Identification method of axis trajectory of hydropower unit

Abstract

The present invention discloses a method for identifying the axis trajectory of a hydroelectric unit. The axis trajectory signal is de-noised by an improved wavelet threshold to synthesize an axis trajectory image. The features of the axis trajectory image are extracted by using a directional gradient histogram. The feature dimension is reduced by using principal component analysis. Then, SVM is used for classification and identification. The SVM uses a transient search optimization algorithm to optimize two important parameters, a penalty factor and a kernel parameter, to achieve the best identification effect. The method of the present invention can identify the axis trajectory of a hydroelectric unit with high efficiency and accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of fault identification of hydroelectric generator sets, and relates to a method for identifying the axis trajectory of a hydroelectric generator set. Background Art

[0002] With the development of science and technology and production needs, hydropower units tend to be large-scale and intelligent, and the status monitoring and fault diagnosis of hydropower units are becoming more important. In the fault diagnosis of hydropower units, the vibration signal is often processed to extract the signal spectrum characteristics for analysis. As a rotating device, the axis trajectory of the rotor of the hydropower unit can reflect different operating conditions. When diagnosing faults, the fault mode of the unit can be judged according to the shape of the axis trajectory: mild rotor misalignment corresponds to a banana shape; severe rotor misalignment corresponds to an outer figure 8 shape; rotor mass imbalance corresponds to an ellipse; in addition, there are shapes such as an inner figure 8 and a petal shape. The identification of the axis trajectory provides another important way for fault diagnosis of hydropower units.

[0003] The axis trajectory is a two-dimensional image, and the recognition of the axis trajectory mainly involves image processing. Guo Pengcheng et al. extracted the HU invariant moment features of the image, removed redundant data through the particle swarm algorithm, and combined it with the improved BP neural network to realize the recognition of the axis trajectory. Zhang Xudong et al. extracted the envelope features of the axis trajectory as well as the time domain and frequency domain features, and extracted the fault sensitive features after calculating the weights. Wen Guangrui et al. proposed a method based on quadrant information entropy to extract image features, divided the image into four quadrants, and calculated the information entropy of the four quadrants as image features. In addition, there are statistical fuzzy vector coding, popular sensitive features, Fourier descriptors and other methods. In recent years, deep learning has been widely used in the field of image processing. Xu Jingjun et al. used formulas to simulate the axis trajectory and used deep convolutional networks for classification and recognition. Guo Mingjun et al. obtained the axis trajectories of different faults in the simulation test bench. However, since the deep learning training set requires a large amount of data, the fault data set of the axis trajectory cannot meet the needs, so deep learning methods are rarely used in the recognition of axis trajectories. Summary of the invention

[0004] The purpose of the present invention is to provide a method for identifying the axis center track of a hydroelectric generator set, which can identify the axis center track of the hydroelectric generator set with high efficiency and high accuracy.

[0005] The technical solution adopted by the present invention is a method for identifying the axis trajectory of a hydropower unit, which is specifically implemented according to the following steps:

[0006] Step 1, obtaining the axis trajectory signal of the hydropower unit;

[0007] Step 2, denoising the axis trajectory signal of the hydropower unit obtained in step 1 by using an improved wavelet threshold method;

[0008] Step 3, synthesizing the axis trajectory signal of the hydropower unit after denoising in step 2 into an axis trajectory image, and extracting the features of the axis trajectory image using a directional gradient histogram feature extraction method;

[0009] Step 4, the directional gradient histogram feature of the axis trajectory image extracted in step 3 is reduced in dimension using the PCA method to obtain the feature quantity of the axis trajectory image after dimensionality reduction;

[0010] Step 5, construct a TSO-SVM classification model;

[0011] Step 6, repeat steps 1-4 to obtain the feature quantities of the axis trajectory after dimensionality reduction in the fault state and the normal state, divide the obtained feature quantities of the axis trajectory after dimensionality reduction into a training set and a test set, input the training set into the TSO-SVM model constructed in step 5 for training, obtain the trained TSO-SVM model, and input the test set into the trained TSO-SVM model to verify the training effect.

[0012] The present invention is also characterized in that

[0013] In step 1, the axis trajectory signal of the hydropower unit is divided into an upper guide axis trajectory signal, a lower guide axis trajectory signal and a water guide axis trajectory signal. The upper guide axis trajectory signal is collected by two eddy current sensors installed at a 90° angle at the upper guide bearing. The collection method of the lower guide axis trajectory signal and the water guide axis trajectory signal is the same as that of the upper guide, and is collected by eddy current sensors installed at the lower guide bearing and the water guide bearing.

[0014] In step 2, the improved wavelet threshold processing function expression is:

[0015]

[0016] In formula (5), d is the wavelet decomposition signal, sign is the sign function;

[0017] Among them, considering the influence of noise standard deviation and wavelet decomposition layer number on the threshold, the improved threshold function is as follows:

[0018]

[0019] In formula (4), n is the signal length, σ is the standard deviation of the noise, and μ is the coefficient;

[0020] μ=1 / ln(2a+1) (3)

[0021] In formula (3), a is the number of wavelet decomposition levels.

[0022] In step 3, the process of extracting the features of the axis trajectory image using the Histogram of Oriented Gradients (HOG) feature extraction method is as follows:

[0023] Step 3.1, use the gradient operator to perform convolution operation on the axis trajectory image to obtain the gradient components in the horizontal and vertical directions. The horizontal gradient operator is [-1, 0, 1], and the vertical gradient operator is [-1, 0, 1]T. Then calculate the gradient and direction of each pixel point. The calculation formulas are shown in equations (6) and (7);

[0024]

[0025]

[0026] In formulas (6) and (7), G x (x, y) represents the lateral gradient at the pixel point (x, y) of the axis trajectory image, G y (x,y) represents the longitudinal gradient at the axis track image pixel point (x,y), H(x+1,y) represents the pixel value of the axis track image pixel point (x,y) with a positive distance of 1 on the x-axis, H(x-1,y) represents the pixel value of the axis track image pixel point (x,y) with a positive distance of -1 on the x-axis, H(x,y+1) represents the pixel value of the axis track image pixel point (x,y) with a positive distance of 1 on the y-axis, H(x,y-1) represents the pixel value of the axis track image pixel point (x,y) with a positive distance of -1 on the y-axis, G(x,y) represents the gradient at the pixel point (x,y), and α(x,y) represents the direction at the pixel point (x,y);

[0027] Step 3.2, construct the gradient direction histogram of each cell;

[0028] Specifically, in each cell, the gradient direction is evenly divided into 9 bins in the range of 0-180°. Formula (6) and formula (7) are used to calculate the gradient and direction of all pixels in each cell. Weighted voting is performed in the gradient direction histogram, and the weight is the gradient size. The gradient direction histogram of each cell can form a 9-dimensional feature vector.

[0029] Step 3.3, each 2×2 cell unit is combined into a block, each block has a 4×9-dimensional feature vector, and a window of the block size is sequentially slid on the entire axis trajectory image, with a step size of the cell size. Finally, the features of all blocks are connected in series to form the HOG feature of the axis trajectory image. The HOG feature dimension calculation formula is as follows:

[0030]

[0031] In formula (8), l p Indicates the number of pixels of the horizontal coordinate of the axis trajectory image, h p Indicates the number of pixels of the image's ordinate, lc Is the size of the cell.

[0032] The specific process of step 5 is: input the feature quantity of the axis trajectory image obtained in step 4 after dimension reduction into the support vector machine for classification, and then use the transient search optimization algorithm to optimize the SVM model to obtain the TSO-SVM classification model.

[0033] The process of support vector machine classification is as follows:

[0034] For the set V = {(v i ,y i )|y i ∈{-1,1}, i=1,2,...,N}, where v i represents the sample data, i.e., the feature quantity of the axis trajectory image after dimensionality reduction, i represents v i The sample label y represents the sample category, and SVM transforms the solution of the optimal hyperplane into the following:

[0035]

[0036] In formula (9), w represents the weight vector, b represents the partial vector, C is the penalty factor, ξ is the slack variable, and the Lagrange multiplier and kernel function are introduced. The classification problem of SVM can be expressed as:

[0037]

[0038] In formula (10), e is the Lagrange multiplier, K(v i ,v j ) represents the kernel function and satisfies in and They are variables v i and v j Mapping in high-dimensional space; the final classification results of the SVM model can be distinguished in the following ways:

[0039]

[0040] In the SVM model, the radial basis function (RBF) is used as the SVM kernel function, and its expression is as follows:

[0041] K(v i ,v j )=exp(-g||v i -v j || 2 ) (12)

[0042] Where g is the kernel parameter of RBF.

[0043] The expression optimized by the transient search optimization algorithm is:

[0044]

[0045] Y=l b +rand×(u b -l b ) (14)

[0046] T=2×z×r2-z (15)

[0047] C1=k×z×r3+1 (16)

[0048] z=2-2(l / l max ) (17)

[0049] In formulas (13)-(17), Y is the initialized search agent; u b is the upper bound of the search area; l b is the lower bound of the search area; rand is a random number; z varies linearly from 2 to 0; T and C1 are random coefficients; r1, r2, and r3 are numbers uniformly distributed between [0,1], and r1 is used to balance the exploration behavior r1≥0.5 and the development behavior r1<0.5; Y l Represents the location of the search agent; Y l * is the optimal search agent position; k is a constant (k = 0, 1, 2, ...); l is the number of iterations; l max is the maximum number of iterations.

[0050] The beneficial effects of the present invention are:

[0051] (1) The method for identifying the axis trajectory of a hydropower unit of the present invention adopts an improved wavelet threshold denoising method. Compared with the general wavelet soft threshold denoising, the improved algorithm reduces the constant deviation generated by denoising and has a better denoising effect;

[0052] (2) The method for identifying the axis trajectory of the hydropower unit of the present invention adopts the HOG combined with TSO-SVM method, which has a good recognition effect on the axis trajectory. Compared with PSO-SVM, ABC-SVM and SOA-SVM, TSO-SVM has better classification accuracy and the shortest time to complete the classification, which proves that the TSO optimization algorithm is superior to the PSO, ABC and SOA optimization algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the method for identifying the axis trajectory of a hydroelectric unit of the present invention;

[0054] Figure 2It is a schematic diagram of dividing bins of gradient directions in a directional gradient histogram in a method for identifying the axis trajectory of a hydropower unit of the present invention;

[0055] Figure 3 It is a denoised waveform diagram of the x-axis axis trajectory signal in the method for identifying the axis trajectory of a hydropower unit of the present invention;

[0056] Figure 4 It is a denoised waveform diagram of the Y-axis axis trajectory signal in the method for identifying the axis trajectory of a hydropower unit of the present invention;

[0057] Figure 5 It is the original axis track image in the method for identifying the axis track of the hydropower unit of the present invention;

[0058] Figure 6 It is the axis trajectory image after denoising in the method for identifying the axis trajectory of a hydropower unit of the present invention;

[0059] Figure 7 1 is an image of the axis trajectory of different faults in the method for identifying the axis trajectory of a hydropower unit of the present invention; (a) is an outer figure 8 shape, (b) is an inner figure 8 shape, (c) is an ellipse, (d) is a banana shape, and (e) is a circle;

[0060] Figure 8 It is a visualization diagram of HOG features in the method for identifying the axis trajectory of a hydropower unit of the present invention;

[0061] Fig. 9 It is a classification result diagram of the TSO-SVM model in the method for identifying the axis trajectory of the hydropower unit of the present invention;

[0062] Fig.10 It is the fitness image of the TSO-SVM model in the method for identifying the axis trajectory of the hydropower unit of the present invention. DETAILED DESCRIPTION

[0063] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0064] The present invention provides a method for identifying the axis trajectory of a hydroelectric unit, the process of which is as follows: Figure 1 As shown, the specific implementation steps are as follows:

[0065] Step 1, obtaining the axis trajectory signal of the hydropower unit;

[0066] The axis trajectory signal of the hydropower unit is divided into the upper guide axis trajectory signal, the lower guide axis trajectory signal and the water guide axis trajectory signal. The upper guide axis trajectory signal is collected by two eddy current sensors installed at 90 degrees radially at the upper guide bearing. The lower guide axis trajectory signal and the water guide axis trajectory signal are collected in the same way as the upper guide, and are collected by eddy current sensors installed at the lower guide bearing and the water guide bearing.

[0067] The axis trajectory signal includes a fault axis trajectory signal and an axis trajectory signal under normal operating conditions;

[0068] Step 2, denoising the axis trajectory signal of the hydropower unit obtained in step 1 by using an improved wavelet threshold method;

[0069] Wavelet threshold denoising is essentially filtering the signal. The selection of the threshold determines the quality of the denoising effect. The Sqtwolog general threshold function is the most commonly used among the four threshold functions. Its formula is shown in the following formula.

[0070]

[0071]

[0072] In equations (1) and (2), λ is the threshold, n is the signal length, σ is the standard deviation of the noise, and d a (k) is the a-th layer signal of wavelet decomposition, k is the number of wavelet coefficients in each layer, and median is the median function;

[0073] When the above formula is used to calculate the threshold, the influence of the number of decomposition layers is not considered. In wavelet transform, as the number of decomposition layers increases, the noise in the wavelet detail coefficient decreases, and the threshold calculated by the above formula is inaccurate. The present invention introduces a coefficient μ to reduce the threshold as the number of decomposition layers increases.

[0074] μ=1 / ln(2a+1) (3)

[0075] In formula (3), a is the number of wavelet decomposition layers;

[0076] Taking into account the influence of noise standard deviation and wavelet decomposition layer number on the threshold, the improved threshold function is as follows:

[0077]

[0078] There are two types of threshold processing functions: hard threshold function and soft threshold function. The hard threshold processing function will cause discontinuity in the signal, and although the soft threshold processing function has good continuity, it will over-compress the signal and distort it. The present invention adopts an improved threshold processing function to avoid the discontinuity of the hard threshold function and the constant deviation of the soft threshold function. The improved wavelet threshold processing function is shown as follows:

[0079]

[0080] In formula (5), d is the wavelet decomposition signal, sign is the sign function;

[0081] Step 3, synthesizing the axis trajectory signal of the hydropower unit after denoising in step 2 into an axis trajectory image, and extracting the features of the axis trajectory image using a histogram of oriented gradients (HOG) feature extraction method;

[0082] HOG obtains image features by calculating and counting the gradient direction histogram of the local area of ​​the image; the image is divided into cells of equal size, and the gradient direction histogram in each cell is counted. Every 2×2 cells form a block, and the statistical histograms of all blocks are connected to form the HOG feature of the image;

[0083] The HOG feature extraction process is:

[0084] Step 3.1, use the gradient operator to perform convolution operation on the axis trajectory image to obtain the gradient components in the horizontal and vertical directions. The horizontal gradient operator is [-1, 0, 1], and the vertical gradient operator is [-1, 0, 1]T. Then calculate the gradient and direction of each pixel point. The calculation formulas are shown in equations (6) and (7);

[0085]

[0086]

[0087] In formulas (6) and (7), G x (x, y) represents the lateral gradient at the pixel point (x, y) of the axis trajectory image, G y (x,y) represents the longitudinal gradient at the axis track image pixel point (x,y), H(x+1,y) represents the pixel value of the axis track image pixel point (x,y) with a positive distance of 1 on the x-axis, H(x-1,y) represents the pixel value of the axis track image pixel point (x,y) with a positive distance of -1 on the x-axis, H(x,y+1) represents the pixel value of the axis track image pixel point (x,y) with a positive distance of 1 on the y-axis, H(x,y-1) represents the pixel value of the axis track image pixel point (x,y) with a positive distance of -1 on the y-axis, G(x,y) represents the gradient at the pixel point (x,y), and α(x,y) represents the direction at the pixel point (x,y);

[0088] Step 3.2, construct the gradient direction histogram of each cell;

[0089] Specifically: Figure 2As shown, in each cell, the gradient direction is evenly divided into 9 bins in the range of 0-180°. Formula (6) and formula (7) are used to calculate the gradient and direction of all pixels in each cell. Weighted voting is performed in the gradient direction histogram, and the weight is the gradient size. The gradient direction histogram of each cell can form a 9-dimensional feature vector.

[0090] Step 3.3, each 2×2 cell unit is combined into a block, each block has a 4×9-dimensional feature vector, and a window of the block size is sequentially slid on the entire axis trajectory image, with a step size of the cell size. Finally, the features of all blocks are connected in series to form the HOG feature of the axis trajectory image. The HOG feature dimension calculation formula is as follows:

[0091]

[0092] In formula (8), l p Indicates the number of pixels of the horizontal coordinate of the axis trajectory image, h p Indicates the number of pixels of the vertical coordinate of the image, l c Is the size of the cell.

[0093] Step 4, the HOG features of the axis trajectory image extracted in step 3 are reduced in dimension using the PCA (Principal Component Analysis) method to obtain the feature quantity of the axis trajectory image after dimensionality reduction;

[0094] Step 5, construct the TSO-SVM classification model, and use the transient search optimization algorithm (TSO) to optimize the penalty factor C and kernel parameter g of SVM. The parameter settings are as follows: the search population size is 30, the number of iterations is 100, the search range of the two optimization parameters is [0.1, 100], and the sample data in the SVM is the feature quantity of the axis trajectory image after dimensionality reduction.

[0095] The specific process is as follows: the feature quantity of the axis trajectory image obtained in step 4 after dimension reduction is input into the support vector machine (SVM) for classification, and then the transient search optimization algorithm (TSO) is used to optimize the SVM model to obtain the TSO-SVM classification model;

[0096] The process of support vector machine (SVM model) classification is as follows:

[0097] For the set V = {(v i ,y i )|y i ∈{-1,1}, i=1,2,...,N}, where v i represents sample data, i represents v iThe sample label y represents the sample category, and SVM transforms the solution of the optimal hyperplane into the following:

[0098]

[0099] In formula (9), w represents the weight vector, b represents the partial vector, C is the penalty factor, ξ is the slack variable, and the Lagrange multiplier and kernel function are introduced. The classification problem of SVM can be expressed as:

[0100]

[0101] In formula (10), e is the Lagrange multiplier, K(v i ,v j ) represents the kernel function and satisfies in and They are variables v i and v j Mapping in high-dimensional space; the final classification results of the SVM model can be distinguished in the following ways:

[0102]

[0103] In the SVM model, the selection of kernel function and kernel parameters will affect the classification accuracy. The present invention adopts radial basis function (RBF) as the SVM kernel function, and its expression is as follows:

[0104] K(v i ,v j )=exp(-g||v i -v j || 2 ) (12)

[0105] In formula (12), g is the kernel parameter of RBF.

[0106] The penalty factor C and the kernel parameter g have a significant impact on the classification accuracy and generalization ability of the SVM model. Therefore, it is necessary to optimize these two parameters through an optimization algorithm to obtain the best SVM model.

[0107] The optimization process of the TSO algorithm is as follows:

[0108] The exploration behavior of the TSO algorithm is inspired by the oscillation of the second-order RLC circuit around zero, and the exploitation behavior of the TSO is inspired by the exponential decay of the first-order discharge; the random number r1 is used to balance the exploration behavior (r1≥0.5) and the exploitation behavior (r1<0.5);

[0109]

[0110] Y=lb +rand×(u b -l b ) (14)

[0111] T=2×z×r2-z (15)

[0112] C1=k×z×r3+1 (16)

[0113] z=2-2(l / l max ) (17)

[0114] In formulas (13)-(17), Y is the initialized search agent, u b is the upper bound of the search area, l b is the lower bound of the search area, rand is a random number; z varies linearly from 2 to 0, T and C1 are random coefficients, r1, r2 and r3 are numbers uniformly distributed between [0,1], and Y l Represents the location of the search agent, Y l * is the optimal search agent position, k is a constant (k = 0, 1, 2, ...), l is the number of iterations, l max is the maximum number of iterations.

[0115] Step 6, repeat steps 1-4 to obtain the feature quantities of the axis trajectory after dimensionality reduction in the fault state and the normal state, divide the obtained feature quantities of the axis trajectory after dimensionality reduction into a training set and a test set (the sample size of the training set and the test set is 3:1), input the training set into the TSO-SVM model constructed in step 5 for training, obtain the trained TSO-SVM model, and input the test set into the trained TSO-SVM model to verify the training effect.

[0116] Example

[0117] The axis trajectory signals of the hydropower unit are divided into upper guide, lower guide and water guide axis trajectory signals. The upper guide axis trajectory signal is collected by two eddy current sensors installed at 90° radially at the upper guide bearing. The lower guide and water guide axis trajectory signals are collected in the same way as the upper guide, and are collected by eddy current sensors installed at the lower guide and water guide bearings. Multiple sets of fault axis trajectory data and axis trajectory data under normal operating conditions were collected, including external 8-shaped (corresponding fault is severe rotor misalignment), elliptical (corresponding fault is rotor mass imbalance), internal 8-shaped (corresponding fault is oil film vortex), banana-shaped (corresponding fault is mild rotor misalignment) and normal state circular.

[0118] Taking the No. 1 unit of a power station as an example, the unit fault is serious rotor misalignment, the corresponding axis trajectory shape is an outer 8 shape, the unit speed is 300r / min, the sampling frequency of the two eddy current sensors installed at the water-guided bearing is 2000Hz, and the sampling signal of 1s is intercepted. The improved wavelet threshold mentioned above is used for denoising. The wavelet basis function selects Sym8 wavelet, and the decomposition layer number is 5. The signal waveforms before and after denoising are as follows: Figure 3 and Figure 4 The axis trajectory images before and after denoising are shown in Figure 6 shown.

[0119] The evaluation methods of signal denoising effect usually choose signal-to-noise ratio (SNR) and root mean square error (RMSE). SNR describes the ratio of signal to noise. The larger the value, the better the denoising effect. The smaller the RMSE value, the closer the denoised signal is to the real signal, and the better the denoising effect. The formulas of SNR and RMSE are as follows.

[0120]

[0121]

[0122] In the formula, q is the original signal, p is the denoised signal, and n is the signal length.

[0123] The denoising method of the present invention is compared with the wavelet general soft threshold method, Xie Bo's method and Zhang Shuli's method. Taking the x-axis signal denoising as an example, the results are shown in Table 1. The SNR obtained by the method of the present invention is 81.3475 and the RMSE is 0.0303; the SNR of the wavelet soft threshold is 79.7097 and the RMSE is 0.0442; the SNR of Xie Bo's method is 80.7854 and the RMSE is 0.0345; the SNR of Zhang Shuli's method is 80.7730 and the RMSE is 0.0346. It can be seen that the result obtained by the denoising method of the present invention has the highest SNR and the lowest RMSE. The denoising effect is better than the wavelet general soft threshold method, and is also better than the Xie Bo method and Zhang Shuli method. The denoising effect is improved while reducing the error generated by denoising.

[0124] Table 1 Comparison of several denoising methods

[0125]

[0126] After the axis trajectory signal is denoised, the axis trajectory image is synthesized. In order to obtain enough samples, the generated image is a single-cycle axis trajectory with a size of 128×128 pixels. To facilitate feature extraction, the axis trajectory is thickened, such as Figure 7 As shown in the figure, finally, 120 images of each of the four types of fault axis trajectories and normal state axis trajectories were obtained, for a total of 600 sample images.

[0127] Then the HOG method is used to extract image features. The size of the cell has a significant impact on the dimension of the extracted features and the extraction time. The smaller the cell, the higher the feature dimension extracted, and the longer the feature extraction time, which also affects the final recognition effect. The feature dimension, extraction time and feature dimension after PCA dimensionality reduction corresponding to different cells are shown in Table 2.

[0128] Table 2 Comparison of features extracted from different cells

[0129]

[0130] From Table 2, we can see that when the cell size is 4×4, the time used for feature extraction is the longest, reaching 694.58s, and the feature dimension after dimensionality reduction is 127, which is much higher than the other three sizes; and when the cell size is 32×32, the time used for feature extraction is the shortest, which is 16.60s, and the feature dimension after dimensionality reduction is also the smallest at 7 dimensions. Since the image of the axis trajectory is relatively simple and the requirements for details are not high, the present invention selects a 32×32 cell to extract features. Taking the outer 8-shaped axis trajectory image as an example, the HOG features extracted by selecting a 32×32 cell are visualized as shown below Figure 8 As shown, there are 16 cells in total, and the direction and gradient size of each cell are obviously different.

[0131] The 600 feature samples after PCA dimension reduction were randomly divided into training set and test set in a ratio of 3:1, and the axis trajectory fault samples were trained and classified using the SVM optimized by TSO. The upper and lower bounds of the penalty factor C and the kernel parameter g were set to [0.01, 100], the search population size was 30, and the number of iterations was 100. The TSO-SVM model training classification results are shown in Figure 2. Fig. 9 As shown, the obtained fitness image is as follows Fig.10 As shown, the optimized penalty factor C is 17.8564 and the kernel parameter g is 1.5385.

[0132] Depend on Fig. 9 It can be seen that the classification accuracy of TSO-SVM is 99.33%, with only one misclassification, which is the inner 8 shape being misclassified as a banana shape. The classification time is 14.76s.

[0133] To verify the performance of the TSO algorithm, the classification results of TSO-SVM are compared with those of SVM optimized by particle swarm algorithm (PSO), artificial bee colony algorithm (ABC) and seagull optimization algorithm (SOA). The experimental platform is MATLAB R2018a, and the laptop configuration is as follows: CPU is i5 8300H 2.3GHz, graphics card is NVIDIA GTX1060, memory is 8GB 2666MHz, and 256G solid state drive. The parameters are uniformly set to the penalty factor C and the upper and lower bounds of the kernel parameter g are set to [0.01,100], the search population size is 30, the number of iterations is 100, and the comparison of classification results is shown in Table 3.

[0134] Table 3 Classification comparison of different methods in multiple directions

[0135]

[0136] As shown in Table 3, the classification accuracy of TSO-SVM is 99.33%, which is 0.66%, 0.66% and 1.33% higher than that of PSO-SVM, ABC-SVM and SOA-SVM respectively. At the same time, the time taken by TSO-SVM is 14.76s, which is 0.7s, 1.15s and 2.48s less than that of PSO-SVM, ABC-SVM and SOA-SVM respectively. It proves that TSO is better than PSO, ABC and SOA and is more suitable for optimizing SVM.

Claims

1. A method for identifying the axis trajectory of a hydropower unit, characterized in that: Follow the steps below to implement it: Step 1, obtaining the axis trajectory signal of the hydropower unit; Step 2, denoising the axis trajectory signal of the hydropower unit obtained in step 1 by using an improved wavelet threshold method; In step 2, the improved wavelet threshold processing function expression is: （5） In formula (5), d is the wavelet decomposition signal, sign is the sign function; Among them, considering the influence of noise standard deviation and wavelet decomposition layer number on the threshold, the improved threshold function is as follows: （4） In formula (4), n is the signal length, σ is the standard deviation of the noise, μ is the coefficient; （3） In formula (3), a is the number of wavelet decomposition levels; Step 3, synthesizing the axis trajectory signal of the hydropower unit after denoising in step 2 into an axis trajectory image, and extracting the features of the axis trajectory image using a directional gradient histogram feature extraction method; Step 4, the directional gradient histogram feature of the axis trajectory image extracted in step 3 is reduced in dimension using the PCA method to obtain the feature quantity of the axis trajectory image after dimensionality reduction; Step 5, construct a TSO-SVM classification model; Step 6, repeat steps 1-4 to obtain the feature quantities of the axis trajectory after dimensionality reduction in the fault state and the normal state, divide the obtained feature quantities of the axis trajectory after dimensionality reduction into a training set and a test set, input the training set into the TSO-SVM model constructed in step 5 for training, obtain the trained TSO-SVM model, and input the test set into the trained TSO-SVM model to verify the training effect.

2. The method for identifying the axis trajectory of a hydroelectric generator set according to claim 1, characterized in that: In step 1, the axis trajectory signal of the hydropower unit is divided into an upper guide axis trajectory signal, a lower guide axis trajectory signal and a water guide axis trajectory signal. The upper guide axis trajectory signal is collected by two eddy current sensors installed at a 90° angle at the upper guide bearing. The lower guide axis trajectory signal and the water guide axis trajectory signal are collected in the same way as the upper guide, and are collected by eddy current sensors installed at the lower guide bearing and the water guide bearing.

3. The method for identifying the axis trajectory of a hydroelectric generator set according to claim 1, characterized in that: In step 3, the process of extracting the features of the axis trajectory image using the directional gradient histogram feature extraction method is as follows: Step 3.1, use the gradient operator to perform convolution operation on the axis trajectory image to obtain the gradient components in the horizontal and vertical directions. The horizontal gradient operator is [-1, 0, 1], and the vertical gradient operator is [-1, 0, 1]T. Then calculate the gradient and direction of each pixel point. The calculation formulas are shown in equations (6) and (7); （6） （7） In formulas (6) and (7), G x ( x , y ) represents the axis trajectory image pixel point ( x , y ), G y ( x , y ) represents the axis trajectory image pixel point ( x , y ), H ( x +1, y ) represents the axis trajectory image pixel point ( x , y )The pixel value of the pixel point whose positive distance on the x-axis is 1, H ( x -1, y ) represents the axis trajectory image pixel point ( x , y )The pixel value of the pixel point with a positive distance of -1 on the x-axis. H ( x , y +1) indicates the axis trajectory image pixel point ( x , y )The pixel value of the pixel point with a positive distance of 1 on the y-axis. H ( x , y -1) represents the axis trajectory image pixel point ( x , y )The pixel value of the pixel point with a positive distance of -1 on the y-axis. G ( x , y ) represents pixel points ( x , y ), α ( x , y ) represents pixel points ( x , y ) direction; Step 3.2, construct the gradient direction histogram of each cell unit; Specifically, in each cell unit, the gradient direction is evenly divided into 9 bins in the range of 0-180°. Formula (6) and formula (7) are used to calculate the gradient and direction of all pixels in each cell unit. Weighted voting is performed in the gradient direction histogram, and the weight is the gradient size. The gradient direction histogram of each cell unit can form a 9-dimensional feature vector. Step 3.3, every 2×2 cell units are grouped into a block, each block has a 4×9-dimensional feature vector, and a window of the block size is sequentially slid on the entire axis track image, with a step size of the cell unit size. Finally, the features of all blocks are connected in series to form the HOG feature of the axis track image. The HOG feature dimension calculation formula is as follows: （8） In formula (8), l p Represents the number of pixels of the horizontal coordinate of the axis trajectory image, h p Represents the number of pixels of the image's ordinate. l c Is the size of the cell unit.

4. The method for identifying the axis trajectory of a hydroelectric generator set according to claim 1, characterized in that: The specific process of step 5 is: input the feature quantity of the axis trajectory image obtained in step 4 after dimension reduction into the support vector machine for classification, and then use the transient search optimization algorithm to optimize the SVM model to obtain the TSO-SVM classification model.

5. The method for identifying the axis trajectory of a hydroelectric generator set according to claim 4, characterized in that: The process of support vector machine classification is as follows: For the set V={( v i , y i )| y i ∈{-1,1}, i =1,2,..., N },in v i represents the sample data, that is, the feature quantity of the axis trajectory image after dimensionality reduction, i represent v i The sample labels of y Represents the sample category, SVM transforms the solution of the optimal hyperplane into the following: （9） In formula (9), w represents the weight vector, b represents a partial vector, C is the penalty factor, ξ As slack variables, Lagrange multipliers and kernel functions are introduced, and the SVM classification problem can be expressed as: （10） In formula (10), e is the Lagrange multiplier, K ( v i ,v j ) represents the kernel function and satisfies K ( v i ,v j ) =<φ ( v i ) ·φ ( v j ) > ,in φ ( v i )and φ ( v j ) are variables v i and v j Mapping in high-dimensional space; the final classification results of the SVM model can be distinguished in the following ways: (11) In the SVM model, the radial basis function RBF is used as the SVM kernel function, and its expression is as follows: (12) In the formula, g is the kernel parameter of RBF.

6. The method for identifying the axis trajectory of a hydroelectric generator set according to claim 5, characterized in that: The expression optimized by the transient search optimization algorithm is: （13） （14） （15） （16） （17） In formulas (13)-(17), Y is the initialized search agent; u b is the upper bound of the search area; l b is the lower bound of the search area; rand is a random number; z Changes linearly from 2 to 0; T and C 1 is the random coefficient; r 1. r 2 and r 3 is a number uniformly distributed between [0,1], r 1 for balanced exploration behavior r 1 ≥ 0.5 and development behavior r 1<0.5; Y l Represents the location of the search agent; Y l * is the optimal search agent location; k is a constant ( k =0,1,2,…); l is the number of iterations; l max is the maximum number of iterations.

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