A Novel Open Set Adaptation Network for Marine Machinery Fault Diagnosis

Abstract

Domain adaptation techniques have effectively tackled fault diagnosis under varying operational conditions. Many existing studies presume that machine health states remain consistent between training and testing data. However, in real-world scenarios, fault modes during testing are often unpredictable, introducing unknown faults that challenge the effectiveness of domain adaptation-based fault diagnosis methods. To address these challenges, this paper proposes a Deep Open Set Domain Adaptation Network (DODAN). Firstly, a feature extraction module based on multi-scale depthwise separable convolutions is constructed for discriminative feature extraction. To improve the model’s adaptability, an adversarial training strategy is implemented to learn generalized features that are resilient to unknown domain shifts. Additionally, an outlier detection module is employed to determine the optimal decision boundaries for each class representation space, enabling the classification of known fault modes and the identification of unknown ones. Extensive diagnostic experiments on two marine machinery datasets validate the effectiveness of the proposed method. Furthermore, ablation studies verify the efficacy of the proposed modules and strategies, highlighting significant potential for practical applications.

1. Introduction

Marine diesel engines are the most critical mechanical equipment in a ship’s engine room due to their complex system structure. Any malfunction in these engines can severely impact the ship’s navigation safety. With increasing automation, marine equipment structures have become more complex and integrated, making reliable diagnosis an indispensable part of modern engineering systems’ safety [1]. Components in marine machinery are prone to faults in various industrial scenarios, affecting system reliability. Machine learning, a current research focus in areas such as speech recognition and image processing, has been widely adopted to address complex practical application challenges [2,3,4]. The development of artificial intelligence technology, especially machine learning algorithms based on deep learning, has made great breakthroughs in the fields of image and speech recognition. Therefore, some scholars have introduced deep learning into the field of rolling bearing fault diagnosis and achieved good results [5,6].

Zhao et al. [7] proposed a novel incremental learning method that is based on classification and feature-level information. This method utilizes an adaptive dual-branch residual network and adversarial network to enhance model robustness under noisy conditions and overcome catastrophic forgetting. Experimental results showed superior performance in diagnosing complex mechanical equipment faults compared to existing methods. Wang et al. [8] introduced a deep reinforcement network (MDAQN) method to address data imbalance in gearbox fault diagnosis. By incorporating an imbalanced classification Markov decision process and a multi-scale attention convolutional network, the method improves feature extraction and generalization capabilities, achieving over 99.0% accuracy across three datasets. Lu et al. [9] proposed an enhanced active learning intelligent fault diagnosis method to tackle sample imbalance in rolling bearing fault diagnosis. By using Gaussian mixture models and density peak clustering techniques, the method intelligently labels unmarked samples from limited labeled samples, enhancing classification performance and reducing the number of labeled samples needed for training. Experimental results indicated a significant improvement in fault diagnosis accuracy for imbalanced samples with fewer training data. Dong et al. [10] introduced a multi-scale dynamic supervised contrastive learning (MDSupCon) framework. This approach employs a multi-scale adaptive feature extraction network combined with a channel-spatial joint attention mechanism to improve feature extraction and fault recognition under varying conditions. Li et al. [11] introduced a domain adversarial graph convolution network (DAGCN) that models class labels, domain labels, and data structures within a unified deep network. This method aims to improve unsupervised domain adaptation (UDA) performance in varying working conditions for mechanical fault diagnosis. By combining classifiers, domain discriminators, and graph convolution networks, the method more comprehensively extracts and utilizes feature information. Experimental results showed that DAGCN outperforms other methods in two case studies, enabling the extraction of transferable features for domain adaptation. In the context of marine machinery, Wang et al. [12] put forward a graph convolution network (GCN) fault diagnosis approach based on distance and probability topology graphs (DPGCN). By constructing two topological graphs (distance and probability topology graphs) to handle class imbalance in marine diesel engine condition monitoring data and by combining graph learning and self-attention mechanisms, his method enhances the classification accuracy and stability in imbalanced datasets. Experimental results demonstrate the superior performance of the DPGCN model in handling imbalanced data. Wang et al. [13] introduced a self-supervised contrastive learning framework (SCLNNM) based on nearest-neighbor matching in order to obtain discriminative feature representations from large-scale unlabeled data, addressing the issue of limited labeled samples in the maritime industry. By designing a reasonable data augmentation strategy and by identifying the nearest neighbor positive instances of input signals, combined with a 1D CNN model and contrastive learning, the method effectively learns robust and comprehensive representations derived from various augmented signals. Experimental results show that this framework significantly improves fault diagnosis classification accuracy under limited labeled datasets. Velasco-Gallego et al. [14] introduced the Mar-RUL system, which aims to optimize predictive maintenance in the maritime industry by integrating deep learning models. Using a degradation data simulation module and a case study on the turbo-charger of a tanker diesel generator, results indicate that time-series imaging and integrated methods yield promising results in predicting the remaining useful life (RUL). Liu et al. [15] combined convolutional neural networks (CNN) and bidirectional gat-ed recurrent units (BiGRU) to develop a model for predicting marine diesel engine exhaust temperatures. The predictive performance yielded a mean squared error (MSE) of 0.1156, a mean absolute error (MAE) of 0.2501, and a mean absolute percentage error (MAPE) of 0.0005336. By setting alarm thresholds based on the residual distribution and standard deviation calculated through a sliding window and by validating under abnormal conditions, the method accurately identifies diesel engine fault warnings, providing new references for intelligent marine equipment health management. Li et al. [16] investigated the issue of current waveform analysis failing to accurately determine the operational state of large multi-cylinder marine diesel engines (MCMDE) by proposing an intrinsic multi-scale dispersion entropy (IMDE) framework based on intrinsic reconstructed instantaneous angular velocity (IAS) signals. The method first decomposes IAS signals using intrinsic feature scale decomposition, selects appropriate components to re-construct denoised IAS signals, and finally quantifies the intrinsic reconstructed IAS signals using MDE to identify operational states. Simulation and experimental results demonstrate that IMDE effectively extracts fault features under different conditions, with classification accuracy superior to existing methods such as MDE, multi-scale sample entropy (MSE), and multi-scale fuzzy entropy (MFE). Fu et al. [17] introduced a state monitoring method for marine engines by establishing a test bench to record various temperature and pressure data. By employing principal component analysis, sparse autoencoder, and physics-based models, the study conducted a comparative analysis of anomaly detection and fault isolation for typical issues such as lubrication oil filter blockage and cylinder leakage. Results showed that data points for filter blockage faults were typically twice the threshold set by data-driven models, with lubrication oil pressure dropping from 3.2–3.8 bar to approximately 2.3 bar. For cylinder leakage faults, the test data showed a nearly four-fold increase in the threshold, with exhaust temperature dropping from an estimated 150–200 °C to about 100 °C. The study delved into the transferability and interpretability of the models, offering guidance for effective state monitoring of marine engines. Dong et al. [18] addressed the high cost and difficulty of acquiring fault sample data by establishing a multi-body dynamic model of marine turbochargers and using simulation methods to obtain turbocharger vibration signals. A diagnostic model developed using the TrAdaBoost transfer learning method achieved an accuracy of 87% with 20 samples and 96% with 40 samples in the validation of 2040 simulated fault samples. The diagnostic model can transfer diagnostic information between actual turbochargers and simulation models. Cai et al. [19] proposed a VGG16-based transfer learning convolutional neural network model for diagnosing valve leakage faults in marine diesel engines. Initially, the vibration signals of diesel engine cylinder heads were converted into time-domain, frequency-domain, and wavelet decomposition images. Subsequently, the pre-trained VGG16 network from the ImageNet dataset was fine-tuned using image enhancement methods and pre-trained parameters. Finally, the well-trained model was utilized to train and test the target dataset. The cosine annealing learning rate setting method was applied to ensure that the learning rate approached the global optimum. Experimental results indicated that, in comparison to traditional methods and other deep learning models, this approach achieved higher accuracy and noise robustness in small sample datasets. The study not only provides a new method for diagnosing valve leakage in diesel engines but also offers applicable diagnostic insights for other similar issues.

The literature reviewed indicates that fault diagnosis methods based on deep learning have demonstrated promising results. However, optimal application scenarios for deep learning share several key characteristics: the training dataset (source domain) and the testing dataset (target domain) must have the same distribution and there must be a large amount of labeled data available during the training phase. Despite this, the variability of mechanical working conditions often leads to inconsistencies in data distribution, causing domain shifts. Furthermore, unpredictable and unknown fault modes may emerge during testing, which were not present in the training dataset, resulting in category gaps known as open-set fault diagnosis. These challenges hinder the further development and implementation of deep learning in intelligent fault diagnosis (IFD).

Domain adaptation techniques utilize knowledge acquired from labeled data in the source domain to identify the health status of unlabeled data in the target domain. These techniques have been widely employed in industrial fault diagnosis and have produced significant results [20,21]. In their study, Lu et al. [22] introduced a new model for diagnosing faults in wind turbine drivetrains, known as the Class Imbalance-Aware Deep Adversarial Network (CIDAA). This model was designed to tackle challenges associated with varying environmental conditions and limited fault-related data. Wind turbines operate under constantly changing conditions, making it challenging for traditional machine learning models trained on standard conditions to adapt to different domain distributions. Moreover, the scarcity of fault-labeled data in real wind turbines results in imbalanced training data. The CIDAA model addresses these issues by learning domain-invariant features through a class imbalance-aware layer and by enhancing the discriminatory structure of the imbalanced feature space. As a result, it effectively generalizes from labeled source domains to unlabeled target domains. The performance of the CIDAA model was evaluated using a high-fidelity 5 MW reference drivetrain model’s bearing damage dataset under three environmental conditions, demonstrating its superior accuracy in fault classification when handling varying environmental conditions and imbalanced data. Zhang et al. [23] introduced a Feature Discard and Augment Module (FD-DAML)-based domain adaptive meta-learning network to address performance degradation in actual industrial applications due to data scarcity and varying equipment, load, and operational conditions. This method alternates source and target domain meta-learning within a unified framework, combined with domain adversarial training, addressing issues such as differences in labeled sample distribution, label space mismatch, and scarcity of samples in the target domain; the FD-DAML has been designed to incorporate a plug-and-play feature discard–augment module to enhance the model’s generalization capability. Zhang et al. [24] proposed a Pseudo-Label Transfer Domain Adaptive Network (PLTDAN) for fault diagnosis, addressing domain shift issues in cross-bearing transfer. The authors provide empirical selection criteria to ensure the appropriate intermediate domain is selected to better bridge the source and target domains. By adding TDANs in the intermediate domain, the direct transfer process is split into source-intermediate and intermediate-target gradual transfers, progressively correcting domain shifts. Additionally, they propose a Cross-Domain Pseudo-Label Constraint (CDPLC) to select high-confidence intermediate domain samples and generate corresponding pseudo-labels, thus reducing TDAN’s accumulated errors. Lu et al. [25] introduced a novel domain adaptation method, named DASSL-FC, which is based on self-supervised learning and feature clustering. The purpose of this method is to address the issues where feature learning in domain adaptation tends to favor the source domain and unreliable pseudo-labels affect conditional domain adaptation. To mitigate these issues, this method employs unbiased feature learning and pseudo-label updating strategies. Specifically, different transformation methods are used to train neural networks with transformed data and their original data in a self-supervised learning (SSL) manner. In terms of pseudo-labels, clustering is used as auxiliary information to correct network-predicted labels according to the “strong clustering” rule. Then, the updated pseudo-labels and their confidence are further used to estimate conditional distribution differences and their confidence weights. In order to verify the effectiveness of this method, platform-specific and cross-platform simulations were conducted. The results demonstrate significant advantages of DASSL-FC in intelligent fault diagnosis.

Zhang et al. [26] proposed a two-stage Multi-Source Partial Domain Adaptation (MSPDA) method based on Pseudo-Balanced Target Domains (PBTD) to address domain shift issues faced in multi-source domain adaptation (MSDA) and the possibility that target domain class labels might be a subset of source domain class labels. In the initial stage, a weighted adversarial partial domain adaptation method is employed, which is based on a double progressive strategy to align each source domain with the target domain in order to construct a series of PBTDs. In the subsequent stage, an alternating learning scheme is utilized to align the remaining source domains with the PBTDs, thereby fully leveraging multi-source information to bridge differences between domains. To enhance the algorithm’s representation capability, a multi-scale convolutional neural network, incorporating a three-branch attention mechanism, is proposed to capture cross-dimensional interactions of scale, channel, and space. Xia et al. [27] introduced an innovative deep adversarial domain adaptation approach for the fault diagnosis of industrial robot bearings operating under diverse working conditions. In response to the challenges presented by evolving work environments, a new approach is being introduced to ensure an equal distribution between the target and source domains, improving adversarial training stability. Furthermore, a timestamp-based method is proposed to improve the efficiency of preprocessing vibration signals. Experimental results demonstrate superiority over CNN and conditional adversarial network-based methods in accuracy and excel in handling classic handling tasks in industrial robots. Guo et al. [28] addressed the urgent need for intelligent fault diagnosis technology in developing intelligent ships by proposing a method called the Multi-Scale Multi-View Domain Adversarial Network (MMDAN) to tackle fault diagnosis challenges in high-power marine diesel engines operating under various complex conditions. Due to a lack of fault labels in extensive working condition data and asymmetrical fault modes across different conditions, knowledge transfer from source conditions to target conditions was designed and the method was validated using operational data from the 6S50MC-C7 marine diesel engine system.

Despite these advancements, the diagnostic performance of these algorithms significantly degrades in open-set scenarios. Therefore, it is crucial to develop open-set fault diagnosis models for industrial applications. The effectiveness of open-set domain adaptation fault diagnosis methods relies on learning domain-invariant representations and detecting outlier samples. However, there is limited research in this area, so further exploration is necessary.

The main contributions of this paper are the following:

• Addressing the fault diagnosis problem in open-set domain adaptation scenarios for marine machinery fault diagnosis, filling a research gap in multi-sensor collaborative diagnosis under open-set domain adaptation scenarios;
• The proposed method extracts fault features using multi-scale separable convolution kernels and proposes a weighted adversarial learning strategy to learn domain-invariant features. The outlier detection module identifies unknown class samples;
• Conducting experiments and comparative studies on two marine machinery datasets, demonstrating high accuracy in open-set domain adaptation problems with the proposed model.

2. Preliminaries

2.1. Problem Definition

In fault diagnosis, data collected under the same working conditions constitute a domain. Let $D_s={\left\{(x_i^s,y_i^s)\right\}}_{i=1}^{n_s}$ represent the labeled source domain and $D_t={\left\{(x_i^t)\right\}}_{i=1}^{n_t}$ represent the unlabeled target domain, where $n_s$ and $n_t$ are the numbers of samples in the source and target domains, respectively. Due to changes in working conditions, the data distributions of the source and target domains differ, i.e., $P_t(x^t)\ne P_s(x^s)$. We denote the class labels of the target and source domains as $C_s$ and $C_t$, respectively. The shared label space is represented as $C=C_s\cap C_t$. The private label space is ${\overline{C}}_t=C_t\backslash C$; label settings specific to the target domain should be identified as “unknown”.

In this type of open set domain adaptation, the target domain is entirely unlabeled during training and $C_t$ is unknown, making it challenging to identify the shared part of the target and source label spaces. Distinguishing shared and unknown target samples is particularly challenging due to the absence of any traces of target sample labels.

Table 1. Comparison between open-set domain adaptation fault diagnosis and related topics.

Topic	Ps versus Pt		Cs versus Ct			Target Data for Training
	=	≠	Cs = Ct	Cs⊃Ct	Cs⊂Ct	Labeled data	Unlabeled data
DL	√		√			√
DA [21]		√	√				√
PSDA [28]		√		√			√
OSDA		√			√		√

compares the fault diagnosis scenarios of OSDA with related topics. TDL represents the traditional training paradigm of deep learning. DA stands for domain adaptation, PSDA stands for partial set domain adaptation, and OSDA stands for open set domain adaptation.

Figure 1 illustrates the schematic diagram of closed set, partial set, and open set domain adaptation in fault diagnosis. The open set domain adaptation scenario includes fault classes in the target domain that are not present in the source domain, making OSDA fault diagnosis more challenging.

2.2. Multi-Scale Lightweight Feature Extraction Module

Convolutional Neural Networks (CNNs) are among the most widely used models in deep learning and are studied extensively for various recognition tasks. The combination of convolutional and fully connected layers allows CNNs to automatically extract and classify features. Recently, many advanced lightweight CNNs have emerged, utilizing depthwise separable convolutions to reduce model size and computational load. Figure 2 shows an example with a data segment containing $K$ channels, where the convolution kernel’s width and height are $D_m$ and $D_n$, respectively. The parameters for this part are $D_m\times D_n\times K$. After pointwise convolution, the convolution kernel’s size is $1\times 1\times K$. If we need $N$ feature maps, the parameters for pointwise convolution are $K\times 1\times 1\times N$. The parameters for depthwise separable convolutions (DSC) are $P_{DSC}=D_m\times D_n\times K+K\times 1\times 1\times N$, while the parameters for regular convolutions (PCNN) are $P_{CNN}=D_m\times D_n\times K\times N$. The optimization equations for both are shown below (multiplication calculations are much more significant than additions and hence are disregarded).

$${\mathrm{z}}^{{\displaystyle \frac{P_{DSC}}{P_{CNN}}}}={\displaystyle \frac{D_m\times D_n\times K+K\times 1\times 1\times N}{D_m\times D_n\times K\times N}}={\displaystyle \frac{1}{K}}+{\displaystyle \frac{1}{D_m\times D_n}}$$

(1)

3. Proposed Method

3.1. DODAN

The DODAN structure is shown in Figure 3. Firstly, a multi-scale extraction module based on DSC is constructed for distinguishing feature extraction. A weighted adversarial learning scheme is proposed to carry out domain invariant learning of shared fault modes between the source domain and target domain. Adversarial learning is implemented between the feature extraction module and the domain discriminator. In the process of model training, the domain discriminator is optimized to correctly identify the domain label of the input data, and the feature extractor is trained to confuse the domain discriminator, that is, to increase the domain prediction error. Through the iteration of adversarial training, the learned features can become more and more domain invariant. This bridges the domain gap and allows generalized features to be used for subsequent fault diagnosis. Finally, an outlier detection module is proposed to learn the optimal decision boundary of each class representation space to classify known fault modes and identify unknown fault modes.

The specifics of the proposed architecture and parameters are detailed in

Table 2. Structure of the modules in DODAN.

Module	Layer Name	Layer (Receptive Field Size Channels—Stride—Padding)	Output
Feature Extractor G	L1	Dsc 9 × 1-128-1-3 (BN, LReLU)
		Maxpooling 2 × 1-1-2	512 × 128
	L2	Dsc 7 × 1-64-1-2 (BN, LReLU)
		Maxpooling 2 × 1-1-2	256 × 64
	L3	Dsc 5 × 1-64-1-1
		Maxpooling 2 × 1-1-2	128 × 64
	L4	Dsc 3 × 1-32
		Maxpooling 2 × 1-1-2	64 × 32
Domain discriminator D	/	Fully Connected 100	100
Condition classifier C	/	Fully Connected 100	C

. The notation Dsc A × 1-B denotes a Depthwise Separable Convolution (DSC) layer with a filter size of A × 1 and B pointwise convolution kernels. Maxpooling 2 × 1 refers to a max-pooling layer with a 2 × 1 filter. FC represents fully connected neural layers. BN indicates batch normalization layers, which enhance computational efficiency and stabilize the training process. LReLU refers to the Leaky ReLU activation function.

Based on the supervised training method, the labelled source domain data $\left(x^s,y^s\right)$ are used to train the feature extractor G and classifier C. The network adopts the standard cross entropy loss function $L_C$ to construct the following objective function [29].

$$L_C\left({\theta }_G,{\theta }_C\right)=E_{\left(x^s,y^s\right)\in D^s}-{\displaystyle \sum _{k=1}^K{1}_{\left[y^s=k\right]}\log \left({\widehat{y}}^s\right)}$$

(2)

where ${\widehat{y}}^s$ represents the classification score output and $K$ is the number of classes in the source domain.

${\theta }_G$ represents network parameters feature extractor. ${\theta }_C$ represents the network parameter of the classifier.

The parameters ${\theta }_G$ and ${\theta }_C$ of the network can be obtained by solving the objective function, as follows:

$$\left({\widehat{\theta }}_G,{\widehat{\theta }}_C\right)=\underset{{\theta }_G,{\theta }_C}{\arg \min } L_C\left({\theta }_G,{\theta }_C\right)$$

(3)

This study aims to achieve cross-domain fault diagnosis under varying working conditions, with domain-invariant learning as a fundamental strategy to address this issue. To this end, we introduce a domain adversarial neural network (DANN) to reduce discrepancies in feature distribution. In DANN, adversarial learning strategies are employed for domain-invariant learning. The optimization objective is described as

$$L_d\left(x^s,x^t\right)={\displaystyle \frac{1}{n_s+n_t}}{\displaystyle \sum _{x_i\in D^s\cup D^t}{L}_{ce}\left(D\left(F\left(x_i^{s,t}\right)\right),d_i\right)}$$

(4)

where $d_i$ denotes the domain label and $F$ represents the shared feature space between the two domains. $L_{ce}$ is the cross entropy loss, which can be expressed as

$$L_{ce}\left(x,y\right)=-E_{\left(x,y\right)\in D}\left[{\displaystyle \sum _{k=1}^K{1}_{\left[k=y\right]}\log \left(\widehat{y}\right)}\right]$$

(5)

where $y$ is the input sample’s label and $\widehat{y}$ is the predicted label. A Gradient Reversal Layer (GRL) is introduced during adversarial training for domain adaptation.

In open-set domain adaptation scenarios, the fault categories in the source domain are typically a subset of those in the target domain. Under such circumstances, achieving global domain adaptation between the source and target domains may lead to negative transfer due to the presence of outlier conditions in the target domain. To address this issue, it is necessary to filter out samples with outlier conditions from the target domain during the domain adaptation process.

To align non-identical health condition spaces between the source and target domains, a selective adversarial network is introduced for domain adaptation (DA) learning. In the context of Selective Adversarial Networks, domain discriminators are divided into $\left|C_s\right|$ class domain discriminators $D^k$, where $k=1,2,...,\left|C_s\right|$. Each $D^k$ carries out DA for health condition $k$ of the two domains. For an input sample $x_i$, its predicted output ${\widehat{y}}_i=C\left(F\left(x_i\right)\right)$ is a probability distribution on the source label space, effectively representing the probability allocation $x_i$ to each health condition $\left|C_s\right|$.

Thus, using the probability output ${\widehat{y}}_i$ as the probability allocation for each data point $x_i$ to the $D^k$, the class-domain adaptation (CDA) loss based on probability-weighted adversarial learning is formulated as

$$L_{CDA}\left(x^s,x^t\right)=-{\displaystyle \frac{1}{m_s+m_t}}{\displaystyle \sum _{k=1}^{\left|C_s\right|}{\displaystyle \sum _{x_i\in D_s\cup D_t}{\widehat{y}}_i^k{L}_{ce}^k\left(D^k\left(F\left(x_i\right)\right),d_i\right)}}$$

(6)

where $D^k$ denotes the $k$ domain discriminator for each class. Minimizing $L_{CDA}$ seeks optimal ${\theta }_G$ and ${\theta }_D$; the training process can be described as follows:

$$\left({\widehat{\theta }}_G,{\widehat{\theta }}_D\right)=\underset{{\theta }_G,{\theta }_D}{\arg \min } L_{CDA}$$

(7)

where ${\theta }_D$ denotes the domain discriminator’s network parameters, with GRL introduced in the shared feature layer during training.

3.2. Class-Wise Decision Boundary-Based Outlier Detection

Previous research has demonstrated the superiority of spherical boundaries in open classification [30]. However, employing a unified decision boundary for a single class is suboptimal for Open-Set Domain Generalization Fault Diagnosis (OSDGFD) problems. While target known class samples tend to be closer to their corresponding source clusters than target unknown class samples, there remains uncertainty in the dissociation of target-known class samples around source samples. Hence, the optimal boundary shape for known classes may vary among classes. To mitigate these deficiencies, the designed method adjusts to the unique representation spaces of each class.

The learned feature embedding $z_{k,i}^s$ is formulated as

$$z_{k,i}^s=F\left(x_{k,i}^s\right)$$

(8)

The class prototype can then be computed as the mean vector of the embeddings, as follows:

$$c_n={\displaystyle \frac{1}{\left|S_n\right|}}{\displaystyle \sum _{\left(z_{k,i}^s,y_{k,i}^s\right)\in S_n}{z}_{k,i}^s}$$

(9)

where $S_n$ is the set of samples labeled as n and $\left|S_n\right|$ is the number of samples in $S_n$.

To accurately distinguish known and unknown fault modes, the samples of known classes ${\Delta }_n$ should be confined within a spherical region around the decision boundary, as follows:

$$\forall z_{k,i}^s\in S_n,d\left(z_{k,i}^s,c_n\right)\le {\Delta }_n$$

(10)

where $d(·,·)$ represents a suitable distance function and the study utilizes the Euclidean distance. In order to adapt the decision boundary to different class feature spaces, a deep model is employed to optimize the learnable parameter $\widehat{{\Delta }_n}\in ℝ$. To meet the following requirements $\widehat{{\Delta }_n}>0$, the Softplus activation function maps $\widehat{{\Delta }_n}$ to ${\Delta }_n$, as follows:

$${\Delta }_n=\log (1+e^{\widehat{{\Delta }_n}})$$

(11)

The decision boundary should adapt to include known samples while rejecting unknown samples. For instance, if $d(z_{k,i}^s,c_n)>{\Delta }_n$, known samples outside the boundary increase empirical risk. Conversely, if $d(z_{k,i}^s,c_n)<{\Delta }_n$, unknown samples may be misclassified as known classes, increasing open space risk. In order to address these issues, a boundary loss function is employed, as follows:

$$L_a={\displaystyle \frac{1}{K}}{\displaystyle \sum _k^K\frac{1}{n_k^s}{\displaystyle \sum \frac{n_k^s}{i=1}[{\delta }_{k,i}\left(d\left(z_{k,i}^s,c_{yk,1}\right)-{\Delta }_{yki}\right)]+\left(1-{\delta }_{k,i}\right)\left({\Delta }_{yki}-d\left(z_{k,i}^x,c_{yk,i}\right)\right)}}$$

(12)

where ${\delta }_{k,j}$ is denoted:

$${\delta }_{k,j}:=\left\{\begin{array}{c}1,\begin{array}{c}if d\left(z_{k,i}^s,c_{yk,i}\right)>{\Delta }_{yk,i}\end{array}\\ 0,\begin{array}{c}if d\left(z_{k,i}^s,c_{yk,i}\right)\le {\Delta }_{yk,i}\end{array}\end{array}\right.$$

(13)

Adaptive boundary learning customizes the boundary according to class feature spaces and learns appropriate values for $d(z_{k,i}^s,c_n)$. The decision boundaries effectively surround most known class samples near each class prototype to identify unknown fault modes.

3.3. Optimization Objectives

The ultimate objective function can be formulated as follows:

$$L=L_c+{\beta }_1{L}_{CDA}+{\beta }_2{L}_a$$

(14)

where ${\beta }_1$ and ${\beta }_2$ are trade-off parameters.

4. Experimental Research

To assess the effectiveness of the proposed open set domain adaptation method for marine machinery fault diagnosis, experiments were carried out using two marine datasets. The code was implemented in PyTorch 1.2 and run on a Core i7-9700K CPU with 16 GB RAM. The results were averaged over 10 runs. The important network hyperparameters are mainly selected by Grid Search technology in the Scikit-Learn framework or set according to experimental verification. Adam optimization algorithm is adopted to optimize and update MCCNN model parameters [31].

4.1. Dataset Description

4.1.1. Diesel Engine Dataset

Real-world fault data from marine main engine systems were collected. Detailed information is presented in

Table 3. Main specifications of the 6S50MC diesel engine.

Parameters	Value
Cylinder numbers	6
Number of stroke	2
Rated speed (r/min)	127
Continuous output (kW)	9480
Mean effective pressure (bar)	1.9
Bore (mm)	500
Stroke (mm)	2000
Stroke/bore	4
Brake Specific Fuel Consumption (g/kWh)	178.35

,

Table 4. Main specifications of the TCA66 turbocharger.

Parameters	Value
Exhaust turbine type	Axial Flow
Compressor type	Centrifugation style
Compressor pressure ratio	3.75
Compressor flow rate (kg/s)	24
Nominal speed (rpm)	14,250
Maximum allowable temperature (/°C)	500
Maximum allowable speed (rpm)	16,000
Turbine pressure ratio	3.24
Weight (kg)	5500

and

Table 5. Label information for the experimental dataset.

Data Type	Engine Conditions	Label
Health condition	Without any fault	1
Performance Breakdown	Turbocharger filter screen dirty blocked	2
	Dirty blockage of air inlet	3
	Dirty blockage of exhaust port	4
	Air cooler smudge	5
	Turbine nozzle carbon deposits	6
	Air plug of cylinder liner cooling water cavity	7
Abnormal boundary condition	Insufficient cooling of cylinder liner	8
	Insufficient cooling of piston	9
	Air cooler cooling water inlet temperature too high	10
	Air cooler cooling water inlet temperature too low	11

. The data collection involved the main engine system under 90% load and 75% load conditions.

The test data consist of normal data of the host system, six types of performance fault data (turbocharger filter screen dirty blocked, dirty blockage of air inlet, dirty blockage of exhaust port, air cooler smudge, turbine nozzle carbon deposits, and air plug of cylinder liner cooling water cavity) and four types of abnormal boundary condition data (insufficient cooling of cylinder liner, insufficient cooling of piston, air cooler cooling water inlet temperature too high, and air cooler cooling water inlet temperature too low), and the dataset is classified as shown in Table 5.

4.1.2. Bearing Dataset

Provided by Paderborn University, this dataset further validates the model’s effectiveness. All vibration signals were collected from the equipment shown in the figure. Three load conditions were selected from the Paderborn University bearing data as three different working conditions. Each condition had four health statuses: Health (H), Artificial outer ring fault (AOR), Artificial inner ring fault (AIR), and Real outer ring fault (ROR), all at 1500 rpm. The vibration signals were sampled at 64 kHz. Each condition had 8000 samples, with 1200 data points per sample. The bearing dataset design is detailed in

Table 6. Paderborn University bearing datasets of different operating conditions.

NO	Load Torque (Nm)	Radial Force (N)	Health Status	Label
A	0.7	1000	H	0
	0.7	1000	AOR	1
	0.7	1000	AIR	2
	0.7	1000	ROR	3
B	0.1	1000	H	0
	0.1	1000	AOR	1
	0.1	1000	AIR	2
	0.1	1000	ROR	3
C	0.7	400	H	0
	0.7	400	AOR	1
	0.7	400	AIR	2
	0.7	400	ROR	3

.

Based on Table 5 and Table 6, two fault diagnosis tasks were created as shown in

Table 7. Diesel engine experimental task.

Transfer Task Number	Source to Target	Source Domain	Openness
D1	90%→75%	All	0
D2	75%→90%	All	0
D3	90%→75%	0 1 2 3 4 5 6 7 8 9	0.09
D4	75%→90%	0 1 2 3 4 5 6 7 8 10	0.09
D5	90%→75%	0 1 2 3 4 5 6 7 8	0.18
D6	75%→90%	0 1 2 3 4 5 6 7 9	0.18
D7	90%→75%	0 1 2 3 4 5 6 7	0.27
D8	75%→90%	0 1 2 3 4 5 6 8	0.27
D9	90%→75%	0 1 2 3 4 5 6	0.36
D10	75%→90%	0 1 2 3 4 5 7	0.36

and

Table 8. Bearing experimental task.

Transfer Task Number	Source to Target	Source Domain	Openness
B1	A→B	All	0
B2	B→C	All	0
B3	A→C	All	0
B4	B→A	0 1 2	0.25
B5	A→C	0 1 2	0.25
B6	C→B	0 1 2	0.25
B7	C→B	0 1	0.50
B8	B→A	0 1	0.50
B9	A→C	3	0.50
B10	B→A	3	0.75
B11	C→A	3	0.75
B12	A→C	3	0.75

. For open-set DA, the target domain encompasses all operating conditions, while the source domain includes partial operating conditions. Openness $1-\left|{\displaystyle \frac{C_s}{C_t}}\right|$ is defined to describe the label space difference between the two domains. Different levels of openness were set in the experiments, with higher openness indicating more outlier classes in the target domain.

4.2. Compared Methods

The performance of DODAN was evaluated through various experimental tasks designed to test the effectiveness of the proposed open-set domain adaptation method. Specifically, the following methods were implemented:

• Transformer (Baseline): This method directly applies the model trained on source domain data to target domain data;
• DANN [32]: This is a typical closed-set DA transfer learning method, which performs distribution matching through adversarial learning. Specifically, the domain discriminator cannot distinguish whether the input sample belongs to the source domain or the target domain so that the source domain and the target domain are aligned in distribution;
• OSBP [33]: It applies a new adversarial learning method to enable the generator to separate target samples of unknown classes. It mainly solves the data processing problem when the source domain is a subset of the target domain. The main parameters are shown in [33];
• OSWA [34]: A deep learning-based DA method for open-set mechanical fault diagnosis using an instance-level weighting strategy to indicate the detected instance’s similarity to known classes. The main parameters are shown in [34].

The details of the comparison method are shown in

Table 9. The detailed structure of the comparison method.

Method	Layer Type	Details	Output Shape
Transformer (Baseline)	Input layer	Raw input data	1024
	Dense	Dense(512)->Relu	512
	Dense	Dense(256)->Relu	256
	Dense	Dense(128)->Relu	128
	Output Layer	Dense(C)->Softmax	(C)
DANN	Feature Extractor	Conv2D(128)->Relu	(128,256)
		MaxPooling2D	(128,128)
		Conv2D(64)->Relu	(64,128)
		MaxPooling2D	(64,64)
		Conv2D(32)->Relu	(32,64)
		MaxPooling2D	(32,32)
	Label Predictor	Dense(128)->Relu	128
		Dense(C)->Softmax	(C)
	Domain Discriminator	GRL->Dense(128)->Relu	128
		Dense(1)->Softmax	1
OSBP	Feature Extractor	Conv2D(128)->Relu	(128,256)
		MaxPooling2D	(128,128)
		Conv2D(64)->Relu	(64,128)
		MaxPooling2D	(64,64)
		Conv2D(32)->Relu	(32,64)
		MaxPooling2D	(32,32)
	Domain Discriminator	GRL->Dense(128)->Relu	128
		Dense(1)->Softmax	1
	Open Set Recognition	GRL->Dense(128)->Relu	128
		Dense(2)->Softmax	2
	Label Predictor	Dense(128)->Relu	128
		Dense(C)->Softmax	(C)
OSWA	Feature Extractor	Conv2D(128)->Relu	(128,256)
		MaxPooling2D	(128,128)
		Conv2D(64)->Relu	(64,128)
		MaxPooling2D	(64,64)
		Conv2D(32)->Relu	(32,64)
		MaxPooling2D	(32,32)
	Domain Discriminator	GRL->Dense(128)->Relu	128
		Dense(1)->Softmax	1
	Outlier Classifier	GRL->Dense(128)->Relu	128
		Dense(2)->Softmax	2
	Label Predictor	Dense(128)->Relu	128
		Dense(C)->Softmax	(C)

.

4.3. Evaluation Metrics

Four evaluation metrics were utilized to assess the performance of different methods. Furthermore, the following symbols were defined to provide clarity on the evaluation metrics:

$M_s$: Number of correctly recognized shared-class test samples.

$M_u$: Number of precisely detected unknown-class test samples.

$A_s$: Number of all shared-class test samples.

$A_u$: Number of all unknown-class test samples.

The evaluation metrics employed in this study are as follows:

• $U_k=M_s+M_u/A_s+A_u$: Accuracy of all target samples over $K+1$ classes. All unknown samples are considered as one class.
• $U_s=M_s/A_s$: Accuracy of shared classes.
• $U_u=M_u/A_u$: Accuracy of unknown classes.
• $H-score=2\cdot U_s\cdot U_u/\left(U_s+U_u\right)$: The harmonic mean of shared-class accuracy and unknown-class accuracy is high only when both $U_s$ and $U_u$ are high, effectively evaluating different methods.

4.4. Experimental Results

4.4.1. Experimental Results of the Diesel Engine Dataset

The classification accuracy of DODAN on the diesel engine dataset tasks is shown in

Table 10. The classification accuracy (%) of the diesel engine dataset.

Task	Transformer	DANN	OSBP			OSWA			DODAN
	Uk	Uk	Uk	Us	Uu	Uk	Us	Uu	Uk	Us	Uu
D1	70.6	83.3	88.8	81.5	/	86.2	90.5	/	93.7	94.1	/
D2	69.2	82.5	89.0	88.2	/	86.1	89.4	/	93.4	94.4	/
D3	67.3	75.7	85.3	81.4	59.4	85.3	87.6	68.4	92.5	93.0	95.2
D4	68.2	73.2	84.6	85.0	54.7	85.7	88.2	68.1	92.1	93.7	95.6
D5	65.5	70.4	80.4	82.1	49.6	85.4	86.4	67.8	90.8	91.5	93.7
D6	61.9	69.0	81.2	82.4	48.8	85.5	86.9	66.3	90.2	91.6	92.1
D7	60.3	67.8	76.5	78.3	43.2	82.4	83.1	68.5	89.0	90.3	93.5
D8	60.7	66.6	75.7	77.4	44.3	79.1	84.7	67.3	90.3	90.6	91.4
D9	60.1	65.9	73.4	75.8	41.5	70.5	75.4	67.8	88.2	91.4	90.8
D10	59.3	64.5	72.8	74.9	41.8	71.3	76.8	66.6	88.4	90.5	90.4
Avg	64.3	71.9	80.8	80.7	47.9	81.6	84.9	67.6	90.9	92.1	92.8

. It can be observed that DODAN exhibits strong open-set fault diagnosis capabilities, obtaining the highest diagnostic accuracy among various fault diagnosis methods, with an average diagnostic accuracy of 90.9%. This is 26.6% higher than the baseline Transformer model, while the highest accuracy achieved by the compared methods is 86.2%. In each diagnostic task, the proposed method’s accuracy exceeds 88% and outperforms all comparison methods. The DANN method exhibits outstanding classification accuracy in closed-set fault diagnosis tasks, confirming its effectiveness in transfer learning. However, its performance significantly degrades with increased interference from target outliers. Additionally, compared to the baseline, OSBP and OSWA effectively improved accuracy by 10.1% and 9.3%, respectively. Nevertheless, the proposed method outperformed OSBP and OSWA in all open-set domain adaptation tasks. The proposed method attained over 90% accuracy in all diagnostic tasks, indicating accurate classification of most shared class samples. Furthermore, the method successfully detected 92.8% of unknown class samples across all diagnostic tasks.

4.4.2. Experimental Results of the Bearing Dataset

The bearing diagnosis results are shown in

Table 11. The classification accuracy (%) of the diesel bearing dataset.

Task	Transformer	DANN	OSBP			OSWA			DODAN
	Uk	Uk	Uk	Us	Uu	Uk	Us	Uu	Uk	Us	Uu
B1	65.2	82.3	87.3	81.4	/	86.2	84.5	/	91.5	91.3	/
B2	64.6	81.4	86.4	80.3	/	84.5	84.7	/	90.1	92.8	/
B3	65.1	82.0	83.7	81.3	/	85.3	85.3	/	90.3	91.0	/
B4	64.5	70.5	84.2	86.1	53.5	84.6	87.5	66.0	91.9	92.8	96.2
B5	63.7	71.7	83.2	85.3	50.2	84.8	87.2	66.4	91.5	92.2	94.3
B6	64.9	69.9	82.4	81.5	49.4	85.7	85.4	67.8	92.2	91.7	94.0
B7	61.4	66.7	77.5	77.0	45.1	81.0	80.6	67.9	90.2	94.3	94.3
B8	61.6	65.4	72.8	77.2	46.3	80.5	84.8	68.2	91.4	91.6	93.5
B9	60.3	67.1	73.4	76.8	45.4	79.9	84.0	68.4	91.2	92.5	91.7
B10	60.6	66.8	71.6	75.4	43.6	70.2	75.7	67.7	90.4	90.0	91.5
B11	60.5	65.7	70.8	75.7	44.5	69.5	75.5	68.4	90.5	90.3	90.6
B12	59.3	65.8	70.9	74.6	43.7	70.8	74.7	67.5	90.8	90.7	90.8
Avg	62.6	71.3	78.7	79.4	46.9	80.3	82.5	67.6	91.0	91.8	93.0

. Among all of the methods, the Transformer still exhibits the worst diagnostic performance: the average diagnostic accuracy is 62.6%. The improvements in DANN, OSBP, and OSWA are relatively limited. The proposed DODAN outperforms other methods in all tasks, with an average diagnostic accuracy of 91.0%. Similar to the diesel engine dataset results, OSBP and OSWA showed better clustering performance than closed-set DA methods, improving accuracy by 11.6% and 10.7%, respectively. However, the proposed method outperformed OSBP and OSWA in all open-set domain adaptation tasks. The method achieved more than 90% accuracy in all diagnostic tasks; the results indicate that the majority of shared class samples were accurately classified. Additionally, the method successfully detected 91.8% of unknown class samples across all diagnostic tasks.

4.4.3. Feature Visualization Analysis

In addition to mean accuracy, the H-score was utilized as a key performance metric for multi-class classification and the H-score was used as an important multi-class performance metric. To illustrate the advantages of the DODAN method, H-scores for selected tasks from the Diesel Engine and Bearing datasets were calculated. The results are shown in Figure 4. The proposed DODAN method achieved the highest H-score in all tasks, indicating its effectiveness in handling OSFD problems.

To visually demonstrate the effectiveness of the DODAN method, confusion matrices for tasks D9 and B4 are presented in Figure 5.

The confusion matrices in Figure 5 reveal that the Transformer method failed to recognize unknown fault modes. Although OSBP and OSWA improved the recognition accuracy of health states, their overall performance was still average. DODAN effectively classified known fault modes and accurately detected unknown fault modes. According to Figure 5, the proposed DODAN method demonstrated high accuracy (>90%) in all tasks, further highlighting its advantages in addressing OSFD problems.

Using task D10 as an example, Figure 6 displays the t-SNE results of target test data for various methods. The fused feature distribution of the proposed method demonstrates the most effective clustering effect, clearest class boundaries, and minimal misclassification. In contrast, other methods’ feature maps show overlapping features among different classes, indicating that the proposed method effectively extracts domain-invariant representations of known classes and identifies unknown health conditions in the source domain.

4.5. Discussion

The experimental results indicate that model performance generally degrades as the types of fault samples increase. This aligns with the current understanding that fault diagnosis problems become more challenging when fewer classes are shared across domains. In closed-set diagnosis tasks (D1–D2 and B1–B3), all methods, except the baseline, achieved satisfactory diagnostic results. Due to the lack of a distribution matching process, the Transformer has limited ability to transfer diagnostic knowledge, leading to lower accuracy compared to other methods. In open-set diagnosis tasks (D3–D10 and B4–B12), traditional transfer learning implemented by DANN largely fails due to outlier classes. DANN focuses on matching marginal distribution and learning domain-invariant features for known classes but it struggles to learn specific discriminative features for unknown classes. As a result, the diagnostic knowledge learned in the source domain cannot be applied to the target domain, resulting in negative transfer due to interference from target outliers. In low-openness diagnosis tasks (D3–D10 and B4–B9), OSBP, OSWA, and the proposed DODAN achieved good diagnostic results. In high-openness diagnosis tasks (B10–B12), OSBP and OSWA performed poorly because OSWA uses a single metric to detect open classes and OSBP uses a supervised classifier to predict outliers. The proposed method significantly improved upon OSBP and OSWA, demonstrating the benefits of adversarial training and the outlier detection module in mitigating the negative impact of newly emerged fault classes in the target domain.

Table 12. Calculation times for different methods.

Method	Transformer	DANN	OSBP	OSWA	DODAN
Train time(s)	176.4	293.5	287.2	268.3	249.2
Test time(s)	0.75	0.85	0.89	0.81	0.74

also displays average training and testing times for various methods. Apart from the Transformer, the training times for the other methods were not significantly different, with all methods completed within 5 min. Given that domain adaptation fault diagnosis tasks are mostly performed offline, the computational burden is acceptable. Compared to others, the Transformer method has a faster training speed but lower accuracy, limiting its practical application. The proposed DODAN method employs depthwise separable convolutions, reducing computation time and proving its potential for practical applications.

5. Conclusions

This paper discusses a valuable and realistic application scenario for marine machinery fault diagnosis using open-set domain adaptation. A multi-scale depthwise separable convolution-based feature extraction module was constructed for discriminative feature extraction. An adversarial training strategy was designed to learn generalized features that can resist unknown domain shifts. Finally, an outlier detection module was proposed to learn the optimal decision boundaries for each class representation space, enabling the classification of known fault modes and the identification of unknown fault modes. Extensive experiments on two marine datasets demonstrated that the proposed method accurately identified known fault categories and effectively detected unknown fault categories, outperforming other domain adaptation methods in various open-set fault diagnosis tasks. Feature visualization further aided in the interpretation of diagnostic results. These findings suggest that the proposed method holds significant potential for achieving higher performance in other industrial applications. Future research will focus on exploring new methods that combine data-driven approaches with expert knowledge to achieve both fault prediction and root cause analysis.