Method for mining mapping relationship between performance of aero-engine gas path components and performance of whole engine

Abstract

The present application relates to the technical field of maintenance and repair of aero-engine gas path components, in particular to a method for mining the mapping relationship between the performance of aero-engine gas path components and the performance of the whole machine, which can significantly improve the use and maintenance efficiency of aero-engines, the method comprises the following steps: constructing a regression model to mine the mapping relationship between the performance of aero-engine gas path components and the performance of the whole machine, adding a convolution attention mechanism to a multivariate time series regression model based on CNN-LSTM to construct a CBA-LSTM aero-engine gas path component performance and whole machine performance multivariate time series regression model, and incorporating a traditional linear regression model into the model to improve the sensitivity of the model to linear changes in input parameters, the model can regress and predict the whole machine performance index EGTM based on the aero-engine gas path multi-component performance evaluation results of fingerprint maps and gas path parameter deviation values, thereby providing performance early warning for the whole machine before maintenance in actual operation and maintenance.

Description

Technical fields:

[0001] This invention relates to the field of maintenance and repair technology for aero-engine air path components, specifically a method for mining the mapping relationship between the performance of aero-engine air path components and the overall performance, which can solve the problem that the deviation values ​​of existing aero-engine air path parameters are difficult to directly apply to the performance evaluation of the engine air path, and significantly improve the efficiency of aero-engine use and maintenance. Background technology:

[0002] As the "heart" of an aircraft, timely and accurate performance assessment of the aero-engine is crucial for ensuring flight safety and developing reasonable maintenance plans. Currently, engine performance monitoring and assessment, a critical component of engine health management, still relies on the original equipment manufacturer (OEM). This forces airlines to passively execute engine maintenance according to the manufacturer's rules. As characteristic parameters representing the performance status of engine pneumatic components, as shown in the fingerprint diagram, pneumatic parameter deviations are inevitably affected by non-component performance degradation and engine operating conditions, resulting in significant gross errors and noise in the data.

[0003] As an assembly of main units and sub-components, the performance of an engine depends on the performance of each component. Especially when defining the scope of maintenance work during engine overhaul, the scope of maintenance for each aerodynamic component needs to be determined with the overall engine performance recovery target in mind. This enables component-based engine maintenance management. However, current engine performance evaluation methods primarily use autoregressive approaches based on overall performance indicators, neglecting the impact of component performance on overall engine performance. This means that the overall performance evaluation results can only be used for pre-overhaul performance warnings, offering no guidance for actual engine maintenance. Therefore, it is necessary to study the mapping relationship between the performance of aero-engine aerodynamic components and overall engine performance, thereby providing technical support for defining the scope of maintenance work for both the entire engine and its components, and for post-overhaul performance evaluation.

[0004] Aircraft engine maintenance and management is typically conducted on a fleet basis. The service status of each engine within the same fleet is affected by factors such as performance degradation, life-limiting components, component damage, and airworthiness directives / service notices. Therefore, to ensure flight missions, guarantee flight safety, and reduce maintenance costs, it is necessary to comprehensively consider factors that may interfere with the normal service of engines in order to plan the maintenance of both in-service and servicing engines. In addition to engine maintenance prediction factors based on life-limiting components, component damage, and airworthiness directives / service notices, engine performance degradation assessment can provide relevant support for aircraft engine maintenance work.

[0005] Exhaust Gas Temperature Margin (EGTM) is one of the most important performance indicators of an engine. Figure 1 As shown, it is defined as the difference between the exhaust gas temperature (EGT) and the EGT redline value when the engine takes off at full thrust under standard weather conditions at sea level. The EGT redline value is a fixed value set by the engine OEM based on the limited operating temperature of the materials used in the combustion chamber and turbine components in the gas path.

[0006] like Figure 2 As shown in the diagram, under typical conditions, the performance degradation of newly generated components is almost negligible, thus allowing for a large margin in EGTM. However, during engine service, as the overall performance of the engine and its various air passage components deteriorates, EGT slowly increases, and EGTM slowly decreases. When EGTM drops to near the EGTM redline, the engine needs to be disassembled and sent for repair. A repair target, i.e., the overall engine performance recovery amount, is determined by comprehensively considering repair costs and post-repair service requirements. In reality, the overall engine performance degradation is caused by the performance degradation of its air passage components. Therefore, during repair, the overall engine performance recovery amount is used as an indicator to guide the repair of each air passage component. That is, based on the repair target, different operating ranges are used for repairing each air passage component, restoring their performance and thus bringing the overall engine EGTM back to an acceptable range.

[0007] It is evident that in actual engine maintenance, the performance recovery of the entire engine depends on the performance recovery of its airflow components; that is, there is a certain dependency between the overall engine performance and the component performance. This means that the overall engine performance is actually a collection of the performance of its various airflow components based on a certain mapping relationship. If the mapping relationship between the performance of each airflow component and the overall engine performance can be extracted based on the performance evaluation results of multiple engine airflow components, it will be of great benefit to pre-repair performance warnings, the determination of the working range of airflow components during repair, and post-repair performance evaluation of the entire engine in actual operation and maintenance.

[0008] The current engine performance evaluation mainly relies on historical data of EGTM. Following the idea of ​​formula (1), a data-driven method is used to perform autoregression on EGTM data. By mining the data change patterns, the trend of EGTM is predicted, and thus the performance changes of the engine can be predicted in advance.

[0009]

[0010] In the formula —Predicted values ​​for EGTM;

[0011] τ — Length of historical data;

[0012] y i —Historical real data of EGTM.

[0013] This method can better predict the long-term performance trend of the engine as a whole, so as to formulate maintenance plans in advance, but it cannot help to determine the scope of maintenance work for engine air circuit components during actual maintenance. Summary of the Invention:

[0014] This invention addresses the shortcomings and deficiencies of existing technologies by proposing a method for mining the mapping relationship between the performance of aero-engine air path components and the overall performance. This method can solve the problem that the deviation values ​​of existing aero-engine air path parameters are difficult to directly apply to the evaluation of engine air path performance and significantly improve the efficiency of aero-engine use and maintenance.

[0015] This invention achieves its purpose through the following measures:

[0016] A method for mining the mapping relationship between the performance of aero-engine air passage components and the overall engine performance, characterized by comprising the following steps:

[0017] Step 1: Data acquisition and preprocessing;

[0018] Step 2: Establish and train a regression model for the performance of multiple components in the engine's airflow path and the overall engine performance based on CBAM.

[0019] Step 2-1: Based on the collected samples, perform sample pairing and use the Grubbs criterion and EEMD-SG filtering algorithm to perform noise reduction filtering on the EGTM data;

[0020] Step 2-2 normalizes the dataset and constructs the model input in the form of a sliding window;

[0021] Steps 2-3 divide the model training set and test set in a 7:3 ratio;

[0022] Steps 2-4: Construct a performance regression model for engine components and the entire engine based on CBAM;

[0023] Steps 2-5: Set the model hyperparameters and train the model using the Adam algorithm combined with a loss function;

[0024] Steps 2-6: Search for the optimal value of the hyperparameter to be adjusted;

[0025] Steps 2-7: Fix the hyperparameters and train the final model;

[0026] Step 3: Apply a regression model of engine airflow multi-component performance and overall engine performance based on CBAM.

[0027] The present invention describes a CBA-LSTM-based multi-component performance and overall engine performance regression model for engine airflow based on CBAM. This model incorporates a convolutional attention mechanism into a multivariate time-series regression model constructed using CNN-LSTM, thereby creating a CBA-LSTM multivariate time-series regression model for engine airflow component performance and overall engine performance. The model uses the performance degradation of each engine airflow component over a time period of T and with a feature parameter of 5. As input to the model, the overall system performance metric EGTM, with the same time duration, is used as the regression target. First, according to equation (7), n 3×3 convolution kernels are used to linearly map the single-channel input features to n different channels with the same input feature scale, and non-linear feature mapping is performed through a non-linear activation function. Here, the method of filling one row of 0 at the beginning and end is adopted to ensure that the parameter dimensions of the input and output are consistent.

[0028]

[0029] In the formula X i,j —The j-th eigenvalue of the i-th convolutional feature surface, i∈(1,n);

[0030] —The input value of the u-th row and v-th column of the convolution region corresponding to the j-th row, j∈(1,T);

[0031] —The weights of the i-th convolutional kernel in the u-th row and v-th column to be learned;

[0032] σ c —Non-linear activation function, using the ReLU function;

[0033] Secondly, the mapped multi-channel features Input into the CBAM module, and obtain the weighted mapping features after channel attention and spatial attention weighting according to equations (4) and (6). Then, the weighted mapping feature X″ is input into a convolutional layer with n 3×3 convolutional kernels for feature compression.

[0034] Similarly, we also use a method of padding the beginning and end with one row of 0s to ensure that the parameters of the input and output are consistent.

[0035]

[0036] In the formula Z i,j —The j-th eigenvalue of the i-th convolutional feature surface, i∈(1,n);

[0037] —The input value of the u-th row and v-th column of the convolution region corresponding to the j-th row, j∈(1,T);

[0038] —The weights of the i-th convolutional kernel in the u-th row and v-th column to be learned;

[0039] σ c —A non-linear activation function, here we use the ReLU function;

[0040] Next, the compression features will be... Input the time series features sequentially into the LSTM initialized with h0 and c0 in state 0, and obtain the time series feature values ​​according to equations (9)-(13).

[0041] f t =sigmoid(W f [h t-1 ;z t ]+b f (9)

[0042] i t =sigmoid(W i [h t-1 ;z t ]+b i (10)

[0043] m t =sigmoid(W o [h t-1 ;z t ]+b o (11)

[0044] c t =f t ·c t-1 +i t ·tanh(W s [h t-1 ;z t ]+b s (12)

[0045] h t =m t ·tanh(c t (13)

[0046] In the formula W f b f W i b i W o b o W s b s —Model parameters to be learned;

[0047] [h t-1 ;zt ]——h t-1 With z i splicing;

[0048] Finally, the time series feature values ​​M are mapped to a nonlinear regression term through a fully connected layer.

[0049]

[0050] In the formula W nl ,b nl —Model parameters to be learned;

[0051] Furthermore, as a linear complement to the nonlinear regression model, a linear regression model is directly added to the nonlinear mapping model to obtain the linear regression term of the model.

[0052]

[0053] In the formula W l ,b l —Model parameters to be learned;

[0054] By combining the nonlinear regression terms according to equation (16) With linear regression term Obtain CBA-LSTM

[0055] Predicted values ​​from the regression model

[0056]

[0057] Using the root mean square error as shown in equation (17) as the loss function of the model, the error between the model's predicted value and the regression target is examined;

[0058]

[0059] The principle of the dual attention mechanism in the regression model of engine airflow multi-component performance and overall engine performance based on CBAM in step 2 of this invention is as follows:

[0060] Channel attention can effectively capture the performance synergy of each component in the gas path, that is, the working state of each component in the gas path under the current synergistic working state. According to equation (3), the input features after mapping the performance degradation of the gas path components are first mapped. Perform mean pooling and max pooling on the channel separately to obtain the mean performance hidden state of the gas path components. With degraded performance in hidden state Then and Information compression is performed in a single hidden-layer MLP with shared parameters, and finally the compressed information is processed. and The summation is performed and activation is applied using a nonlinear mapping function to output the attention weights for each channel.

[0061]

[0062] In the formula σ o —The channel attention non-linear activation function, here we use the Sigmoid function;

[0063] σ i —The nonlinear activation function for the multilayer perceptron, here we use the ReLU function;

[0064] W i —MLP input layer weights;

[0065] W o —MLP output layer weights.

[0066] After obtaining the channel attention weights, the input features mapped to the performance degradation of the gas path components are processed according to equation (4-4). Assign channel attention weights.

[0067]

[0068] In the formula — Multiply corresponding elements,

[0069] Spatial attention can effectively capture the temporal and spatial correlations of various gas path components, i.e., when and which component's performance degrades and its impact on the performance of other gas path components. According to equation (5), the input feature X′ after channel attention weighting is first subjected to mean pooling and max pooling along the channel direction to obtain the current spatiotemporal mean hidden state of the gas path components. With the hidden state of spatiotemporal degradation Then, the features are spliced ​​along the channel direction for feature fusion, and then the convolutional layer is used to extract the time and component features that need attention to generate spatial attention.

[0070]

[0071] In the formula, σ is the spatial attention nonlinear activation function, and the Sigmoid function is used here;

[0072] Conv k — Convolution operation with kernel size k

[0073] After obtaining the spatial attention weights, spatial attention weights are assigned to the input feature X′ after channel attention weighting according to equation (6).

[0074]

[0075] In the formula — Multiply corresponding elements.

[0076] By introducing CBAM, the regression model can better uncover the spatiotemporal relationship between the collaborative performance degradation of pneumatic components and the overall engine performance EGTM.

[0077] In step 2 of this invention, the time step T, the number of CNN convolutional kernels k, and the number of RNN hidden neurons h are the hyperparameters of the model to be adjusted. A grid search method is used to search for hyperparameters. The specific steps are as follows: Let the time step T = {10, 15, 20}, the number of CNN convolutional kernels n = {32, 64, 128}, and the number of RNN hidden neurons h = {16, 32}. The parameters selected for each experiment are trained 10 times. The mean of the standard deviation is taken as the performance index of the set of hyperparameters. The hyperparameter with the smallest standard deviation is selected as the model hyperparameter. Finally, the optimal time step T = 15, the number of CNN convolutional kernels k = 128, and the number of RNN hidden neurons h = 32 are selected.

[0078] The data acquisition and data preprocessing in step 1 of this invention specifically includes the following steps:

[0079] Step 1-1: Use the collected full-life cruise data to train the gas path multi-component performance evaluation model, and use the trained model to evaluate the gas path multi-component performance of sample-paired data.

[0080] Step 1-2: Perform data pairing. If the deviation value of the air path parameters recorded in the cruise data at time t is used as the input of the air path multi-component performance evaluation model, and the output of the model, i.e. the performance degradation of each component, is used as the input of the CBA-LSTM engine component and whole engine performance multivariate time series regression model, then the EGTM recorded in the takeoff data immediately following time t is used as the regression target of the model. Filter the dataset and discard mismatched cruise / takeoff data.

[0081] After data pairing, since the EGTM data recorded in the takeoff data and the air path parameter deviation value recorded in the cruise data are physically collected in the same way, there is also a lot of noise signal in the EGTM data. Therefore, it is also necessary to reduce the noise of the EGTM data. The coarse error removal and EEMD-SG filtering algorithm are used to preprocess the EGTM data.

[0082] Steps 1-3: After sample pairing, the data is normalized using the linear function normalization (Min-MaxNormalization) method shown in equation (18):

[0083]

[0084] In the formula, x represents the data to be preprocessed.

[0085] x * —Data after normalization;

[0086] x min —The minimum value of the data to be preprocessed;

[0087] x max —The maximum value of the data to be preprocessed.

[0088] In this invention, step 1-1 uses the collected full-life cruise data to train a performance evaluation model for multiple gas path components, specifically including the following steps:

[0089] Step 1-1-1: Establish a nonlinear encoder model and perform feature extraction. The nonlinear encoder consists of a one-dimensional convolutional neural network and a traditional encoder. A traditional 1D-CNN typically contains three basic units: convolutional layers, nonlinear activation layers, and pooling layers. The convolutional layers and nonlinear activation layers work together to extract parametric features, while the pooling layers are used to downsample the model parameters. Since an autoencoder is used to reconstruct the input and output, it is necessary to ensure that the data before and after reconstruction is consistent. Therefore, the pooling layers used to reduce the model parameters need to be removed. The feature extraction process of the 1D-CNN after removing the pooling layers is as follows:

[0090] Construct the input feature surface of the 1D-CNN using ΔD with time length T and feature parameters of 3. By using n 3×3 convolution kernels to perform convolution operations on the input feature surface according to equation (19), and then inputting the result of the convolution operation into a nonlinear activation layer, n convolution feature surfaces Y are output. i ;

[0091] Because a 3×3 convolution kernel is used, the output feature surface Y is [value missing] without data padding. i This will reduce the time steps by 2 compared to the original input feature surface X. To ensure that the data length before and after the input is consistent, zeros need to be padded at the beginning and end of the input feature surface X. The padded feature surface

[0092]

[0093]

[0094] In the formula Y i,j —The j-th eigenvalue of the i-th convolutional feature surface, i∈(1,n);

[0095] —The input value of the u-th row and v-th column of the convolution region corresponding to the j-th row, j∈(1,T);

[0096] —The weights of the i-th convolutional kernel in the u-th row and v-th column to be learned;

[0097] σ c —Nonlinear activation function;

[0098] Introducing a non-linear activation function after convolution can transform the original linear mapping feature surface K. i *x j Mapping to a nonlinear space, the original linearly inseparable linear mapping features will have the opportunity to find a linearly separable path in the mapped nonlinear space, thereby decoupling the performance degradation H of each gas path component under nonlinear coupling working state. The ELU function is used as the nonlinear activation function of the network, as shown in equation (20):

[0099]

[0100] In the formula, α is the combination weight coefficient, and α = 1.

[0101] Step 1-1-2: Perform non-linear encoding:

[0102] After extracting features using 1D-CNN, the input of a nonlinear encoder is constructed using convolutional feature surfaces with a time length of T and a number of features of n. It is mapped onto a hidden layer H, which is used to characterize the performance degradation of each gas path component after decoupling, through a nonlinear encoder composed of a multilayer perceptron (MLP). The nonlinear mapping relationship is shown in equations (21) and (22):

[0103] Z = σ e (YW′ e +b′ e (21), H=ZW e +b e (twenty two)

[0104] In the formula, Z represents the nonlinear output of the encoder input layer.

[0105] H – The encoder output, i.e., the performance degradation of the pneumatic components after decoupling.

[0106] W′ e —The input layer weights of the encoder to be learned.

[0107] σ e—The non-linear activation function of the encoder;

[0108] b′ e —The encoder input layer bias to be learned

[0109] W e —The encoder output layer weights to be learned

[0110] b e —The encoder output layer bias to be learned

[0111] Step 1-1-3: Perform linear decoding:

[0112] After obtaining the performance degradation H of the decoupled gas path components through feature extraction and nonlinear coding, the influence of the unit performance degradation of each gas path component on the deviation value of the gas path parameters in the fingerprint image can be used as a weight W. d The constructed linear decoder reconstructs the gas path parameter deviation values The linear decoding method is shown in equation (23).

[0113]

[0114] In the formula b d —The decoder bias to be learned

[0115] Step 1-1-4: Parameter optimization: Since the nonlinear encoder model aims to minimize the reconstruction error of the air path parameter deviation before and after reconstruction, the mean square error function as shown in equation (24) can be used as one of the optimization objectives.

[0116]

[0117] In the formula, L1 represents the root mean square error of the deviation values ​​of the gas path parameters before and after reconstruction.

[0118] n — number of samples;

[0119] θ — the model parameters to be learned, θ = {K} i ,W′ e ,b′ e W e ,b e ,b d};

[0120] —The difference between the reconstructed deviation value of the i-th gas path parameter and the baseline;

[0121] Δd i —The difference between the deviation value of the i-th gas path parameter before reconstruction and the baseline;

[0122] Furthermore, as aero-engines are highly reliable thermomechanical machines, the performance degradation of each component under non-fault conditions should be slow and stable. Considering the collaborative working characteristics of each gas path component, the performance degradation of these components during service should also be synergistic, meaning the performance degradation of each component should be roughly within the same order of magnitude. However, since the impact of unit performance degradation of each gas path component on the aero-engine is not uniform—that is, the degree of disturbance to the gas path parameter deviations differs—to eliminate the inconsistency in performance fluctuation indicators caused by the inconsistent force dimensions of each gas path component, the influence W of unit performance degradation of each gas path component on the gas path parameter deviations can be used as a reference. d The norm of column vectors eliminates the influence of dimensions, so a loss function L2 as shown in equation (25) can be constructed to narrow the search range of optimal parameters and reduce the difficulty of model training:

[0123]

[0124] In the formula, L2 represents the performance degradation loss function of each gas path component.

[0125] η i,j —Performance degradation of the j-th pneumatic component in the i-th sample;

[0126] η 0,j —The initial performance degradation of pneumatic component j, taken as η 0,j =0;

[0127] ||w j ||2——Weight matrix W d The Euclidean norm of the j-th column vector;

[0128] The loss function of the engine multi-airway component performance evaluation model is shown in equation (26):

[0129]

[0130] In this invention, the Grubbs criterion and EEMD-SG are used to preprocess the deviation values ​​of the air path parameters, effectively eliminating the influence of the engine's unsteady operating conditions on the deviation values ​​of the air path parameters, removing gross errors in the data, and reducing data noise. Specifically:

[0131] Step (1): For the deviation value of the gas path parameters The correction formula based on the fingerprint image is as follows:

[0132]

[0133] In the formula —The uncorrected deviation value of the original gas path parameters at time i;

[0134] xij —The unit opening angle or unit bleed air leakage of VSV and VBV at time i;

[0135] w j —x in the fingerprint image j The offset caused by deviations in gas path parameters;

[0136] Step (2): Use the Grubbs criterion to remove gross errors from the grouped gas path parameter deviations. The specific steps of step 2 are as follows:

[0137] Step (2-1): For a set of corrected gas path parameter deviations that follow a Gaussian distribution The mean μ and standard deviation σ of this set of data can be calculated using equations (28) and (29).

[0138]

[0139] Step (2-2): This set of data Arrange in ascending order according to formula (30): d (1) <d (2) <…<d (n) (30);

[0140] Step (2-3): Calculate the sorted data according to formula (31). The corresponding statistic g (i) :

[0141] If data point d (i) The corresponding statistic g (i) >g (0) If (n, α), then this point represents a gross error and needs to be removed from the data set, where g (0) (n,α) is the critical value of the statistic when the number of repeated measurements is n and the confidence probability is α, which can be obtained by consulting the Grubbs critical value table;

[0142] Step (2-4): To ensure data integrity, the data d to be removed... i The data is completed using interpolation method (32):

[0143]

[0144] Step (3): Use EEMD-SG to filter and reduce noise in the gas path parameter deviation value D after removing coarse errors: The specific steps are as follows:

[0145] Step (3-1): Based on the EEMD decomposition of gas path parameter deviation values, step 3-1 specifically includes the following steps:

[0146] Step (3-1-1): Set the number of repetitions m of the superimposed Gaussian white noise and the amplitude α of the white noise relative to the standard deviation of the original signal.

[0147] Step (3-1-2): According to formula (33), add Gaussian white noise N with amplitude α to the gas path parameter deviation value D after gross error removal. i The new signal obtained is denoted as

[0148] Step (3-1-3): Use EMD to analyze the new signal The decomposition is performed, and it is decomposed into n intrinsic mode components I according to equation (34). i,j and one residual component R i :

[0149] Step (3-1-4): Repeat steps 3-1-2 and 3-1-3 m times, and calculate the mean values ​​of each IMF component and residual component obtained according to equations (35) and (36) as the intrinsic mode components I after decomposition of the gas path parameter deviation value D. j and residual components R:

[0150]

[0151] Data noise is mainly contained in the high-frequency intrinsic mode components I. h In the above, the noise component is considered, while the signal trend is mainly reflected in the low-frequency intrinsic mode component I. l In the residual component R, it can be regarded as an evolutionary component, so data denoising mainly depends on the high-frequency intrinsic mode component I. h The processing;

[0152] Step (3-2): Use a one-sample t-test to perform a zero-mean test on the cumulative sum of IMF components to distinguish between high-frequency and low-frequency IMFs. Those that pass the test are high-frequency IMFs, and those that fail are low-frequency IMFs. The specific steps are as follows:

[0153] Step (3-2-1): Calculate the cumulative IMF component I according to formula (37). s :

[0154]

[0155] Step (3-2-2): Establish the test hypothesis and determine the significance level: Let the test mean μ = 0, and the null hypothesis H0: μ Is =μ, Alternative hypothesis H1: μ Is ≠μ, significance level α=0.05, where μ Is For the cumulative IMF component I s The mean;

[0156] Step (3-2-3): Select the test method and calculate the test statistic: Calculate the statistic using the one-sample T-test formula (38) and perform a two-tailed test:

[0157]

[0158] In the formula, k——I s The number of samples;

[0159] σ Is —I s Standard deviation;

[0160] Step (3-2-4): Determine the P-value and draw inferences: Calculate t according to equation (38). α,k-1 The value is determined by consulting the T-distribution table. If P > α, then H0 is accepted, and the IMF component I is accumulated. s Pass the zero-mean t-test; if P < α, then accept H1 and accumulate the IMF component I. s The zero-mean t-test was not passed when the cumulative IMF component that passed the test was I. d When j < d, the IMF components are high-frequency signals, and the IMF components with j > d are low-frequency signals.

[0161] Step (4): Smoothing the high-frequency IMF signal using the Savitzky-Golay filter. The specific steps are as follows:

[0162] Step (4-1): For high-frequency IMF components I h Within an overlapping sliding window of equal length, there are 2m+1 consecutive values ​​x. i , i∈(-m,m), and fit the data by constructing a k-th order polynomial (k≤2m+1) according to equation (39).

[0163]

[0164] In the formula a j —Undetermined coefficients of the polynomial;

[0165] Step (4-2): Determine the undetermined coefficients a of the polynomial j The residual E between the data and the original data can be fitted using the least squares method according to equation (40):

[0166]

[0167] Step (4-3): To minimize the residual E, the reciprocal of E with respect to the undetermined coefficients of each polynomial must be zero.

[0168]

[0169] Solving for:

[0170]

[0171] The center point estimate of the window is calculated using the fitted polynomial, and then the high-frequency intrinsic mode components I at any time step are traversed using an equal-length overlapping sliding window. h The signal smoothing process can be completed to obtain the reconstructed high-frequency IMF signal I′. h ;

[0172] Step (5): Reconstruct the deviation value of the gas path parameters after noise reduction: According to formula (43), the high-frequency IMF component I′ obtained after smoothing by the SG filter is... h Low-frequency IMF component l By summing the residual component R, the deviation value D′ of the reconstructed gas path parameters can be obtained.

[0173]

[0174] In the formula I′ i —High-frequency IMF components processed by the SG filter;

[0175] I i —Low-frequency IMF components not processed by the SG filter;

[0176] R is the residual component obtained from EEMD decomposition.

[0177] This invention explores the mapping relationship between the performance of aero-engine airflow components and overall engine performance by constructing a regression model. By adding a convolutional attention mechanism to a multivariate time-series regression model based on CNN-LSTM, a CBA-LSTM multivariate time-series regression model for engine airflow component performance and overall engine performance is built. Furthermore, by incorporating a traditional linear regression model into the model, its sensitivity to linear changes in input parameters is enhanced. This model can predict the overall engine performance index EGTM based on the performance evaluation results of multiple aero-engine airflow components using fingerprint diagrams and airflow parameter deviation values. This provides assistance for pre-repair engine performance warnings, determining the working range of airflow components during repairs, and post-repair engine performance evaluations during actual engine maintenance. Attached image description:

[0178] Appendix Figure 1 This is a graph of the EGTM calculation method in this invention.

[0179] Appendix Figure 2 This is a schematic diagram of the engine EGT and EGTM data in this invention.

[0180] Appendix Figure 3 This is a schematic diagram of the CBAM model structure.

[0181] Appendix Figure 4 This is a schematic diagram of the channel attention structure.

[0182] Appendix Figure 5 This is a schematic diagram of spatial attention structure.

[0183] Appendix Figure 6 This is a schematic diagram of the engine air passage components and overall engine performance regression model based on CBAM in this invention.

[0184] Appendix Figure 7 It is the pre-processed overall performance index EGTM in this invention.

[0185] Appendix Figure 8 It is the mean square error of different hyperparameter pairs on the test set in this invention.

[0186] Appendix Figure 9 This is a structural schematic diagram of the CFM56-5B2 / 3 aircraft engine.

[0187] Appendix Figure 10 This is a schematic diagram of an automatic encoder in an embodiment of the present invention.

[0188] Appendix Figure 11 This is a schematic diagram of the performance evaluation model of multiple components of the engine air passage in an embodiment of the present invention.

[0189] Appendix Figure 12 This is a statistical chart showing the flight mission frequency of the 76 engines in the embodiment.

[0190] Appendix Figure 13 It is the mean squared error of different hyperparameters on the test set in the embodiment.

[0191] Appendix Figure 14 This is a schematic diagram illustrating the performance degradation of the air passage components during the engine's service life, as shown in the embodiment.

[0192] Appendix Figure 15 This is a schematic diagram comparing the input and output of the model reconstruction in the embodiment. Detailed implementation method:

[0193] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0194] To address the performance evaluation needs during actual engine operation and maintenance, this invention constructs a time-series mapping regression model between the performance degradation of engine pneumatic components and the overall engine performance index EGTM, thereby uncovering the mapping relationship between the performance of multiple engine pneumatic components and the overall engine performance.

[0195]

[0196] The mechanical mechanism of engine airflow performance degradation is complex, and the working states of the whole machine and its components are coupled. Therefore, it is difficult to analyze the relationship between engine components and the whole machine by constructing traditional mechanistic models. Furthermore, general multiple linear regression models are difficult to capture the feature evolution trends hidden in the time series, which can easily lead to problems such as low regression model accuracy and difficulty in mining complex mapping relationships.

[0197] The time-series regression model built using deep learning technology can rely on the powerful nonlinear mapping capability of neural networks to autonomously learn the nonlinear mapping function between the performance degradation characteristics of engine air path components and the overall engine performance index EGTM, thereby realizing the mapping relationship between the performance of multiple engine air path components and the overall engine performance.

[0198] This invention first introduces a convolutional attention mechanism into a multivariate time series regression model of engine air path component performance and overall engine performance using a CBA-LSTM engine.

[0199] The convolutional attention mechanism is included in the convolutional attention module.

[53] In the Convolutional Block Attention Module (CBAM), it interacts with the squeezing and excitation networks.

[54] Squeeze-and-Excitation Networks (SENet) and Selective Kernel Networks

[55] Similar to Selective Kernel Networks (SKNet), it is a type of convolutional attention mechanism.

[0200] like Figure 3 As shown, compared to SENet and SKNet, CBAM includes dual attention (DA) in both spatial and channel dimensions. With the help of this dual attention mechanism, the convolutional neural network can focus on important features and suppress unnecessary features during training, thereby improving the model accuracy.

[0201] The principle of the dual attention mechanism in CBAM is as follows:

[0202] (1) Channel Attention (CA)

[0203] Channel attention can effectively capture the performance synergy of each component in the gas path, that is, the working state of each component in the gas path under the current synergistic working state. According to equation (3), it first maps the input features after the performance degradation of the gas path components. Perform mean pooling and max pooling on the channel separately to obtain the mean performance hidden state of the gas path components. With degraded performance in hidden state Then and Information compression is performed in a single hidden-layer MLP with shared parameters, and finally the compressed information is processed. and The summation is performed and activation is applied using a nonlinear mapping function to output the attention weights for each channel.

[0204]

[0205] In the formula σ o —The channel attention non-linear activation function, here we use the Sigmoid function;

[0206] σ i —The nonlinear activation function for the multilayer perceptron, here we use the ReLU function;

[0207] W i —MLP input layer weights;

[0208] W o —MLP output layer weights.

[0209] After obtaining the channel attention weights, the input features mapped to the performance degradation of the gas path components are processed according to Equation (4). Assign channel attention weights.

[0210]

[0211] In the formula — Multiply corresponding elements.

[0212] (2) Spatial Attention (SA)

[0213] Spatial attention can effectively capture the temporal and spatial correlations of various gas path components, i.e., when and which component's performance degrades and its impact on the performance of other gas path components. According to equation (5), the input feature X′ after channel attention weighting is first subjected to mean pooling and max pooling along the channel direction to obtain the current spatiotemporal mean hidden state of the gas path components. With the hidden state of spatiotemporal degradation Then, the features are spliced ​​along the channel direction for feature fusion, and then the convolutional layer is used to extract the time and component features that need attention to generate spatial attention.

[0214]

[0215] In the formula, σ is the spatial attention nonlinear activation function, and the Sigmoid function is used here;

[0216] Convk — Convolution operation with kernel size k.

[0217] After obtaining the spatial attention weights, spatial attention weights are assigned to the input feature X′ after channel attention weighting according to Equation (6).

[0218]

[0219] In the formula — Multiply corresponding elements.

[0220] By introducing CBAM, the regression model can better uncover the spatiotemporal relationship between the collaborative performance degradation of pneumatic components and the overall engine performance EGTM.

[0221] This invention introduces a CBAM module into a two-layer nested CNN structure, and then uses convolutional layers to identify short-term temporal features, performance synergy, and spatiotemporal correlations hidden in the performance degradation of airflow components. The extracted features are then fed into a Long Short-Term Memory (LSTM) network to mine long-term trends. Finally, a CBA-LSTM mapping regression model between engine airflow component performance and overall engine performance is constructed using a linear regression model. Figure 6 As shown.

[0222] The model uses a time length of T and a characteristic parameter of 5 to measure the performance degradation of each component in the engine's airflow path. As input to the model, the overall system performance metric EGTM, with the same time duration, is used as the regression target. First, according to equation (4-7), n 3×3 convolutional kernels are used to linearly map the single-channel input features to n different channels with the same input feature scale, and then a non-linear activation function is used for non-linear feature mapping. Here, a row of zeros is used at the beginning and end to ensure that the parameter dimensions of the input and output are consistent.

[0223]

[0224] In the formula X i,j —The j-th eigenvalue of the i-th convolutional feature surface, i∈(1,n);

[0225] —The input value of the u-th row and v-th column of the convolution region corresponding to the j-th row, j∈(1,T);

[0226] —The weights of the i-th convolutional kernel in the u-th row and v-th column to be learned;

[0227] σ c —Non-linear activation function, here we use the ReLU function.

[0228] Secondly, the mapped multi-channel features Input into the CBAM module, and obtain the weighted mapping features after channel attention and spatial attention weighting according to equations (4) and (6).

[0229] Then, the weighted mapped feature X″ is input into a convolutional layer with n 3×3 kernels for feature compression. Similarly, a row of zeros is used at the beginning and end to ensure that the input and output parameter dimensions are consistent.

[0230]

[0231] In the formula Z i,j —The j-th eigenvalue of the i-th convolutional feature surface, i∈(1,n);

[0232] —The input value of the u-th row and v-th column of the convolution region corresponding to the j-th row, j∈(1,T);

[0233] —The weights of the i-th convolutional kernel in the u-th row and v-th column to be learned;

[0234] σ c —Non-linear activation function, here we use the ReLU function.

[0235] Next, the compression features will be... Input the time series features sequentially into the LSTM initialized with h0 and c0 in state 0, and obtain the time series feature values ​​according to equations (9) to (13).

[0236] f t =sigmoid(W f [h t-1 ;z t ]+b f (9)

[0237] i t =sigmoid(W i [h t-1 ;z t ]+b i (10)

[0238] m t =sigmoid(W o [h t-1 ;z t ]+b o (11)

[0239] c t=f t ·c t-1 +i t ·tanh(W s [h t-1 ;z t ]+b s (12)

[0240] h t =m t ·tanh(c t (13)

[0241] In the formula W f b f W i b i W o b o W s b s —Model parameters to be learned;

[0242] [h t-1 ;z t ]——h t-1 With z i splicing.

[0243] Finally, the time series feature values ​​M are mapped to a nonlinear regression term through a fully connected layer.

[0244]

[0245] In the formula W nl ,b nl —Model parameters to be learned.

[0246] Furthermore, as a linear complement to the nonlinear regression model, a linear regression model is directly added to the nonlinear mapping model to obtain the linear regression term of the model.

[0247]

[0248] In the formula W l ,b l —Model parameters to be learned.

[0249] By combining the nonlinear regression terms according to equation (16) With linear regression term Obtain CBA-LSTM

[0250] Predicted values ​​from the regression model

[0251]

[0252] Using the root mean square error as shown in equation (17) as the loss function of the model, we can test the error between the model's predicted value and the regression target.

[0253]

[0254] Example:

[0255] This study focuses on the CFM56-5B2 / 3 aero engine, which employs a modular design, comprising three main units and six major aerodynamic components. The engine's specific structure is as follows: Figure 9 As shown, this is a typical twin-rotor turbofan aero-engine.

[0256] Based on the properties and functions of fingerprint diagrams, they serve as an important theoretical basis and diagnostic tool in the performance evaluation of engine airflow components. For example, friction between the HPT blades and the casing leads to an increase in blade tip clearance, which in turn reduces HPT efficiency, ultimately reflected in an abnormal increase in the engine exhaust temperature deviation value ΔEGT. Since fingerprint diagrams can be used to explain small deviations in engine airflow parameter values ​​under conditions of efficiency degradation or malfunction of different airflow components, they can be used as mechanistic knowledge to assess the aging or damage of engine airflow components.

[0257] If a decrease in the efficiency of a pneumatic component is considered a performance degradation of that component, then, according to the fingerprint diagram, the symptoms of different faults or performance degradation in the CFM56-5B2 / 3 aero-engine manifest differently in the pneumatic parameter deviation values. When evaluating the performance of a single pneumatic component, it is usually only necessary to consider the pneumatic parameter deviation value D at the time of evaluation. i Deviation D from a certain reference gas path parameter b The difference ΔD between the fingerprints

[0258] The linear relationship between the unit working efficiency decrease of each air circuit component shown in the figure and the influence w of the air circuit parameter deviation value can be used to determine the performance degradation of the air circuit component to be evaluated in the engine, as shown in Equation (1).

[0259]

[0260] In the formula —The uncorrected deviation value of the original gas path parameters at time i;

[0261] x ij —The unit opening angle or unit bleed air leakage of VSV and VBV at time i;

[0262] w j —x in the fingerprint image j The offset caused by deviations in gas path parameters.

[0263] When R=1, it means that the deviation of the gas path parameter caused by the performance degradation of the gas path component being evaluated is consistent with the deviation of the gas path parameter caused by the theoretical unit performance degradation, that is, the performance of the gas path component has degraded by 1%. When R∈(0,1) or R>1, it means that the actual performance degradation is less severe or more severe than the theoretical unit performance degradation, respectively.

[0264] In reality, during actual engine operation, the working states of engine air circuit components are nonlinearly coupled with each other and with the whole engine. The performance degradation of multiple components may be consistent with the performance degradation of a single component in ΔD. If fingerprint diagrams are used directly to evaluate the performance of a single air circuit component, the evaluation will fail during anomaly detection or fault diagnosis.

[0265] In addition, when using fingerprint diagrams to evaluate the performance of multiple gas path components, if the deviation values ​​of gas path parameters are regarded as the set of influences caused by the performance degradation of each gas path component, then according to the fingerprint diagram, the underdetermined equation set shown in equation (2) can be constructed.

[0266] H = W d -1 (ΔD-b) (2)

[0267] In the formula, b is the bias coefficient, b = [b ΔEGT ,b ΔFF ,b ΔN2 ] T ;

[0268] H—Performance degradation of engine air passage components, H = [η] FAN ,η LPC ,η HPC ,η HPT ,η LPT ] T ;

[0269] W d —Based on the fingerprint diagram, the influence weight of the unit performance degradation of each gas path component on the deviation value of the gas path parameter is extracted, as shown in Equation (3).

[0270]

[0271] There are two difficulties in solving this system of equations: 1) W d Since it is not a square matrix, it is difficult to solve for the inverse matrix. 2) The unknowns of this underdetermined equation system (performance degradation of each gas path component) are 5 greater than 3 known quantities (gas path parameter deviation values), and it is impossible to solve by introducing other relevant conditions to construct 2 constraint equations. Therefore, it is impossible to directly use the fingerprint diagram and gas path parameter deviation values ​​to realize the performance evaluation of multiple gas path components under collaborative working conditions.

[0272] Therefore, a data-driven approach can be used, employing deep learning technology to learn the performance H of multiple components in the gas path.

[0273] The deviation value D of the pre-treated air circuit parameters of the engine is compared with the reference value D of the air circuit parameter deviation of this engine model. b The nonlinear mapping relationship between the difference ΔD is shown in Equation (4). Combined with the fingerprint diagram, we can verify whether the learned gas path component performance degradation H is accurate, that is, whether the offset of the gas path parameter deviation value can be restored by using the fingerprint diagram.

[0274] H=f(ΔD=f(DD) b (4)

[0275] In the formula, f is a nonlinear mapping function between the offset ΔD of the gas path parameter deviation value and the performance degradation H of the multiple gas path components.

[0276] As mentioned above, the pre-processed gas path parameter deviation value D can be considered to be the same as the gas path parameter deviation D at a certain reference time. b The fluctuation in the difference ΔD is caused by the performance degradation of various airflow components under the nonlinear coupling operating condition of the engine. As shown in the fingerprint diagram, if the performance degradation H of each airflow component is known, ΔD can be linearly reconstructed from the fingerprint diagram. Therefore, this example utilizes... Figure 2 The automatic encoder shown proposes, as Figure 3 The engine air passage multi-component performance evaluation model is shown.

[0277] Figure 3 The model treats the performance degradation H of each gas path component as an intermediate latent variable, i.e., the encoding target, and uses the preprocessed gas path parameter deviation value D relative to the baseline D. b The inter-component difference ΔD is used as the model input. The nonlinear mapping capability of the encoder is used to mine the performance degradation of each decoupled pneumatic component. Then, the influence of the unit performance degradation of each pneumatic component on the deviation value of the pneumatic parameter in the fingerprint is used as the weight W. d The constructed linear decoder approximates the reconstruction difference ΔD as follows: To minimize ΔD before and after reconstruction Using the loss function L as the objective, the network model parameters θ of the encoder and decoder are trained through the backpropagation algorithm, thereby achieving performance evaluation of multiple components in the engine's air path with the help of the trained encoder.

[0278] Furthermore, due to the collaborative working characteristics of various air passage components in the engine, the degradation process of each component maintains a slow, dynamically balanced degradation characteristic during its service life. This characteristic is hidden in the air passage parameter deviation values, which have one-dimensional time-series features. In the construction of nonlinear encoders, traditional encoders often fail to fully extract these hidden features. Considering the powerful data feature extraction capabilities of Convolutional Neural Networks (CNNs), characterized by weight sharing and local connectivity, a one-dimensional convolutional neural network (1D-CNN) can be specifically used to identify the engine's degradation characteristics. These characteristics can then be input into a traditional encoder, thereby constructing a more powerful nonlinear mapping encoder to uncover the performance degradation of each air passage component hidden in the engine's air passage parameter deviation values.

[0279] The detailed steps for evaluating the performance of multiple components in the engine's airflow system in this example are as follows:

[0280] (1) Feature extraction

[0281] The nonlinear encoder of this model mainly consists of a one-dimensional convolutional neural network and a traditional encoder.

[0282] Traditional 1D-CNNs typically consist of three basic units: convolutional layers, activation layers, and pooling layers. The convolutional and activation layers work together to extract parametric features, while the pooling layers are used to downsampling model parameters. Since this invention uses an autoencoder to reconstruct the input and output, it's necessary to ensure consistency between the data before and after reconstruction. Therefore, the pooling layers used to reduce model parameters need to be removed. The feature extraction process of the 1D-CNN after removing the pooling layers is as follows:

[0283] Construct the input feature surface of the 1D-CNN using ΔD with time length T and feature parameters of 3. By using n 3×3 convolution kernels to perform convolution operations on the input feature surface according to equation (3-5), and then inputting the result of the convolution operation into a nonlinear activation layer, n convolutional feature surfaces Y are output. i .

[0284] Because a 3×3 convolution kernel is used, the output feature surface Y is [value missing] without data padding. i This will reduce the time steps by 2 compared to the original input feature surface X. To ensure that the data length before and after the input is consistent, zeros need to be padded at the beginning and end of the input feature surface X. The padded feature surface

[0285]

[0286]

[0287] In the formula Y i,j —The j-th eigenvalue of the i-th convolutional feature surface, i∈(1,n);

[0288] —The input value of the u-th row and v-th column of the convolution region corresponding to the j-th row, j∈(1,T);

[0289] —The weights of the i-th convolutional kernel in the u-th row and v-th column to be learned;

[0290] σ c —Nonlinear activation function.

[0291] Introducing a non-linear activation function after convolution can transform the original linear mapping feature surface K. i *x j Mapping to a nonlinear space. In the mapped nonlinear space, the original linearly inseparable linear mapping features will have the opportunity to find a linearly separable path, thereby decoupling the performance degradation H of each gas path component under nonlinear coupling working conditions. Commonly used nonlinear activation functions include the Sigmoid function, the Tanh function, and the ReLU function. During use, the Sigmoid function and the Tanh function have the problem of gradient vanishing, and the ReLU function will cause the neurons to "die" due to the negative gradient being set to 0. Therefore, this invention uses the ELU function as the nonlinear activation function of the network, as shown in equation (6).

[0292]

[0293] In the formula, α is the combined weight coefficient, and α = 1.

[0294] This function combines the Sigmoid and ReLU functions, making the network more robust to input features.

[0295] (2) Nonlinear coding

[0296] After extracting features using 1D-CNN, the input of a nonlinear encoder is constructed using convolutional feature surfaces with a time length of T and a number of features of n. It is mapped to a hidden layer H, which is used to characterize the performance degradation of each gas path component after decoupling, through a nonlinear encoder composed of a multilayer perceptron (MLP). The nonlinear mapping relationship is shown in equations (7) and (8).

[0297] Z = σ e (YW′ e +b′ e (7)

[0298] H = ZW e +b e (8)

[0299] In the formula, Z represents the nonlinear output of the encoder input layer.

[0300] H – The encoder output, i.e., the performance degradation of the pneumatic components after decoupling.

[0301] W′ e —The input layer weights of the encoder to be learned.

[0302] σ e —The non-linear activation function of the encoder;

[0303] b′ e —The encoder input layer bias to be learned

[0304] W e —The encoder output layer weights to be learned

[0305] b e —The encoder output layer bias to be learned

[0306] (3) Linear Decoding

[0307] After obtaining the performance degradation H of the decoupled gas path components through feature extraction and nonlinear coding, the influence of the unit performance degradation of each gas path component on the deviation value of the gas path parameters in the fingerprint image can be used as a weight W. d The constructed linear decoder reconstructs the gas path parameter deviation values The linear decoding method is shown in equation (9).

[0308]

[0309] In the formula b d —The decoder bias to be learned

[0310] (4) Parameter optimization

[0311] Since the model aims to minimize the reconstruction error of the gas path parameter deviation before and after reconstruction, the mean square error function as shown in equation (10) can be used as one of the optimization objectives.

[0312]

[0313] In the formula, L1 represents the root mean square error of the deviation values ​​of the gas path parameters before and after reconstruction.

[0314] n — number of samples;

[0315] θ — the model parameters to be learned, θ = {K} i W e ′,b e ′,W e ,b e ,b d};

[0316] —The difference between the reconstructed deviation value of the i-th gas path parameter and the baseline;

[0317] Δd i —The difference between the deviation value of the i-th gas path parameter before reconstruction and the baseline.

[0318] Furthermore, as aero-engines are highly reliable thermomechanical machines, the performance degradation of each component under non-fault conditions should be slow and stable. Considering the collaborative working characteristics of each gas path component, the performance degradation of these components during service should also be synergistic, meaning the performance degradation of each component should be roughly within the same order of magnitude. However, since the impact of unit performance degradation of each gas path component on the aero-engine is not uniform—that is, the degree of disturbance to the gas path parameter deviations differs—to eliminate the inconsistency in performance fluctuation indicators caused by the inconsistent force dimensions of each gas path component, the influence W of unit performance degradation of each gas path component on the gas path parameter deviations can be used as a reference. d The norm of the column vector eliminates the influence of dimensions, so the loss function L2 shown in equation (11) can be constructed to narrow the search range of the optimal parameters and reduce the difficulty of model training.

[0319]

[0320] In the formula, L2 represents the performance degradation loss function of each gas path component.

[0321] η i,j —Performance degradation of the j-th pneumatic component in the i-th sample;

[0322] η 0,j —The initial performance degradation of pneumatic component j, taken as η 0,j =0;

[0323] ||w j ||2——Weight matrix W d The Euclidean norm of the j-th column vector.

[0324] In summary, the loss function of the engine multi-airway component performance evaluation model is shown in equation (12).

[0325]

[0326] This example uses the Adaptive Momentum Estimation (Adam) algorithm to update the parameter θ of the loss function L calculated by forward propagation of the model using back propagation (BP), thereby obtaining the optimal performance evaluation model for multi-gas-path components.

[0327] Experimental verification:

[0328] First, data selection and preprocessing are performed:

[0329] Over 510,000 data points of full-lifecycle operational monitoring data from 76 CFM56-5B2 / 3 aircraft engines with different serial numbers collected from an airline were used as the data basis for model validation. Analysis revealed that the collected operational data included engine takeoff and cruise data. Cruise data acquisition requires stable aircraft and engine operation for more than 5 minutes, with no data changes from onboard sensors within 12 seconds. Therefore, this chapter uses this relatively stable monitoring data to analyze the long-term and slow performance degradation of engine pneumatic components.

[0330] To address the various "imperfections" in the original operating data, the deviation values ​​of the air path parameters were preprocessed. The Grubbs criterion and EEMD-SG were used to preprocess the deviation values ​​of the air path parameters, which effectively eliminated the influence of the engine's unsteady operating conditions on the deviation values ​​of the air path parameters, removed gross errors in the data, and reduced data noise. The deviation values ​​of the air path parameters that were not preprocessed are shown in Table 2.

[0331] Table 2 Deviation values ​​of air path parameters for CFM56-5B2 / 3 aircraft engines

[0332]

[0333] Furthermore, the calculation methods for the deviation values ​​of each gas path parameter are different, resulting in different dimensions among the deviation values ​​of each gas path parameter after preprocessing. To address this, the Euclidean norm of the column vector can be used to standardize it according to equation (13).

[0334]

[0335] In the formula D i —Dimensional deviation of gas path parameters;

[0336] —Pre-processed gas path parameter deviation values;

[0337] ||w i ||2——Weight matrix W d The Euclidean norm of the i-th row vector.

[0338] Performance evaluation model benchmark established:

[0339] Due to differences in manufacturing levels, even engines of the same model may have slightly different factory performance. However, as mentioned in the current research, traditional comprehensive evaluation methods can only reflect the performance differences of the air passage components at different times within the same engine. They cannot provide a unified evaluation benchmark for all engines of that model. That is, they cannot show the changes in component performance at different times for different engine numbers under a certain model relative to a certain benchmark performance of that model. Therefore, it is necessary to reasonably select a set of air passage parameter deviation values ​​for that model of engine as the benchmark D for evaluating the component performance of that engine type. b .

[0340] Therefore, statistical analysis can be performed on the deviation values ​​of the air path parameters generated by new engines of this model within a certain period of service after leaving the factory, and a set of air path parameter deviation values ​​can be determined as the benchmark for evaluating the performance of engine components based on actual needs.

[0341] Statistical analysis of uncorrected engine operating data revealed the daily flight mission frequency of the 76 engines as follows: Figure 3-4 As shown, different color layers correspond to different engine numbers under the same model. It can be seen that for a single engine, the daily flight mission frequency is generally less than 6 times, with 2 flight missions per day being typical.

[0342] Since the task has the highest frequency, the basic data is grouped into sets of two points.

[0343] To avoid the impact of control parameter fine-tuning on the deviation of the gas path parameters during the initial service period of a new engine, 2156 data points were selected from the first two weeks (14 days) of service for each new engine. The worst initial performance point D of the gas path parameter deviation of this type of engine was calculated according to formulas (14) and (15). worst With average initial performance point D average D serves as a benchmark for evaluating the performance of engine components. average .

[0344] D worst =max(D) (14)

[0345]

[0346] In the formula, n represents the sample data size, and n = 2156.

[0347] By solving for the worst initial performance point D of the air path parameter deviation value of the CFM56-5B2 / 3 aero-engine, the worst initial performance point D of the CFM56-5B2 / 3 aero-engine was determined. worst With average initial performance point D average The corresponding deviation values ​​of the gas path parameters are shown in equations (16) and (17).

[0348] As shown.

[0349] D worst = [-57.3590, 2.9160, -9.8380] T (16)

[0350] D average = [-27.3598, 2.2572, -4.7204] T (17)

[0351] Model training and hyperparameter tuning:

[0352] The training steps for the engine airflow multi-component performance evaluation model based on fingerprint diagrams and airflow parameter deviation values ​​are as follows:

[0353] (1) Perform data preprocessing and standardization on the deviation value D of the gas path parameter;

[0354] (2) Select a certain initial performance point as the benchmark, and compare the gas path parameter deviation value D with the benchmark D. b The difference ΔD is used to construct the model dataset;

[0355] (3) Combine 1DCNN and AE to construct a multi-component performance evaluation model of aero-engine air path based on fingerprint diagram and air path parameter deviation value;

[0356] (4) Divide the model training set and test set in a 7:3 ratio;

[0357] (5) Set the model hyperparameters according to Table 3, where the time step T and the number of convolutional kernels n are hyperparameters to be adjusted;

[0358] (6) Use the Adam algorithm combined with the loss function to train the model and search for the optimal value of the hyperparameter to be adjusted;

[0359] (7) Determine the hyperparameters and train the final model;

[0360] (8) Use the trained nonlinear encoder to evaluate the performance of multiple components of the pneumatic circuit;

[0361] (9) Compare the performance evaluation results of the gas circuit components with the maintenance report to verify the accuracy of the model evaluation.

[0362] The time step T and the number of convolutional kernels n are the hyperparameters of the model to be adjusted. The specific steps for parameter search are as follows:

[0363] Given a time step set T = {10, 20, 30} and a kernel number n = {32, 64, 128}, a grid search method is used to determine the hyperparameter values ​​based on the mean squared error on the test set after model training. To avoid interference from the randomness of the neural network and different initialization methods on the model training results, the parameters are trained 10 times for each experiment. The average of the 10 mean squared errors is taken as the mean squared error of that set of parameters, and the set of parameters with the smallest mean squared error is selected as the optimal value of the hyperparameter to be adjusted. The grid search results are as follows: Figure 5 As shown, considering both network model parameters and training accuracy, the optimal time step T = 20 and the number of convolutional kernels n = 64 are selected.

[0364] Table 3 Model Hyperparameters

[0365]

[0366] Application examples of performance evaluation for multi-airway components:

[0367] Due to space limitations, this study only uses the deviation values ​​of the air path parameters during the full life cruise state of a certain CFM56-5B2 / 3 engine from its factory commissioning to its first major overhaul as an example to evaluate the performance of multiple air path components. The performance degradation of each air path component during service, decoupled by the nonlinear encoder of the trained model, is shown in the following figures: Figure 6 The model output and input reconstructed based on the performance evaluation results of the gas path components are as follows: Figure 7 The superscript 'a' indicates that the data has undergone preprocessing and standardization. It is evident that the performance of each decoupled gas path component can be approximately reconstructed from the model's input parameters using the fingerprint diagram.

[0368] The performance of the engine's air passage components before the overhaul, the performance of the air passage components before the overhaul, and the performance of each air passage component are shown in Table 3-4. It can be seen that before the overhaul, the HPT performance of the engine's air passage components deteriorated the most, at 0.6150%.

[0369] Table 4 Performance of the engine's air passage components

[0370]

[0371] Since the actual performance degradation of engine airflow components needs to be measured through physical experiments, and such experimental conditions were not available during the research process of this invention, in order to verify the accuracy of the evaluation results, the diagnostic results of the engine repair work-scope were consulted, which revealed that the cause of engine disassembly was HPT leading edge ablation. This is consistent with the model's evaluation results, which indirectly proves that the model can effectively evaluate the performance degradation of engine airflow components.

[0372] This invention addresses the performance degradation assessment needs of multiple airflow components in aircraft engines. Based on fingerprint images and airflow parameter deviations, and combined with deep learning methods, a performance assessment model for multiple airflow components of aircraft engines is proposed. This model treats the performance degradation of each airflow component as a latent variable. First, the difference between the pre-processed and standardized airflow parameter deviations and the benchmark airflow parameter deviations for this engine model is used as the model input. Then, a nonlinear encoder constructed using 1DCNN and MLP decouples the performance degradation of each airflow component hidden in the airflow parameter deviations. Next, a linear decoder is constructed using the impact of unit performance degradation of the airflow component on the airflow parameter deviations extracted from the fingerprint image as weights. This linear decoder is used to reconstruct the input. The neural network model is then trained with the goal of minimizing the difference between input and output to obtain the optimal decoder parameters. Finally, the trained decoder is used to assess the performance degradation of airflow components. Experiments verify that the airflow component with the most severe performance degradation in the assessment results is consistent with the disassembly and re-engine reasons recorded in the engine's repair work kit, indirectly verifying the effectiveness of the model's assessment results.

[0373] The acquisition of engine cruise data has stringent requirements, while takeoff data acquisition is only recommended when it is closest to the peak EGT of the engine model at takeoff. In practice, it can be measured at full thrust or reduced thrust takeoff under any ambient temperature. The deviation values ​​of the gas path parameters on which the engine gas path multi-component performance evaluation model depends are recorded from the cruise data, but the EGTM, which represents the overall engine performance, is recorded from the takeoff data. Therefore, there is a sample mismatch problem between the gas path multi-component performance evaluation results and the overall engine performance index EGTM, with a data mismatch ratio of approximately 1:1.2.

[0374] To ensure the accuracy of the performance evaluation results for multiple gas path components and to address the mismatch between the performance of multiple gas path components and the overall system performance in the mapping and regression samples, this invention makes the following adjustments to the collected dataset:

[0375] (1) Use the collected full-life cruise data to train the gas path multi-component performance evaluation model, and use the trained model to evaluate the gas path multi-component performance of sample-paired data.

[0376] (2) Perform data pairing. If the deviation value of the air path parameters recorded in the cruise data at time t is used as the input of the air path multi-component performance evaluation model, and the output of the model, i.e. the performance degradation of each component, is used as the input of the CBA-LSTM engine component and whole engine performance multivariate time-series regression model, then the EGTM recorded in the takeoff data immediately following time t is used as the regression target of the model. Filter the dataset and discard mismatched cruise / takeoff data.

[0377] After data pairing, because the EGTM data recorded in the takeoff data and the air path parameter deviation values ​​recorded in the cruise data are physically acquired in the same way, a large amount of noise signals also exist in the EGTM data, such as... Figure 2 As shown in the figure, EGTM data also needs to be denoised. Taking the engine used for multi-component performance evaluation of the gas path as an example, coarse error removal and EEMD-SG filtering algorithms are used to preprocess the EGTM data. The EGTM data before and after preprocessing are shown in the figure. Figure 7 As shown in the figure. After sample pairing, the performance degradation of multiple gas path components and the pre-processed EGTM data are shown in Table (1).

[0378] Table 1 Performance degradation of multiple components in the gas path and EGTM data after pretreatment.

[0379]

[0380] Considering the differences in the dimensions of the data and their respective distribution characteristics, the linear function normalization (Min-Max Normalization) method shown in Equation (18) is used to normalize the data.

[0381]

[0382] In the formula, x represents the data to be preprocessed.

[0383] x * —Data after normalization;

[0384] x min —The minimum value of the data to be preprocessed;

[0385] x max —The maximum value of the data to be preprocessed.

[0386] The training steps for the CBAM-based regression model of engine airflow multi-component performance and overall engine performance are as follows:

[0387] 1) Based on the collected samples, sample pairing was performed, and the Grubbs criterion and EEMD-SG filtering algorithm were used to perform noise reduction filtering on the EGTM data;

[0388] 2) Normalize the dataset and construct the model input in the form of a sliding window;

[0389] 3) Divide the model training set and test set in a 7:3 ratio;

[0390] 4) Construct a performance regression model for engine components and the entire engine based on CBAM;

[0391] 5) Set the model hyperparameters according to Table 4-2, and train the model using the Adam algorithm combined with the loss function;

[0392] 6) Search for the optimal value of the hyperparameter to be adjusted;

[0393] 7) Fix the hyperparameters and train the final model;

[0394] 8) Conduct experiments to compare and verify the model's advancement.

[0395] The time step T, the number of CNN convolutional kernels k, and the number of RNN hidden neurons h are the hyperparameters to be adjusted. Similar to Chapter 3, a grid search method is used to search for hyperparameters. The specific steps are as follows: Let the time step T = {10, 15, 20}, the number of CNN convolutional kernels n = {32, 64, 128}, and the number of RNN hidden neurons h = {16, 32}. For each experiment, the selected parameters are trained 10 times. The mean of the standard deviation is taken as the performance index of this set of hyperparameters, and the hyperparameter with the smallest standard deviation is selected as the model hyperparameter. The grid search results are as follows: Figure 4-8 As shown in a) and 4-8b), the optimal time step T = 15, the number of CNN convolutional kernels k = 128, and the number of RNN hidden neurons h = 32 were finally selected.

[0396] Table 2 Model Hyperparameters

[0397]

[0398] To verify the advancement of the proposed method in mining the mapping relationship between the performance of multiple gas path components and the overall system performance, multiple linear regression (MLR), backpropagation neural network (BPNN), long short-term memory (LSTM) regression network, and temporal convolutional network were employed respectively.

[58] The regression results of Temporal Convolutional Network (TCN), LSTNet, and TPA-LSTM were used as comparative experiments, and the hyperparameter settings of each model were kept as consistent as possible.

[0399] The following are used: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE), and Coefficient of Determination (R-Square, R0). 2 ) and the adjusted R-squared (Adjusted R-squared) 2 As used as a model performance evaluation index to assess the mapping relationship mining effect, as shown in formulas (19) to (23), where RMSE, MAPE, and SMAPE are better the smaller they are. 2 and Adjusted R 2 The closer to 1, the better.

[0400]

[0401]

[0402]

[0403]

[0404]

[0405] In the formula y i —The true value of EGTM;

[0406] —Sample mean of EGTM;

[0407] n — number of samples;

[0408] p — characteristic number.

[0409] Similarly, to avoid interference from neural network initialization and randomness in a single experiment, each experiment was performed 10 times, and the average value of each evaluation index was taken as the evaluation result of the method. The experimental results are shown in Table 3.

[0410] Table 3 Evaluation indicators for different regression methods

[0411]

[0412] It is evident that the engine air path component and overall engine performance mapping regression model constructed based on the convolutional attention mechanism has certain advantages over other time series regression models in various evaluation indicators. Specifically, the CBA-LSTM proposed in this invention achieves a better fit to the overall engine performance EGTM by utilizing the performance degradation of engine air path components.

Claims

1. An aero-engine gas path component performance and engine performance mapping relationship mining method, characterized in that, Includes the following steps: Step 1: Data acquisition and preprocessing, including: Step 1-1-1: Establish a nonlinear encoder model and perform feature extraction. The nonlinear encoder consists of a one-dimensional convolutional neural network and a traditional encoder. A traditional 1D-CNN typically contains three basic units: convolutional layers, nonlinear activation layers, and pooling layers. The convolutional layers and nonlinear activation layers work together to extract parameter features, while the pooling layers are used to downsample the model parameters. Since an autoencoder is used to reconstruct the input and output, it is necessary to ensure consistency between the data before and after reconstruction. Therefore, the pooling layers used to reduce model parameters need to be removed. The feature extraction process of the 1D-CNN after removing the pooling layers is as follows: (The text then continues with a description of a time-length feature extraction process.) The feature parameter is 3 Constructing the input feature surface of 1D-CNN By adopting indivual The convolution kernel performs a convolution operation on the input feature surface according to equation (19), and then inputs the result of the convolution operation into the nonlinear activation layer to output the result. Convolutional feature surfaces ; Because of the adoption The convolution kernel is such that, without data padding, the output feature surface is obtained. It will be relative to the original input feature surface To reduce the number of time steps by two, and to ensure consistent data length before and after input, it is necessary to modify the input feature surface. Fill the beginning and end with 0, and the filled feature surface ; （19）， In the formula, For the first The first convolutional feature surface 1 eigenvalue, ; For the first The first row of the convolution region OK The column's input value, ; The first to be learned The first convolutional kernel OK The weight of the column; It is a non-linear activation function; A non-linear activation function is introduced after convolution to transform the original linear mapping feature surface. Mapping to a nonlinear space, the original linearly inseparable linear mapping characteristics will have the opportunity to find a linearly separable path in the mapped nonlinear space, thereby decoupling the performance degradation of each gas path component under nonlinear coupling operating conditions. The ELU function is used as the nonlinear activation function of the network, as shown in equation (20): (20), where, These are the combined weighting coefficients, taken as follows: ; Step 1-1-2: Perform non-linear encoding: After extracting features using 1D-CNN, the input of a nonlinear encoder is constructed using convolutional feature surfaces with a time length of T and a number of features of n. It is then mapped to a hidden layer, which is used to characterize the performance degradation of each gas path component after decoupling, through a nonlinear encoder composed of a multilayer perceptron (MLP). The nonlinear mapping relationship is shown in equations (21) and (22): (twenty one), (22), where, It is the nonlinear output of the encoder input layer. ; It is the encoder output, i.e., the performance degradation of the pneumatic components after decoupling. ; These are the input layer weights of the encoder to be learned. ; It is the non-linear activation function of the encoder; It is the encoder input layer bias to be learned. ; These are the encoder output layer weights to be learned. ; It is the encoder output layer bias to be learned. ; Step 1-1-3: Perform linear decoding: The performance degradation of decoupled gas path components is obtained through feature extraction and nonlinear coding. Subsequently, the impact of the unit performance degradation of each gas path component on the deviation value of the gas path parameters can be used as a weight in the fingerprint diagram. The constructed linear decoder reconstructs the gas path parameter deviation values The linear decoding method is shown in equation (23): （23）， In the formula, It is the decoder bias to be learned. Step 1-1-4: Parameter optimization: Since the nonlinear encoder model aims to minimize the reconstruction error of the air path parameter deviation before and after reconstruction, the mean square error function as shown in equation (24) is used as one of the optimization objectives. （24）， In the formula, It is the mean square error of the deviation values ​​of the gas path parameters before and after reconstruction; It is the number of samples; These are the model parameters to be learned. ; It is the reconstructed first The difference between the deviation value of each gas path parameter and the reference value; It is the first before the reconstruction The difference between the deviation value of each gas path parameter and the reference value; To eliminate the inconsistency in performance fluctuation indicators caused by the different force dimensions of various gas path components, the influence of unit performance degradation of each gas path component on the deviation value of gas path parameters is utilized. The norm of the column vector eliminates the influence of dimensions, and the loss function is constructed as shown in equation (25). To reduce the difficulty of model training by narrowing the search range for optimal parameters: (25), where, It is a function of the performance degradation loss of each gas path component; It is the first The first sample Performance degradation of individual pneumatic components; It is a pneumatic component The initial performance degradation amount, take ; It is a weight matrix No. The Euclidean norm of a column vector; The loss function of the engine multi-airway component performance evaluation model is shown in equation (26): （26）； Step 2: Establish and train a regression model for the performance of multiple components in the engine's airflow path and the overall engine performance based on CBAM. Step 2-1: Based on the collected samples, perform sample pairing and use the Grubbs criterion and EEMD-SG filtering algorithm to perform noise reduction filtering on the EGTM data; Step 2-2 normalizes the dataset and constructs the model input in the form of a sliding window; Steps 2-3 divide the model training set and test set in a 7:3 ratio; Steps 2-4: Construct a performance regression model for engine components and the entire engine based on CBAM; Steps 2-5: Set the model hyperparameters and train the model using the Adam algorithm combined with a loss function; Steps 2-6: Search for the optimal value of the hyperparameter to be adjusted; Steps 2-7: Fix the hyperparameters and train the final model; Step 3: Apply a regression model of engine airflow multi-component performance and overall engine performance based on CBAM.

2. The method for mining the mapping relationship between the performance of aero-engine gas path components and the overall engine performance according to claim 1, characterized in that, The time step of the model in step 2 Number of CNN convolutional kernels and the number of hidden neurons in RNN To find the hyperparameters of the model to be adjusted, a grid search method is used. The specific steps are as follows: Set the time step. Number of CNN convolutional kernels and the number of hidden neurons in RNN Each experiment uses a fixed set of parameters and trains the model 10 times. The mean of the root mean square error is used as the performance index of the hyperparameters. The hyperparameter with the smallest root mean square error is selected as the model hyperparameter, and finally, the optimal time step is determined. Number of CNN convolution kernels and the number of hidden neurons in RNN .

3. The method for mining the mapping relationship between the performance of aero-engine air passage components and the overall engine performance according to claim 1, characterized in that, Step 1, data acquisition and preprocessing, specifically includes the following steps: Step 1-1: Use the collected full-life cruise data to train the gas path multi-component performance evaluation model, and use the trained model to evaluate the gas path multi-component performance of sample-paired data. Step 1-2: Perform data pairing. If the deviation value of the air path parameters recorded in the cruise data at time t is used as the input of the air path multi-component performance evaluation model, and the output of the model, i.e. the performance degradation of each component, is used as the input of the CBA-LSTM engine component and whole engine performance multivariate time series regression model, then the EGTM recorded in the takeoff data immediately following time t is used as the regression target of the model. Filter the dataset and discard mismatched cruise / takeoff data. After data pairing, since the EGTM data recorded in the takeoff data and the air path parameter deviation value recorded in the cruise data are physically collected in the same way, there is also a lot of noise signal in the EGTM data. Therefore, it is also necessary to reduce the noise of the EGTM data. The coarse error removal and EEMD-SG filtering algorithm are used to preprocess the EGTM data. Steps 1-3: After sample pairing, the data is normalized using the linear function normalization method shown in equation (18): (18); In the formula, The data to be preprocessed; The data has been normalized. The minimum value of the data to be preprocessed; This represents the maximum value of the data to be preprocessed.

4. The method for mining the mapping relationship between the performance of aero-engine gas path components and the overall engine performance according to claim 3, characterized in that, The Grubbs criterion and EEMD-SG were used to preprocess the air path parameter deviation values ​​to eliminate the influence of engine unsteady-state operating conditions on the air path parameter deviation values, thereby removing gross errors and reducing data noise. Specifically: Step (1): For the deviation value of the gas path parameters The correction formula based on the fingerprint image is as follows: （27）， In the formula, yes The uncorrected deviation value of the original gas path parameters at any given time; yes The unit opening angle or unit bleed air leakage of VSV and VBV at any given time; Fingerprint The offset caused by deviations in gas path parameters; Step (2): Use the Grubbs criterion to remove gross errors from the grouped gas path parameter deviations. The specific steps of step 2 are as follows: Step (2-1): For a set of corrected gas path parameter deviations that follow a Gaussian distribution The mean of the data can be calculated using equations (28) and (29). with standard deviation , （28）， （29）， Step (2-2): Transfer the data Arrange in ascending order according to formula (30): (30); Step (2-3): Calculate the sorted data according to formula (31) Corresponding statistics : (31) If data points Corresponding statistics If the data points are large errors, they need to be removed from the data. The number of repeated measurements is The confidence probability is The critical value of the statistical measure at that time was obtained by consulting the Grubbs critical value table. Steps (2-4): To ensure data integrity, the data that was removed... The data is completed using interpolation method (32): (32); Step (3): Use EEMD-SG to analyze the deviation values ​​of the gas path parameters after gross error removal. Noise reduction filtering is performed using the following steps: Step (3-1): Based on the EEMD decomposition of gas path parameter deviation values, step 3-1 specifically includes the following steps: Step (3-1-1): Set the number of repetitions for the superimposed Gaussian white noise. The amplitude of white noise relative to the standard deviation of the original signal Step (3-1-2): According to formula (33), the deviation value of the gas path parameters after gross error removal is calculated. Mid-stack amplitude Gaussian white noise The new signal obtained is denoted as , (33), Step (3-1-3): Use EMD to analyze the new signal Decompose it according to equation (34) into Each intrinsic mode component and 1 residual component : (34), Step (3-1-4): Repeat In steps 3-1-2 and 3-1-3, the mean values ​​of each IMF component and residual component obtained by calculating according to equations (35) and (36) are used as the gas path parameter deviation values. The intrinsic mode components after decomposition and residual components : （35）， （36）， Data noise is mainly contained in the high-frequency intrinsic mode components. In the above, the noise component is considered, while the signal trend is mainly reflected in the low-frequency intrinsic mode components. and residual components In this context, the eigenmode components can be considered as evolutionary components, so data denoising mainly relies on the high-frequency intrinsic mode components. The processing; Step (3-2): Use a one-sample t-test to perform a zero-mean test on the cumulative sum of IMF components to distinguish between high-frequency and low-frequency IMFs. Those that pass the test are high-frequency IMFs, and those that fail are low-frequency IMFs. The specific steps are as follows: Step (3-2-1): Calculate the cumulative IMF component according to formula (37). : （37）， Step (3-2-2): Establish the test hypothesis and determine the significance level: Set the test mean. Null hypothesis H0: Alternative hypothesis H1: Significance level ,in To accumulate IMF components The mean; Step (3-2-3): Select the test method and calculate the test statistic: Calculate the statistic using the one-sample T-test formula (38) and perform a two-tailed test: (38), where, yes The number of samples; yes Standard deviation; Step (3-2-4): Determine the P-value and draw inferences: Calculate the P-value according to equation (38). The value is obtained by referring to the T-distribution table to find the P-value. Then accept H0 and accumulate IMF components. Pass the zero-mean t-test; if Then accept H1 and accumulate IMF components. The zero-mean T-test was not passed when the cumulative IMF component that passed the test was... At that time, in the IMF component The IMF component is a high-frequency signal. The IMF component is a low-frequency signal; Step (4): Smoothing the high-frequency IMF signal using the Savitzky-Golay filter. The specific steps are as follows: Step (4-1): For high-frequency IMF components The corresponding sliding window of equal length with overlapping inner dimensions consecutive values , Construct a by formula (39) polynomial of order Fitting data; (39), where, These are the undetermined coefficients of the polynomial; Step (4-2): Determine the undetermined coefficients of the polynomial. The residuals between the data and the original data can be fitted using the least squares method according to equation (40). : （40）； Step (4-3): To make the residual Minimum, must be made The reciprocal of the undetermined coefficients of each polynomial is 0. （41） Solving for: （42） The center point estimate of the window is calculated using the fitted polynomial, and then the high-frequency intrinsic mode components at any time step are traversed using an equal-length overlapping sliding window. The signal smoothing process can be completed in this way to obtain the reconstructed high-frequency IMF signal. ; Step (5): Reconstruct the deviation value of the gas path parameters after noise reduction: According to formula (43), the high-frequency IMF component obtained after smoothing by the SG filter is converted into the deviation value. Low-frequency IMF components and residual components By summing the values, we can obtain the deviation values ​​of the reconstructed gas path parameters. ; (43), where, It is a high-frequency IMF component processed by an SG filter; It is the low-frequency IMF component that has not been processed by the SG filter; These are the residual components obtained from EEMD decomposition.

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