A ship diesel engine fault diagnosis method based on nonlinear intuitionistic fuzzy support tensor machine

Abstract

A nonlinear intuitionistic fuzzy support tensor machine-based fault diagnosis method for marine diesel engines is proposed. Firstly, the multi-source sensor signals are converted into time-frequency images, and then grayed and cropped. Finally, the coupling structure information in the time domain, frequency domain and spatial domain is fully mined by stacking and reconstructing the tensor samples along the forward slice. Secondly, a nonlinear non-membership function is designed to construct an intuitionistic fuzzy set, and the score of each tensor sample is obtained to highlight the contribution of different samples and alleviate the impact of noise on the model. Thirdly, the tensor robust principal component analysis is used to accurately recover the low-rank feature tensor without noise from the original noisy tensor sample. Finally, the nonlinear intuitionistic fuzzy support tensor machine model is established, and the inner product is performed with the low-rank feature tensor without noise instead of the original tensor, which avoids the loss of structural information and coupling information of multi-source monitoring signals and enhances the robustness of the model to noise, thus effectively improving the fault diagnosis performance of marine diesel engines.

Description

Technical Field

[0001] This invention belongs to the field of marine diesel engine fault diagnosis technology, and relates to a marine diesel engine fault diagnosis method based on a nonlinear intuitionistic fuzzy support tensor machine model. Background Technology

[0002] Marine diesel engines, as reciprocating internal combustion engines, are widely used in marine propulsion systems and have become a crucial source of power for ships. Their operating status plays a vital role in ensuring safe navigation. Marine diesel engines consist of numerous complex nonlinear subsystems. During operation, these subsystems interact, causing violent vibrations in the engine body. Furthermore, the components are subjected to high-temperature, high-pressure impact loads, which can easily lead to a series of abnormalities or malfunctions, thus affecting the safe operation of the ship. Fault diagnosis of marine diesel engines can accurately estimate their operating status, ensuring safe ship operation, and also enable timely repairs, greatly reducing the workload of maintenance personnel and lowering maintenance costs. Therefore, strengthening fault diagnosis of marine diesel engines has significant economic and social value.

[0003] Currently, the main methods for diagnosing faults in marine diesel engines are as follows:

[0004] 1) Fault diagnosis method based on mechanism model.

[0005] This method primarily involves establishing a mechanistic model of the monitored diesel engine equipment and diagnosing faults through the construction of a complete mathematical model. The focus of this method is on achieving a complete and accurate system model of the marine diesel engine. However, due to the high coupling between the internal components of the diesel engine and its complex, time-varying nature, the actual models often neglect this coupling and dynamics. This leads to a discrepancy between the established mechanistic model and the actual system, failing to accurately reflect the true operating conditions of the marine diesel engine system. Furthermore, as the performance of the diesel engine equipment degrades, the mechanistic model is prone to failure.

[0006] 2) Fault diagnosis methods based on expert qualitative experience and knowledge.

[0007] This method utilizes the accumulated experience and knowledge of diagnostic experts to construct comprehensive fault diagnosis rules, such as expert systems and fault trees. However, this method often requires experts with many years of experience in the field to accurately analyze and diagnose marine diesel engine faults, heavily relying on expert experience. Any deviation in this experience can affect the accuracy of the fault diagnosis.

[0008] 3) Data-driven fault diagnosis methods.

[0009] This method is one of the important research directions in marine diesel engine fault diagnosis in recent years, including data statistics, signal conversion, and machine learning methods. Based on a large amount of process data generated by various sensors under different operating conditions, this method achieves fault diagnosis by extracting and analyzing features from this sensor data. The machine learning algorithms include neural networks, support vector machines, and decision trees. They primarily mimic human experts' intelligent judgment of the diesel engine's condition, thus avoiding the construction of complex mechanistic models and excessive reliance on expert experience to some extent. However, neural network algorithms require a large amount of data for calculating network layer weights and are prone to getting trapped in local minima. Support vector machines, based on the VC dimension theory and the principle of structural risk minimization in statistical learning theory, seek the optimal trade-off between model complexity and learning ability with limited sample information. They have good generalization capabilities and can solve practical problems such as small samples, nonlinearity, high dimensionality, and local minima. Therefore, they have become a hot research topic in the machine learning community and have been successfully applied to the field of marine diesel engine fault diagnosis.

[0010] However, Support Vector Machines (SVMs) are only suitable for one-dimensional vector data composed of signals from a single-source sensor, and cannot directly process tensor data composed of signals from multiple sources (such as multiple thermal parameter sensors). One-dimensional signals provide limited effective information; in contrast, signals obtained from sensors installed at different locations have a certain correlation and contain rich operational status information, which can comprehensively reflect the operating status of the marine diesel engine. To model tensor data, SVMs flatten the feature tensors into a vector as the model input. This vectorization of tensors generates high-dimensional feature vectors, increasing computational complexity and leading to overfitting. Furthermore, it destroys the inherent structural information of the original feature tensor data, losing coupling information between different monitoring signals, ultimately significantly affecting the performance of marine diesel engine fault diagnosis. Because marine diesel engines operate under complex conditions, the condition monitoring signals are always nonlinear and non-stationary time-varying, meaning that the transient frequency of the signal changes over time. In this case, time-frequency analysis methods are needed to extract time-varying features from non-stationary signals. In addition, the actual sensor signal acquisition process is susceptible to noise interference, and the acquired multi-source monitoring signals often contain a lot of noise, which will also reduce the accuracy of fault diagnosis.

[0011] Based on the above discussion, it is necessary to establish a fault diagnosis method for marine diesel engines that can extract time-varying noise-free features from non-stationary, noisy multi-source sensor monitoring signals, while preserving the inherent structural information of the multi-source sensor monitoring signals and the coupling information between different monitoring signals. Summary of the Invention

[0012] This invention aims to address the problem of low fault diagnosis accuracy caused by a large amount of noise in the non-stationary signals of multi-source sensors in marine diesel engine systems. It proposes a fault diagnosis method for marine diesel engines based on a nonlinear intuitionistic fuzzy support tensor machine, which can combine signals from multiple sensors for diagnosis, fully explores the time, frequency, and spatial domain features of the signals, effectively mitigates noise interference, and significantly improves the performance of fault diagnosis.

[0013] To improve the accuracy of fault diagnosis, the technical solution adopted in this invention is as follows:

[0014] A fault diagnosis method for marine diesel engines based on a nonlinear intuitionistic fuzzy support tensor machine includes the following steps:

[0015] Step 1: Reconstruct the original multi-source monitoring signal into a third-order tensor based on the wavelet time-frequency plot. The reconstruction process is as follows:

[0016] 1.1) Divide the multi-source sensor monitoring signal into a sample at every L time points, and obtain the multi-source signal of each sample as follows: Where K is the total number of monitored signals or parameters, and L is the length of the signal.

[0017] 1.2) For each column in X, use continuous wavelet transform to convert it into a wavelet time-frequency image, and perform grayscale processing to obtain K grayscale images. Crop each grayscale image to size I×J and normalize the pixels to [0,1] to obtain a normalized K pixel matrix.

[0018] 1.3) Stack these K pixel matrices along the forward slice direction of the tensor, and reconstruct each sample as follows: The third-order tensor. The first order corresponds to the time domain information of the multi-source signal, the second order corresponds to the frequency domain information of the multi-source signal, and the third order corresponds to the spatial domain information of the multi-source signal.

[0019] Step 2: Since this invention addresses a binary classification problem, assuming the faults to be diagnosed are fault 1 and fault 2, repeat step 1 for the monitoring signals under each fault to obtain their respective tensor samples. Divide each tensor sample into a training set and a test set (the ratio of training set to test set data is 1:1). Assume a total of m tensor samples are selected from the two faults. Training is performed, thus obtaining the training set D:

[0020]

[0021] Where m represents the number of tensor samples, y i Representative sample The corresponding tags.

[0022] Step 3: For each tensor sample in the training set, calculate its nonlinear membership and non-membership functions using equation (2) to obtain the score for each sample. For the i-th tensor sample... Its membership degree Non-membership degree The calculation formula is:

[0023]

[0024] Where δ>0 is an adjustable parameter; r + r - These represent the positive and negative radii, respectively. These represent the positive and negative class centers, respectively; s + s represents the maximum distance between the centers of positive and negative samples; - This represents the maximum distance between the centers of the negative class and the positive class; it can be calculated using (3-5):

[0025]

[0026]

[0027]

[0028] Where, m + m represents the number of positive class samples. - y represents the number of positive class samples. i =+1 indicates a sample The corresponding label is 1, y i =-1 indicates a sample The corresponding label is -1.

[0029] Next, construct Intuitive Fuzzy Sets (IFSs): Finally, tensor samples are obtained through equation (6). Score s i :

[0030]

[0031] Step 4: Process the original tensor samples Tensor robust principal component analysis is performed to accurately recover noise-free low-rank feature tensors. This process mainly involves solving the following convex optimization problem:

[0032]

[0033] in, Indicates low-rank eigenvalues; ε i Indicates sparse noise components; Represents low-rank eigenvalues nuclear norm; λ i Denotes slack variables; ||ε i ||1 represents the sparse noise component ε i 1-norm;

[0034] The solution to the above problem is obtained using the alternating direction method of multipliers.

[0035] Step 5: Establish the primal problem of the nonlinear intuitionistic fuzzy support tensor machine model and obtain its dual problem. Specifically:

[0036] Introducing a nonlinear feature mapping function Low-rank feature tensor samples Mapping to Hilbert space: The primal optimization problem of the nonlinear intuitionistic fuzzy support tensor machine model is:

[0037]

[0038] in, Hyperplane representing classification Weight vectors; c0, s i ξ i b and b represent the penalty factor, sample score, slack variable, and unknown bias, respectively.

[0039] To obtain the optimal solution to the original problem (8), it is necessary to transform the original problem into its dual problem. To do this, the Lagrangian function of the original problem is constructed as follows:

[0040]

[0041] Where, α i and β i Represents the Lagrange multiplier.

[0042] By taking the partial derivatives with respect to the variables and setting them to zero, we obtain the Karush-Kuhn-Tucker (KKT) conditions:

[0043]

[0044] Substituting the KKT conditions into the original optimization problem (8), we derive its dual problem:

[0045]

[0046] By introducing kernel tricks: choosing an appropriate tensor kernel function Replace inner product The final dual optimization model of the nonlinear intuitionistic fuzzy support tensor machine model (8) is obtained, as shown in (12):

[0047]

[0048] It is worth noting that this invention uses [the following] in the dual problem. Inner product of the original tensor sample It avoids the vectorization process of tensor data, and preserves the intrinsic structural information of each monitoring signal and the coupling information of different monitoring signals.

[0049] Step 6: Obtain the solution vector by solving the final dual optimization problem (12). Therefore, we get:

[0050]

[0051]

[0052] Where, L={i|0 α i c0s i {i = 1, 2, ..., m} represents the set of indices for all supporting tensors, p represents an element in set L, and y p Representative sample The tag. The optimal solution representing the weights, b * This represents the optimal solution for the bias.

[0053] For unknown samples to be diagnosed First, obtain the low-rank feature tensor through tensor robust principal component analysis. Substituting the result into the decision function shown in equation (15), we obtain the predicted label:

[0054]

[0055] Step 7: Perform tensor robust principal component analysis on each tensor sample in the test set to obtain the low-rank feature tensor of each sample. Substitute it into the decision function (15) to obtain the predicted label of each sample, and determine whether the predicted label is equal to the true label. Use the formula Accuracy = Number of correctly classified samples / Total number of samples to obtain the classification accuracy of the model.

[0056] The beneficial effects of this invention are as follows:

[0057] This invention provides a fault diagnosis method for marine diesel engines. Addressing the shortcomings of current diagnostic methods, such as their inability to effectively extract multi-sensor time-varying features and susceptibility to noise, leading to low diagnostic accuracy, this invention constructs a fault diagnosis method for marine diesel engines based on a nonlinear intuitionistic fuzzy support tensor machine model. Compared to existing methods, this approach can extract multi-sensor time-varying features and highlight the contributions of different samples, effectively mitigating the impact of noise and outliers on the optimal hyperplane and improving the model's robustness. Furthermore, by introducing tensor robust principal component analysis, low-rank noise-free feature tensors are accurately extracted from noisy tensor samples and used as approximations of the original tensors. This avoids the destruction of inherent structural information of the monitoring signals and coupling information between different monitoring signals during the vectorization process, and also prevents this information from being overwhelmed by noise, ultimately significantly improving the accuracy of fault diagnosis. Attached Figure Description

[0058] Figure 1 (a) is the intercooler pressure signal of fault 1;

[0059] Figure 1 (b) is the exhaust pipe pressure signal of fault 1;

[0060] Figure 2 This is the wavelet time-frequency diagram corresponding to the first 15 time points of the intercooler pressure signal in fault 1. Figure 2 a) and grayscale image ( Figure 2 b);

[0061] Figure 3 This is the wavelet time-frequency plot of the exhaust pipe pressure signal of fault 1 at the first 15 time points. Figure 3 a) and grayscale image ( Figure 3 b);

[0062] Figure 4 (a) is the intercooler pressure signal of fault 2;

[0063] Figure 4 (b) is the exhaust pipe pressure signal for fault 2;

[0064] Figure 5 This is the wavelet time-frequency diagram corresponding to the first 15 time points of the intercooler pressure signal in fault 2. Figure 5 a) and grayscale image ( Figure 5 b);

[0065] Figure 6 This is the wavelet time-frequency plot of the exhaust pipe pressure signal of fault 2 at the first 15 time points. Figure 6 a) and grayscale image ( Figure 6 b);

[0066] Figure 7 This is a flowchart of the present invention. Detailed Implementation

[0067] To make the problems solved by the present invention, the solutions adopted, and the effects achieved clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should also be noted that, for ease of description, only the parts relevant to the present invention are shown in the drawings, not all of them.

[0068] A fault diagnosis method for marine diesel engines based on nonlinear intuitionistic fuzzy support tensor machines, the method comprising the following steps:

[0069] Step 1: In this example, we take two common faults that occur during the actual operation of a diesel engine: exhaust pipe blockage (fault 1, labeled 1) and insufficient air cooler cooling (fault 2, labeled -1). All operational data are from the operation of a 6S35ME-B9 diesel engine manufactured by MAN. Data from the first 300 sampling time points of faults 1 and 2 are selected. The collected measurement data of 15 different types of variables (monitoring signals) are used as multi-source monitoring signals. Specific monitoring signals include: diesel engine power (kW), maximum burst pressure (Bar), pressure flow (kg / °C), press outlet temperature (°C), press outlet pressure (Bar), intercooler after-temperature (°C), intercooler temperature difference (°C), intercooler after-pressure (Bar), intercooler pressure difference (Bar), scavenging air box temperature (°C), scavenging air box pressure (Bar), exhaust pipe temperature (°C), exhaust pipe pressure (Bar), turbocharger inlet temperature (°C), and turbocharger outlet temperature (°C).

[0070] Step 2: Check the 15 monitoring signals under fault 1 (e.g., the 8th monitoring signal - intercooler afterpressure). Figure 1 (a) and the 13th monitoring signal - exhaust pipe pressure ( Figure 1 (b) , fs = 30), the time window L is set to 15 for sample division, resulting in 20 samples, where the multi-source monitoring signal of each sample is represented as: Using continuous wavelet transform (here, 'morse' wavelet, fs=5), each column in X is converted into a wavelet time-frequency plot (e.g. Figure 2 (a) and Figure 3 (a)) and then convert it to grayscale to obtain the corresponding grayscale image (e.g. Figure 2 (b) and Figure 3 (b) After cropping the image to 64×64 and normalizing the pixels to [0,1], the 15 monitoring signals are converted into 15 grayscale images of size 64×64. The pixel matrices corresponding to these grayscale images are stacked along the direction of the forward slice, and the sample X is reconstructed into a third-order tensor sample of size 64×64×15. A total of 20 tensor samples were obtained for fault 1. Half of the samples were randomly selected for training, and the other half were used for testing. For each monitoring signal under fault 2 (e.g., the 8th monitoring signal - the pressure after the cooler), Figure 4 (a) and the 13th monitoring signal - exhaust pipe pressure ( Figure 4 (b) Perform the same processing to obtain its wavelet time-frequency plot (e.g. Figure 5 (a) and Figure 6 (a)) and the corresponding grayscale image (e.g. Figure 5 (b) and Figure 6 (b)) Finally, 20 tensor samples of fault 2 were obtained. Half of the samples were randomly selected for training, and the other half were used for testing.

[0071] Step 3: Calculate the membership degree and non-membership degree of each tensor sample using formula (2), and then obtain the score of the tensor sample using formula (6).

[0072] Step 4: For training set D: Tensor samples in Tensor robust principal component analysis is performed, that is, by solving the optimization problem (7), the noise-free low-rank feature tensor is accurately recovered. Combine the sample scores obtained in step 3 Substitute this into the dual optimization model (12) of the nonlinear intuitionistic fuzzy support tensor machine. In this embodiment, we use a Gaussian kernel function, namely: The parameters q and c0 are both in [2]. -7 ,2 -6 ,2 -5 ,2 -4 ,2 -3 ,2 -2 ,2 -1 ,2 0 ,2 1 ,2 2 ,2 3 ,2 4 ,2 5 ,2 6 ,2 7 The parameters are selected within a certain range, and the optimal parameter values ​​are determined using a grid search method. The solution vector is obtained by solving model (12). Substituting the solution vector into equations (13) and (14) respectively, we obtain the weight vector. and bias b * Finally, the decision function of the invented nonlinear intuitionistic fuzzy support tensor machine model is obtained using equation (15).

[0073] Step 5: Perform tensor robust principal component analysis on each tensor sample in the test set, and then substitute it into the decision function (15) to obtain the predicted label of the test sample. Determine whether the predicted label is equal to the true label. Use the accuracy = number of correctly classified samples / total number of samples to obtain the classification accuracy.

[0074] In addition, to further illustrate the effectiveness of the invented fault diagnosis method, we repeated the above experiment 5 times, and the confusion matrix of the 5 experiments is shown in Table 1. The accuracy of the 5 experiments and their corresponding optimal parameter values ​​are shown in Table 2.

[0075] Table 1. Confusion matrix of five replicate experiments

[0076]

[0077] Table 2. Accuracy and optimal parameter values ​​of five repeated experiments.

[0078] first The second The third Fourth Fifth average accuracy 90％ 95％ 100％ 90％ 85％ 92％ Optimal q value 64 0.0078 32 128 32 —— <![CDATA[Optimal c0 value]]> 8 0.0078 4 16 2 ——

[0079] As shown in Table 1, the method of this invention exhibits good predictive performance for both positive samples (exhaust pipe blockage fault samples) and negative samples (insufficient air cooler cooling fault samples), further verifying that the method of this invention can more accurately diagnose marine diesel engine faults. The accuracy rates of the five repeated experiments in Table 2 are all greater than or equal to 85%, with an average accuracy rate as high as 92%, further demonstrating the good diagnostic performance of the invented method for marine diesel engine faults. This is mainly attributed to the fact that, on the one hand, this invention combines multiple sensor signals for diagnosis, and the constructed tensor samples fully exploit the time-varying and spatial domain features of the signals. By assigning different scores to each tensor sample, the contributions of different samples are highlighted, effectively mitigating the influence of noise and improving the robustness of the model. On the other hand, it accurately extracts low-rank, noise-free feature tensors from noisy tensor samples, fundamentally alleviating noise interference and ultimately achieving a significant improvement in fault diagnosis accuracy.

[0080] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A ship diesel engine fault diagnosis method based on nonlinear intuitionistic fuzzy support tensor machine, characterized in that, The method comprises the following steps: Step 1: Reconstruct the original multi-source monitoring signal into a third-order tensor based on wavelet time-frequency map Step 2: For the binary classification problem, assuming that the faults to be diagnosed are fault 1 and fault 2, repeat step 1 to obtain the respective tensor samples under the two faults, and divide the training set and the test set for each tensor sample respectively, assuming that a total of m tensor samples are selected in the two faults Training is performed to obtain the training set D: wherein m represents the number of tensor samples, y i representative samples corresponding labels; Step 3: Calculate the membership and non-membership functions of each tensor sample in the training set using formula (2) to obtain the score of each sample; for the i-th tensor sample The membership and non-membership of the i-th tensor sample are calculated as follows: where δ > 0 is a tunable parameter; r + , r - denote the positive and negative class radius, respectively; denote the positive and negative class center, respectively; s + denotes the maximum distance between positive class samples and negative class center; s - denotes the maximum distance between negative class samples and positive class center; and can be computed by (3-5), respectively: where m + represents the number of positive class samples, m - represents the number of positive class samples, y i = +1 indicates that the sample corresponding label is 1, y i = -1 indicates that the sample corresponding label is -1; Reconstructed Intuitionistic Fuzzy Sets IFSs: The score value s of the tensor sample is finally obtained by equation (6) i : Step 4: Robust Principal Component Analysis on the original tensor sample Tensor Robust Principal Component Analysis is performed to exactly recover the noise-free low-rank feature tensor The procedure mainly solves the following convex optimization problem: wherein, denotes a low-rank feature component; ε i denotes a sparse noise component; denotes a low-rank feature component denotes a nuclear norm of i denotes a slack variable; ||ε i denotes a 1-norm of the sparse noise component ε i denotes a 1-norm of the sparse noise component ε solutions to the above problem are obtained by the alternating direction method of multipliers Step 5: establish the original problem of the nonlinear intuitive fuzzy support tensor machine model, and obtain the dual problem thereof; Step 6: Obtain the solution vector by solving the final dual optimization problem (12) Further, we obtain: Where, L={i|0 α i c0s i {i = 1, 2, ..., m} represents the set of indices for all supporting tensors, p represents an element in set L, and y p Representative sample Tags; The optimal solution representing the weights, b * The optimal solution represents the bias; then For an unknown sample to be diagnosed First, a low-rank feature tensor is obtained by tensor robust principal component analysis Then, the predicted label of the unknown sample is obtained by substituting the decision function shown in equation (15). Step 7: tensor robust principal component analysis is performed on each tensor sample in the test set to obtain a low-rank feature tensor of each sample, the prediction label of each sample is obtained by substituting the low-rank feature tensor into the decision function (15), and it is judged whether the prediction label is equal to the true label; the classification accuracy of the model is obtained by using the accuracy rate = the number of correctly classified samples / the total number of samples.

2. The method according to claim 1, wherein, The reconstruction process of step 1 is: 1.1) Divide the multi-source sensor monitoring signals into one sample for every L time points, and get the multi-source signal representation of each sample as where K is the total number of monitoring signals or parameters, and L is the length of the signal; 1.2) using continuous wavelet transform to convert each column in X into a wavelet time-frequency diagram, and performing gray processing to obtain K gray diagrams, cutting each gray diagram into I*J size and normalizing the pixels to [0, 1] to obtain K normalized pixel matrices; 1.3) stack these K pixel matrices along the forward slice direction of the tensor, reconstructing each sample into a third order tensor of size ; the first order corresponds to the time domain information of the multi-source signal, the second order corresponds to the frequency domain information of the multi-source signal, and the second order corresponds to the spatial domain information of the multi-source signal.

3. The method according to claim 1, wherein, The step 5 is specifically: Introducing a nonlinear feature mapping function map low-rank feature tensor samples to a Hilbert space: The original optimization problem of the nonlinear intuitive fuzzy support tensor machine model is: wherein, represents a weight vector of the classification hyperplane ; c0, s i , ξ i and b represent a penalty factor, a sample score, a slack variable and an unknown bias, respectively; In order to obtain the optimal solution of the original problem (8), the original problem needs to be converted into its dual problem, and therefore the Lagrange function of the original problem is constructed as follows: where a i and β i represent the Lagrange multipliers; By taking partial derivatives of the variables and setting the partial derivatives to 0, the KKT condition is obtained: The KKT condition is substituted into the original optimization problem (8) to derive the dual problem: By introducing the kernel trick: choosing a suitable tensor kernel function Substitute inner product The final dual optimization model of the nonlinear intuitive fuzzy support tensor machine model (8) is obtained, as shown in (12):

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