Fan health evaluation method based on Koopman spatial transformation and mahalanobis distance

Abstract

The invention discloses a Koopman spatial transformation and mahalanobis distance-based fan health evaluation method, which comprises the following steps of: firstly, acquiring a low-frequency signal and a high-frequency vibration signal of a system, preprocessing data, then, constructing a second-order polynomial basis function by utilizing extended dynamic mode decomposition, and solving a Koopman operator to realize global linearization of a nonlinear system; key modes which are low in attenuation rate and are matched with gear abrasion and bearing fault characteristic frequency are screened through eigenvalue decomposition; real-time data is projected to a modal space, the standardized mahalanobis distance between the real-time data and normal state distribution is calculated, a health index model is constructed in combination with historical data, and health degree quantification and graded early warning are achieved. According to the method, the Koopman theory and the statistical distance are combined, the high-dimensional modeling problem of a nonlinear fan system is solved, accurate mapping of fault severity and service life loss is achieved, and the method is suitable for health management of key parts such as gearboxes and bearings and is expanded to the field of rotary machinery such as water pumps and compressors.

Description

Technical Field

[0001] The invention belongs to the technical field of wind turbine status monitoring and fault diagnosis, and in particular relates to a wind turbine health evaluation method based on Koopman space transformation and Mahalanobis distance. Background Art

[0002] At present, mainstream wind turbine health assessment methods include vibration analysis, SCADA data modeling, data-driven AI, etc. However, the above methods still face the following key problems: Low efficiency of multi-source data fusion: Existing unit condition monitoring methods rely on simple weighting or manual feature extraction for the fusion of multi-source heterogeneous data such as vibration, temperature, and power, and fail to effectively explore the dynamic coupling relationship between data, resulting in low information utilization.

[0003] Lack of physical explainability: The diagnostic models used in traditional fault detection methods are generally black box models based on deep learning (such as LSTM and CNN). Although LSTM and CNN can fit complex fault modes, they lack explicit expression of fault mechanisms and are difficult to support causal reasoning for operation and maintenance decisions. Summary of the invention

[0004] The purpose of the present invention is to provide a fan health evaluation method based on Koopman space transformation and Mahalanobis distance, which solves the problems of low efficiency of multi-source data fusion and lack of physical interpretability in nonlinear fan system life prediction methods.

[0005] The technical solution adopted by the present invention is: a fan health evaluation method based on Koopman space transformation and Mahalanobis distance, and the specific operation steps are as follows: Step 1: Collect multi-source operation data of the wind turbine, including low-frequency signals based on the data acquisition and supervisory control system SCADA and high-frequency vibration signals based on the content management system CMS; Step 2: Perform missing value interpolation, noise reduction and time alignment on the multi-source operation data to generate a standard data set; Step 3: Linearize the standard data set in step 2 through Koopman space transformation; decompose it using EDMD extension module to approximately solve the K operator; Step 4: Extract the characteristic modes that characterize the system dynamics in the Koopman space and calculate the Mahalanobis distance between the fault state data and the standard data set; Step 5: Based on the correlation between Mahalanobis distance and historical health data, a fan health evaluation model is established to quantify the health status of the equipment.

[0006] The present invention is also characterized in that: Step 2 is as follows: denoise the high-frequency vibration signal based on wavelet threshold; interpolate the missing values ​​of the low-frequency signal using linear interpolation; and time-align the high-frequency vibration data using the sliding window mean method to make it consistent with the frequency of the low-frequency signal.

[0007] First, the high-frequency vibration signal Decompose into low-frequency approximate coefficients and high frequency detail factor :

[0008] Among them, the low-frequency approximation coefficient Represents the equipment operation trend, high-frequency detail coefficient Represents noise or fault pulses; Again Perform soft thresholding:

[0009] Among them, the threshold Noise standard deviation ; Q is the signal length; It is the highest level detail coefficient in wavelet transform decomposition; right Use low-pass filtering and downsampling to get a low-frequency approximation ; Then reconstruct the high-frequency vibration signal: .

[0010] The missing values ​​of the low-frequency signal are interpolated by linear interpolation, wherein the low-frequency signal includes power P ( t ), speed R ( t ),temperature T ( t ); Calculation time interval [ , ] Power missing value within P ( t ),but:

[0011] in, and Respectively represent the collected and Power data at the moment; speed R ( t ) and temperature T ( t ) is handled in the same way as the power P (t ); The sliding window mean method is used to align the high-frequency vibration data, as follows: Define the high frequency vibration data sampling window width , take the average of all high-frequency vibration signal data in the window, the formula is as follows:

[0012] in, is the vibration signal of the target frequency, is the number of window data points, yes The vibration signal at the moment, is the sampling interval, is the sampling time; if the sampling frequency is 1 Hz, set Δt=0.5s; Step 3 is as follows: Construct second-order polynomial basis functions; Among them, the second-order polynomial basis function contains the following items: The system data processed in step 2 is used as the state observation data, including the current state and the next moment state in, is the time step; ∈Rn is the state vector, Rn represents the spatial domain;

[0013] Construct a second-order polynomial basis function vector, which contains square terms and cross terms:

[0014] in, :temperature, P :power, : rotation speed, : Vibration effective value, : Bearing outer ring fault frequency energy, : wind speed, : represents the frequency ~ Band energy, :Wavelet packet decomposition extraction Band energy; Indicates the decomposition level, Represents a decomposition node.

[0015] Let the total number of basis functions be , the order should be 2 according to the system complexity. n is the system characteristic number, and this basis function designs 8 characteristics in total;

[0016] Each state point x i Mapped to the basis function space, forming a basis function matrix:

[0017]

[0018] Solving the approximate Koopman operator matrix by the least squares method , m is the number of basis functions;

[0019]

[0020] in represents the Moore-Penrose pseudoinverse, which is calculated as:

[0021] Then the Koopman operator matrix K Perform eigenvalue decomposition:

[0022] Among them, Λ is the eigenvalue diagonal matrix, Φ is the eigenvector matrix, and the eigenvector corresponds to the spatial distribution of the mode; Then use the Koopman operator to predict system dynamics:

[0023] Compare the predicted results with the real data, calculate the mean square error (MSE) or visualize the trajectory, and verify the accuracy of the Koopman operator matrix.

[0024] Step 4 is as follows: Step 4.1: Koopman operator matrix K Perform eigenvalue decomposition: KΦ=ΦΛ Where Λ is the eigenvalue diagonal matrix, Λ=diag(λ1,λ2,…,λ m );Eigenvalues ​​λ1,λ2,…,λ m The amplitude and phase of reflect the attenuation rate and frequency of the mode, Φ is the eigenvector matrix, , Represents the modality; Step 4.2: Screening Koopman modes related to physical faults: Step 4.2.1: Decay rate screening: Select the mode Re(λ) whose real part of eigenvalue is close to zero i )≥ , = 0.1; these modes correspond to long-term dynamic or steady-state oscillations of the system; Step 4.2.2: Energy sorting: Calculate the modal energy corresponding to the modes selected in step 4.2.1 , retaining the highest energy k modality; k The value ranges from 10 to 50; Step 4.2.3: Combined with the fault characteristic frequency, the mode of the corresponding fault frequency band is further selected on the basis of step 4.2.2; the fault characteristics include gear wear, broken teeth, tooth surface chipping, gear eccentricity, bearing internal and external gear failure, and shaft crack; Step 4.2 is as follows: ① Screening modal frequency Koopman eigenvalue λ i = a i +j b i , matrix K The real part of a i : Determines the stability or decay rate of the mode if a i is negative, the mode will decay over time; if a i is positive, the mode will grow; matrix K Learning the evolution of basis functions over time, for FFT band energy terms , whose evolution is modeled as a linear combination:

[0025] The FFT band energy terms affect the Koopman matrix through the periodicity of their time evolution K Even if the energy term itself is real, its dynamic changes (such as fluctuations modulated by speed) will be K The oscillation frequencies captured as complex eigenvalues. The proposed method incorporates the speed design basis function to ensure that the fault frequencies are transferred to the eigenvalues ​​through the coupling mechanism.

[0026] So the matrix K The imaginary part j b i : The oscillation frequency of the corresponding mode, that is, the vibration frequency of the system in this mode, j represents the imaginary part; the key modes are screened by calculating the eigenvalue frequency; Calculating modal frequencies :

[0027] ② Screening the key modes that match the fault characteristic frequency: the screening conditions are: ,After the screening is completed, a key modal matrix is ​​formed; is the fault characteristic frequency threshold, is the frequency of each type of fault, Based on expert experience; ③ After screening out the key modes, normal state modeling is performed; Get from the preprocessed canonical dataset Status data of normal operating units Substituting into the basis function we get

[0028]

[0029]

[0030] in, is the key mode matrix after screening; , is the number of modes screened out, m is the total number of basis functions; ④Calculation The mean and covariance of :

[0031]

[0032] in, Representative i samples, yes The number of samples, N ≥100, express Each sample in ⑤According to the method in step ③, the fault data Projected into the same modal space, , and finally calculate the fault state Mahalanobis distance.

[0033] Step 4 The calculation of Mahalanobis distance is as follows:

[0034] : Pseudo-inverse of the regularized covariance matrix; Step 5 is as follows: Dynamically associate the Mahalanobis distance with the health index and output a health score of 0% to 100%; the health index is used to trigger graded warnings; the graded warnings include three states: normal, warning, and emergency; calculate the Mahalanobis distance between the fault data and the normal state, and set the distance threshold Dth; Taking gear wear as an example, according to historical data statistics, the average Mahalanobis distance of normal gear wear is D≤20, the range of D is about 20~80 for slight wear, and D>80 for severe wear. Therefore, Dth=80 is set according to expert experience, that is, when D≥80, it is considered that wear has affected operation. Health Index

[0035] Among them, α is the time attenuation coefficient, the initial value is 0.5%; β: distance attenuation coefficient, the initial value is 2%; T over: the cumulative time of the Mahalanobis distance exceeding the distance threshold Dth, Tover =∑(ti | Di≥Dth); D max: maximum Mahalanobis distance during the fault period; Through the health index formula, a linear regression model is constructed to obtain historical data of the SCADA and CMS systems, calculate the time series Mahalanobis distance D, the over-threshold duration Tover, and the maximum Mahalanobis distance Dmax during the fault period, feed the regression model, optimize α and β, and adjust Dth.

[0036] When HI<50%, it indicates an emergency state; When 50% ≤HI≤70%, it indicates a warning state; When HI>70%, it indicates normal status.

[0037] The beneficial effects of the present invention are: the present invention introduces the Koopman operator into the multi-source data fusion analysis of the fan, breaking through the bottleneck of nonlinear system modeling; it realizes the accurate mapping of fault severity and life loss, which is suitable for the health management of key components such as gearboxes and bearings, and is extended to the field of rotating machinery such as water pumps and compressors. Specific advantages also include: engineering practicality: quantifying the impact of faults through Mahalanobis distance, directly supporting operation and maintenance decisions (such as spare parts scheduling, maintenance priority); compatibility: it can be extended to the life prediction scenarios of other rotating machinery (water pumps, compressors). BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of the fan health evaluation method based on Koopman space transformation and Mahalanobis distance of the present invention; Figure 2 It is a schematic diagram of Koopman space transformation and feature extraction of the present invention. DETAILED DESCRIPTION

[0039] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] Example 1 The present invention proposes a fan health evaluation method based on Koopman space transformation and Mahalanobis distance, such as Figure 1-2 As shown, it mainly includes the following steps: Step 1: Collect multi-source operation data of the wind turbine, including low-frequency signals based on the data acquisition and supervisory control system SCADA and high-frequency vibration signals based on the content management system CMS; Step 2: performing noise reduction, missing value interpolation and time alignment on the multi-source operation data, and generating a standard data set after standardization; Step 3: Linearize the standard data set in step 2 through Koopman space transformation; decompose it using EDMD extension module to approximately solve the K operator; Step 4: Extract the characteristic modes that characterize the system dynamics in the Koopman space and calculate the Mahalanobis distance between the fault state data and the standard data set; Step 5: Based on the correlation between the Mahalanobis distance and the historical health data, a fan health evaluation model is established to quantify the health status of the equipment.

[0041] Example 2 Based on Example 1, step 2 is as follows: denoising the high-frequency vibration signal based on wavelet threshold; interpolating missing values ​​of the low-frequency signal using linear interpolation; and time-aligning the high-frequency vibration data using a sliding window mean method to make it consistent with the frequency of the low-frequency signal.

[0042] First, the high-frequency vibration signal Decompose into low-frequency approximate coefficients and high frequency detail factor :

[0043] Among them, the low-frequency approximation coefficient Represents the equipment operation trend, high-frequency detail coefficient Represents noise or fault pulses; Again Perform soft thresholding:

[0044] Among them, the threshold Noise standard deviation ; Q is the signal length; It is the highest level detail coefficient in wavelet transform decomposition; right Use low-pass filtering and downsampling to get a low-frequency approximation ; Then reconstruct the high-frequency vibration signal: .

[0045] The missing values ​​of the low-frequency signal are interpolated by linear interpolation, wherein the low-frequency signal includes power P ( t ), speed R ( t ),temperature T ( t ); Calculation time interval [ , ] Power missing value within P ( t ),but:

[0046] in, and Respectively represent the collected and Power data at the moment; speed R ( t ) and temperature T ( t ) is handled in the same way as the power P ( t ); The sliding window mean method is used to align the high-frequency vibration data, as follows: Define the high frequency vibration data sampling window width , take the average of all high-frequency vibration signal data in the window, the formula is as follows:

[0047] in, is the vibration signal of the target frequency, is the number of window data points, yes The vibration signal at the moment, is the sampling interval, is the sampling time; if the sampling frequency is 1 Hz, set Δt=0.5s; Example 3 Based on Example 2, step 3 is as follows: Construct second-order polynomial basis functions; Among them, the second-order polynomial basis function contains the following items: The system data processed in step 2 is used as the state observation data, including the current state and the next moment state in, is the time step; ∈Rn is the state vector;

[0048] Construct a second-order polynomial basis function vector (including square terms and cross terms)

[0049] in, :temperature, P :power, : rotation speed, : Vibration effective value, : Bearing outer ring fault frequency energy, : wind speed, : represents the frequency ~ Band energy, :Wavelet packet decomposition extraction Band energy; Indicates the decomposition level, Represents a decomposition node; The total number of basis functions is , , according to the complexity of the system, the order is selected as 2, n is the system characteristic number, n =8;

[0050] Each state point x i Mapped to the basis function space, forming a basis function matrix:

[0051]

[0052] Solving the approximate Koopman operator matrix by the least squares method , m is the number of basis functions;

[0053]

[0054] in, represents the Moore-Penrose pseudoinverse, which is calculated as:

[0055] Then the Koopman operator matrix K Perform eigenvalue decomposition:

[0056] Among them, Λ is the eigenvalue diagonal matrix, Φ is the eigenvector matrix, and the eigenvector corresponds to the spatial distribution of the mode; Then use the Koopman operator to predict system dynamics:

[0057] Compare the predicted results with the real data, calculate the mean square error (MSE) or visualize the trajectory, and verify the accuracy of the Koopman operator matrix.

[0058] Example 4 Based on Example 3, step 4 is as follows: Step 4.1: Koopman operator matrix K Perform eigenvalue decomposition: KΦ=ΦΛ Where Λ is the eigenvalue diagonal matrix, Λ=diag(λ1,λ2,…,λ m ), the amplitude and phase of the eigenvalue reflect the attenuation rate and frequency of the mode, Φ is the eigenvector matrix, ; Step 4.2: Screening Koopman modes related to physical faults: Step 4.2.1: Decay rate screening: Select the mode Re(λ) whose real part of eigenvalue is close to zero i )≥ , = 0.1; these modes correspond to long-term dynamic or steady-state oscillations of the system; Step 4.2.2: Energy sorting: Calculate the modal energy corresponding to the modes selected in step 4.2.1 , retaining the highest energy k modality; k The value ranges from 10 to 50; Step 4.2.3: Combined with the fault characteristic frequency, the mode of the corresponding fault frequency band is further selected on the basis of step 4.2.2; the fault characteristics include gear wear, broken teeth, tooth surface chipping, gear eccentricity, bearing internal and external gear failure, and shaft crack; Among them, the gear meshing frequency f GM=

[0059] N m : number of gear teeth, fr : Shaft speed (Hz) Bearing fault frequency (such as outer ring fault frequency )

[0060] Nb : Number of rolling elements; d: rolling element diameter; D 0 : bearing pitch diameter; : Contact angle Step 4.2 is as follows: ① Screening modal frequency Koopman eigenvalue λ i = a i +j b i , Real part a i : Determines the stability or decay rate of the mode if a i is negative, the mode will decay over time; if a i is positive, the mode will grow; Imaginary part b i : b i The oscillation frequency of the corresponding mode, that is, the vibration frequency of the system in this mode, j represents the imaginary part; Calculating modal frequencies :

[0061] ② Screening the key modes that match the fault characteristic frequency: the screening conditions are: ,After the screening is completed, a key modal matrix is ​​formed; is the fault characteristic frequency threshold, is the frequency of each type of fault, Based on expert experience; ③ After selecting the key modes, normal state modeling is performed. Projection into the critical modal space: First, collect 100 sets of 8 features of data X _normal is extended to the basis function,

[0062] in, is the key mode matrix after screening; , is the number of modes screened out, m is the total number of basis functions; ④Calculation The mean and covariance of :

[0063]

[0064] in, Representative i samples, yes The number of samples, express Each sample in .

[0065] ⑤According to the method in step ③, the fault data Projected into the same modal space, , and finally calculate the fault state Mahalanobis distance.

[0066] The projection of step ③ and step ⑤ can be understood as projecting the system into an infinite-dimensional space. Taking three-dimensional space as an example, a certain fault mode is a corresponding line in three-dimensional space. The direction of the line is fixed, and a certain point on the line is The entire line is , projected in a certain direction. This direction represents a certain fault type. The system is linear. Now calculate its Mahalanobis distance according to the projection of the linear system.

[0067] Step 4 The calculation of Mahalanobis distance is as follows:

[0068] : Pseudo-inverse of the regularized covariance matrix; Example 5 Based on Example 4, step 5 is specifically as follows: Dynamically associate the Mahalanobis distance with the health index and output a health score of 0% to 100%; the health index is used to trigger graded warnings; the graded warnings include three states: normal, warning, and emergency; calculate the Mahalanobis distance between the fault data and the normal state, and set the distance threshold D th =80 Building a health index model

[0069] Among them, α is the time attenuation coefficient, the initial value is 0.5%; β: distance attenuation coefficient, the initial value is 2%; T over: The cumulative time of the Mahalanobis distance exceeding the distance threshold Dth, Tover =∑(t i | D i ≥Dth); D max: maximum Mahalanobis distance during the fault period; Through the health index formula, a linear regression model is constructed, the historical data of the SCADA and CMS systems are obtained, the time series Mahalanobis distance D, the over-threshold duration Tover, and the maximum Mahalanobis distance Dmax during the fault are calculated, the regression model is fed, and α and β are optimized. When HI<50%, it indicates an emergency state; When 50% ≤HI≤70%, it indicates a warning state; When HI>70%, it indicates normal status.

[0070] Example 6 Step 1: Collect 30-day operation data of a wind turbine, including: SCADA low-frequency signal (1Hz): power P(t), speed R(t), gearbox temperature T(t).

[0071] CMS high-frequency vibration signal (10kHz): axial vibration acceleration V(t), bearing outer ring fault frequency f extracted by FFT bpfo =85Hz, gear meshing frequency f mesh =320Hz.

[0072] Step 2: Data Preprocessing Time Alignment: The CMS data (10kHz→1Hz) was aggregated using a sliding window mean with Δt=0.5s and window data points Nwindow=10,000.

[0073] Missing values ​​of SCADA data (e.g., power loss at a certain time t=12:05) are completed by linear interpolation.

[0074] Wavelet threshold denoising: Decompose the vibration signal x(t) into 5 layers, estimate the noise standard deviation σ=0.12, and the threshold λ=0.25.

[0075] After denoising, the signal-to-noise ratio is improved to SNR=28.6dB.

[0076] Step 3: Koopman space transformation Construct second-order polynomial basis functions, including , Equal original variables and cross terms, total dimension m =45.

[0077] Solving the Koopman operator matrix K ∈R45×45, verification prediction error MSE=0.023.

[0078] Step 4: Key mode extraction and Mahalanobis distance calculation Feature value screening: Decompose K to get the eigenvalue λi, screening condition: Re(λi)≥-0.1, retain the previous k =20 high energy modes. Matching the characteristic frequency of gear wear =320Hz, filter out the mode =318Hz( =2Hz).

[0079] Normal state modeling: Select 100 groups of normal data and project them into the key modal space, and calculate the mean μ=[1.2,-0.4,...,0.7] T and the covariance matrix Σ.

[0080] Fault Data Projection: The fault data X fault After basis function mapping, we get =[2.8,-1.1,...,3.5] T .

[0081] Calculate the Mahalanobis distance: .

[0082] Step 5: Health assessment and graded warning Set the threshold Dth=80, and the accumulated time of exceeding the threshold T over =6h, maximum distance D max=92.3; Health Index Calculation:

[0083] Output result: Current HI=72.4%>70%, triggering the warning state, indicating that the gear is slightly worn.

Claims

1. A wind turbine health assessment method based on Koopman space transformation and Mahalanobis distance, characterized in that: The specific steps are as follows: Step 1: Collect multi-source operation data of the wind turbine, including low-frequency signals based on the data acquisition and supervisory control system SCADA and high-frequency vibration signals based on the content management system CMS; Step 2: Perform noise reduction, missing value interpolation and time alignment on the multi-source operation data to generate a standard data set; Step 3: Linearize the standard data set in step 2 through Koopman space transformation; decompose it using EDMD extension module to approximately solve the K operator; Step 4: Extract the characteristic modes that characterize the system dynamics in the Koopman space and calculate the Mahalanobis distance between the fault state data and the standard data set; Step 5: Based on the correlation between the Mahalanobis distance and the historical health data, a fan health evaluation model is established to quantify the health status of the equipment.

2. The wind turbine health evaluation method based on Koopman space transformation and Mahalanobis distance according to claim 1 is characterized in that: Step 2 is as follows: denoise the high-frequency vibration signal based on wavelet threshold; interpolate the missing values ​​of the low-frequency signal using linear interpolation; and time-align the high-frequency vibration data using the sliding window mean method.

3. The wind turbine health evaluation method based on Koopman space transformation and Mahalanobis distance according to claim 2 is characterized in that: Step 2: For high-frequency noise and fault impact in high-frequency vibration signals, wavelet threshold denoising is used, as follows: First, the high-frequency vibration signal Decompose into low-frequency approximate coefficients and high frequency detail factor : Among them, the low-frequency approximation coefficient Represents the equipment operation trend, high-frequency detail coefficient Represents noise or fault pulses; Again Perform soft thresholding: Among them, the threshold Noise standard deviation ; Q is the signal length; It is the highest level detail coefficient in wavelet transform decomposition; right Use low-pass filtering and downsampling to get a low-frequency approximation ; Then reconstruct the high-frequency vibration signal: 。 4. The wind turbine health evaluation method based on Koopman space transformation and Mahalanobis distance according to claim 3 is characterized in that: ① Use linear interpolation to interpolate missing values ​​of low-frequency signals, including power P ( t ), speed R ( t ),temperature T ( t ); Calculation time interval [ , ] Power missing value within P ( t ),but: in, and Respectively represent the collected and Power data at the moment; speed R ( t ) and temperature T ( t ) is handled in the same way as the power P ( t ); ② The sliding window mean method is used to align the high-frequency vibration data, as follows: Define the high frequency vibration data sampling window width , take the average of all high-frequency vibration signal data in the window, the formula is as follows: in, is the vibration signal of the target frequency, is the number of window data points, yes The vibration signal at the moment, is the sampling interval, is the sampling time; if the sampling frequency is 1 Hz, set Δt=0.5s.

5. The wind turbine health evaluation method based on Koopman space transformation and Mahalanobis distance according to claim 4 is characterized in that: Step 3 is as follows: The system data processed in step 2 is used as state observation data. The state observation data includes the current state and the next moment state in, is the time step; ∈Rn is the state vector; Construct second-order polynomial basis functions: Construct a second-order polynomial basis function vector: in, :temperature, P :power, : rotation speed, : Vibration effective value, : Bearing outer ring fault frequency energy, : wind speed, : represents the frequency ~ Band energy, :Wavelet packet decomposition extraction Band energy, Indicates the decomposition level, Represents a decomposition node; Let the total number of basis functions be , according to the complexity of the system, the order is selected as 2, n is the system characteristic number; Each state point x i Mapped to the basis function space, forming a basis function matrix: Solving the approximate Koopman operator matrix by the least squares method : in represents the Moore-Penrose pseudoinverse, which is calculated as: Then the Koopman operator matrix K Perform eigenvalue decomposition: Among them, Λ is the eigenvalue diagonal matrix, Φ is the eigenvector matrix; Then use the Koopman operator to predict system dynamics: Compare the predicted results with the real data to verify the accuracy of the Koopman operator matrix.

6. The wind turbine health evaluation method based on Koopman space transformation and Mahalanobis distance according to claim 5 is characterized in that: Step 4 is as follows: Step 4.1: Koopman operator matrix K Perform eigenvalue decomposition: K F=FL Where Λ is the eigenvalue diagonal matrix, Λ=diag(λ1,λ2,…,λ m );Eigenvalues ​​λ1,λ2,…,λ m The amplitude and phase reflect the attenuation rate and frequency of the mode, and the eigenvector matrix ; Represents the modality; Step 4.2: Screening Koopman modes related to physical faults: Step 4.2.1: Attenuation rate screening: Select the eigenvalue real part Re(λ i )≥ The modality, =0.1; Step 4.2.2: Energy sorting: Calculate the modal energy corresponding to the modes selected in step 4.2.1 , retaining the highest energy k modality; k The value ranges from 10 to 50; Step 4.2.3: Combined with the fault characteristic frequency, the mode of the corresponding fault frequency band is further selected on the basis of step 4.2.2; the fault characteristics include gear wear, broken teeth, tooth surface chipping, gear eccentricity, bearing internal and external tooth faults, and shaft cracks.

7. The wind turbine health evaluation method based on Koopman space transformation and Mahalanobis distance according to claim 6 is characterized in that: Step 4.2 is as follows: ① Screening modal frequency Koopman eigenvalue λ i = a i +j b i , matrix K The real part of a i : Determines the stability or decay rate of the mode, if a i If it is negative, the mode will decay over time; if a i is positive, the mode will grow; matrix K The imaginary part j b i : b i The oscillation frequency of the corresponding mode, that is, the vibration frequency of the system in this mode, j represents the imaginary part; the key modes are screened by calculating the eigenvalue frequency, Calculating modal frequencies : ② Screening the key modes that match the fault characteristic frequency: The screening conditions are: ,After the screening is completed, a key modal matrix is ​​formed; is the fault characteristic frequency threshold, is the frequency of occurrence of each type of fault; ③ After selecting the key modes, normal state modeling is performed: Obtained from the preprocessed canonical dataset N Normally operating units and State data at the same time step Substituting into the basis function we get ; in, is the key mode matrix after screening; , is the number of modes screened out, m is the total number of basis functions; ④Calculation The mean and covariance of : in, Representative i samples, yes The number of samples, express Each sample in ⑤According to the method in step ③, the fault data Projected into the same modal space, , , and finally calculate the fault state Mahalanobis distance.

8. The wind turbine health evaluation method based on Koopman space transformation and Mahalanobis distance according to claim 7 is characterized in that: Step 4 The calculation of Mahalanobis distance is as follows: : Pseudoinverse of the regularized covariance matrix.

9. The wind turbine health assessment method based on Koopman space transformation and Mahalanobis distance according to claim 8 is characterized in that: Step 5 is as follows: Dynamically associate the Mahalanobis distance with the health index formula to output a health score of 0% to 100%; the health index is used to trigger graded warnings and maintain priority sorting; the graded warnings include three states: normal, warning, and emergency; Calculate the Mahalanobis distance between the fault data and the normal state, and set the distance threshold Dth; Health index HI = 100% - α T over-β D max Among them, α is the time attenuation coefficient, the initial value is 0.5%; β is the distance attenuation coefficient, the initial value is 2%; T over is the cumulative time of the Mahalanobis distance exceeding Dth; D max is the maximum Mahalanobis distance during the fault period; Through the health index formula, a linear regression model is constructed to obtain historical data of the SCADA and CMS systems, calculate the time series Mahalanobis distance D, the over-threshold duration Tover, and the maximum Mahalanobis distance Dmax during the fault period, feed the linear regression model, optimize α and β, and adjust Dth; When HI < 50%, it indicates an emergency state; When 50% ≤HI≤70%, it indicates a warning state; When HI>70%, it indicates normal status.

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