Pump turbine S characteristic braking area identification method based on self-organizing kernel regression

Abstract

The invention discloses a pump turbine S characteristic braking area identification method based on self-organizing kernel regression. The method specifically comprises the following steps that 1, pressure pulsation signals and vibration signals of all measuring points on a pump turbine under the operation working condition are collected in real time; step 2, constructing a feature index vector in an ith window length time period corresponding to each measuring point; 3, constructing a characteristic matrix X containing the pressure pulsation signal and the vibration signal, and standardizing the characteristic matrix X to obtain a standardized matrix Y; step 4, calculating the similarity between the standardized characteristic values of each window length time period; 5, solving expected state data; 6, solving a diagonal covariance matrix according to the variance of the expected state data; 7, solving a health index according to the diagonal covariance matrix; and 8, judging whether the operating condition of the pump turbine enters an S characteristic braking area or not. By adopting the method, whether the pump turbine enters the S characteristic braking area or not can be accurately judged.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydraulic machinery and relates to a method for identifying the "S" characteristic braking area of a pump-turbine based on self-organizing kernel regression. Background Art

[0002] As a hydraulic machinery device capable of realizing energy storage, the pump-turbine is widely used in the power system, so its operation stability is crucial to the safety of the power system. The pump-turbine has an ineliminable "S" characteristic braking area. After entering the "S" characteristic braking area, the phenomenon of hydraulic characteristic fluctuation will occur, which will further cause the vibration of the pump-turbine and the oscillation of the runner torque, seriously affecting the stability of the unit and resulting in the adverse consequence of grid connection failure. Therefore, it is crucial to propose a method for accurately determining whether the pump-turbine enters the "S" characteristic braking area for improving the operation stability of the pump-turbine and upgrading the operation and maintenance strategy. In previous studies, there is a lack of a quantitative criterion for determining whether the pump-turbine enters the "S" characteristic braking area, and there is also a lack of a method for determining whether the pump-turbine enters the "S" characteristic braking area based on measured vibration and pressure pulsation data, and it is impossible to provide effective early warning technical measures when the pump-turbine enters the "S" characteristic braking area during actual operation. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for identifying the "S" characteristic braking area of a pump-turbine based on self-organizing kernel regression. By using this method, it is possible to accurately determine whether the pump-turbine enters the "S" characteristic braking area.

[0004] The technical solution adopted by the present invention is a method for identifying the "S" characteristic braking area of a pump-turbine based on self-organizing kernel regression, which specifically includes the following steps:

[0005] Step 1, collect the pressure pulsation signals and vibration signals of each measurement point on the pump-turbine in real time under the operating conditions;

[0006] Step 2, construct the characteristic index vector in the i-th window length time period corresponding to each measurement point;

[0007] Step 3, construct a characteristic matrix X including the pressure pulsation signal and the vibration signal, and standardize the characteristic matrix X to obtain a standardized matrix Y;

[0008] Step 4, calculate the similarity between the standardized characteristic values in each window length time period;

[0009] Step 5, obtain the expected state data through the calculation result of Step 4;

[0010] Step 6, obtain the diagonal covariance matrix according to the variance of the expected state data;

[0011] Step 7, obtain the health index according to the diagonal covariance matrix;

[0012] Step 8: Calculate the standard deviation of the health index vector, and determine whether the operating condition of the pump-turbine enters the "S" characteristic braking zone according to the standard deviation.

[0013] The features of the present invention also lie in:

[0014] The specific process of step 2 is as follows:

[0015] Step 2.1: Perform time-domain windowing calculation on each collected pressure pulsation and vibration signal, and determine the window function as the Hanning window;

[0016] Step 2.2: Calculate the mean value F of the signal in each window length time period through the following formulas (1) to (7) 1p , variance F 2p , root mean square value F 3p , peak-to-peak value F 4p , absolute mean value F 5p , skewness F 6p , kurtosis F 7p , and impulse factor F 8p , where the subscript p represents the number of the pressure pulsation or vibration measurement point, p = 1, 2, 3,..., 8;

[0017]

[0018] F 4p = max[x(k)] - min[x(k)] (4)

[0019]

[0020] F 8p = max[x(k)] / F 5p (8)

[0021] Among them, x(k) represents the signal data to be analyzed, k = 1, 2,..., N, and N is the length of the signal data to be analyzed;

[0022] Step 2.3: Construct the characteristic index vector x corresponding to the index of each measurement point in the i-th window length time period p , x p , and the expression is as shown in formula (9):

[0023] x p = [F 1p , F 2p , F 3p , F 4p , F 5p , F 6p , F 7p , F 8pp = 1, 2, 3, …, 8 (9).

[0024] The specific process of step 3 is as follows:

[0025] Step 3.1: The characteristic index vector x of the vibration and pressure pulsation signals extracted in step 2 is uniformly constructed into a characteristic matrix X. The size of the matrix X is n×m, where n is the number of window length time periods and m is the number of characteristics. Each row X(i, :) represents the characteristic values of the i-th window length time period, and each column X(:, j) represents the j-th characteristic: p X = [x1, x2, …, x

[0026] p = 1, 2, 3, …, 8 (10) p Step 3.2: The characteristic matrix X is standardized through formula (11) to obtain a standardized matrix Y, such that the mean of each characteristic is 0 and the standard deviation is 1:

[0027]

[0028]

[0029] where μ j is the mean of the j-th column of characteristic values, and σ j is the standard deviation of the j-th column of characteristics.

[0030] The specific process of step 4 is as follows:

[0031] The similarity between the characteristic values of each window length time period is calculated using the Gaussian kernel function. Each element K(a, b) in the kernel matrix represents the similarity between the standardized characteristic vectors of the a-th and b-th window length time periods. The calculation formula of the kernel matrix K is:

[0032]

[0033] where Y(a, :) and Y(b, :) are the standardized characteristic vectors of the a-th and b-th window length time periods respectively, σ is the width parameter of the kernel function, and ∥Y(a, :) - Y(b, :)∥ 2 is the square of the Euclidean distance, representing the difference between the two standardized characteristic vectors.

[0034] The specific process of step 5 is as follows:

[0035] The expected state data f nc is obtained through weighted average calculation, and the formula is as follows:

[0036]

[0037] w ab = K(a, b) (15)

[0038] Among them, f nc (a, :) is the expected state data of the standardized feature vector in the a-th window length period; Y(b, :) is the standardized feature vector in the b-th window length period; w ab is the similarity weight between the standardized feature vectors in the a-th and b-th window length periods, and n is the number of window length periods.

[0039] The specific process of step 6 is as follows:

[0040] Step 6.1, for each feature dimension, calculate the mean μ nc of the expected state data f j1 :

[0041]

[0042] Among them, f nc (a, j) is the expected state value of the standardized feature vector in the a-th window length period on the j-th feature, and μ j1 is the mean of the j-th feature;

[0043] Step 6.2, for each feature dimension, calculate the variance of the expected state data in this dimension:

[0044]

[0045] Among them, V j is the variance of the j-th feature;

[0046] Step 6.3, the diagonal covariance matrix S is a diagonal matrix, where each diagonal element is the variance V j of the corresponding feature dimension, that is:

[0047] S = diag(V j ) = [V1, V2, …, V m (18)

[0048] Among them, m is the number of features.

[0049] The specific process of step 7 is as follows:

[0050] Step 7.1, calculate the weighted Euclidean distance between the standardized feature vector of each window length period and the expected state through formula (18), where the weighting is completed through the inverse S -1 of the covariance matrix of the expected state data, and the specific formula is as follows:

[0051] HI E (a) = (Y(a, :) - f nc (a, :)) T S -1 (Y(a, :) - fnc (a, :) (19)

[0052] Wherein, S -1 Covariance matrix of the expected state data; HI E (a) Weighted Euclidean distance between the normalized eigenvector and the expected state in the ath window length period; f nc (a, :) is the expected state data of the normalized eigenvector in the ath window length period; Y(a, :) is the normalized eigenvector in the ath window length period;

[0053] Step 7.2, calculate the cosine similarity between the normalized eigenvector and the expected state in each window length period through the following formula (20), and the calculation formula is:

[0054]

[0055] Wherein, HI c (a) Cosine similarity between the normalized eigenvector and the expected state in the ath window length period;

[0056] Step 7.3, calculate the health index HI(a) through HI E (a) and HI C (a), and the calculation formula is as follows:

[0057]

[0058] Step 7.4, calculate the vector HI of the health state of all window length periods through the following formula (22), and the formula is as follows:

[0059] HI = [HI(1), HI(2), …, HI(a), …, HI(n)] (22)

[0060] Wherein, each element HI(a) is the health index of the ath window length period.

[0061] The specific process of Step 8 is as follows:

[0062] Step 8.1, calculate the standard deviation δ of the health index vector through formula (23):

[0063]

[0064] In the formula, is the mean value of the health index vector;

[0065] Step 8.2: Determine whether the operating condition of the pump-turbine enters the "S" characteristic braking zone according to the value of the standard deviation δ of the health index vector. If the standard deviation δ of the health index vector is greater than 68.94, it is considered that the pump-turbine enters the "S" characteristic; otherwise, it is considered that the pump-turbine does not enter the "S" characteristic.

[0066] The beneficial effects of the present invention are as follows: The method for identifying the "S" characteristic braking zone of the pump-turbine based on self-organizing kernel regression of the present invention has the advantages of high precision and strong robustness. It can perform real-time nonlinear modeling based on the measured vibration and pressure pulsation signals of the pump-turbine, and then calculate the health index of the pump-turbine in real time. By comparing the health index with the threshold, it can quickly determine whether the pump-turbine enters the "S" characteristic braking zone, thus providing a scientific criterion for the early warning of the pump-turbine entering the "S" characteristic braking zone. Brief Description of the Drawings

[0067] Figs. 1(a) and 1(b) are schematic diagrams of the measuring point positions of the pump-turbine unit test system in the method for identifying the "S" characteristic braking zone of the pump-turbine based on self-organizing kernel regression of the present invention;

[0068] Figure 2 is the characteristic curve of the pump-turbine in the method for identifying the "S" characteristic braking zone of the pump-turbine based on self-organizing kernel regression of the present invention.

[0069] In the figures, 1. Vibration measuring point in the X direction of the vaneless area, 2. Vibration measuring point in the Y direction of the vaneless area, 3. Pressure pulsation measuring point in the X direction of the vaneless area, 4. Pressure pulsation measuring point in the Y direction of the vaneless area, 5. Measuring point A on the conical pipe wall, 6. Measuring point B on the conical pipe wall, 7. Measuring point on the outer side of the elbow pipe, 8. Measuring point on the elbow pipe. Detailed Embodiment

[0070] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0071] Embodiment 1

[0072] The method for identifying the braking area of the "S" characteristic of a pump-turbine based on self-organizing kernel regression first uses a hydraulic excitation test system to synchronously and real-time collect vibration and pressure pulsation data at typical positions under operating conditions. The system includes 8 key measurement points: as shown in Fig. 1(a) (top view of the pump-turbine), it includes the vibration measurement point 1 in the X direction in the vaneless area (in front of the runner's guide vane), the vibration measurement point 2 in the Y direction in the vaneless area, the pressure pulsation measurement point 3 in the X direction in the vaneless area, and the pressure pulsation measurement point 4 in the Y direction in the vaneless area; as shown in Fig. 1(b) (front view of the pump-turbine), the conical pipe wall measurement point A 5, the conical pipe wall measurement point B 6, the outer elbow measurement point 7, and the elbow measurement point 8. Among them, the vertical distance between the conical pipe wall measurement point A 5 and the conical pipe wall measurement point B 6 and the runner inlet is L, and the value of L is 0.3 times the runner outlet diameter, and the two measurement points are arranged at 90°. During the test, a pressure pulsation sensor is used to collect the pressure pulsation signals at the pressure pulsation measurement point 3 in the X direction in the vaneless area, the pressure pulsation measurement point 4 in the Y direction in the vaneless area, the conical pipe wall measurement point A 5, the conical pipe wall measurement point B 6, and the elbow measurement point 8. An acceleration sensor is used to collect the vibration signals at the vibration measurement point 1 in the X direction in the vaneless area, the vibration measurement point 2 in the Y direction in the vaneless area, and the outer elbow measurement point 7. The 8 collected signals are all synchronously collected through a multi-channel acquisition card, and the sampling frequency must be set to be greater than or equal to 12.8 kHz, and the total duration of the working condition acquisition is 5 s.

[0073] Example 2

[0074] The method for identifying the braking area of the "S" characteristic of a pump-turbine based on self-organizing kernel regression is specifically implemented according to the following steps:

[0075] Step 1, perform time-domain windowing calculation on each collected pressure pulsation and vibration signal. The window function is determined to be a Hanning window, and the window length is determined to be Δt = 0.1 s.

[0076] Step 2, during the time-domain windowing calculation of each pressure pulsation and vibration signal in Step 1, calculate the mean value F of the signal within each window length period through formulas (1)-(7) 1p 、variance F 2p 、root mean square value F 3p 、peak-to-peak value F 4p 、absolute mean value F 5p 、skewness F 6p 、kurtosis F 7p and impulse factor F 8p , where the subscript p represents the number of the pressure pulsation or vibration measurement point, and p = 1, 2, 3,..., 8.

[0077]

[0078] F 4p =max[x(k)]-min[x(k)] (4)

[0079]

[0080]

[0081] F 8p = max[x(k)] / F 5p (8)

[0082] Among them, x(k) represents the signal data to be analyzed, k = 1, 2, ……, N, and N is the length of the signal data to be analyzed. Thus, within each same window length time period, the total number of signal index quantities of 8 measurement points is 8×8 = 64, and these 64 indices can form a characteristic index vector x corresponding to each window length time period p , x p The expression of is shown in Equation (9).

[0083] x p = [F 1p , F 2p , F 3p , F 4p , F 5p , F 6p , F 7p , F 8p p = 1, 2, 3, …, 8 (9)

[0084] Step 3, uniformly construct the eigenvalues of the vibration and pressure pulsation signals extracted in Step 2 into a characteristic matrix X. The size of matrix X is n×m, where n is the number of window length time periods and m is the number of characteristics, and n and m are 50 and 64 respectively. Each row X(i, :) represents the eigenvalue of the i-th window length time period, and each column X(:, j) represents the j-th characteristic:

[0085] X = [x1, x2, …, x p p = 1, 2, 3, …, 8 (10)

[0086] Among them, p represents the signals collected from 8 key measurement points; F 1p represents the mean value of the signals collected from the p-th measurement point; F 2p represents the variance of the signals collected from the p-th measurement point; F 3p represents the root mean square value of the signals collected from the p-th measurement point; F 4p represents the peak-to-peak value of the signals collected from the p-th measurement point; F 5p represents the absolute average value of the signals collected from the p-th measurement point; F 6p represents the skewness of the signals collected from the p-th measurement point; F 7p represents the kurtosis of the signals collected from the p-th measurement point; F 8pdenotes the pulse factor of the signal collected at the p-th measurement point; X p denotes the eigenvalue matrix corresponding to the p-th measurement point.

[0087] Step 4, standardize the eigenmatrix X through Equation (11) to obtain the standardized matrix Y, such that the mean of each eigen is 0 and the standard deviation is 1:

[0088]

[0089] where, μ j is the mean of the eigenvalues in the j-th column, and σ j is the standard deviation of the eigenvalues in the j-th column.

[0090] Step 5, use the Gaussian kernel function to calculate the similarity between the eigenvalues for each window length period. Each element K(a, b) in the kernel matrix represents the similarity between the eigenvectors of the a-th and b-th window length periods. The calculation formula for the kernel matrix K is:

[0091]

[0092] where, Y(a, :) and Y(b, :) are the standardized eigenvectors of the a-th and b-th window length periods respectively, σ is the width parameter of the kernel function for adjusting the measurement of similarity, σ = 0.5; ∥Y(a, :) - Y(b, :)∥ 2 is the square of the Euclidean distance, representing the difference between the two standardized eigenvectors.

[0093] Step 6, the expected state data f nc is obtained by weighted average, and the formula is:

[0094]

[0095] w ab = K(a, b) (15)

[0096] where, f nc (a, :) is the expected state data of the standardized eigenvector of the a-th window length period; X(b, :) is the standardized eigenvector of the b-th window length period; w ab is the similarity weight between the standardized eigenvectors of the a-th and b-th window length periods, and n is the number of window length periods, n = 50.

[0097] Step 7, the diagonal covariance matrix S is obtained by calculating the variance of the expected state data f nc . The variance of each eigen dimension represents the variability of that eigen in the expected state data.

[0098] Step 8. The health index HI(a) is used to evaluate the deviation between the standardized eigenvector of the ath window length period and its desired state, so as to determine whether the device is healthy. The health index combines the Euclidean distance and the cosine similarity, reflects the differences and similarities between the data segment and the desired state, and calculates the health index according to the diagonal covariance matrix;

[0099] Step 9. Calculate the standard deviation of the health index vector, and determine whether the operating condition of the pump-turbine enters the "S" characteristic braking region according to the standard deviation.

[0100] Example 3

[0101] The specific process of Step 7 is as follows:

[0102] Step 7.1. For each feature dimension, calculate the mean value μ nc of the desired state data f j1 :

[0103]

[0104] where f nc (a,j) is the desired state value of the standardized eigenvector of the ath window length period on the jth feature, and μ j1 is the mean value of the jth feature.

[0105] Step 7.2. For each feature dimension, calculate the variance of the desired state data in this dimension:

[0106]

[0107] where V j is the variance of the jth feature.

[0108] Step 7.3. The diagonal covariance matrix S is a diagonal matrix, where each diagonal element is the variance V j of the corresponding feature dimension, that is:

[0109] S = diag(V j ) = [V1, V2, …, V m (18)

[0110] where m is the number of features.

[0111] Example 4

[0112] The specific process of Step 8 is as follows:

[0113] Step 8.1. Calculate the weighted Euclidean distance between the standardized eigenvector of each window length period and the desired state through Equation (19) to measure the difference, where the weighting is through the inverse S of the covariance matrix of the desired state data-1 Completed.

[0114] HI E (a) = (Y(a, :) - f nc (a, :)) T S -1 (Y(a, :) - f nc (a, :)) (19)

[0115] Where S -1 Covariance matrix of the expected state data; HI E (a) Weighted Euclidean distance between the standardized eigenvector and the expected state in the ath window length period; f nc (a, :) is the expected state data of the standardized eigenvector in the ath window length period; Y(a, :) is the standardized eigenvector in the ath window length period.

[0116] Step 8.2: Use cosine similarity to measure the directional similarity between the standardized eigenvector and the expected state in each window length period. If the similarity is high, the health index is low, indicating that the data point is more consistent with the expected state. The calculation formula is:

[0117]

[0118] Where HI c (a) Cosine similarity between the standardized eigenvector and the expected state in the ath window length period.

[0119] Step 8.3: Calculate the health index HI(a) by combining HI E (a) and HI C (a) to quantify the abnormality degree of the standardized eigenvector in the ath window length period. The calculation formula is as follows:

[0120]

[0121] Step 8.4: The health index HI is a vector containing the health status of all window length periods, where each element HI(a) is the health index of the ath window length period.

[0122] HI = [HI(1), HI(2), …, HI(a), …, HI(n)] n = 50 (22)

[0123] Example 5

[0124] Calculate the standard deviation δ of the health index vector through Equation (23) and use it as the evaluation criterion.

[0125]

[0126] In the formula, is the mean value of the health index vector.

[0127] Example 6

[0128] Determine whether the operating condition of the pump-turbine enters the "S" characteristic braking area according to the value of the standard deviation δ of the health index vector. If the standard deviation δ of the health index vector is greater than 68.94, it is considered that the pump-turbine enters the "S" characteristic. If δ is less than or equal to 68.94, it is considered that the pump-turbine does not enter the "S" characteristic, and the recognition result is as Figure 2 shown (where the abscissa n 11 is the unit speed and the ordinate Q 11 is the unit flow rate).

[0129] The present invention first collects the pressure pulsation and vibration data of the pump-turbine under different operating conditions and extracts the time-domain characteristic values, then uses self-organizing kernel regression to perform non-linear modeling on the data, and calculates the health index of this operating condition. By comparing the size of the standard deviation of the health index vector with the specified threshold, it is judged whether the pump-turbine enters the "S" characteristic braking area. This method can determine in real time whether the pump-turbine enters the "S" characteristic braking area according to the vibration and pressure pulsation signals measured on-site of the pump-turbine, thereby providing a scientific basis for the fault warning and operation and maintenance decision-making of the pump-turbine.

Claims

1. A method for identifying the braking area of the "S" characteristic of a pump-turbine based on self-organizing kernel regression, characterized in that: Specifically, it includes the following steps: Step 1: Real-time collect the pressure pulsation signals and vibration signals of each measuring point on the pump-turbine under operating conditions; Step 2: Construct the characteristic index vector within the i-th window length time period corresponding to each measuring point; Step 3: Construct the characteristic matrix X containing the pressure pulsation signals and vibration signals, and standardize the characteristic matrix X to obtain the standardized matrix Y; Step 4: Calculate the similarity between the standardized eigenvalues of each window length time period; Step 5: Obtain the expected state data through the calculation results of Step 4; Step 6: Calculate the diagonal covariance matrix according to the variance of the expected state data; Step 7: Calculate the health index according to the diagonal covariance matrix; Step 8: Calculate the standard deviation of the health index vector, and determine whether the operating condition of the pump-turbine enters the "S" characteristic braking area according to the standard deviation.

2. The method for identifying the braking area of the "S" characteristic of a pump-turbine based on self-organizing kernel regression according to claim 1, wherein: The specific process of Step 2 is as follows: Step 2.1: Perform time-domain windowing calculation on the collected pressure pulsation and vibration signals, and the window function is determined as the Hanning window; Step 2.2, calculate the mean value F of the signal in each window length time period through the following formulas (1) to (7) 1p , variance F 2p , root mean square value F 3p , peak-to-peak value F 4p , absolute mean value F 5p , skewness F 6p , kurtosis F 7p and impulse factor F 8p , where the subscript p represents the number of the pressure pulsation or vibration measurement point, p = 1, 2, 3, …, 8; F 4p = max[x(k)] - min[x(k)] (4) F 8p = max[x(k)] / F 5p (8) Among them, x(k) represents the signal data to be analyzed, k = 1, 2, ……, N, and N is the length of the signal data to be analyzed; Step 2.3, construct the characteristic index vector x corresponding to each measuring point index within the i-th window length time period p , x p , and the expression is as shown in Equation (9): x p = [F 1p , F 2p , F 3p , F 4p , F 5p , F 6p , F 7p , F 8p where p = 1, 2, 3, …, 8 (9).

3. The method for identifying the braking zone of the "S" characteristic of a pump-turbine based on self-organizing kernel regression according to claim 2, wherein: The specific process of Step 3 is as follows: Step 3.1: Extract the characteristic index vector x of the vibration and pressure pulsation signals obtained in Step 2 p Unify and construct them into a characteristic matrix X. The size of matrix X is n×m, where n is the number of window length time periods and m is the number of characteristics. Each row X(i,:) represents the characteristic values of the i-th window length time period, and each column X(:,j) represents the j-th characteristic: X = [x1, x2, …, x p p = 1, 2, 3, …, 8 (10) Step 3.2: Standardize the characteristic matrix X through Equation (11) to obtain the standardized matrix Y, so that the mean of each characteristic is 0 and the standard deviation is 1: where μ j is the mean of the eigenvalues of the j-th column, and σ j is the standard deviation of the features of the j-th column.

4. The method for identifying the braking area of the "S" characteristic of a pump-turbine based on self-organizing kernel regression according to claim 3, characterized in that: The specific process of Step 4 is as follows: Use the Gaussian kernel function to calculate the similarity between the eigenvalues of each window length time period. Each element K(a, b) in the kernel matrix represents the similarity between the standardized eigenvectors of the a-th and b-th window length time periods. The calculation formula of the kernel matrix K is: where Y(a,:) and Y(b,:) are the normalized feature vectors of the ath and bth window length time periods respectively, σ is the width parameter of the kernel function, and ∥Y(a,:) - Y(b,:)∥ 2 is the square of the Euclidean distance, representing the difference between the two normalized feature vectors.

5. The method for identifying the braking area of the "S" characteristic of a pump-turbine based on self-organizing kernel regression according to claim 4, characterized in that: The specific process of Step 5 is as follows: The expected state data f is obtained by weighted average calculation nc , and the formula is as follows: w ab = K(a, b) (15) Among them, f nc (a, :) is the expected state data of the standardized feature vector in the a-th window length time period; Y(b, :) is the standardized feature vector in the b-th window length time period; w ab is the similarity weight between the standardized feature vectors in the a-th and b-th window length time periods, and n is the number of window length time periods.

6. The method for identifying the braking area of the "S" characteristic of a pump-turbine based on self-organizing kernel regression according to claim 5, characterized in that: The specific process of Step 6 is as follows: Step 6.1, for each feature dimension, calculate the mean value μ nc of j1 the expected state data f where f nc (a, j) is the expected state value of the standardized feature vector in the a-th window length period on the j-th feature, and μ j1 is the mean of the j-th feature; Step 6.2: For each characteristic dimension, calculate the variance of the expected state data in this dimension: Among them, V j is the variance of the j-th feature; Step 6.3, the diagonal covariance matrix S is a diagonal matrix, where each diagonal element is the variance V of the corresponding eigen-dimension j , that is: S = diag(V j ) = [V1, V2, …, V m (18) Among them, m is the number of characteristics.

7. The method for identifying the braking area of the "S" characteristic of a pump-turbine based on self-organizing kernel regression according to claim 6, characterized in that: The specific process of Step 7 is as follows: Step 7.1, calculate the weighted Euclidean distance between the normalized eigenvector and the desired state for each window length period, where the weighting is done through the inverse S of the covariance matrix of the desired state data, and the specific formula is as follows: -1 This is achieved as follows: HI E (a) = (Y(a, :) - f nc (a, :)) T S -1 (Y(a, :) - f nc (a, :)) (19) Among them, S -1 Covariance matrix of the desired state data; HI E (a) Weighted Euclidean distance between the normalized eigenvector and the desired state in the ath window length period; f nc (a, :) is the desired state data of the normalized eigenvector in the ath window length period; Y(a, :) is the normalized eigenvector in the ath window length period; Step 7.2: Calculate the cosine similarity between the standardized eigenvector of each window length time period and the expected state through the following formula (20), and the calculation formula is: Among them, HI c (a) The cosine similarity between the standardized feature vector of the a-th window length time period and the expected state; Step 7.3, through HI E (a) and HI C (a) Calculate the health index HI(a), and the calculation formula is as follows: Step 7.4: Calculate the vector HI of the health state of all window length time periods through the following formula (22), and the formula is as follows: HI = [HI(1), HI(2), …, HI(a), …, HI(n)] (22) Among them, each element HI(a) is the health index of the a-th window length time period.

8. The method for identifying the braking area of the "S" characteristic of a pump-turbine based on self-organizing kernel regression according to claim 7, characterized in that: The specific process of Step 8 is as follows: Step 8.1: Calculate the standard deviation δ of the health index vector through Equation (23); In the formula, is the mean of the health index vectors; Step 8.2: Determine whether the operating condition of the pump-turbine enters the "S" characteristic braking area according to the value of the standard deviation δ of the health index vector. If the standard deviation δ of the health index vector is greater than 68.94, it is considered that the pump-turbine enters the "S" characteristic. Otherwise, it is considered that the pump-turbine does not enter the "S" characteristic.

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