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Article

Early Fault Diagnosis and Prediction of Marine Large-Capacity Batteries Based on Real Data

by
Yifan Liu
,
Huabiao Jin
,
Xiangguo Yang
*,
Telu Tang
,
Qijia Song
,
Yuelin Chen
,
Lin Liu
and
Shoude Jiang
School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430070, China
*
Author to whom correspondence should be addressed.
J. Mar. Sci. Eng. 2024, 12(12), 2253; https://doi.org/10.3390/jmse12122253
Submission received: 31 October 2024 / Revised: 29 November 2024 / Accepted: 6 December 2024 / Published: 8 December 2024
(This article belongs to the Special Issue Advancements in Power Management Systems for Hybrid Electric Vessels)
Browse Figures
Figure 1
<p>Network topology of the battery system.</p> "> Figure 2
<p>Some of the data used in this article. (<b>a</b>) is the electric boat speed, (<b>b</b>) is the battery cluster voltage sampled by the electric boat BMS, and (<b>c</b>) is the right pod power.</p> "> Figure 3
<p>Alarm flow chart of BMU, BCU, and BAU in Marine BMS.</p> "> Figure 4
<p>Time-stamped ship alarm status and differential signals on 1 January 2023.</p> "> Figure 5
<p>Schematic diagram of DBSCAN clustering method.</p> "> Figure 6
<p>Comparison of fault points and true labels based on DBSCAN.</p> "> Figure 7
<p>DBSCAN clustering result evaluation indicator value in each month.</p> "> Figure 8
<p>Cloud-based data platform for iTransformer fault prediction.</p> "> Figure 9
<p>Transformer-related structural design diagram.</p> "> Figure 10
<p>iTransformer-related structural design diagram.</p> "> Figure 11
<p>PCC (<b>a</b>) and Spearman (<b>b</b>) correlation coefficient calorific value map.</p> "> Figure 12
<p>Voltage difference in the battery cluster and fault alarm status for the fault segment on 3 January 2023.</p> "> Figure 13
<p>Voltage prediction results and errors based on the transformer model.</p> "> Figure 14
<p>Voltage prediction results and errors based on the iTransformer model.</p> ">
Versions Notes

Abstract

:
The inconsistency of battery voltages in all-electric ships is a significant issue for electric vehicle battery systems, leading to numerous safety concerns during vessel operation. Therefore, timely fault diagnosis and accurate fault prediction are crucial for the safe operation of ships. This study examines the fault alarm system of marine battery management systems in conjunction with the unique operating conditions of ships, focusing on the system’s latency. To facilitate prompt fault detection, a fault diagnosis method based on the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is proposed, utilizing the voltage data of battery clusters. Results indicate that the DBSCAN clustering algorithm demonstrates superior effectiveness and accuracy in identifying irregular battery clusters. Furthermore, the fault prediction method based on the iTransformer model is introduced to forecast variations in battery cluster voltages. Experimental findings suggest that this model can effectively predict consistency faults and over-/under-voltage conditions based on battery cluster voltage values and corresponding fault thresholds.

1. Introduction

Entering this century, as the global energy crisis worsens and environmental problems intensify, addressing energy depletion and environmental degradation has become a top priority worldwide. The gradual enforcement of the International Maritime Organization’s (IMO) sulfur cap regulation has placed new technological and environmental demands on the global shipping industry, making energy conservation and emission reduction an inevitable trend for ships. Compared to traditional fuel-powered vessels, all-electric ships, with their zero emissions, high transmission efficiency, lower operating costs, and higher technological value, are increasingly gaining prominence in the industry and showing broad potential for application [1,2]. The battery system is a core component of all-electric ships, and its performance largely determines the ship’s power, safety, and endurance during navigation [3,4]. Unlike electric vehicles, marine battery systems face far more challenging operating conditions due to the complex and variable marine environment [5,6]. Frequent temperature changes, humidity, vibrations, and prolonged high-load operations significantly increase the risk of system failure. In extreme conditions, such failures could even lead to thermal runaway, posing serious threats to the safe operation of the vessel. Recent studies have shown that voltage anomalies in batteries are a key factor triggering system malfunctions [7,8,9,10]. These anomalies can typically be classified into four categories: overvoltage, undervoltage, rapid voltage fluctuations, and poor voltage consistency. Among these, inconsistency is one of the most common issues in battery management systems [11,12]. It results in uneven capacity utilization, where weaker batteries reach their charge or discharge limits first, reducing the efficiency of other batteries and lowering overall system capacity utilization. Furthermore, inconsistency accelerates system aging, leading to the premature failure of underperforming batteries, shortening the overall lifespan of the battery pack and increasing maintenance costs. After identifying the inconsistencies, it is necessary to isolate certain battery cells or perform balancing charge and discharge operations to improve the overall performance and safety of the battery pack. Therefore, promptly detecting and addressing voltage anomalies, particularly inconsistency issues, is crucial to ensuring the safe and efficient operation of all-electric ships. This not only helps meet industry standards for energy savings and emissions reduction but also plays a vital role in guaranteeing the safety of ships navigating complex marine environments.
The main lithium battery fault diagnosis algorithms today are typically categorized into knowledge-based, model-based, and data-driven approaches [13]. Knowledge-based lithium battery fault diagnosis algorithms draw on historical data to extract fundamental insights about battery behavior, which are then used for diagnosis by comparison with a knowledge base [14]. For instance, expert systems use fuzzy logic to establish a knowledge base that improves through self-optimization during diagnostics [15].
Model-based lithium battery fault diagnosis algorithms develop models to simulate lithium-ion battery behavior, then compare the predicted and actual values to generate residuals for fault detection. Kumara et al. [16] developed a connection fault diagnosis algorithm using a Luenberger observer, creating a first-order equivalent circuit model to simulate fault scenarios and using the observer to generate residual signals. LIN et al. [17] applied hybrid system theory to design automata for capturing both the continuous and discrete states of lithium battery packs, using dual extended Kalman filters to estimate parameters and diagnose sensor and relay faults.
Data-driven methods analyze extensive offline and online operational data to establish input-output mappings and extract diagnostic features without needing detailed battery models, though data quality is critical. Numerous global new energy data centers now host extensive datasets on electric vehicle performance, supporting data-driven fault diagnosis validation [18]. Xia et al. [19] used correlations between adjacent cell voltages to diagnose faults, while Kang et al. [20] employed a joint fault diagnostic method, combining staggered voltage measurement topology and modified correlation analysis to detect internal and external short-circuit faults. Sun et al. [21] used wavelet transforms to denoise voltage data and calculated Shannon entropy to diagnose faults, validating the method’s effectiveness through battery vibration tests. To address challenges with traditional Shannon entropy, such as computational complexity and high hardware demands, Wang et al. [22] applied an improved Shannon entropy method, using a sliding window for iterative entropy calculations, and introduced a Z-score-based strategy for predictive maintenance. Liu et al. [23] used entropy weighting to assign objective weights to battery voltage, identifying anomalies through battery scoring. To address early fault-detection issues, where fault characteristics may be subtle, Hong et al. [24] proposed an enhanced multi-scale entropy method to accurately predict fault timing and locations, helping prevent thermal runaway.
With advancements in artificial intelligence and machine learning, effective battery fault diagnosis and prediction now rely on inputting feature factors and labels into models. For example, Qiu et al. [25] applied a nonlinear autoregressive exogenous (NARX) neural network for voltage prediction and fault diagnosis, while Fang et al. proposed a noise-applied DBSCAN clustering algorithm for fault diagnosis, paired with least-squares support vector regression (LS-SVR) for cell voltage change prediction [26]. However, much of this research focuses on electric vehicles, with few studies specifically addressing the unique requirements of all-electric vessels.
Existing battery voltage prediction methods have been validated primarily on electric vehicles, with little testing on all-electric ships. This paper addresses this gap by introducing a new approach for predicting voltage and detecting potential abnormal voltage fluctuations based on actual data from electric ships. The paper aims to make three notable contributions and improvements to current technology:
  • Adapting Fault Detection for All-Electric Ships: We adapt fault detection methods traditionally used for electric vehicles to all-electric ships, using real operational data to examine battery inconsistency.
  • Analyzing Ship Fault Alarm Mechanisms: This study investigates the delay issues in alarm communications, proposing a voltage anomaly diagnosis method based on battery clusters, specifically tailored to the operational context of ships.
  • Introducing an iTransformer-Based Fault Prediction Method: We propose a fault prediction method using the iTransformer algorithm to forecast trends in battery cluster behavior, revealing potential hazards associated with inconsistency faults.
The remainder of this paper is organized as follows: Section 2 gives a brief introduction of the real-world driving data details. Section 3 analyzes the alarm mechanism of the ship’s battery management system and uses real data to illustrate the delay in alarms, from which a DBSCAN-based identification method is proposed. Section 4 utilizes iTransformer for voltage prediction. Section 5 summarizes the main conclusions of the paper.

2. Data Description and Preprocessing

In actual ship operations, battery voltage can experience significant and random fluctuations due to unpredictable environmental and operational factors, creating a more complex operating environment compared to electric vehicles. The dataset used in this study originates from a monitoring platform provided by a domestic research institute. This platform tracks the real-time status of over ten electric ships, delivering timely feedback to the vessels and their operators. Additionally, the platform provides IT support and data services for electric ship companies and government agencies, enabling the collection of extensive operational data and expanding the application potential of machine learning techniques, such as the Transformer network architecture proposed in this paper.
The data examined in this study specifically pertains to the Junlu, an all-electric ship developed collaboratively by the China State Shipbuilding Corporation’s 712th and 702nd Research Institutes. Capable of carrying up to 300 passengers, it is the first large passenger ship in China to meet the *Inspection Guidelines for All-Battery Electric Ships* set by the China Classification Society. The ship’s battery system consists of multiple clusters connected in parallel, providing a total capacity of 2240 kWh; the specific battery system topology is shown in Figure 1. The battery system in the “Junlvhao” ship is divided into two parts (left and right), each containing 6 battery clusters. After the 6 battery clusters are connected in parallel, they supply power to the pod and other loads through the ship’s DMSB. Additional specifications are presented in Table 1. Data collection spanned from October 2022 to October 2023, including essential information such as timestamps, state of charge (SoC), battery cluster voltage lists, battery consistency status, fault alarms, alarm severity, total current, voltage, and power, as shown in Figure 2.
In the diagnostic phase, the DBSCAN clustering method is employed for fault detection and localization, while the iTransformer model is used for the prediction algorithm. The operational principles, specific parameters, and further technical details of these methods are discussed in subsequent sections.
For fault diagnosis and localization, the DBSCAN clustering method is utilized, while the prediction algorithm is based on the iTransformer model. The system principles, detailed parameters, and further technical specifics of these methods are discussed in the following sections.

3. Inconsistency Fault Analysis and Diagnosis

3.1. Inconsistency Fault Analysis

3.1.1. Fault Alarm Mechanism in Marine BMS

In practical applications, the BMS alarm system primarily responds to faults caused by individual battery cells, as the terminal voltage of individual cells is easily measurable. To further diagnose the fault, it is essential to establish the voltage differential threshold used for fault detection. In the battery management system, each data sample records the relevant information of individual cells, including their voltage data. By comparing the calculated feature factors with pre-calibrated thresholds, any value exceeding the threshold is flagged as a fault, and the corresponding alarm thresholds and levels are outlined in Table 2. These fault thresholds are set by the manufacturer based on specific conditions and are defined according to national standards. In our study, the design manual of the battery system from the Junlvhao vessel was used as the source of these thresholds.
The battery management system (BMS) adopts a distributed design, as shown in Figure 3. The distributed BMS consists of the Battery Assembly Unit (BAU), Battery Control Unit (BCU), and Battery Management Unit (BMU), which work together to monitor the battery pack’s status and ensure the safe operation of the battery. The BAU is the system-level control unit responsible for the monitoring, management, and control of the entire system. It directly monitors the status of each battery module within the battery system and can also monitor the battery pack’s information. The BCU is a module-level control unit, with each battery module having a corresponding BCU. The BCU is responsible for monitoring the status of individual cells within the battery module and reporting status information to the higher-level control unit. The BMU is the cell-level control unit, responsible for monitoring the status of individual cells and communicating this information to the BCU, which in turn passes it to higher-level units. The entire system communicates through a CAN network. Therefore, when a fault occurs at the cell level, the fault reporting process follows a hierarchical flow: from the BMU to the BCU to the BAU.
When using the CAN network for BMS communication on ships, significant delays often occur due to the ship’s complex system architecture and challenging operating environment. First, ships have many interconnected subsystems, with considerable physical distances between them. Coupled with a large number of nodes, this setup often results in data congestion and delays. Second, environmental factors such as temperature, humidity, and salt fog significantly impact the battery system, increasing the monitoring demand and necessitating redundant design features, which in turn prolong the data processing time. Additionally, interference from high-power electromagnetic equipment on board may affect the stability of communication, and the shielding measures implemented to ensure signal integrity can further contribute to delays.
In summary, due to the design of the ship’s BMS, the individual cell fault alarm mechanism may have inherent delays. To address this issue, this study proposes a fault detection method based on the voltage of the battery pack, which directly uses data from the BAU monitoring the battery pack voltage. This method ensures higher real-time performance and can improve the overall fault detection process.

3.1.2. Fault Fragment Analysis

Battery inconsistency faults typically persist over an extended period, manifesting as an increasing voltage difference between cells and battery clusters. This voltage disparity may lead to the progression of faults from an initial level 1 to levels 2 or even 3. For instance, in Figure 4, an alarm event that occurred at 10:00 PM on 1 January 2023, clearly illustrates the temporal relationship between voltage difference changes and alarm states. Initially, the figure shows that the trend of voltage difference changes began to emerge before the alarm was triggered, indicating that voltage anomalies often serve as early warning signals for potential faults. In the alarm segment at 10:38 PM, it was observed that the voltage difference increased rapidly to its peak; however, the alarm did not trigger immediately but only after the voltage difference exceeded a specific threshold. This phenomenon indicates that the alarm mechanism relies not solely on instantaneous changes in voltage difference but rather on the cumulative effect of voltage differences over time. Additionally, after the voltage returns to normal levels, the alarm state persists for a period to ensure that all anomalies have been resolved. This process highlights the persistence of voltage anomalies in battery clusters and their critical role in fault detection. Therefore, it is evident that the occurrence of faults is often accompanied by abnormal voltage changes in battery clusters, which frequently precede the triggering of alarm states. These early voltage changes provide crucial insights for the timely detection and diagnosis of battery faults. Consequently, continuous monitoring of voltage differences in battery clusters is essential within battery management systems, as it enhances the accuracy and responsiveness of fault diagnostics.

3.2. Inconsistency Fault Diagnosis

Based on Table 2, overvoltage and undervoltage faults in individual battery cells can be detected by setting specific voltage thresholds using raw data. However, as analyzed above, this method does not provide immediate fault detection, leading to delays in alarms and assessments. To address this issue, this study proposes directly detecting anomalies at the battery cluster level, significantly reducing detection latency. A DBSCAN-based clustering method is introduced to automatically identify and classify faults across multiple battery cluster voltage curves. Unlike K-means, this method uses outlier detection to identify abnormal clusters.
K-means is a widely used unsupervised learning algorithm primarily employed for clustering tasks, with the goal of partitioning a dataset into K clusters such that data points within each cluster are as similar as possible, while data points in different clusters are as distinct as possible. The core idea of K-means is to iteratively update the centroid of each cluster, optimizing the cluster assignments over time. However, K-means requires a predefined number of clusters, K, which is often difficult to determine in practice. For example, when diagnosing voltage anomalies in battery cells using K-means, if K is set to 2, certain special cases may lead to underdiagnosis, requiring an increase in K to achieve more accurate clustering results. In cases where the voltage anomaly distribution is variable, it becomes challenging to accurately identify all anomalous cells with a fixed number of cluster centers. Therefore, the K-means-based anomaly detection method has certain limitations in such scenarios. The DBSCAN algorithm does not require setting the number of clusters, making it more effective in identifying the occurrence of multiple fault situations.
The DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clustering algorithm, developed by Ester M., Kriegel H.P. et al. in 1996, is a density-based method that classifies data points with similar characteristics based on distances between them, automatically dividing data into distinct clusters. Widely applied in fields such as battery voltage balancing and thermal runaway diagnostics, DBSCAN is highly effective for identifying patterns and anomalies. A cluster is formed when data points satisfy a minimum point threshold (minpts) within a specified neighborhood (eps).
The algorithm’s operation, shown in Figure 5, classifies data points as core points, boundary points, or noise points. Initially, minpts is set to 5, and orange-marked core points are identified. The algorithm then expands clusters by transferring from one core sample to neighboring points to locate additional core points, completing the clustering task. In the figure, light red points have only three neighbors and thus do not qualify as core points; however, they remain within reach of the core point density, classifying them as boundary points. Blue points, which cannot be reached from any core point, are considered noise.
Before implementing DBSCAN, it is essential to intelligently set the neighborhood radius (eps) and minimum neighborhood sample count (minpts), as these parameters directly impact clustering outcomes. The detailed steps for implementing the DBSCAN algorithm are outlined as follows:
Step 1: Select a Core Point, p: A data point is randomly selected as a core point, p, to begin forming a cluster.
Step 2: Form Cluster C: Using core point p as the starting point, a cluster, C, is created by adding p and all data points within a specified radius, r (i.e., the r-neighborhood), to the cluster.
Step 3: Expand Cluster C: For each unprocessed point in the neighborhood, the cluster is expanded. If a neighboring point, q, also qualifies as a core point, all points within q’s neighborhood that are not yet assigned to another cluster are added to C, continuing the cluster expansion.
Step 4: Repeat Expansion: This process is repeated until all points that can be included have been assigned to a cluster, ensuring that every sample point is processed.
Step 5: Output Clusters and Noise Point: Finally, the algorithm outputs the set of clusters, C, and any points that could not be assigned to a cluster are labeled as noise and placed in the noise set O.
Based on data from January 2023, this study applied the DBSCAN clustering method to analyze voltage anomalies in battery clusters within the marine BMS. Figure 6 illustrates the correspondence between noise points identified by the method and actual fault points. In the figure, blue solid points represent detected noise or anomaly points, while orange hollow points denote actual labeled fault points. The figure shows that, in most cases, potential faults within the battery clusters were detected early, as these anomalies were marked as noise points, often preceding alerts from the ship’s BMS. Additionally, during the period from 3 January to 18 January, several potential fault points were detected, with timing differences from the BMS fault alarms. Around 23 January, noise points identified by the algorithm appeared noticeably earlier than actual fault alerts, demonstrating the clustering method’s significant predictive capability.
To conclude, the DBSCAN algorithm has proven effective in fault detection, as it can identify potential issues in the battery system before the BMS issues an alert. This early-warning capability provides valuable response time for maintenance personnel, enabling timely interventions and reducing potential losses associated with delayed fault reporting.
To evaluate DBSCAN’s effectiveness in identifying abnormal voltage in battery clusters, this study introduces the F1 Score, a common classification metric. The F1 Score provides a straightforward assessment of the DBSCAN algorithm’s performance in detecting voltage anomalies. Since fault anomalies are typically rare in battery systems, and sample classes are imbalanced, relying solely on precision or recall can be misleading. The F1 Score calculation follows these steps:
  • True Positive (TP): The number of correctly clustered samples for a specific class.
  • False Positive (FP): The number of samples incorrectly clustered into a specific class.
  • False Negative (FN): The number of samples that belong to a specific class but were not correctly identified.
Using these definitions, the formulas for precision, recall, and F1 Score are as follows:
Precision = TP TP + FP
Recall = TP TP + FN
F 1 = 2 × Precision × Recall Precision + Recall
As shown in Figure 7, the DBSCAN clustering method’s results for detecting voltage anomalies in battery clusters demonstrate a consistently high detection precision, with precision values remaining at 1.0 across all months, indicating excellent accuracy in identifying voltage anomalies. The recall rate, however, shows some fluctuations, particularly in September (0.92) and November (0.92946), where recall rates are relatively lower. This variability may relate to operational factors, such as climate, sea conditions, and maintenance schedules, which could increase the complexity of anomaly patterns and contribute to missed detections.
The F1 score, which integrates both precision and recall, generally ranges between 0.9423 and 0.99692, indicating stable and strong overall model performance. Notably, the F1 score approaches 1.0 in June, October, and December, reflecting optimal detection performance during these months. In summary, the model performs well throughout most of the year, effectively detecting voltage anomalies, though a few missed detections may occur in certain months.

4. Inconsistency in Fault Prediction Based on iTransformer

The primary indicator for detecting inconsistency faults in large-capacity battery clusters on ships is the voltage residual of the battery pack. In the initial stages of a fault, before individual cell inconsistency alarm signals are triggered, the voltage range gradually expands over time. Typically, in maritime applications, reporting of individual cell faults is subject to delays. However, since the Battery Control Unit (BCU) directly monitors the battery cluster voltage without passing through the CAN0 network, using cluster voltage as a consistency indicator avoids such delays, providing a more immediate reflection of the overall health of the battery pack. Thus, in addition to accurately diagnosing faults in ship batteries, effectively predicting faults at the battery pack level would significantly enhance operational safety. To address this, this study proposes an iTransformer-based predictive method for early warning of voltage anomalies and forecasting fault progression trends.
The proposed iTransformer fault prediction method can be supported by the cloud-based big data platform for fully electric ships. This platform enables real-time information exchange between the ship and the platform, meaning the ship can upload relevant data to the platform, and the platform can return the predicted signals to the ship. Cloud-based cyber-physical systems and platform technologies provide an excellent environment for creating self-improving models that can effectively and efficiently enhance the safety of the ship during operation. Figure 8 demonstrates how we utilize the cloud data platform for fault prediction.
Our iTransformer plays a critical role in predicting voltage anomalies in large-capacity ship battery clusters. Given the influence of environmental factors, predicting the voltage of ship battery clusters requires capturing the complex dependencies in a multivariate time series. Traditional Transformer architectures often struggle with long time-series data due to performance declines and increased computational complexity. By utilizing an inverted dimensional structure, iTransformer more accurately captures the interdependencies among battery cells, providing greater stability in handling multivariate data. This capability aids in the earlier identification of inconsistency faults within battery clusters and enables effective forecasting of future voltage trends, ultimately enhancing the operational safety of ship battery systems.

4.1. Transformer Architecture

The Transformer model is a widely popular deep learning architecture, first introduced in the groundbreaking paper * “Attention is All You Need”. * Unlike traditional sequence models such as LSTMs, the Transformer captures dependencies between input and output elements using a self-attention mechanism, allowing it to process the entire sequence in parallel rather than sequentially across time steps. This capability enables the Transformer to capture long-range dependencies more efficiently, significantly enhancing model performance. The schematic diagram of the relevant transformer principles is shown in Figure 9. The following sections outline the key components of the Transformer model.

4.1.1. Positional Encoding

In the Transformer model, the embedding process typically combines token and positional embeddings to capture sequence order. In this study, positional and operational embeddings are used to represent the position of battery charge and discharge curves within the sequence, as shown by the following formula:
PE p o s , 2 i = s i n ( p o s 10,000 2 i d mod e l ) PE p o s , 2 i + 1 = c o s ( p o s 10,000 2 i d mod e l )
The PE refers to the Positional Embedding matrix, where pos indicates a specific position, i represents a particular dimension, and d_model denotes the dimension of the model.

4.1.2. Self-Attention Mechanism

The self-attention mechanism is central to the Transformer model, enabling each position (token) in the input sequence to relate to all other positions, capturing dependencies throughout the sequence. The self-attention mechanism follows these main steps:
1. Calculate Query, Key, and Value Vectors: For each position in the input sequence, a linear transformation generates a query vector (Q), a key vector (K), and a value vector (V), using the following formulas:
Q i = W Q x i K i = W K x i V i = W V x i
where W Q , W K , and W V are learned weight matrices that map the input into subspaces for query, key, and value. The Q represents the token seeking information, the K contains the information, and the V holds the data used for the output.
2. Compute Attention Scores: The attention scores are obtained by calculating the dot product between the query and key vectors, representing the relevance of each position to others in the sequence.
A t t e n t i o n ( Q i , K j ) = Q i K j T d k
The Q is compared to K using a similarity measure (usually dot product) to calculate how much attention one token should pay to another.
3. Apply Softmax Function: To normalize the attention scores into probabilities, they are passed through a softmax function, ensuring that the weights sum to 1:
α i j = softmax ( Q i K j T d k )
The attention scores are normalized with softmax, turning them into probabilities so that they sum to 1, determining the attention weight each token should have.
4. Weighted Sum to Obtain Output: Finally, the output for each query position is a weighted sum of all value vectors V, with weights determined by the attention scores:
O u t p u t i = ∑ j α i j V j

4.1.3. Multi-Head Attention

The multi-head attention mechanism extends self-attention by allowing the model to learn different types of dependencies in parallel across multiple subspaces. The formula for multi-head attention is as follows:
MultiHead ( Q , K , V = Concat ( head 1 , head 2 , … , head h ) W O
Each head is calculated similarly to single-head self-attention:
head i = Attention ( Q i , K i , V i )
where W O is the weight matrix for the final linear transformation, and concatenation combines the outputs from each attention head. Multiple attention mechanisms (heads) run in parallel, each focusing on different parts of the input. The results are combined to capture different relationships between tokens.

4.1.4. Feed-Forward Network

The feed-forward network further processes and transforms feature representations. The formula is as follows:
FFN ( x ) = max ( 0 , x W 1 + b 1 ) W 2 + b 2
where W 1 and W 2 are weight matrices, b 1 and b 2 are biases, and ReLU is the activation function. It transforms and refines data through two layers with a ReLU activation to learn complex patterns.

4.1.5. Layer Normalization

To accelerate model training and improve stability, the Transformer applies layer normalization between the input and output of each sub-layer. Layer normalization helps mitigate issues like gradient vanishing or explosion during training and promotes faster convergence. The layer normalization formula is:
LayerNorm ( x ) = x − μ σ + ϵ ⋅ γ + β
where μ and σ are the mean and standard deviation of the input, ϵ is a small constant for numerical stability, and γ and β are learnable parameters. It normalizes the output to stabilize training, improving convergence and reducing learning rate dependency.

4.1.6. Residual Connections

Residual connections directly pass the input of each layer to the next layer to avoid information loss and ensure better gradient backpropagation. Specifically, input x is added to the output of the layer:
Output = LayerNorm ( x + SubLayer ( x ) )

4.1.7. Final Output

The decoder’s final output is passed through a linear layer, followed by a softmax function to produce predicted values.
Target ( y | x ) = softmax ( H W + b )
The Transformer combines self-attention, multi-head attention, feed-forward networks, positional encoding, layer normalization, and residual connections to build a highly parallelized model architecture. The self-attention mechanism allows the model to focus on multiple positions within the input sequence, capturing long-range dependencies, while the multi-head mechanism enhances flexibility and expressiveness. The feed-forward network provides nonlinear transformation, positional encoding manages sequence order, and layer normalization and residual connections ensure stability and efficient training. Together, these components make the Transformer a powerful and widely adopted model.

4.2. iTransformer Architecture

The iTransformer model is an adaptation of the classic Transformer architecture, designed specifically for time series prediction using an inverted dimension approach. Unlike the traditional structure, the improved model inverts the time series dimensions, enabling the attention mechanism and feed-forward network to operate across different dimensions, capturing correlations and trends in multivariate time series more effectively. The schematic diagram of the relevant iTransformer principles is shown in Figure 10. Key iTransformer functions compared to the Transformer are as follows:

4.2.1. Inverted Dimension Design and Embedding Process

In traditional architectures, the input time series X ∈ R T × N , which consists of T time steps and N variables, is embedded so that multiple variables at each time step form a single time-step token. This approach focuses primarily on dependencies across time steps, potentially overlooking correlations among variables. In contrast, the iTransformer uses an inverted dimension design, embedding each variable’s entire time series as a separate variable token, thus allowing the attention mechanism to capture inter-variable relationships. The embedding process is as follows:
h 0 n = Embedding ( X : , n ) ,   n = 1 , 2 , … , N
where X : , n represents the entire time series for the n-th variable, and h 0 n is the representation after embedding each variable.

4.2.2. Inverted Application of Self-Attention Mechanism

In traditional models, the self-attention mechanism operates along the time dimension, capturing temporal dependencies by calculating the relationships between each time step. In the iTransformer, however, self-attention is applied across the variable dimension. By calculating correlations among different variables, the model can capture inter-variable dependencies. The formula is as follows:
Q n , K n , V n = h n W Q , h n W K , h n W V
Attention ( Q n , K n , V n ) = softmax ( Q n K n T d k ) V n

4.2.3. Application of Feed-Forward Network (FFN) in the Time Dimension

The FFN is applied to each variable’s time-series representation, allowing the model to better capture temporal changes for each variable. The formula is:
H l + 1 n = F F N ( H l n )

4.2.4. Omitting Positional Encoding

Since the iTransformer applies attention across the variable dimension rather than the time dimension, positional encoding is omitted. Temporal sequence information is implicitly captured through the FFN and attention mechanism.

4.2.5. Multivariable Correlation Handling

A key innovation of this model is its ability to specifically address variable correlations in multivariate time series. By applying attention across the variable dimension, the model generates a multivariable correlation map, which helps capture the influence among different variables. The attention score matrix A is calculated as follows:
A i j = softmax ( Q i K j ⊤ d k )
This matrix describes the correlation between variables i and j, which is critical for accurate multivariate time-series prediction.

4.3. Feature Selection

This section addresses the selection of features most relevant to predicting battery cluster voltage. These features represent various operating conditions and state variables, such as temperature, load, current, and voltage history. Although the self-attention mechanism adjusts weights based on input features, selecting a higher-correlation feature set improves model convergence and performance. The Pearson Correlation Coefficient (PCC) and Spearman Coefficient are used for feature selection. PCC measures linear correlation with battery cluster voltage, while the Spearman Coefficient captures nonlinear relationships. Together, these metrics comprehensively identify features with strong relevance to the target variable.

4.3.1. Pearson Correlation Coefficient

PCC is a standard measure of linear correlation between two variables. It is used to select features with strong linear relationships to battery cluster voltage. The PCC formula is:
r x , y = ∑ ( x i − x ¯ ) ( y i − y ¯ ) ∑ ( x i − x ¯ ) 2 ∑ ( y i − y ¯ ) 2
where r x , y is the correlation coefficient between feature x and voltage y. PCC values range from −1 to 1, with values closer to 1 or −1 indicating a stronger linear correlation.

4.3.2. Spearman Coefficient

The Spearman Coefficient, a rank-based correlation measure, is suitable for selecting features with nonlinear relationships. It assesses correlation by comparing variable ranks, calculated as follows:
ρ x , y = 1 − 6 ∑ d i 2 n ( n 2 − 1 )
where ρ x , y is the Spearman coefficient, d is the rank difference between feature x and voltage y, and n is the sample size. Like PCC, Spearman values range from −1 to 1, with values closer to 1 or −1 indicating a stronger correlation.
The combined use of PCC and Spearman can provide a comprehensive assessment of both linear and nonlinear relationships. PCC effectively evaluates linear relationships, while Spearman is suitable for identifying monotonic relationships in the data. Therefore, the combination of both can offer a thorough evaluation of the various associations between variables. Additionally, this approach enhances robustness, as PCC requires specific data distribution, particularly linear relationships and normality, while Spearman does not require normal distribution and is better suited for handling nonlinear or non-normally distributed data. Thus, the joint use of these two methods can offer more accurate correlation analysis across different types of data.

4.3.3. Feature Selection Based on Real Ship Data

In battery voltage prediction for electric vehicle BMSs, voltage characteristics or fluctuations during operation or charging may be influenced by various external factors, including meteorological conditions, vessel operational states, and inherent battery characteristics. To enhance prediction accuracy, this study comprehensively considers these three dimensions—meteorological factors, vessel operating conditions, and battery system characteristics—forming a more robust framework for predicting ship battery voltage.
Regarding meteorological factors, environmental conditions significantly impact battery voltage, especially in maritime applications. However, due to the variability and unpredictability of marine weather, variables such as humidity, precipitation, atmospheric pressure, temperature, visibility, and wind speed may not fully represent actual operational conditions, as they lack direct correlations with a vessel’s dynamic state and do not sufficiently capture voltage fluctuation patterns. To address this limitation, this study incorporates a feature combination of “pod power + speed”. This pairing effectively reflects the vessel’s power demand and operating state in complex maritime environments, indirectly capturing real-time environmental effects on battery voltage. For example, pod power and speed indicate current power output demands and operational conditions, providing insights beyond environmental factors alone. Consequently, this feature combination enables more precise voltage predictions under varying conditions.
At the battery system level, several features closely related to battery voltage were selected, including voltage, probe temperature, state of charge (SOC), and current. These variables directly represent the real-time status and health of the battery system. While driver behavior may influence battery voltage fluctuations—especially as operational inputs can alter battery load (e.g., sudden acceleration or deceleration)—this impact is typically indirect and difficult to quantify. Furthermore, complex interactions exist between driver behavior and environmental factors; for instance, different driver actions in the same environment can uniquely impact the battery system, making precise modeling challenging. In light of this, this study excludes driver behavior as a factor and instead focuses on meteorological factors, vessel operating conditions, and battery characteristics, reducing model complexity and improving predictive accuracy. Ultimately, the selected features include SOC, temperature, current, total voltage, left pod power, right pod power, and speed.
As shown in Figure 11, An analysis of the Pearson correlation coefficient (PCC) and Spearman coefficient for features related to battery cluster voltage prediction reveals a strong positive correlation between current and battery cluster voltage, with a PCC of 0.905716 and a Spearman coefficient of 0.823703. Therefore, current should be prioritized as a key feature. The power of the left and right pods also demonstrates significant negative correlation, with Spearman coefficients of −0.78632 and −0.78287, respectively, indicating strong nonlinear effects and establishing them as important predictive indicators. The Spearman coefficient between the total voltage of the battery system and the battery cluster voltage is 0.697869, indicating a complex nonlinear relationship, which should be considered as an auxiliary feature. A negative linear relationship exists between speed and probe temperature with battery cluster voltage; however, the low Spearman coefficients suggest weak nonlinear effects, allowing these features to be considered as secondary. The state of charge (SOC) shows low correlation, n, with battery cluster voltage, indicating that it may not play a significant role in voltage prediction.
Although the analysis using PCC and Spearman coefficients revealed a strong correlation between battery cluster voltage and the left and right pod power, potential multicollinearity between these features may lead to information redundancy. Multicollinearity can affect model stability and interpretability; feature redundancy was further evaluated by calculating the Variance Inflation Factor (VIF). VIF is a tool that assesses linear relationships among features, calculated as follows:
V I F i = 1 1 − R i 2
where R i 2 represents the coefficient of determination, showing how well a feature can be predicted by the other features. A VIF > 10 typically indicates a strong linear relationship with other features, suggesting redundancy. Our calculations yielded VIF values of 15.438989 for both left and right pod power, significantly exceeding the threshold of 10, which suggests overlapping information. As a result, only one feature, left pod power, was retained to reduce redundancy. The final selected features were left pod power, probe temperature, current, system voltage, and speed.
To comprehensively evaluate model performance, three standard regression metrics were employed:
1. Root Mean Square Error (RMSE): RMSE measures the standard deviation of prediction errors, reflecting the magnitude of prediction error. The formula is:
RMSE = 1 n ∑ i = 1 n ( y ^ i − y i ) 2
2. Mean Absolute Error (MAE): MAE measures the average absolute difference between predictions and actual values, representing the actual magnitude of prediction errors. The formula is:
MAE = 1 n ∑ i = 1 n | y ^ i − y i |
3. Mean Absolute Percentage Error (MAPE): MAPE evaluates prediction error as a percentage of actual values, showing the relative magnitude of prediction error. The formula is:
MAPE = 100 % n ∑ i = 1 n | y ^ i − y i y i |

4.4. Prediction Results and Discussion

In this study, the electric ship has 12 battery clusters. Training and building separate models for each cluster would be time-consuming, and invoking multiple models simultaneously during real-time voltage prediction could substantially reduce prediction efficiency. To address this issue, the data from all 12 clusters were sequentially combined into a new, unified battery cluster voltage dataset. This combined data were then used to train a generalized voltage prediction model. By incorporating the voltage information from each individual cluster, this approach enabled the creation of a well-calibrated model capable of predicting voltage across all clusters simultaneously. The prediction and fault diagnosis responses were evaluated using an alarm scenario that occurred around 9:50 AM on 3 January 2023, as shown in Figure 12.
In Figure 12, the voltage difference fluctuated over time, remaining small between 09:56 and 10:05 before gradually increasing, peaking at a significant voltage difference around 10:10, and then slowly declining. The alarm status is indicated by a dashed line, with 0 representing no alarm and 1 indicating an active alarm. Whenever the voltage difference increased, the alarm status shifted from 0 to 1, signifying that the system detected an anomaly. This also illustrates the inherent delay in the alarm response.
This study combined Transformer and iTransformer models to predict short-term voltage range variations in segments with active alarms. Each input sequence consisted of voltage difference data across 30 consecutive time points, which were preprocessed as input to the model, with the goal of predicting the next 10 time points’ voltage values. During training, the Mean Squared Error (MSE) was used as the loss function, and the model was optimized with the Adam optimizer. Learning rates were adjusted to ensure that the model converged quickly and stabilized at an optimal prediction performance. Transformer-based prediction results and relative error are shown in Figure 13 The analysis shows that the model effectively captures the overall trend of voltage changes, particularly in periods of gradual voltage increase. However, the model’s response lagged during sharp declines in voltage difference, resulting in a spike in error, with prediction errors reaching up to 15 V during sudden events and alarms.
Applying the iTransformer model to the same alarm segment with identical sequences, the voltage data from the previous 20 time points were used as the training sample to predict the following 10 time points. The prediction results and errors for the sliding data window over the fault segment are shown in Figure 14. The iTransformer model captured fluctuations more accurately, with reduced amplitude and frequency of oscillations, indicating improved handling of noise and minor local variations. Overall, errors remained within a 5 V range, demonstrating strong predictive accuracy when voltage differences were relatively stable. Table 3 summarizes the model’s prediction performance across all battery clusters, showing that iTransformer outperformed Transformer in RMSE, MAE, and MAPE, with predictions closer to actual values, confirming its superior predictive capability.
To predict fault alarms, the predicted results were compared with fault detection thresholds, enabling fault identification and providing short-term predictions 90 s in advance. In fault prediction analysis, FP, FN, TP, and TN are calculated. From these, accuracy, recall, and F1 score are derived, which help us evaluate the model’s performance in predicting faults. Based on fault alarms recorded during a year of operations in the ship data utilized in this study, and using iTransformer and threshold analysis, the following evaluation metrics were obtained in Table 4.

5. Conclusions

This paper utilizes real driving data from the all-electric ship Junlv to diagnose and predict inconsistent faults under complex operating conditions. Initially, an analysis of the actual driving data revealed that the fault alarms of the marine BMS exhibit latency and that faults often coincide with anomalies in battery cluster voltage. A fault diagnosis method based on DBSCAN clustering of battery cluster voltage and a fault prediction method using the iTransformer model are proposed. Based on real driving data, the DBSCAN method effectively identifies the locations of fault units. Throughout the year of study, the accuracy of this clustering method was consistently 1, with a recall rate around 0.96 and an F1 score around 0.98, significantly outperforming the K-means clustering algorithm. This demonstrates the superiority of the DBSCAN model in the context of this research. Additionally, the iTransformer prediction method can diagnose faults up to 90 s in advance. Its RMSE for voltage prediction is 0.390, its MAE is 0.343, its MAPE is 0.03%, and the F1 score for fault diagnosis is 94.87%. Overall, this work demonstrates the potential of integrating real data with deep learning modeling to achieve accurate predictions of real-world physical problems characterized by hidden physics and lacking predefined initial or boundary conditions. Timely and accurate detection and prediction of battery fault risks under complex operating conditions are crucial for ensuring the safe operation of battery systems in real all-electric ship environments. Future research will focus on further optimizing detection and prediction models, as well as assessing multiple faults, including consistency faults caused by capacity, state of charge (SoC), and internal resistance.

Author Contributions

Conceptualization, X.Y. and Y.L.; methodology, H.J. and Y.L.; software, Y.L.; validation, Y.L., H.J. and T.T.; formal analysis, Y.L., H.J. and L.L.; investigation, Q.S.; resources, H.J. and Q.S.; data curation, Y.C.; writing—original draft preparation, X.Y. and S.J.; writing—review and editing, H.J. and Y.L.; visualization, Y.L. and H.J.; supervision, X.Y.; project administration, X.Y.; funding acquisition, X.Y. All authors have read and agreed to the published version of the manuscript.

Funding

This work is supported by the China National Key Research and Development Project (Grant No: 2023YFB4301704), the National Natural Science Foundation of China (Grant No: 52271329) and the China National Key Laboratory of Electromagnetic Energy Technology Open Fund (Grant No: 61422172220403).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data will be made available on request.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Network topology of the battery system.
Figure 1. Network topology of the battery system.
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Figure 2. Some of the data used in this article. (a) is the electric boat speed, (b) is the battery cluster voltage sampled by the electric boat BMS, and (c) is the right pod power.
Figure 2. Some of the data used in this article. (a) is the electric boat speed, (b) is the battery cluster voltage sampled by the electric boat BMS, and (c) is the right pod power.
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Figure 3. Alarm flow chart of BMU, BCU, and BAU in Marine BMS.
Figure 3. Alarm flow chart of BMU, BCU, and BAU in Marine BMS.
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Figure 4. Time-stamped ship alarm status and differential signals on 1 January 2023.
Figure 4. Time-stamped ship alarm status and differential signals on 1 January 2023.
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Figure 5. Schematic diagram of DBSCAN clustering method.
Figure 5. Schematic diagram of DBSCAN clustering method.
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Figure 6. Comparison of fault points and true labels based on DBSCAN.
Figure 6. Comparison of fault points and true labels based on DBSCAN.
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Figure 7. DBSCAN clustering result evaluation indicator value in each month.
Figure 7. DBSCAN clustering result evaluation indicator value in each month.
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Figure 8. Cloud-based data platform for iTransformer fault prediction.
Figure 8. Cloud-based data platform for iTransformer fault prediction.
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Figure 9. Transformer-related structural design diagram.
Figure 9. Transformer-related structural design diagram.
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Figure 10. iTransformer-related structural design diagram.
Figure 10. iTransformer-related structural design diagram.
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Figure 11. PCC (a) and Spearman (b) correlation coefficient calorific value map.
Figure 11. PCC (a) and Spearman (b) correlation coefficient calorific value map.
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Figure 12. Voltage difference in the battery cluster and fault alarm status for the fault segment on 3 January 2023.
Figure 12. Voltage difference in the battery cluster and fault alarm status for the fault segment on 3 January 2023.
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Figure 13. Voltage prediction results and errors based on the transformer model.
Figure 13. Voltage prediction results and errors based on the transformer model.
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Figure 14. Voltage prediction results and errors based on the iTransformer model.
Figure 14. Voltage prediction results and errors based on the iTransformer model.
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Table 1. The specifications of the electric ship studied.
Table 1. The specifications of the electric ship studied.
ParameterSpecification
TypePassenger Ship
Length55 m
Width10 m
Draft Depth1.6 m
Coordinates114–17.414 E, 30–34.296 N
DestinationWuhan Port
Battery Capacity 2240 kWh
Maximum Speed 10 knots/h
Number of Battery Clusters12
Nominal Voltage3.2 V
Rated Capacity280 Ah
Table 2. Common faults and thresholds.
Table 2. Common faults and thresholds.
Fault TypeLevelThreshold
Cell overvoltage (V)13.5
23.6
33.65
Cell Undervoltage (V)13.1
23.0
32.8
Cell Voltage Deviation (mV)1350
2400
3500
Cluster Overvoltage (V)13.55 * N
23.6 * N
33.65 * N
Cluster Undervoltage (V)13.1 * N
23.0 * N
32.8 * N
Table 3. Model’s prediction performance.
Table 3. Model’s prediction performance.
Prediction MethodRMSEMAEMAPE (%)
Transformer1.1920.8400.16
iTransiformer0.3900.3430.03
Table 4. Model fault prediction evaluation index.
Table 4. Model fault prediction evaluation index.
Performance MetricValue
Accuracy93.25%
Precision94.28%
Recall95.47%
F1 Score94.87%
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MDPI and ACS Style

Liu, Y.; Jin, H.; Yang, X.; Tang, T.; Song, Q.; Chen, Y.; Liu, L.; Jiang, S. Early Fault Diagnosis and Prediction of Marine Large-Capacity Batteries Based on Real Data. J. Mar. Sci. Eng. 2024, 12, 2253. https://doi.org/10.3390/jmse12122253

AMA Style

Liu Y, Jin H, Yang X, Tang T, Song Q, Chen Y, Liu L, Jiang S. Early Fault Diagnosis and Prediction of Marine Large-Capacity Batteries Based on Real Data. Journal of Marine Science and Engineering. 2024; 12(12):2253. https://doi.org/10.3390/jmse12122253

Chicago/Turabian Style

Liu, Yifan, Huabiao Jin, Xiangguo Yang, Telu Tang, Qijia Song, Yuelin Chen, Lin Liu, and Shoude Jiang. 2024. "Early Fault Diagnosis and Prediction of Marine Large-Capacity Batteries Based on Real Data" Journal of Marine Science and Engineering 12, no. 12: 2253. https://doi.org/10.3390/jmse12122253

APA Style

Liu, Y., Jin, H., Yang, X., Tang, T., Song, Q., Chen, Y., Liu, L., & Jiang, S. (2024). Early Fault Diagnosis and Prediction of Marine Large-Capacity Batteries Based on Real Data. Journal of Marine Science and Engineering, 12(12), 2253. https://doi.org/10.3390/jmse12122253

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