products and Methods Objective of this Research 7 Chapter 2: Methodology Cross Correlation Artificial Neural Network 11 Chapter 3: System Implementation Modelling: Simulate the Leak Data Acquisition System Matlab and Data Flow 25 Chapter 4: Data Analysis and Results Velocity Test Pipeline Monitoring System Leak Localization More Discussion in Weight and Learning Rate More Discussion in Training Database 50 Chapter 5: Conclusion 55 References 56 Appendix A 57 Appendix B 61 iii

4 LIST OF TABLES ' Table 4-1 t lag in Six Velocity Tests 31 Table 4-2 The Slopes of Approximation Lines in 10 Leak-Free Experiments 38 Table 4-3 The Reliability in Different Slope Ranges 38 Table 4-4 Validation and Its Mean Square Error 46 Table 4-5 Estimation of Lagged Time for Ten Data Sets 46 Table 4-6 Statistics of Experiments 50 Table 4-7 Statistics of Additional Experiments 53 iv

5 LIST OF FIGURES Figure 1-1 Pipleline Buried in Soil 3 Figure 1-2 Pipleline Exposed in Air 4 Figure 1-3 Sonic Leak Detection Equipment 5 Figure 1-4 Digital Pipeline Leak Detection 6 Figure 2-1 Schematic of a Pipe with a Leak Bracketed by Two Sensors 9 Figure 2-2 Alternate Cross Correlation Method 10 Figure 2-3 Neuron Structure 11 Figure 2-4 Structure of Three-Layer Network 12 Figure 3-1 System Block Diagram 17 Figure 3-2 Leak Simulation 17 Figure 3-3 ADXL2.3EB 19 Figure 3-4 Relationship between Output and Acceleration 19 Figure C300PA4K 20 Figure 3-6 Relationship between Output and Pressure 20 Figure 3-7 FDT Figure 3-8 Relationship between Output and Flow Rate 21 Figure 3-9 Arduino Duemilanove 22 Figure 3-10 Circuits Design for Data Collection 23 Figure 3-11 Filter Design and Analysis Tool 26 Figure 3-12 Signal Processing Tool 27 Figure 3-13 Data Flow 28 Figure 4-1 Schematic of Velocity Test 30 Figure 4-2 Frequency Spectrum of Flow Rate 32 Figure 4-3 Flow Rate Filter 33 Figure 4-4 Frequency Spectrum of Pressure 33 Figure 4-5 Pressure Filter 34 Figure 4-6 Frequency Spectrum of Non-Leak Signal and Leak Signal 35 Figure 4-7 Approximation of Flow Rate Data 36 Figure 4-8 Approximation of Pressure Data 37 Figure 4-9 Frequency Spectrum of Filtered Acceleration 39 Figure 4-10 Schematic of Leak Localization System 40 Figure 4-11 Structure of ADALINE 40 Figure 4-12 Data Flow of Training Procedures 43 Figure 4-13 Weights during the Iterations 44 Figure 4-14 Mean Square Error during the Iterations 45 Figure 4-15 Weights Initialized at 0 47 v

6 Figure 4-16 Weights Training Initialized at Random Number 47 Figure 4-17 Weight Training when α equals Figure 4-18 Weight Training when α equals Figure 4-19 Weight Training when α equals Figure 4-20 Weight Training Using the Previous Database Repeatedly 51 Figure 4-21 Weight Training Using the Universal Learning Rate 52 Figure 4-22 Physical and Estimated Lagged Times 53 Figure 4-23 Absolute Values of Errors 54 vi

7 ABSTRACT Water Leak Detection and Localization Using Multi-Sensor Data Fusion By Fei Yang Master of Science in Electrical Engineering Modern cities can no longer tolerate insufficiencies in water supply systems. Of the many options available for conserving water, detecting a leakage from a sealed pipe is an effective low cost method. The quality of the leak detection system is determined by accuracy. The aims of this study were developing a system to minimize the probability of false alarm and miss detection, and to detect the leak in time by using a multi-sensor network. Cross correlation and the Artificial Neural Network (ANN) algorithm were utilized to pinpoint the leak location. The results showed that the probabilities of false alarm and miss detection have been decreased. In addition, an analysis of the results in leak localization implies that the error of estimated location and physical location decreases if more data is fed to the ANN algorithm and it finally stabilizes within ±27.22 mm. The results of this study are presented such that they can be used as an aid to a water pipeline monitoring system. vii

8 Chapter 1 Motivation and Background Research Current metropolises such as Las Vegas, Los Angeles and Cairo rely on water distribution systems for drinking water. These systems involve long distance water transportation and water distribution networks under the city. The water service provided by these systems not only meets the need of living, but also serves vitally important commercial customers and the industrial world. In addition, these systems provide sufficient water for fire stations to put out fires in emergencies and save lives. Unfortunately, since the pipelines in the water distribution system have been in place over a long period, water leaks and breaks have developed. Therefore various methods have been investigated to detect the leak and find out its location when the leak happens. In this chapter, after describing the necessity of leak detection and localization, an analysis of current solutions is presented in Section 1.2, followed by some leak examples and finally the contribution to the field. 1

9 1.1 The Necessity of Leak Detection and Localization Water is critical to life on earth, so it is critical to not waste water. On November 8, 2011 two water mains in Studio City broke, causing the closure of Ventura Boulevard and depriving nearly 100 customers of water service. In September 2009, a 62-inch water main burst, washed away cars and flooded several homes [1]. Detecting a water leakage from sealed pipes is of crucial importance in many aspects. First, by solving this problem, tons of fresh water can be saved. The amount of water leaked from U.S. homes exceeds more than 1 trillion gallons per year, which is equivalent to the annual water use of Los Angeles, Chicago, and Miami combined [2]. In the meantime, detecting the leakage as soon as possible reduces the risk of public health hazard, because the drinking water can be easily contaminated by bacteria in soil or anything surrounding the water pipeline. In addition, the commercial loss could be reduced. According to an assessment of the public water system by the US Environmental Protection Agency (EPA) in 2009, $334.8 billion is needed to improve the infrastructure over the next 20 years for thousands of miles of pipe as well as thousands of treatment plants, storage tanks, and other key assets [3]. This is an increase by 20.87% compared with the year Those pipes were laid many years ago. For instance, the water main broken in Studio City was laid in They are too old and become so fragile that even a very small physical damage can cause a rupture. The rupture does not happen frequently but its consequences can be severe. Before performing practical experiments, it is important to understand how water was transported and the main reasons for leaks. Typically in the modern world, a long 2

10 distance water distribution system is used to transport water from a water reservoir to a metropolis. The system consists of large scale sealed pipelines that are buried in soil or exposed directly to air. Figure 1-1 and Figure 1-2 show these two situations respectively. There are many possible causes of leaks, and often a combination of factors leads to their occurrence. The material, composition, age, and joining methods of the distribution system components can influence leak occurrence. Water and external conditions, including temperature, pressure, contact with other structures, and stress from traffic vibrations, frost loads, and freezing soil around a pipe are also factors which contribute to leaks. Figure 1-1 Pipeline Buried in Soil [4] 3

11 Figure 1-2 Pipeline Exposed to Air [5] 1.2 Products and Literature Review To solve the water leak problem, there are two kinds of products in the current water leak detection and localization market. One category specializes in short distance water leak locating, and an example of such equipment is Sonic Leak Detection as shown in Figure 1-3. This kind of product requires a leak report before locating. Though leak location can be determined precisely by the products in this category, leaks are not detected until the amount of leakage is large enough that people can sense it. By this time significant environmental damage may already have occurred. Furthermore it needs to be 4

12 manipulated manually in most circumstances; in some places, this may be dangerous for human beings. The second category of product is designed for long distance leak detection and localization. This typically features a long distance, sensor-functioned cable which has to be deployed along with the water pipelines. For instance, Digital Pipeline Leak Detection utilizes a fiber optic cable to detect temperature changes caused by the leak. Figure 1-4 shows the principle of this approach. These products detect the leak and pinpoint it within a range of several meters. However, they require large investments in system installation, which, in the current economic environment, may not be approved by the government. Figure 1-3 Sonic Leak Detection Equipment [6] 5

13 Figure 1-4 Digital Pipeline Leak Detection [7] In order to improve the effectiveness and efficiency of these products, some theoretical models are built and experiments are conducted. These models and experiments can be divided into two classes. One class uses a single kind of sensor. The leak, in this case, can be located precisely in an ideal environment. However, such models are not reliable in the practical world due to false alarm and miss detection. An example of the second class is PIPENET: a Wireless Sensor Network for Pipeline Monitoring. This network utilizes hydraulic, water quality and acoustic/vibration data to detect and locate the leak and uses Global Pointing System (GPS) and Precise Positioning Service (PPS) to synchronize the whole system. As the author [8] claimed, however, the leak localization algorithm localized leaks to within 30 cm when sensors were separated by 3m or less. 6

14 1.3 Objective of this Research In this project, a multi-sensor monitoring system is designed for the following three purposes: (1) decreasing the probabilities of false alarm and miss detection; (2) detecting the leakage as soon as possible; and (3) precisely pinpointing leak location. In a system with a single type of sensor such as acoustic leak detection system, the received signal is easily affected by external factors such as wind and railroads, in which case a false alarm may be triggered. Similarly, if a system collects data solely from a pressure sensor, misses may occur when the leak is very small. In our system, three kinds of sensors are applied to decrease the probability of occurrences of false alarm and miss detection. In addition, thresholds are designed in the detection section to increase the reliability of the system. Secondly, the water distribution system needs to be monitored continuously in case of a sudden leak caused by significant outside force. If a leak is not detected in time, significant environmental damage, commercial loss, or health hazard may occur as illustrated in the two systems above. On the other hand, it is also crucial to detect the leak when it is still small to avoid a leak leading to a break. To solve this problem, three approaches are developed in this project using three different types of sensors and using the perceptron to detect a small leak. Finally, in addition to using the cross-correlation method to pinpoint the leak location, a neural network is applied to minimize the location error and thus make the result more accurate. 7

15 Chapter 2 Methodology In this thesis, two mathematical tools are utilized to accomplish Water Leak Detection and Localization. The first one is cross correlation, a typical method to pinpoint the leak location, which has been used in water distribution systems in many big cities. Typically, two acoustic signals are required by this method to determine the location of the leak. The second tool is the Artificial Neural Network (ANN). ANN has been widely used in the field of engineering nowadays. With its remarkable feature of deriving outcomes from complicated noisy data, a network system is built in this thesis to minimize the probability of false alarm and miss detection. In addition, the cross correlation method is embedded in the neural network and accuracy of the leak location has been further increased. This chapter has been divided into two parts. In the first part, the classical cross correlation method is introduced, followed by the data flow of the method in this thesis. In the second part, the theory and concept of ANN are explained, followed by our neural network design. The advantages and disadvantages of this network are discussed in the end. 8

16 2.1 Cross Correlation Accelerometer1 Leak Accelerometer2 Water Pipe d d 1 d 2 Figure 2-1 Schematic of a Pipe with a Leak Bracketed by Two Sensors Classical Cross Correlation Method Using cross correlation to pinpoint the leak location is very straightforward. As showed in Figure 2-1, two accelerometers are installed to collect vibration information generated by the leak along the water pipe on either side of a suspected leak. These two signals are set to have zero mean, and then fed to filters to get rid of noise. After that, the cross correlation function is applied with filtered input signals. Cross correlation function is defined as [9] R x1 x 2 (τ) = E[x 1 (t)x 2 (t + τ)] where τ is the lag time; E[] is the expectation operator. The variable τ leak, which represents the time difference in arrival of the signal at the accelerometer, is calculated by maximizing R x1 x 2 (τ). Then by using simple algebra, the location of the leak can be easily obtained by the following equation: d 1 = d cτ peak 2 where c is the wave speed propagation along the pipe. 9

17 2.1.2 Modified Cross Correlation Method There are two reasons that the above cross correlation method needs to be modified in this project. One reason is that the signal is collected discretely and for a limited time interval in our experiments. Another reason is that the lag of time in our experiments is less than 50 milliseconds, and the time interval of data collection is 1000 milliseconds. There is no necessity to calculate R x1 x 2 (τ) when τ is greater than 50ms. To reduce the calculation burden, an altered cross correlation method is shown in Figure 2-2. x 2 x 1 T D R x1 x 2 (0) R x1 x 2 (1) D Max τ leak D R x1 x 2 (49) Figure 2-2 Alternate Cross Correlation Method First, the discrete cross correlation is calculated at τ ranging from 0 to 49 respectively. Then, the time lag τ leak can be found by determining the largest cross correlation value. 10

18 2.2 Artificial Neural Network Artificial Neural Network, inspired by the biological characteristics of brain functions, has been widely used in many fields, not only in engineering, science and mathematics, but in banking, entertainment, and even literature. It is simply good at solving problems. Moreover, faster computation speed and more effective algorithms make it possible to use neural networks in more areas and more complex problems Neuron Structure A general neuron, shown in Figure 2-3, usually consists of five parts. They are input, weight, bias, transfer function, and output. The input vector o is multiplied by the weight matrix w and then sent to the adder. Another element passed to adder is bias b. The output of the adder, n, also named as net output, is fed to the transfer function f, which provides the output of a [10]. o w b n + f a Figure 2-3 Neuron Structure The dimension of the input vector o is R 1. It is decided by the external specification of the problem. The dimension of the weight matrix w is S R where S is the number of interested outputs. The dimension of the bias vector b and transfer function f 11

19 are S 1. Finally the dimension of the output a is S 1. The output can be written in the following equation: a = f(wo + b) Two more points need to be mentioned here: (1) the elements of the input and output can be from different sensors and may represent various physical meanings; and (2) the transfer function in each neuron is not necessarily the same Layers and Network The definition of layer varies between different areas. In this thesis, a Neuron described in the former section can be treated as a single layer. With multiple layers comes a network. The layer whose output is the network output is called the output layer. The rest of the layers are called hidden layers. The typical structure of a three-layer neural network is shown in Figure 2-4. Note that the superscripts do not mean the power, but indicate the different layers. o w 1 + n 1 a 1 w 2 f 1 + f 2 a 2 a 3 w 3 + f 3 b 1 b 2 b 3 Figure 2-4 Structure of Three-Layer Network The output of first layer is a 1, which can be obtained in the following equation[10]: a 1 = f 1 (w 1 o + b 1 ) 12

20 Similarly, a 2 and a 3 can be calculated in the following equations respectively: a 2 = f 2 (w 2 a 1 + b 2 ) a 3 = f 3 (w 3 a 2 + b 3 ) By substituting the first two equations in to the third equation, we can write the general output equation of three-layer network as: a 3 = f 3 (w 3 f 2 (w 2 f 1 (w 1 o + b 1 ) + b 2 ) + b 3 ) Multilayer networks are more powerful than single-layer networks. For instance, a two-layer network having a sigmoid first layer and a linear second layer can be trained to approximate most functions arbitrarily well. However a single-layer neuron is not able to do this[10] Performance Learning and Performance Index Besides defining input and output of ANN, another very important thing to do is parameter training in neural network design. Parameter training, which is a procedure of finding the weight matrix and bias, is called performance learning. During this learning process, the network parameters are modified (trained) to optimize the performance of the system. The performance index is a quantitative measure of network performance. Usually the smaller the performance index is, the better the network performance. There are two steps in the training process. The first step is to define a proper performance index that can well reflect the network performance. The second step is finding a path (by adjusting weights and biases) on the performance surface in order to reduce the performance index. 13

21 2.2.4 Least Mean Square (LMS) Algorithm The LMS algorithm was introduced by Bernard Widrow and Marcian Hoff in It is a very powerful learning rule and has been found to be very practical in many fields. Since it minimizes the mean square error, this algorithm tries to adjust the parameters so that the performance index gets to a minimum as fast as possible [10]. In the LMS algorithm, the mean square error is defined by F(x) = (t a) 2 = s 2 where t(k) is the correct output (target), and a(k) is the network output. Then to find the minimum of F(x), take the derivative with respect to the weights and biases: s w 2 = s2 w s b 2 = s2 b Assume the transfer function is pure linear, Therefore, = 2s s w = 2s s b a = f(wo + b) = wo + b s = t f(wo + b) = t wo b s w = o s b = 1 Finally, the LMS algorithm can be summarized in the following equations: w(k + 1) = w(k) + 2s(k)α o(k) where α is the learning rate. b(k + 1) = b(k) + 2s(k)α 14

22 2.2.5 Hessian Matrix and Convergence Analysis The Hessian Matrix for this algorithm is defined by [10]: where E is the expectation operator. R = E{ o 1 [ot 1]} The learning rate α defines the learning speed. If α is not chosen properly, the network system would not converge. It can be shown that if 0 < α < 1 λ max where λ max is the max eigenvalue of Hessian Matrix, the system is will converge. 15

23 Chapter 3 System Implementation To solve the problem and make the model practical, a leak simulation system was set up in the outer field. In the new system, microphones have been replaced by accelerometers in order to have a clean background. The system consists of two leak locations, two accelerometers, two pressure sensors, and two flow rate sensors, as shown in Figure 3-1. This chapter will discuss the new leak simulation system in Section 3.1. In Section 3.2, a data acquisition system including sensors and a microcontroller is described. Finally circuits that are used to interface the microcontroller and the sensors will be discussed, as well as the software that is used to implement the ANN algorithm. Accelerometer Water Pipe Sensor Node 1 Sensor Node 2 Flow Pressure Flow Pressure Figure 3-1 System Block Diagram 16

24 3.1 Modeling: Simulate the Leak In our experiment setups, water goes through ¾ PVC pipe, the length of which is over 70 feet long. There are two kinds of leak on the pipe. As shown in Figure 3-1, one leak (on the left) is an open-ending pipe and its size can be controlled by a valve. The vibration generated by the leak can be captured by accelerometers. The advantages of this leak type are (1) the size of the leak can be controlled; and (2) the signal generated by the leak is very strong that can be easily collected by the sensors. The disadvantage is that the acquired signal is very noisy; More specifically, the frequency spectrum of the signal changes when the size of the leak changes. Also, the leak signal can be affected by other elements such as wind. Another leak (on the right) is a hole drilled on the pipe. The diameter of the hole is 4 mm. Accelerometers are still used to collect the data. This kind of leak generates a very steady signal and it is hardly influenced by other elements. However, the signal that contains the leak information is so weak that it can be barely captured by the sensors. Figure 3-2 Leak Simulation 17

25 The reasons that we created the above two types of leaks are as follows. The first type of leak can be used to simulate the leak caused by the pipe aging, physical or chemical corrosion, and external conditions. This kind of leak usually has smaller size and then grows to a bigger size as time passed by. The second one is to simulate the leak generated by the joining methods. The size of this kind of the leak changes very slow compared with the first one. 3.2 Data Acquisition System There are three kinds of sensors in this model used to collect data. They are accelerometer, pressure sensor, and flow rate sensor. Both of them have analog outputs. Arduino is used as the microcontroller to convert these analog outputs to digital data and then transfer them to a PC Sensors ADXL203EB is an accelerometer manufactured by Analog Device as shown in Figure 3-2. It is powered by 5V dc. The measurement range is ±1.7g and the sensitivity is 1000mV/g. The output is analog voltage. The relationship between the output and the acceleration is defined in Figure

26 Figure 3-3 ADXL203EB Figure 3-4 Relationship between Output and Acceleration 19

27 19C300PA4K is pressure sensor manufactured by Honeywell as shown in Figure 3-4. It is powered by 15V dc. The measurement range is 0 pound per square inch (psi) to 300 psi, and the sensitivity is 0.5mV/psi. The output is analog voltage. The relationship between the output and the pressure is defined in Figure 3-5. Figure C300PA4K Figure 3-6 Relationship between Output and Pressure 20

28 FDT-32 is a transit time ultrasonic flow meter manufactured by Omega as shown in Figure 3-6. It is powered by 15V dc. The measurement range is one gallon per minute (GPM) to 55 GPM, and the sensitivity is mA/GPM. The output is analog current. The relationship between the output current and the flow rate is defined in Figure 3-7. Figure 3-7 FDT-32 Figure 3-8 Relationship between Output and Flow Rate 21

29 3.2.2 Arduino Board and Circuit Connection Arduino is an open-source electronics prototyping platform. The microcontroller on the board is programmed using Arduino language via Arduino software. The Arduino board used in this thesis is called Arduino Duemilanove. As shown in Figure 3-8, this microcontroller board is based on the ATmega328. It has 14 digital input/output pins, 6 analog inputs, a 16 MHz crystal oscillator, a USB connection, a power jack, and a reset button. In the experiments, the analog input pins are used to collect all kinds of data. Figure 3-9 Arduino Duemilanove The circuit design is shown in Figure 3-9. Since the Arduino analog inputs only accept the voltage between 0 to 5 volts, an amplifier with a gain 50 is applied to pressure sensor in order to convert its output to 0 to 4.5 volts, and also a 250-ohm resistor is added to the flow rate sensor in order to convert its output to the range of 1 to 5 volts. 22

30 23 Figure 3-10 Circuit Design for Data Collection

31 As depicted in Figure 3-9, analog input number 0 and 1 are set to Accelerometer 2 and analog input number 2 and 3 are set to Accelerometer 1. The output of the pressure sensor is connected to analog input 4 and the output of flow rate sensor is connected to analog input Arduino Programming Firstly these analog input pins are described as constants in Arduino language: const int y1pin = A3; const int x1pin = A2; const int y2pin = A1; const int x2pin = A0; const int flowpin = A4; const int pressurepin = A5; Then we initialize the serial communication: Serial.begin(9600); and read the pressure and flow rate data with: float flow = getvoltage(flowpin); float pressure = getvoltage(pressurepin); The signals x1, y1, x2, and y2 are separated by a tab space respectively. The sampling frequency is at 1000 Hz. The first column is x1, then y1, followed by x2 and y2. Each time 10-second data is collected, after that a 5-second pause is inserted. These data collections are realized with the code below: for (int i=0; i<1000; i++) { 24

32 Serial.print(analogRead(x1pin)); Serial.print("\t"); Serial.print(analogRead(y1pin)); Serial.print("\t"); Serial.print(analogRead(x2pin)); Serial.print("\t"); Serial.print(analogRead(y2pin)); Serial.print("\t"); Serial.println(); delay(1);} 3.3 MATLAB and Data Flow MATLAB is a programming environment for algorithm design, data analysis, etc. It is used in a very wide range of applications such as signal processing, communications, control, and system simulations. In this thesis, MATLAB is used to design a filter, process the signal, develop an algorithm, analyze data, and compute the results Data Preprocessing If the data contains only a dc value, the result of cross correlation is a triangle, which has the largest value at origin. Therefore, the data collected from accelerometers needs to eliminate the dc value. In MATLAB, by subtracting its mean, we can remove the dc component from the data. 25

33 3.3.2 Filter Design There are two reasons that filters are necessary before analyzing data. One reason is that there is always noise in signals. By filtering the data, some noise can be greatly weakened. Another reason is to eliminate the same signal that exists both in leak-free and leak conditions. By plotting the frequency spectrum of this signal, we can filter out this signal from the leak signal. The filter design tool syntax in MATLAB is fdatool and a screenshot is shown in Figure Figure 3-11 Filter Design and Analysis Tool 26

34 3.3.3 Signal Processing In this thesis, signal processing mainly means signal filtering. Some filters have high orders and cannot be converted to a single section for export to the workspace in MATLAB. Therefore, the Signal Processing Tool is used to filter the signal without exporting the filter to the workspace. The Signal Processing Tool window is shown in Figure Figure 3-12 Signal Processing Tool Data Flow in MATLAB In the first step, the data collected from the pressure sensor and the flow rate sensor are sent through a low pass filter (LPF) to filter out the noise. In the meantime, frequency spectrum of data from the accelerometer needs to be calculated. Secondly, design a MATLAB function to determine whether there is a leak based on single type of 27

35 sensor. Then the results from the second step are sent to a detection algorithm to recognize if a leak occurs. If the answer of former step is positive, use cross correlation and ANN to pinpoint the leak location. The whole data flow is shown in Figure Pressure Flow Rate Acceleromete LPF LPF Frequency Spectrum Check Leak/Non-leak Leak/Non-leak Leak/Non-leak Detection Non-leak Leak Cross Correlation ANN Leak Figure 3-13 Data Flow 28

36 Chapter 4 Data Analysis and Results In this chapter, we utilize and evaluate the procedures for detecting and localizing leaks that have been introduced in the previous chapters. Since the data analysis system is implemented in MATLAB, those procedures use offline data to simulate real time pipe monitoring, leak detecting and localizing. The key component of the research work conducted here is developing an ANN algorithm to localize the leak. This includes performance index choosing, weights and biases updating, LMS analysis while iteration, weights and biases analysis when in steady state, and finally the error analysis. We start with velocity test which is used to calculate the velocity of leak signal propagating along the pipeline. After that we introduce leak detection which includes the data preprocessing and the detection system. At last the leak localization system is described and its results are presented and discussed. 29

37 4.1 Velocity Test In order to apply the cross correlation method, the velocity of the leak signal travelling along the pipe needs to be calculated priorly Velocity Test Modeling Accelerometer1 Accelerometer2 Leak Water Pipe d = 2142 mm y1 y2 Water Pipe x1 x2 Figure 4-1 Schematic of Velocity Test As shown in Figure 4-1, one accelerometer is installed at the leak location, another one is d away. Each accelerometer measures acceleration in two directions which, as depicted in the above figure, are y1 and x1 for the accelerometer 1; y2 and x2 for the accelerometer 2. Once the lagged time, which is consumed by the leak signal traveling from accelerometer 1 to 2, has been captured by the cross correlation, the velocity can be easily calculated by the following equation: v = d t lag 30

38 4.1.2 Steps to Calculate Velocity and Results Due to the limit of the sampling rate, the minimum unit of lagged time this system can capture is 1 millisecond (ms), which results in an inaccuracy on velocity of the leak signal. Therefore, six experiments have been conducted and the lagged time is calculated as the mean of cross correlation. Unit: ms xcorr(y1,y2) xcorr(x1,x2) xcorr(y1,x2) xcorr(x1,y2) Test Test Test Test Test Test Table 4-1 t lag in Six Velocity Tests Table 4-1 shows the lagged time captured from different velocity tests. It is notable that the lagged time from xcorr(y1,y2) in test 2 is much larger than the others. Therefore it is assumed that this number is out of the range of lagged time and not counted in calculation of the lagged time. As a result, the time lag and the velocity are given as: t lag = = v = d = 2142 = s/s t lag Pipeline Monitoring System Pipeline monitoring system aims to supervise all the interested characteristics of the water distribution system. The purpose of surveying these data is to detect the leak as 31

39 soon as possible after it occurs and prevent it from growing to a break and causing more damage. In the model of this project, the interested characteristics include data collected from pressure sensor, flow rate sensor, and accelerometer. At first, these data are preprocessed by low pass filters and notched filters to filter out the noise. Then they are fed into check functions, which are designed for each type of the sensors, in order to detect the leak and tell how reliable the result is from each sensor Low Pass Filter Design Ideally, the flow rate should remain constant before or after the leak happens. From the frequency spectrum of flow rate, it is very clear to see that the frequency of the noise is around 43 Hz. Therefore the LPF for flow rate sensor has a stop frequency at 40 Hz. The frequency spectrum of flow rate and the filter for that is shown in Figure 4-2 and Figure 4-3 respectively. Figure 4-2 Frequency Spectrum of Flow Rate 32

40 Figure 4-3 Flow Rate Filter Similarly, the frequency of noise in pressure signal is around 32 Hz. Therefore the LPF for pressure sensor has a stop frequency at 30 Hz. The frequency spectrum of pressure signal and the filter for that is shown in Figure 4-4 and Figure 4-5 respectively. Figure 4-4 Frequency Spectrum of Pressure 33

41 Figure 4-5 Pressure Filter Notched Filter Design Unlike the pressure or flow rate data, the acceleration always exists on the pipe. It contains information not only from the leak, but from the other sources such as vibration caused by water flowing and pressure changing. The objective is to separate the interested information which is leak information. In this project, by comparing the frequency spectrum of leak and non-leak signal, two notched filters are designed. Figure 4-6 (a) and (b) shows the frequency spectrums of non-leak signal and leak signal respectively. By comparing the two, it is very clear that there is a signal at two specific frequencies generated when leak does not happen. This signal also exists when leak happens. Therefore two notched filters are designed to eliminate this signal. The two frequencies are at 192 Hz and 384 Hz respectively. 34

42 (a) (b) Figure 4-6 Frequency Spectrums of (a) Non-Leak Signal, and (b) Leak Signal 35

43 4.2.3 Check Function for Flow Rate and Pressure This check function utilizes data collected in 5 seconds with a sampling rate at 100 Hz (500 samples). It has three steps in this function: (1) dividing 500 samples into 50 parts; (2) calculating the mean of each part and saving the result as a vector; (3) approximating the result from step 2 with a first order polynomial. The criteria used by the check function for leak detection is the slope of the first order polynomial approximation. For the flow rate, as shown in Figure 4-7, the dots are the means of 50 parts and the line is the approximation of the data. It is very clear that the flow rate drops from 10.4 GPM to 10.1 GPM which implies there is a leak. Figure 4-7 Approximation of Flow Rate Data 36

44 For the pressure, similar to the flow rate as depicted in Figure 4-8, the approximation line indicates that the leak causes pressure-drop from about 25 psi to 24.7 psi. Figure 4-8 Approximation of Pressure Data However, since the noise cannot be eliminated, the result of this check function is not reliable if the leak is very small. Therefore, thresholds are set based on the slopes of approximation lines for non-leak flow rate and pressure data. Table 4-2 shows the slopes of approximation lines in 10 different leak free experiments. Based on this, the threshold is set to be , which means the leak occurs if the slope of the fitting line is less than In addition, the result of the check function is more reliable if the slope is far less than the threshold. On the contrary, it is really hard to tell whether the slope very close to 37

45 threshold is caused by leak or just by noise. Thus it is necessary to define a standard that demonstrates how reliable the result of check functions is. As shown in Table 4-3, the reliability is small if the slope is close to threshold and it becomes larger when the slope is away from threshold. Experiment Number Flow Rate Slope *e-03 Pressure Slope *e Table 4-2 the Slopes of Approximation Lines in 10 Leak-Free Experiments Range of Slope (m) m > > m > > m Reliability Unreliable Less reliable Reliable Table 4-3 the Reliability in Different Slope Ranges 38

46 Figure 4-9 Frequency Spectrum of Filtered Acceleration Check Function for Acceleration The check function for acceleration differs from the previous one. It analyzes the frequency spectrum of filtered acceleration data. If x-axis, whose magnitude is over 500, is not limited in the range 187 to 197 Hz and 379 to 389 Hz, the function will return 1 which means there is a leak, and 0 otherwise. As shown in Figure 4-9, the frequency spectrum in the four circles illustrates there is a leak Rules of Leak Detection System The basic idea of leak detection system follows 3 rules: (1) it is leak-free if the results from both flow rate and pressure are in the unreliable range; (2) it is leak if the results from both flow rate and pressure are in the reliable range; (3) otherwise the result depends on acceleration check function. 39

47 4.3 Leak Localization Accelerometer1 Leak d 1 (unknown) Leak Water Pipe d 2 (unknown) d = 2142 mm Accelerometer2 y1 Leak Water Pipe y2 x1 x2 Figure 4-10 Schematic of Leak Localization System Theoretically, the cross correlation function provides the accurate t lag. The distance between the leak location and accelerometer 1 can be calculated by using the equation given in the Section However, the interested information always comes with noises. To make it more accurate, an ANN algorithm is designed so that the noise can be minimized and the accuracy of the results can be improved Adaptive Linear Neuron Network (ADALINE) Y1 X1 Y2 X2 t yy t xx t yy t xx w b + f l ssssss oooooo Figure 4-11 Strcture of ADALINE 40

48 As depicted in Figure 4-11, y1, x1, y2, and x2 are the data collected from accelerometers. The relationship between first column and second column on the left is defined as: t yy t xx t yx xcorr(s1, s2) xcorr(x1, x2) = = t xcorr(s1, x2) lag = x l t xy xcorr(x1, s2) where x l is the system input. w and b are weight and bias of the system, respectively. The transfer function f l is purelin, which actually means pure linear and its transfer function is 1. The system output is the estimation of the time lag t lag and it can be defined in the following equation: t lag = f l (x l w + b) = t lag w + b Performance Index and Learning Rules In this system, the error is defined as following: The performance index is the LMS error: s(k) = T lag (k) t lag(k). F (x) = s 2 (k). Since the purpose of learning rules is to minimize the performance index, the directions of learning rules are the negative derivative of performance index with respect to the weights and biases respectively: [ s 2 (k)] wi = s2 (k) s(k) = 2s(k) w i (k) w i (k) = 2s(k) T lag(k) t lag(k) w i (k) T lag (k) t lagi (k)w i (k) b(k) = 2s(k) = 2s(k)t w i (k) lagi (k) 41

49 Similarly, [ s 2 (k)] b = s2 (k) b(k) = 2s(k) s(k) b(k) = 2s(k) Therefore, combined with the learning rate α, the learning rules can be written as: w i (k + 1) = w i (k) + 2αs(k)t lagi (k) b(k + 1) = b(k) + 2αs(k) Limitation of Learning Rate The learning rate defines how fast the algorithm converges. However, if the learning rate is chosen improperly, the system may spend infinite time to converge, which means the system is not stable. Therefore finding the limitation of learning rate is also the study of system stability. Assume that: R = E x l x l T = 1 n x(i)x(i)t And λ max is the maximum eigenvalue of R. It can be proven that if α satisfies that n i=1 0 < a < 1 λ max the system will converge, otherwise the system is not stable Training Procedures There are seven steps to train the system, there are listed as following: 1) set the bias equal to zero; 2) use the 80% previous database to update the weights; 42

50 3) use the rest 20% data to validate the results, and calculate the mean square error; 4) choose the set that has the least mean square error, and calculate the bias; 5) use the current database, weights, and bias to estimate the current leak location; 6) based on the estimation, localize the physical leak location; and 7) repeat step 2 when next leak happens. Previous Leak Data Current Leak Data Figure 4-12 Data Flow of Training Procedures Results In this section, signals with known leak information containing 100 sets of data, are used to train the weight and bias. Following the procedure step 1) to 6), we could finally have a better approximation of the leak location. The initial weights have been chosen as following: w = [ ] T 43

51 Actually, how the initial weight vector has been chosen is irrelevant to its final values. More results about this are discussed in Section The range of learning rate α is 0 < α < We chose α = 0.1. The final value of weight vector depends on the value of α. In other words, the weight vector changes if α changes. First, the bias is set to be zero. Then 80% data is randomly chosen from the database to train the weights. After 80 iterations, the weights shown in Figure 4-13 finally converged at w = The mean square error during the iterations is shown in Figure Figure 4-13 Weights during the Iterations 44

52 Figure 4-14 Mean Square Error during the Iterations In step 3), the rest 20% data from the database is used to validate the result. In the meantime, mean square error is calculated. In Table 4-4, the left two columns are the estimation of lagged time and the right two columns are corresponding mean square error. The physical lagged time of this initialization database is 1.15ms. The bias is calculated in step 4). In this procedure, the minimum mean square error needs to be found Table 4-4. In this experiment, the minimum mean square is shown in the red rectangle. The corresponding estimation of lagged time is ms. Therefore, the bias is calculated as following: b new = b old + 2αs l = ( ) =

53 Estimation of Lagged Time (Unit: ms) s l = t lag Mean Square Error *e Table 4-4 Validation and Its Mean Square Error Estimation of Lagged Time Data Set Number (Unit: ms) Mean Table 4-5 Estimation of Lagged Time for Ten Data Sets In step 5), the current leak location is estimated by applying the weight vector and bias to the ten sets of current leak data and then finding the mean of the ten estimations. These data is shown in Table 4-5. Based on the mean of the estimations, the estimation of the distance between accelerometer 1 and leak can be calculated. The physical leak location is found at 587mm away from accelerometer 1 based on d 1. d 1 = d vt lag 2 = = ss

54 4.4 More Discussions in Weight and Learning Rate This section discusses what would happen if the weights and α change Weight Figure 4-15 Weights Initialized at 0 Figure 4-16 Weights Training Initialized at Random Number 47

55 Figure 4-15 shows the weights training iterations initialized at 0. Figure 4-16 shows the weights are initialized at random numbers from 0 to 1. It is safety to conclude that, no matter where the weights start, they eventually converge to the similar value Learning Rate α condition: As mentioned in Section 4.4.3, the learning rate should satisfy the following 0 < α < 1 λ max The λ max in previous chapter is Therefore the range of α is 0 < α < Figure 4-17, Figure 4-18, and Figure 4-19 are the weights trained during iterations when α is 0.218, , and respectively. It is obvious that weights do not converge if α is out of its range. In addition, α cannot be too small, or it needs more iterations to converge which would increase the computational burden. Figure 4-17 Weight Training when α equals

56 Figure 4-18 Weight Training when α equals Figure 4-19 Weight Training when α equals

57 4.5 More Discussion in Training Database One feature of ANN is that more data is used in training, the better the results will be. However in our case, the above algorithm only utilizes data from previous one leak to train the weight and bias. The learning rate, which depends on the input vector, determines the convergence of the weights. Therefore we cannot simply apply all the previous leaks data to train the weights. In fact, there are three options here: (1) using the previous leaks data to train with different α repeatedly; (2) finding a universal α and then applying the entire past leaks data to train weights; and (3) changing the structure of ANN by adding more weights. Before carrying out these three approaches, a few experiments need to be conducted to simulate the leaks which should have already happened. Table 4-6 lists the statistics of these experiments. We assume that leak 0 has been used for initialization, leaks 1 through 4 have been already happened, detected and localized, and leak 5 is currently happening and not yet localized. d 1 is the physical distance between accelerometer 1 and leak location; T lag is the physical lagged time; and limit of learning rate. 1 λ max is the upper Leak 0 Leak 1 Leak 2 Leak 3 Leak 4 Leak 5 d T lag λ max Table 4-6 Statistics of Experiments 50

58 4.5.1 Repeatedly Training the System Using the Previous Data As depicted in Figure 4-20, the weights start to repeat themselves and become periodic when the previous leaks database is used to train the system repeatedly. They are not going to converge no matter how many times that the whole database is used repeatedly to train the system. Therefore, this option is inappropriate. Figure 4-20 Weight Training Using the Previous Database Repeatedly Training the System with an Universal Learning Rate This approach treats the inputs of past leaks database as one input vector and then, finds a universal learning rate that satisfies all the requirement for the leaks that already happened. According to the definition of learning rate, it has to satisfy all the conditions for different leaks respectively. 0 < α < The value of α is chosen as half of its upper limit, which is

59 Figure 4-21 Weight Training Using the Universal Learning Rate From Figure 4-21, it can be observed that the weights still do not converge. Therefore we can draw the conclusion that the weight training not only depends on the learning rate, but also relies on the target output which, in our algorithm, means the physical lagged time. The result also indicates that our ANN model is not sophisticated for the problem in consideration Adding More Weights In previous approaches, only one leak database is used during each algorithm cycle no matter how many leak databases are used totally. Thus the size of the weight remains the same which is a 1*4 vector. From the previous discussion, the weights do not converge due to the difference of learning rate or target output (physical lagged time). 52

60 However, if multiple leak databases are used in one algorithm circle, the size of weight vector grows as the increasing size of input increases. In this way, not only do the weights converge, but also all the previous leak databases are used in ANN. With more and more data used to train the system, the results are getting more and more accurate. Table 4-7 lists the statistics of four additional experiments which are used for verification. Leak6 Leak 7 Leak 8 Leak 9 d T lag λ max Table 4-7 Statistics of Additional Experiments As shown in Figure 4-22, bars on the left refer to the physical lagged time and bars on the right indicate the estimated lagged time. Figure 4-22 Physical and Estimated Lagged Times 53

61 Figure 4-23 shows the absolute value of errors for the estimations. It is obvious this number decreases when more leaks occur. From the figure we can see that the error increases at the third leak. In experiment 3, one accelerometer is installed very far to the leak location while the other one is installed very close to the leak. This indicates that the signal from accelerometer 1 is very weak and thus make the result less accurate as the other experiments. Ideally, the absolute value of error will always decrease when more data is fed into the training system. However, due to the noise and the low sampling rate, the error may increase occasionally and fluctuate around zero. Figure 4-23 Absolute Values of Errors 54

62 Chapter 5 Conclusion In this research work, a multi-sensor monitor system is designed to detect the leak and determine the leak location. In the meantime, this system effectively decreases the possibility of having false alarm and miss detection. However, the system can be improved further in the following ways. First of all, in the leak localization part, only data collected by the accelerometers are used to localize the leak, which make the results depend on the acceleration data. If one of the accelerometers is malfunctioning, the result is not reliable. Secondly, being exposed under the sun for a long time, the PVC pipe became soft and distorted; therefore the data may not be very accurate. In the future work, the localization part should include the information not only from accelerometers but from pressure sensors, flow rate sensors, and even other types of sensors. The algorithm should be redesigned so that the computational burden can be reduced. More importantly, the system should be installed in a practical water distribution system to test its application, get practical data, and then, make further improvements on the algorithms according to actual scenarios. 55