A deep learning-based turbofan engine multi-level predictive maintenance method

Abstract

The application discloses a kind of based on deep learning's turbofan engine multistage predictive maintenance method.Firstly, the sensor data and operation setting data of turbofan engine are collected, preprocessed to form data set and divided into training set and test set.Secondly, the training set is input into C-Transformer network, and the remaining life of the component is predicted, and the training set and the remaining life are labeled again using classification criteria, thereby forming a new training data set.Then, the new training data set is input into the convolutional neural network CNN to predict the failure probability of the component and calculate the system failure probability, and the trial-and-error method is used to obtain the system maintenance level.Finally, the optimization model is combined with the MDU-ABC-K algorithm, with the goal of minimizing the total comprehensive cost, and the optimal dynamic maintenance strategy is output.The application can provide technical support for the active operation and maintenance of aircraft engines, avoid unpredictable failures, reduce operating costs, reduce unexpected shutdowns and improve operation and maintenance efficiency.

Description

Technical Field

[0001] This invention belongs to the field of intelligent operation and maintenance technology for aero-engines, and in particular relates to a multi-level predictive maintenance method for turbofan engines based on deep learning. Background Technology

[0002] As one of the key components of aero engines, turbofan engines operate under extremely complex conditions, and any accident could lead to catastrophic consequences. Therefore, predictive maintenance of aero engines is necessary, which typically includes two key parts: remaining life prediction and decision-making. Traditional predictive maintenance is mostly implemented through model-driven methods. This method models the remaining life of turbofan engines, requires updating model parameters with measured data, and assumes that the component life follows a parametric process model, which cannot be effectively applied to industry. Currently, with the development of sensor technology and the accumulation of a large amount of engineering data, feature learning can be integrated into the model construction process through deep learning, reducing the defects caused by human feature design, thereby establishing a remaining life model, and on this basis, achieving the optimal solution of the decision model and outputting the optimal maintenance scheme. However, the following problems still exist: (1) Existing data-driven predictive maintenance methods all use fixed features to predict remaining life, which greatly reduces the generalization and accuracy of the network. (2) Due to the nonlinear changes in parameters, the complexity of the system increases rapidly, and the difficulty of decision-making also increases. However, most engineering projects consider single maintenance capabilities rather than multi-level maintenance, which increases the computational complexity of the decision-making process. (3) When selecting the optimal instantaneous maintenance strategy, most dynamic optimization models consider minimizing the specified maintenance resources under a specific threshold, which cannot balance maintenance resources. (4) Existing optimization algorithms used for model solving are prone to getting trapped in local optima, which limits the computation speed of model solving to the millisecond level. (5) Since the maintenance strategy depends on the failure probability and the current state of each component in the series and parallel system, it is unreasonable to not consider the multi-state maintenance of the turbofan engine. Summary of the Invention

[0003] The purpose of this invention is to address the problems existing in the prior art by providing a deep learning-based multi-level predictive maintenance method for turbofan engines, which provides technical support for proactive operation and maintenance of aero engines, avoids unpredictable failures, reduces operating costs, minimizes unexpected downtime, and improves operation and maintenance efficiency.

[0004] To achieve the above objectives, the present invention employs the following technical solution.

[0005] A deep learning-based multi-stage predictive maintenance method for turbofan engines includes the following steps:

[0006] Step 1: Collect sensor data and operating setting data of the turbofan engine;

[0007] Step 2: Preprocess the sensor data collected in Step 1 to form a dataset, and divide the dataset into a training set and a test set in an 8:2 ratio;

[0008] Step 3: Input the training set divided in Step 2 into the C-Transformer network, adaptively extract features from the dataset, and perform remaining lifetime prediction;

[0009] Step 4: A new training dataset is formed by combining the training set with the component remaining life predicted in Step 3 and relabeling it using classification criteria.

[0010] Step 5: Input the new training dataset obtained in Step 4 into the convolutional neural network (CNN) to predict the component failure probability;

[0011] Step 6: Based on the component failure probability obtained in Step 5, calculate the system failure probability, and use a trial-and-error method to determine the system maintenance level;

[0012] Step 7: Feed the test set divided in Step 2 into the C-Transformer and CNN networks trained in Steps 3-5, and based on the system maintenance level obtained in Step 6, combine the optimization model with the MDU-ABC-K algorithm. The objective function of the optimization model is the total comprehensive cost, and finally output the optimal dynamic maintenance strategy.

[0013] Further optimization, in step 1, the specific content and method of collecting the sensor data and operation setting data of the turbofan engine is to use C-MAPSS to perform engine degradation simulation, and simulate four different units under different operating conditions and fault mode combinations, which includes 21 sensor data and 3 operation setting data.

[0014] Further preferred, in step 2, the specific content and method of preprocessing the data collected in step 1 includes standardization, normalization, and removal of mutation points and null values ​​to form a dataset.

[0015] Further preferred, in step 3, the specific content and method of inputting the training set divided in step 2 into the C-Transformer network for adaptive feature extraction involves removing redundant features through two convolutional layers and adaptively extracting key information from the features. Based on different datasets, multiple different features are adaptively selected and fed into the network for remaining lifetime prediction.

[0016] Further optimization, in step 4, the classification criteria are:

[0017] Category 0: When the remaining lifetime is greater than or equal to the preset time window w,

[0018] Category 1: When the remaining lifetime is less than the preset time window w.

[0019] In a further preferred embodiment, in step 5, the convolutional neural network (CNN) consists of an input layer, a convolutional layer, a flattening layer, a fully connected layer, and a softmax activation function, and is used to predict the component failure probability in order to obtain the current state of the component and the system failure probability.

[0020] Further optimized, in step 6, the specific content and method for calculating the system failure probability based on the component failure probabilities obtained in step 5 are as follows: The failure probabilities of each subsystem composed of identical components are calculated using the probability union rule. The system performance is determined by the lowest performance of the subsystems, i.e., the system failure probability is determined by the highest failure probability of the subsystems. The system maintenance level is determined using a trial-and-error method. All data used in this method comes from a new training dataset.

[0021] Further optimization, in step 7, the specific content and method steps of the MDU-ABC-K algorithm are to combine the bee colony ABC algorithm with multidimensional update and k-nearest neighbor algorithm, and the final output result is the optimal maintenance strategy with the lowest total comprehensive cost, which consists of maintenance time and maintenance cost.

[0022] Advantages and beneficial effects of the present invention:

[0023] (1) This invention proposes a novel adaptive C-Transformer network that can adaptively extract features based on different datasets to effectively predict remaining lifetime, thereby improving the network's generalization and increasing classification accuracy by 4%-6%.

[0024] (2) This invention constructs a multi-level predictive maintenance decision model for a series-parallel multi-state system based on deep learning. By introducing multi-level maintenance, the computational complexity of the decision-making process is reduced by about 50%.

[0025] (3) By allocating appropriate weights for maintenance time and maintenance costs, and taking the minimum overall cost as the optimization objective, this invention can allocate maintenance resources more rationally and shorten decision-making time by 40%.

[0026] (4) This invention provides a new MDU-ABC-K optimization algorithm, which combines multidimensional update and k-nearest neighbor algorithm to better escape local optima, thereby improving the decision-making speed to within 10ms.

[0027] (5) The present invention constructs a predictive maintenance decision model that considers component status and component failure probability, which can not only overcome the shortcomings of existing maintenance that relies solely on intelligent algorithms, but also save the cost of verifying the correctness of the results. Attached Figure Description

[0028] Figure 1 This is a flowchart of a deep learning-based multi-stage predictive maintenance method for turbofan engines.

[0029] Figure 2 This is a network diagram for deep learning-based prediction of remaining lifetime and failure probability.

[0030] Figure 3 This is a flowchart of the trial-and-error method.

[0031] Figure 4 The figures show the prediction results, where (a) represents the prediction results for engine 21 in the test set, (b) represents the prediction results for engine 31 in the test set, (c) represents the prediction results for engine 34 in the test set, and (d) represents the prediction results for engine 81 in the test set.

[0032] Figure 5 This is a schematic diagram of an example turbofan engine system. Detailed Implementation

[0033] To better understand the above-mentioned objectives, features, and advantages of the present invention, the technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the present invention can be implemented in various forms and should not be limited to the embodiments described herein. Rather, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0034] like Figure 1 As shown, this invention provides a multi-stage predictive maintenance method for turbofan engines based on deep learning, comprising the following steps:

[0035] Step 1: Engine degradation simulation was performed using C-MAPSS to collect turbofan sensor data and operating setting data. Four different engine units were simulated under varying operating conditions and fault mode combinations, including data from 21 sensors and 3 operating settings. During the mission, C-MAPSS was used to collect sensor data and operating setting data for engine degradation simulation. Four different engine units were simulated under varying operating conditions and fault mode combinations, including data from 21 sensors and 3 operating settings. Historical data were all from before mission m. Figure 1 As shown, the data includes historical data and new runtime data during the execution of task m.

[0036] Step 2: Preprocess the data collected in Step 1, including standardization and normalization. The raw data will be uniformly scaled to a statistical probability distribution between 0 and 1, and abrupt changes and null values ​​will be removed, thus forming a dataset. This invention divides the dataset into training and test sets in an 8:2 ratio.

[0037] Step 3: The training set partitioned in Step 2 is fed into the C-Transformer network for training. The network can adaptively select multiple different features based on different datasets to predict the remaining life of turbofan engines, laying the foundation for the CNN prediction of component failure probability in Step 5. This invention proposes a novel adaptive C-Transformer to solve sequence-to-sequence tasks. It relies entirely on a self-attention mechanism, reducing training time and performance degradation caused by long-term dependencies. The structure of this adaptive C-Transformer network is as follows: Figure 2 As shown at the top, it includes a feature extraction layer, input layer, encoder block, decoder block, and output layer, specifically as follows: The C-Transformer mainly includes the following structure:

[0038] Feature Extraction Layer: The feature extraction layer consists of convolutional layers, fully connected layers, and a ReLU activation function. To streamline the feature extraction network, pooling layers are omitted, and only convolutional operations are used. The convolutional layers extract features from the input data using convolutional kernels. During data training, the convolutional kernels periodically scan the input features. Then, the ReLU activation function is applied to better fit the complex nonlinear feature data. Finally, the features are input into the fully connected layer for linear transformation, effectively obtaining the feature extraction results. After unifying the dimensionality, the features are input into the input layer for residual lifetime network training.

[0039] Input layer: Consists of an input embedding layer, an output embedding layer, and a positional encoding layer. The embedding layer maps the data to a dimension d according to the network computation task requirements. model A 3D vector. Since the Transformer does not contain recursion and convolution, this model adds positional encoding to represent the absolute or relative position of information in the sequence, allowing the network to utilize sequence information. Positional encoding uses sine and cosine functions, as shown in the following formula:

[0040]

[0041]

[0042] Where pos is the position and i is the dimension. Therefore, each dimension of the position encoding corresponds to a sine signal, and experiments have shown that this function allows the model to easily learn the pattern of position.

[0043] The encoder consists of N stacked encoder layers, each connected sequentially to two sub-layers, a multi-head attention mechanism, and a feedforward network. Residual jumpers are used between sub-layers, and layer normalization is employed to reduce the training difficulty of deep neural networks and accelerate model convergence. MHA addresses the limitation of self-attention mechanisms, which tend to overemphasize their own position when encoding current location information. It learns different query matrices (Q), key matrices (K), and value matrices (V) by using h different attention groups to perform different linear projections on the data. Then, the h groups of different Q, K, and V matrices are merged in parallel. Finally, the pooled outputs of the h groups are concatenated and transformed through another learnable linear projection to produce the final output. The calculation formula is shown below:

[0044] MH(Q,K,V)=Concat(head1,head2,…head h W O

[0045] where head i =Attention(QW i Q KW i K VW i V )

[0046] The learnable parameters include and Based on this design, each head can focus on different parts of the input data.

[0047] The decoder consists of N stacked decoder layers, each with three sequentially connected sub-layers: a masked multi-head attention layer, a multi-head attention mechanism, and a feedforward network. The masked multi-head attention layer comprises a padding mask and a sequence mask. Since the lengths of each batch of input sequences are not uniform, it is necessary to use a padding mask to align the input sequences. The purpose of the sequence mask is to mask (set to -∞) all values ​​so that when predicting the remaining lifetime at time t, the attention mechanism only depends on the output data prior to time t.

[0048] Output layer: After passing through N layers of encoders and decoders, the input features undergo a linear transformation and are activated by the sigmoid activation function to obtain the final output.

[0049] Step 4: To provide a new training dataset for the CNN to predict component failure probabilities in Step 5, the training set and the remaining lifespan predicted in Step 3 are relabeled using a classification criterion, thus forming a new training dataset. The classification criterion is:

[0050] Category 0: When the remaining lifetime is greater than or equal to the preset time window w.

[0051] Category 1: When the remaining lifetime is less than the preset time window w.

[0052] Assume the time window w equals the length of the next task. Therefore, if the remaining lifetime of a component is less than this time window, the component belongs to category 1, and the system will completely fail in the next task. Conversely, when the remaining lifetime of a component is greater than the time window, it belongs to category 0, and the system is considered to function normally in the next task. In this invention, the time window w is set to 30 cycles, meaning the task time is set to 30 cycles.

[0053] Step 5: Input the new training dataset obtained in Step 4 into the CNN network to predict the component failure probability, so as to obtain the current state of the component and the system failure probability.

[0054] CNN network structure as follows Figure 2 As shown at the bottom, it consists of an input layer, convolutional layers, flattening layers, fully connected layers, and a softmax activation function. In this work, the CNN has 6 layers to better learn features, where the convolutional kernels are two-dimensional tensors. The flattening layers are used to transform the data into one dimension, which is then used as the input to the fully connected layers. The fully connected layers integrate and compute the previously extracted features, serving as the final stage of the entire network. Softmax is an activation function for classification problems and can be expressed as:

[0055]

[0056] Among them, z i c and c represent the output values ​​of the i-th node and the numbered classification category, respectively. The output values ​​can be transformed into a probability distribution in the range of [0,1] using the softmax function to obtain the failure probability value of the turbofan engine.

[0057] Step 6: Based on the component failure probabilities obtained in Step 5, evaluate the engine's pre-state values. The state value evaluation criteria are shown in Table 1. The system consisting of a turbofan engine can be considered as a series-parallel system. According to the probability union rule, the formula for calculating the failure probability of a multi-component subsystem can be expressed as:

[0058]

[0059] Among them RUL n This represents the remaining lifespan of the nth component in the subsystem. The failure probabilities of multiple subsystems can be calculated. Since the system's performance is determined by the minimum performance of its subsystems (i.e., the system's failure probability is determined by the maximum failure probability of its subsystems), the system's failure probability is the maximum value among the subsystem failure probabilities.

[0060] Table 1

[0061]

[0062] To reduce computational complexity and maintenance costs during decision-making, a maintenance level considering incomplete maintenance is proposed based on a trial-and-error learning method according to the system failure probability. This invention addresses multi-level system failures by employing a five-level maintenance approach to formulate a system maintenance strategy. The maintenance level represents the maximum step size of the state transition before and after maintenance. The maximum step size is used to determine the maximum state that can be repaired in the current system state without wasting redundant maintenance resources. For example, Level 4 represents a maximum step size of 5 before and after maintenance, Level 3 represents a maximum step size of 4, and so on for Levels 1 and 2, with Level 0 meaning no maintenance. The trial-and-error testing process is as follows: Figure 3 As shown, the state of each component after repair is used as the criterion; the highest state cannot be greater than the optimal state plus 1, and the lowest state cannot be less than the intermediate state. Since the same system failure probability can result in multiple sets of different component failure probabilities, the above process can be repeated multiple times using the new training dataset obtained in step 4 to extract the system failure probability boundary for the maintenance level. The maintenance level evaluation criteria for various failure probabilities of the entire system are shown in Table 2.

[0063] Table 2

[0064]

[0065] Step 7: Feed the test set partitioned in Step 2 into the C-Transformer and CNN networks trained in Steps 3-5. Based on the system maintenance level obtained in Step 6, combine the optimization model with the new MDU-K-ABC algorithm. The objective function of the optimization model is the total comprehensive cost. This invention uses a novel bee colony algorithm, MDU-ABC-K, which enhances solution search and improves solution quality by utilizing multi-dimensional updates and k-neighborhood radii, respectively, thus facilitating escape from local optima and ultimately outputting the optimal dynamic maintenance strategy. The maintenance optimization model defined in this invention can be described by a nonlinear integer programming model, with the objective of minimizing the comprehensive cost, as shown in the following formula.

[0066] Minimize f(x) = k1C M (X)+k2T M (X)

[0067] X ij <Y ij <K,X ij Let i be an integer, i = 1, 2, ..., M; j = 1, 2, ..., N i

[0068] Where k1 and k2 represent the weights of maintenance costs and time consumption when calculating the overall cost (k1+k2=1), and the specific values ​​depend on the actual needs in industry. Based on the decision optimization model, this invention addresses the shortcomings of the original ABC algorithm, such as fast early convergence speed, easy getting trapped in local optima, loss of diversity and slow convergence speed in the later stages. It proposes a new MDU-ABC-K metaheuristic algorithm to output the optimal dynamic maintenance strategy.

[0069] In the proposed MDU-ABC-K algorithm, it is assumed that there are N nectar sources (X1, X2, ..., X...). N Each nectar source has D components. That is, the solution space of the problem to be optimized contains N feasible solutions (X...). i =x i1 x i2 , ..., x iD Each feasible solution is a d-dimensional vector. The proposed MDU-ABC-K algorithm consists of the following four stages:

[0070] Population initialization phase: For any solution x id (d = 1, 2, 3, ..., D), each component will be initialized, which can be represented as:

[0071] x id =x idmin +rand(0,1)·(x idmax -x idmin )

[0072] Where, x idmax and x idmin represents the upper and lower bounds of the d-dimensional components of the feasible solution space, respectively, and rand(0,1) represents a random number between 0 and 1.

[0073] Hired Bee Phase: In this phase, the convergence time of the original strategy of updating the solution by dimension increases with the increasing dimension of the function, affecting the accuracy of the final solution. To solve this problem, the update method of this invention updates all dimensions simultaneously, which can be expressed as:

[0074]

[0075] Where j∈{1,2,...,N}, j≠i represents the selected nectar source and x i different.

[0076] Observer bee phase: After all hired bees have completed their search, information about the solution and its suitability is shared with the observer bees. The observer bees select the solution based on probability P. i The probability of each observer bee being tracked can be expressed as:

[0077]

[0078] Among them, fit k This is the fitness function value of the k-th solution. Observer bees use a roulette wheel rule to select which hired bees to follow. The higher the selection probability of a hired bee for a nectar source, the more observer bees will follow it. In other words, nectar sources with higher fitness values ​​have a wider neighborhood search range for the corresponding solution.

[0079] Scout bee phase: In this phase, after all the observer bees have completed their follow-up search, if a nectar source has not been updated after being searched and repeatedly mined a certain number of times, it is considered that the nectar source has been exhausted, and the corresponding solution is trapped in a local optimum. The corresponding foraging bees and observer bees will abandon the nectar source and switch to scout bee mode, performing a global random search to find a new nectar source to replace the abandoned one. The original formula is as follows:

[0080] x id =low d +rand(0,1)·(up d -low d )

[0081] Where, d∈{1,2,...,D},[low d up d [] represents the boundary value.

[0082] To more effectively escape local optima, this invention proposes a novel and efficient method for scout bees to find new nectar sources based on the concept of k-neighborhood. When X is abandoned... i When U1 and U2 are generated, then X i It will be replaced by the optimal solution between U1 and U2. U1 is obtained from the original formula mentioned above, and U2 is X. i The best solution X in the k-neighborhood ib The optimal value is given by the following formula:

[0083] u id =x ibd +rand(0,1)·(x r1d -x r2d )

[0084] Where r1≠i2≠ib indicates that the selected nectar source is different from x. ib .

[0085] The results were validated using the FD001 test set, and the remaining lifetime experimental results are as follows: Figure 4 As shown, Figure 4Figure (a) shows the prediction results for engine 21 in the test set, Figure (b) shows the prediction results for engine 31 in the test set, Figure (c) shows the prediction results for engine 34 in the test set, and Figure (d) shows the prediction results for engine 81 in the test set. The results indicate that the method has good accuracy and generalization ability. Figure 5 As shown, an application scenario of the deep learning-based multi-stage predictive maintenance decision-making method for turbofan engines provided in this embodiment of the invention is further illustrated:

[0086] exist Figure 5 In this study, a system consisting of three subsystems connected in series was considered, where each component in the subsystems is a turbofan engine. The failure probabilities of each turbofan engine were predicted using C-Transformer and CNN, as shown in Table 3.

[0087] Table 3

[0088]

[0089] The states of each turbofan engine can be obtained from Table 1, and can be represented as follows:

[0090] or x = [3 2 2 1 3 4 2 2]

[0091] According to the formula in step 6, the failure probabilities of each subsystem are 0.8962, 0.8330, and 0.8442, respectively. The overall system failure probability is 0.8962. According to Table 2, the maintenance level of this system is level 3. Based on the current state and maintenance level combined with the decision optimization model, this invention uses the MDU-ABC-K algorithm to solve the model and obtain the optimal dynamic maintenance strategy, as shown in Table 4 below.

[0092] Table 4

[0093]

[0094] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the above figures and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the present invention.

Claims

1. A multi-stage predictive maintenance method for turbofan engines based on deep learning, characterized in that, Includes the following steps: Step 1: Collect sensor data and operating setting data of the turbofan engine; Step 2: Preprocess the sensor data collected in Step 1 to form a dataset, and divide the dataset into a training set and a test set in an 8:2 ratio; Step 3: Input the training set divided in Step 2 into the C-Transformer network, adaptively extract features from the dataset, and perform remaining lifetime prediction; Step 4: A new training dataset is formed by combining the training set with the component remaining life predicted in Step 3 and relabeling it using classification criteria. Step 5: Input the new training dataset obtained in Step 4 into the convolutional neural network (CNN) to predict the component failure probability; Step 6: Based on the component failure probability obtained in Step 5, calculate the system failure probability, and use a trial-and-error method to determine the system maintenance level; Step 7: Feed the test set divided in Step 2 into the C-Transformer and CNN networks trained in Steps 3-5, and based on the system maintenance level obtained in Step 6, combine the optimization model with the MDU-ABC-K algorithm. The objective function of the optimization model is the total comprehensive cost, and the final output is the optimal dynamic maintenance strategy. The specific content and method steps of the MDU-ABC-K algorithm are to combine the bee colony ABC algorithm with multidimensional update and k-nearest neighbor algorithm, and the final output result is the optimal maintenance strategy with the lowest total comprehensive cost, which consists of maintenance time and maintenance cost.

2. The deep learning-based multi-stage predictive maintenance method for turbofan engines as described in claim 1, characterized in that, In step 1, the specific content and method of collecting sensor data and operation setting data of the turbofan engine is to use C-MAPSS to perform engine degradation simulation, and simulate four different units under different operating conditions and fault mode combinations, which includes 21 sensor data and 3 operation setting data.

3. The deep learning-based multi-stage predictive maintenance method for turbofan engines as described in claim 1, characterized in that, In step 2, the specific content and methods for preprocessing the data collected in step 1 include standardization, normalization, and removal of mutation points and null values ​​to form a dataset.

4. The deep learning-based multi-stage predictive maintenance method for turbofan engines as described in claim 1, characterized in that, In step 3, the specific content and method of inputting the training set divided in step 2 into the C-Transformer network for adaptive feature extraction are described. Redundant features are removed through two layers of convolution and key information in the features is extracted adaptively. Multiple different features are adaptively selected according to different datasets and fed into the network for remaining lifetime prediction.

5. The deep learning-based multi-stage predictive maintenance method for turbofan engines as described in claim 1, characterized in that, In step 4, the classification criteria are: Category 0: When the remaining lifetime is greater than or equal to the preset time window w, Category 1: When the remaining lifetime is less than the preset time window w.

6. The deep learning-based multi-stage predictive maintenance method for turbofan engines as described in claim 1, characterized in that, In step 5, the convolutional neural network (CNN) consists of an input layer, a convolutional layer, a flattening layer, a fully connected layer, and a softmax activation function, and is used to predict the component failure probability in order to obtain the current state of the component and the system failure probability.

7. The deep learning-based multi-stage predictive maintenance method for turbofan engines as described in claim 1, characterized in that, In step 6, the specific content and method steps for calculating the system failure probability based on the component failure probability obtained in step 5 are as follows: the failure probability of each subsystem composed of the same component is calculated using the probability union rule. The system performance is determined by the lowest performance of the subsystem, that is, the system failure probability is determined by the highest failure probability of the subsystem. The system maintenance level is obtained by using a trial-and-error method. All data used in this method comes from a new training dataset.

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