Study on Methods Using Multi-Label Learning for the Classification of Compound Faults in Auxiliary Equipment Pumps of Marine Engine Systems

Abstract

The impact of the Fourth Industrial Revolution has brought significant attention to Condition-based maintenance (CBM) for autonomous ships. This study aims to apply CBM to the fuel supply pump of a ship. Five major failures were identified through reliability analysis, and structural analysis was conducted to investigate the mechanisms by which one failure induces another, leading to the identification of three compound failure scenarios. Data were collected on a test bed under normal conditions, five single failure conditions, and three compound failure conditions. The acceleration data from the experiments were transformed into 2D arrays corresponding to a single pump rotation, and a method was proposed to compensate for the errors accumulated during the repeated array generation. The data were vectorized using a simplified CNN structure and applied to six multi-label learning methods, which were compared to identify the optimal approach. Among the six methods, the Label Powerset (LP) was found to be the most effective. Multi-label learning captures correlations between labels, similar to the failure-inducing mechanisms learned from structural analysis.

1. Introduction

As part of the impact of the Fourth Industrial Revolution, autonomous ships have been receiving significant attention. The current maintenance technology for autonomous ships relies on timely maintenance. This approach requires ships to dock regularly at predetermined intervals for repairs and inspections. Consequently, this results in frequent interruptions and high costs due to the replacement of parts that may still have remaining useful life [1]. To address this issue, condition-based maintenance (CBM) technology is being introduced. Condition-based maintenance involves monitoring the equipment’s condition in real time and performing maintenance based on the actual condition of the equipment rather than at set intervals.

In the ship’s fuel supply system, the pump plays a crucial role. This system consists of a fuel tank, heater, purifier, service tank, and supply pump. The pump’s primary function is to quickly and reliably deliver refined fuel to the engine. After the crude oil is refined in the purifier and filtered through the service tank, the supply pump transfers the refined fuel to the engine. The stable operation of this pump ensures a smooth fuel supply to the ship, thereby guaranteeing the ship’s stable operation. Therefore, the maintenance and management of the pump are essential for the normal operation of the ship and play a critical role in preventing operational loss costs and other related issues.

Through the investigation of failure cases and a literature review, the primary causes of the failures were analyzed, and the main five failure modes were selected using reliability analysis techniques. A test bed was installed to experiment on the selected failures. Experiments were conducted to collect data on the temperature, pressure, flow rate, noise vibration, and RPM (revolutions per minute). Figure 1 shows the test-bed setup.

The vibration data were collected at a sampling rate of 25,600 Hz, with each experiment lasting for 10 min, utilizing a sensor that collects three-axis data simultaneously. These data can be used to diagnose the current state of the equipment and classify faults. The major failure modes include bearing failure, elastomer failure, misalignment, mechanical seal failure, and cavitation failure, totaling five main failure modes.

Table 1. Overview of the five major failure modes.

Failure Modes	Failure Test Plan	Failure Simulation Diagram
Bearing lubrication/particle injection	- Complete removal of lubrication - Particle injection
Jaw-coupling elastomer wear	- Normal: 0% - Removal 1: 25% - Removal 2: 50% - Removal 3: 75%
Misalignment	- Angular: max. 9° - Lateral: max. 0.25 mm - Offset: max. 4 mm
Mechanical seal degradation	- 120 °C, 90 h degradation
Cavitation	- Outlet pressure change

presents these failures. In the jaw-coupling elastomer wear section, the 25%, 50%, and 75% wear represent the removal of one, two, and three wings out of the six wings of the elastomer, respectively.

These failures can induce other types of failures. The correlation of these failures was analyzed through structural analysis. Among the five failure modes, cavitation, which occurs due to the vaporization of fluid, was excluded from the structural analysis. Structural analysis was conducted on the remaining four failure modes to understand their impact on other components and the mechanisms by which they cause additional failures. As a result, three additional compound failure modes were identified. The overall experimental conditions included the normal state, five primary failures, and three compound failures, totaling nine conditions for the experiments.

The aforementioned failures were tested using the test bed. Through these experiments, data on the flow rate, pressure, temperature, noise, vibration, and RPM were acquired. Vibration data are primarily used for diagnosing rotating machinery [2,3,4]. Diagnosis through vibration is more accurate and cost-effective compared to other diagnostic methods. Therefore, using vibration data to diagnose failures is an efficient choice.

In this study, the vibration data for a consistent single rotation were processed and converted into a 2D array. To create a consistent single rotation array, the sampling rate and real-time RPM data are required. As the data for one rotation are repeatedly generated, slight errors accumulate. We propose two simple and intuitive methods to compensate for these errors. The arrays generated using these methods are intended for learning via a 2D Convolutional Neural Network (CNN). Specifically, the arrays pass through the convolutional and pooling layers of the CNN, where spatial features are learned. Afterward, a flattening process converts these features into a one-dimensional vector. In traditional CNNs, these vectorized data would be further processed and classified through fully connected layers. In this research, after extracting the features through the convolutional and pooling layers and converting them into vectors via the flattening process, we applied six different multi-label methods for classification. Various evaluation metrics were then used to compare the results and identify the optimal method. Multi-label learning techniques can learn the correlations between labels.

Research on the classification of failures in rotating machinery has been conducted for many years [5,6]. Most studies have utilized sound or vibration data to classify failures. Dong et al. (2024) [7] introduced a dynamic normalization supervised contrastive network (DNSCN) that addressed the issue of imbalanced fault diagnosis in gearboxes by using a multiscale compound attention mechanism. Additionally, research has been carried out to classify compound failures in rotating machinery [8,9]. Traditional research on compound failures in rotating machinery has primarily been conducted by detecting the signal characteristics of compound failures using complex signal processing methods [10]. With the advancements in machine learning, many studies have adopted simpler signal processing or statistical feature learning methods [11]. A more recent study, Wang et al. (2023) [12] introduced an adaptive variational autoencoding generative adversarial network (AVAEGAN) for rolling bearing fault diagnosis. This method significantly improved compound fault classification performance by using data augmentation to supplement imbalanced datasets, demonstrating its effectiveness in multi-class comparison experiments. In [13], the Multi-labeling method was first applied to classify compound failures in rotating machinery. Although many subsequent studies have been conducted, it remains rare to find research that classifies six different states and simultaneously simulates and classifies three types of failure conditions.

Multi-label learning is primarily applied in fields such as image and video annotation, music categorization, and text classification [14,15]. In this study, Multi-label learning was used to classify compound failures in rotating machinery. The application of Multi-label learning to diagnose failures in rotating machinery has only recently begun to be explored [16,17,18]. Multi-label learning can consider the dependencies between labels depending on the classifier used [19]. This means it can account for how closely related specific labels are to one another. This can be understood as operating through a similar mechanism to the correlation between failures, where a specific failure causes another failure, as identified through structural analysis.

The structure of this paper is as follows. Section 2 investigates the process through which a single failure leads to another failure via correlation, identified through structural analysis. Through this analysis, two or more compound failure modes that commonly occur in pumps were identified. Additionally, we simulated conditions where two or more failures occurred simultaneously and collected data through experiments. Section 3 explains the data preprocessing procedure for the experimental data. We propose a simple and intuitive method for converting the data into a 2D array for a single rotation. Section 4 discusses the multi-label problems, which differ from those used for multi-class problems. Section 6 shows the results of evaluating the methods introduced in Section 4 using the evaluation metrics described in Section 5. Finally, Section 7 summarizes the entire content and presents the final conclusions.

2. Compound Failures

A single failure can lead to another failure. To investigate these correlations between failures, structural analysis was conducted through the modeling of the pump. Among the five previously selected failure modes, cavitation was excluded from the structural analysis, as it occurs due to fluid vaporization. Therefore, structural analysis was performed on the remaining four failure modes. Figure 2 shows the 3D modeling of the pump and the names of its various components.

The structure of the pump can be broadly divided into four main components: coupling, bearing, mechanical seal, and shaft. The coupling transfers power from the motor to the pump’s shaft. The bearing is an essential component for any rotating machinery. The mechanical seal prevents the internal oil of the pump from leaking to the outside. The shaft is connected to the rotor and helps to form the internal pressure of the pump. These components of the pump are arranged in a serial structure, meaning that the failure of one component can significantly impact the others. To understand how a failure propagates to other components and to evaluate the potential for compound failures, a structural analysis was conducted. If a structural analysis assuming failure mode indicates that significant stress is exerted on other components, it is likely that those components may also develop failure. Figure 3 shows the structural analysis results of a bearing sticking failure.

When a bearing sticking occurs, it can be observed that significant stress is applied to the coupling, shaft, and mechanical seal. This indicates that a bearing failure can lead to coupling failure, shaft misalignment, and mechanical seal failure. Using this approach, we identified the factors causing additional failures for the four primary failure modes. Figure 4 shows the failures induced by bearing failure and misalignment.

Through structural analysis, we understood the mechanisms by which one failure induces another, leading to the selection of compound failure modes. Figure 5 shows the five single failure modes and the three selected compound failure modes.

The selected failure modes were tested using the test bed, and data on the temperature, flow rate, pressure, noise, vibration, and RPM were acquired. In this research, we focused on utilizing the vibration data.

3. Data Preprocessing

Through experiments, various data such as the temperature, flow rate, pressure, noise, vibration, and RPM were collected. In this research, we focused on utilizing the vibration data. Vibration data are widely used in many fault diagnosis studies. There are various methods to analyze vibration data. Statistical indicators of vibration data are commonly used for analysis [20], and time–frequency analysis methods like Short-Time Fourier Transform (STFT) [21], Wavelet Transform (WT) [22], and Hilbert–Huang Transform (HHT) [23] are frequently employed. In recent failure diagnosis research, most of the methods relied on deep learning for training and classification [24]. When using deep learning, it is efficient to transform the data into a form that is easy for the computer to learn without undergoing complex signal processing. This is because both signal processing and the subsequent learning and classification processes require time and computational resources. Therefore, simpler signal processing methods are advantageous.

In this research, we aimed to transform vibration data corresponding to one rotation into a 2D array and used this for training a 2D CNN. This method is both simple and intuitive. A critical aspect of this process is creating arrays that consistently represent a single rotation of data. To construct such arrays, we must consider the pump’s rotational speed (RPM) and the sampling rate. By accounting for real-time RPM data and the sampling rate, we generated consistent one-rotation arrays. The target operational rotational speed of the pump was 1770 RPM, with a sampling rate of 25,600 Hz. While the motor controls the rotational speed, it can still exhibit variations. When the RPM was 1770, considering the RPM and sampling rate, the number of data points per rotation was calculated to be approximately 867.79661 data/rev. To create the array, the number of data points must be an integer. Therefore, we rounded and used 868 data points to form a 28 × 31 array. Assuming the actual RPM was exactly 1770, an error of 0.2033 occurred each time an array was created. This error depends on the RPM at the moment the array is generated. Although this error might seem minor, it can accumulate significantly over time. Given that data are collected at sampling rate of 25,600 Hz for 10 min, approximately 17,000 arrays are generated, potentially leading to substantial cumulative errors. Therefore, it is crucial to implement methods to compensate for these errors. We propose two straightforward and intuitive error compensation methods to address this issue.

Compensation Method 1: This method involves skipping one data point whenever the accumulated error exceeds 1. By doing so, the error can be corrected when it becomes positive, ensuring the creation of consistent single rotation arrays. When the actual RPM is 1770, the error accumulates to about 1 every five arrays, leading to the skipping of one data point. This means about six data points are skipped every second, which corresponds to 6/25,600 = 0.0023% of the total data, a very small portion. Thus, using Compensation Method 1 to skip data points is considered to keep the overall data valid.

However, an issue arises when the data for one rotation exceed 868 data points (i.e., when the rotation speed is faster). In this case, a negative error occurs for each array generated. When creating consistent single rotation data, 868 data points include slightly more than one full rotation. Therefore, a compensation method for negative errors is needed.

Compensation Method 2: Each time the negative error reaches-1, we generate one data point by interpolating between the 867th and 868th data points. This method addresses the need for new data due to negative errors, but instead of introducing arbitrary data that might disrupt the existing data trend, it maintains the data trend by creating new data points through interpolation. Figure 6 compares the arrays before and after applying the compensation method.

Figure 6a shows the arrays before applying the error compensation. While the first, second, and third arrays appear consistent, the 100th, 200th, and 300th arrays exhibit slight delays. The images in Figure 6b show the arrays after applying the error compensation. Consistent arrays are generated not only for the first, second, and third arrays but also for the 100th, 200th, and 300th arrays. The images in Figure 6 visualize the generated arrays. These images are not directly used for training; instead, the data from the 2D arrays are utilized. Figure 7 shows the arrays for the normal state and the five failure states. The consistent appearance of the features across the fault patterns, from the first to the 300th array, can be observed. Figure 7 intuitively represents the differences in the vibration patterns that occur with each fault, allowing for the identification of unique array structures for each fault. This figure enables the visual verification of the data that the CNN model will use to extract the features.

The reason for converting the data into 2D arrays is that CNNs are highly effective at learning structural features from images or 2D data. Since CNNs are specialized in recognizing spatial patterns, converting the acceleration data into 2D arrays allows the model to extract meaningful patterns more easily. Furthermore, transforming the data in this way does not require complex calculations or formulas, unlike other transformation methods. This approach is simple to implement and does not take much time. The acceleration data were then transformed into 2D arrays using Compensation Methods 1 and 2, specifically to utilize the 2D CNNs. In the CNN process, only the convolutional and pooling layers were employed, with the fully connected layer excluded.

By applying convolutional layers to the arrays, the spatial features of the arrays were learned, and the data was vectorized through a flattened layer to be used as input data for various classifiers. CNNs are typically applied to data with a two-dimensional grid structure, such as images. In the case of standard RGB images, each image has a two-dimensional structure of width and height, with each pixel having three channel values: R, G, and B. The vibration data obtained from the experiments were collected using sensors that capture data along three axes simultaneously. The input data used for CNN training had a structure of (31, 28, 3), with each of the three axes of data forming an array. This is analogous to how a 2D color image is trained with three channels (R, G, B). The structure of the CNN used was as follows. It consisted of 32 filters of size (3, 3), and the activation function used was ReLU. Zero padding was applied to maintain the data at the edges of the 2D array. A max-pooling layer with a window size of (2, 2) was then used to reduce the dimensionality of the feature maps and improve the computational efficiency. After the max-pooling layer, the data were passed through a flattening layer, which converted the 2D feature maps into a 1D vector, preparing the data for classification by various classifiers. This overall flowchart is shown in Figure 8. Through this structure, the CNN can learn the structural features of the 2D arrays representing the acceleration data for one rotation of the pump.

4. Multi-Label Learning

The challenge of single-label classification involves training on examples where each instance is tagged with a single label ${\mathsf{\lambda }}_i$ from a finite set of mutually exclusive labels $\mathrm{L}=\{{\mathsf{\lambda }}_1,{\mathsf{\lambda }}_2,\dots ,{\mathsf{\lambda }}_Q\}$. When Q is greater than 2, this becomes a multi-class classification problem. Conversely, in multi-label classification, the goal is to assign a set of labels $Y\subseteq L$ to an example $x\in X$ (where $X$ is the domain of examples). Unlike multi-class classification, where each label is exclusive, multi-label classification allows multiple labels to be associated with a single example, indicating that an example can belong to multiple labels. Labels in the set $Y$ are considered relevant, while those in $L\setminus Y$ are deemed irrelevant for that example.

Multi-label learning methods are continuously being developed and can be broadly categorized into three categories [25,26]: (1) problem transformation methods, (2) algorithm adaptation methods, and (3) ensemble methods.

(1)

Problem transformation methods approach multi-label problems by transforming them into traditional single-label problems. This approach has the advantage of allowing the use of well-established single-label learning algorithms. examples of these methods include binary relevance (BR), classifier chain (CC), and label powerset (LP).

(2)

Algorithm adaptation methods modify existing single-label learning algorithms to handle multi-label problems. Examples of these methods include ML-KNN (multi-label k-nearest neighbor) and Rank-SVM.

(3)

Ensemble methods improve performance by combining multiple models. Examples of these methods include RAKEL (random k-labelsets) and ensemble of classifier chains (ECC).

In this study, we compared six multi-label learning methods. The input data consisted of the vectorized feature data obtained through the convolutional layer of the previously created arrays. The six methods compared were as follows: three problem transformation methods (binary relevance (BR), classifier chain (CC) [27], and label powerset (LP)), two ensemble methods (random k-labelsets D (RAKEL D) and random k-labelsets O (RAKEL O) [28]), and one algorithm adaptation method (multi-label k-nearest neighbor (ML-KNN) [29]). These methods were selected because they are widely used in many studies and have relatively simple structures [30,31]. In this study, the scikit-multilearn library was used, and for the parameters not explicitly mentioned, the default values provided by the library were applied [32] Below is an introduction to each method.

(1)

Binary Relevance (BR)

Binary relevance (BR) is a simple yet efficient method for solving multi-label learning problems. BR decomposes the multi-label problem into several independent binary classification problems, each predicting the presence or absence of a label individually. This method is easy to implement and can be quickly trained on large datasets, because it learns independent classifiers for each label. Additionally, when new labels are added, there is no need to modify the existing model; only a new classifier needs to be added. However, a drawback of BR is that it does not consider the correlations between labels.

(2)

Classifier Chain (CC)

Classifier chain (CC) is designed to overcome the limitations of BR by leveraging the correlations between labels. While BR handles each label independently, CC models the relationships between labels by forming a chain structure that takes label order into account. For a multi-label dataset, an order is established for all labels, forming a chain based on this order. The order of labels can be determined by the characteristics of the dataset.

(3)

Label Powerset (LP)

Label powerset (LP) is a method that treats each unique combination of labels as a single distinct class. LP naturally models the correlations between labels by identifying all possible label combinations in the dataset and considering each combination as a unique class. This transforms the multi-label problem into a traditional single-label classification problem, specifically a multi-class problem.

(4)

Random k-Labelsets D (RAKEL D), Random k-Labelsets O (RAKEL O)

Random k-labelsets (RAKEL) is an ensemble method based on a label powerset (LP), which processes label sets by dividing them into multiple subsets. There are two main variants of RAKEL: RAKEL D and RAKEL O. RAKEL D stands for “Disjoint”. In this variant, the entire label set is divided into non-overlapping subsets. This approach trains independent LP classifiers for each subset and aggregates the results from all classifiers. Since it deals with fewer label combinations, rather than using the entire label set, this method reduces the model complexity. In this study, we used a label size of 3, meaning that each subset was composed of three labels, which helps balance the computational efficiency and label interaction. However, because the subsets do not overlap, the method cannot capture the correlations between labels that belong to different subsets. This reduces the computational burden but may result in information loss, as it may fail to capture the correlation between some labels. RAKEL O stands for “Overlap”. This variant allows for overlapping labels between subsets. By designing each subset to overlap to some extent, RAKEL O can better capture correlations between labels. The degree of overlap can be adjusted to suit different datasets. While RAKEL O can more effectively capture label dependencies, it also increases the model complexity and may lead to longer training times due to the larger number of combinations that need to be learned. In summary, RAKEL D focuses on computational efficiency by reducing the number of label combinations at the expense of potentially missing some label interactions. In contrast, RAKEL O aims to capture more label dependencies by allowing overlaps, resulting in a more complex model with increased training time.

(5)

Multi-Label k-Nearest Neighbors (ML-KNN)

Multi-label k-nearest neighbors (ML-KNN) is an adaptation of the traditional KNN algorithm for multi-label learning. For each test instance, it identifies the k nearest neighbors from the training dataset. It then calculates how frequently each label appears among these k neighbors, evaluating the presence likelihood of each label. To determine the presence likelihood of each label, ML-KNN counts the number of instances among the k neighbors that have each label. This count is then combined with prior probabilities derived from the training data to make a final decision. A label is assigned to the test instance if its probability exceeds a certain threshold; otherwise, it is not assigned. ML-KNN is a simple and intuitive algorithm that is easy to implement. However, its computational cost increases significantly with the size of the dataset. Additionally, finding the optimal threshold for binary decisions can be challenging. One of the key parameters of ML-KNN is k, which represents the number of nearest neighbors considered during prediction. To balance the computation time and efficiency, k was set to 3 in this study.

5. Evaluation Metrics

Evaluating the performance of multi-label learning systems requires different evaluation metrics compared to traditional single-label learning systems. In multi-label learning, it is essential to include a variety of evaluation metrics to address the additional complexity introduced by the multi-label environment. The performance evaluation metrics used in this paper were as follows: Precision, Recall, F1 Score, Hamming Loss, Subset Accuracy, and Training and Testing Time. In the definitions below, $Y_i$ represents the set of true labels for the example $x_i$, and $h\left(x_i\right)$ represents the set of predicted labels for the same example. The symbol $\left|·\right|$ denotes the number of elements in a set, and N refers to the total number of instances in the dataset.

• Precision, Recall, F1 Score

Precision measures the proportion of predicted labels that are actually correct. It is defined as follows.

$$\mathrm{Precision}(\mathrm{h})={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\displaystyle \frac{\left|h(x_i)\cap Y_i\right|}{\left|Y_i\right|}}$$

(1)

Recall measures the proportion of actual labels that are correctly predicted by the model. It is defined as follows.

$$\mathrm{Recall}(\mathrm{h})={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\displaystyle \frac{\left|h(x_i)\cap Y_i\right|}{\left|h(x_i)\right|}}$$

(2)

The F1 Score is the harmonic mean of Precision and Recall, taking both metrics into account to provide an overall measure of a model’s performance. It is defined as follows.

$$\mathrm{F}1 \mathrm{Score}(\mathrm{h})={\displaystyle \frac{1}{N}}{\sum }_{i=1}^{N}2\times {\displaystyle \frac{\left|h(x_i)\cap Y_i\right|}{\left|h(x_i)\right|+\left|Y_i\right|}}$$

(3)

2.

Hamming Loss

The Hamming Loss measures the discrepancy between the predicted label set and the true label set, indicating the proportion of misclassified labels. Hamming Loss is calculated by dividing the number of incorrectly predicted labels by the total number of labels for each instance and then averaging this value over all instances. Mathematically, it is defined as follows. N is the number of examples, and L is the total number of possible class labels, where $\Delta$ stands for the symmetric difference between two sets.

$$\mathrm{Hamming} \mathrm{Loss}(\mathrm{h})={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\displaystyle \frac{1}{\left|L\right|}}\left|h(x_i)\Delta Y_i\right|$$

(4)

3.

Subset Accuracy

The Subset Accuracy measures whether the model’s predictions exactly match the true label sets. This metric is also known as the “exact match”. It is calculated as 1 if the predicted label set is exactly the same as the true label set and 0 otherwise. Mathematically, it is defined as follows.

$$\mathrm{Subset} \mathrm{Accuracy}(\mathrm{h})={\displaystyle \frac{1}{N}}{\sum }_{i=1}^{N}I(h\left(x_i\right)=Y_i)$$

(5)

The indicator function I returns 1 if the condition inside the parentheses is true and 0 if it is false. This strict evaluation criterion means that even a small number of label errors can significantly impact the overall performance.

4.

Training and Testing Time

The final evaluation metric is the Training and Testing Time. Time is used to assess the efficiency of the algorithm. It measures the time taken to build the predictive model and the time required to make predictions on unseen examples.

6. Classification Results

The data from one pump rotating were converted into an array and used as input data, with the pump rotating at 1770 RPM and collecting data for 10 min, generating a total of 17,700 arrays. Each array consisted of an array of size 28 × 31, which included data from the x, y, and z axes, ultimately forming a 28 × 31 × 3 2D array. This array was fed into a 2D CNN for feature extraction, resulting in a 6720 feature vector for each array. This 6720 feature vector was then used as a single instance in the input data for the multi-label learning algorithm. The performance of various classifiers was evaluated using the evaluation metrics introduced in Section 5.

Table 2. Comparative classification results of six multi-label learning methods.

	Binary Relevance	Classifier Chain	Label Powerset	RAKEL O	RAKEL D	ML-KNN
Precision	0.9995	0.9985	0.9980	0.9993	0.9976	0.9654
Recall	0.9105	0.9256	0.9976	0.9713	0.9519	0.9844
F1-Score	0.9468	0.9563	0.9978	0.9841	0.9719	0.9743
Hamming Loss	0.0230	0.0193	0.0010	0.0075	0.0129	0.0131
Subset Accuracy	0.8674	0.8866	0.9970	0.9562	0.9284	0.9768
Training and Testing Time	901.47	853.99	238.68	975.62	171.76	1703.49

shows the performance evaluation results for each classifier. Note that the Training and Testing Time can vary depending on the size of the dataset and the performance of the computer. Therefore, these times should be considered as relative values when comparing different methods.

First, the binary relevance showed the worst performance across most of the metrics. On the other hand, the label powerset demonstrated high performance in most of the metrics, and although its Training and Testing Time were not the best, they were the second-best. A well-known disadvantage of the label powerset is that as the number of labels increases, the number of combinations grows exponentially, leading to increased computational costs. However, in this dataset, the number of label combinations was not large; so, this disadvantage did not apply. Thus, based on various metrics, the label powerset can be chosen as the method with the best overall performance.

7. Conclusions

This study aimed to implement condition-based maintenance for the fuel supply pump of a ship. Five major failures of the pump were identified, and a test bed was set up to experiment with these failures. Through structural analysis of the pump, the impact of one failure on other failures was understood. As a result, three compound failure modes were selected. These selected compound failure modes were tested on the test bed, and data were collected.

A simple and intuitive method was proposed to transform the acquired acceleration data into consistent single rotation arrays. The generated 2D arrays were then used to learn the features of the arrays through a CNN. The learned features were applied to six multi-label learning methods.

Research on applying multi-label learning to classify compound failures in rotating machinery has only recently begun, and studies attempting to classify as many failures simultaneously as this one are rare. Among the six multi-label methods applied, the label powerset showed the most positive results across most performance metrics. Multi-label learning enables the learning of correlations between labels, which is similar to the mechanism used in structural analysis to identify compound failure modes. In other words, it can learn the correlations where specific failures frequently occur together or not, aligning with the findings of the structural analysis.

For future work, we aim to verify whether the proposed method can be effectively applied to other datasets. This would involve addressing the domain discrepancy issue to ensure the generalizability of the approach across different environments and systems.