A method for extracting dominant factors of strong vortex band working condition area of hydroelectric generating set based on LDA analysis

Abstract

The present application relates to the technical field of hydroelectric generating set state monitoring and fault diagnosis, in particular to a kind of dominant factor extraction method of hydroelectric generating set strong vortex band operating condition area based on LDA analysis.The present application includes: by constructing linear discriminant analysis model, with the multi-condition measured data of hydroelectric generating set under different loads as high-dimensional input characteristics;By linear discriminant analysis algorithm, the optimal projection direction that makes the maximum between-class dispersion and the minimum within-class dispersion between the two kinds of samples of "strong vortex band condition" and "non-strong vortex band condition" is automatically found, so that high-dimensional monitoring data is fused and reduced to one-dimensional discriminant feature Z (Z can maximize the distinction between the two kinds of working conditions).The present application designs the component size of LDA projection vector, and quantitatively evaluates its contribution to distinguish strong vortex band condition;The method effectively extracts the dominant factor of strong vortex band operating condition area through data-driven mode, and provides a scientific basis for the state evaluation and optimal operation of hydroelectric generating set.

Description

Technical Field

[0001] This invention relates to the field of hydropower unit condition monitoring and fault diagnosis technology, specifically to a method for extracting the dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis. Background Technology

[0002] With the large-scale integration of intermittent renewable energy sources such as wind and solar power into the power grid, hydropower units are undertaking increasingly heavy regulation tasks, and their operating conditions are becoming more complex and variable. In addition to fulfilling basic power generation tasks, hydropower units, with their rapid start-up and shutdown and flexible regulation characteristics, are playing an increasingly important role in power grid peak shaving, frequency regulation, and emergency backup.

[0003] Strong vortex band operation is a hydraulic imbalance phenomenon that occurs when a hydropower unit operates under partial load. It has four significant characteristics: First, strong hydraulic excitation, where the vortex band rotates at 0.2 to 0.5 times the rotational frequency and impacts the draft tube, causing pressure pulsations of tens of kilopascals. Second, significantly increased vibration amplitude, with vibration amplitudes in the upper frame, lower frame, and top cover reaching several times that of normal operating conditions, and a significant increase in guide bearing runout, which may exceed limits in severe cases. Third, the impact of the vortex band with the draft tube wall easily generates low-frequency noise, which may be accompanied by high-frequency noise. Fourth, the reduced pressure at the center of the vortex band leads to cavitation, causing cavitation erosion damage to the runner blades and draft tube wall. Statistics show that approximately 30% of hydropower unit vibration exceeding the standard accident is directly related to strong vortex band operation, resulting in increased maintenance costs and power generation losses. Therefore, accurate identification of strong vortex band operation has become a key technical requirement for the safe operation of hydropower stations.

[0004] Currently, the condition monitoring of hydropower units mainly relies on single threshold alarms. This method has three limitations: First, each monitoring parameter participates in the judgment independently, which cannot accurately reflect the coupling relationship between multiple physical quantities such as vibration, sway, and pressure pulsation, and it is difficult to comprehensively characterize the comprehensive characteristics of strong vortex belt conditions. Second, there is a dilemma in setting the threshold: too high a threshold is prone to missed alarms, and too low a threshold is prone to false alarms. Moreover, a general threshold is difficult to apply to different units and different operating conditions. Third, threshold alarms are a post-event diagnosis. When parameters are found to exceed the standard, the unit may already be in a serious fault state, which cannot achieve early warning and maintenance.

[0005] To address the limitations of single-threshold methods, researchers have explored various analytical approaches. Spectral analysis is a common method for studying the vibration and pressure pulsation characteristics of hydropower units. It uses Fourier transform to convert the time-domain signal to the frequency domain, identifying characteristic frequency components. Under strong vortex zone conditions, low-frequency components of 0.2 to 0.5 times the revolutions frequency appear in the pressure pulsation signal. However, the operating conditions of hydropower units change frequently, and the vibration and pressure pulsation signals exhibit significant non-stationary characteristics. Traditional Fourier analysis struggles to accurately capture time-frequency features, and spectral characteristics rely heavily on the experience of engineers. Multi-parameter correlation analysis methods, such as principal component analysis and independent component analysis, can reveal the correlation between parameters to some extent. However, unsupervised methods like principal component analysis only consider the variance structure of the data, and the extracted features may not be directly related to the strong vortex zone condition. While deep learning methods such as neural networks can establish complex nonlinear mapping relationships, the internal model struggles to explain the intrinsic relationships and contributions of various physical quantities. More importantly, existing methods cannot quantitatively assess the contribution of each monitoring parameter to the strong vortex zone condition and cannot clearly identify the dominant factors leading to its formation.

[0006] Linear Discriminant Analysis (LDA), a classic pattern recognition method, differs from unsupervised methods such as Principal Component Analysis (PCA) by fully utilizing the class label information of samples to find the optimal projection direction that maximizes inter-class dispersion and minimizes intra-class dispersion. Applying LDA to extract the dominant factors of strong vortex zones in hydropower units offers several key advantages: First, LDA utilizes the class label information of strong and non-strong vortex zones to extract features directly related to operating condition discrimination, avoiding interference from irrelevant information. Second, each component of the LDA projection vector directly reflects the importance of the corresponding feature for discrimination; a larger weight indicates greater importance for distinguishing between the two operating conditions, giving the model good interpretability. Third, LDA can fuse multiple monitoring parameters into a one-dimensional discriminant feature, comprehensively reflecting the coupling effect of multiple physical quantities such as vibration, sway, and pressure pulsation. Fourth, both LDA model training and feature extraction have analytical solutions, making it suitable for online monitoring and real-time analysis applications. Fifth, based on the LDA projection vector, the contribution of each monitoring parameter to the discrimination of strong vortex zones can be quantitatively calculated, and the dominant factors can be clearly identified by ranking the contributions, providing a basis for operational optimization.

[0007] In view of this, in order to solve the problem that existing technologies are unable to effectively identify and quantify the dominant factors leading to strong vortex zone conditions from multi-physics monitoring data, we propose a method for extracting the dominant factors of strong vortex zone conditions in hydropower units based on LDA analysis. Summary of the Invention

[0008] The purpose of this invention is to address the aforementioned problems in the existing technology by providing a method for extracting the dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis. This method achieves feature fusion of multi-source monitoring data by constructing an LDA model, extracts one-dimensional discriminative features, and quantitatively calculates the contribution of each monitoring parameter to the discrimination of the strong vortex zone, thereby solving the problems mentioned in the background technology.

[0009] To address the aforementioned technical problems, the present invention aims to provide a method for extracting the dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis, comprising the following steps:

[0010] S1. Collect the status monitoring data of the hydropower unit under different load conditions, and perform standardization processing and Z-score standardization processing on the measured status monitoring data in accordance with national standards to eliminate dimensional differences.

[0011] S2. Construct a linear discriminant analysis (LDA) model, using the processed state monitoring data as the sample set for model input;

[0012] S3. Based on the characteristics of active power and pressure pulsation, define the discrimination rules for strong vortex zone conditions and generate binary classification labels for the sample set; mark the samples with active power in the partial load range and tailrace pipe pressure pulsation exceeding the threshold as strong vortex zone conditions, and mark the remaining samples as non-strong vortex zone conditions.

[0013] S4. Based on the generated binary classification labels, the standardized samples are divided into two categories: strong vortex zone and non-strong vortex zone. The mean vector and covariance matrix of the two classes of samples are calculated, and then the intra-class scatter matrix is ​​calculated and a regularization term is added to obtain the optimal projection direction under the Fisher discriminant criterion. The original high-dimensional data is projected onto this direction to obtain the discriminant feature Z.

[0014] S5. Based on the magnitude of each component of the LDA projection vector, calculate the contribution of each monitoring parameter to the identification of strong vortex zones; sort each feature from largest to smallest contribution to obtain the ranking of dominant factors of strong vortex zones; and divide the key feature subset that plays a dominant role in the identification of strong vortex zones by the cumulative contribution ranking.

[0015] As a further improvement to this technical solution, in step S1, the status monitoring data (i.e., operating parameters) includes at least one or more of the following: unit load, guide vane opening, volute pressure pulsation, tailrace pipe pressure pulsation, unit top cover vibration amplitude, unit frame vibration amplitude (upper and lower frame vibration), guide bearing swing (upper guide swing, lower guide swing, water guide swing) and rotational speed.

[0016] The formula for Z-score standardization is:

[0017] ;

[0018] In the formula, and These are the mean and standard deviation of each feature, respectively; It is a matrix of parameters without normalization, such as guide vane opening, and dimensionless normalized values ​​(such as sway, vibration, and pressure pulsation data); the standardized data matrix is ​​denoted as... .

[0019] As a further improvement to this technical solution, in step S2, when constructing the LDA model, the sample set is constructed using the standardized feature vectors. The calculation formula is as follows:

[0020]

[0021] In the formula, This represents the feature vector of the i-th sample after standardization. Indicates the first Labels for each sample.

[0022] As a further improvement to this technical solution, in step S3, the discrimination rule for the strong vortex zone condition is as follows:

[0023] ;

[0024] In the formula, The low load threshold is typically set at 30% of the unit's rated load. The high load threshold is typically set at 70% of the unit's rated load. Active power; This is due to pressure pulsation in the tailrace pipe; The threshold value for pressure pulsation in the tailrace pipe;

[0025] Based on the above discrimination rules, the binary classification label is defined as follows:

[0026] ;

[0027] in, This indicates a strong vortex zone operating condition label. This indicates a label for non-strong vortex zone operating conditions.

[0028] As a further improvement to this technical solution, in step S4, the LDA model finds the optimal projection direction by maximizing the ratio of inter-class distance to minimizing intra-class distance, compressing the multi-dimensional feature space into a one-dimensional discriminative feature Z, so that samples from strong eddy zones and non-strong eddy zones are highly clustered in the same class and separated from the opposite class in the projection space.

[0029] The steps for calculating the discriminant feature Z are as follows:

[0030] S4.1 Calculate the mean vector of the two classes of samples based on the generated binary classification labels:

[0031] ;

[0032] In the formula, , These are the mean vectors of the two types of samples: non-strong vortex zone and strong vortex zone. This indicates the number of samples in the non-strong vortex zone operating condition. This indicates the number of samples for the strong vortex zone condition. Indicates the first One standardized sample;

[0033] S4.2 Calculate the covariance matrix:

[0034] ;

[0035] In the formula, , These are the covariance matrices for the two types of samples: non-strong vortex zone and strong vortex zone. Indicates vector transpose;

[0036] The within-class scatter matrix is ​​defined as the sum of the covariance matrices of the two classes of samples, denoted as . The calculation formula is as follows:

[0037] ;

[0038] In the formula, It describes the degree of signal diffusion within the same operating condition category;

[0039] The inter-class scatter matrix is , The physical meaning of describing the average distribution difference between two types of working conditions is "the separability between strong vortex zones and non-strong vortex zones", and its calculation formula is as follows:

[0040] ;

[0041] S4.3 Calculate the optimal projection direction:

[0042] ;

[0043] In the formula, It is the direction of the mean difference between strong vortex zones and non-strong vortex zones; It is a contraction operator for intra-class diffusion;

[0044] To prevent Singularity (the number of features may be greater than the number of samples), add a regularization term:

[0045] ;

[0046] in, , It is the identity matrix;

[0047] get Then, normalize it to: ;

[0048] S4.4 Calculate the discriminant feature Z:

[0049] ;

[0050] In the formula, This represents the standardized monitoring data matrix. The Z value represents the optimal projection direction; the larger the Z value, the closer it is to the statistical center of the strong vortex zone in the discrimination space of the LDA model.

[0051] As a further improvement to this technical solution, in step S5, the formula for calculating the contribution of each monitoring parameter to the strong vortex zone discrimination based on the magnitude of each component of the LDA projection vector is as follows:

[0052] ;

[0053] In the formula, The contribution of the j-th parameter, The larger the value, the stronger its dominant role. Let j be the j-th component in the projection vector. It is the sum of the absolute values ​​of all feature weights.

[0054] As a further improvement to this technical solution, it also includes:

[0055] S6. Use the obtained discrimination threshold to classify the samples, construct the confusion matrix and calculate the performance indicators, such as: confusion matrix and accuracy, recall;

[0056] Plot the ROC (Receiver Operating Characteristic) curve and calculate the AUC (Area Under the Curve) value to evaluate the model's discriminative ability.

[0057] As a further improvement to this technical solution, in step S6, the process of classifying samples using the obtained discrimination threshold is as follows:

[0058] The discriminant feature values ​​for the two types of samples, namely, non-strong vortex zone and strong vortex zone, are denoted as follows: and To classify new samples, the midpoint between the two class means is taken as the classification threshold. The formula for calculating the classification threshold is:

[0059] ;

[0060] In the formula, The threshold used to classify new samples. and These are the mean values ​​of the discrimination features for non-strong vortex zone and strong vortex zone classes, respectively. The physical meaning of the discrimination threshold is: as a classification boundary, when the discriminative features of a new sample... If the value is greater than or equal to this threshold, it is determined to be a strong vortex zone condition; otherwise, it is a non-strong vortex zone condition.

[0061] The confusion matrix construction process is as follows: The discriminative features are classified according to the aforementioned discrimination threshold to obtain the predicted labels. The confusion matrix is ​​then constructed as follows:

[0062] ;

[0063] The performance metrics include one or more of accuracy, precision, recall, and F1 score;

[0064] The formulas for calculating performance metrics such as accuracy and recall are as follows:

[0065] ;

[0066] ;

[0067] ;

[0068] .

[0069] As a further improvement to this technical solution, in step S6, the AUC value is the area under the ROC curve, and the value ranges from 0.5 to 1. The closer the AUC value is to 1, the stronger the discrimination ability of the LDA model.

[0070] As a further improvement to this technical solution, it also includes:

[0071] S7. Add the LDA discriminant features to the original data and save the analysis results;

[0072] Draw discriminant feature distribution maps, probability density curves, box plots, etc., to visually demonstrate the separation effect between the two types of samples;

[0073] Draw a bar chart ranking the contribution of features to identify the dominant factors in the strong vortex belt.

[0074] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0075] 1. This invention integrates n-dimensional monitoring parameters into a one-dimensional discriminant feature Z using an LDA model. This feature can amplify the difference between strong vortex zones and non-strong vortex zones to the greatest extent, thereby maximizing the differentiation between the two operating conditions and achieving accurate identification of the strong vortex zone operating area. This significantly improves the sensitivity of identifying key operating areas. Compared with the traditional single threshold alarm method, the discriminant feature Z of this invention can comprehensively reflect the coupling effect of multiple physical quantities such as vibration, sway, and pressure pulsation, and more accurately characterize the essential characteristics of the strong vortex zone operating condition.

[0076] 2. This invention analyzes the discriminant coefficient matrix generated by the LDA model and quantitatively calculates the contribution of each monitoring parameter to the discrimination of strong vortex zones based on the absolute value of the projection weights of each original monitoring variable in the discrimination direction (where variables with significantly higher projection weights are identified as key dominant factors inducing or leading the formation of this operating condition zone). The parameters are then sorted from largest to smallest contribution to clearly identify the key factors that play a dominant role in the formation of strong vortex zones. Compared with traditional empirical judgments or qualitative analyses, this invention provides a scientific quantitative basis, enabling maintenance personnel to accurately grasp the main causes of strong vortex zone operating conditions.

[0077] 3. This invention comprehensively evaluates the model's discriminative ability through multiple indicators such as accuracy, recall, F1 score, and AUC value. The ROC curve intuitively shows the model's performance at different thresholds, providing a reliable evaluation for the model's practical application.

[0078] 4. The technical solution of the present invention does not depend on specific unit models and parameter settings, and has good universality; for different types of hydropower units, only the corresponding monitoring data needs to be collected and appropriately adjusted, and this method can be applied to extract the dominant factors of strong vortex bands. Attached Figure Description

[0079] Figure 1 This is an exemplary overall flowchart of the method of the present invention;

[0080] Figure 2 A schematic diagram of the sample set effect of the one-dimensional discriminant feature Z extracted by the LDA model of measured data from a power plant provided in an embodiment of the present invention;

[0081] Figure 3 The probability distribution of discriminant features based on measured data from a power plant provided in this embodiment of the invention;

[0082] Figure 4 This invention provides a relationship between measured data of water conductor X-direction swing and discrimination features from a power plant, as provided in an embodiment of the invention.

[0083] Figure 5 This invention provides a relationship between measured data of pressure pulsation and discrimination features from a power plant, as provided in an embodiment of the invention.

[0084] Figure 6 This is a threshold classification effect of measured data from a power plant provided in an embodiment of the present invention.

[0085] Figure 7 Ranking of the contribution of 15 features from measured data of a power plant provided in this embodiment of the invention to the identification of strong vortex zones;

[0086] Figure 8 Trend diagrams of normalized parameters versus load in embodiments of the present invention;

[0087] Figure 9 The ROC curve of the LDA model of a power plant provided in an embodiment of the present invention. Detailed Implementation

[0088] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0089] Example 1

[0090] like Figure 1 As shown in the figure, this embodiment provides a method for extracting the dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis. This technical solution fully utilizes the advantages of LDA supervised learning, strong interpretability, and quantitative analysis of contribution, effectively solving the problems of unclear dominant factors and poor interpretability in existing methods, and providing strong technical support for the safe and stable operation of hydropower units. The specific steps include the following:

[0091] S1. Collect condition monitoring data of the hydropower unit under different load conditions. The condition monitoring data (i.e., operating parameters) shall include at least one or more of the following: unit load, guide vane opening, volute pressure pulsation, tailrace pressure pulsation, unit top cover vibration amplitude (e.g., top cover X-vibration, top cover vertical vibration, etc.), unit frame vibration amplitude (e.g., upper frame X-vibration, upper frame Y-vibration, lower frame X-vibration, lower frame vertical vibration, etc.), guide bearing runout (e.g., upper guide runout - upper guide X-vibration, upper guide Y-vibration, lower guide runout - lower guide X-vibration, lower guide Y-vibration, water guide runout - water guide X-vibration, water guide Y-vibration, etc.) and rotational speed. Due to the different dimensions of the multivariate data and the large differences in amplitude variation in different parts, the measured condition monitoring data shall be standardized according to national standards. Furthermore, since the dimensions of the guide vane opening and other standardized data are different, Z-score standardization shall be performed to eliminate the dimensional differences.

[0092] In this step, the formula for Z-score standardization is:

[0093] ;

[0094] In the formula, and These are the mean and standard deviation of each feature, respectively; It is a matrix of parameters without normalized values ​​(such as guide vane opening and dimensionless normalized values, including data on sway, vibration, and pressure pulsation); the standardized data matrix is ​​denoted as... .

[0095] S2. Construct a linear discriminant analysis (LDA) model, using the processed state monitoring data as the sample set for model input;

[0096] In this step, when constructing the LDA model, the sample set is built using the standardized feature vectors. The calculation formula is as follows:

[0097]

[0098] In the formula, Indicates the standardized number The feature vector of each sample Indicates the first Labels for each sample.

[0099] S3. Based on the characteristics of active power and pressure pulsation, define the discrimination rules for strong vortex zone conditions and generate binary classification labels for the sample set; mark the samples with active power in the partial load range and tailrace pipe pressure pulsation exceeding the threshold as strong vortex zone conditions, and mark the remaining samples as non-strong vortex zone conditions.

[0100] In this step, the criteria for identifying the strong vortex belt condition are as follows:

[0101] ;

[0102] In the formula, The low load threshold is typically set at 30% of the unit's rated load. The high load threshold is typically set at 70% of the unit's rated load. Active power; This is due to pressure pulsation in the tailrace pipe; The threshold value for pressure pulsation in the tailrace pipe;

[0103] Based on the above discrimination rules, the binary classification label is defined as follows:

[0104] ;

[0105] in, This indicates a strong vortex zone operating condition label. This indicates a label for non-strong vortex zone operating conditions.

[0106] S4. Based on the generated binary classification labels, the standardized samples are divided into two categories: strong vortex zone and non-strong vortex zone. The mean vector and covariance matrix of the two classes of samples are calculated, and then the intra-class scatter matrix is ​​calculated and a regularization term is added to obtain the optimal projection direction under the Fisher discriminant criterion. The original high-dimensional data is projected onto this direction to obtain the discriminant feature Z.

[0107] In this step, the LDA model finds the optimal projection direction by maximizing the ratio of inter-class distance to minimizing intra-class distance, compressing the multi-dimensional feature space into a one-dimensional discriminative feature Z, so that samples from strong eddy zones and non-strong eddy zones are highly clustered in the same class and separated from the opposite class in the projection space.

[0108] The steps for calculating the discriminant feature Z are as follows:

[0109] S4.1 Calculate the mean vector of the two classes of samples based on the generated binary classification labels:

[0110] ;

[0111] In the formula, , These are the mean vectors of the two types of samples: non-strong vortex zone and strong vortex zone. This indicates the number of samples in the non-strong vortex zone operating condition. This indicates the number of samples for the strong vortex zone condition. Indicates the first One standardized sample;

[0112] S4.2 Calculate the covariance matrix:

[0113] ;

[0114] In the formula, , These are the covariance matrices for the two types of samples: non-strong vortex zone and strong vortex zone. Indicates vector transpose;

[0115] The within-class scatter matrix is ​​defined as the sum of the covariance matrices of the two classes of samples, denoted as . The calculation formula is as follows:

[0116] ;

[0117] In the formula, It describes the degree of signal diffusion within the same operating condition category;

[0118] The inter-class scatter matrix is , The physical meaning of describing the average distribution difference between two types of working conditions is "the separability between strong vortex zones and non-strong vortex zones", and its calculation formula is as follows:

[0119] ;

[0120] S4.3 Calculate the optimal projection direction:

[0121] ;

[0122] In the formula, It is the direction of the mean difference between strong vortex zones and non-strong vortex zones; It is a contraction operator for intra-class diffusion;

[0123] To prevent Singularity (the number of features may be greater than the number of samples), add a regularization term:

[0124] ;

[0125] in, , It is the identity matrix;

[0126] get Then, normalize it to: ;

[0127] S4.4 Calculate the discriminant feature Z:

[0128] ;

[0129] In the formula, This represents the standardized monitoring data matrix. The Z value represents the optimal projection direction; the larger the Z value, the closer it is to the statistical center of the strong vortex zone in the discrimination space of the LDA model.

[0130] S5. Based on the magnitude of each component of the LDA projection vector, calculate the contribution of each monitoring parameter to the identification of strong eddy zones; sort each feature from largest to smallest contribution to obtain the ranking of dominant factors of strong eddy zones; divide the key feature subset that plays a dominant role in the identification of strong eddy zones by the cumulative contribution ranking.

[0131] In this step, based on the magnitude of each component of the LDA projection vector, the formula for calculating the contribution of each monitoring parameter to the strong eddy zone identification is as follows:

[0132] ;

[0133] In the formula, The contribution of the j-th parameter, The larger the value, the stronger its dominant role. Let j be the j-th component in the projection vector. It is the sum of the absolute values ​​of all feature weights.

[0134] S6. Use the obtained discrimination threshold to classify the samples, construct the confusion matrix and calculate the performance index;

[0135] In this step, the process of classifying samples using the obtained discrimination threshold is as follows:

[0136] The discriminant feature values ​​for the two types of samples, namely, non-strong vortex zone and strong vortex zone, are denoted as follows: and To classify new samples, the midpoint between the two class means is taken as the classification threshold. The formula for calculating the classification threshold is:

[0137] ;

[0138] In the formula, The threshold used to classify new samples. and These are the mean values ​​of the discrimination features for non-strong vortex zone and strong vortex zone classes, respectively. The physical meaning of the discrimination threshold is: as a classification boundary, when the discriminative features of a new sample... If the value is greater than or equal to this threshold, it is determined to be a strong vortex zone condition; otherwise, it is a non-strong vortex zone condition.

[0139] The confusion matrix construction process is as follows: Classify the discriminative features according to the aforementioned discrimination threshold to obtain the predicted labels. The confusion matrix is ​​then constructed as follows:

[0140] ;

[0141] Performance metrics include one or more of the following: accuracy, precision, recall, and F1 score;

[0142] The formulas for calculating performance metrics such as accuracy and recall are as follows:

[0143] ;

[0144] ;

[0145] ;

[0146] .

[0147] Plot the ROC (Receiver Operating Characteristic) curve and calculate the AUC (Area Under the Curve) value to evaluate the model's discriminative ability;

[0148] The AUC value is the area under the ROC curve, ranging from 0.5 to 1. The closer the AUC value is to 1, the stronger the discrimination ability of the LDA model.

[0149] S7. Add the LDA discriminant features to the original data and save the analysis results;

[0150] Draw discriminant feature distribution maps, probability density curves, box plots, etc., to visually demonstrate the separation effect between the two types of samples;

[0151] Draw a bar chart ranking the contribution of features to identify the dominant factors in the strong vortex belt.

[0152] Application Examples

[0153] This embodiment analyzes actual monitoring data from a power plant, and the process is as follows: Figure 1 As shown, the specific steps are as follows:

[0154] Step 1: Collect historical operating data through the hydropower unit's online monitoring system. The collected data includes: vibration signals: such as X / Y vibration of the upper and lower frames (unit: μm); sway signals: such as X / Y sway of each guide bearing (unit: μm); pressure pulsation signals: pressure pulsation at the spiral casing inlet and tailrace pipe inlet (unit: kPa); operating parameters: active power (unit: MW).

[0155] Step 2: Normalize the collected data according to national standards. For example, according to GB / T32584-2016, the maximum allowable value of the X-direction runout of the lower guide bearing is 280 μm. Therefore, divide the collected X-direction runout of the upper guide bearing by 280, which is step S1, to obtain the normalized data. Figure 8 As shown.

[0156] Then, Z-score standardization was performed on all parameters. In this embodiment, a total of n=120 sample points were collected, forming the original data matrix. .

[0157] Step 3: Extract features closely related to the strong vortex zone condition from the sample set. Based on the discriminant formula, divide the processed data into two sample sets: samples under the strong vortex zone condition are labeled as 1, and samples not under the strong vortex zone condition are labeled as 0. Set the pressure pulsation threshold to pth = 20.0 kPa. In this embodiment, the actual unit's rated power is 600 MW. The low load threshold is typically set at 30% of the unit's rated load. ; The high load threshold is typically set at 70% of the unit's rated load. The value is 420MW; that is, step S3.

[0158] Step 4: Calculate the mean vector and covariance matrix of the two classes of samples, and then calculate the within-class scatter matrix; project the data onto the optimal direction to obtain the discriminant feature Z (example data is shown in the image). Figures 2-6 As shown in the figure, that is, step S4.

[0159] Step 5: Based on the magnitude of each component of the LDA projection vector, calculate the contribution and discrimination weight of each monitoring parameter to the strong eddy zone discrimination, as shown in Table 1 below; each feature is sorted from largest to smallest contribution, such as... Figure 7 As shown, the ranking of the dominant factors of the strong vortex belt is obtained, i.e., step S5;

[0160] Table 1 Ranking of the relative contributions of dominant factors

[0161] Tailwater pipe pressure pulsation 0.5283 16.47 1 Upper guide X swing 0.5104 15.64 2 Water conduction X-swivel -0.3349 10.45 3 X-vibration on the upper frame -0.2709 8.45 4 Lower guide Y swing 0.2250 7.02 5 Water-conducting Y-swivel 0.2209 6.89 6 Lower guide X swing -0.2062 6.43 7 Top cover vertical vibration -0.1911 5.96 8 Lower frame vertical vibration -0.1866 5.82 9 upper guide Y swing -0.1544 4.81 10 Guide vane opening -0.1465 4.57 11 Upper frame Y vibration 0.1429 4.46 12 Top cover X vibration -0.0645 2.01 13 Lower frame X vibration 0.0275 0.86 14 volute pressure pulsation -0.0055 0.17 15

[0162] Step 6: Classify the samples using the obtained discrimination threshold, calculate the confusion matrix and performance metrics such as precision and recall; plot the ROC curve and calculate the AUC value to evaluate the model's discrimination ability; in this example, the calculated precision is 97.5%, the recall is 100%, and the F1 score is 0.930. Figure 9 The AUC value shown is 1.000, which corresponds to step S6.

[0163] Those skilled in the art will understand that the process of implementing all or part of the steps of the above embodiments can be carried out by hardware or by a program instructing the relevant hardware.

[0164] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for extracting dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis, characterized in that, Includes the following steps: S1. Collect the status monitoring data of the hydropower unit under different load conditions, and perform standardization processing and Z-score standardization processing on the measured status monitoring data in accordance with national standards. S2. Construct a linear discriminant analysis (LDA) model, using the processed state monitoring data as the sample set for model input; S3. Based on the characteristics of active power and pressure pulsation, define the discrimination rules for strong vortex belt conditions and generate binary classification labels for the sample set. Samples with active power in the partial load range and tailrace pipe pressure pulsation exceeding the threshold are marked as strong vortex zone conditions, and the remaining samples are marked as non-strong vortex zone conditions. S4. Based on the generated binary classification labels, the standardized samples are divided into two categories: strong vortex band and non-strong vortex band. Calculate the mean vector and covariance matrix of the two classes of samples, then calculate the within-class scatter matrix and add a regularization term to obtain the optimal projection direction under the Fisher discriminant criterion; project the original high-dimensional data onto this direction to obtain the discriminant feature Z; S5. Based on the magnitude of each component of the LDA projection vector, calculate the contribution of each monitoring parameter to the identification of strong vortex zones; sort each feature from largest to smallest contribution to obtain the ranking of the dominant factors of strong vortex zones. The key feature subset that plays a dominant role in the identification of strong vortex zones is identified by ranking the cumulative contribution.

2. The method for extracting dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis according to claim 1, characterized in that: In step S1, the status monitoring data includes at least one or more of the following: unit load, guide vane opening, volute pressure pulsation, tailrace pipe pressure pulsation, unit top cover vibration amplitude, unit frame vibration amplitude, guide bearing swing and rotational speed. The formula for Z-score standardization is: ； In the formula, and These are the mean and standard deviation of each feature, respectively; It is a matrix of parameters without normalized values; The standardized data matrix is ​​denoted as .

3. The method for extracting dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis according to claim 2, characterized in that: In step S2, when constructing the LDA model, the sample set is constructed using the standardized feature vectors. The calculation formula is as follows: ； In the formula, Indicates the standardized number of The feature vector of each sample Indicates the first Labels for each sample.

4. The method for extracting dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis according to claim 3, characterized in that: In step S3, the discrimination rule for the strong vortex zone condition is as follows: ； In the formula, For low load threshold, For high load threshold, Active power; This is due to pressure pulsation in the tailrace pipe; The threshold value for pressure pulsation in the tailrace pipe; Based on the above discrimination rules, the binary classification label is defined as follows: ； in, This indicates a strong vortex zone operating condition label. This indicates a label for non-strong vortex zone operating conditions.

5. The method for extracting dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis according to claim 4, characterized in that: In step S4, the LDA model finds the optimal projection direction by maximizing the ratio of inter-class distance to minimizing intra-class distance, compressing the multi-dimensional feature space into a one-dimensional discriminative feature Z, so that samples with strong eddy bands and non-strong eddy bands are highly clustered in the same class and separated from each other in the projection space. The steps for calculating the discriminant feature Z are as follows: S4.1 Calculate the mean vector of the two classes of samples based on the generated binary classification labels: ； In the formula, , These are the mean vectors of the two types of samples, namely, the non-strong vortex zone working condition and the strong vortex zone working condition; This indicates the number of samples in the non-strong vortex zone operating condition. This indicates the number of samples for the strong vortex zone condition. Indicates the first One standardized sample; S4.2 Calculate the covariance matrix: ； In the formula, , These are the covariance matrices for the two types of samples: non-strong vortex zone and strong vortex zone. Indicates vector transpose; The within-class scatter matrix is ​​defined as the sum of the covariance matrices of the two classes of samples, denoted as . The calculation formula is as follows: ； In the formula, It describes the degree of signal diffusion within the same operating condition category; The inter-class scatter matrix is , The physical meaning of describing the difference in average distribution between two types of operating conditions is "the separability between strong vortex zones and non-strong vortex zones", and its calculation formula is as follows: ； S4.3 Calculate the optimal projection direction: ； In the formula, It is the direction of the mean difference between strong vortex zones and non-strong vortex zones; It is a contraction operator for intra-class diffusion; Add regularization to prevent Strange: ； in, , It is the identity matrix; get Then, normalize it to: ; S4.4 Calculate the discriminant feature Z: ； In the formula, This represents the standardized monitoring data matrix. The Z value represents the optimal projection direction; the larger the Z value, the closer it is to the statistical center of the strong vortex zone in the discrimination space of the LDA model.

6. The method for extracting dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis according to claim 5, characterized in that: In step S5, the formula for calculating the contribution of each monitoring parameter to the strong vortex zone discrimination based on the magnitude of each component of the LDA projection vector is as follows: ； In the formula, The contribution of the j-th parameter, The larger the value, the stronger its dominant role. Let j be the j-th component in the projection vector. It is the sum of the absolute values ​​of all feature weights.

7. The method for extracting dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis according to claim 6, characterized in that, Also includes: S6. Use the obtained discrimination threshold to classify the samples, construct the confusion matrix and calculate the performance index; Plot the ROC curve and calculate the AUC value to evaluate the model's discriminative ability.

8. The method for extracting dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis according to claim 7, characterized in that: In step S6, the process of classifying samples using the obtained discrimination threshold is as follows: The discriminant feature values ​​for the two types of samples, namely, non-strong vortex zone and strong vortex zone, are denoted as follows: and To classify new samples, the midpoint between the two class means is taken as the classification threshold. The formula for calculating the classification threshold is: ； In the formula, The threshold used to classify new samples. and These are the mean values ​​of the discrimination features for non-strong vortex zone and strong vortex zone classes, respectively. The physical meaning of the discrimination threshold is: as a classification boundary, when the discriminative features of a new sample... When the value is greater than or equal to this threshold, it is determined to be a strong vortex zone condition; Otherwise, it is a non-strong vortex zone; The performance metrics include one or more of accuracy, precision, recall, and F1 score.

9. The method for extracting dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis according to claim 8, characterized in that: In step S6, the AUC value is the area under the ROC curve, and the value ranges from 0.5 to 1. The closer the AUC value is to 1, the stronger the discrimination ability of the LDA model.

10. The method for extracting dominant factors in the strong vortex zone operating condition of hydropower units based on LDA analysis according to claim 9, characterized in that, Also includes: S7. Add the LDA discriminant features to the original data and save the analysis results; Draw discriminant feature distribution maps and probability density curves to visually demonstrate the separation effect between the two types of samples; Draw a bar chart ranking the contribution of features to identify the dominant factors in the strong vortex belt.

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