Synthetic Leak Data Generation Using Variational Autoencoders to Address Data Imbalance in Acoustic Emission-Based Pipe Leak Detection

Featured Application

The proposed method can be applied beyond pipe monitoring to structural monitoring and the detection of abnormal states that may occur during the manufacturing process.

Abstract

A synthetic data generation method is proposed to mitigate data imbalance in pipeline leak detection using acoustic emission (AE) sensors. Collecting sufficient AE signals in the leak state is challenging due to the rarity of leaks and safety concerns. The rarity of leaks leads to highly imbalanced datasets. The performance of leak detection methods may be degraded because the models tend to be biased towards the normal state. The proposed method utilizes a variational autoencoder (VAE) to probabilistically model the difference between the normal-state and leak-state spectrograms. After training the VAE with the spectrogram differences, the decoder of the VAE generates spectrogram differences from random latent vectors. Synthetic leak-state spectrograms are created by adding the generated spectrogram differences to normal-state spectrograms. The effectiveness of the proposed method is evaluated by comparing the leak detection performance of models trained with and without the proposed method. A leak detection model trained with synthetic leak data generated by the proposed method shows improved detection performance compared to models trained using existing oversampling methods.

1. Introduction

Pipes are widely used in manufacturing facilities and chemical plants to efficiently transport gases or liquids. However, if a leak occurs, it can lead to major accidents causing casualties or environmental pollution. Therefore, real-time monitoring of vibrations generated by the pipes is necessary for early leak detection [1,2].

Various sensors are used to monitor the condition of pipes, such as flow meters, pressure sensors, fiber-optic sensors, and acoustic emission (AE) sensors [3,4,5,6]. Among these sensors, AE sensors are suitable for collecting vibration signals from a pipe because they can detect small high-frequency vibrations despite their compact size and low power consumption [7,8]. AE sensors made of flexible materials can be attached to curved pipe surfaces to collect AE signals effectively [9]. However, signals collected by AE sensors contain ambient noise from various sources in manufacturing facilities or chemical plants because of their high sensitivity [10].

Various machine learning-based leak detection methods have been proposed [11,12]. To train models of these methods, a dataset containing both normal-state and leak-state signals is required. However, collecting such a dataset from real manufacturing facilities or chemical plants presents challenges. For effective training of a leak detection model, a dataset containing both normal-state and leak-state signals is required. Collecting signals from AE sensors during normal operation is relatively easy in real manufacturing facilities or chemical plants where pipes are actively in use. In contrast, collecting AE signals during leakage events is considerably more challenging. This is because leaks rarely occur in practice, and intentionally inducing leaks for data collection is restricted due to safety concerns. As a result, depending on the data collection environment and conditions, it may be possible to collect only a small number (one or a few) of leak-state signals. This often leads to a significant imbalance between normal-state AE signals and leak-state AE signals. In practice, the ratio of normal-state signals to leak-state signals can easily reach 100:1 or even higher. If the imbalance issue is not addressed, the leak detection performance of the trained models may be degraded because the models are biased towards the normal state.

To address the imbalance issue, this paper proposes a synthetic leak data generation method. Unlike the existing oversampling methods that rely on simple duplication or interpolation of the limited leak-state data [13,14], the proposed method generates synthetic leak-state data by probabilistically modeling the difference between normal and leak states. First, both normal and abnormal data are converted into spectrograms [15], and the differences between these spectrograms are calculated. Second, these spectrogram differences are used to train a variational autoencoder (VAE) [16]. The probabilistic distribution of the spectrogram differences is learned through the encoder–decoder architecture of the VAE. Finally, the decoder of the trained VAE generates spectrogram differences. The generated differences are then added to the normal-state spectrograms to synthesize leak-state spectrograms.

The proposed method assumes a scenario where normal-state data is abundant and abnormal-state data is very limited. In this scenario, the proposed method mitigates data imbalance by generating a large amount of synthetic leak-state data from a small amount of real leak-state data along with abundant normal-state data. The proposed method is an oversampling strategy used to reduce the class bias of leak detection models. It does not alter the prior probability of leak events in real-world environments. If the proposed method is applied appropriately, it can reduce the false detection rate by improving the discrimination boundary characteristics. Experimental results support the effectiveness of the proposed method in improving leak detection performance by reducing the false detection rate. The applications of the proposed method can be extended beyond pipe leak detection to include monitoring other manufacturing equipment.

This paper is organized as follows. In Section 2, related work on pipe leak detection using AE sensors and data imbalance handling methods is reviewed. Section 3 describes the data acquisition process using AE sensors in a testbed that simulates pipe leaks. Section 4 explains the proposed method for synthetic leak-data generation using VAE. Section 5 presents experimental results that validate the effectiveness of the proposed method. Section 6 discusses conclusions and future works.

2. Related Work

2.1. Pipe Leak Detection Using Acoustic Emission Sensors

Various methods have been proposed to detect pipe leaks using AE sensors. The proposed methods commonly employ an approach that extracts features from AE signals containing noise, and then uses a classifier to detect leaks using the extracted features. A leak detection method using support vector machines (SVMs) with rough set theory and artificial bee colony (ABC) has been proposed [17]. Wavelet double thresholding has been proposed to remove white noise from AE signals before feature extraction [18]. Capturing the unique time-frequency signature generated by leaks in AE signals using short-time Fourier transform (STFT) and tuned wavelet transform has been proposed to detect pipe leaks [19]. A method has been proposed to detect leaks by applying K-means clustering to the intrinsic mode function (IMF) containing leak signals after decomposing AE signals using empirical mode decomposition (EMD). The reliability of the detection results was verified by the consistent distribution of statistical features within the clusters identified as leaks [20]. A pipe leak detection method has been proposed to accurately estimate the time delay of AE signals by integrating the energy and frequency characteristics of AE signals based on the wavelet transform [21]. End-to-end leak detection using a convolutional neural network (CNN) has been proposed [22]. Widely used CNN architectures such as ResNet18 have been employed to detect pipe leaks using spectrograms of AE signals [23]. A CNN–LSTM hybrid model using scalogram images generated by continuous wavelet transform (CWT) has been proposed for pipe leak detection [24].

The methods described above generally require sufficient acquisition of both normal-state data and leak-state data during model training to accurately detect pipe leaks.

2.2. Data Imbalance Handling

Although its severity depends on the data collection environment and conditions, data imbalance is difficult to avoid when training classification models. The ideal strategy is collecting a sufficient amount of data for each class, but this is often impractical. Consider the leak detection problem in pipes addressed in this paper. Data collection under normal operating conditions is relatively straightforward, whereas collecting data under leak conditions is considerably more challenging. As a result, acquiring a balanced number of data points for both normal and leak states is difficult.

To address the data imbalance issue, various methods have been proposed for handling data imbalance when training classification models. One common approach involves assigning different weights to the minority and majority classes when calculating the loss. This reduces the influence of the majority class [25,26].

Undersampling and oversampling methods have been proposed to resolve the imbalance issue at the data level. Random undersampling removes samples from the majority class in a random manner until the number of samples in the majority class matches that of the minority class [27]. Tomek Links deletes the data point belonging to the majority class when two data points are the closest neighbors but belong to different classes [28]. Unlike random undersampling or its variants, oversampling methods generate new data points from the minority class until the number of samples in the minority class matches that of the majority class. Random oversampling simply duplicates existing data points in the minority class [14]. Synthetic minority oversampling technique (SMOTE) is one of the most widely used methods. New data points are generated by interpolating between existing minority class data points [29]. Adaptive synthetic sampling (ADASYN) is an approach that improves SMOTE to generate more data points from hard-to-classify minority data [30].

The methods mentioned above may not be effective when the minority class data is too small or when the data has high dimensionality [29].

3. Data Acquisition

Collecting leak data from gas pipelines in operational settings is difficult and dangerous. Therefore, a testbed was constructed using a 35 mm galvanized pipe, similar to those used in actual manufacturing facilities, to simulate leaks (Figure 1). Nitrogen gas is injected at one end of the pipe, and a gas leak that commonly occurs at flange connections between pipes in chemical plants can be simulated by loosening the flange at the opposite end. The pressure of the injected nitrogen gas controls the flow rate of the leak. Normal-state data is collected when the flange is securely tightened (zero-leak flow), while leak-state data is collected when the flange is loosened to simulate a leak. The flexible AE sensor [9] was attached 150 mm from the leak location. The sensor is a prototype manufactured by Rina Solution [31]. A flexible AE sensor is fabricated with a three-layer thin-film structure. The outer layer consists of electrodes for signal transmission and polyimide. The sensor is 0.2 mm thick, and its first resonant frequency is approximately 20 kHz [9]. The middle layer is made of piezoelectric PZT fibers embedded in epoxy, which convert mechanical vibrations into electrical signals. Signals collected by the AE sensor are amplified with a gain of 40 dB and then sampled at 200 kHz. Figure 2 shows the normal- and leak-state AE signals collected from the testbed.

The collected AE signal is converted into a spectrogram [15]. A spectrogram represents the frequency variation of a signal over time in a two-dimensional time-frequency domain by applying STFT [32] to a one-dimensional time-domain signal.

A collected AE signal is represented as $s\left[n\right]$:

$$S=\left\{s\right[0],s[1],\dots ,s[N-1\left]\right\}.$$

(1)

The AE signal is divided into overlapping frames. The m-th frame signal $s_m\left[l\right]$ is represented as

$$s_m\left[l\right]=s[l+mH],l=0,1,\dots ,L-1,$$

(2)

where H and L are the hop size and frame length, respectively.

The windowed m-th frame signal $x_m\left[l\right]$ is obtained by multiplying the frame signal $s_m\left[l\right]$ with the window function:

$$x_m\left[l\right]=s_m\left[l\right]·w\left[l\right],$$

(3)

where $w\left[l\right]$ is the window function to reduce spectral leakage [33] caused by the discontinuities at the edges of each frame.

$$w\left[l\right]=a_0-a_{1}cos\left({\displaystyle \frac{2\pi l}{L-1}}\right),$$

(4)

where $a_0$ and $a_1$ are constants of the window function. The windowed signal $x_m\left[l\right]$ is transformed into the frequency representation $X(m,k)$ by applying the discrete Fourier transform (DFT) [34]:

$$X(m,k)=\sum _{l=0}^{L-1}{x}_m\left[l\right]exp\left(-j{\displaystyle \frac{2\pi kl}{L}}\right),k=0,1,\dots ,L-1.$$

(5)

The frequency representation $X(m,k)$ is converted into the spectrogram $P(m,k)$ by calculating the squared magnitude:

$$P(m,k)={\left|X(m,k)\right|}^2.$$

(6)

Figure 3 shows spectrograms of the normal and leak states of the AE signals. Compared to the spectrograms in the normal state, those in the leak state exhibit increased signal responses across multiple time frames and frequency bins.

The normal-state spectrograms above (Figure 3a) show a small number of dominant frequency components maintaining constant positions and intensities throughout time with low background noise. In contrast, the leak-state spectrogram in Figure 3b reveals that the dominant frequency components’ energy has dispersed and noise has increased across a broad frequency range.

4. Synthetic Leak Data Generation

4.1. Difference of Spectrograms

The proposed method mitigates the data imbalance issue by synthesizing the spectrograms of the leak state using multiple normal-state spectrograms and a limited number of leak-state spectrograms. For this purpose, the differences between the leak-state and the normal-state spectrograms are initially calculated (Figure 4).

$$D_{i,j}=P_i-P_j,P_i\in {\mathcal{P}}_{leak},P_j\in {\mathcal{P}}_{normal},$$

(7)

where $D_{i,j}$ is the difference-of-spectrogram (DoS) image calculated by subtracting the normal-state spectrogram $P_j$ from the leak-state spectrogram $P_i$.

The number of leak-state spectrograms is much lower than that of normal-state spectrograms because the acquisition of leak-state spectrograms is more difficult than that of normal-state spectrograms:

$$|{\mathcal{P}}_{leak}|\ll |{\mathcal{P}}_{normal}|.$$

(8)

Although the number of leak-state spectrograms is far lower than the number of normal-state spectrograms, a large number of DoS images can still be computed and then used to train the VAE model. This is because the total number of possible leak–normal spectrogram pairs is $|{\mathcal{P}}_{leak}|\times |{\mathcal{P}}_{normal}|$. Figure 5 shows examples of DoS images by subtracting normal-state spectrograms from leak-state spectrograms.

4.2. Training of Variational Autoencoder Using Differences-of-Spectrogram Images

If a DoS image can be generated, it can be combined with a normal-state spectrogram to synthesize the leak-state spectrogram. VAE is used to synthesize DoS images by modeling the probabilistic distribution of the DoS images (Figure 6). VAE is one of the generative models. By transforming input data into a latent space and then sampling from that space, VAE reconstructs the input data [16].

A VAE model has three components: an encoder, a latent space module, and a decoder (Figure 6). The distribution of the training data D is mapped to a probabilistic distribution in the latent space by the encoder:

$$q_{\varphi }\left(z\right|d):D\to Z,$$

(9)

where $q_{\varphi }\left(z\right|d)$ is the encoder network parameterized by $\varphi$, d is the input DoS image, and z is the latent variable. $\mu$ and $\sigma$ are the mean vector and standard deviation vector of the distribution in the latent space, respectively.

By using the reparameterization trick, the latent space module samples the latent variable $\tilde{z}$ from the distribution:

$$\tilde{z}=\mu +\sigma \odot ϵ,ϵ\sim \mathcal{N}(0,I),$$

(10)

where $ϵ$ is a random vector sampled from $\mathcal{N}(0,I)$. The decoder reconstructs the input data from the latent variable $\tilde{z}$:

$$p_{\theta }\left(d\right|\tilde{z}):\tilde{Z}\to D,$$

(11)

where $p_{\theta }\left(d\right|\tilde{z})$ is the decoder network parameterized by $\theta$.

To compute the parameters of the VAE model, the following loss function is used [35]:

$$L=-{\mathbb{E}}_{q_{\varphi }\left(z\right|d)}[log{p}_{\theta }\left(d\right|z)]+\beta D_{KL}(q_{\varphi }\left(z\right|d)\parallel p\left(z\right)),$$

(12)

where $p\left(z\right)$ is the prior distribution of the latent variable, and $D_{KL}$ is the Kullback–Leibler divergence (KLD) [36]. $\beta$ is a weighting factor that balances the two terms in the loss function. The first term is the reconstruction loss. The second term is the KLD between the latent distribution produced by the encoder and the prior distribution $p\left(z\right)=\mathcal{N}(0,I)$.

Table 1. Architecture of the encoder.

Layer Name	Kernel	Output Shape
conv2d	3 × 3, 512, stride 2	128 × 64
conv2d	3 × 3, 256, stride 2	64 × 32
conv2d	3 × 3, 128, stride 2	32 × 16
conv2d	3 × 3, 64, stride 2	16 × 8
conv2d	3 × 3, 32, stride 2	8 × 4
linear	-	1024

,

Table 2. Architecture of the latent space module.

Layer Name	Kernel	Output Shape
linear (mean)	-	128
linear (logvar)	-	128
reparameterization	-	128

and

Table 3. Architecture of the decoder.

Layer Name	Kernel	Output Shape
decoder input	-	1024
pixel shuffle	3 × 3, 64, stride 2, upscale 2	16 × 8
pixel shuffle	3 × 3, 128, stride 2, upscale 2	32 × 16
pixel shuffle	3 × 3, 256, stride 2, upscale 2	64 × 32
pixel shuffle	3 × 3, 512, stride 2, upscale 2	128 × 64
interpolation	bilinear, upscale 2	256 × 128
	3 × 3, 1, stride 1

show the detailed architectures of the encoder, latent space module, and decoder, respectively. DoS images are normalized to the range $[0,1]$ before training the VAE model, and then resized to 256 × 128 pixels. The encoder has five convolutional layers and one linear layer (Table 1). The latent space module has two linear layers to produce the mean and log-variance vectors and a reparameterization layer to sample the latent variable (Table 2). The decoder consists of four pixel shuffle layers and one interpolation layer (Table 3). The pixel shuffle layers [37] are used to upsample the feature maps to reduce checkerboard artifacts that may occur during the upsampling process. The interpolation layer is used to refine the upsampled feature maps and produce the final output DoS images.

Every layer in the VAE model, except for the interpolation layer in the decoder, uses Leaky ReLU as the activation function [38]. To normalize the output values of the interpolation layer between 0 and 1, the sigmoid function is used as its activation function.

After training, the decoder of the VAE model is used to generate DoS images from randomly sampled latent variables [16]. The generated DoS images are denormalized to the original scale, and then added to randomly sampled normal-state spectrograms to synthesize leak-state spectrograms. Synthetic leak-state spectrograms are generated by adding the generated DoS images to normal-state spectrograms (Figure 7).

4.3. Training of Leak Detection Models

Synthetic leak-state spectrograms can be used to resolve the imbalance of data between normal and leak states. When training a supervised leak detection model, generated leak-state spectrograms are used along with real leak-state spectrograms whose number is far lower than that of normal-state spectrograms (Figure 8).

5. Experimental Results

The effectiveness of the proposed method was evaluated under a severe data imbalance scenario where normal data were abundant and leak data were extremely limited. This assumption reflects the practical constraint that obtaining sufficient leak data from gas pipelines in real manufacturing facilities or chemical plants is challenging. To reflect the constraint and verify that the proposed method can effectively work under conditions where only an extremely limited number of leak-state data points are available, a highly challenging experimental setting was intentionally designed by restricting the number of leak-state spectrograms to just two.

The prototype flexible AE sensor [31] (Rina Solution, Cheonan-si, Chungcheongnam-do, Republic of Korea) was used to collect AE signals from the testbed. Each AE signal was collected at a sampling rate of 200 kHz for 1 s in the testbed and downsampled to 144 kHz before converting to a spectrogram. The flow rate of the leak was set to 4 L/min, which corresponds to a small-scale leak [39], by loosening the flange in the testbed for collecting leak-state AE signals. The parameters used for the STFT to convert the AE signals into spectrograms are shown in

Table 4. STFT parameters for converting AE signals into spectrograms.

Parameter	Value
Frame length	1024
Hop size	512
Window type	Hann window

.

5.1. VAE Model Training Using Differences-of-Spectrogram Images

PyTorch (2.7.1) was used to implement the VAE model, and it is trained on a computer with an NVIDIA GeForce RTX 3090 GPU (NVIDIA Corporation, Santa Clara, CA, USA).

Before training the VAE, DoS images were generated using normal-state spectrograms and leak-state spectrograms. A total of 2300 DoS images were created from 1150 normal-state spectrograms and two leak-state spectrograms.

The VAE model was trained for 500 epochs. AdamW optimizer was used for training the VAE model with a learning rate of 0.0001 and a batch size of 32. The weighting factor $\beta$ in the loss function was set to 0.001 to balance the reconstruction loss and the KLD. The input size of the VAE model was set to 256 × 128 by resizing the DoS images.

Samples of the generated DoS images are shown in Figure 9. The generated DoS images seem to have similar patterns to the real DoS images shown in Figure 5. This indicates that the VAE model has learned the distribution of the real DoS images and the decoder of the VAE model can generate DoS images that follow the learned distribution.

5.2. Leak Detection Models

The decoder of the trained VAE model was used to generate synthetic DoS images. The synthetic leak-state spectrogram was generated by adding the generated DoS images to normal-state spectrograms sampled from a statistical model defined by the mean and variance of the normal-state spectrograms. Figure 10 shows examples of the generated synthetic leak-state spectrograms. This figure demonstrates that the proposed method can generate diverse synthetic leak-state spectrograms by combining different normal-state spectrograms with generated DoS images.

The magnified view of real and synthetic leak-state spectrograms (Figure 11) shows that the synthetic leak-state spectrograms have similar characteristics to the real leak-state spectrograms. Both the real leak spectrograms on the left and the synthetic leak spectrograms on the right show multiple high-energy responses resembling broken bands in the mid-to-low frequency range, along with weak energy responses appearing as noise-like patterns around them. This similarity indicates that the synthetic leak-state spectrograms effectively mimic the distinctive characteristics of the real leak-state spectrograms.

Two hundred normal-state spectrograms and two real leak-state spectrograms were used to train the leak detection model. To mitigate data imbalance, 198 synthetic leak-state spectrograms were generated using the proposed method, random oversampling [27], SMOTE [29], and ADASYN [30]. The generated synthetic leak-state spectrograms were combined with the real leak-state spectrograms to create a balanced training dataset. We also used the unbalanced dataset without oversampling as a baseline to compare the performance of the proposed method and other oversampling methods. Four different leak detection models were implemented: (1) logistic regression, (2) decision tree [40], (3) support vector machine (SVM) [41], and (4) gradient boosting [42]. One thousand normal-state spectrograms and 1000 leak-state spectrograms were used as the test dataset to compare the performance of the trained leak detection models. Before training the leak detection models, the spectrograms were flattened into one-dimensional vectors, and the dimensionality was reduced using principal component analysis (PCA) to 128 dimensions because spectrograms have high dimensions (256 × 128) [43].

The performance of leak detection models trained using the proposed method and other oversampling methods is compared in

Table 5. Leak detection performance comparison under different oversampling methods when the input vector dimension is 128. The “Baseline” column indicates the performance obtained using the original dataset without oversampling. Upper values in each cell indicate accuracies, and lower values indicate F1-scores.

Model	Oversampling Method
	Baseline	Random	SMOTE	ADASYN	Proposed
Logistic Regression	0.901	0.890	0.890	0.889	0.990
	0.901	0.901	0.901	0.900	0.990
Decision Tree	0.518	0.519	0.519	0.519	0.973
	0.037	0.071	0.071	0.071	0.972
SVM	0.500	0.585	0.629	0.630	0.926
	0.000	0.289	0.409	0.413	0.920
Gradient Boosting	0.518	0.543	0.543	0.543	0.973
	0.037	0.157	0.157	0.157	0.972

. The table shows accuracies and F1-scores of leak detection models trained using naive (no oversampling), random oversampling, SMOTE, ADASYN, and the proposed method. The proposed method outperforms the other oversampling methods across all four leak detection models. Both the accuracies and F1-scores are higher when the models are trained using the proposed method. When trained using other oversampling methods, the logistic regression model achieves higher accuracy and F1-score than the other models, but its performance is still lower than that of the models trained using the proposed method. In contrast, decision tree, SVM, and gradient boosting show poor performance when trained using other oversampling methods. However, these models show considerable performance improvements when trained using the proposed method.

The performances of SMOTE and ADASYN are similar to those of random oversampling because the effectiveness of SMOTE is limited when only a few leak-state spectrograms are available for training. They generate synthetic data by interpolating between two data points in the minority class. This indicates that more minority-class samples than in the current scenario are required to generate more diverse synthetic samples. The diversity of synthetic samples generated by SMOTE or ADASYN is constrained when the quantity of minority-class samples is very limited, as in our scenario. As a result, the performance improvements achieved by SMOTE and ADASYN are similar to those of random oversampling, which simply duplicates existing minority-class samples without introducing new variations.

The leak detection models trained using the proposed method show improved performance compared to those trained with widely used oversampling methods, such as SMOTE and ADASYN. SMOTE and ADASYN generate synthetic samples by interpolating between existing samples in the feature space. If the number of leak samples is very limited, SMOTE and ADASYN may not generate diverse synthetic samples. Meanwhile, the proposed method generates more diverse synthetic spectrograms by learning a latent distribution of DoS spectrograms using a VAE.

Figure 12 shows the confusion matrices of leak detection models trained using SMOTE and the proposed method. Logistic regression model trained with SMOTE incorrectly classifies some normal-state spectrograms as leak-state spectrograms. The decision tree, SVM, and gradient boosting models trained with SMOTE demonstrate poor leak detection performance. These models misclassify most leak-state spectrograms as normal-state spectrograms. Meanwhile, all four leak detection models trained with the proposed method show substantially fewer misclassifications for both normal- and leak-state spectrograms. This verifies that the proposed method can effectively mitigate the data imbalance by generating more diverse synthetic leak-state spectrograms than other oversampling methods.

6. Conclusions and Future Work

This paper proposes a method to generate synthetic leak-state spectrograms using a VAE model for mitigating data imbalance in leak detection. The proposed method generates DoS images using the VAE model trained on a few leak-state spectrograms and many normal-state spectrograms. The decoder of the trained VAE model generates DoS images from randomly sampled latent variables. The synthetic leak-state spectrograms are generated by combining the generated DoS images with normal-state spectrograms. The proposed method effectively mitigates data imbalance by generating synthetic leak-state spectrograms using only a small number of leak-state spectrograms. Its effectiveness is evaluated by comparing the performance of various leak detection models trained using different oversampling methods.

The proposed method presents a preliminary result on resolving the data imbalance issue using generative models. The proposed method can be extended in several directions. The generative model using the proposed method can be improved to generate higher-quality leak-state spectrograms that more closely resemble real leak-state spectrograms. A smaller generative model can be developed to synthesize leak-state data by using an alternative representation instead of a spectrogram. The degree of leakage can be considered as an additional condition for generating leak-state spectrograms. AE sensors can be attached not only to pipes but also to other manufacturing equipment to detect various types of faults. The application of the proposed method can be extended to other fault detection tasks in manufacturing facilities that suffer from data imbalance issues.