Research on Multi-Parameter Fault Early Warning for Marine Diesel Engine Based on PCA-CNN-BiLSTM (2024)

1. Introduction

Marine diesel engines play a vital role in the operation of ships, but due to prolonged high-load operation, harsh marine environment and other factors, MDEs are prone to various failures [1]. For the safety and operational efficiency of the vessel, early detection and warning of these faults is critical [2]. The study of a deep learning (DL)-based multi-parameter fault early warning (EW) system for marine diesel engines can use deep learning algorithms to monitor and analyze multiple parameters during diesel engine operation to provide EW of potential faults [3]. By monitoring and analyzing various parameters of the diesel engine in real time, it can accurately determine if there are any signs of diesel engine failure and take maintenance action in advance to avoid the serious impact of failures on ship operations [4]. The study of a DL-based multi-parameter fault warning system for marine diesel engines can not only improve the safety and reliability of ships but also reduce maintenance costs and improve operational efficiency [5]. Therefore, this research has important practical significance and application prospects.

Concepts such as smart ships and unmanned aircraft cabins have become key directions for future research in the maritime industry [6]. The concept of a ‘smart ship’ was first introduced in Det Norske Veritas’ Future Shipping Industry publication in 2014, and since then, countries around the world have been conducting extensive research into smart ships [7]. In 2015, the China Classification Society (CCS) published the world’s first smart ship code, enabling China to make great strides in the development of smart ships [8]. In 2017, Lloyd’s Register published Design Rules for Intelligent Ship Systems, a document that serves as a guide in the field of intelligent ships [9]. In order to accelerate the development of ship intelligence, Prognostics and Health Management (PHM) technology has been gradually introduced into the shipping industry [10]. PHM technology has come a long way in the last few decades, from the early sensors and data loggers to today’s cloud computing and artificial intelligence, which continue to improve the reliability and availability of devices [11]. Li et al. studied the application of PHM technology in the field of diesel engines, described the characteristics of traditional diesel engine fault diagnosis, constructed the system architecture of diesel engine PHM, summarized its key technologies, and provided an outlook on data analysis, fault diagnosis, fault EW, and health management [12]. The PHM system is used extensively on the International Space Station (ISS) [13]. By collecting and analyzing sensor data, the PHM system monitors and predicts the health of various subsystems and components of the ISS, such as the life support system, the electrical power system, the attitude control system, etc., and is able to ensure the normal operation of the ISS and the safety of the astronauts to the greatest extent possible [14]. The Health and Usage Monitoring System (HUMS) is widely used in military helicopters and fixed-wing aircraft, and is a composite system that integrates avionics, ground support equipment, on-board computer monitoring, and equipment diagnostics to develop effective predictive maintenance strategies for the aircraft [15].

In recent years, when investigating the problem of predicting the thermal parameters of MDE, researchers have often taken the EGT as an important research object [16]. Liu et al. proposed an MDE fault warning model that combines the feature extraction capability of a CNN and the time-series data prediction capability of a bi-directional gated recirculation unit (BiGRU) to predict the exhaust temperature of an MDE [17]. Liu et al. combined the feature extraction capability of the attention mechanism and the time-series memory capability of the Long Short-Term Neural Network (LSTM) to construct an exhaust temperature prediction model for MDE and set the fault threshold for exhaust temperature prediction based on the distribution of residuals between the model’s predicted value and the actual value using a process control method [18]. Ji et al. proposed a hybrid neural network prediction model based on deep learning for MDE exhaust temperature (EGT) prediction and demonstrated that the proposed CNN-BiLSTM-Attention prediction accuracy is higher by comparing experiments with other neural network prediction models [19].

Predictive technology refers to the monitoring and analysis of equipment or systems to detect and predict potential failures or anomalies in advance so that appropriate maintenance or preventive action can be taken [20]. At present, fault EW technology is widely used in industry, power, transportation, and other fields, and some important progress has been made [21]. Li et al. proposed an aircraft engine EGT prediction model based on the optimization of the BAT algorithm with a chaotic rate, improved the convergence rate and accuracy of the BAT algorithm by introducing the chaotic rate, and applied it to the optimized prediction model to predict the EGT, and the prediction results showed that the method is suitable for aircraft engine condition monitoring [22]. Li et al. studied the possibility of implementing fault warning in an automotive engine fault diagnostic model; through the establishment of fault domains, the engine state is divided into domain values. They established a combination model based on a variety of machine learning methods to diagnose multiple types of faults at the same time, and after experimental verification of the method, it can ensure the accuracy of engine fault warning and is suitable for real-time warning of multiple faults [23]. Yang et al. designed a fault risk warning method for a distribution network based on multi-source information fusion technology, which was verified through simulation experiments to have real-time and accuracy of fault warning and provided reliable technical support for risk warning for efficient and safe operation of power systems [24]. Li et al. proposed an engine failure EW model for liquefied natural gas buses based on an improved random forest algorithm, which helps to detect potential failure situations in advance and take appropriate repair or preventive measures, thus improving the reliability and safety of buses [25]. Tan et al. proposed a hydraulic turbine fault early warning system, and the experimental results show that the method has superior performance indexes and can meet the requirements of hydraulic turbine fault early warning [26]. Li et al. combined LSTM with an equivalent circuit model to investigate a new power battery fault diagnosis and EW method that will provide accurate fault diagnosis and localization of thermal runaway battery packs for potential battery failures [27].

As far as current research is concerned, the traditional methods of fault warning in marine diesel engines cannot be better adapted to the development and progress of intelligent ships. Therefore, this paper adopts the state prediction method and proposes a prediction model based on a PCA-CNN-BiLSTM neural network for the research on the multi-parameter thermodynamic parameter prediction problem of MDE and combines the mathematical modelling method to propose the MDE operation state assessment index for the research of MDE fault EW. The main work of this paper is as follows: Introduce the principles of the deep learning network model structure used and lay the foundation for the subsequent construction of combinatorial network prediction models; thermal parameter data prediction process using normalization, PCA, and other methods to select the characteristic parameters; the PCA-CNN-BiLSTM neural network prediction model is built, and the model hyper-parameter selection is carried out using the method of artificial experience and control variables to establish a multi-input multi-output prediction model for MDE; use standardized Euclidean distance to set the total deviation of MDE thermal parameters, combined with the standard deviation of the deviation to set the marine diesel engine fault warning threshold for MDE operating condition monitoring and fault warning research; and experimental verification.

2. Principles of Deep Learning Models

2.1. The Convolutional Neural Networks (CNNs)

The concept of CNNs can be traced back to the 1980s and 1990s [28]. The main difference between CNNs and general neural networks (NNs) is their feature extraction structure, which can automatically extract the features of the input data compared with traditional NNs, thus achieving efficient classification and recognition of the input data [29].

The traditional NN model must take the whole image as the input to the NN when performing the data input problem, and as the size of the image increases, there are more and more parameters involved, which brings great difficulties to the calculation [30]. The information content in the local region is highly correlated, so in the process of image perception, only part of the region needs to be perceived, and then this highly correlated local information can be integrated to obtain the overall information [31]. The neurons in the network structure of a CNN are connected in this way (locally connected mode). The CNN structure is shown in Figure 1.

The following is an analysis of the structural principles of the components of the CNN model:

Input layer: as in traditional neural network machine learning, the input layer receives and preprocesses the original image or data, and common preprocessing methods in the input layer include normalization, standardization, de-averaging, etc. [32];
Convolutional layer: The layers of this convolutional neural network consist of multiple convolutional units, the parameters of each of which are optimized using a back-propagation algorithm [33]. The convolutional operation aims to extract multi-level features, whereas a single-layer convolutional network can only extract low-level features such as edges, lines, corners, etc.; a multi-layer network can obtain more complex features by iterating over low-level features. In this paper, we take a 4 × 4 input data and design two 2 × 2 convolution kernels to perform convolution operations to explain in detail. The step size of the convolution kernel is set to 1, i.e., sliding to the right one unit at a time with a fixed window of 2 × 2. The schematic diagram of convolutional computation is shown in Figure 2. The formula is provided in Equation (1).

$C_{t} = (N_{i 1} - f_{1} + 2 p_{1}) / s_{1} + 1$

(1)

where C_t is the size of the output matrix of the convolutional layer operation, N_i₁ is the size of the input matrix, f₁ is the number of convolutional kernels of the convolutional layer, p₁ is the number of padding fills in the convolutional layer, and s₁ is the step size of the convolutional layer;

3.: Activation layer: There is an excitation function in the activation layer, and under the condition that no excitation function is used, the output of each layer is linearly related to the input of the previous layer. Tanh and ReLU functions are commonly used. The formula is shown in Equations (2)–(4)

$s i g m o i d (x) = \frac{1}{1 + \exp (- x)}$

(2)

$\tanh (x) = \frac{1 - \exp (- 2 x)}{1 + \exp (- 2 x)}$

(3)

$Re L U (x) = \max (x, 0);$

(4)

4.: Pooling layer: The role of the pooling layer is mainly to retain the salient features of the extracted information, reduce the feature dimension, and increase the perceptual field of the kernel function. Currently, there are two general pooling methods, namely maximum pooling (MP) and average pooling (AP). In this paper, the MP process is further detailed under the assumption that the pooling layer size is 2 × 2 and the step size is 1. The MP computation is performed on image data with an input of 3 × 3. The schematic diagram of the pooling layer calculation is shown in Figure 3. The calculation formula is shown in Equation (5).

$P_{t} = (N_{i 2} - f_{2} + 2 p_{2}) / s_{2} + 1$

(5)

where P_t is the size of the output matrix of the pooling layer operation, N_i₂ is the size of the input matrix, f₂ is the number of convolution kernels of the pooling layer, p₂ is the number of padding fills in the pooling layer, and s₂ is the step size of the pooling layer;

5.: Full connectivity layer: The neurons in each layer are connected with specific weights, and the fully connected neurons are often at the end of the CNN. It acts as a classifier and completes the final feature extraction and classification [34].

2.2. Recurrent Neural Networks (RNNs)

An RNN is an NN structure which introduces information transfer on the time series based on a fully connected neural network, so that it can capture the correlation between before and after time series, and it can better deal with time-series-related problems such as machine translation, etc. [35]. It has a strong ability to deal with the time series data, and the RNN deals with the whole sequence processing, and it can generalize a long sequence to obtain the required results [36]. The schematic of the RNN structure is shown in Figure 4.

The RNN structure U, V, and W are the shared parameters, i.e., the shared weights of each layer. X_t is the input at time t. The hidden layer and the output layer are computed as shown in Equation (6).

$\{\begin{cases} s_{t} = f (U x_{t} + W s_{t - 1}) \\ o_{t} = s o f t \max (V s_{t}) \end{cases}$

(6)

where f is the non-linear activation function, s_t and s_t−₁ are the hidden layer state vector units, and o_t is the current instant of the RNN calculated output value.

Each training sample in an RNN is a set of time series, and the data at the two time points before and after the same training sample have some correlation; if the data samples are too long, it is easy to produce the problem of gradient disappearance, and the LSTM model is proposed to solve this problem.

2.3. Bidirectional Long- and Short-Term Memory Neural Network Unit (BiLSTM)

BiLSTM is an NN unit commonly used in deep learning models [37]. It combines the advantages of LSTM and BiRNN to better capture long-term dependencies in sequential data [38]. The BiLSTM cell has two directions of hidden states, one of which receives information from the forward propagation direction and the other from the backward propagation direction [39]. This allows for a more comprehensive understanding of the contextual information in the sequence data and improves the ability of the model to model sequence data. The introduction of BiLSTM units greatly improves the model’s ability to process sequential data and is one of the key components of deep learning. The structure of the BiLSTM network is shown in Figure 5.

If the hidden state of the forward propagation output of BiLSTM at time t is a and the hidden state of the backward propagation output is b, then the hidden state of the overall output of BiLSTM is provided with Equation (7), and the output is the combined output of the forward and backward networks at each time.

$h_{t} = h_{a} \oplus h_{b}$

(7)

where $\oplus$ is a fully connected layer operation.

2.4. CNN-BiLSTM Prediction Model

With the traditional single NN prediction model, it has been difficult to meet the demand of multi-parameter time series prediction for MDEs [40]. Therefore, this paper proposes a combined NN prediction model for the study of the MDE thermal parameter prediction problem. The CNN-BiLSTM combination NN prediction model is a deep learning model that is a combination of CNN and BiLSTM. The CNN in the model is used to extract local features from the input data and capture the spatial information in the data through convolutional and pooling layers. BiLSTM then processes the CNN-extracted feature sequences to capture long-term dependencies and contextual information in the sequence data. BiLSTM’s bidirectional structure allows a better understanding of the temporal relationships in the sequential data, improving the predictive power of the model. The structure of the CNN-BiLSTM prediction model is shown in Figure 6.

3. PCA-CNN-BiLSTM-Based Multi-Parameter Fault Prediction for Marine Diesel Engines

3.1. Data Processing

3.1.1. Data Acquisition

Actual operating data of a 6L34DF dual-fuel power-generating diesel engine on an LNG carrier are chosen for the study. The technical parameters of the MDE are shown in Table 1.

The experimental data used in this paper are the actual operation data of the 6L34DF dual-fuel marine diesel engine collected by sensors under the normal sailing condition of the ship, and the sensor recording adopts the principle of recording once per second for data collection. In order to reduce the influence of cabin noise and improve the training speed of the combined neural network prediction model, this paper adopts the method of taking points at intervals for parameter selection and takes a thermal parameter monitoring point every 5 s, and a total of 5000 monitoring points are selected. In this paper, seven representative thermal parameters of the MDE are preselected for the study, as shown in Table 2.

In this paper, a sample parameter collection is carried out in the stable operating conditions of an MDE. The collected sample data serve as important thermodynamic parameters of the ship’s diesel engine, and each sample parameter can reflect the operating work of the MDE to a certain extent. EGT can indicate the combustion efficiency and heat load of the MDE; the supercharger outlet EGT can indicate the working condition and boosting effect of the supercharger; the supercharger speed can indicate the rotational speed and boosting effect of the supercharger; the high-temperature water air cooler is the temperature at which the cooling water in a high-temperature water air cooler flows out of the unit. The temperature value can reflect the cooling effect and working condition of the high-temperature water-to-air cooler, which is an important reference value for the performance and operating safety of diesel engines; the differential pressure in a lube filter is the difference in pressure between the inlet and outlet of the filter, caused mainly by the resistance within the cartridge and the build-up of contaminants on the surface of the cartridge. When the differential pressure of the lube filter exceeds the set limit, it can be used as a timing indicator for maintenance. By monitoring the differential pressure of the lube oil filter, it is possible to detect the situation of filter element clogging in time, prevent poor lubrication or equipment failure due to filter element clogging, and ensure safe operation of the equipment; the gas inlet pressure of the host computer can indicate the gas inlet pressure of the MDE; the low-temperature oil cooler outlet temperature can indicate the working effect of the MDE cooling system.

Some of the actual operation data for the 6L34DF dual-fuel marine engine on board the LNG carrier selected in the paper is shown in Table 3.

3.1.2. Principal Component Analysis (PCA)

PCA is a popular method for reducing the dimensionality of data, transforming high-dimensional data into a lower-dimensional representation while preserving the essential information of the original data [41]. The composite index obtained after the conversion is known as the principal component (PC), which is somehow superior to the original variable. When processing multi-parameter data sets, a single PC may not be sufficient to fully capture all N variables in the original data using PCA. Therefore, it is essential to identify additional principal components, such as the second, third, or even fourth PC. The second PC should not contain redundant information from the first PC, and the two principal components should have a covariance of zero, indicating that they are geometrically orthogonal to each other. The steps of PCA are as follows:

The raw data are standardized to eliminate the effect of scale. The formula is provided in (8).

$z = \frac{x - u}{σ}$

(8)

where z is the output results, x is the input raw data, u is the total data mean, and $σ$ is the total data standard deviation.

A matrix of correlation coefficients between the variables, R, is constructed and calculated as shown in Equation (9).

$\{\begin{cases} R = {(r_{i j})}_{m \times m} \\ r_{i j} = \frac{\sum_{k = 1}^{n} {\tilde{x}}_{k i} \cdot {\tilde{x}}_{k j}}{n - 1} \end{cases}$

(9)

where r_ij is the correlation coefficient between the i-th indicator and the j-th indicator.

Calculate the eigenvalues and eigenvectors of R. The calculation formula is provided in Equation (10).

$\{\begin{cases} u_{j} = {(u_{1 j}, u_{2 j}, \cdot \cdot \cdot, u_{n j})}^{T} \\ y_{m} = u_{1 m} {\tilde{x}}_{1} + u_{2 m} {\tilde{x}}_{2} + \cdot \cdot \cdot + u_{n m} {\tilde{x}}_{n} \end{cases}$

(10)

where u_j is the eigenvector corresponding to the eigenvalue and y_m is the mth principal component.

The principal component contribution and the cumulative contribution are identified and each principal component score is calculated as shown in Equation (11).

$\{\begin{cases} F_{i} = \sum_{j = 1}^{j} W_{i j} X_{j} \\ W_{i j} = \frac{θ_{i}}{\sqrt{λ_{i}}} \end{cases}$

(11)

In this context, F_i represents the score of the i-th principal component, X_j denotes the sample parameter, W_ij signifies the weight of each variable in the principal component, $θ_{i}$ corresponds to the coefficients of each variable in the component matrix, and $\sqrt{λ_{i}}$ represents the square root of the eigenvalues associated with the principal components.

The principal component composite score is calculated and the formula is shown in Equation (12).

$F = \sum_{i = 1}^{n} α_{i} F_{i}$

(12)

where $α_{i}$ is the variance contribution of the ith principal component. F_i is the score of the ith principal component.

Characterization of thermal parameters using the above methods: The table of correlation coefficient evaluation indicators is shown in Table 4, and the table of correlation coefficients of sample parameters is shown in Table 5.

At the same time, the collected sample data were subjected to principal component analysis and the pre-selected seven thermal parameters were subjected to data dimensionality reduction to extract the main features of the data. Before conducting factor analysis of the data, KMO and Bartlett’s spherical test are conducted on the sample data to verify the structural validity of the sample data and whether the reliability and validity of the data meet the requirements of PCA. The KMO and the test results, and whether they meet the requirements of factor analysis, are evaluated in the table as shown in Table 6.

Bartlett’s spherical test is used to test whether the correlation matrix is a unit matrix, i.e., whether there is a correlation between the variables, and the range of evaluation indicators for the p-value of the test results, as shown in Table 7.

The sample data in this paper were calculated to obtain a KMO value of 0.725 and a Sig value of 0.000, indicating that the sample has a high degree of correlation between the parameter characteristic factors, which meets the requirements of PCA. Principal and cumulative contributions are shown in Table 8.

PCA was performed to extract principal components with a cumulative variance contribution rate of approximately 95%. The cumulative variance contribution rate of the first five principal components was 93.026%, indicating that these five components capture 93.026% of the information from the original seven sample parameters. This indicates that they effectively represent the total data of the selected samples. Thus, in this paper, the EGT T_p, supercharger EGT T₁, supercharger speed N, high-temperature water cooler outlet temperature T₂, and main engine lube oil filter differential pressure P₁ are used for the multi-parameter fault EW study of MDE.

The cumulative variance contribution of the first two principal components accounted for more than half of the characteristics of the sample data. Therefore, specific analyses were carried out for the first two principal components, each of which was obtained from the composition of seven sample parameters via linear fitting, and the linear coefficients of the original variables of the first two principal components, Z1 and Z2, are shown in Table 9 and Table 10.

As can be seen from the table, the linear coefficients of exhaust temperature T_P, supercharger speed N, and high-temperature water-to-air cooler outlet temperature T₂ in the PC Z1 are all greater than 0.7, indicating that these three sample parameters occupy larger components in the PC Z1. The linear coefficient of the low-temperature water slide oil cooler outlet temperature T₃ in the PC Z2 is greater than 0.7, indicating that this sample parameter has a large influence in the principal component Z2. Combining the performance of the linear coefficients of each parameter in the two principal components of Z1 and Z2, this paper selects the two parameters of exhaust temperature T_P and supercharger speed N as the research object of multi-parameter prediction of MDE.

Some of the sample parameter data after completion of data processing are shown in Table 11.

3.2. Multi-Parameter Prediction of Early Warning Processes

3.2.1. Model Evaluation Indicators

Model evaluation metrics can help determine how accurate and effective a model is, and they serve two main purposes: first, they are used to look at the model’s ability to replicate, i.e., by comparing multiple models using the same metrics, it is possible to determine which are better and which are worse. The second is to use the evaluation metrics to optimize the model step by step. In this paper, a commonly used prediction evaluation metric in deep learning, the Mean Absolute Percentage Error (MAPE), is chosen. The formula is shown in (13).

$M A P E = \sum_{i = 1}^{N} |\frac{y_{i} - {\hat{y}}_{i}}{y_{i}}| \times \frac{1}{n}$

(13)

where ${\hat{y}}_{i}$ is the predicted value and $y_{i}$ is the actual value.

The MAPE is a measure of the degree of difference between the estimated and the predicted quantities, which avoids the problem of error cancellation, and is itself often used as a statistical measure of forecast accuracy, such as in time-series forecasting.

3.2.2. CNN-BiLSTM Prediction Model Hyperparameter Selection

The number of neurons in the input layer of the CNN-BiLSTM prediction model is determined by the dimensionality of the input parameters. According to the preliminary results of data processing in Section 3.1.2 above, the prediction model has an input sample parameter of five outputs, and the outputs are the two types of exhaust temperatures and the speed of the supercharger, so the neuron in the input layer is set to 5, and the neuron in the output layer is set to 2. The CNN-BiLSTM prediction model has a large number of hyperparameters, and the hyperparameters are essential for training the model. The selection of appropriate hyperparameters can improve the training effect and generalization ability of the model, while inappropriate choices will lead to a decline in the performance of the model. Therefore, in this paper, hyper-parameter optimization is carried out using the method of control variables, and MAPE is used as the evaluation index of the combined prediction model. First, under the premise that all grid parameters of the BiLSTM model are guaranteed to be unchanged, the effect of the number of layers of the CNN model on the prediction results is tested, and the experimental results are shown in Table 12.

The CNN model hyperparameters were set to constant values and the BiLSTM model layers were tested for the accuracy of the prediction results. The results of the BiLSTM model layer test are shown in Table 13.

The other hyperparameters of the combined prediction model are tested and determined according to the method used above, where parameters such as hidden layer state dimensions, input sequence step size, sample training batch, etc., can be determined using the control variable approach to determine the optimal values. The optimal parameters of the CNN-BiLSTM model are shown in Table 14.

3.2.3. Projected Results Analysis

The PCA-CNN-BiLSTM-based multi-input multi-output prediction model for MDE thermal parameters is obtained as shown in Figure 7 for the prediction curve of MDE exhaust temperature. As can be seen in the figure, there is a high degree of agreement between the predicted value and the actual value, and the predicted value can well reflect the change in the EGT of the MDE in the future. Combined with the exhaust temperature residual curves in Figure 8, it can be seen that most of the standardized residuals between the predicted and actual values are in the range of −2 to 2. This indicates that the overall deviation of the prediction model is small, and the model has a high accuracy in predicting the exhaust temperatures of the MDE.

The output results of the predicted values of the supercharger speed and the residuals between the predicted and actual values are shown in Figure 9 and Figure 10. As shown in Figure 8, the predicted curve of supercharger speed is very close to the actual curve, and the predicted trend is basically the same as the actual trend. Combined with the residual curve of the supercharger speed shown in Figure 9, it can be seen that the residual value is distributed between −2 and 2, indicating that the PCA-CNN-BiLSTM prediction model established in this paper has a high prediction accuracy and the prediction of the supercharger speed is in line with the expected target.

The table of evaluation metrics for the prediction results obtained from the PCA-CNN-BiLSTM prediction model is shown in Table 15.

4. Failure Early Warning Study

4.1. Deviation Index Setting Based on Standardized Euclidean Distance

This paper investigates the prediction of thermal parameters of MDEs, focusing on the prediction of two thermal parameters, namely MDE exhaust temperature and supercharger speed. Through the comprehensive performance of the two thermodynamic parameters, we can judge whether the MDE is in normal operating condition or not and carry out research into EW of MDE failure. For the multi-parameter prediction problem, the deviation calibration between the predicted value and the actual value should be carried out. The commonly used time series similarity analysis is a data mining method based on distance to evaluate the degree of correlation between different signals.

Euclidean distance is commonly used to study the deviation of multidimensional data. Therefore, this paper proposes a fault warning method for MDEs based on standardized Euclidean distance. The Euclidean distance, also known as the Euclidean metric, is a widely used and intuitive distance measure that calculates the distance between two points in Euclidean space. Calculate the points X (x₁, x₂,…, x_n) and Y (y₁, y₂,…, y_n) in two n-dimensional spaces according to Equation (14).

$D (X, Y) = \sqrt{\sum_{k = 1}^{n} {(x_{1} - y_{1})}^{2}}$

(14)

where D(X, Y) is the Euclidean distance between points X and Y and n is the size of the spatial dimension.

Euclidean distance is one of the most intuitive distance measures, and the calculation is straightforward and easy to implement [42]. However, it is more sensitive to outliers in the calculation process, and the calculation process is limited in high-dimensional spaces, which can lead to inaccurate results. In the process of calculating the Euclidean distance, if the parameter size is different, the calculation results will produce a large deviation, and the value solved by applying the simple Euclidean distance will be very large and of no practical significance. Therefore, this paper deals with the combination of standardized residuals based on simple Euclidean distance in the problem of a multi-parameter fault warning threshold setting for MDE. The standardized formula is provided in Equation (8).

The mathematical formula for standardized residuals is provided in Equation (15).

$e_{k} = x_{k} - y_{k}$

(15)

where x_k is the result after standardizing the predicted values, y_k is the result after standardizing the true values and e_k is the result of calculating the standardized residuals.

Euclidean distance measures the similarity between predicted and actual values, and the normalized residual values are substituted into the Euclidean distance formula, and the calculated values are defined as the total deviation between the predicted and actual values of the exhaust temperature and supercharger speed, as shown in Equation (16).

$D = \sqrt{\sum_{k = 1}^{n} e_{k}^{2}}$

(16)

where D is the overall bias indicator and k is the data dimension.

During the fault warning process, when the diesel fuel is operating under normal conditions, the relevant deviation indicator monitoring points show good correlation and the standardized Euclidean distance is maintained within a specified interval with random fluctuations up and down. If the operating conditions are abnormal, this can be indicated by the fluctuation trend and relative value of the Standardized Euclidean Distance indicator, where the strong correlation of the Deviation indicator is broken, leading to abnormal relative fluctuations and ultimately exceeding the set threshold of the Standardized Euclidean Distance Deviation indicator under normal operating conditions. This is the basis of this paper’s implementation of multi-parameter fault warning for MDEs based on standardized Euclidean distances. The multi-parameter fault warning flow diagram for an MDE is shown in Figure 11.

As shown in the figure, the MDE multi-parameter fault warning process is divided into three parts, the process is as follows:

Based on the data collected with the MDE sensors, seven MDE thermal parameters were selected in the same way as in Section 3.1;
To obtain the processed predictive model input data set, data pre-processing is performed on the acquired raw MDE operating data;
The CNN-BiLSTM prediction model is constructed, the structural parameters of the model are determined, and the input data set is used to train the model;
The real-time operating parameters of the ship’s diesel engine are obtained and fed into the trained combinatorial neural network prediction model for MDE exhaust temperature and supercharger speed prediction;
Calculate the total deviation between predicted and actual values of thermal parameters of an MDE based on standardized Euclidean distances and set the fault warning threshold;
Analyze the variation in the deviation index of the MDE and determines whether the MDE is operating abnormally. If the deviation index exceeds the threshold, a fault warning is issued.

In the process of MDE operating condition monitoring and prediction, abnormal monitoring condition points are generally due to sensor failure or MDE structural failure, caused by significant deviation from the true value of monitoring data. Therefore, in this paper, the total deviation of predicted and actual values of EGT and supercharger speed of an MDE under normal working condition are calculated with the above method, and the distribution of deviation index is shown in Table 16, and the total deviation curve of an MDE is shown in Figure 12. Combined with graphical analysis, the results of multi-parameter condition monitoring of a MDE based on standardized Euclidean distances show that the deviation index fluctuates smoothly, with large fluctuations at individual monitoring points but is able to recover to a stable fluctuation range very quickly. It can be seen that when the MDE is running under normal operating conditions, most of the overall deviation index is below 1.6, but due to the model calculation there may be reasonable errors; the individual deviation index value is larger close to about 3.

According to the above study, if the deviation index threshold is set to 3, it may cause the problem of failure to warn of faults, and if it is set to 1.6, the problem of false alarms of faults may occur. Therefore, in this paper, in order to avoid the random error when running the model, the setting of the deviation index threshold for the deviation index not only considers the threshold of the total deviation curve, but also sets the fault alarm threshold based on the standard deviation of the total deviation in the sliding window. The sliding window provides instantaneously updated standard deviation values. Calculating the standard deviation through the sliding window allows data to be smoothed, reduces data fluctuations and noise, and better reflects the overall trend of the data. The standard deviation is a statistic value used to measure the degree of dispersion or volatility of a set of data. The larger the standard deviation, the more volatile the data; the smaller the standard deviation, the less volatile the data. The formula for calculating the standard deviation is provided in Equation (17).

$λ = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {(x_{i} - \bar{x})}^{2}}$

(17)

where $λ$ is the standard deviation, N is the number of data points, x_i is the ith data point, and $\bar{x}$ is the mean of the data. The deviation index is introduced into the formula, and, based on manual experience, the sliding window size is set to 20, the standard deviation of the total deviation is calculated, and the standard deviation plot of the deviation is obtained, as shown in Figure 13.

The standard deviation value of the total deviation is obtained via calculation, and the maximum value of the standard deviation of the deviation under the stable working condition of the diesel engine is 0.595. The maximum value of the standard deviation of the deviation represents the upper limit of the degree of variability or dispersion of the data. Setting the threshold at the maximum value of the standard deviation means that the maximum degree of variability is considered. The maximum value of the standard deviation is often compared to observations within a typical range of data and is used to identify data points that may be outliers or anomalies. Therefore, in this paper, the standard deviation warning value of the ship’s diesel engine is set at 0.595. The deviation index warning value between the predicted and actual values of the MDE multi-parameter is set to 1.6, and the deviation standard deviation warning value based on the sliding window is set to 0.595, and the MDE multi-parameter failure warning is issued only when the monitoring index exceeds the warning values of the two indices at the same time.

This paper also presents an experimental verification of the accuracy of the alarm threshold setting for marine diesel engines using Monte Carlo simulation. Monte Carlo simulation is a numerical computational method based on random sampling to solve complex stochastic or mathematical problems that cannot be solved by analytical methods. It is used to simulate an experiment or process by generating a large number of random samples to approximate the solution to a problem or to derive statistical properties. According to the real ship operation data of the marine diesel engine selected in this paper, the cabin noise impact is added on the basis of ensuring the normal operation condition of the marine diesel engine. Using Monte Carlo simulation sampling to generate 5000 groups of random numbers, the random sample data was generated by the simulation through the proposed multi-parameter prediction and early warning method for ship diesel engine alarm threshold verification. The standard deviation threshold of the deviation set above is 0.595, so a uniform random function is used to generate 5000 random numbers on the interval [0,0.595] of the total deviation values, and if the random numbers are within the interval, they are recorded as the random sample size. The result of running the program is that a total of 4951 random numbers meet the evaluation requirements and a total of 49 do not meet the requirements. The results of the Monte Carlo simulation of the random sample and probability distribution are shown in Table 17 below.

As shown in Table 17, more than 99% of the random number points are within the sampling interval, indicating that the standard deviation alarm thresholds for the total deviation proposed in this paper satisfy the monitoring and warning needs of ship diesel engines when noise is introduced under normal sailing conditions. Among them, 0.98% of the random number points do not meet the evaluation requirements, and the false alarm problem for exceeding the threshold can be solved by combining the error setting method in this paper.

In summary, this paper proposes an MDE fault EW method based on the combination of standardized Euclidean distance and sliding windows to achieve multi-parameter fault EW for MDEs, which can meet the needs of monitoring the state of MDEs in operation and fault EW in the future period.

4.2. Experimental Validation of Fault Warning

The thermal parameters selected for the experiments in this paper are the actual operating parameters of the 6L34DF model MDE, the sample parameters collected are under stable operating conditions, and the operating parameters during the fault condition are not collected. Therefore, in order to verify the effectiveness of the fault early warning method proposed in this paper, this paper adopts the method of manual linear adjustment of the data set to simulate the abnormal operating conditions of a ship’s diesel engine due to abnormally high cooling water temperature. The advantages of the artificial linear adjustment data set are high accuracy, strong interpretability, flexibility, controllability and good ability to calibratable, which can effectively improve the quality and applicability of the data set. Since the MDE failures to be detected are all the result of equipment degradation and accumulation of failures, the failures are represented as a set of monitoring indicator points exceeding the warning value. Linear adjustments were made to the test set data to set the sequence point at 490, where the MDE operating conditions were abnormal, causing parameters such as EGT and supercharger speed to change. In this paper, in order to avoid the problem of false alarms, the total deviation and standard deviation of the ship’s diesel engine error setting, when there is a value that exceeds the monitoring threshold, will be based on the current value and the two values before and after comparison; if the two values before and after current value are outside the normal monitoring range, taking into account the special working environment of the cabin, the point will be judged as a point of error caused by the cabin noise of the monitoring error and will not issue fault alarm prompts. After the CNN-BiLSTM prediction model and normalized Euclidean distance calculation, the bias index plot is obtained as shown in Figure 14.

As shown in the figure, the deviation index fluctuates within the warning value before time series point 490, and occasionally fluctuates more than the warning value at point 264, but does not continue to exceed the limit, combined with the standard deviation value of the monitoring point at point 264 as shown in Figure 15 which does not appear to exceed the limit, indicating that the ship’s diesel engine is in a stable operating condition. After the artificial introduction of MDE failures (after time series 490), the ship’s diesel engine deviation index fluctuated strongly, continued to rise, and, after exceeding the warning value, did not fluctuate into the normal range but continued to rise. Therefore, it was initially concluded that the MDE was in an abnormal operating condition after the 490-timing sequence.

The standard deviation of the total deviation is calculated using the standard deviation formula to obtain the standard deviation plot of the MDE fault warning deviation as shown in Figure 15.

As depicted in the figure, the value of the standard deviation of the deviation fluctuates within the normal threshold up to time series 490 and therefore no fault warning is issued at point 264 of the time series of the deviation index above. After the fault is introduced (after point 490 of the time series) the standard deviation value crosses the warning line and continues to fluctuate above the warning line. In summary, during operation of an MDE, no fault warning is issued before time series 490. After time series 490, the MDE is in an abnormal operating condition and the deviation index and the standard deviation of deviation simultaneously exceed the set failure warning value, and the MDE failure warning is issued. Through the fault warning experiment, the effectiveness of the multi-parameter fault warning method for an MDE proposed in this paper is verified, which can not only monitor the operating status of an MDE, but also issue a fault warning for abnormal operating conditions in the future period, to meet the needs of modern MDE fault warning.

5. Conclusions

In this paper, a multi-parameter fault warning method for MDEs based on a PCA-CNN-BiLSTM prediction model is designed and implemented for predicting the thermal parameters of an MDE and for fault warning. The key findings are summarized as follows:

The representative thermal parameters of the MDE are selected as sample data, and data pre-processing is carried out using normalization and principal component analysis to eliminate the problem of different magnitudes among the sample parameters and to extract the characteristic parameters. The parameters with larger linear coefficients in the principal components are used as the output parameters of the multi-parameter prediction results for the MDE, which improves the efficiency of the model operation as well as the accuracy of the model prediction results.

In the proposed CNN-BiLSTM prediction model, the CNN can extract features from time-series data, while the BiLSTM can autonomously learn these extracted features from time-series data. The model is able to better capture the feature sequences related to the failure of an MDE, compensate for the limitations of the traditional single NN, and is able to extract the temporal and spatial features of the exhaust temperature of an MDE in a more comprehensive way, which improves the prediction accuracy. By performing residual analysis between predicted and actual values, as well as evaluating the model using performance metrics, it was found that the CNN-BiLSTM prediction model proposed in this study has higher prediction accuracy. This suggests that the neural network model proposed in this paper has advantages in predicting temporal sequences.

For the fault warning problem, this paper proposes a multi-parameter deviation index setting method based on the standardized Euclidean distance, while two fault warning thresholds are set by calculating the standard deviation of the total deviation using a sliding window. When the predicted value crosses the two fault warning thresholds at the same time, the MDE fault warning is issued. Through the fault warning experiment verification, the method can meet the needs of marine diesel engine fault warning and can realize the multi-parameter fault warning for MDEs.

In summary, the MDE fault warning method based on a PCA-CNN-BiLSTM prediction model and standardized Euclidean distance integrates various techniques such as PCA, CNN, and BiLSTM to improve the prediction performance and accuracy of the model. The standardized Euclidean distance, as part of the fault warning method, quantifies the similarity between different parameters and helps to detect abnormal MDE operation in a timely manner. This paper makes extensive use of a variety of technical methods to improve the comprehensiveness and reliability of the MDE fault warning system, which helps to ensure the safety and stability of ship operations.

In this work, we select a 6L34DF model diesel engine in a real ship for power generation of a diesel engine, of which the working condition is stable and there is little change in load. In the future, one can select the ship’s main power output diesel engine as the research object, set the dynamic deviation index and the standard deviation index failure warning value according to the thermal parameters of different loads, and thus contribute to the universality of this model. Furthermore, the monitoring and early warning system of the ship diesel engine can be developed on the basis of our current research to achieve an automatic fault classification function based on fault prediction. Future research and development should collect as many diesel engine fault operation parameters as possible on the real ship or bench experiments, so as to provide fault classification and diagnosis at the same time as fault early warning and to offer early support for the subsequent repair and maintenance.

Author Contributions

Conceptualization, H.G.; Formal analysis, Y.S.; Investigation, Y.S.; Methodology, Y.S.; Supervision, H.G.; Writing—original draft, Y.S.; Writing—review and editing, Y.S., H.G., and Z.J. All authors have read and agreed to the published version of the manuscript.

Funding

This work is supported by the China Ministry of Industry and Information Technology Project: Innovation Engineering of the Offshore LNG Equipment Industry Chain under Grant CBG3N21-2-7.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data is contained within the article.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1.Structure of CNN.

Figure 2.Schematic diagram of convolution calculation. The red outline indicates the required calculation area.

Figure 3.Schematic diagram of pooling layer calculation. The red outline indicates the required calculation area.

Figure 4.Structure of RNN.

Figure 5.Structure of BiLSTM.

Figure 6.Structure of CNN-BiLSTM.

Figure 7.Comparison of EGT prediction results.

Figure 8.EGT normalized residual value.

Figure 9.Results of the supercharger speed prediction.

Figure 10.Supercharger speed normalized residual plot.

Figure 11.Flowchart for diesel engine fault warning.

Figure 12.Total deviation curve of marine diesel engine.

Figure 13.Standard deviation plot of the deviation index.

Figure 14.Diesel engine fault warning deviation index plot.

Figure 15.Standard deviation plots of diesel engine fault warning deviations.

Table 1.Technical parameters of diesel engine.

Technical Parameters	Unit	Numeric
Number of cylinders	\	6
Bore (i.e., diameter of a cylinder)	mm	340
Power rating	KW	2700
Rated speed	rpm	750
Compression ratio	\	12
Piston stroke	mm	400
Firing sequence of cylinders	\	1-5-3-6-2-4

Table 2.Type of feature parameter.

Thermal Parameters	Icon	Unit
EGT	T_P	°C
EGT at turbocharger outlet	T₁	°C
Speed of supercharger (SOC)	N	r/min
High-temperature water air cooler	T₂	°C
Oil filter differential pressure	P₁	MPa
Mainframe gas inlet	P₂	MPa
Outlet temperature of low-temperature oil cooler	T₃	°C

Table 3.Operating data related to marine diesel engine section.

T_P	T₁	N	T₂	P₁	P₂	T₃
496.8	511.6	9420	88	0.31	7.47	54.9
469.8	511.6	9420	88	0.31	7.49	54.8
469.8	511.6	9440	88	0.35	7.49	54.8
470	511.6	9420	88	0.31	7.49	54.8
470	511.6	9420	88.1	0.4	7.49	54.8
…	…	…	…	…	…	…
…	…	…	…	…	…	…
…	…	…	…	…	…	…
470.6	512.5	9420	88	0.28	7.49	55.7
470.8	512.4	9420	88	0.26	7.49	55.7
470.5	512.4	9440	88	0.26	7.47	55.8
470.5	512.4	9440	88	0.26	7.47	55.8
470.5	512.4	9430	88	0.26	7.49	55.8

Table 4.Indicators for the evaluation of correlation coefficients.

Range of Values	Correlation
$\|ρ\| \in [0.0, 0.3)$	Very weak may be considered irrelevant
$\|ρ\| \in [0.3, 0.5)$	Low relevance
$\|ρ\| \in [0.5, 0.8)$	Moderate relevance
$\|ρ\| \in [0.8, 1.0)$	High relevance

Table 5.Correlation coefficients of sample parameters.

	T_P	T₁	N	T₂	P₁	P₂	T₃
T_P	1.000	0.367	0.961	0.640	0.006	−0.062	0.069
T₁	0.367	1.000	0.339	0.343	0.013	−0.024	0.012
N	0.961	0.399	1.000	0.599	0.012	−0.060	0.052
T₂	0.640	0.343	0.599	1.000	0.018	−0.029	−0.095
P₁	0.006	0.013	0.012	0.018	1.000	−0.006	−0.013
P₂	−0.062	−0.024	−0.060	−0.029	−0.006	1.000	0.033
T₃	0.069	0.012	0.052	−0.095	−0.013	0.033	1.000

Table 6.Index table for evaluation of KOM test results.

KMO Range	Factor Analysis
KMO ∈ [0.0, 0.5)	Highly unsuitable
KMO ∈ [0.5, 0.6)	Unsuitable
KMO ∈ [0.6, 0.7)	Generally suitable
KMO ∈ [0.7, 0.8)	Suitable
KMO ∈ [0.8, 1.0)	Well suited

Table 7.Indicator table for evaluation of Bartlett’s spherical test results.

Range of Values	Correlation
p ∈ [0.00, 0.05)	Correlation
p ∈ [0.05, 1.00)	irrelevant

Table 8.Table of principal contributions and total variance contributions.

	Variance Contribution	Cumulative Variance Contribution
1	38.914%	38.914%
2	15.007%	53.920%
3	14.234%	68.155%
4	13.977%	82.131%
5	10.895%	93.026%
6	6.464%	99.491%
7	0.509%	100.00%

Table 9.The linear coefficients of the original variables in Z1.

Sample Parameters	Principal Component Linear Coefficients
T_P	0.941
T₁	0.575
N	0.936
T₂	0.789
P₁	0.022
P₂	−0.088
T₃	0.025

Table 10.The linear coefficients of the original variables in Z2.

Sample Parameters	Principal Component Linear Coefficients
T_P	0.075
T₁	0.010
N	0.067
T₂	−0.141
P₁	−0.301
P₂	0.481
T₃	0.835

Table 11.Table of input parameters for the prediction model (partial).

	T_P	T₁	N	T₂	P₁
1	0.51797	−1.81596	0.49688	0.11596	0.58422
	…	…	…	…	…
1500	−1.00500	0.34461	−0.73264	0.11596	−1.24825
	…	…	…	…	…
3000	1.00646	0.34461	0.49688	1.59102	0.43151
	…	…	…	…	…
4500	−0.77512	−0.37558	−0.73264	−0.62156	0.73692
	…	…	…	…	…

Table 12.Table of CNN model layer test results.

CNN Layers	T_P	N
1	0.0004238	0.001503
2	0.0004541	0.001560
3	0.0004625	0.001596

Table 13.Table of results of the BiLSTM model layer test.

BiLSTM Layers	T_P	N
1	0.0004241	0.001606
2	0.0004545	0.001689
3	0.0004560	0.001750

Table 14.Table of optimal parameters of the CNN-BiLSTM.

Hyperparameter	Optimum Value
Cnn kernel	32
Activation function	ReLU
Pooling_layer	Max Pool
Hidden_size	64
Seq_len	5
Batch_size	100
Epochs	500
Learning_rate	0.0005
Dropout	0.5

Table 15.Summary of indicators for the evaluation of the forecast results.

Thermal Parameters	MAPE
T_P	0.004038
N	0.00147

Table 16.Deviation index distribution table.

Range	Percent (%)	Cumulative Percent	Range	Percent (%)	Cumulative Percent
0 ≤ D < 0.2	20.85200	20.85200	1.4 ≤ D < 1.6	1.113361.6	98.18115
0.2 ≤ D < 0.4	22.36842	43.22042	1.6 ≤ D < 1.8	0.40486	98.58601
0.4 ≤ D < 0.6	17.40891	60.62933	1.8 ≤ D < 2.0	0.30364	98.88965
0.6 ≤ D < 0.8	19.13077	79.76010	2.0 ≤ D < 2.2	0.30364	99.19329
0.8 ≤ D < 1.0	12.65182	92.41192	2.2 ≤ D < 2.4	0.20243	99.39572
1.0 ≤ D < 1.2	2.73279	95.14471	2.4 ≤ D < 2.6	0.40486	99.80058
1.2 ≤ D < 1.4	1.92308	97.06779	2.6 ≤ D < 3.0	0.10121	99.90179

Table 17.Monte Carlo simulation of rounding distributions and probability tables.

	Number of Random Points	Probability Distribution
Meeting assessment needs	4951	99.02%
Failure to meet assessed needs	49	0.98%

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