Aero-engine health index modeling method fusing linear and nonlinear features

Abstract

The application proposes an aero-engine health index modeling method fusing linear and nonlinear characteristics, specifically comprising the following steps: arranging a multi-source sensor detection system to collect aero-engine operation state multi-source data; normalizing the collected data and performing reliability screening; based on the remaining sensor data after screening, respectively using VAE to extract nonlinear degradation features and SPCA to extract linear degradation features; according to the obtained nonlinear and linear degradation features, designing dynamic fusion weights, and combining a weighted moving average optimization algorithm to construct a composite health index. The application effectively fuses multi-source sensor data, fully utilizes the complementary characteristics of linear and nonlinear methods, constructs a more reliable composite health index, and can intuitively reflect the degradation state of the aero-engine, providing an important reference for the evaluation of the aero-engine operation state, the prediction of the remaining life and the scientific formulation of the maintenance strategy.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of health state assessment of aero-engines, and in particular to a health index modeling method of aero-engines fusing linear and nonlinear features. BACKGROUND

[0002] Aero-engines are the core power source of aircrafts, and as key components of aircrafts, their operating conditions directly affect the flight performance and safety of aircrafts. With the complication of aircraft equipment and the diversification of operating environment, it is essential to assess the health state of aero-engines and timely monitor their degradation trend for the purpose of ensuring flight safety and improving operating reliability. Accurate prediction of the remaining useful life (RUL) of aero-engines can help airlines effectively arrange maintenance, reduce costs, and improve efficiency and safety. In the past few decades, significant progress has been made in RUL prediction technology, and various methods and techniques have been developed. Among them, the remaining useful life prediction method based on health index construction has become a research hotspot due to its intuitiveness and effectiveness.

[0003] Traditional health state assessment methods mostly rely on single-variable or single-sensor observation data, which is difficult to fully capture the complex degradation process of aero-engines. With the rapid development of sensor technology, multi-source sensor monitoring systems can record real-time multi-dimensional heterogeneous data of engine operating conditions, providing rich information for health index modeling. However, how to effectively fuse multi-source sensor data to construct a comprehensive index that accurately reflects the health state of the equipment remains a difficult point in current research.

[0004] Existing multi-source data processing methods usually include independent component analysis, singular value decomposition, factor analysis based on linear feature extraction, and kernel principal component analysis, long short-term memory network, convolutional neural network based on nonlinear feature extraction. SPCA captures the dominant direction of data through linear dimension reduction, which is suitable for processing data with strong linear correlation, but performs poorly when facing complex nonlinear degradation features. VAE, on the other hand, can better capture the nonlinear degradation patterns of multi-source sensor data by constructing the probability distribution of the latent space and realizing nonlinear feature extraction of complex data.

[0005] In order to fully utilize the complementary advantages of VAE and SPCA in feature extraction, the present application proposes a health index modeling method of aero-engines fusing linear and nonlinear features. This method can maintain the data dimension reduction effect while constructing a comprehensive health index with high discriminability and robustness, providing an important reference for the health state assessment and maintenance decision of aero-engines. SUMMARY

[0006] In view of the problems in the prior art, the aero-engine health index modeling method fusing linear and nonlinear features is provided to solve the technical problems of lack of comprehensiveness and robustness in constructing aero-engine health indexes by fusing multi-source data with the prior art.

[0007] To achieve the above technical purposes, the present application provides the following technical solutions:

[0008] The aero-engine health index modeling method fusing linear and nonlinear features specifically includes the following steps:

[0009] S1, a multi-source sensor detection system is arranged to collect multi-source data of the running state of the aero-engine;

[0010] S2, the collected multi-source data of the running state is normalized and then the reliability is screened by using the Pearson coefficient;

[0011] S3, the remaining multi-source data of the running state after screening is fused by using the variational autoencoder VAE to obtain nonlinear degradation features;

[0012] S4, the remaining multi-source data of the running state after screening is fused by using the sparse principal component analysis SPCA method to obtain linear degradation features;

[0013] S5, the dynamic fusion weight is designed according to the obtained nonlinear and linear degradation features, and a composite health index is constructed by combining the weighted moving average optimization algorithm.

[0014] Further, step S1 specifically includes:

[0015] S11, a plurality of sensors for measuring different physical quantities are installed and connected on the aero-engine;

[0016] S12, data transmission mode, sampling frequency, and data storage format parameters are configured;

[0017] S13, after determining that the sensors are in a normal working state, the multi-source data of the running state of the aero-engine is collected, and the formula is expressed as:

[0018]

[0019] Wherein, A i is the multi-source data of the running state of the aero-engine i; is the running state data collected by the sensor j on the aero-engine i at the running moment k.

[0020] Further, step S2 specifically includes:

[0021] S21, the collected aero-engine operating state multi-source data is normalized to avoid the influence of different sensor dimensions; the normalized operating state multi-source data is represented as:

[0022]

[0023] wherein, U i is the normalized operating state multi-source data of the aero-engine i; is the normalized operating state data collected by the sensor j on the aero-engine i at the operating time k;

[0024] S22, the Pearson coefficient is used for reliability screening on the normalized operating state multi-source data, and the operating state data collected by the sensor with a small Pearson coefficient, i.e. weak correlation, is removed; the screened operating state multi-source data is denoted as Y=(y i,1 ,y i,2 ,...,y i,j ); the calculation formula of the Pearson coefficient is:

[0025]

[0026] wherein, is the mean value of the sum of historical time values of the aero-engine i, is the kth operating time of the aero-engine i, is the mean value of the normalized operating state data collected by the sensor j on the aero-engine i; K is the maximum operating time of the aero-engine i.

[0027] Further, step S3 specifically includes:

[0028] S31, the screened operating state multi-source data is taken as the input variable of VAE, and the hidden variable, i.e. the nonlinear degradation feature Z=(z1, z2,..., z j ) of the aero-engine is obtained through nonlinear dimension reduction processing; and the learning process of VAE is optimized by maximizing the objective function; the formula expression of the objective function is

[0029] logp(y)=log∫p(z)p(y|z);

[0030] wherein, p(y) and p(z) represent the probability distribution of the screened operating state multi-source data and the nonlinear degradation feature respectively; p(y|z) is the conditional probability distribution, which represents the distribution of y given z;

[0031] S32, the posterior distribution q(z|y) is introduced to approximate p(y|z), and the objective function is converted to:

[0032]

[0033] wherein, is the lower bound of evidence, D KL (q(z|ys)||p(z|y)) is the KL divergence;

[0034] S33, according to the KL divergence is always not less than 0, the maximum objective function is converted into maximizing the lower bound of evidence The formula of the lower bound of evidence is:

[0035]

[0036] wherein, E q(z|y) [logp(y|z)] is the reconstruction loss;

[0037] By maximizing the lower bound of evidence, the hidden variable close to the distribution of the input variable is obtained.

[0038] Further, the step S4 specifically comprises:

[0039] S41, based on the screened running state multi-source data, the running state data mean μ of the sensor j on the aero-engine i collected within the complete running time is calculated; the formula is:

[0040]

[0041] S42, the covariance matrix ψ is calculated, and the formula is:

[0042]

[0043] wherein, is the transpose matrix of matrix ;

[0044] S43, the covariance matrix is subjected to sparse principal component analysis, and the sparse principal component direction vector s is obtained by optimizing the following objective function:

[0045] maxs T ψs-α||s||1;

[0046] Wherein, α is a sparse regularization parameter, which controls the sparsity degree, s is a sparse principal component direction vector, is a unit vector, s T Indicates the transpose vector of the sparse principal component direction vector, ||s||1 indicates the L1 norm of s, which is used to introduce sparsity;

[0047] S44, the linear transformation is performed on the running state multi-source data screened by reliability by using the obtained sparse principal component vector, and the linear degradation feature Q=sY=(q1,q2,...,q j ) is obtained.

[0048] Further, step S5 specifically comprises:

[0049] S51, set the dynamic fusion weight of degradation features as γ(t) = [γ1(k), γ2(k)];

[0050] wherein γ1(k), γ2(k) are respectively the fusion weights of linear degradation features and nonlinear degradation features; representing the importance and weight distribution of the corresponding degradation features, which dynamically changes with k moment;

[0051] S52, in the initial state, it is considered that the importance of linear degradation features and nonlinear degradation features is equal, so the weight is set as:

[0052] γ1(1) = γ2(1) = 0.5;

[0053] S53, calculate the change rate of linear degradation features and nonlinear degradation features for any k moment; the formula is expressed as:

[0054]

[0055] wherein Q(k), Z(k) represent respectively the linear degradation features and nonlinear degradation features at k moment, Q(k-1), Z(k-1) represent respectively the linear degradation features and nonlinear degradation features at k-1 moment; Δk = k-(k-1);

[0056] S54, normalize the feature change rate to obtain respectively:

[0057]

[0058] S55, according to the normalized change rate, the dynamic fusion weight is obtained by using the exponential weighted moving average algorithm; the formula is expressed as:

[0059] γ1(k) = β·r SPCA,norm (k) + (1-β)·γ1(k-1)

[0060] γ2(k) = β·r VAE,norm (k) + (1-β)·γ2(k-1);

[0061] wherein β is a weight adjustment rate factor, which controls the response sensitivity of weight update to current feature change;

[0062] S56, based on the degradation features obtained in steps S3, S4 and the dynamic fusion weight in step S55, a composite health index H is constructed, and the formula is expressed as:

[0063] H = γ1(k)Q + γ2(k)Z;

[0064] Wherein, Q and Z are linear degradation characteristics and nonlinear degradation characteristics respectively.

[0065] In addition, the application also provides a device equipment comprising a memory and a processor, wherein:

[0066] The memory is used for storing a computer program capable of running on the processor;

[0067] The processor is used for executing the aero-engine health index modeling method of fusing linear and nonlinear characteristics as described above when running the computer program.

[0068] The application also provides a computer readable storage medium storing computer instructions for making the processor execute the aero-engine health index modeling method of fusing linear and nonlinear characteristics as described above.

[0069] Based on the above technical solution, the application has at least the following beneficial effects:

[0070] 1. The operation state multi-source data of the aero-engine are fused, the linear and nonlinear characteristics collected by the multi-source sensor data acquisition are fully mined, and the accuracy of the health state evaluation is improved;

[0071] 2. The advantages of the nonlinear method and the linear method are combined, and the robustness of the data processing, the high efficiency and the interpretability of the feature expression are improved;

[0072] 3. The aero-engine health index constructed by the method has higher quality, and can more intuitively reflect the degradation trend of the aero-engine, and provides strong support for the subsequent residual life prediction and maintenance decision. BRIEF DESCRIPTION OF DRAWINGS

[0073] The drawings described herein are used to provide further understanding of the application, and constitute a part of the application. The illustrative embodiments of the application and their descriptions are used to explain the application, and do not constitute an improper limitation on the application. In the drawings:

[0074] Figure 1 The flow chart of the method for aero-engine health index modeling proposed by the application;

[0075] Figure 2 The operation state data collected by 21 sensors on a single aero-engine in the training set in the embodiment of the application is shown in the time variation trend graph;

[0076] Figure 3 The composite health index obtained by using different methods for the four test aero-engines involved in the embodiment of the application is shown in the time variation trend graph. DETAILED DESCRIPTION

[0077] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and not used to limit the present application.

[0078] The steps in the present application are arranged by using labels, but are not used to limit the sequence of the steps. Unless the sequence of the steps is explicitly described or the execution of a certain step needs other steps as a basis, the relative sequence of the steps can be adjusted. It can be understood that the term "and / or" used herein involves and covers any and all possible combinations of one or more of the associated listed items.

[0079] As shown in Figures 1-3 , the present application proposes an aero-engine health index modeling method fusing linear and nonlinear characteristics; as shown in Figure 1 , which specifically includes the following steps:

[0080] S1, arranging a multi-source sensor detection system to collect multi-source data of the running state of the aero-engine;

[0081] As a preferred embodiment, step S1 specifically includes:

[0082] S11, installing and connecting a plurality of sensors for measuring different physical quantities on the aero-engine;

[0083] The aero-engine involved in the present embodiment mainly includes a fan, a combustion chamber, a low-pressure turbine, a low-pressure compressor, a high-pressure compressor, a high-pressure turbine and a nozzle; in the initial stage of component degradation, the engine is normally operated. As the service time of the engine continues, the performance of the engine gradually degrades until the entire engine completely fails. Therefore, in the present embodiment, 21 sensors such as pressure, temperature and speed are installed inside the engine to measure the degradation state of the performance of the aero-engine in each dimension over time.

[0084] S12, configuring data transmission mode, sampling frequency and data storage format parameters;

[0085] S13, after determining that the sensor is in a normal working state, collecting multi-source data of the running state of the aero-engine, which is expressed by the formula:

[0086]

[0087] Wherein, A i is the multi-source data of the running state of the aero-engine i; is the running state data collected by the sensor j on the aero-engine i at the running moment k;

[0088] It should be further noted that, represents the running state data collected by sensor j on aero-engine i at full running time.

[0089] S2, normalize the collected running state multi-source data, and then use the Pearson coefficient for reliability screening;

[0090] As a preferred embodiment, step S2 specifically comprises:

[0091] S21, normalize the collected running state multi-source data of the aero-engine to avoid the influence of different sensor dimensions; the normalized running state multi-source data is represented as:

[0092]

[0093] Wherein, U i is the normalized running state multi-source data of aero-engine i; is the normalized running state data collected by sensor j on aero-engine i at running time k; u i,j The specific form refers to a i,j ;

[0094] S22, use the Pearson coefficient to screen the reliability of the normalized running state multi-source data, eliminate the running state data collected by the sensors with weak correlation, i.e. small Pearson coefficient, and mark the screened running state multi-source data as Y=(y i,1 ,y i,2 ,...,y i,j ); The calculation formula of the Pearson coefficient is:

[0095]

[0096] Wherein, is the mean of the sum of historical time values of aero-engine i, is the kth running time of aero-engine i, is the mean of the normalized running state data collected by sensor j on engine i; K is the maximum running time of aero-engine i.

[0097] In this embodiment, the Pearson coefficient is used to measure the correlation between the state data collected by different sensors and the engine running time, i.e. to screen out the weakly correlated sensor data related to the degradation of engine health state, and to ensure the reliability of the extracted nonlinear features and linear features subsequently.

[0098] S3, data fusion is performed on the remaining running state multi-source data after screening by using the variational autoencoder VAE to obtain nonlinear degradation features;

[0099] As a preferred embodiment, step S3 specifically comprises:

[0100] S31, taking the screened running state multi-source data as the input variable of VAE, and obtaining the hidden variable, i.e. the nonlinear degradation feature Z=(z1, z2,..., z j ) of the aero-engine through nonlinear dimension reduction processing; and optimizing the learning process of VAE by maximizing the objective function; the formula expression of the objective function is

[0101] logp(y) = log∫p(z)p(y|z);

[0102] Wherein, p(y) and p(z) represent the probability distribution of the screened running state multi-source data and the nonlinear degradation feature respectively; p(y|z) is the conditional probability distribution, which represents the distribution of y given z;

[0103] S32, by introducing the posterior distribution q(z|y) to approximate p(y|z), the objective function is converted to:

[0104]

[0105] Wherein, is the lower bound of evidence, D KL (q(z|ys)||p(z|y)) is the KL divergence, which is used to measure the difference between the probability distribution of the input variable and the hidden variable;

[0106] S33, according to the fact that the KL divergence is always not less than 0, the maximization of the objective function is converted to the maximization of the lower bound of evidence The formula expression of the lower bound of evidence is:

[0107]

[0108] Wherein, E q(z|y) [logp(y|z)] is the reconstruction loss; which is used to measure the similarity between the input variable and the hidden variable;

[0109] By maximizing the lower bound of evidence, the hidden variable close to the distribution of the input variable is obtained.

[0110] S4, performing data fusion on the remaining running state multi-source data after screening by the sparse principal component analysis (SPCA) method, and obtaining the linear degradation feature;

[0111] As a preferred embodiment, step S4 specifically comprises:

[0112] S41, based on the screened running state multi-source data, calculating the running state data mean μ of the sensor j on the aero-engine i collected within the complete running time; the formula expression is:

[0113]

[0114] S42, calculate the covariance matrix ψ, which is expressed by the formula:

[0115]

[0116] wherein, is the transpose matrix of matrix ;

[0117] S43, perform sparse principal component analysis on the covariance matrix, and obtain sparse principal component direction vectors s by optimizing the following objective function:

[0118] maxs T ψs-α||s||1;

[0119] wherein, α is a sparse regularization parameter, which controls the degree of sparsity, and s is a sparse principal component direction vector, which is a unit vector, s T represents the transpose vector of the sparse principal component direction vector, and ||s||1 represents the L1 norm of s, which is used to introduce sparsity;

[0120] S44, linearly transform the operation state multi-source data after reliability screening by using the obtained sparse principal component vector, to obtain linear degradation features Q=sY=(q1,q2,...,q j ).

[0121] S5, design dynamic fusion weights according to the obtained nonlinear and linear degradation features, and construct a composite health index combined with a weighted moving average optimization algorithm;

[0122] As a preferred embodiment, step S5 specifically includes:

[0123] S51, set the dynamic fusion weight of the degradation feature as γ(t)=[γ1(k),γ2(k)];

[0124] wherein, γ1(k) and γ2(k) are the fusion weights of the linear degradation feature and the nonlinear degradation feature, respectively; represent the importance and weight allocation of the corresponding degradation feature, and dynamically change with k time;

[0125] S52, in the initial state, it is considered that the importance of the linear degradation feature and the nonlinear degradation feature is equal, and then the weight is set as:

[0126] γ1(1)=γ2(1)=0.5;

[0127] S53, calculate the change rate of the linear degradation feature and the nonlinear degradation feature for any k time, which is expressed by the formula:

[0128]

[0129] wherein Q(k), Z(k) represent linear degradation feature and nonlinear degradation feature at k time respectively, Q(k-1), Z(k-1) represent linear degradation feature and nonlinear degradation feature at k-1 time respectively; Δk = k-(k-1) ;

[0130] S54, the feature change rate is normalized again, respectively:

[0131]

[0132] S55, according to the normalized change rate, the dynamic fusion weight is obtained by using exponential weighted moving average algorithm; The formula is expressed as:

[0133] γ1(k) = β·r SPCA,norm (k) + (1-β)·γ1(k-1)

[0134] γ2(k) = β·r VAE,norm (k) + (1-β)·γ2(k-1) ;

[0135] Wherein, β is the weight adjustment rate factor, control weight update response sensitivity to the current feature change;

[0136] S56, based on the degradation features obtained in steps S3, S4 and the dynamic fusion weight in step S55, a composite health index H is constructed, and the formula is expressed as:

[0137] H = γ1(k) Q + γ2(k) Z;

[0138] Wherein, Q, Z are linear degradation feature and nonlinear degradation feature respectively.

[0139] So far, the specific process of the method proposed in the application has been described, and the superiority of the method proposed in the application is verified through specific experimental examples. In the present embodiment, in order to verify the performance of the aero-engine health index modeling method combining linear and nonlinear features proposed in the application, the present method is performed on the aero-engine public degradation data set provided by NASA. In the offline stage, 100 groups of complete time series from the start of operation to the end of failure contained in the "train_FD001.txt" file in the data set are used, which contains sensor data transmitted to the central processing unit in real time based on wireless communication technology, the sampling frequency is set to 1 per cycle to ensure efficient monitoring of the engine operating state, and the data storage format uses the standard text file (.txt) format, each line record contains the engine number, timestamp, operating condition parameters and 21 sensor data for subsequent analysis and processing. In the verification stage, the state monitoring sequence of 100 groups of incomplete test engines contained in the "test_FD001.txt" file in the data set is used.

[0140] In the present embodiment, the engine operating state raw data collected by the sensors is first preprocessed according to the reliability screening method in step S2; the operating state data collected by the 21 sensors in the training set is as shown in FIG. 2, it can be seen that the values of the operating state data collected by some sensors have significant changes over time, reflecting the degradation of the performance of the aero-engine over time; and the sensor data without obvious changes in the figure is considered to have weak correlation and is screened out and does not participate in subsequent feature extraction. Through the reliability screening of step S2, the present application selects as much as possible the degradation features collected by the sensors that are strongly related to the performance degradation of the aero-engine, which helps to improve the rationality and reliability of the subsequent construction of the composite health index. Figure 2

[0141] According to steps S3 and S4, nonlinear degradation features and linear degradation features are extracted from the remaining operating state multi-source data after screening by the variational autoencoder VAE and the sparse principal component analysis SPCA method respectively, and the composite health index is constructed by feature fusion according to step S5, and the fusion coefficient γ = [γ1, γ2] of the degradation feature vector is optimized by the exponential weighted moving average algorithm.

[0142] After training, the expression of the composite health index and the dynamic fusion weight is obtained, at this time, the incomplete state detection data in the "test_FD001.txt" file is tested according to the above steps; the test result is as shown in FIG. 4, which describes the health index values obtained by using the method proposed in the application and using VAE or SPCA alone. Figure 3 Figure 3 ​​As can be seen, compared with the VAE or SPCA alone, the composite health index obtained by the method has small fluctuations and a generally stable trend over time, and the index values calculated at the initial and final stages of engine operation are not too small or too large, which shows that the method has better robustness. In addition, after calculating the Pearson coefficient, the Pearson coefficient of the single sensor data in the untreated original aero-engine multi-source data and the running time is 0.811; after using VAE or SPCA alone to construct the degradation feature vector, the Pearson coefficient is 0.823 and 0.837 respectively, while the Pearson coefficient of the degradation feature constructed by the method and the running time is 0.851, which shows that the composite health index designed by the method has better correlation with the engine health state. Therefore, the composite health index modeling method is reliable.

[0143] It will be obvious to a person skilled in the art that, without departing from the spirit or essential characteristics of the application, the present application can be implemented in other specific forms. The present examples are therefore to be considered in all respects as illustrative and not restrictive, the scope of the application being indicated by the appended claims rather than by the specification as previously given. Any reference signs in the claims should not be construed as limiting the scope of the claims.

[0144] In addition, it should be understood that, although the present specification is described in terms of embodiments, not every embodiment contains only one independent technical solution, and the description of the specification is only for the sake of clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be combined appropriately to form other embodiments that those skilled in the art can understand.

Claims

1. A method for modeling aero-engine health indicators that integrates linear and nonlinear features, characterized in that, Specifically, the following steps are included: S1. Deploy a multi-source sensor detection system to collect multi-source data on the operating status of the aero-engine; S2. Normalize the collected multi-source operational status data and then use the Pearson coefficient for reliability screening. S3. Data fusion is performed on the remaining multi-source data of the operating status after filtering by variational autoencoder (VAE) to obtain nonlinear degradation characteristics; S4. The remaining multi-source data of the operating status after screening are fused using the sparse principal component analysis (SPCA) method to obtain linear degradation characteristics. S5. Based on the obtained nonlinear and linear degradation characteristics, design dynamic fusion weights and construct a composite health index by combining a weighted moving average optimization algorithm; specifically including: S51. Set the dynamic fusion weights for degradation features as follows: ; in, These represent the fusion weights for linear and nonlinear degradation features, respectively; they characterize the importance and weight allocation of the corresponding degradation features, and vary with... Constantly changing; S52. In the initial state, assuming that linear degradation features and nonlinear degradation features are of equal importance, the weights are set as follows: ； S53. Calculate the rate of change of the linear degradation characteristic and the nonlinear degradation characteristic for any time k; the formula is expressed as: ； in, These represent the linear and nonlinear degradation characteristics at time k, respectively. Represent Linear and nonlinear degradation characteristics at time points; ; S54. Then, normalize the characteristic rate of change to obtain: ； S55. Based on the normalized rate of change, the dynamic fusion weights are obtained using an exponentially weighted moving average algorithm; the formula is expressed as: ； in, The weight adjustment rate factor controls the sensitivity of weight updates to changes in current features. S56. Based on the degradation features obtained in steps S3 and S4 and the dynamic fusion weights obtained in step S55, construct a composite health index. The formula is expressed as: ； in, , These are linear degradation characteristics and nonlinear degradation characteristics, respectively.

2. The method for modeling aero-engine health indicators by integrating linear and nonlinear features according to claim 1, characterized in that, Step S1 specifically includes: S11. Install and connect multiple sensors on the aircraft engine to measure different physical quantities; S12. Configure data transmission method, sampling frequency, and data storage format parameters; S13. After confirming that the sensor is in normal working condition, collect multi-source data on the operating status of the aero-engine, expressed by the following formula: ； in, For aircraft engines Multi-source data on operational status; For aircraft engines Sensors on The running status data collected at runtime k.

3. The method for modeling aero-engine health indicators by integrating linear and nonlinear features according to claim 2, characterized in that, Step S2 specifically includes: S21. Normalize the collected multi-source data on the operating status of the aero-engine to avoid the influence of different sensor dimensions; the normalized multi-source data on the operating status is represented as follows: ； in, For aircraft engines Normalized operational status multi-source data; For aircraft engines Sensors on Normalized runtime status data collected at runtime k; S22. The normalized multi-source operational status data is subjected to reliability screening using the Pearson coefficient. Operational status data collected by sensors with small Pearson coefficients (i.e., weak correlation) are discarded. The filtered multi-source operational status data is denoted as... The formula for calculating the Pearson coefficient is: ； in, , For aircraft engines The average of the sum of historical moment values, For aircraft engines The Each running moment, For engine Upper sensor The mean of the collected normalized operating status data; For aircraft engines Maximum runtime.

4. The method for modeling aero-engine health indicators by integrating linear and nonlinear features according to claim 1, characterized in that, Step S3 specifically includes: S31. Using the filtered multi-source operational status data as the input variables of the VAE, latent variables, namely the nonlinear degradation characteristics of the aero-engine, are obtained through nonlinear dimensionality reduction processing. The learning process of the VAE is optimized by maximizing the objective function; the objective function is expressed as follows: ； in, and These represent the probability distributions of the filtered multi-source data on operational status and the nonlinear degradation features, respectively. It is a conditional probability distribution, which represents the distribution of y given z; S32, By introducing a posterior distribution approximate Transform the objective function into: ； in, As the lower bound of evidence, Let KL divergence be a metric. S33. Based on the fact that the KL divergence is always not less than 0, the objective function is transformed into maximizing the lower bound of evidence. The formula for the lower bound of evidence is expressed as: ； in, For reconstruction loss; By maximizing the lower bound of evidence, we obtain latent variables that closely approximate the distribution of the input variables.

5. The method for modeling aero-engine health indicators by integrating linear and nonlinear features according to claim 3, characterized in that, Step S4 specifically includes: S41. Based on the filtered multi-source operational status data, calculate the aero-engine... Sensors on The average value of the running status data collected during the complete running time. The formula is expressed as: ； S42. Calculate the covariance matrix. The formula is expressed as: ； in, For matrix The transpose of the matrix; S43. Perform sparse principal component analysis on the covariance matrix, and obtain the sparse principal component direction vectors by optimizing the following objective function. : ； in, This is a sparsity regularization parameter that controls the degree of sparsity. Let be the sparse principal component direction vector, and be a unit vector. This represents the transpose of the sparse principal component direction vector. express The L1 norm is used to introduce sparsity; S44. Using the obtained sparse principal component vectors, perform a linear transformation on the multi-source data of the operating status after reliability screening to obtain linear degradation features. .

6. An electronic device, characterized in that, The electronic device includes a memory and a processor, wherein: Memory is used to store computer programs that can run on a processor; A processor is configured to, while running the computer program, execute the aero-engine health index modeling method that integrates linear and nonlinear features as described in any one of claims 1-5.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause a processor to execute the aero-engine health index modeling method that integrates linear and nonlinear features as described in any one of claims 1-5.

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