An eGBDT-based long-term voltage stability fine evaluation method

Abstract

The application discloses an eGBDT-based long-term voltage stability fine evaluation method and belongs to the field of power system operation and maintenance. The bus voltage amplitude and phase angle data of wide-area online measurement can be used to calculate a load margin index and realize fine classification of voltage stability. Meanwhile, the one-side gradient sampling method and the mutual exclusion feature bundling technology are adopted in the method to realize dimension reduction and feature compression of the high-dimensional measurement data space, effectively improving the processing efficiency of the traditional GBDT method on massive measurement data. The method inherits the high-precision estimation effect of the traditional GBDT method and greatly improves the processing capacity for massive measurement data. The application has stronger robustness for the uncertainty analysis caused by large-scale access of renewable energy sources and has good applicability when incomplete measurement data and different training data set sizes are processed. Therefore, the method has good practical application value.

Description

Technical Field

[0001] This invention belongs to the field of power system operation and maintenance technology, and in particular relates to a long-term voltage stability refined assessment method based on eGBDT. Background Technology

[0002] With the expansion of interconnected power grids, the high proportion of renewable energy integration, and the gradual increase in electricity load, power systems are approaching their limiting states, increasing the risk of voltage instability. Therefore, long-term online monitoring and assessment of voltage stability are crucial for ensuring the safety and stability of power systems. Scholars and researchers have proposed methods for voltage stability assessment, including the PV curve method based on continuous power flow (CPF) calculation, optimal power flow methods, and methods based on Thevenin equivalents. However, these methods suffer from difficulties in modeling and low online computational efficiency. With the widespread application of wide-area measurement devices in power systems, numerous research results on online voltage stability assessment based on machine learning have emerged, such as voltage stability assessment methods based on support vector machines (SVM), artificial neural networks (ANN), and decision trees (DT). In recent years, methods that integrate and enhance DT have received widespread attention. Random forest (RF) and gradient boosting decision tree (GBDT) algorithms are outstanding representatives of ensemble learning. However, due to the continuous expansion of system scale and the large-scale integration of renewable energy, the dimensionality of system measurement data has increased dramatically, leading to low computational efficiency when using GBDT methods to assess voltage stability, severely impacting the formulation and implementation of subsequent stability control measures.

[0003] In summary, there is an urgent need in the existing technology for an effective and high-performance method for rapid processing of large-scale, high-dimensional measurement data to solve this problem, thereby enabling rapid online assessment of voltage stability. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a long-term voltage stability fine-grained evaluation method based on eGBDT to solve the technical problem of low computational efficiency of traditional gradient descent tree (GBDT) algorithm in scenarios of gradual expansion of power system scale and large-scale integration of new energy sources.

[0005] A refined evaluation method for long-term voltage stability based on eGBDT includes the following steps, which are performed sequentially:

[0006] Step 1: Establish the load margin index K for voltage stability assessment p Furthermore, the load margin index K p The magnitude of the voltage and the bus voltage amplitude are used to finely divide the system voltage stability state into: safe state, warning state and emergency state.

[0007] Step 2: Using the Gradient Descent Tree (GBDT) method, construct a GBDT model that integrates multiple different regression trees. Based on the given training set data, with the goal of minimizing the logarithmic approximate loss function, iteratively train the GBDT model along the direction of the maximum negative gradient to construct a refined voltage stability evaluation model.

[0008] Step 3: The measurement data obtained by the voltage stability fine evaluation model is spatially reduced and feature compressed using the one-sided gradient sampling method GOSS and the mutually exclusive feature binding technique HEEFB. This achieves dimensionality reduction of massive measurement data and further constructs a voltage stability evaluation model based on eGBDT, thereby improving the evaluation efficiency of the GBDT model.

[0009] Step 4: Input the online measured data of each bus voltage and bus phase angle into the eGBDT model to obtain the refined voltage stability assessment results and specifically display whether the voltage is in a safe state (S), a warning state (W), or an emergency state (E), thereby realizing the refined online assessment of the long-term voltage stability of the power system with a high proportion of new energy.

[0010] The load margin index K in step one p The formula is as follows:

[0011]

[0012] Among them, K p λ0 is the load margin index, representing the distance from the current operating point of the busbar to the voltage stability critical point; λ0 is the load parameter of the current state of the busbar. max These are the load parameters for the critical state of bus voltage stability.

[0013] In step one, the system voltage stability state is finely divided into three states: safe state, warning state, and emergency state. The specific conditions for these states are as follows:

[0014] (1) Safety status: K under normal operating conditions p >7% and V i ≥0.9 pu or K under fault conditions p >5% and V i ≥0.9pu;

[0015] (2) Warning status: K under normal operating conditions p >7% and V i ≤0.9pu;

[0016] (3) Emergency state: K under normal operating conditions p <7% or under fault conditions K p <5%;

[0017] Among them, V iThe voltage amplitude is represented by pu, which indicates the per-unit value.

[0018] The second step of constructing a refined voltage stability evaluation model specifically includes the following steps:

[0019] Given a training set, which includes input data and corresponding voltage stability state labels, where the label for a safe state is S, the label for a warning state is W, and the label for an emergency state is E, as shown in equation (2):

[0020]

[0021] Where n represents the number of load buses; i represents the i-th system operating condition; This represents the voltage magnitude of the i-th bus. x represents the voltage phase angle of the i-th bus; i y represents the input sample under the i-th operating condition; i This represents the sample label corresponding to the i-th working condition;

[0022] Define the logarithmic approximation loss function L(y,f(x)) as the difference between the predicted and actual voltage stability values, and obtain formula (3):

[0023]

[0024] Wherein, the probability function p k (x) is the predicted probability that sample x belongs to class k: y i These are sample labels, y i If y ∈{0,1}, the target classification and the predicted classification are consistent, then y i =1, otherwise, if the target classification and the predicted classification are inconsistent, then y i =0; f(x) is a GBDT model ensembled from k different regression trees;

[0025] The gradient descent tree GBDT model is repeatedly trained in the direction of the negative gradient error function defined by formula (4) to minimize the loss function, thus obtaining the final enhanced gradient descent tree eGBDT model:

[0026] Negative gradient error function:

[0027] Where t is the number of iterations; x is the negative gradient error function of the class k corresponding to the i-th sample in the t-th iteration; i , These are the fitted sample parameters obtained from the previous iteration; p k t (x if(x) represents the probability of predicting sample x in the t-th iteration; i ) represents the GBDT model ensemble of the first i regression trees;

[0028] During the training of the Gradient Descent Tree (GBDT) model, the objective is to minimize the logarithmic approximate loss function. The model iterates continuously along the direction of the maximum negative gradient, thus utilizing the sample values ​​x from the previous iteration. i , Update the current sample value x i , Ultimately, the GBDT model was transformed from f t-1 (x) is updated to f t (x) means that the GBDT model is completed.

[0029] The specific steps for further constructing the voltage stability evaluation model based on eGBDT are as follows:

[0030] (1) The single-sided gradient sampling method GOSS reduces the voltage stability fine evaluation model by arranging the gradient in descending order to obtain the dimensionality-reduced measurement data, thereby improving the computational efficiency.

[0031] In each iteration of the one-sided gradient sampling method GOSS, the sample gradient of the measurement data is first calculated, and then the samples are sorted in descending order according to the absolute value of the gradient. A proportion threshold a is set, and the first a% of the sorted samples are defined as large gradient samples, which are all retained; the remaining (1-a)% of the samples are small gradient samples, which are randomly sampled at a sampling ratio of b%.

[0032] To ensure the original distribution of the small sample data obtained by sampling, the small gradient sample data is multiplied by a coefficient (1-a) / b to amplify the weight of the small gradient sample.

[0033] (2) The HEEFB (mutually exclusive feature binding) technique is used to compress the feature of measurement data.

[0034] The obtained dimensionality-reduced measurement data is processed by HEEFB (Hybrid Feature Bundling) to extract features from each measurement data. The extracted features are sorted according to the number of non-zero features. The conflict ratio between different features is calculated and obtained. The features are then merged to obtain the feature with the smallest conflict ratio, thus completing feature compression.

[0035] Through the above design scheme, the present invention can bring the following beneficial effects:

[0036] This invention proposes a fully data-driven, eGBDT-based method for refined long-term voltage stability assessment. This method utilizes wide-area online bus voltage amplitude and phase angle data to calculate load margin indices and achieve refined voltage stability classification. Simultaneously, it employs One-Sided Gradient Sampling (GOSS) and Mutually Exclusive Feature Bundling (HEEFB) techniques to achieve dimensionality reduction and feature compression of high-dimensional measurement data space, effectively improving the processing efficiency of traditional GBDT methods for massive measurement data. While inheriting the high-precision estimation performance of traditional GBDT methods, the proposed method significantly enhances its ability to process massive measurement data. Compared with existing methods, this invention demonstrates better real-time application in efficiently analyzing high-dimensional measurement data, exhibits stronger robustness to uncertainties arising from large-scale renewable energy integration, and shows good applicability when handling incomplete measurement data and training datasets of varying sizes. Therefore, the proposed method has significant practical application value. Attached Figure Description

[0037] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0038] Figure 1 This is a flowchart illustrating the workflow of a long-term voltage stability fine evaluation method based on eGBDT in an embodiment of the present invention.

[0039] Figure 2 This is a comparison chart of estimation accuracy and training time under different parameter combinations in the embodiments of the present invention.

[0040] Figure 3 This is a schematic diagram of the confusion matrix calculation results in an embodiment of the present invention.

[0041] Figure 4 This is a comparison chart of estimation accuracy under different dataset sizes in the embodiments of the present invention. Detailed Implementation

[0042] To better understand the purpose, structure, and function of this invention, the following detailed description of a long-term voltage stability refined evaluation method based on eGBDT, in conjunction with the accompanying drawings, is provided.

[0043] like Figures 1-4 As shown, this invention provides a refined long-term voltage stability assessment method based on eGBDT. This method utilizes eGBDT to evaluate load margin parameters from widely measured voltage amplitude and phase angle, thereby assessing the voltage stability of the power system online. The calculation process includes the following steps:

[0044] S1: Establish a load margin index K for voltage stability assessment p And further based on Kp The magnitude and bus voltage amplitude are used to refine the determination of the system voltage stability state: safe state, warning state, and emergency state.

[0045] S2: Using the Gradient Descent Tree (GBDT) method, with the goal of minimizing the logarithmic approximate loss function, the model is iteratively trained along the direction of the maximum negative gradient to construct a refined evaluation model for voltage stability.

[0046] S3: The single-sided gradient sampling method (GOSS) and the mutually exclusive feature binding technique (HEEFB) are used to realize spatial dimensionality reduction and feature compression of measurement data, and further construct a voltage stability evaluation model based on eGBDT to improve the evaluation efficiency of GBDT model.

[0047] S4: Using online measurement data of system voltage amplitude and voltage phase angle as input to the eGBDT model, a refined assessment of voltage stability is achieved.

[0048] In S1, the load margin index K shown in formula (1) is established. p Furthermore, it provides a refined voltage stability state of the power system, including the following steps:

[0049]

[0050] Among them, K p λ0 is the load margin index, representing the distance from the current operating point of the busbar to the voltage stability critical point; λ0 is the load parameter of the current state of the busbar. max These are the load parameters at the critical state of bus voltage stability;

[0051] Furthermore, based on the bus voltage stability state, the voltage stability state is further refined into: Secure (S), Warning (W), and Emergency (E) states, with the conditions for each state being as follows:

[0052] (1) Safety state: K under normal conditions p >7% and V i ≥0.9 pu or K under fault conditions p >5% and V i ≥0.9pu;

[0053] (2) Warning state: K under normal conditions p >7% and V i ≤0.9pu;

[0054] (3) Emergency situation: Under normal circumstances, K p <7% or under fault conditions K p <5%;

[0055] Among them, Vi The value represents the bus voltage amplitude, and pu indicates the per-unit value.

[0056] In S2, based on the given training set data, the GBDT model is built by iteratively training and minimizing the loss function. This includes the following steps:

[0057] Given a training set, which includes input data and corresponding voltage stability state labels (safe state S, warning state W, and emergency state E), as shown in Equation (2):

[0058]

[0059] Where n represents the number of load buses; i represents the i-th system operating condition; This represents the voltage magnitude of the i-th bus. x represents the voltage phase angle of the i-th bus; i y represents the input sample under the i-th operating condition; i This represents the sample label corresponding to the i-th working condition;

[0060] Define the logarithmic approximation loss function L(y,f(x)) as the difference between the predicted and actual voltage stability values, and obtain formula (3):

[0061]

[0062] Wherein, the probability function p k (x) is the predicted probability that sample x belongs to class k: y i These are sample labels, y i If y ∈{0,1}, the target classification and the predicted classification are consistent, then y i =1, otherwise, if the target classification and the predicted classification are inconsistent, then y i =0; f(x) is a GBDT model ensembled from k different regression trees;

[0063] The gradient descent tree GBDT model is repeatedly trained in the direction of the negative gradient error function defined by formula (4) to minimize the loss function, thus obtaining the final enhanced gradient descent tree eGBDT model:

[0064] Negative gradient error function:

[0065] Where t is the number of iterations; x is the negative gradient error function of the class k corresponding to the i-th sample in the t-th iteration; i , These are the fitted sample parameters obtained from the previous iteration; p k t (xi f(x) represents the probability of predicting sample x in the t-th iteration; i ) represents the GBDT model ensemble of the first i regression trees;

[0066] During the training of the Gradient Descent Tree (GBDT) model, the objective is to minimize the logarithmic approximate loss function. The model iterates continuously along the direction of the maximum negative gradient, thus utilizing the sample values ​​x from the previous iteration. i , Update the current sample value x i , Ultimately, the GBDT model was transformed from f t-1 (x) is updated to f t (x) means that the GBDT model is completed.

[0067] In S3, the single-sided gradient sampling method GOSS and the mutually exclusive feature binding technique HEEFB are used to achieve spatial dimensionality reduction and feature compression of measurement data, and a voltage stability fine evaluation model based on eGBDT is constructed to improve the computational efficiency of the gradient descent tree GBDT algorithm.

[0068] (1) One-sided gradient sampling method GOSS. This method reduces the dimensionality of the dataset by sorting gradients in descending order, thereby improving computational efficiency. Each iteration first calculates the sample gradient, then sorts the samples in descending order of their absolute gradient values. A threshold 'a' is set, defining the first 'a'% of the sorted samples as large gradient samples, which are all retained; the remaining (1-a)% are small gradient samples, randomly sampled at a sampling ratio of b%. To preserve the original distribution of the sampled small samples as much as possible, a coefficient (1-a) / b is applied to amplify the weight of the small gradient samples. The gradient calculation in GOSS focuses more on datasets with large gradients, giving more weight to system operation points with higher risks, thus reducing the spatial dimensionality of the database. On the other hand, the weight amplification prevents excessive influence on the original data distribution.

[0069] (2) HEEFB (Helper Exclusive Feature Bundling) technique. HEEFB bundles closely related features together, while compressing less related features without compromising the information provided by the data, thus achieving overall feature compression. The dimensionality-reduced measurement data is processed using HEEFB to extract features from each measurement data point. The extracted features are then sorted by the number of non-zero features. The conflict ratio between different features is calculated and obtained. Each feature is iterated over, and features are attempted to be merged to minimize the conflict ratio, thus obtaining the feature with the lowest conflict ratio and completing feature compression.

[0070] In summary, by employing spatial dimensionality reduction based on the one-sided gradient sampling method GOSS and feature compression based on the mutually exclusive feature binding technique HEEFB, we can achieve efficient dimensionality reduction of massive measurement data and improve the efficiency of the gradient descent tree GBDT algorithm.

[0071] In S4, an enhanced gradient descent tree (eGBDT) model is established by integrating the one-sided gradient sampling method (GOSS), the mutually exclusive feature binding technique (HEEFB), and the gradient descent tree (GBDT) model. Furthermore, by using online measurements of bus voltages and phase angles as the eGBDT model, a refined voltage stability assessment result (safe state S, warning state W, emergency state E) is obtained, thus enabling a refined online assessment of the long-term voltage stability of power systems with a high proportion of renewable energy.

[0072] In summary, the calculation of the refined evaluation method for long-term voltage stability of power systems with a high proportion of new energy sources based on eGBDT has been completed.

[0073] The present invention will be further described in detail below with reference to embodiments:

[0074] like Figure 1 As shown, the Nordic 32-node system was used for testing, simulating three scenarios for simulation analysis. Measurement datasets from different operating scenarios were used as input, with voltage stability state classification (safe state S, warning state W, and emergency state E) as the target. The resulting datasets were randomly divided into 70% training data and 30% test data. The specific settings for each scheme are shown in Table 1.

[0075] Table 1. Datasets used in the case study

[0076]

[0077] To illustrate the impact of parameters (iteration number T and number of bins h in the histogram) on the voltage stability assessment results, the model was trained and analyzed using a combination of parameter values ​​(h, T), including the accuracy of the estimation results and the training time. The results are as follows: Figure 2 As shown. From Figure 2 It can be seen that the accuracy of the scheme increases with the increase of the number of bins h and the number of iterations T in the histogram, up to the combination (20, 5). Compared with the accuracy obtained with parameter value (15, 15), the combination (15, 10) can achieve the same accuracy in less time. Therefore, in order to balance model accuracy and training time, the case study of this system selects the combination (15, 10) as the parameter in voltage stability evaluation.

[0078] A confusion matrix was used to evaluate the classification performance of the proposed scheme. The confusion matrix represents the percentage of classification results that are the same as or different from the sample labels; the values ​​on the diagonal represent the probability of correct classification, while the values ​​outside the diagonal represent the probability of misclassification. The training dataset in Table 1 was used as the data input for training the eGBDT model with the selected parameter combinations, and then the accuracy of the training results was evaluated using the test set. Figure 3 This is the result of the confusion matrix calculation. (From...) Figure 3 It can be seen that the misclassification rates for the three voltage stability classification states are all within the acceptable range. Among them, the highest misclassification probability is for a safe state to be misclassified as a warning state, with a misclassification probability of 0.022. Under normal circumstances, the probability of misclassifying the system as an emergency state or a warning state is extremely low. This greatly ensures that voltage stability emergency states and early warning states are detected in a timely manner before the system's safety and stability deteriorate further, effectively guaranteeing the reliability of the proposed voltage stability assessment framework.

[0079] To further verify the superiority of the proposed method, eGBDT was compared with several other commonly used machine learning methods (Multi-kernel Support Vector Machine (MCSVM), Decision Tree (DT), and Neural Network (ANN). The comparison results are shown in Table 2. The statistical analysis results in Table 2 show that, compared with other manual algorithms, eGBDT has the highest evaluation accuracy and overall accuracy (the average of the evaluation accuracy in the three scenarios) in different scenarios, effectively demonstrating the effectiveness of the proposed method in voltage stability evaluation.

[0080] Table 2 Comparison of evaluation accuracy of different methods

[0081]

[0082] To investigate the impact of the amount of training data on the accuracy of voltage stability assessment, the training data was randomly sampled to form datasets of different sizes (20%, 30%, 40%, 50%, 60%, and 70%). Voltage stability assessments were then conducted using four analytical methods, and the results are as follows: Figure 4 As shown. From Figure 4As can be seen, the overall accuracy of all four methods increases significantly with the increase of the training dataset, and the overall accuracy of the proposed method is higher than that of the other methods for all given datasets. Even with a small amount of training data (20% of the dataset), the accuracy of the proposed method is reduced to 96.12%, which is far higher than the other three methods. The simulation results show that the proposed method can accurately assess the voltage stability of power systems even with limited data, further validating its effectiveness. Furthermore, less training data reduces the burden on data transmission and processing, further demonstrating the effectiveness and superiority of the proposed method in practical engineering applications.

Claims

1. An eGBDT-based long-term voltage stability refinement evaluation method, characterized by: Comprise the following steps and the following steps are sequentially performed: Step two, using gradient descent tree GBDT method, a GBDT model integrated by multiple different regression trees is constructed, according to the given training set data, the log approximation loss function is minimized as the goal, the GBDT model is iteratively trained according to the direction of the maximum negative gradient, and a voltage stability fine evaluation model is constructed; Step one, establish the load margin index K for voltage stability assessment p And further, the size of the load margin index K p The system voltage stability state is finely divided into safe state, warning state and emergency state according to the size of the load margin index K and the bus voltage amplitude. The voltage stability fine evaluation model is constructed, specifically comprising the following steps: Given the training set, the training set includes input data and corresponding voltage stability state labels, wherein the label of the safe state is S, the label of the warning state is W, and the label of the emergency state is E, as shown in formula (2): Define the log approximation loss function L(y,f(x)), which represents the difference between the voltage stability classification prediction value and the true value, as shown in formula (3): wherein n represents the number of load buses; i represents the i-th system operating condition; represents the voltage amplitude of the i-th bus; represents the voltage phase angle of the i-th bus;x i represents the input sample under the i-th operating condition; y i represents the sample label corresponding to the i-th condition; According to the negative gradient error function direction defined by formula (4), the gradient descent tree GBDT model is repeatedly trained, so that the loss function is minimized, and the final enhanced gradient descent tree eGBDT model is obtained: wherein the probability function p k (x) is the probability that the predicted sample x belongs to the k class: y i is the sample label, y i ∈{0,1}, the target classification is consistent with the predicted classification, then y i =1, otherwise, the target classification is inconsistent with the predicted classification, then y i =0; f(x) is a GBDT model integrated by k different regression trees; Wherein, the negative gradient error function is as follows: Step three, using one-sided gradient sampling method GOSS and mutual exclusion feature bundling technology HEEFB, the measurement data obtained by the voltage stability fine evaluation model is subjected to spatial dimension reduction and feature compression, the dimension reduction of massive measurement data is realized, and a voltage stability evaluation model based on eGBDT is further constructed to improve the evaluation efficiency of the GBDT model; In the formula, t is the iteration number; is the negative gradient error function of the i-th sample corresponding to the category k in the t-th iteration; x i , is the fitting sample parameter obtained in the last round of iteration; p k t (x i ) represents the probability of the predicted sample x in the t-th iteration; f(x i ) represents the GBDT model of the first i regression tree ensemble. In the training process of the gradient boosting decision tree (GBDT) model, the minimum of the logarithmic approximation loss function is taken as the target, and the direction of the maximum negative gradient is iterated constantly, so that the sample value x of the previous iteration is used i , The current sample value x is updated i , Finally, the GBDT model is updated from f t-1 (x) to f t (x), that is, the construction of the GBDT model is completed; Step four, taking the online obtained bus voltage and bus phase measurement data as the input of the eGBDT model, the voltage stability fine evaluation result is obtained and the voltage is specifically displayed in the safe state S, the warning state W or the emergency state E, so as to realize the long-term voltage stability fine online evaluation of the new energy high proportion power system. The specific conditions of the fine division of the system voltage stability state in step one are as follows:

2. The eGBDT-based long-term voltage stability refinement evaluation method according to claim 1, characterized in that: The load margin index K in step one p The formula is as follows: where K p is the load margin index, which represents the distance from the current operating point of the bus to the voltage stability critical point; λ0is the load parameter of the current state of the bus, and λ max is the load parameter of the voltage stability critical state of the bus.

3. The eGBDT-based long-term voltage stability refinement evaluation method according to claim 2, characterized in that: The specific steps of further constructing the voltage stability evaluation model based on eGBDT are as follows: (1) secure state: K p > 7% and V i ≥ 0.9 p.u. or fault case: K p > 5% and V i ≥ 0.9 p.u.; (2) Warning state: K p > 7% and V i ≤ 0.9 p.u. (3) Emergency: K p <7% or failure condition K p <5%; where V i is the system voltage magnitude, p.u. denotes per unit.

4. The eGBDT-based long-term voltage stability refinement evaluation method according to claim 1, characterized in that: (1) The one-sided gradient sampling method GOSS is used to reduce the dimension of the measurement data obtained by the voltage stability fine evaluation model by arranging the gradient in descending order, so as to improve the calculation efficiency; Each step of iteration of the one-sided gradient sampling method GOSS first calculates the sample gradient of the measurement data, then arranges the samples in descending order according to the gradient absolute value, sets a proportion threshold a, defines the first a% of the sorted samples as large gradient samples, and all are reserved; the remaining (1-a)% samples are small gradient samples, which are randomly sampled with a sampling proportion of b%; In order to ensure the original distribution of the small sample data obtained by sampling, the small gradient sample data is multiplied by the coefficient (1-a) / b to adjust the weight of the small gradient sample data; (2) The mutual exclusion feature bundling technology HEEFB is used to realize feature compression of the measurement data; The reduced measurement data is extracted by the mutual exclusion feature bundling technology HEEFB, the features of the extracted measurement data are sorted according to the number of non-zero values, the conflict ratio between different features is calculated and obtained, and feature merging is performed, so as to obtain the feature with the minimum conflict ratio and complete feature compression. ​

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