Xichen Han1,a，Peng Wei1,b*
1Maritime College, Tianjin University of Technology, Tianjin, China, 300384
aEmail:hanxichen@stud.tjut.edu.cn
bEmail:weipeng0925@sina.com
Abstract: Based on the existing framework of marine electric propulsion system, the article establishes the equipment health assessment model of marine electric propulsion system from the equipment degradation model of marine electric propulsion system by using the fuzzy AHP method to optimize the selection of equipment health status monitoring parameters and combining with the variable power theory. The equipment failure characteristics of the electric propulsion system are obtained through wavelet packet decomposition, and the migration learning VCTL mechanism is introduced to assist the Bayesian network for parameter learning, and in this way, the early failure prediction model of the equipment of the marine electric propulsion system based on the migration learning-Bayesian network framework is established. Simulations are carried out to verify the effectiveness of the above methods. The results show that the system health degree calculated by combining the fuzzy AHP method and the variable weight theory is in good agreement with the standard health degree, with a difference of only 3.95 percentage points. The average running time of the transfer learning-Bayesian network model is only 12.54 s. Applying the transfer learning-Bayesian network framework to the early failure prediction of the marine electric propulsion system has the advantages of fast efficiency and high accuracy, which can assist the operation and maintenance personnel to carry out the optimization and maintenance of the marine electric propulsion system in time to ensure the safety of the electric propulsion system. It can assist the operation and maintenance personnel to optimize the maintenance of the marine electric propulsion system in time and ensure the safety of electric propulsion system.
Keywords: marine electric propulsion system; equipment degradation model; fuzzy AHP; variable power theory; transfer learning; Bayesian network; early failure prediction
1. Introduction
At present, the international marine competition is unprecedentedly fierce, and the dispute over maritime rights and interests is becoming increasingly severe, the state attaches great importance to marine scientific research, formulates the strategic goal of strengthening the development of the distant sea and the strategic layout of moving from the shallow sea to the deep sea, and from the near sea to the ocean, and proposes to make a major breakthrough in the deep sea exploration and research, so as to effectively enhance China’s position in the international marine scientific research. As the power system of marine vessels has the related demands such as low vibration noise, large electric load for scientific research equipment, good maneuverability, and valuable cabin space [1-2]. The electric propulsion system can fully satisfy the various large-load electricity needs of the ship by virtue of its advantages of high degree of automation, flexible arrangement, low vibration and noise, good speed distribution performance, flexible operation, and green environmental protection [3-6]. Therefore, the integrated electric propulsion system is the leapfrog development of modern ship technology, which is of great significance to solve the problem of ship power platform.
However, affected by the operating environment, coupled with the system itself is a tightly coupled and complex network structure, once the electrical system fails in the process of ship navigation, it will threaten the safety and stability of ship navigation [7-9]. In order to enhance the reliability of the electric propulsion system operation, a set of scientific and reliable fault diagnosis methods should be constructed according to the characteristics of the ship electric propulsion system [10-11]. It can quickly detect and locate different types of faults in the system under different operating conditions of the ship, and provide guarantee for the safe operation of the ship electric propulsion system [12-13]. For this reason, the establishment of the degradation model and fault detection framework of the electric propulsion system is of great significance for improving the stability and reliability of the operation of the electric propulsion system of Chinese ships [14-15].
In this paper, on the basis of combing the marine electric propulsion system, a system equipment degradation model is established from the perspective of the electric propulsion system equipment, and a health assessment model of the marine electric propulsion system equipment is established through the fuzzy AHP method and variable power theory. The parameter learning of Bayesian network is then optimized by using the migration learning technique, and an early failure prediction model of marine electric propulsion system is established. The feasibility of the application of the transfer learning-Bayesian network framework is verified through experiments on the health assessment and early failure prediction of marine electric propulsion system equipment.
2. Degradation model for marine electric propulsion system equipment
In order to ensure the safe and reliable operation of the energy-based marine electric propulsion system and improve the defect warning capability of electric equipment, it is imminent to carry out digital and intelligent transformation of the health management and operation and maintenance mode of marine electric propulsion system equipment. Based on this, this paper carries out modeling of the relevant equipment degradation of the marine electric propulsion system to assist in realizing the fault identification of the marine electric propulsion system, and better enhance the stability and reliability of the marine electric propulsion system.
2.1 Framework analysis of marine electric propulsion systems
2.1.1 Electric propulsion system framework
For the marine electric propulsion system, the brushless DC motor is mostly used as the driving motor, and the double closed-loop feedback control strategy is mostly adopted. The PID controller controls the size of the output voltage by adjusting the error of speed and current to achieve the purpose of controlling the rotational speed of the brushless DC motor, and then controlling the rotational speed of the propeller. The basic framework of the marine electric propulsion system is shown in Fig. 1, which adds the effect of ocean disturbance on the dynamic load of the propeller to the input of the control system for compensation, thus effectively improving the dynamic performance of the electric propulsion system.
Figure 1 Electric propulsion control system model
The torque loss of the propeller under wave disturbance is used as a measurable disturbance signal, which is added to the input of the control system through the feed-forward control link to compensate for the influence of the disturbance on the propeller thruster. The outer loop is the speed loop, which adopts PID control to suppress the load disturbance, eliminate the rotor speed fluctuation, and ensure the dynamic tracking performance of the system. The inner loop is the current loop, which adopts hysteresis loop control to improve the current response speed, limit the maximum current and keep the system running stably. The output of the current controller is used to adjust the duty cycle of the PWM waveform to change the phase voltage size and thus adjust the speed.
2.1.2 Electric propulsion system equipment
Marine electric propulsion system devices generally refer to devices that use electro-mechanically driven propellers to propel the movement of a ship. Marine electric propulsion devices generally consist of propellers, electric motors, generators, prime movers and control and regulation equipment. Among them, the mechanical energy of the prime mover is changed into electric energy by the generator and transmitted to the propulsion motor, which changes the electric energy into mechanical energy and transmits it to the propeller to promote the ship’s movement. The prime mover for electric propulsion can adopt diesel engine, steam turbine or gas turbine. At present, high-speed or medium-high speed diesel engine is generally used, and steam turbine or gas turbine is used for high power. Generator can be used brushless DC it excitation, differential compound excitation motor or AC synchronous generator. The electric motor can adopt DC it excitation motor or AC synchronous motor, asynchronous motor and so on. Propellers are generally used for marine propulsion because of their high efficiency and small size.
Marine electric propulsion system device also has the following characteristics:
(1) Flexible maneuvering and good maneuverability.
(2) Easy to obtain the ideal towing characteristics, improve the technical and economic performance of the ship.
(3) The total power of the propulsion device can be borne by multiple units, increasing the flexibility of equipment selection and improving the ship’s vitality.
(4) Middle and high speed non-reversing prime mover can be used. And the middle and high speed diesel engine maintenance management and overhaul is relatively simple, replacement is also more convenient.
(5) There is no rigid connection between the prime mover and propeller. This can prevent shock vibration, favorable noise reduction, so that the propeller speed can choose the best value, and do not have to be restricted by the speed of the prime mover. The diesel engine speed can be allowed to select the best value without being limited by the propeller speed. Since the propeller does not have to be directly connected to the main engine, the propulsion system can be arranged more flexibly, which is more favorable for the arrangement of some special ship power equipment.
2.2 Modeling of equipment degradation in electric propulsion systems
2.2.1 System equipment degradation model
Equipment degradation refers to the existence of mechanical and electrical reliability reduction, aging and failure behavior of power equipment over time, which is a random phenomenon of continuous time trajectory. Simple degradation models have low accuracy, while complex models are difficult to adjust parameters and have low generalization, and the equipment degradation model used for its own evaluation needs to have both accuracy and generalization. Therefore, the traditional degradation model can be improved in the following aspects, based on the easy-to-adjust differential equations for degradation modeling, synchronized equipment degradation information for real-time model adjustment, and improve its fit to the equipment’s own state [16].
First of all, power equipment degradation modeling based on stochastic processes, the data collection process to consider the possibility of extreme behavior and the real average degradation behavior information. After that, the degradation model of the intelligent power equipment is established based on the state data, and the nonlinear function of the degraded state at the moment is solved based on the time variable and the random variable, that is:
(1)
where is the stochastic factor, and are the drift and diffusion coefficients, respectively.
The stochastic differential equation is decomposed according to the following equation, i.e:
(2)
where is the standard Brownian motion about and , and is the Brownian motion function. The device degradation state is derived by counting the probability of transition from to at in the following equation. Namely:
(3)
Finally, the model is trained based on the power equipment’s own dataset to improve the fit and generalization of the model to the data. The degradation model should also be synchronized with the equipment degradation information to adjust the parameters in real time to improve the model fit to the equipment’s own state.
2.2.2 Optimized selection of monitoring parameters
On the basis of clarifying the degradation model of the marine electric propulsion system, due to the fact that more system equipment is involved, the correlation relationship between each system equipment needs to be clarified when carrying out the degradation state analysis, so as to make the accurate health assessment results of the system equipment. Based on this, this paper proposes a monitoring parameter optimization selection method based on the fuzzy AHP method, and its specific process is as follows:
(1) Analyze the correlation relationship between equipment factors and establish a hierarchical structure model of the system. The target layer is the process of equipment health state degradation, the criterion layer is the principle of monitoring parameter selection, denoted as , and the scenario layer P is the set of parameters to be selected for monitoring, denoted as .
(2) Compare the relative importance of each element in the same level about a criterion in the previous level and construct a fuzzy judgment matrix. Firstly, the judgment matrix is constructed according to the conventional hierarchical analysis, and then the conventional scales in are replaced by the triangular fuzzy numbers of the form to form the fuzzy judgment matrix , that is:
(4)
(3) Calculate the relative weights under a single criterion, i.e., hierarchical single sorting, and perform consistency test. The calculation method of weights generally adopts the eigenroot method: the largest eigenroot and the corresponding eigenvector of and the corresponding eigenvector can be found from the fuzzy judgment matrix , and the maximum eigenvector is normalized, that is, the single-ranking weights are found. The ratio is used to determine the degree of inconsistency of the matrix , where , and is the average stochastic consistency index of the matrix , which can be obtained by looking up the table. When , the judgment matrix is considered to have satisfactory consistency, otherwise the judgment matrix needs to be adjusted to have satisfactory consistency [17].
(4) Calculate the total ranking weights of the program level elements on the stem system objectives, and perform the total hierarchical ranking and consistency test. The ultimate goal of hierarchical analysis is to determine the total ranking weights of the elements in the bottom level, i.e., the scenario level, with respect to the objectives in order to select an optimized scenario. The criterion layer has elements and the solution layer has elements. Let the single ordering weight vector of the elements of the criterion layer with respect to the objective layer be denoted as , and the single ordering weight vector of the elements of the solution layer with respect to the criterion be denoted as , and the single-ordered weight vectors of the elements of the scheme layer with respect to all the elements of the criterion layer form a matrix of , i.e.:
(5)
The total ranking weights of the elements of the scheme layer on the target layer are then:
(6)
Or written as:
(7)
Hierarchical total ordering consistency test: let the consistency metric when is the criterion be , and the average stochastic consistency metric be , then the total ordering stochastic consistency ratio of the elements of the scheme hierarchy for the target hierarchy is:
(8)
Similarly, when , the results of hierarchical total ranking are considered to have satisfactory consistency, otherwise the judgment matrix needs to be adjusted.
(5) Based on the normalized total ranking weight vector, the monitoring parameters are selected. The judgment principle is as follows:
(9)
Given a weight threshold , the monitoring parameter is chosen if .
2.2.3 System equipment health assessment
In the actual health assessment process of the system, the weight of the lower level equipment tends to change with the change of the state, and when the health of the lower level equipment is seriously reduced, the damage to the whole system will be significantly aggravated. According to the trend of weight change, variable weight can be divided into 2 kinds of incentive-type variable weight and penalty-type variable weight. Obviously, in the process of health assessment of marine electric propulsion system equipment, the penalty-type variable weight should be selected, i.e., when the state value of an indicator decreases, the weight of its corresponding indicator should rise [18]. The weight change of each indicator should satisfy the following conditions:
(1) Normalizability, i.e., .
(2) Continuity, i.e., is continuous with respect to each variable.
(3) decreases monotonically about , i.e., . For the changed weights, the following relationship should be satisfied compared with the fixed weights:
(10)
where is the changed weight, is the fixed weight, and is the change function with respect to the actual state value, and for penalized variable weights such as health assessment, increases as the actual state value decreases and increases.
Construct the variable weight function as:
(11)
Where is the actual state value of the device, is the number of juxtaposed indicators in the same level with the device , is the starting point for the change of weights, to control the speed of change of the weights with the actual state, and is the coefficient of punishment, to control the size of the degree of punishment.
The coefficients and need to be determined according to the specific equipment, different equipment weights and its actual health state of the relationship between the change is not the same, should be considered mainly from the following aspects:
(1) The degree of equipment importance. Some of the main units of function realization, the degree of importance is extremely high, and its performance degradation will have a great impact on the whole system, and even the failure or not of a single unit will play a decisive role in the health of the whole system, so its weight will be significantly increased with the performance degradation. As for some devices, their degree of importance is small, when the performance is slightly degraded, the whole system is still able to realize the main functions well, so the amount of change in its weight with the performance degradation is also relatively small.
(2) Performance degradation speed. For the degradation speed is faster, or because of the detection conditions and technical constraints are not easy to detect the degradation phenomenon of the device, its weights should be more punitive to the degree of performance degradation.
(3) Task and technical requirements. Different equipment in the technical performance requirements are somewhat different.
Based on this, this paper divides different marine electric propulsion system equipment into four types: failure, degradation, performance degradation and health, with respect to their degradation status and health condition. On this basis, the health assessment of marine electric propulsion system equipment is carried out, which also provides the basis for the early failure prediction of marine electric propulsion system later.
3. Fault prediction based on migration learning-Bayesian network
Marine electric propulsion system related equipment presents a wide distribution, a variety of types, different structures and other characteristics, in the operation will inevitably appear insulation aging, structural damage and equipment function degradation and other problems, the operation of the marine electric propulsion system will also have a greater impact. In view of the problems in the operation of the marine electric propulsion system, relevant scholars in the study proposed to start from the basic features of equipment health management and intelligent operation and maintenance, to adopt advanced and effective management mode, and at the same time, to play the advantages of the intelligent key technology, which can provide support for the better operation of the marine electric propulsion system.
3.1 Migration Learning and Bayesian Networks
3.1.1 Transfer Learning Techniques
Transfer learning is the learning problem of obtaining data and information from similar neighborhoods in order to solve the learning problem in the domain with insufficient amount of data. The target network is the network whose parameters are to be estimated, compared to the target network which has sufficient amount of data and is similar to the target network is called resource network which is the provider of data and information in transfer learning [19].
Denote the target network as , where denotes the data of the target network, denotes the structure of the target network, and denotes the dimension of the target network. Similarly, the resource network is represented as , where denotes the data of the resource network, denotes the structure of the resource network, and denotes the dimension of the resource network. In the process of using transfer learning to find a source network that matches the target network, the following conditions must be satisfied:
(1) Structural consistency. The number of parent nodes owned by the child nodes corresponding to the resource sub-network is the same as the number of parent nodes owned by the child nodes corresponding to the target sub-network.
(2) Parameter dimension consistency. It is guaranteed that the number of states of each parent node as well as the number of states of the child nodes of the target sub-network and the resource sub-network are the same.
On the basis of satisfying the above conditions, some researchers have proposed a migration aggregation method for LP. The probability is a probability-weighted sum from the target and resource networks, denoted as:
(12)
where denotes the conditional probability of the th model out of models involving , is the weight associated with that probability, and is the normalization factor.
3.1.2 Bayesian networks and parameter learning
(1) Basic principle of Bayesian theory
The method of dealing with positional parameters by setting up random variables while reflecting the uncertainty of the variables through the associated probabilities is called the Bayesian method. Bayesian statistics refers to the method of determining the conditional probability of an unknown variable using fixed observations: by making assumptions before the statistical analysis and then refuting them through fixed observations, we can update the obtained results several times each time new, available observations appear in the statistical model. As the amount of available data increases, the impact of the assumptions made on the assessment results decreases, and the conclusions reached through Bayesian analysis are closer to those reached using frequency analysis methods [20]. The mathematical formula used to describe the Bayesian approach is as follows:
(13)
Where is the probability of event A and event B occurring simultaneously, is the prior probability of event A i.e., the probability of A occurring without collecting information about event B, is the posterior probability of A i.e., the conditional probability of event A after event B occurs, and as for , it is similar to the case of . The value of can be obtained by the full probability formula, i.e.:
(14)
From Eq. As the information related to event B is updated, the probabilistic confidence of event A is also updated.
The Bayesian network analysis method is a means used for information gathering, risk assessment, and prediction of future consequences. In the process of constructing the Bayesian network model, in order to ensure the convenience and feasibility of the model in the operation and analysis stages, it is necessary to integrate various factors in the fault tree and construct the model with the least number of parameters and the most concise interdependencies to ensure that the model can operate properly.
(2) Bayesian network parameter learning
After determining the structure of the Bayesian network and clarifying the logical relationship between each node, the parameter learning of the Bayesian network is carried out, and the conditional probability of each node can be obtained through the method of parameter learning. Generally, the expectation maximization algorithm is used to carry out model parameter learning on the sample data of the existence of data situations, and after the Bayesian network structure is adjusted using the correlation method, the Bayesian network parameter learning is carried out on the accident sample dataset through the EM algorithm, and the maximum expectation method is used to deal with the sample data.
Step1 Input sample data, convergence threshold for missing dataset, and calculate the likelihood value of network parameters according to Bayesian network related formula. If is a set of observed sample variable data, and is the hidden variable data, i.e., the set of all the missing-value variables in , and let be the currently known parameter estimate, is the complete data based on supplemented with , and the log-likelihood function of defining as is:
(15)
where , is the expected log-likelihood function of based on , and the observed sample data remains unchanged during EM algorithm The observed sample data remains unchanged during the iteration process, so can be expressed as .
Step2 Enter the loop body. During the th iteration of the expectation maximization algorithm, the expected log-likelihood function is first computed, and the value of the parameter is found when reaches its maximum, and the expression of the expectation step is as follows:
(16)
Among them:
(17)
(18)
To find the value of , substitute into the following equation:
(19)
At this point, the new value is obtained and compared with the old value, and if it is within the convergence threshold, the iteration ends. The new value is the final result. Otherwise. The new value becomes the old value, the number of iterations is added by one and the iteration continues. Following the above method can be used to learn the parameters of this Bayesian network and build a Bayesian network model.
3.2 Early Failure Prediction for Electric Propulsion Systems
3.2.1 System Failure Characterization
(1) Wavelet packet decomposition
Feature extraction is the current bottleneck problem in mechanical fault diagnosis, which is directly related to the accuracy of fault diagnosis and the reliability of early prediction. Wavelet analysis is a new time-frequency analysis method, wavelet transform has a good frequency domain resolution for low-frequency signals and a good time domain resolution for high-frequency signals. Wavelet packet decomposition can decompose the signal into the projection of the original signal in different frequency bands, and the analysis of the signal in these bands is called the band analysis technique.
If and the permissibility condition is satisfied:
(20)
Where denotes the Fuchsian transform of and denotes the circular frequency, then is said to be the fundamental wavelet.
The binary discrete wavelet generated from the fundamental wavelet is:
(21)
If the binary discrete wavelet clusters form the standard orthogonal basis of , then there is an orthogonal wavelet decomposition of as:
(22)
where is the number of decomposition layers, are the coefficients, are the scale coefficients of the layers, and is the binary quadrature scale function.
When , the binary orthogonal scale function obtained from the fundamental wavelet is:
(23)
Denoting the scale function and the wavelet function as and , respectively, then by:
(24)
The defined function ( or ) is called the wavelet packet of the orthogonal scale function . In the above equation, , i.e., the two coefficients also satisfy the orthogonality relation. This generalizes the orthogonal wavelet decomposition in multiresolution analysis to wavelet packet decomposition, yielding a wavelet packet representation of the signal as:
(25)
where coefficients from decomposition.
(2) Fault feature sample acquisition and processing
The fault signal of the marine electric propulsion system equipment is decomposed into wavelet packets to form preliminary feature components to be diagnosed. In order to speed up the Bayesian network model inference calculation speed, the wavelet packet decomposition should also be processed and discretized after the data feature extraction, to form the final fault inference feature vector.
Let the length of the original vibration signal be , where are all positive integers. Following the wavelet packet decomposition algorithm to decompose the original signal into layers of wavelet packets, the component can be obtained. The size of each frequency band data volume will become . The designed early fault feature extraction function is:
(26)
Where is the th component of the initial vibration signal decomposed by the layer wavelet packet, , is the number of summation, is the number of final formation of the feature vectors, and is a natural number. By the above equation, each wavelet coefficients can be formed into a set of feature vectors.
Using the maximum discretization method, the maximum value of each component is noted as , and the resulting eigenvectors are discretized into discrete eigenvalues to form the eigenvectors, i.e.:
(27)
The parameter is taken as 3, and is taken as 0.618. Depending on the amplitude of the vibration characteristic signal of the corresponding equipment, the value of 1, 2, or 3 is taken after discretization and quantitative unification according to the magnitude of the corresponding equipment, respectively.
3.2.2 System Early Failure Prediction Models
The early fault prediction process of marine electric propulsion system based on migration learning and Bayesian network designed in this paper is shown in Fig. 2. It makes full use of the data and information acquired in the source domain and migrated to the target domain model for learning by introducing the migration learning VCTL mechanism, establishes the final early fault prediction model of the marine electric propulsion system, and carries out the early fault prediction using Bayesian network.
Figure 2 System early fault prediction model
The steps of early fault prediction based on migration learning-Bayesian network are as follows:
Step1 Set the early fault feature attribute threshold .
Step2 Perform feature fusion and normalization on the features obtained by wavelet packet decomposition algorithm, and use SVM classification to obtain AU feature samples (including the source domain AU sample set and the target domain AU sample set ).
Step3 Determine whether to build a BN model for early failure prediction of electric propulsion system. If yes, jump to Step8, otherwise execute Step4 to Step7 for modeling.
Step4 Establish the BN structure for early failure prediction of electric propulsion system equipment by analyzing the relationship between early failure characteristics of electric propulsion system equipment and each AU.
Step5 Statistical sample size according to the source domain sample set and calculate the source domain BN parameter , that is:
(28)
Step6 Statistical sample size according to the target sample set and calculate to get the target initial BN parameter , that is:
(29)
Where , denotes the number of states of the parent node variable, denotes the number of states of the child node variable, and is a constant close to zero.
Step7 Determine the final target BN parameters based on and as well as the BN parameter fusion model, and design a balancing factor , i.e.:
(30)
(31)
where C is the small dataset sample threshold and .
From the above two equations, it can be seen that when is larger, is larger, at this time, the final target BN parameters tend to utilize the target domain data for parameter learning, otherwise it is more inclined to utilize the source domain data for parameter learning.
Step8 Perform fault prediction using Bayesian network model on the acquired samples to be predicted, and get the attribute probability of early fault features .
Step9 Perform the determination of early fault features. If the early fault feature attribute probability is greater than or equal to the threshold , output the early fault feature attribute, i.e. the early fault feature prediction result. Otherwise, return to Step2 and reacquire new feature samples.
4. Marine electric propulsion system health assessment and fault prediction
For marine electric propulsion system to carry out state detection, fault diagnosis and health management, through a variety of sensor data and historical data, the use of relevant intelligent algorithms to realize the system monitoring state assessment, early failure prediction and other functions, and combined with a variety of available resource information for maintenance personnel to provide equipment maintenance and security strategy basis. Based on this, the health assessment and fault prediction of marine electric propulsion system equipment is very necessary, and it plays a very important role in enhancing the stable operation performance of marine electric propulsion system.
4.1 Electric propulsion system equipment health assessment
4.1.1 Comparative validation of different methods
In this paper, on the basis of establishing the degradation model of marine electric propulsion system equipment, combining the fuzzy AHP method to select the equipment monitoring parameters, and introducing the variable power theory to carry out the health state assessment of marine electric propulsion system equipment. In order to verify the validity of the methodology in this paper, the system equipment health is quantified from the perspective of the gearbox in the marine electric propulsion system equipment without considering the remaining component failures, and this is used as a comparison standard for the health of marine electric propulsion systems. This comparison criterion is justified since this calculation example is a failure of the actuating equipment but the measuring equipment is normal. Taking the system equipment gearbox health as the standard and choosing the constant-weight AHP as the comparison method, the health simulation curve of the marine electric propulsion system is obtained as shown in Fig. 3.
From the comparison results of the system health degree, it can be seen that the results of the system health degree calculated by the fuzzy AHP combined with the variable weight theory proposed in this paper have a better consistency with the results of the standard health degree under the perspective of the gearbox, while the gap between the calculated results of the constant-weight AHP method and the standard health degree reaches 40.59 percentage points. This indicates that the health assessment method of marine electric propulsion system based on fuzzy AHP and variable weight theory proposed in this paper is reasonable and can effectively obtain the health status of marine electric propulsion system. In addition, the latest system health management requires that environmental factors be taken into account, and it is also easier to carry out subsequent research using the method in this paper, as long as appropriate parameters can be selected to reflect the dynamic impact of the environment.
Figure 3 The health of the Marine electric propulsion system
4.1.2 Transmission Health Assessment
The gearbox is a commonly used component in marine electric propulsion system equipment, and it is used as an object to further validate the use of the health assessment methodology in this paper. For ease of illustration, the transmission model is simplified by examining the transmission model consisting of only the three main components (i.e., gears, bearings, and shafts) that cause the main failure modes of the transmission, and examining only the main failure modes of these three main components (which account for more than 90% of the transmission failures). The three components of gears, shafts and bearings of the transmission have multiple failure modes, which mainly include input-side gear damage, output-side gear damage, input-side shaft mechanical loosening, input-side bearing collar damage, output-side shaft mechanical loosening, and output-side bearing ring damage, and are defined as H1~H6 respectively.Different failure modes are categorized by reading the vibration signals corresponding to the frequency bands of the accelerometer measurements, and using the relevant The experimental data in the literature on the growth of cracks in the gearbox gears are used to verify the effectiveness of this paper’s method in the health assessment of marine electric propulsion system equipment. Figure 4 shows the health assessment results of the gearbox.
At the beginning of the time scale, the gearbox of the marine electric propulsion system is normal, and after injecting crack faults in the gears, when the time scale is 20, high vibration levels beyond the normal limits occur at the intrinsic frequency of the gearbox gears, and the inference calculations yielded the likelihood of gear failures on the output and input sides to be 16.74%% and 31.58%, respectively. When the time scale is 25, with the gear intrinsic frequency as the center of the side frequency band interval for the damage to the gear rotation frequency value for the input side of the wheel tooth frequency, reasoning failure for the input side gear failure, and according to the model information forecast input side gear node sub-node input side shaft and output side gear in the failure risk components. The reason is that the crack damage of the input side gear grows during operation, and the vibration caused by it is transmitted to the output side gear and the input side shaft, which are directly related to it, and so on. The vibration caused by the opening and closing of cracks in the input side gear during rotation causes the shaft motion to start rotating away from the axial direction and eventually leads to mechanical loosening of the input side shaft. At a time scale of 30, the high harmonic band of the shaft speed is exceeded, leading to the conclusion that the input shaft is mechanically loose and predicting that the input bearing is the next component at risk of failure. This is due to the fact that the vibration caused by both the input gear and shaft failures can cause the input bearing performance to deteriorate. At a time scale of 35, the 2x shaft speed band is exceeded, and the inference model concludes the fault diagnosis of bearing collar damage. Comprehensive results can be seen, this paper in the marine electric propulsion system equipment degradation model on the basis of the introduction of fuzzy AHP and variable weight theory can be realized on the system equipment health state for effective assessment, which is conducive to further development of the system equipment early failure prediction.
Figure 4 Results of transmission health assessment
4.2 Failure prediction of electric propulsion system equipment
4.2.1 Parameter learning under different migration strategies
In this section, a variety of parameter learning algorithms for Bayesian network models are comparatively analyzed. These parameter learning algorithms for Bayesian network models can be categorized into two types of algorithms according to the learning strategy they follow, those without knowledge transfer (e.g., MLE and MAP algorithms) and those with knowledge transfer. The latter can be further categorized into two types, fixed learning methods (where the parameter learning directly uses the data in the resource domain without relying on the samples in the target domain) and fine-tuned learning methods (where the results of the parameter learning are dependent on both the target domain samples and the resource domain samples.) The LoLP algorithm and the VCTL mechanism applied in this paper belong to the strategy of fine-tuned learning.
Based on the previous description of the failures of the marine electric propulsion system equipment, which mainly includes four categories (F1~F4) of failure, degradation, performance degradation, and health, a Bayesian network model is built according to each of the four types, and 1000 sets of instance samples of the marine electric propulsion system equipment are collected for each of them. In the parameter learning, the information of the resource samples is utilized to obtain the Bayesian network parameters of the target domain through knowledge transfer learning. In order to facilitate the comparison of the performance of different Bayesian network parameter learning algorithms, MLE, MAP, Freeze, LoLP and VCTL algorithms are used in the experiments, respectively, to obtain the CPT values of the Bayesian network using parameter learning, and then evaluate the learning results by calculating the average KL dispersion (KLD) between it and the true CPT, and the smaller the KLD represents that the estimated parameters are closer to the parameters’ true value. Each experiment was conducted 20 times, and the mean and variance of the experimental results were counted to obtain the learning results of different Bayesian network models as shown in Table 1, with * in the table indicating the best learning results.
Based on the results in the table, the following conclusions are drawn:
(1) In terms of whether the migration learning strategy is used or not, when the sample size of the target domain for parameter learning is small, compared with the methods without knowledge migration (MLE or MAP), the parameter learning using knowledge migration methods (Freeze, LoLP or VCTL) can better reduce the KLD, i.e., the CPT value of the Bayesian network obtained by knowledge migration learning, is closer to the real CPT value. The analysis shows that the information migration mechanism can compensate for the inaccuracy of Bayesian network parameter valuation in the target domain due to too few samples, thus helping to improve the results of Bayesian network parameter estimation.
(2) Among several parameter learning methods that have adopted the migration learning strategy, the comparison results between the fixed learning method (which does not utilize the sample information of the target domain) and the fine-tuning learning method show that the fine-tuning method effectively utilizes the Bayesian network parameter information embedded in the target domain samples, and improves the performance of parameter learning within the target domain of the Bayesian network.By utilizing the informational potentials of the data of both the resource domain and the target domain, the VCTL The best parameter learning results are obtained by winning with the smallest KLD in almost every experiment.
Table 1 The learning results of different Bayesian network models
| Method | F1 | F2 | F3 | F4 |
| MLE | 0.24±0.03 | 0.38±0.25 | 0.56±0.35 | 0.47±0.26 |
| MAP | 0.15±0.09 | 0.13±0.09 | 0.27±0.18 | 0.21±0.15 |
| Freeze | 0.06±0.04 | 0.06±0.03 | 0.08±0.04 | 0.07±0.06 |
| LoLP | 0.04±0.01* | 0.03±0.02 | 0.04±0.02 | 0.04±0.02 |
| VCTL | 0.04±0.01* | 0.03±0.01* | 0.03±0.01* | 0.03±0.01* |
In addition, this paper also conducts statistics for the average running time consumption of Bayesian network model migration learning, and its specific results are shown in Table 2. Along with the increasing number of nodes and parameter dimension complexity of the Bayesian network model, the time consumption of almost all Bayesian network parameter learning algorithms is incrementing, but the average running time does not have an overly significant surge in the order of magnitude. Among them, the computational complexity of the VCTL algorithm is similar to that of the MAP algorithm.
Table 2 The Average operating time consumption of different Bayesian (ms)
| Method | F1 | F2 | F3 | F4 |
| MLE | 0.98±0.15 | 1.03±0.25 | 1.13±0.15 | 1.17±0.25 |
| MAP | 1.04±0.16 | 1.32±0.14 | 1.58±0.16 | 1.61±0.18 |
| Freeze | 1.08±0.14 | 1.53±0.16 | 1.61±0.13 | 1.69±0.22 |
| LoLP | 1.12±0.17 | 1.67±0.23 | 1.65±0.27 | 1.72±0.34 |
| VCTL | 1.26±0.12 | 1.84±0.15 | 1.78±0.24 | 1.81±0.18 |
In summary, the migration learning strategy helps to improve the accuracy of Bayesian network parameter learning when the sample size of the target domain is small. Utilizing the information potential of the resource domain and target domain data, the VCTL mechanism can obtain more accurate parameter learning results for the target domain model. Therefore, in this paper, it is feasible to utilize the migration learning VCTL mechanism for parameter learning of Bayesian network models, which can provide reliable migration learning results for early failure prediction of marine electric propulsion system equipment.
4.2.2 Analysis of equipment early failure prediction results
In order to verify the practical application effect of the migration learning-Bayesian network early fault prediction model proposed in this paper, relevant experiments are conducted. At the same time, the fault prediction method based on GCA-MLP and the fault prediction method based on VFS theory are selected for experimental comparison to compare the prediction accuracy and prediction time of the three methods. According to the actual values of early failure prediction of marine electric propulsion system equipment, the relevant affiliation degree of the prediction process is calculated, and the interval is set to analyze whether the affiliation degree belongs to the interval, and if it is not inside the interval, the affiliation degree is judged to be located on the left or right side of the interval. After obtaining the relevant judgment results, the final results are obtained through normalization. Analyzing the eigenvalues, calculating the evaluation results, and comparing the frequency change of the equipment signal in the fault state, the experimental results obtained are shown in Fig. 5. Among them, Fig. 5(a)~(d) shows the fault prediction results of the actual frequency, GCA-MLP, VFS, and the method of this paper, respectively.
According to the comparison in the figure, it can be seen that the failure frequency fluctuation of the predicted object marine electric propulsion system equipment is very obvious, which indicates that there are multiple failures. At the same time, three prediction methods are selected for prediction, and the predicted load accuracy obtained by the prediction method based on the migration learning-Bayesian network framework proposed in this paper is more consistent with the actual load fluctuation. Compared with the traditional prediction methods, the early failure prediction method proposed in this paper has a higher prediction accuracy and can accurately determine whether there is a risk in the marine electric propulsion system equipment.
(a) Actual frequency (b) GCA-MLP
(c) VFS (d) This article
Figure 5 Early failure prediction results of equipment
Compare the time spent by the three methods in the process of predicting the early failure of marine electric propulsion system equipment. In order to ensure the authenticity of the experiment, the paper sets the number of predictions to be 12 times, and the experimental results obtained are shown in Table 3. According to the results in the table, it can be seen that the offshore electric propulsion system equipment early failure prediction method based on the migration learning-Bayesian network framework can make the offshore electric propulsion system equipment early failure prediction in a shorter time, and the average value of the prediction time in the prediction process of 12 times is 12.54 s. The traditional offshore electric propulsion system equipment early failure prediction method based on the grey correlation analysis and the multilayer perceptron and the offshore electric propulsion system equipment early failure prediction method based on the theory of variable fuzzy sets has the average value of the prediction time. The average prediction time of traditional gray correlation analysis and multilayer perceptron-based and variable fuzzy set theory-based methods for offshore electric propulsion system is 60.55s and 55.58s respectively, which is 2.83 times and 2.43 times higher than that of this paper’s method. It can be seen that the early failure prediction method of offshore electric propulsion system equipment proposed in this paper can accurately determine the early failure of offshore electric propulsion system equipment in a short period of time, which has high practical application value.
Table 3 Predict the experimental results of time (s)
| Number | GCA-MLP | VFS | Ours |
| 1 | 61.43 | 55.49 | 12.79 |
| 2 | 60.38 | 55.72 | 12.58 |
| 3 | 60.46 | 55.38 | 12.64 |
| 4 | 60.51 | 55.37 | 12.73 |
| 5 | 60.79 | 55.52 | 12.51 |
| 6 | 60.42 | 55.37 | 12.29 |
| 7 | 60.75 | 55.89 | 12.37 |
| 8 | 60.43 | 55.93 | 12.64 |
| 9 | 60.65 | 55.81 | 12.28 |
| 10 | 60.32 | 55.72 | 12.67 |
| 11 | 60.17 | 55.46 | 12.43 |
| 12 | 60.26 | 55.31 | 12.58 |
| Means | 60.55 | 55.58 | 12.54 |
5. Conclusion
Based on the framework of marine electric propulsion system, the article establishes a system equipment degradation model and utilizes fuzzy AHP and variable power theory for optimal selection of monitoring parameters and equipment health assessment. Then migration learning is applied to Bayesian network parameter learning to establish an early failure prediction model for marine electric propulsion system equipment. The simulation found that the system health results calculated by fuzzy AHP combined with variable weight theory are in good agreement with the standard health results under the gearbox angle, and its error with the standard health is only 3.95 percentage points. The early failure prediction results of the marine electric propulsion system equipment based on the migration learning-Bayesian network framework are more consistent with the actual failure frequency, and the overall failure prediction mean value is only 12.54s, which has a higher computational efficiency compared to the two comparison algorithms. It is feasible to apply migration learning and Bayesian network in the early fault identification of marine electric propulsion system, which can better guarantee the stable operation of marine electric propulsion system.
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