Novel EMD with Optimal Mode Selector, MFCC, and 2DCNN for Leak Detection and Localization in Water Pipeline

Abstract

Significant water loss caused by pipeline leaks emphasizes the importance of effective pipeline leak detection and localization techniques to minimize water wastage. All of the state-of-the-art approaches use deep learning (DL) for leak detection and cross-correlation for leak localization. The existing methods’ complexity is very high, as they detect and localize the leak using two different architectures. This paper aims to present an independent architecture with a single sensor for detecting and localizing leaks with enhanced performance. The proposed approach combines a novel EMD with an optimal mode selector, an MFCC, and a two-dimensional convolutional neural network (2DCNN). The suggested technique uses acousto-optic sensor data from a real-time water pipeline setup in UTAR, Malaysia. The collected data are noisy, redundant, and a one-dimensional time series. So, the data must be denoised and prepared before being fed to the 2DCNN for detection and localization. The proposed novel EMD with an optimal mode selector denoises the one-dimensional time series data and identifies the desired IMF. The desired IMF is passed to the MFCC and then to 2DCNN to detect and localize the leak. The assessment criteria employed in this study are prediction accuracy, precision, recall, F-score, and R-squared. The existing MFCC helps validate the proposed method’s leak detection-only credibility. This paper also implements EMD variants to show the novel EMD’s importance with the optimal mode selector algorithm. The reliability of the proposed novel EMD with an optimal mode selector, an MFCC, and a 2DCNN is cross-verified with cross-correlation. The findings demonstrate that the novel EMD with an optimal mode selector, an MFCC, and a 2DCNN surpasses the alternative leak detection-only methods and leak detection and localization methods. The proposed leak detection method gives 99.99% accuracy across all the metrics. The proposed leak detection and localization method’s prediction accuracy is 99.54%, precision is 98.92%, recall is 98.86%, F-score is 98.89%, and R-square is 99.09%.

1. Introduction

A water pipeline is the optimal and most productive mode of transporting water. However, the structure of pipelines deteriorates over time due to aging, corrosion, weather, and various external factors. This deterioration causes pipeline leaks, which lead to water wastage. A few pipeline incidents are given here to show the significance of water wastage. A significant water pipeline rupture occurred in Pune, India, resulting in the wastage of thousands of liters of water [1]. Another incident involved a leakage near Maharashtra Industrial Developmental Corporation (MIDC), India, where one lakh liters of water were wasted [2]. In Thane, Maharashtra, India, a burst water pipeline caused waterlogging in the area, creating obstacles for the residents [3].

Similarly, in Dehradun, India, a pipeline leak caused by human negligence resulted in the squandering of gallons of drinking water [4]. Additionally, in Erode, India, another pipeline leak led to the wastage of a substantial amount of water, measuring many lakh liters [5]. Further, another pipeline burst in a high-pressure water pipeline led to the entrapment of three people in Assam, India [6]. These incidents show that the water pipeline leak should be attended to as early as possible to minimize wastage with appropriate leak detection and localization methods.

The categories of pipeline leak detection and localization methods are exterior methods, interior methods, and visual or biological-based methods [7]. Visual or biological methods help to locate the leak more precisely, but they need constant and frequent monitoring. The exterior methods involve sensing devices to monitor the outer parts of the pipeline, whereas the interior methods deal with monitoring the inner parts of the pipeline. The exterior and interior methods give more precise detection and localization results but are more costly.

A few monitoring devices used in pipeline leak detection and localization are acoustic emission sensors [8,9,10,11,12,13,14,15,16,17,18,19], infrared thermography [20,21], microphones [22], CCTV, vibration sensors [23,24], accelerometers [25], pressure sensors [26,27,28,29], flow meters [30,31], and pipeline robots [32]. The acoustic emission and vibration sensors capture the vibration in the pipeline. Microphones record the sound created by the leak. At the same time, the flow meters estimate the amount of water flow. Infrared thermography captures the energy dissipated. CCTV captures the state of the issue through images. This paper utilizes the acousto-optic sensor data from a real-time setup to implement the proposed method. Like the acoustic emission sensor, the acousto-optic sensor captures the acoustic vibrations in the pipeline.

Widely used machine learning (ML) and DL algorithms to detect a pipeline leak are the support vector machine (SVM) [15,29,30,31], naïve Bayes (NB) [31], logistic regression (LR), decision tree (DT) [24,30,31,33], multi-layer perceptron (MLP), k-nearest neighbors (KNN) [24,34], random forest (RF) [18,24], gradient boosting [24], LightGBM [24], XGBoost [24], CatBoost [24], long short-term memory (LSTM) [35], and convolutional neural network (CNN) [8,9,10,14,16,17,20,21,22,23,36,37,38,39,40,41,42]. Data collected from acoustic emission sensors, acousto-optic sensors, microphones, and vibration sensors must be feature-extracted for ML classifiers like SVM, NB, and DT.

Xiao et al. implemented a leak detection mechanism for acoustic signal data after using wavelet denoising, feature extraction, and SVM [15]. The feature extraction techniques used were mean, standard deviation, crest factor, short-time entropy, kurtosis, skewness, frequency centroid, frequency band, peak frequency, wavelet mean frequency, and wavelet entropy. Using SVM for the extracted features, the achieved accuracy was 99.4%. Zeng et al. implemented a leak detection mechanism with an in-pipe optical fiber-based pressure sensor and impulse response function, achieving great accuracy [28]. Zhang et al. implemented a leak zone identification system using a multiclass SVM with pressure sensor data [29]. The highest accuracy obtained by the multiclass SVM was 98.07%.

Shravani et al. compared LR, DT, NB, SVM, and MLP to identify the best classifier to detect a leak using flow meters and obtained an accuracy of 95% with LR [31]. Further, Shravani et al. implemented a hybrid approach using SVM and MLP to improve flow meter-based leak detection accuracy [30]. The hybrid SVM-MLP combination gave a leak detection accuracy of 99%. Valizadeh et al. implemented KNN for pipeline leak detection with time-domain features and achieved a 94.34% correct classification rate [34]. Wang et al. designed a burst detection method using LSTM with flow meter data in district metering areas [35]. The LSTM detected the burst with 99.80% accuracy.

Lee et al. explored machine learning models like KNN, DT, RF, extra trees, gradient boosting, LightGBM, XGBoost, and CatBoost for leak detection in water pipelines using vibration sensors [24]. Time and frequency domain features were extracted and passed to these classifiers to detect leaks. The XGBoost gave the best leak detection accuracy of 99.79% among the classifiers. Nguyen et al. implemented a leak size identification system using an acoustic emission intensity index using RF [18]. The data were collected using an acoustic emission sensor. The b-value was extracted from the acoustic emission sensor data for the acoustic emission intensity index curve construction. After the leak was confirmed, the data were passed to the RF for leak size identification. The RF gave an accuracy of 99.2% for 18-bar pressure data. Ullah et al. implemented a leak detection mechanism using acoustic emission sensors with machine learning algorithms [19]. Twenty-five time and frequency domain features were extracted from the acoustic emission sensor data before passing them to the ML classifiers for leak detection. With the system, the overall classification accuracy achieved was 99%.

Types of CNN applied in pipeline leak detection are one-dimensional and two-dimensional. The data collected from acousto-optic sensors, acoustic emission sensors, microphones, and vibration sensors are one-dimensional and applied directly to one-dimensional CNNs. Further, the one-dimensional data are converted into two-dimensional data and applied with 2DCNN for leak detection. At the same time, the data collected by infrared thermography and CCTV are two-dimensional and can be applied directly by two-dimensional CNNs to detect a leak. Li et al. detected a pipeline defect using videos collected from a camera installed in the pipeline robot. The video was converted into grayscale, fed to the VGGNet for feature extraction, and the extracted features were then classified using a SVM [32].

Kang et al. proposed an architecture to detect a leak in a water pipeline using an ensemble 1DCNN-SVM with accelerometer data [25]. The 1DCNN performed the feature extraction process, and the SVM tailored in the 1DCNN detected the leak with great accuracy. Bohorquez et al. implemented a leak detection mechanism using a 1DCNN with pressure data [36]. The 1DCNN detected the leak with 95% accuracy. Further, Bohorquez et al. implemented a leak detection system using a 1DCNN with pressure sensor data. The 1DCNN detected the leak with a 0.59% average error [37]. Choi et al. implemented a mechanism to detect and classify leaks in water pipelines using pipeline vibrations [42]. The observed accuracy of leak detection and classification using the CNN was 95.8%.

A few methods that help to convert one-dimensional data to two-dimensional are mel-frequency cepstral coefficients (MFCCs) [10,14,17], Bartlet beamforming [43], Hilbert–Huang transform (HHT) [16], continuous wavelet transform (CWT) [8], scaleogram [8], short-time Fourier transform (STFT) [22], and spectrogram [23]. The MFCC is widely used in speech recognition to identify the speaker and tone. It helps capture the essential frequency parameters from the data. Using acoustic signals, Chuang et al. implemented a MFCC and 2DCNN to detect underground water pipelines and achieved good accuracy [10].

Similarly, Li et al. implemented MFCC and 2DCNN to detect gas pipeline leaks using acoustic emission data. The paper aims to improve the signal-to-noise ratio by introducing a discrete stochastic resonance approach [14]. Using a convolutional neural network, Tsai et al. implemented an AI-based leak diagnostic instrument for water pipelines [17]. The leak diagnostic module consisted of an acoustic vibration sensing unit and a communication module to capture the audio data. The communication module helped store the data in the cloud. The CNN helped detect the leak after extracting essential features using MFCC. With MFCC and CNN, the observed leak detection accuracy was 95%.

A few pipeline leak localization methods available are cross-correlation (CC) [44,45,46,47,48,49,50] and generalized cross-correlation (GCC) [11,12,13]. CC and GCC localize the leak based on time difference estimation. So, CC and GCC need two sensors to localize a leak. The data collected from the pipeline using sensors are noisy. A few noise removal methods used for noise removal are empirical mode decomposition (EMD) [11], independent component analysis (ICA) [12,13], and wavelet packet [13,49]. Pan et al. implemented a leak localization method using wavelet packet analysis and CC [49]. With this method, the achieved localization error was less than 8%.

Another leak localization method implemented by Kothandaraman et al. combined adaptive ICA with GCC using two acousto-optic sensors’ data and achieved an accuracy of 93% [12]. Further, to improve localization accuracy, Kothandaraman et al. introduced EMD-ICA and GCC using two acousto-optic sensors’ data and achieved an accuracy of 96.47% [11]. Furthermore, to improve the localization accuracy using two acousto-optic sensors’ data, Kothandaraman et al. implemented a wavelet packet-ICA-based GCC and achieved improved accuracy [13].

Research gaps and key findings identified in the literature survey are:

• The ML and DL algorithms have been explored only for pipeline leak detection with various sensor inputs.
• Even though the ML and DL have shown good leak detection accuracy, they have not been applied to localize leaks.
• Another critical advantage observed in the literature with ML and DL algorithms is that detection is possible with only one leak sensor.
• For localizing leaks, the most predominantly applied tool is cross-correlation. However, two sensors are needed for correlation, leading to an increase in system complexity.
• The existing leak detection and localization methods use two different architectures: ML/DL architecture for leak detection and cross-correlation for localization.
• The ML and DL detect the leak with reasonable accuracy, irrespective of the sensor used to collect data.
• With an appropriate denoising technique, the cross-correlation gives an improved accuracy.
• The MFCC helps to extract essential features and convert one-dimensional data to two-dimensional data.

The primary objective of this paper is to propose a novel standalone architecture to detect and localize leaks with a single sensor with more accurate leak detection and localization accuracy to overcome all the research gaps listed above. This paper proposes a novel EMD with an optimal mode selector, an MFCC, and a 2DCNN for detecting and localizing the leak with a single acousto-optic sensor. As EMD is the most potent denoising technique, this paper studies the variants of EMD before proposing a novel EMD with an optimal mode selector. The structure of this paper is as follows: (1) background study on pipeline leak detection methods, (2) experimental setup, (3) proposed leak detection and localization method, (4) results and discussion, and (5) conclusion.

2. Background Study on Pipeline Leak Detection Methods

2.1. Empirical Mode Decomposition (EMD)

Empirical mode decomposition (EMD) helps to denoise a signal by breaking it down into multiple IMFs and a residual component [51]. Each IMF has a part that oscillates at a single instantaneous frequency. The two primary conditions an IMF must satisfy are as follows:

• The extrema and zero crossing counts should be the same or not exceed one.
• The local maxima defines the envelope’s mean value. This envelope is zero at the energy point.

Algorithm 1 helps to obtain a set of IMFs and a residue. The sifting process continues, treating the $r_1\left(t\right)$ as a new signal until the primary conditions are satisfied. The highest frequency oscillations are in the first IMF, the further IMFs contain low frequencies, and the residue contains no frequency component. The original signal can be written with the IMFs and residues, as shown in Equation (1):

$$S\left(t\right)=\sum _{i=1}^n{I}_1\left(t\right)+r_n\left(t\right)$$

(1)

EMD is a dynamic data analysis tool that operates by adapting to the local characteristics of data, effectively capturing nonlinear, non-stationary oscillations. EMD functions as a filter bank with a dyadic structure. The only disadvantage of EMD is that the dyadic property cancels out when the data are intermittent.

Algorithm 1 EMD algorithm steps

Step 1: Identify the local minima and maxima in the observed signal Step 2: Using the cubic spline method to interpolate local extrema to obtain the lower and upper envelope Step 3: Calculate local mean lm1(t) for lower and upper envelopes Step 4: The first component f1(t) estimated by subtracting the lm1(t) from the original signal S(t). f1(t) = S(t) − lm1(t). Step 5: Check f1(t) satisfies both primary conditions. If it satisfies, then the component is first IMF. Step 6: If f1(t) does not satisfy the primary conditions, the f1(t) is considered as a new original signal, and the process repeats itself until f1(t) is a designated IMF I1(t). This process is known as sifting. The residue formula is r1(t) = S(t) − I1(t).

2.2. Ensemble Empirical Mode Decomposition (EEMD)

Ensemble empirical mode decomposition (EEMD) helps to resolve the mode mixing problem in EMD by introducing white noise to the signal [51]. The mode mixing problem occurs in EMD when the IMF includes significantly different scales during sifting. The added white noise helps extract the original signal from the data, even when the data are intermittent.

The introduction of a series of white noise nullifies each other in Algorithm 2, step 4. As a result, the necessary outcome stays within the dyadic filter windows, substantially reducing the likelihood of mode mixing and preserving the dyadic property. The disadvantage of EEMD is that the decomposition is incomplete, and there is a possibility of producing different number modes due to different signal-to-noise realizations.

Algorithm 2 EEMD algorithm steps

Step 1: Generate $\begin{array}{c}{S}^i\left(t\right)=S\left(t\right)+\beta W{n}^i\hfill \end{array}\mathit{,}\mathit{where}\begin{array}{c}\beta >0\hfill \end{array}\mathit{,}\mathit{and}\begin{array}{c}W{n}^i\hfill \end{array}\mathit{is}a\mathit{white}\mathit{noise}$ with zero mean unit variance Step 2: Decompose each $\begin{array}{c}{S}^i\left(t\right)\hfill \end{array}\begin{array}{c}(i=1,\dots ,I)\hfill \end{array}\mathit{completely}\mathit{by}\mathit{EMD}\mathit{and}$ obtain the modes $\begin{array}{c}{I}_k^i,\hfill \end{array}\mathit{where}\begin{array}{c}k=1,\dots K\hfill \end{array}$ indicated the mode. Step 3: Assign $\begin{array}{c}\left({\overline{I}}_k\right)\hfill \end{array}\mathit{as}\mathit{the}\begin{array}{c}{k}^{th}\hfill \end{array}$ mode (average of corresponding modes $\begin{array}{c}{\overline{I}}_k=\frac{1}{I}{\sum }_{i=1}^I{I}_k^i\hfill \end{array})of\begin{array}{c}S\hfill \end{array}$

2.3. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN)

CEEMDAN addresses the drawbacks of EEMD [51]. The CEEMDAN process is as follows: the first IMF and the first mode generation are the same as EEMD, and then, from the noise realization, the first residue is obtained. Then, the first EMD mode is computed with the ensemble of residues having different noise realizations. Then, these modes are averaged to obtain the second mode, and the next residue is generated. This process repeats until the stopping criterion.

Using Algorithm 3, iterating through steps 4 to 6 is continued until either the EMD cannot decompose the residue while satisfying the IMF criteria or the residue exhibits fewer than three local extrema. The final residue $r_k$ is obtained by the CEEMDAN as in Equation (2):

$$r_k=S\left(t\right)-\sum _{k=1}^K\widetilde{I_k}$$

(2)

The original signal $S\left(t\right)$ is as in Equation (3):

$$S\left(t\right)=\sum _{k=1}^K\widetilde{I_k}+r_k$$

(3)

Algorithm 3 CEEMDAN algorithm steps

Step 1: $\mathit{For}\mathit{every}\begin{array}{c}i=1,\dots ,I\hfill \end{array}\mathit{decompose}\mathit{each}\begin{array}{c}{S}^i\left(t\right)=S\left(t\right)+{\beta }_{0}W{n}^i\hfill \end{array}\mathit{using}\mathit{EMD}$ until the first mode and compute $\begin{array}{c}\widetilde{I_1}=\frac{1}{I}{\sum }_{i=1}^I{I}_1^i=\overline{I_1}\hfill \end{array}$ Step 2: $\mathit{For}\begin{array}{c}k=1\hfill \end{array}\mathit{obtain}\mathit{the}\mathit{first}\mathit{residue}\begin{array}{c}{r}_1=S\left(t\right)-\widetilde{I_1}\hfill \end{array}$ Step 3: Obtain the first mode of $\begin{array}{c}{r}_1+{\beta }_1{E}_1\left(W{n}^i\right),i=1,\dots ,I\hfill \end{array}$, define the second CEEMDAN mode using EMD $\begin{array}{c}\widetilde{I_2}=\frac{1}{I}{\sum }_{i=1}^I{E}_1(r_1+{\beta }_1{E}_1\left(W{n}^i\right))\hfill \end{array},\mathit{where}$ Ek(∗) is the operator produces the kth mode with EMD. Step 4: $\mathit{For}\begin{array}{c}k=2,\dots K\hfill \end{array}\mathit{estimate}\mathit{the}\begin{array}{c}{k}^{th}\hfill \end{array}\mathit{residue}\begin{array}{c}{r}_k=r_{(k-1)}-\widetilde{I_k}\hfill \end{array}.$ Step 5: Obtain the kth mode of $\begin{array}{c}{r}_k+{\beta }_k{E}_k\left(W{n}^i\right),i=1,\dots ,I\hfill \end{array}$ using EMD until defining the $\begin{array}{c}{(k+1)}^{th}\hfill \end{array}\mathit{CEEMDAN}\mathit{mode}\begin{array}{c}\widetilde{I_{(k+1)}}=\frac{1}{I}{\sum }_{i=1}^I{E}_1(r_k+{\beta }_k{E}_k\left(W{n}^i\right))\hfill \end{array}$ Step 6: Go to step 4 for the next k

2.4. Mel-Frequency Cepstral Coefficients (MFCC)

The mel-frequency cepstral coefficient (MFCC) method’s application is mainly in speech signal processing as a feature extraction technique for emotional state analysis [41]. Its application is extended to pipeline leak detection, as the data collected from a pipeline are a non-stationary signal [10]. The MFCC captures the frequency component from the time domain and represents it in both the time and frequency domains. Figure 1 shows the process of the MFCC.

Figure 1 gives detailed information on the process of MFCC extraction. First, the raw input signal is pre-emphasized. After that, the pre-emphasized signal is split into some frames. The frames are passed through the hamming window before performing the discrete Fourier transform (DFT). The DFT converts the time to the frequency domain representation. After the conversion into the frequency domain, the mel filter bank helps capture the frequency component in the way humans perceive the frequencies. After the filter bank application, the discrete cosine transform (DCT) helps convert the data into an aggregate of cosine functions oscillating at distinct frequencies. This DCT conversion helps to obtain MFCCs.

Equation (4) gives the formula for the DFT.

$$D\left(k\right)=\sum _{t=0}^{T-1}{I}_d\left(t\right)e^{-j2\pi k\frac{t}{T}}$$

(4)

where $t=0,1,2,\dots T-1$. The spectrum obtained from Equation (6) has a wide range. The leak signal does not apply on a linear scale. The mel filter bank helps to view the frequency level the way humans hear with the help of Equations (5) or (6).

$$mel\left(f\right)=2595lo{g}_{10}(1+\frac{f}{700})$$

(5)

$$mel\left(f\right)=1127ln(1+\frac{f}{700})$$

(6)

By applying a DCT on the log energy ($E_l$), ‘N’ MFCCs are obtained with triangular bandpass filters. Equation (7) gives the formula for the DCT.

$$D{C}_m=\sum _{c=1}^S\left(E_{l}cos(m*c-\frac{1}{2})\frac{\pi }{S}\right)$$

(7)

where $m=1,2,3,\dots N$, S is the count of log spectral coefficients, and N is the obtained MFCC. Chuang et al. introduced a leak-detection method using a MFCC and a 2DCNN for acoustic signals collected using listening devices [10]. The schematic representation of the same is in Figure 2.

The flow of the layers in the schematic shown in Figure 2 is input, convolutional, max pool, convolutional, max pool, fully connected, and output. The input for the 2DCNN architecture is the acoustic signal’s MFCC. The convolutional layer’s filter size is 32, with a kernel size of 2 × 2 and an activation function ReLU. The pool size of both max pool layers is 2 × 2. The number of neurons in the fully connected and output layers is 128 and 2, respectively.

3. Experimental Setup

For this paper, the experimental arrangement, located in UTAR, Malaysia, helped to collect data. The experimental configuration comprises a 1-kiloliter water reservoir, a water pumping system with a capacity of 4 kW, and a 40 m pipeline (galvanized iron) with specifications of inner, outer, and simulated leak aperture diameters of 80, 90, and 5 mm, respectively. The simulated leak diameter is 5 mm, and there is one acousto-optic sensor [52]. Five components of the acousto-optic sensor are a 980/1500 nm wavelength division multiplexer (WDM), a 980 nm pump, fiber laser cavity/sensing fiber, Erbium-doped fiber, and a photodetector. The 980 nm pump helps deliver the laser particles into sensing fiber via the 980/1550 nm WDM. The laser-filled sensing fiber on the pipeline measures acoustic vibrations, and the photodetector detects the vibration. The diagrammatic representation of the experimental arrangement is in Figure 3. Figure 4 shows a sensing fiber positioned on the aperture for leak simulation, and Figure 5 shows the experimental arrangement.

System specifications used to collect the data, data preprocessing, training, testing, and predicting, are below:

• Processor: AMD Ryzen 5 4600HS with Radeon Graphics, Nvidia GeForce GTX 1650Ti;
• Memory: 24 GB;
• System type: 64-bit operating system, x64-based processor;
• Operating system: Windows 11.

L in Figure 3 is the length between the leak aperture and the sensor. In the event of a pipeline leak, vibrations occur. The sensor records this vibration. This paper uses two sets of data, which are each split into four classes. The water pressure of the first set is 2-bar, and the second is 3-bar. At these two different pressures, the four classes of collected data are no leak, leak at a 1 m distance, leak at a 2 m distance, and leak at a 3 m distance. The non-leak data are captured with the sensor placed 1 m from the leak point on the pipeline setup with the leak aperture closed. Each set comprises 1200 data samples collected over a 50-millisecond interval. Thus, the recorded samples are 4800 in a single pressure set. Therefore, 9600 samples are in both pressure sets. The response changes based on the distances at which the sensors are connected.

4. Proposed Leak Detection and Localization Method

Four steps are involved in the proposed novel EMD with an optimal mode selector, an MFCC, and a 2DCNN. The proposed leak detection and localization method’s steps are as follows: (1) Decomposing the data collected from the sensor using EMD; (2) Using the novel optimal mode selector algorithm to choose the desired IMF based on the energy of the IMF; (3) Converting the one-dimensional data to two-dimensional data and extracting essential features using an MFCC by capturing the frequency components; (4) Passing the MFCCs to the 2DCNN for leak detection and localization. The proposed architecture’s workflow is shown in Figure 6.

4.1. Novel EMD with Optimal Mode Selector, MFCC, and 2DCNN

EMD helps to denoise any non-stationary signal, and the only problem with the EMD is its mode mixing. Contrarily, the EEMD and CEEMDAN aid in mitigating the issue of mode mixing. Although all three methods help to denoise, none gives a rule of thumb by which to select the appropriate IMF. This paper addresses this issue by proposing a novel EMD with an optimal mode selector for noise removal. The novel EMD with an optimal mode selector chooses the IMF automatically based on the energy value of the IMF. Equation (8) gives the formula for calculating the energy of a signal, and Figure 7 gives the flowchart of the novel EMD with an optimal mode selector. The novel EMD with an optimal mode selector algorithm is in Algorithm 4.

$$E=\sum _{n=-\infty }^{\infty }{\left|I_n\left(t\right)\right|}^2$$

(8)

where E is the energy calculated and $I_n\left(t\right)$ is the IMF. The average energy of the desired IMF ($I_d\left(t\right)$) is in

Table 1. The average energy of desired IMFs.

Sl No	Class	Average Energy (mV${}^2$)
1	No leak	328.16
2	Leak at a 1 m distance	2554.71
3	Leak at a 2 m distance	13,137.34
4	Leak at a 3 m distance	24,754.25

. The range of the average energy varies from −1000 mV${}^2$ to +1000 mV${}^2$ for each class.

Algorithm 4 Novel EMD with optimal mode selector algorithm steps

Step 1: Identify IMFs using the EMD algorithm Step 2: Leave the first IMF, as the first IMF is the predominant noise, and estimate the energy of the IMFs using the energy equation. Step 3: Choose the desired IMF Id(t) based on the required average energy listed in Table 1 ±1000 mV2 Step 4: Pass the Id(t) to the next level.

The EMD and the other EMD variants denoise any signal by identifying the local minima and maxima. The first IMF considers the highest frequency content captured from the signal. The frequency content reduces as the order of the IMFs increases. The desired energy of the frequency component that holds the information about the necessary pipeline leak data is in Table 1. The proposed novel EMD with an optimal mode selector is designed in such a way that it screens the signal and chooses the appropriate IMF. After selecting the optimal IMF, the one-dimensional data are feature-extracted and converted into two-dimensional data using MFCC. Then, the MFCC with the shape of 13 × 40 is converted and saved as a JPEG image with the dimensions of 640 × 480 and a resolution of 100 dpi in a folder with the name of the sample’s category name. Similarly, 9600 images of the novel EMD with an optimal mode selector and an MFCC are created and stored under their corresponding category names under both pressure sets.

4.2. 2DCNN

The layers in the proposed 2DCNN architecture in this study contain one input, five convolutional, four max pools, one flatten, two dense, and one output. A max pool layer follows each convolutional layer. A convolutional layer executes a convolutional operation involving the input to the layer along with its weights and bias, as described by the given Equation (9).

$$Con{v}_{out}=Conv(\sum A_{in}\ast w_i+\alpha )$$

(9)

where $Con{v}_{out}$ is convolutional layer-generated output, $A_{in}$ is the convolutional layer’s input, $w_i$ is the weight variable, and $\alpha$ is a bias variable. Convolutional layers can employ various activation functions, such as ReLU, sigmoid, tanh, and linear. Due to its ability to mitigate exponential computational growth, practitioners commonly use the ReLU function among these options, as defined in Equation (10).

$$R_{out}=Relu\left(Con{v}_{out}\right)$$

(10)

Equation (10) defines the ReLU function, which yields an output of either $max\left(Con{v}_{out}\right)$ or 0. Following the convolutional layer, a max pooling layer reduces the number of parameters.

$$M{P}_{out}=maxpool(R_{out},poolsize=n)$$

(11)

Equation (11) involves the max pool operation, which selects the maximum value from a set of pool size n. The last layer in a CNN is the classification layer, which categorizes according to the defined classes. The configurations and quantities of the convolutional and max pooling layers differ based on the specific applications. In general, the optimal kernel size is 3 × 3 and the kernel size is 1 × 1, which are applied for dimensionality reduction. When the kernel size is greater than 5 × 5, it leads to a longer training time. Meanwhile, the even kernel sizes of 2 × 2 and 4 × 4 do not have the same capacity as odd-size filters to divide the pixels in the previous layer more symmetrically. The filter size should grow gradually to learn the features appropriately.

Figure 8 shows the architectural diagram of a 2DCNN with its dimensions after considering the above criteria. The input layer dimension is 150 × 150 × 3. All the convolutional layer’s kernel sizes are 3 × 3. The convolutional layer’s filter sizes are as follows: (1) first convolutional layer—8, (2) second convolutional layer—16, (3) third convolutional layer—32, (4) fourth convolutional layer—64, and (5) fifth convolutional layer—128. The pool size of all max pool layers is 2 × 2. The first and second dense layers’ neuron sizes are 256 and 128, respectively. The output layer’s activation function is softmax, and the number of neurons is kept at four to match the categories the model is supposed to detect and localize the leak with. The optimizer used in this paper for this architecture is Adam, which is used to optimize the hyperparameters. The number of convolutional layers is kept at five because after five layers, the model overfits, and the model does not classify as accurate as with fewer layers. The flatten layer helps to convert the two-dimensional feature size of the convolutional layer to one dimension to make it suitable for the dense layers. The two dense layers help to reduce the dimension of the flatten layer gradually to keep the input to the output layer simpler.

5. Results and Discussion

This paper implements (1) MFCC–2DCNN [10], (2) MFCC with a proposed 2DCNN architecture, (3) EMD–MFCC with a proposed 2DCNN architecture, (4) EEMD–MFCC with a proposed 2DCNN architecture, and (5) CEEMDAN–MFCC with a proposed 2DCNN architecture to compare the performance of the proposed novel EMD with an optimal mode selector, an MFCC, and a 2DCNN. As the existing 2DCNN models are implemented only for leak detection, the proposed 2DCNN is also modified and implemented for detecting the leak only by keeping the number of neurons in the output layer as two. Similarly, the existing 2DCNN model’s output layer is modified to have four neurons in the output layer for leak detection and localization. Therefore, this paper implements six leak detection and localization models for 2-bar and 3-bar pressure sets. All the model’s epochs and batch sizes are set to 50 and 20, respectively. The train, test, and predict ratios, containing 4800 samples in each pressure dataset, are 80%, 16%, and 4%, respectively.

Implementing all the methods takes two steps: (1) data preparation, and (2) leak detection and localization. The times taken to process the MFCC, EMD–MFCC, EEMD–MFCC, CEEMDAN–MFCC, and the novel EMD with an optimal mode selector and MFCC are 819.26, 3748.15, 189,667.23, 395,188.37, and 3988.15 s, respectively. The times taken for the leak detection models 2DCNN [10] and the proposed 2DCNN are 504.12 and 356.22 s, respectively. Meanwhile, the time taken for the leak detection and localization models modified from the existing 2DCNN and the proposed 2DCNN is 1162.15 and 842.74, respectively. The assessment metrics used to evaluate the models’ performance are prediction accuracy, precision, recall, F-score, and R-square. The observation results are in

Table 2. Results for leak detection at 2-bar pressure.

Sl No	Models	Prediction Accuracy	Precision	Recall	F-Score	R2
1	MFCC–2DCNN [10]	96.95	96.23	95.98	96.1	96.78
2	MFCC-proposed 2DCNN	99.41	99.33	99.31	99.32	97.22
3	EMD–MFCC-proposed	99.68	99.58	99.58	99.58	98.33
	2DCNN
4	EEMD–MFCC-proposed	99.78	99.71	99.73	99.72	98.88
	2DCNN
5	CEEMDAN–MFCC-	99.98	99.97	99.87	99.92	99.97
	proposed 2DCNN
6	Proposed novel EMD	99.99	99.99	99.99	99.99	99.99
	with optimal mode
	selector, MFCC, and
	2DCNN

,

Table 3. Results for leak detection at 3-bar pressure.

Sl No	Models	Prediction Accuracy	Precision	Recall	F-Score	R2
1	MFCC–2DCNN [10]	97.53	96.68	96.12	96.39	96.78
2	MFCC-proposed 2DCNN	99.31	99.21	99.29	99.25	97.22
3	EMD–MFCC-proposed	99.72	99.62	99.69	99.65	98.88
	2DCNN
4	EEMD-MFCC-proposed	99.86	99.82	99.84	99.83	99.44
	2DCNN
5	CEEMDAN–MFCC-	99.89	99.91	99.92	99.91	99.88
	proposed 2DCNN
6	Proposed novel EMD	99.99	99.99	99.99	99.99	99.99
	with optimal mode
	selector, MFCC, and
	2DCNN

,

Table 4. Results for leak detection and localization at 2-bar pressure.

Sl No	Models	Prediction Accuracy	Precision	Recall	F-Score	R2
1	Modified MFCC–2DCNN	84.97	83.56	83.99	83.77	85.72
2	MFCC-proposed 2DCNN	90.56	89.98	89.05	89.51	90.12
3	EMD–MFCC-proposed	98.63	98.66	98.63	98.64	98.37
	2DCNN
4	EEMD–MFCC-proposed	98.82	98.81	98.76	98.78	98.68
	2DCNN
5	CEEMDAN–MFCC-	98.86	98.83	98.82	98.82	98.72
	proposed 2DCNN
6	Proposed novel EMD	99.53	98.89	98.85	98.87	99.01
	with optimal mode
	selector, MFCC, and
	2DCNN

and

Table 5. Results for leak detection and localization at 3-bar pressure.

Sl No	Models	Prediction Accuracy	Precision	Recall	F-Score	R2
1	Modified MFCC–2DCNN	85.42	83.56	83.99	83.77	85.72
2	MFCC-proposed 2DCNN	92.63	93.86	92.63	93.24	90.88
3	EMD–MFCC-proposed	98.79	98.67	98.69	98.68	98.01
	2DCNN
4	EEMD–MFCC-proposed	98.83	98.85	98.73	98.79	98.69
	2DCNN
5	CEEMDAN–MFCC-	98.93	98.88	98.83	98.85	98.77
	proposed 2DCNN
6	Proposed novel EMD	99.55	98.95	98.87	98.91	99.18
	with optimal mode
	selector, MFCC, and
	2DCNN

.

Table 2 and Table 3 give the leak detection results at 2-bar and 3-bar pressure, respectively. All the models give good results. The detection methods utilizing the noise removal methods give better accuracy, and the proposed novel EMD with an optimal mode selector, an MFCC, and a 2DCNN detects the leak with the best accuracy. Table 4 and Table 5 give the leak detection and localization results at 2-bar and 3-bar pressure. These tables clearly show the effect of the denoising techniques and the importance of the optimal node selector algorithm. The prediction accuracy, precision, recall, and F-score of the EMD variants are very close. The R-square metric helps to reveal how well the model fits and shows visible differences. The R-square metric value increases as the level of the EMD variant changes. The CEEMDAN gives a better R-square value than the EEMD and EMD. It shows that EEMD and CEEMDAN helped to solve the mode mixing issue. The proposed novel EMD with an optimal mode selector gives the best prediction accuracy, precision, recall, F-score, and R-square as the algorithm is designed to choose the optimal IMF based on the requirements. This paper also utilizes cross-correlation to validate the proposed novel EMD with an optimal mode selector, an MFCC, and a 2DCNN. Four samples from the 2-bar pressure dataset assist in implementing the cross-correlation. An additional twelve data samples are taken from the 2-bar set at a 1 m distance, as the cross-correlation needs two sensors for localization. The results of the cross-correlation are in

Table 6. Results of cross-correlation at 2-bar pressure.

Sl No	Actual Distance	Calculated Distance	Relative Error	Accuracy %
1	L1 = 1 L2 = 1	L1 = 1.007 L2 = 0.993	0.007	99.31
2	L1 = 1 L2 = 1	L1 = 1.133 L2 = 0.867	0.133	86.71
3	L1 = 1 L2 = 1	L1 = 1.108 L2 = 0.892	0.108	89.21
4	L1 = 1 L2 = 1	L1 = 1.221 L2 = 0.779	0.221	77.92
5	L1 = 1 L2 = 2	L1 = 0.985 L2 = 2.015	0.011	98.87
6	L1 = 1 L2 = 2	L1 = 0.928 L2 = 2.072	0.054	94.63
7	L1 = 1 L2 = 2	L1 = 1.162 L2 = 1.838	0.122	87.85
8	L1 = 1 L2 = 2	L1 = 0.928 L2 = 2.072	0.054	94.62
9	L1 = 1 L2 = 3	L1 = 0.694 L2 = 3.306	0.204	79.61
10	L1 = 1 L2 = 3	L1 = 1.253 L2 = 2.747	0.169	83.13
11	L1 = 1 L2 = 3	L1 = 0.824 L2 = 3.176	0.117	88.27
12	L1 = 1 L2 = 3	L1 = 1.012 L2 = 2.988	0.008	99.27
Average accuracy				89.95

.

Table 6 lists the cross-correlation results along with the relative error and accuracy. Among the results, the highest observed accuracy is 99.31%, the lowest observed accuracy is 77.92%, and the average accuracy is 89.95%. The average accuracy of the cross-correlation is closer to the localization accuracy of the modified existing MFCC–2DCNN. The results conclude that the proposed novel EMD with an optimal mode selector, an MFCC, and a 2DCNN detects and localizes the leak more accurately at the two different pressures than all of the other methods discussed in this paper.

6. Conclusions

In conclusion, this paper significantly contributes to water pipeline leak detection and localization by introducing a novel and practical approach. This paper’s proposed independent pipeline leak detection and localization architecture comprises a novel EMD with an optimal mode selector, an MFCC, and a 2DCNN with a single acousto-optic sensor. This paper also implemented a modified existing MFCC–2DCNN, variants of EMD–2DCNN, and cross-correlation to validate the leak localization credibility of the novel EMD with an optimal mode selector, an MFCC, and a 2DCNN. The findings demonstrate that the novel EMD with an optimal mode selector, an MFCC, and a 2DCNN gives higher leak detection and localization accuracy than traditional signal processing and state-of-the-art DL techniques. The EMD variants help to overcome the mode mixing problem in EMD. Even though the EMD variants denoise more accurately, the time taken for the EMD variants to denoise is very high. The proposed novel EMD with optimal mode selector helps to denoise more accurately in less time. Since the novel EMD with an optimal mode selector, an MFCC, and a 2DCNN detects and localizes the leak at different pressures with similar accuracies, the proposed method is reliable. The proposed method localizes the leak accurately at the new location within the specified range. If the range of the unknown location is exceeded, then it will not localize accurately. This issue can be resolved by introducing more datasets with different locations.