CN114077867A - Aircraft engine fault diagnosis method based on migratable neural network - Google Patents

Aircraft engine fault diagnosis method based on migratable neural network Download PDF

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CN114077867A
CN114077867A CN202111282685.XA CN202111282685A CN114077867A CN 114077867 A CN114077867 A CN 114077867A CN 202111282685 A CN202111282685 A CN 202111282685A CN 114077867 A CN114077867 A CN 114077867A
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赵永平
李兵
陈耀斌
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention provides an aircraft engine fault diagnosis method based on a migratable neural network. The method utilizes the basic idea of migration learning to overcome the problem of the over-idealization assumption that training data and test data sets obey the same distribution in the traditional data-driven aeroengine gas circuit fault diagnosis method, and provides two fault diagnosis algorithms UD-RVFL and UJD-RVFL by combining a domain self-adaption idea and an RVFL algorithm, so that on the premise of keeping the main advantage of simple topology of an original RVFL network, the method can reduce the distribution difference between source domain data and target domain data by learning the characteristic representation of the migratable data, and simultaneously keep the data attribute and the characteristic structure of the source domain as much as possible. The invention adopts the transfer learning strategy, so that the edge distribution and condition distribution difference existing between the data sets can be reduced, and the fault diagnosis precision is improved.

Description

Aircraft engine fault diagnosis method based on migratable neural network
Technical Field
The invention belongs to the field of aircraft engine fault diagnosis, and particularly relates to an aircraft engine fault diagnosis method based on a migratable neural network.
Background
The fault diagnosis system of the aircraft engine is one of effective components of an engine health management system, and is always a focus of attention in the industry and academia, and the fault occurrence probability of an engine gas path component can account for more than 90% of the total fault of the engine, so that the establishment of an effective method for fault diagnosis of the gas path component is very important. Currently, the available methods for engine fault diagnosis focus primarily on model-based methods and data-driven methods. The method based on the model is mainly used for establishing an engine mathematical model according to the real engine running condition to judge the engine health condition, researchers are required to be familiar with the working principle of the engine, the difficulty of establishing an accurate model is continuously improved along with continuous innovation and improvement of the engine, the uncertainty existing in the model and the nonlinear complexity of a system are higher and higher, the judgment accuracy of the method can be influenced, and in addition, the method is required to establish different mathematical models for engines of different models. The data-driven method can detect and isolate the fault of the target according to the real-time data and the historical collected data of the engine sensor, can overcome the difficulty existing in the method, can finish the fault diagnosis task of the engines of different models as long as an effective machine learning algorithm is selected and improved, and adopts the data-driven method to solve the problem existing in the fault diagnosis of the gas circuit of the engine.
However, most studies mainly employ traditional machine learning theory to solve the fault diagnosis problem, which may be impractical in practical application scenarios. In general, these diagnostic methods based on traditional machine learning (including popular deep learning) tend to assume that the training data set and the test data set follow the same data distribution, and this assumption is too idealized in practical applications. In addition, for those diagnostic algorithms that require a large amount of data, the enormous labor and time costs associated with labeling the data are often prohibitive. Thus, while these algorithms may have achieved satisfactory diagnostic accuracy, the potentially idealized assumptions are likely to make them stay only in a well-designed experimental environment, rather than landing on a real engineering application scenario.
To overcome the above challenges, intelligent fault diagnosis based on transfer learning is expected to be one of the most promising solutions. Currently, the migration learning method is adopted by many researchers in various fields, and the research thereof focuses on how to adjust a machine learning model constructed in a Source domain (Source domain) and apply the machine learning model to a Target domain (Target domain) which is different from but related to an initial Source domain. Typically, the data set of labeled information used for training is referred to as the source data set, while the data of the target domain is used for testing. Therefore, the invention develops a technical means for diagnosing the gas circuit fault of the aero-engine based on the transfer learning. By combining the domain self-adaption thought and the RVFL algorithm, two algorithms of UD-RVFL and UJD-RVFL are provided, so that on the premise of keeping the main advantage of simple topology of the original RVFL network, distribution difference between source domain data and target domain data can be reduced by learning migratable data characteristic representation, and simultaneously, data attribute and characteristic structure of the source domain can be kept as much as possible. Of these, the UD-RVFL algorithm deals primarily with cases where only edge distribution differences are considered, while the UJD-RVFL algorithm uses reconstructed source domain data to train classifiers that iteratively learn pseudo-label information for data in the target domain in an attempt to reduce both edge distribution and conditional distribution differences.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defect that a training data set and a test data set are always assumed to obey the same data distribution based on a traditional machine learning diagnosis method, the invention provides a migratable neural network-based aeroengine fault diagnosis method.
The invention relates to an aeroengine fault diagnosis method based on a migratable neural network, which specifically comprises the following steps:
step 1, acquiring aeroengine operation data serving as sample data including normal data samples and fault data samples, and establishing an original RVFL mathematical model;
the objective function is:
Figure BDA0003331784390000021
wherein
Figure BDA0003331784390000022
Is a sample of engine operating data, N is the total number of samples, and d is the number of features. For the ith example, xiIs a d-dimensional feature vector.
Figure BDA0003331784390000023
In order to output the weight, the weight is output,
Figure BDA0003331784390000024
row j of β. w is ajAnd bjFor randomly set weights and biases input to the enhancement layer. T ═ Ti,…tN]TIs the label set of the sample, if xiBelongs to class j, then tijIs 1, the rest is 0. h isj() is the activation function of the jth enhancement node,
for xiIt is defined as:
Figure BDA0003331784390000025
equation (1) can be further expressed in matrix form, with the objective function written as:
Figure BDA0003331784390000026
wherein the matrix
Figure BDA0003331784390000031
Is defined as shown in the following formula
Figure BDA0003331784390000032
The optimal output of the RVFL is then
Figure BDA0003331784390000033
Wherein the content of the first and second substances,
Figure BDA0003331784390000034
a generalized inverse matrix of H.
Step 2, adding a regular term into the original RVFL mathematical model to reduce the overfitting risk, simplify the complexity of the model and optimize the objective function;
Figure BDA0003331784390000035
wherein
Figure BDA0003331784390000036
Is an error vector, C is a predefined balance factor, and further has h (x)i)＝[h(w1,xi,b1),…,h(wL,xi,bL),xi]。
Step 3, solving the mathematical model to obtain an output weight;
and 4, calculating reconstructed data representation according to the obtained output weight, and performing a fault diagnosis task according to the reconstructed data representation.
Further, step 2 further includes using a strategy for reducing edge distribution in the transfer learning, and integrating the engine data information to obtain a mathematical model of the UD-RVFL, and reconstructing equation (6), where the objective function can be written as:
Figure BDA0003331784390000037
wherein
Figure BDA0003331784390000038
Is the reconstruction error of the ith sample in the source domain, the sample labeled t represents the sample in the target domain. Phi (-) consists of the connection weights of the network, including randomly initialized and optimized.
Figure BDA0003331784390000039
For the output weights, λ and C are predefined balance factors;
through simplified calculations, equation (9) can be changed to:
Figure BDA0003331784390000041
wherein
Figure BDA0003331784390000042
Is a diagonal balance matrix, and the matrix
Figure BDA0003331784390000043
Is defined as follows
Figure BDA0003331784390000044
Wherein HsAnd HtThe definition of (A) is shown in formula (4). In addition to this, the present invention is,
Figure BDA0003331784390000045
is a MMD matrix, which is calculated as shown below
Figure BDA0003331784390000046
For ease of calculation, the two matrices are expanded into suitable dimensions. Suppose that
Figure BDA0003331784390000047
Is composed of
Figure BDA0003331784390000048
And is
Figure BDA0003331784390000049
Wherein
Figure BDA00033317843900000410
All 0 vectors with appropriate dimensions. Therefore, the UD-RVFL algorithm objective function in equation (10) can be further simplified to
Figure BDA00033317843900000411
Step 3, solving the mathematical model to obtain an output weight, specifically:
taking the derivative of the model in equation (14) with respect to β and setting it to zero, one can obtain
β+HTΩHβ-HTΩX+CHTΜHβ＝0. (13)
Then, when (L + d) ≦ (n)s+nt) When true, the solution of equation (15) is
β＝(I+HT(Ω+CΜ)H)-1HTΩX, (14)
Otherwise, the solution can be represented as
β＝HT(I+(Ω+CΜ)HHT)-1ΩX. (15)
Step 4, calculating reconstructed data representation according to the obtained output weight;
for data in the source domain, migratable data representation can be calculated as
X's＝Hsβ, (16)
And the reconstructed feature representation of the target domain data may be calculated by
X't＝Htβ. (17)
From there, the reconstructed target data may be identified by a classifier trained by the reconstructed source marker data.
Further, step 2 includes using the strategy of simultaneously reducing the edge distribution and the condition distribution in the transfer learning, and integrating the engine data information to obtain UJD-RVFL mathematical model, reconstructing equation (6), where the objective function can be shown as:
Figure BDA0003331784390000051
wherein
Figure BDA0003331784390000052
Represents a data set having a kth genuine label category in the source domain, and
Figure BDA0003331784390000053
it represents a data set in the target domain with the kth pseudo tag class. For some simplification, the mathematical model of the above formula for the UJD-RVFL algorithm can be restated in the form
Figure BDA0003331784390000054
Wherein the content of the first and second substances,
Figure BDA0003331784390000055
is a MMD matrix, which is calculated as shown below
Figure BDA0003331784390000061
Furthermore, M0And M, which is defined as shown in formula (12).
Step 3, solving the mathematical model to obtain an output weight, specifically:
the derivative of the model in equation (21) with respect to β is taken and set to zero. When the condition (L + d) is less than or equal to (n)s+nt) When it is established, it can be obtained
Figure BDA0003331784390000062
Otherwise, then there is
Figure BDA0003331784390000063
UJD-RVFL reconstructed data indicates that it cannot be directly acquired and only the edge distribution is aligned during initialization. Then, both margin distribution and condition distribution are considered in an iterative process, and at the same time, the pseudo tag information in the target domain is updated until a termination condition is reached.
Step 4, calculating reconstructed data representation according to the obtained output weight;
for data in the source domain, migratable data representation can be calculated as
X's＝Hsβ, (23)
And the reconstructed feature representation of the target domain data may be calculated by
X't＝Htβ. (24)
From there, the reconstructed target data may be identified by a classifier trained by the reconstructed source marker data.
Further, the aircraft engine fault refers to a low-pressure compressor LPC fault, a high-pressure compressor HPC fault, a high-pressure turbine HPT fault and a low-pressure turbine LPT fault in the engine.
Further, the control variable, the environment variable and the performance degradation amount are adjusted, so that the sample data have different distributions.
In the fault diagnosis of the aircraft engine, firstly, normalizing a data sample, and then taking the sample data and a corresponding sample label as training sample training diagnosis models; and carrying out fault detection on each part of the aircraft engine by using the model obtained by training.
Has the advantages that: by combining the domain self-adaption thought and the RVFL algorithm, the migratable data characteristic representation is learned, the distribution difference between the source domain data and the target domain data is reduced, and the fault diagnosis precision is improved.
Drawings
FIG. 1 is a block diagram of the major components of an aircraft engine.
Fig. 2 is a comparison of the results of the experiment in six groups of cases before the mixed migration experiment.
Fig. 3 is a graph comparing the results of the experiment in six groups of cases after the mixed migration experiment.
Fig. 4 is a graph comparing the results of the experiment for the first six groups of cases of the complete migration experiment.
Fig. 5 is a graph comparing the results of the experiment for six groups of cases after the complete migration experiment.
Detailed Description
In the case of multi-fault diagnosis of the aeroengine, firstly, an objective function of an original RVFL model is established according to all collected engine operation data (including normal data sample information and fault data sample information)
Figure BDA0003331784390000071
Wherein
Figure BDA0003331784390000072
Is a sample, N is the total number of samples, d is the number of features. For the ith example, xiIs a d-dimensional feature vector.
Figure BDA0003331784390000073
In order to output the weight, the weight is output,
Figure BDA0003331784390000074
row j of β. w is ajAnd bjFor randomly set weights and biases input to the enhancement layer. T ═ Ti,…tN]TIs the label set of the sample, if xiBelongs to class j, then tijIs 1, the rest is 0. h isj(. h) activation function for jth enhancement node, for xiIt is defined as:
Figure BDA0003331784390000075
further, equation (1) can be further expressed in a matrix form with an objective function of:
Figure BDA0003331784390000076
wherein the matrix
Figure BDA0003331784390000077
Is defined as shown in the following formula
Figure BDA0003331784390000081
The optimal output of the RVFL is then
Figure BDA0003331784390000082
Wherein the content of the first and second substances,
Figure BDA0003331784390000083
a generalized inverse matrix of H. Generally speaking, a regularization term is added to the RVFL to mitigate the risk of overfitting and simplify the model complexity, and the objective function can be rewritten as follows
Figure BDA0003331784390000084
Wherein
Figure BDA0003331784390000085
Is an error vector, C is a predefined balance factor, and further has h (x)i)＝[h(w1,xi,b1),…,h(wL,xi,bL),xi]. The solution of equation (6) can be expressed as follows from the KKT condition
Figure BDA0003331784390000086
Where I is the identity matrix of the corresponding dimension, and for an unknown test sample x, its prediction label can be expressed as
g(x)＝argmax{h(x)β} (8)
Subsequently, equation (6) is reconstructed, which yields:
Figure BDA0003331784390000087
wherein
Figure BDA0003331784390000088
Is the reconstruction error of the ith sample in the source domain (the set where the training samples are located), and the sample labeled t represents the sample in the target domain (the test data set). Phi (-) consists of the connection weights of the network, including randomly initialized and optimized.
Figure BDA0003331784390000091
For the output weights, λ and C are predefined balance factors. To preserve the inter-class relationship of the source domain, the first constraint in equation (9) is set to force the output of the source domain to approximate the input.
With some simplified calculations, equation (9) can be changed to:
Figure BDA0003331784390000092
wherein
Figure BDA0003331784390000093
Is a diagonal balance matrix, and the matrix
Figure BDA0003331784390000094
Is defined as follows
Figure BDA0003331784390000095
Wherein HsAnd HtThe definition of (A) is shown in formula (4). In addition to this, the present invention is,
Figure BDA0003331784390000096
is a MMD matrix, which is calculated as shown below
Figure BDA0003331784390000097
For ease of calculation, the two matrices are expanded into suitable dimensions. Suppose that
Figure BDA0003331784390000098
Is composed of
Figure BDA0003331784390000099
And is
Figure BDA00033317843900000910
Wherein
Figure BDA00033317843900000911
All 0 vectors with appropriate dimensions. Therefore, the UD-RVFL algorithm objective function in equation (10) can be further simplified to
Figure BDA0003331784390000101
Taking the derivative of the model in equation (14) with respect to β and setting it to zero, one can obtain
β+HTΩHβ-HTΩX+CHTΜHβ＝0. (15)
Then, when (L + d) ≦ (n)s+nt) When true, the solution of equation (15) is
β＝(I+HT(Ω+CΜ)H)-1HTΩX, (16)
Otherwise, the solution can be represented as
β＝HT(I+(Ω+CΜ)HHT)-1ΩX. (17)
Using the solution of the resulting equation, a reconstructed feature representation can be calculated. For data in the source domain, migratable data representation can be calculated as
X's＝Hsβ, (18)
And the reconstructed feature representation of the target domain data may be calculated by
X't＝Htβ. (19)
From there, the reconstructed target data may be identified by a classifier trained by the reconstructed source marker data.
As for the mathematical model of the UJD-RVFL algorithm, equation (6) is reconstructed and can be found:
Figure BDA0003331784390000102
wherein
Figure BDA0003331784390000103
Represents a data set having a kth genuine label category in the source domain, and
Figure BDA0003331784390000111
it represents a data set in the target domain with the kth pseudo tag class. For some simplification, the mathematical model of the above formula for the UJD-RVFL algorithm can be restated in the form
Figure BDA0003331784390000112
Wherein the content of the first and second substances,
Figure BDA0003331784390000113
is a MMD matrix, which is calculated as shown below
Figure BDA0003331784390000114
Furthermore, M0And M, which is defined as shown in formula (12).
The derivative of the model in equation (21) with respect to β is taken and set to zero. When the condition (L + d) is less than or equal to (n)s+nt) When it is established, it can be obtained
Figure BDA0003331784390000115
Otherwise, then there is
Figure BDA0003331784390000116
Unlike UD-RVFL, the reconstructed data representation of UJD-RVFL cannot be directly obtained because the pseudo tag information of the target data is predicted in an iterative manner. Specifically, only the edge distributions are aligned during the initialization phase. Then, both the margin distribution and the conditional distribution are considered in an iterative process. At the same time, the pseudo tag information in the target domain is updated until a termination condition is reached.
Using the solution of the resulting equation, a reconstructed feature representation can be calculated. For data in the source domain, migratable data representation can be calculated as
X's＝Hsβ, (25)
And the reconstructed feature representation of the target domain data may be calculated by
X't＝Htβ. (26)
From there, the reconstructed target data may be identified by a classifier trained by the reconstructed source marker data.
The implementation of the UD-RVFL and UJD-RVFL algorithms is given below, respectively:
Figure BDA0003331784390000121
Figure BDA0003331784390000122
Figure BDA0003331784390000131
the performance of the algorithm is evaluated through a multi-classification algorithm, the evaluation index of the classification algorithm is precision, and the definition of the precision is as follows:
Figure BDA0003331784390000132
where y (x) is the true label information of sample x, and f (x) is the predicted label information of sample x, and the value 1 is the best value to be taken.
All experiments were performed on a desktop computer configured as an intel r core, i7-9750 CPU, 2.60GHz dominant frequency, 8G memory, Windows10 system, and MATLAB2018a version. Notably, since the training set and the test set come from different distributions, the cross-validation technique cannot be used directly to find the best parameter combination. Therefore, we directly use the method of grid search to repeat the experiment 20 times for each parameter combination and give the best average result as the final performance comparison, which is also the most common strategy in the migration learning. To fully verify the practical performance of the algorithms proposed in this chapter, the fault diagnosis results of the two proposed methods are compared here with other widely used methods, mainly including RVFL, CORAL, TCA, GFK and ETL. For CORAL algorithm, no parameters needing to be adjusted exist in the migration learning stage, and a common ELM algorithm is selected as a reference classifier of the CORAL algorithm. For the TCA algorithm, dimension parameters are searched from a candidate set {6,7,8,9,10}, MMD is calculated by using RBF kernel function, and λ and γ are selected from a set {2 }-5，2-4，…，24，25And {2 }-5，2-5，…，24，25It searches and then uses the ELM as its reference classifier as well. For the GRK algorithm, parameters of geodesic flow kernels are searched from the candidate set {1,2,3,4,5 }. For the ETL algorithm, the cosine is adoptedDistance and use ELM as its reference classifier. For the UD-RVFL and UJD-RVFL algorithms, from the alternative set {10 }-4，10-3，…，103，104And {2 }-4，2-3，…，23，24The balance parameters C and λ are searched, and the number of hidden layer nodes is searched from {50,100, …,350,400}, and finally RVFL is also used as its reference classifier.
The present invention uses a dual rotor turbofan engine for testing, as shown in fig. 1, the main components of the engine include an air intake duct, a Low Pressure Compressor (LPC for short), a High Pressure Compressor (HPC for short), a combustor, a High Pressure Turbine (HPT for short), a Low Pressure Turbine (LPT) and a tail nozzle. The air flow flows into the air compressor through the air inlet channel, and the air is high-pressure air after passing through the low-pressure air compressor and the high-pressure air compressor. In the combustion chamber, fuel oil is injected and mixed with high-pressure gas to form mixed gas, and when the mixed gas flows through the high-pressure turbine and the low-pressure turbine, the mixed gas is driven by the high-pressure compressor and the low-pressure compressor which are respectively connected through the high-pressure shaft and the low-pressure shaft. The hot gases are eventually expelled into the atmosphere at high velocity.
The LPC, HPC, HPT and LPT associated with the aircraft engine rotor are prone to failure at high rotational speeds and therefore only failure of these four components is considered. Simulation data for the full flight envelope were collected prior to the experiment and details of the four data sets are listed in table 1. For each data set, they contain an equal number of health conditions, with each health condition having the same number of data samples.
TABLE 1 detailed information of engine data sets collected under different operating conditions
Figure BDA0003331784390000141
As regards the environmental variables of the individual data sets, several typical operating points within the flight range of the engine are selected here to characterize the simulation tests under different operating conditions. Specifically, the operating points for the respective data sets are listed in table 2. It can be seen that data sets a and B share the same operating point. As for the control variables, the data acquisition trials of the different data sets are performed in a dynamic manner that is different from each other.
TABLE 2 environmental variable Specifications to which different data sets relate
Figure BDA0003331784390000151
The invention firstly designs a mixed test scheme, and each data set is divided into a training set and a testing set equally and randomly. Taking data set A as an example, the training set is denoted as A herein0The test set is denoted A1. For conventional fault diagnosis, the learning task is typically A0→A1. In fault diagnosis based on transfer learning, the learning task mainly comprises A0→B1、A0→C1And A0→D1And the like. Notably, since the training set and the test set come from different distributions, the cross-validation technique cannot be used directly to find the best parameter combination. Therefore, we directly use the method of grid search to repeat the experiment 20 times for each parameter combination and give the best average result as the final performance comparison, which is also the most common strategy in the migration learning.
Now referring to the test results listed in table 3, it can be seen that there are 16 mixed validation test combinations, wherein the results shown in bold represent the results of the conventional troubleshooting test tests with the best performance, while the rest are the troubleshooting test results performed in a migration learning manner.
TABLE 3 RVFL algorithm based test results
Figure BDA0003331784390000152
It can be clearly seen that the diagnosis results are higher for the conventional mode (bold marks) than for the migrated mode (diagonal marks). Taking data set C as an example, C0→C1The diagnostic performance of the task was 97.28%, while C0In A1、B1And D1The diagnostic performance of (a) was 78.91%, 80.86% and 81.83%, respectively. The performance degradation is evident due to the distribution difference. In addition, the experimental results of the other three data sets also show similar phenomena. Notably, the performance degradation of data C in the migration experiment was significantly higher than that of the other data sets, which may be due to the large difference in the distribution of C from the other data sets. Thus, the performance degradation indicates that it is necessary to employ a domain adaptation strategy to match the distribution differences.
Extensive experimental validation was then performed according to each comparison algorithm, and the detailed results of the domain adaptation experiments are shown in table 4, and the overall comparison results for 12 diagnosis cases are plotted in fig. 2 and 3. As a basic classifier, the average diagnostic performance of RVFL was 86.97%. Unfortunately, both TCA and GFK exhibit significant negative migratory effects because they are less diagnostic than RVFL. The negative migration phenomenon is common in migration learning and needs to be avoided. Then, ETL and CORAL performed better than RVFL. For the proposed UD-RVFL, the average diagnostic performance of 12 cases was 88.53% better than the original RVFL. The proposed UJD-RVFL is slightly better than UD-RVFL, but the advantages are not particularly great. This may be due to the small total number of tags in the dataset. In general, the diagnostic results of the two proposed methods are significantly better than other comparative algorithms, demonstrating the feasibility of the proposed domain adaptation method, in particular the one-sided alignment strategy employed. With this strategy, the inter-class relationships of the source domain are maintained. With respect to time complexity, TCA has the highest computation time. UJD-RVFL is significantly more computationally expensive than UD-RVFL because the former method introduces an iterative process. The time complexity of the remaining methods remains substantially at a similar level.
TABLE 4 diagnostic Performance (%)
Figure BDA0003331784390000161
Subsequently, the proposed method is further validated using the collected complete data set. Similarly, there were 12 cases, and the results of diagnosis thereof are shown in Table 5. The overall performance comparison is then depicted in fig. 4 and 5. In general, the overall results were similar to those of the mixed migration experiment. In particular, RVFL, as a basic classifier, exhibits similar classification accuracy as before. TCA and GFK still exhibited significant negative transfer effects. For ETL and CORAL, their performance is better than the basic classifier, but not as good as our proposed method. The proposed UJD-RVFL is slightly superior to UD-RVFL and still achieves the best average diagnostic performance in 12 transfer experiments. As for the calculation cost, the calculation time of all algorithms increases as the number of training data sets increases. Notably, the computation time of TCA increases non-linearly with the spread of training samples.
TABLE 5 diagnostic performance (%) -of all comparative methods under complete data set conditions
Figure BDA0003331784390000171

Claims (6)

1. An aircraft engine fault diagnosis method based on a migratable neural network is characterized by specifically comprising the following steps:
step 1, acquiring aeroengine operation data serving as sample data including normal data samples and fault data samples, and establishing an original RVFL mathematical model;
step 2, adding a regular term into the original RVFL mathematical model to optimize a target function;
step 3, solving the mathematical model to obtain an output weight;
and 4, calculating reconstructed data representation according to the obtained output weight, and performing a fault diagnosis task according to the reconstructed data representation.
2. The aircraft engine fault diagnosis method based on the migratable neural network of claim 1, wherein the objective function of the mathematical model of the original RVFL in step 1 is:
Figure FDA0003331784380000011
wherein
Figure FDA0003331784380000012
The method comprises the steps of (1) obtaining engine operation data samples, wherein N is the total number of the samples, and d is a characteristic number; for the ith example, xiIs a d-dimensional feature vector;
Figure FDA0003331784380000013
in order to output the weight, the weight is output,
Figure FDA0003331784380000014
row j, β; w is ajAnd bjWeights and biases for inputs to the enhancement layer that are randomly set; t ═ Ti,…tN]TIs the label set of the sample, if xiBelongs to class j, then tijIs 1, the rest is 0; h isj() is the activation function of the jth enhancement node,
for xiIt is defined as:
Figure FDA0003331784380000015
equation (1) can be further expressed in matrix form, with the objective function written as:
Figure FDA0003331784380000016
wherein the matrix
Figure FDA0003331784380000017
Is defined as shown in the following formula
Figure FDA0003331784380000018
The optimal output of the RVFL is then
Figure FDA0003331784380000021
Wherein the content of the first and second substances,
Figure FDA0003331784380000022
a generalized inverse matrix of H;
step 2, adding a regular term to the mathematical model of the original RVFL to mitigate the risk of overfitting and simplify the model complexity, the objective function can be optimized as follows
Figure FDA0003331784380000023
Wherein
Figure FDA0003331784380000024
Is an error vector, C is a predefined balance factor, and further has h (x)i)＝[h(w1,xi,b1),…,h(wL,xi,bL),xi]。
3. The aircraft engine fault diagnosis method based on the migratable neural network as claimed in claim 2, wherein the step 2 further comprises using a strategy of reducing edge distribution in the migration learning and integrating the engine data information to obtain a mathematical model of the UD-RVFL, reconstructing formula (6), and the objective function can be written as:
Figure FDA0003331784380000025
wherein
Figure FDA0003331784380000026
Is the reconstruction error of the ith sample in the source domain, and the sample marked with t represents the sample in the target domain; phi (-) consists of the connection weights of the network, including randomly initialized and optimized;
Figure FDA0003331784380000027
for the output weights, λ and C are predefined balance factors;
through simplified calculations, equation (9) can be changed to:
Figure FDA0003331784380000028
wherein
Figure FDA0003331784380000029
Is a diagonal balance matrix, and the matrix
Figure FDA00033317843800000210
Is defined as follows
Figure FDA00033317843800000211
Wherein HsAnd HtThe definition of (A) is given by formula (4); in addition to this, the present invention is,
Figure FDA0003331784380000031
is a MMD matrix, which is calculated as shown below
Figure FDA0003331784380000032
For the convenience of calculation, the two matrixes are expanded into appropriate dimensions; suppose that
Figure FDA0003331784380000033
Is composed of
Figure FDA0003331784380000034
And is
Figure FDA0003331784380000035
Wherein
Figure FDA0003331784380000036
All 0 vectors with appropriate dimensions; therefore, the UD-RVFL algorithm objective function in equation (10) can be further simplified to
Figure FDA0003331784380000037
Step 3, solving the mathematical model to obtain an output weight, specifically:
taking the derivative of the model in equation (14) with respect to β and setting it to zero, one can obtain
β+HTΩHβ-HTΩX+CHTΜHβ＝0. (13)
Then, when (L + d) ≦ (n)s+nt) When true, the solution of equation (15) is
β＝(I+HT(Ω+CΜ)H)-1HTΩX, (14)
Otherwise, the solution can be represented as
β＝HT(I+(Ω+CΜ)HHT)-1ΩX. (15)
Step 4, calculating reconstructed data representation according to the obtained output weight;
for data in the source domain, migratable data representation can be calculated as
X′s＝Hsβ, (16)
And the reconstructed feature representation of the target domain data may be calculated by
X′t＝Htβ. (17)
From there, the reconstructed target data may be identified by a classifier trained by the reconstructed source marker data.
4. The aircraft engine fault diagnosis method based on the migratable neural network of claim 2, wherein the step 2 further comprises using a strategy of reducing both the edge distribution and the condition distribution in the migration learning and integrating the engine data information to obtain a mathematical model of UJD-RVFL, reconstructing formula (6), and the objective function can be shown as:
Figure FDA0003331784380000041
wherein
Figure FDA0003331784380000042
Represents a data set having a kth genuine label category in the source domain, and
Figure FDA0003331784380000043
representing a dataset with the kth pseudo tag category in the target domain; for some simplification, the mathematical model of the above formula for the UJD-RVFL algorithm can be restated in the form
Figure FDA0003331784380000044
Wherein the content of the first and second substances,
Figure FDA0003331784380000045
is a MMD matrix, which is calculated as shown below
Figure FDA0003331784380000046
Furthermore, M0M, which is defined as shown in formula (12);
step 3, solving the mathematical model to obtain an output weight, specifically:
taking the derivative of the model in the formula (21) with respect to beta and setting the derivative to zero; when the condition (L + d) is less than or equal to (n)s+nt) When it is established, it can be obtained
Figure FDA0003331784380000051
Otherwise, then there is
Figure FDA0003331784380000052
UJD-RVFL reconstructed data indicate that it cannot be directly acquired, only edge distribution is aligned in initialization phase; then, simultaneously considering marginal distribution and conditional distribution in an iteration process, and updating pseudo label information in a target domain until a termination condition is reached;
step 4, calculating reconstructed data representation according to the obtained output weight;
for data in the source domain, migratable data representation can be calculated as
X′s＝Hsβ, (23)
And the reconstructed feature representation of the target domain data may be calculated by
X′t＝Htβ. (24)
From there, the reconstructed target data may be identified by a classifier trained by the reconstructed source marker data.
5. The method for diagnosing the faults of the aero-engine based on the migratable neural network as claimed in claim 1, wherein the faults of the aero-engine refer to low pressure compressor LPC faults, high pressure compressor HPC faults, high pressure turbine HPT faults and low pressure turbine LPT faults in the engine.
6. The aircraft engine fault diagnosis method based on the migratable neural network of claim 1, wherein the sample data has different distributions by adjusting the control variables, the environmental variables and the performance degradation amount.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116150919A (en) * 2023-04-23 2023-05-23 中国航发四川燃气涡轮研究院 Gas circuit fault diagnosis method based on fault assumption
CN116956048A (en) * 2023-09-19 2023-10-27 北京航空航天大学 Industrial equipment fault diagnosis method and device based on cross-domain generalized label

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116150919A (en) * 2023-04-23 2023-05-23 中国航发四川燃气涡轮研究院 Gas circuit fault diagnosis method based on fault assumption
CN116150919B (en) * 2023-04-23 2023-06-30 中国航发四川燃气涡轮研究院 Gas circuit fault diagnosis method based on fault assumption
CN116956048A (en) * 2023-09-19 2023-10-27 北京航空航天大学 Industrial equipment fault diagnosis method and device based on cross-domain generalized label
CN116956048B (en) * 2023-09-19 2023-12-15 北京航空航天大学 Industrial equipment fault diagnosis method and device based on cross-domain generalized label

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