Water turbine set equipment state comprehensive evaluation method and system
By performing wavelet packet transformation and noise reduction processing on the vibration signal of the hydroelectric unit and using the GWO-SVM model for fault diagnosis, the problems of low efficiency and large error in the judgment of equipment status of the water turbine unit are solved, and higher diagnostic accuracy and speed are achieved.
Patent Information
- Application Number
- CN202411867667.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-18
- Publication Date
- 2025-04-11
AI Technical Summary
In the prior art, the fault judgment efficiency of the equipment status of the turbine unit is low, and errors are prone to occur, resulting in the inability to accurately evaluate the health status of the equipment.
Wavelet packet transformation is used to analyze the time frequency domain signal of the hydroelectric unit vibration signal. After the noise reduction process, the signal is input to the GWO-SVM model for training and fault diagnosis.
Through the combination of noise reduction processing and GWO-SVM model, the accuracy and speed of fault diagnosis of hydroelectric units are improved, errors are reduced, and the fault characteristic information of the equipment can be expressed more accurately.
Smart Images

Figure CN119807955A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of equipment operation monitoring, and in particular relates to a method and system for comprehensively evaluating the equipment status of a water turbine unit. Background Art
[0002] As a key basic equipment of a hydropower station, the turbine has a complex system composition, covering multiple technologies such as mechanics, electronics, and control. The traditional maintenance mode is to shut down for maintenance after a fault occurs, which is not conducive to the long-term stable operation of the hydropower station, resulting in reduced power generation and affecting the reliability of power supply. Since there are many working conditions during the operation of the turbine, the information contained in its health status characterization indicators has obvious uncertainty and ambiguity, which is not conducive to accurately assessing the health status of the equipment.
[0003] At present, the working status of the entire system is evaluated by weighted calculation of the degree of degradation of each detection parameter in the system. The weighting coefficients are mostly fixed values. However, this may result in the following situations: when individual key parameters seriously deviate from normal values or individual key subsystems seriously degrade, manual judgment should be to shut down for inspection, but after several layers of weighting, it may be possible to continue to operate; or, when individual key parameters only slightly deviate from normal values or individual key subsystems slightly degrade, manual judgment should be to continue to operate, but after several layers of weighting, the system may judge that it cannot continue to operate, which may easily lead to problems of misjudgment. Summary of the invention
[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method and system for comprehensively evaluating the status of a hydraulic turbine unit, which solves the problems of low efficiency and large errors in manual fault judgment.
[0005] The technical solution of the present invention is as follows: In a first aspect, the present invention provides a method for comprehensively evaluating the equipment status of a water turbine unit, comprising the following steps:
[0006] S1, obtaining a vibration signal of a hydropower unit, and preprocessing the signal to obtain a vibration signal after noise reduction processing;
[0007] S2, dividing the vibration signal after noise reduction processing into a training set and a test set according to a preset ratio;
[0008] S3, inputting the training set into the GWO-SVM model for training to obtain a trained GWO-SVM model;
[0009] S4. Input the test set into the trained GWO-SVM model to obtain the classification results of hydropower unit fault diagnosis.
[0010] Further: In S1, the method for preprocessing the vibration signal of the hydropower unit is specifically as follows:
[0011] The vibration signals of the hydropower unit under different fault forms are collected, and the vibration signals of the hydropower unit are analyzed in the time and frequency domain using wavelet packet transform. The specific method is as follows:
[0012] The vibration signal of the hydropower unit is decomposed by three-layer wavelet transform, and the wavelet signal generated in the wavelet transform decomposition process is subjected to denoising based on threshold judgment. Wavelet transform reconstruction is performed on the wavelet signal after denoising based on threshold judgment to generate the preprocessed vibration signal of the hydropower unit, which is used as the vibration signal after denoising.
[0013] The beneficial effect of the above further scheme is: the present invention adopts wavelet packet transform to perform time-frequency domain signal analysis on the vibration signal of the hydropower unit, and performs wavelet transform on the vibration signal of the hydropower unit collected on site at multiple decomposition levels, which can reduce the interference of noise on the vibration signal and increase the proportion of effective information in the signal.
[0014] Further: the method of noise reduction processing based on threshold judgment is specifically:
[0015] A corresponding first threshold is set for the wavelet signals generated by wavelet transform decomposition at different layers, and it is judged whether the wavelet signal is greater than the first threshold. If so, a smoothing process is performed on the wavelet signal to obtain a wavelet signal after noise reduction based on the threshold judgment. If not, the wavelet signal is set to zero.
[0016] The expression of the wavelet signal w' after the denoising process based on the threshold judgment is obtained as follows:
[0017] w'=sgn(w)(|w|-a)
[0018] Where sgn(·) is the sign function, a is the first threshold, and w is the wavelet signal.
[0019] Further: S2 is specifically:
[0020] Based on the corresponding faults of the hydropower units, the vibration signals after noise reduction are marked with corresponding fault labels, and the training set and test set are divided into two sets in a ratio of 8:2.
[0021] Further: S3 includes the following sub-steps:
[0022] S31, set the number of gray wolf groups, the maximum number of iterations, the SVM penalty factor and the kernel function;
[0023] S32, randomly generate a gray wolf population, initialize the position of the gray wolf group and the number of iterations, and the position of each gray wolf includes the SVM penalty factor and the kernel function;
[0024] S33, calculating the fitness of each gray wolf, where the fitness of each gray wolf is obtained by training the SVM in the training set;
[0025] S34, dividing the gray wolf pack into three wolves of different levels α, β, δ and the remaining gray wolves according to fitness, and updating the positions of the remaining gray wolves in the gray wolf pack;
[0026] S35. Determine whether the number of iterations is greater than the maximum number of iterations. If so, determine the optimal gray wolf individual and output the best SVM penalty factor and kernel function found. If not, add 1 to the number of iterations and return to S33.
[0027] The beneficial effects of the above further scheme are as follows: in order to increase the diversity of the wolf population, the present invention introduces a nonlinear control strategy into the traditional gray wolf algorithm to improve the global search capability of the gray wolf, and adaptively selects the candidate position with the best fitness during the iteration process. This method helps to find the best SVM penalty factor and kernel function and reduce the risk of premature convergence.
[0028] Further: In said S34, the method for updating the positions of the remaining gray wolves in the gray wolf pack is specifically:
[0029] S341, dividing the gray wolf pack into three wolves of different levels α, β, δ and the remaining gray wolves according to fitness, and calculating the first candidate positions of the remaining gray wolves in the gray wolf pack;
[0030] S342, calculating the search space of each gray wolf among the remaining gray wolves, and determining the gray wolves in the search space;
[0031] S343, calculating the second candidate positions of the remaining gray wolves in the gray wolf pack according to the domain matrix of the search space;
[0032] S344. Select a candidate position with the best fitness from the first candidate position and the second candidate position, and update the positions of the remaining gray wolves in the gray wolf pack.
[0033] Further: In the above 341, the first candidate positions X of the remaining gray wolves in the gray wolf pack are calculated. gwo The specific expression of (t+1) is:
[0034]
[0035] Where X1 is the updated position under the guidance of α wolf, X2 is the updated position under the guidance of β wolf, X3 is the updated position under the guidance of δ wolf, and t is the current iteration number;
[0036] X1=X α -A1|C1X α -X(t)|
[0037] X2=X β -A2|C2X β -X(t)|
[0038] X3=X δ -A3|C3X δ -X(t)|
[0039] In the formula, X α is the current position of wolf α, X β is the current position of β wolf, X δ is the current position of the δ wolf, X(t) is the position of the other gray wolves before updating, C1 is the first coefficient vector, C2 is the second coefficient vector, C3 is the third coefficient vector, A1 is the fourth coefficient vector, A2 is the fifth coefficient vector, and A3 is the sixth coefficient vector.
[0040] The beneficial effect of the above further scheme is: the present invention adopts the gray wolf optimization algorithm to train the SVM, and the gray wolf optimization algorithm continuously iterates and searches for the best by simulating the hunting behavior of wolves, and has strong applicability and search ability for parameter optimization problems.
[0041] Furthermore, the first to third coefficient vectors are updated by a nonlinear control strategy in each iteration to improve the global search capability of the gray wolf. The expression of the updated coefficient vector A′ calculated by the nonlinear control strategy is specifically:
[0042]
[0043] Where A is the coefficient vector before update, T max is the maximum number of iterations, r1 is a random vector whose value range is 0 to 1.
[0044] The beneficial effect of the above further scheme is: the present invention adjusts the size of the coefficient vector through a nonlinear control strategy to avoid falling into the local optimum due to too fast position update speed, and introduces a random vector for disturbance to prevent early falling into the local optimum value and reduce the selection of erroneous positions.
[0045] Further: In S342, the search space R of the i-th gray wolf is calculated i The specific expression of (t) is:
[0046] R i (t)=||X i (t)-X gwo (t+1)||
[0047] In the formula, X i (t) is the position of the i-th gray wolf, X gwo (t+1) is the first candidate position of the i-th gray wolf;
[0048] The gray wolf N in the search space of the i-th gray wolf iThe specific expression of (t) is:
[0049] N i (t) = {X j (t)|E(X j (t),X i (t))≤R i (t)}
[0050] Where, X j (t) is the position of the jth gray wolf, and E(·) is the Euclidean distance.
[0051] Further: In S343, the second candidate position X of the i-th gray wolf is calculated i The specific expression of (t+1) is:
[0052] X i (t+1)=X i (t)+rand×(X n (t)-X r (t))
[0053] In the formula, rand is a random number, its value range is 0 to 1, X n (t) is the position of the randomly selected gray wolf in the search space of the i-th gray wolf, X r (t) is the position of another gray wolf randomly selected from the gray wolf population.
[0054] The beneficial effect of the above further scheme is: the present invention believes that the calculated first candidate position is not the best position for the gray wolf to move, and can also follow the gray wolves in the search space or the gray wolves in the gray wolf population to generate a second candidate position for the gray wolf to move, thereby selecting the candidate position with the best fitness for updating. This method continuously optimizes the position of the gray wolf's movement according to the fitness, which can improve the time efficiency of the optimal SVM penalty factor and kernel function search, and improve the accuracy of the GWO-SVM model.
[0055] In a second aspect, the present invention provides a comprehensive evaluation system for the equipment status of a water turbine unit, comprising:
[0056] A preprocessing module is used to obtain the vibration signal of the hydropower unit, preprocess it, and obtain the vibration signal after noise reduction processing;
[0057] A data division module is used to divide the vibration signal after noise reduction into a training set and a test set according to a preset ratio;
[0058] A model training module is used to input the training set into the GWO-SVM model for training to obtain a trained GWO-SVM model;
[0059] The fault diagnosis module is used to input the test set into the trained GWO-SVM model to obtain the classification results of the fault diagnosis of the hydropower unit.
[0060] Further: the preprocessing module includes:
[0061] A data acquisition submodule, used to collect vibration signals of the hydropower unit under different fault forms;
[0062] The time-frequency domain signal analysis submodule is used to perform time-frequency domain signal analysis on the vibration signal of the hydropower unit by using wavelet packet transform. Specifically, the method comprises: performing three-layer wavelet transform decomposition on the vibration signal of the hydropower unit, performing threshold-based denoising processing on the wavelet signal generated in the wavelet transform decomposition process, performing wavelet transform reconstruction on the wavelet signal after the denoising processing based on the threshold-based denoising processing, generating a pre-processed vibration signal of the hydropower unit, and using it as the vibration signal after the denoising processing.
[0063] Further: the method of performing the noise reduction processing based on threshold judgment in the time-frequency domain signal analysis submodule is specifically as follows:
[0064] A corresponding first threshold is set for the wavelet signals generated by wavelet transform decomposition at different layers, and it is judged whether the wavelet signal is greater than the first threshold. If so, a smoothing process is performed on the wavelet signal to obtain a wavelet signal after noise reduction based on the threshold judgment. If not, the wavelet signal is set to zero.
[0065] The expression of the wavelet signal w' after the denoising process based on the threshold judgment is obtained as follows:
[0066] w'=sgn(w)(|w|-a)
[0067] Where sgn(·) is the sign function, a is the first threshold, and w is the wavelet signal.
[0068] Further: the method of the data division module dividing the vibration signal after noise reduction processing into a training set and a test set according to a preset ratio is specifically as follows:
[0069] Based on the corresponding faults of the hydropower units, the vibration signals after noise reduction are marked with corresponding fault labels, and the training set and test set are divided into two sets in a ratio of 8:2.
[0070] Further: the model training module includes:
[0071] The parameter setting unit is used to set the number of gray wolf groups, the maximum number of iterations, the SVM penalty factor and the kernel function;
[0072] Initialization parameter unit, used to randomly generate gray wolf population, initialize the position of gray wolf group and the number of iterations, the position of each gray wolf includes SVM penalty factor and kernel function;
[0073] A fitness calculation unit is used to calculate the fitness of each gray wolf. The fitness of each gray wolf is obtained by training the SVM in the training set.
[0074] The wolf pack division unit is used to divide the gray wolf pack into three wolves of different levels, namely, α, β, δ, and the rest of the gray wolves according to their fitness, and to update the positions of the rest of the gray wolves in the gray wolf pack;
[0075] The threshold judgment unit is used to judge whether the number of iterations is greater than the maximum number of iterations. If so, the optimal gray wolf individual is determined and the best SVM penalty factor and kernel function found are output. If not, the number of iterations is increased by 1 and returned to the fitness calculation unit.
[0076] Further: the method for the wolf pack division unit to update the positions of the remaining gray wolves in the gray wolf pack is specifically:
[0077] The wolf pack is divided into three wolves of different levels, α, β, δ and the rest of the wolf pack according to their fitness, and the first candidate positions of the rest of the wolf pack are calculated;
[0078] Calculate the search space of each gray wolf among the remaining gray wolves, and determine the gray wolves in the search space;
[0079] Calculate the second candidate positions of the remaining gray wolves in the gray wolf pack according to the domain matrix of the search space;
[0080] Select the candidate position with the best fitness from the first candidate position and the second candidate position, and update the positions of the remaining gray wolves in the gray wolf pack.
[0081] Further: the calculation of the first candidate position X of the remaining gray wolves in the gray wolf pack gwo The specific expression of (t+1) is:
[0082]
[0083] Where X1 is the updated position under the guidance of α wolf, X2 is the updated position under the guidance of β wolf, X3 is the updated position under the guidance of δ wolf, and t is the current iteration number;
[0084] X1=X α -A1|C1X α -X(t)|
[0085] X2=X β -A2|C2X β -X(t)|
[0086] X3=X δ -A3|C3X δ -X(t)|
[0087] Where, X α is the current position of wolf α, X β is the current position of β wolf, X δ is the current position of the δ wolf, X(t) is the position of the other gray wolves before updating, C1 is the first coefficient vector, C2 is the second coefficient vector, C3 is the third coefficient vector, A1 is the fourth coefficient vector, A2 is the fifth coefficient vector, and A3 is the sixth coefficient vector.
[0088] Furthermore, the first to third coefficient vectors are updated by a nonlinear control strategy in each iteration to improve the global search capability of the gray wolf. The expression of the updated coefficient vector A′ calculated by the nonlinear control strategy is specifically:
[0089]
[0090] Where A is the coefficient vector before update, T max is the maximum number of iterations, r1 is a random vector whose value range is 0 to 1.
[0091] Further: the calculation of the search space R of the i-th gray wolf i The specific expression of (t) is:
[0092] Ri(t)=||Xi(t)-X gwo (t+1)||
[0093] Where, X i (t) is the position of the i-th gray wolf, X gwo (t+1) is the first candidate position of the i-th gray wolf;
[0094] The gray wolf N in the search space of the i-th gray wolf i The specific expression of (t) is:
[0095] N i (t) = {X j (t)|E(X j (t),X i (t))≤R i (t)}
[0096] Where, X j (t) is the position of the jth gray wolf, and E(·) is the Euclidean distance.
[0097] Further: the calculation of the second candidate position X of the i-th gray wolf i The specific expression of (t+1) is:
[0098] X i (t+1)=X i (t)+rand×(X n(t)-X r (t))
[0099] In the formula, rand is a random number, its value range is 0 to 1, X n (t) is the position of the randomly selected gray wolf in the search space of the i-th gray wolf, X r (t) is the position of another gray wolf randomly selected from the gray wolf population.
[0100] The beneficial effects of the present invention are:
[0101] (1) The present invention provides a method and system for comprehensively evaluating the equipment status of a hydro-turbine unit, which performs noise reduction processing on the vibration signal of the hydro-turbine unit, reduces the interference of noise on the vibration signal, and increases the proportion of effective information in the signal. The fault characteristic information of the vibration signal of the hydro-turbine unit can be better expressed, and the GWO-SVM model is introduced to perform fault diagnosis of the hydro-turbine unit, so that the results of fault diagnosis of the hydro-turbine unit are more accurate and the fault judgment speed is faster.
[0102] (2) The present invention uses the GWO-SVM model to perform fault diagnosis of hydropower units. The coefficient vector size is changed through a nonlinear control strategy to adjust the global search capability, avoid repeated oscillations caused by excessively fast position update speed, ensure the global optimal search position, improve the reliability of the GWO-SVM model, and further improve the accuracy of the GWO-SVM model output for fault diagnosis of hydropower units.
[0103] (3) The GWO-SVM model of the present invention can identify and analyze the fault vibration signals of various faults occurring in the hydropower unit, thereby quickly determining the fault type and improving the safety management efficiency of the hydropower unit equipment. BRIEF DESCRIPTION OF THE DRAWINGS
[0104] Figure 1 The present invention is a flow chart of a method for comprehensive evaluation of the equipment status of a water turbine unit.
[0105] Figure 2 It is a schematic diagram of a comprehensive evaluation system for the equipment status of a water turbine unit according to the present invention. DETAILED DESCRIPTION
[0106] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.
[0107] Embodiment 1:
[0108] like Figure 1 As shown, in one embodiment of the present invention, a method for comprehensive evaluation of the equipment status of a hydraulic turbine unit includes the following steps:
[0109] S1, obtaining a vibration signal of a hydropower unit, and preprocessing the signal to obtain a vibration signal after noise reduction processing;
[0110] S2, dividing the vibration signal after noise reduction processing into a training set and a test set according to a preset ratio;
[0111] S3, inputting the training set into the GWO-SVM model for training to obtain a trained GWO-SVM model;
[0112] S4. Input the test set into the trained GWO-SVM model to obtain the classification results of hydropower unit fault diagnosis.
[0113] In S1, the method for preprocessing the vibration signal of the hydropower unit is specifically as follows:
[0114] The vibration signals of the hydropower unit under different fault forms are collected, and the vibration signals of the hydropower unit are analyzed in the time and frequency domain using wavelet packet transform. The specific method is as follows:
[0115] The vibration signal of the hydropower unit is decomposed by three-layer wavelet transform, and the wavelet signal generated in the wavelet transform decomposition process is subjected to denoising based on threshold judgment. Wavelet transform reconstruction is performed on the wavelet signal after denoising based on threshold judgment to generate the preprocessed vibration signal of the hydropower unit, which is used as the vibration signal after denoising.
[0116] In this embodiment, the vibration signal of the hydropower unit is obtained and a time-frequency domain signal analysis is performed on it. The present invention uses wavelet packet transform to perform time-frequency domain signal analysis on the vibration signal of the hydropower unit. The vibration signal of the hydropower unit collected on-site is subjected to wavelet transform at multiple decomposition levels, which can reduce the interference of noise on the vibration signal and increase the proportion of effective information in the signal.
[0117] The method of noise reduction processing based on threshold judgment is specifically as follows:
[0118] A corresponding first threshold is set for the wavelet signals generated by wavelet transform decomposition at different layers, and it is judged whether the wavelet signal is greater than the first threshold. If so, a smoothing process is performed on the wavelet signal to obtain a wavelet signal after noise reduction based on the threshold judgment. If not, the wavelet signal is set to zero.
[0119] The expression of the wavelet signal w' after the denoising process based on the threshold judgment is obtained as follows:
[0120] w'=sgn(w)(|w|-a)
[0121] Where sgn(·) is the sign function, a is the first threshold, and w is the wavelet signal.
[0122] In this embodiment, for the decomposed wavelet signal, the wavelet coefficient of the noise signal is smaller than the wavelet coefficient of the useful signal. The present invention sets a first threshold value for threshold judgment, and regards the wavelet coefficient smaller than the first threshold value as noise information to obtain a signal after noise reduction. Among them, for the wavelet coefficients generated by the decomposition of wavelet transform at different layers, the threshold value relative to is:
[0123]
[0124] Where, L is the data length of the original hydropower unit vibration signal, and σ is the noise standard deviation;
[0125] The S2 is specifically:
[0126] Based on the corresponding faults of the hydropower units, the vibration signals after noise reduction are marked with corresponding fault labels, and the training set and test set are divided into two sets in a ratio of 8:2.
[0127] The S3 comprises the following sub-steps:
[0128] S31, set the number of gray wolf groups, the maximum number of iterations, the SVM penalty factor and the kernel function;
[0129] S32, randomly generate a gray wolf population, initialize the position of the gray wolf group and the number of iterations, and the position of each gray wolf includes the SVM penalty factor and the kernel function;
[0130] S33, calculating the fitness of each gray wolf, where the fitness of each gray wolf is obtained by training the SVM in the training set;
[0131] S34, dividing the gray wolf pack into three wolves of different levels α, β, δ and the remaining gray wolves according to fitness, and updating the positions of the remaining gray wolves in the gray wolf pack;
[0132] S35. Determine whether the number of iterations is greater than the maximum number of iterations. If so, determine the optimal gray wolf individual and output the best SVM penalty factor and kernel function found. If not, add 1 to the number of iterations and return to S33.
[0133] In this embodiment, the traditional gray wolf algorithm finds the optimal solution in the process of following the leader, but it limits the diversity of the gray wolf population. This will make the algorithm converge easily and fall into a local optimal solution. In order to increase the diversity of the wolf population, the present invention introduces a nonlinear control strategy into the traditional gray wolf algorithm to improve the global search ability of the gray wolf and adaptively select the candidate position with the best fitness during the iteration process. This method helps to find the best SVM penalty factor and kernel function and reduce the risk of premature convergence.
[0134] In S34, the method for updating the positions of the remaining gray wolves in the gray wolf pack is specifically as follows:
[0135] S341, dividing the gray wolf pack into three wolves of different levels α, β, δ and the remaining gray wolves according to fitness, and calculating the first candidate positions of the remaining gray wolves in the gray wolf pack;
[0136] S342, calculating the search space of each gray wolf among the remaining gray wolves, and determining the gray wolves in the search space;
[0137] S343, calculating the second candidate positions of the remaining gray wolves in the gray wolf pack according to the domain matrix of the search space;
[0138] S344. Select a candidate position with the best fitness from the first candidate position and the second candidate position, and update the positions of the remaining gray wolves in the gray wolf pack.
[0139] In the step 341, the first candidate positions X of the remaining gray wolves in the gray wolf pack are calculated. gwo The specific expression of (t+1) is:
[0140]
[0141] Where X1 is the updated position under the guidance of α wolf, X2 is the updated position under the guidance of β wolf, X3 is the updated position under the guidance of δ wolf, and t is the current iteration number;
[0142] X1=X α -A1|C1X α -X(t)|
[0143] X2=X β -A2|C2X β -X(t)|
[0144] X3=X δ -A3|C3X δ -X(t)|
[0145] In the formula, X α is the current position of wolf α, X β is the current position of β wolf, X δ is the current position of the δ wolf, X(t) is the position of the other gray wolves before updating, C1 is the first coefficient vector, C2 is the second coefficient vector, C3 is the third coefficient vector, A1 is the fourth coefficient vector, A2 is the fifth coefficient vector, and A3 is the sixth coefficient vector.
[0146] In this embodiment, the present invention adopts the gray wolf optimization algorithm to train the SVM. The gray wolf optimization algorithm continuously performs iterative search and optimization by simulating the hunting behavior of wolves, and has strong applicability and search ability for parameter optimization problems.
[0147] The first to third coefficient vectors are updated by a nonlinear control strategy in each iteration to improve the global search capability of the gray wolf. The expression of the updated coefficient vector A′ calculated by the nonlinear control strategy is specifically:
[0148]
[0149] Where A is the coefficient vector before update, T max is the maximum number of iterations, r1 is a random vector whose value range is 0 to 1.
[0150] In this embodiment, the present invention adjusts the size of the coefficient vector through a nonlinear control strategy to avoid falling into the local optimum due to too fast position update speed, and introduces a random vector for disturbance to prevent early falling into the local optimum value and reduce the selection of erroneous positions.
[0151] In S342, the search space R of the i-th gray wolf is calculated. i The specific expression of (t) is:
[0152] R i (t)=||X i (t)-X gwo (t+1)||
[0153] Where, X i (t) is the position of the i-th gray wolf, X gwo (t+1) is the first candidate position of the i-th gray wolf;
[0154] The gray wolf N in the search space of the i-th gray wolf i The specific expression of (t) is:
[0155] N i (t) = {X j (t)|E(X j (t),X i (t))≤R i (t)}
[0156] Where, X j (t) is the position of the jth gray wolf, and E(·) is the Euclidean distance.
[0157] In S343, the second candidate position X of the i-th gray wolf is calculated. i The specific expression of (t+1) is:
[0158] X i (t+1)=X i (t)+rand×(X n (t)-X r (t))
[0159] In the formula, rand is a random number, its value range is 0 to 1, X n (t) is the position of the randomly selected gray wolf in the search space of the i-th gray wolf, X r (t) is the position of another gray wolf randomly selected from the gray wolf population.
[0160] In this embodiment, the present invention believes that the calculated first candidate position is not the optimal position for the gray wolf to move. It is also possible to follow the gray wolves in the search space or the gray wolves in the gray wolf population to generate a second candidate position for the gray wolf to move, thereby selecting the candidate position with the best fitness for updating. This method continuously optimizes the position of the gray wolf's movement according to the fitness, which can improve the time efficiency of the optimal SVM penalty factor and kernel function search, and improve the accuracy of the GWO-SVM model.
[0161] Embodiment 2:
[0162] like Figure 2 As shown, an embodiment of the present invention provides a comprehensive evaluation system for the equipment status of a hydraulic turbine unit, comprising:
[0163] A preprocessing module is used to obtain the vibration signal of the hydropower unit, preprocess it, and obtain the vibration signal after noise reduction processing;
[0164] A data division module is used to divide the vibration signal after noise reduction into a training set and a test set according to a preset ratio;
[0165] A model training module is used to input the training set into the GWO-SVM model for training to obtain a trained GWO-SVM model;
[0166] The fault diagnosis module is used to input the test set into the trained GWO-SVM model to obtain the classification results of the fault diagnosis of the hydropower unit.
[0167] The preprocessing module comprises:
[0168] A data acquisition submodule, used to collect vibration signals of the hydropower unit under different fault forms;
[0169] The time-frequency domain signal analysis submodule is used to perform time-frequency domain signal analysis on the vibration signal of the hydropower unit by using wavelet packet transform. Specifically, the method comprises: performing three-layer wavelet transform decomposition on the vibration signal of the hydropower unit, performing threshold-based denoising processing on the wavelet signal generated in the wavelet transform decomposition process, performing wavelet transform reconstruction on the wavelet signal after the denoising processing based on the threshold-based denoising processing, generating a pre-processed vibration signal of the hydropower unit, and using it as the vibration signal after the denoising processing.
[0170] In this embodiment, the data acquisition submodule obtains the vibration signal of the hydropower unit and performs time-frequency domain signal analysis on it. The present invention uses wavelet packet transform to perform time-frequency domain signal analysis on the vibration signal of the hydropower unit, and performs wavelet transform on the vibration signal of the hydropower unit collected on-site at multiple decomposition levels, which can reduce the interference of noise on the vibration signal and increase the proportion of effective information in the signal.
[0171] The method for the time-frequency domain signal analysis submodule to perform noise reduction processing based on threshold judgment is specifically as follows:
[0172] A corresponding first threshold is set for the wavelet signals generated by wavelet transform decomposition at different layers, and it is judged whether the wavelet signal is greater than the first threshold. If so, a smoothing process is performed on the wavelet signal to obtain a wavelet signal after noise reduction based on the threshold judgment. If not, the wavelet signal is set to zero.
[0173] The expression of the wavelet signal w' after the denoising process based on the threshold judgment is obtained as follows:
[0174] w'=sgn(w)(|w|-a)
[0175] Where sgn(·) is the sign function, a is the first threshold, and w is the wavelet signal.
[0176] In this embodiment, for the decomposed wavelet signal, the wavelet coefficient of the noise signal is smaller than the wavelet coefficient of the useful signal in the time-frequency domain signal analysis submodule. The present invention sets a first threshold value for threshold judgment, and regards the wavelet coefficient smaller than the first threshold value as noise information to obtain the signal after noise reduction. Among them, for the wavelet coefficients generated by the decomposition of wavelet transform at different layers, the threshold value relative to is:
[0177]
[0178] Where, L is the data length of the original hydropower unit vibration signal, and σ is the noise standard deviation;
[0179] The method of the data division module for dividing the vibration signal after noise reduction processing into a training set and a test set according to a preset ratio is specifically as follows:
[0180] Based on the corresponding faults of the hydropower units, the vibration signals after noise reduction are marked with corresponding fault labels, and the training set and test set are divided into two sets in a ratio of 8:2.
[0181] The model training module includes:
[0182] The parameter setting unit is used to set the number of gray wolf groups, the maximum number of iterations, the SVM penalty factor and the kernel function;
[0183] Initialization parameter unit, used to randomly generate gray wolf population, initialize the position of gray wolf group and the number of iterations, the position of each gray wolf includes SVM penalty factor and kernel function;
[0184] A fitness calculation unit is used to calculate the fitness of each gray wolf. The fitness of each gray wolf is obtained by training the SVM in the training set.
[0185] The wolf pack division unit is used to divide the gray wolf pack into three wolves of different levels, namely, α, β, δ, and the rest of the gray wolves according to their fitness, and to update the positions of the rest of the gray wolves in the gray wolf pack;
[0186] The threshold judgment unit is used to judge whether the number of iterations is greater than the maximum number of iterations. If so, the optimal gray wolf individual is determined and the best SVM penalty factor and kernel function found are output. If not, the number of iterations is increased by 1 and returned to the fitness calculation unit.
[0187] In this embodiment, the traditional gray wolf algorithm finds the optimal solution in the process of following the alpha wolf, but it limits the diversity of the gray wolf population. This will make the algorithm converge easily and fall into a local optimal solution. In order to increase the diversity of the wolf population, the present invention innovatively sets a model training module, which introduces a nonlinear control strategy into the traditional gray wolf algorithm to improve the global search ability of the gray wolf and adaptively selects the candidate position with the best fitness during the iteration process. This method helps to find the best SVM penalty factor and kernel function and reduce the risk of premature convergence.
[0188] The method for the wolf group division unit to update the positions of the remaining gray wolves in the gray wolf group is specifically as follows:
[0189] The wolf pack is divided into three wolves of different levels, α, β, δ and the rest of the wolf pack according to their fitness, and the first candidate positions of the rest of the wolf pack are calculated;
[0190] Calculate the search space of each gray wolf among the remaining gray wolves, and determine the gray wolves in the search space;
[0191] Calculate the second candidate positions of the remaining gray wolves in the gray wolf pack according to the domain matrix of the search space;
[0192] Select the candidate position with the best fitness from the first candidate position and the second candidate position, and update the positions of the remaining gray wolves in the gray wolf pack.
[0193] The first candidate position X of the remaining gray wolves in the gray wolf pack is calculated gwo The specific expression of (t+1) is:
[0194]
[0195] Where X1 is the updated position under the guidance of α wolf, X2 is the updated position under the guidance of β wolf, X3 is the updated position under the guidance of δ wolf, and t is the current iteration number;
[0196] X1=X α -A1|C1X α -X(t)|
[0197] X2=X β -A2|C2X β -X(t)|
[0198] X3=X δ -A3|C3X δ -X(t)|
[0199] In the formula, X α is the current position of wolf α, X β is the current position of β wolf, X δ is the current position of the δ wolf, X(t) is the position of the other gray wolves before updating, C1 is the first coefficient vector, C2 is the second coefficient vector, C3 is the third coefficient vector, A1 is the fourth coefficient vector, A2 is the fifth coefficient vector, and A3 is the sixth coefficient vector.
[0200] In this embodiment, the present invention adopts the gray wolf optimization algorithm to train the SVM. The gray wolf optimization algorithm continuously performs iterative search and optimization by simulating the hunting behavior of wolves, and has strong applicability and search ability for parameter optimization problems.
[0201] The first to third coefficient vectors are updated by a nonlinear control strategy in each iteration to improve the global search capability of the gray wolf. The expression of the updated coefficient vector A′ calculated by the nonlinear control strategy is specifically:
[0202]
[0203] Where A is the coefficient vector before update, T max is the maximum number of iterations, r1 is a random vector whose value range is 0 to 1.
[0204] In this embodiment, the present invention adjusts the size of the coefficient vector through a nonlinear control strategy to avoid falling into the local optimum due to too fast position update speed, and introduces a random vector for disturbance to prevent early falling into the local optimum value and reduce the selection of erroneous positions.
[0205] The calculation of the search space R of the i-th gray wolf i The specific expression of (t) is:
[0206] R i (t)=||X i (t)-Xgwo (t+1)||
[0207] Where, X i (t) is the position of the i-th gray wolf, X gwo (t+1) is the first candidate position of the i-th gray wolf;
[0208] The gray wolf N in the search space of the i-th gray wolf i The specific expression of (t) is:
[0209] N i (t) = {X j (t)|E(X j (t),X i (t))≤R i (t)}
[0210] Where, X j (t) is the position of the jth gray wolf, and E(·) is the Euclidean distance.
[0211] The calculation of the second candidate position X of the i-th gray wolf i The specific expression of (t+1) is:
[0212] X i (t+1)=X i (t)+rand×(X n (t)-X r (t))
[0213] In the formula, rand is a random number, its value range is 0 to 1, X n (t) is the position of the randomly selected gray wolf in the search space of the i-th gray wolf, X r (t) is the position of another gray wolf randomly selected from the gray wolf population.
[0214] In this embodiment, the present invention believes that the calculated first candidate position is not the optimal position for the gray wolf to move. It is also possible to follow the gray wolves in the search space or the gray wolves in the gray wolf population to generate a second candidate position for the gray wolf to move, thereby selecting the candidate position with the best fitness for updating. This method continuously optimizes the position of the gray wolf's movement according to the fitness, which can improve the time efficiency of the optimal SVM penalty factor and kernel function search, and improve the accuracy of the GWO-SVM model.
[0215] The beneficial effects of the present invention are as follows: the present invention provides a method and system for comprehensively evaluating the equipment status of a hydro-turbine unit, performs noise reduction processing on the vibration signal of the hydro-turbine unit, reduces the interference of noise on the vibration signal, increases the proportion of effective information in the signal, can better express the fault characteristic information of the vibration signal of the hydro-turbine unit, introduces the GWO-SVM model to perform fault diagnosis of the hydro-turbine unit, and makes the result of fault diagnosis of the hydro-turbine unit more accurate and the fault judgment speed faster.
[0216] The present invention uses the GWO-SVM model to perform fault diagnosis of hydropower units, changes the size of the coefficient vector through a nonlinear control strategy to adjust the global search capability, avoids repeated oscillations caused by excessively fast position update speed, ensures that the search position is globally optimal, improves the reliability of the GWO-SVM model, and further improves the accuracy of the GWO-SVM model output fault diagnosis of hydropower units.
[0217] The GWO-SVM model of the present invention can identify and analyze fault vibration signals of various faults occurring in a hydropower unit, thereby quickly determining the fault type and improving the safety management efficiency of the hydropower unit equipment.
[0218] In the description of the present invention, it is necessary to understand that the orientation or positional relationship indicated by the terms "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", and "third" are used only for descriptive purposes, and cannot be understood as indicating or implying the relative importance or the number of implicitly specified technical features. Therefore, the features defined by "first", "second", and "third" may explicitly or implicitly include one or more of the features.
Claims
1. A method for comprehensive evaluation of the equipment status of a hydraulic turbine unit, characterized in that: The following steps are involved: S1, obtaining a vibration signal of a hydropower unit, and preprocessing the signal to obtain a vibration signal after noise reduction processing; S2, dividing the vibration signal after noise reduction processing into a training set and a test set according to a preset ratio; S3, inputting the training set into the GWO-SVM model for training to obtain a trained GWO-SVM model; S4. Input the test set into the trained GWO-SVM model to obtain the classification results of hydropower unit fault diagnosis.
2. The method for comprehensive evaluation of the equipment status of a hydraulic turbine unit according to claim 1, characterized in that: In S1, the method for preprocessing the vibration signal of the hydropower unit is specifically as follows: The vibration signals of the hydropower unit under different fault forms are collected, and the vibration signals of the hydropower unit are analyzed in the time and frequency domain using wavelet packet transform. The specific method is as follows: The vibration signal of the hydropower unit is decomposed by three-layer wavelet transform, and the wavelet signal generated in the wavelet transform decomposition process is subjected to denoising based on threshold judgment. Wavelet transform reconstruction is performed on the wavelet signal after denoising based on threshold judgment to generate the preprocessed vibration signal of the hydropower unit, which is used as the vibration signal after denoising.
3. The method for comprehensive evaluation of the equipment status of a water turbine unit according to claim 2, characterized in that: The method of noise reduction processing based on threshold judgment is specifically as follows: A corresponding first threshold is set for the wavelet signals generated by wavelet transform decomposition at different layers, and it is judged whether the wavelet signal is greater than the first threshold. If so, a smoothing process is performed on the wavelet signal to obtain a wavelet signal after noise reduction based on the threshold judgment. If not, the wavelet signal is set to zero. The expression of the wavelet signal w' after the denoising process based on the threshold judgment is obtained as follows: w'=sgn(w)(|w|-a) Where sgn(·) is the sign function, a is the first threshold, and w is the wavelet signal.
4. The method for comprehensive evaluation of the equipment status of a water turbine unit according to claim 1, characterized in that: The S2 is specifically: Based on the corresponding faults of the hydropower units, the vibration signals after noise reduction are marked with corresponding fault labels, and the training set and test set are divided into two sets in a ratio of 8:
2.
5. The method for comprehensive evaluation of the equipment status of a water turbine unit according to claim 1, characterized in that: The S3 comprises the following sub-steps: S31, set the number of gray wolf groups, the maximum number of iterations, the SVM penalty factor and the kernel function; S32, randomly generate a gray wolf population, initialize the position of the gray wolf group and the number of iterations, and the position of each gray wolf includes the SVM penalty factor and the kernel function; S33, calculating the fitness of each gray wolf, where the fitness of each gray wolf is obtained by training the SVM in the training set; S34, dividing the gray wolf pack into three wolves of different levels α, β, δ and the remaining gray wolves according to fitness, and updating the positions of the remaining gray wolves in the gray wolf pack; S35. Determine whether the number of iterations is greater than the maximum number of iterations. If so, determine the optimal gray wolf individual and output the best SVM penalty factor and kernel function found. If not, add 1 to the number of iterations and return to S33.
6. The method for comprehensive evaluation of the equipment status of a hydraulic turbine unit according to claim 5, characterized in that: In S34, the method for updating the positions of the remaining gray wolves in the gray wolf pack is specifically as follows: S341, dividing the gray wolf pack into three wolves of different levels α, β, δ and the remaining gray wolves according to fitness, and calculating the first candidate positions of the remaining gray wolves in the gray wolf pack; S342, calculating the search space of each gray wolf among the remaining gray wolves, and determining the gray wolves in the search space; S343, calculating the second candidate positions of the remaining gray wolves in the gray wolf pack according to the domain matrix of the search space; S344. Select a candidate position with the best fitness from the first candidate position and the second candidate position, and update the positions of the remaining gray wolves in the gray wolf pack.
7. The method for comprehensive evaluation of the equipment status of a water turbine unit according to claim 6, characterized in that: In the step 341, the first candidate positions X of the remaining gray wolves in the gray wolf pack are calculated. gwo The specific expression of (t+1) is: Where X1 is the updated position under the guidance of α wolf, X2 is the updated position under the guidance of β wolf, X3 is the updated position under the guidance of δ wolf, and t is the current iteration number; X1=X α -A1|C1X α -X(t)| X2=X β -A2|C2X β -X(t)| X3=X δ -A3|C3X δ -X(t)| Where, X α is the current position of wolf α, X β is the current position of β wolf, X δ is the current position of the δ wolf, X(t) is the position of the other gray wolves before updating, C1 is the first coefficient vector, C2 is the second coefficient vector, C3 is the third coefficient vector, A1 is the fourth coefficient vector, A2 is the fifth coefficient vector, and A3 is the sixth coefficient vector.
8. The method for comprehensive evaluation of the equipment status of a water turbine unit according to claim 7, characterized in that: The first to third coefficient vectors are updated by a nonlinear control strategy in each iteration to improve the global search capability of the gray wolf. The expression of the updated coefficient vector A' calculated by the nonlinear control strategy is specifically: Where A is the coefficient vector before updating, T max is the maximum number of iterations, r1 is a random vector whose value range is 0 to 1.
9. The method for comprehensive evaluation of the equipment status of a water turbine unit according to claim 6, characterized in that: In S342, the search space R of the i-th gray wolf is calculated. i The specific expression of (t) is: R i (t)=||X i (t)-X gwo (t+1)|| Where, X i (t) is the position of the i-th gray wolf, X gwo (t+1) is the first candidate position of the i-th gray wolf; The gray wolf N in the search space of the i-th gray wolf i The specific expression of (t) is: N i (t)={X j (t)|E(X j (t),X i (t))≤R i (t)} Where, X j (t) is the position of the jth gray wolf, and E(·) is the Euclidean distance.
10. The method for comprehensive evaluation of the equipment status of a water turbine unit according to claim 9, characterized in that: In S343, the second candidate position X of the i-th gray wolf is calculated. i The specific expression of (t+1) is: X i (t+1)=X i (t)+rand×(X n (t)-X r (t)) In the formula, rand is a random number, its value range is 0 to 1, X n (t) is the position of the randomly selected gray wolf in the search space of the i-th gray wolf, X r (t) is the position of another gray wolf randomly selected from the gray wolf population.
11. A comprehensive evaluation system for the equipment status of a hydraulic turbine unit, characterized in that: include: A preprocessing module is used to obtain the vibration signal of the hydropower unit, preprocess it, and obtain the vibration signal after noise reduction processing; A data division module is used to divide the vibration signal after noise reduction into a training set and a test set according to a preset ratio; A model training module is used to input the training set into the GWO-SVM model for training to obtain a trained GWO-SVM model; The fault diagnosis module is used to input the test set into the trained GWO-SVM model to obtain the classification results of the fault diagnosis of the hydropower unit.
12. The comprehensive evaluation system for the equipment status of a water turbine unit according to claim 11, characterized in that: The preprocessing module comprises: A data acquisition submodule, used to collect vibration signals of the hydropower unit under different fault forms; The time-frequency domain signal analysis submodule is used to perform time-frequency domain signal analysis on the vibration signal of the hydropower unit by using wavelet packet transform. Specifically, the method comprises: performing three-layer wavelet transform decomposition on the vibration signal of the hydropower unit, performing threshold-based denoising processing on the wavelet signal generated in the wavelet transform decomposition process, performing wavelet transform reconstruction on the wavelet signal after the denoising processing based on the threshold-based denoising processing, generating a pre-processed vibration signal of the hydropower unit, and using it as the vibration signal after the denoising processing.
13. The comprehensive evaluation system for the condition of a hydraulic turbine unit according to claim 12, characterized in that: The method for the time-frequency domain signal analysis submodule to perform noise reduction processing based on threshold judgment is specifically as follows: A corresponding first threshold is set for the wavelet signals generated by wavelet transform decomposition at different layers, and it is judged whether the wavelet signal is greater than the first threshold. If so, a smoothing process is performed on the wavelet signal to obtain a wavelet signal after noise reduction based on the threshold judgment. If not, the wavelet signal is set to zero. The expression of the wavelet signal w' after the denoising process based on the threshold judgment is obtained as follows: w'=sgn(w)(|w|-a) Where sgn(·) is the sign function, a is the first threshold, and w is the wavelet signal.
14. The comprehensive evaluation system for the condition of a water turbine unit according to claim 11, characterized in that: The method of the data division module for dividing the vibration signal after noise reduction processing into a training set and a test set according to a preset ratio is specifically as follows: Based on the corresponding faults of the hydropower units, the vibration signals after noise reduction are marked with corresponding fault labels, and the training set and test set are divided into two sets in a ratio of 8:
2.
15. The comprehensive evaluation system for the condition of a water turbine unit according to claim 11, characterized in that: The model training module includes: The parameter setting unit is used to set the number of gray wolf groups, the maximum number of iterations, the SVM penalty factor and the kernel function; Initialization parameter unit, used to randomly generate gray wolf population, initialize the position of gray wolf group and the number of iterations, the position of each gray wolf includes SVM penalty factor and kernel function; A fitness calculation unit is used to calculate the fitness of each gray wolf. The fitness of each gray wolf is obtained by training the SVM in the training set. The wolf pack division unit is used to divide the gray wolf pack into three wolves of different levels, namely, α, β, δ, and the rest of the gray wolves according to their fitness, and to update the positions of the rest of the gray wolves in the gray wolf pack; The threshold judgment unit is used to judge whether the number of iterations is greater than the maximum number of iterations. If so, the optimal gray wolf individual is determined and the best SVM penalty factor and kernel function found are output. If not, the number of iterations is increased by 1 and returned to the fitness calculation unit.
16. The comprehensive evaluation system for the equipment status of a water turbine unit according to claim 15, characterized in that: The method for the wolf group division unit to update the positions of the remaining gray wolves in the gray wolf group is specifically as follows: The wolf pack is divided into three wolves of different levels, α, β, δ and the rest of the wolf pack according to their fitness, and the first candidate positions of the rest of the wolf pack are calculated; Calculate the search space of each gray wolf among the remaining gray wolves, and determine the gray wolves in the search space; Calculate the second candidate positions of the remaining gray wolves in the gray wolf pack according to the domain matrix of the search space; Select the candidate position with the best fitness from the first candidate position and the second candidate position, and update the positions of the remaining gray wolves in the gray wolf pack.
17. The comprehensive evaluation system for the equipment status of a water turbine unit according to claim 16, characterized in that: The first candidate position X of the remaining gray wolves in the gray wolf pack is calculated gwo The specific expression of (t+1) is: Where X1 is the updated position under the guidance of α wolf, X2 is the updated position under the guidance of β wolf, X3 is the updated position under the guidance of δ wolf, and t is the current iteration number; X1=X α -A1|C1X α -X(t)| X2=X β -A2|C2X β -X(t)| X3=X δ -A3|C3X δ -X(t)| Where, X α is the current position of wolf α, X β is the current position of β wolf, X δ is the current position of the δ wolf, X(t) is the position of the other gray wolves before updating, C1 is the first coefficient vector, C2 is the second coefficient vector, C3 is the third coefficient vector, A1 is the fourth coefficient vector, A2 is the fifth coefficient vector, and A3 is the sixth coefficient vector.
18. The comprehensive evaluation system for the equipment status of a water turbine unit according to claim 17, characterized in that: The first to third coefficient vectors are updated by a nonlinear control strategy in each iteration to improve the global search capability of the gray wolf. The expression of the updated coefficient vector A' calculated by the nonlinear control strategy is specifically: Where A is the coefficient vector before updating, T max is the maximum number of iterations, r1 is a random vector whose value range is 0 to 1.
19. The comprehensive evaluation system for the equipment status of a water turbine unit according to claim 16, characterized in that: The calculation of the search space R of the i-th gray wolf i The specific expression of (t) is: R i (t)=||X i (t)-X gwo (t+1)|| Where, X i (t) is the position of the i-th gray wolf, X gwo (t+1) is the first candidate position of the i-th gray wolf; The gray wolf N in the search space of the i-th gray wolf i The specific expression of (t) is: N i (t)={X j (t)|E(X j (t),X i (t))≤R i (t)} Where, X j (t) is the position of the jth gray wolf, and E(·) is the Euclidean distance.
20. The comprehensive evaluation system for the equipment status of a water turbine unit according to claim 19, characterized in that: The calculation of the second candidate position X of the i-th gray wolf i The specific expression of (t+1) is: X i (t+1)=X i (t)+rand×(X n (t)-X r (t)) In the formula, rand is a random number, its value range is 0 to 1, X n (t) is the position of the randomly selected gray wolf in the search space of the i-th gray wolf, X r (t) is the position of another gray wolf randomly selected from the gray wolf population.