A method for predicting the pump inspection period of pumping unit wells based on feature fusion
Through the feature fusion method, the correlation coefficient method is used to screen static and dynamic data, combined with SVR and convolutional neural network models, the problem of low accuracy in the prediction of the cycle of the pump well inspection pump in the traditional method is solved, and the pump cycle prediction with high accuracy is achieved, and oil field production management is guided.
Patent Information
- Application Number
- CN202110621296.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-06-03
- Publication Date
- 2025-08-05
- Estimated Expiration
- 2041-06-03
AI Technical Summary
The traditional oil pump cycle prediction method has a large workload and low prediction accuracy, making it difficult to meet the economic requirements of oil field production.
The feature fusion method is adopted to filter static and dynamic data through the correlation coefficient method, and a feature extraction model based on SVR and convolutional neural network is established, and a multimodal compression bilinear pooling and hybrid Gaussian model is combined for feature fusion and re-learning, and a pump detection cycle prediction model is established.
It has achieved high accuracy prediction of the well inspection pump cycle of the oil pump, with the prediction accuracy reaching more than 87%, guiding oil field production management and reducing production costs.
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Figure CN115512148B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a method for predicting an oil well pump inspection cycle based on feature fusion, and belongs to the technical field of oil field production. Background Art
[0002] Rod pumping is a predominant production method in oilfields both domestically and internationally. The downhole portion of a rod pumping system primarily consists of the sucker rod string, tubing, and pump. When the pump suffers from sand or wax sticking or severe leakage, it can cause the well to malfunction or even shut down. Sucker rod breakage and other issues prevent energy from being transferred to the pump, disrupting normal production. Tubing corrosion and leakage can also impact pump efficiency. Defective tools, sand filters, and air anchors can also affect pump efficiency. Therefore, regular pump inspections are essential to address downhole failures in pumping wells.
[0003] There are two methods for pump inspection during workover of pumping wells: scheduled inspection and in-well inspection. The interval between inspections is the pump inspection cycle. Various factors, such as sand production, bridging, and well operating systems, affect the inspection cycle. A rational analysis of the factors influencing pump inspections and the determination of an appropriate inspection cycle can reduce oilfield production costs and improve oilfield management, ultimately achieving economic success in oilfield development.
[0004] Traditional pump inspection prediction relies on mechanism analysis, analyzing the failure modes, mechanisms, and impacts of pumping well equipment to determine when failures are likely to occur. However, due to the complex and ever-changing operating conditions of pumping wells and the diverse causes of failures, traditional methods suffer from high workloads and low prediction accuracy. Summary of the Invention
[0005] In view of the above problems, the purpose of the present invention is to provide a method for predicting the pump inspection cycle of a well pumping unit based on feature fusion with high accuracy.
[0006] To achieve the above object, the present invention adopts the following technical solution: a method for predicting the pump inspection cycle of a well pumping unit based on feature fusion, which comprises the following steps:
[0007] 1) Collect sample data of a complete pump inspection cycle of an oilfield pumping well, and divide the data related to the pump inspection cycle of the pumping well into static data and dynamic data according to the degree of data change;
[0008] 2) The correlation coefficient method is used to screen out parameters with strong correlation with the pump inspection cycle in the static and dynamic data;
[0009] 3) Based on the filtered parameters, a static feature extraction model based on SVR and a dynamic feature extraction model based on convolutional neural network are established to extract the static and dynamic features of the parameters respectively;
[0010] 4) Input the extracted static features and dynamic features into the multimodal compression bilinear pooling model for feature fusion;
[0011] 5) Using the mixed Gaussian model to relearn the fusion features and establish a pump inspection cycle prediction model;
[0012] 6) Based on the pump inspection cycle prediction model, the pump inspection cycle of the pumping well is actually predicted.
[0013] In step 1), the static data mainly include parameters such as upstream current, downstream current, pump diameter, pump depth, stroke, stroke frequency, displacement, pump efficiency, maximum load, minimum load, etc., and the dynamic data mainly include parameters such as daily liquid production, daily oil production, daily water production, water cut, oil pressure, casing pressure, flow pressure, dynamic liquid level, wellhead temperature, etc.
[0014] In step 2), the Spearman rank correlation coefficient is used to screen the static parameters, and the correlation coefficient values ρ between the upstream current, downstream current, pump diameter, pump depth, stroke, stroke frequency, displacement, pump efficiency, maximum load, minimum load and pump inspection cycle are calculated respectively. s . Screening ρ s Static parameters with values greater than 0.6 are used as input parameters of the model, including minimum load, pump efficiency, maximum load, stroke frequency, pump depth, and pump diameter.
[0015] In step 2), the Pearson correlation coefficient is used to screen for correlation parameters between dynamic parameters and pump inspection cycle. The pump inspection cycle of the pumping well is used as a feature vector. The absolute value of the linear relationship between daily liquid production, daily oil production, daily water production, water cut, oil pressure, casing pressure, flow pressure, dynamic liquid level, wellhead temperature, and the feature vector is calculated using the Pearson correlation coefficient. The larger the absolute value of the output value, the stronger the linear relationship of the associated feature. Production parameters with an r value greater than 0.6 are selected as input features, including water cut, daily liquid production, flow pressure, daily water production, and daily oil production.
[0016] In step 3), the steps of establishing a static feature extraction model based on SVR are as follows:
[0017] ①Build training samples
[0018] Assume that the historical data of the pump inspection cycle is Y={Y1,Y2,…,Y n}, where n is the data length, Y i is the pump inspection period of the i-th group of data, i∈[1,n]; let the historical data of the static parameters be X N={X1,X2,…,X n}, n = 6, X N is a vector composed of six groups of static characteristics: minimum load, pump efficiency, maximum load, stroke frequency, pump depth, and pump diameter. i ={x1,x2,…,x t}, i∈[1,6] is the data of the i-th static parameter in the time series t, and the training sample {X N ,Y}.
[0019] ② Obtain the optimal penalty factor and kernel function width
[0020] A radial basis kernel function was selected, and a grid search method was used to obtain the optimal penalty factor C and kernel width σ. The parameter C was set to a range of 0 to 100 with a search step of 1, and the parameter σ was set to a range of 0 to 1 with a search step of 0.01. Within the given range, the dataset was divided into 10 subsets of equal size, and a coarse 10×10 grid was obtained for the parameters. SVR was used to learn the samples within all (C, σ) combinations, and the cross-validation mean square error (MSE) was used to express it:
[0021]
[0022] where y i is the actual pump inspection period of the i-th point, y′ i is the predicted pump inspection period of the i-th point. Compare the MSE and select the parameter combination with the smallest MSE as the optimal (C, σ) parameter combination.
[0023] ③Establish a feature extraction model
[0024] The training samples and the optimal (C, σ) parameter combination are brought into the SVR model for training, and the weight ω of each input feature is fitted according to the sample number N and the pump inspection cycle value.
[0025] In step 3), the steps of establishing a dynamic feature extraction model based on a convolutional neural network are as follows:
[0026] ① Parameter reconstruction
[0027] Before training the model, the data is standardized and normalized to eliminate the dimension and regularize the data to a uniform range. The formula is as follows:
[0028]
[0029] in is the characteristic parameter after normalization; x is the original characteristic parameter of the pumping well; X min Indicates the minimum value of the characteristic parameter; X maxRepresents the maximum value of the characteristic parameter. The parameter structure is then reconstructed. For a single well, 30 data points for five dynamic parameters are selected in chronological order as a group. The six data sets are then merged into a 30*30 matrix.
[0030] ②Training model
[0031] The reconstructed dynamic parameters are input into the convolutional neural network for training. The loss function of the model training is defined as:
[0032]
[0033] Among them, P j Y represents the predicted pump detection cycle value output by the convolutional neural network; j It is the actual pump inspection cycle value.
[0034] In step 4), the static characteristics f1 (S n ) and dynamic characteristics f2(D n ), input the Multimodal Compact Bilinear Pooling model for feature fusion. MCBP uses the Count Sketch projection function ψ to convert the outer product of the static feature vector and the dynamic feature vector Projected into a low-dimensional representation space.
[0035] In step 5), the fusion features are relearned using a mixed Gaussian model to establish a pump inspection cycle prediction model for training as follows:
[0036] ①Determine the optimal number of clusters
[0037] Pump inspection cycles ranging from 300 to 1200 days were grouped into 18 clusters and 9 clusters, respectively, at intervals of 50 and 100 days. The Bayesian information criterion (BIC) model selection theory was used to estimate the probability of clustering with 18 and 9 clusters, respectively. The model with the lower BIC value was selected as the optimal model.
[0038] ②Cluster pump inspection cycle
[0039] The fused feature vector is input into the Gaussian mixture model for training to obtain the trained Gaussian mixture model. The expectation-maximization (EM) algorithm is used to fit the k mixed Gaussian distributions to obtain the mean μ of each distribution. j and covariance ε j(1≤j≤k). Using the calculated Gaussian parameters, we traverse all samples and assign them to the class with the highest probability.
[0040] Due to the adoption of the above technical solution, the present invention has the following advantages: the pump inspection cycle prediction method of the present invention first divides the oil field pumping well data into static parameters and dynamic parameters, and extracts features respectively, then adopts multimodal compression bilinear pooling to fuse the features, and then uses a mixed Gaussian model to re-learn the fused features to establish a pump inspection cycle prediction model for training. Experimental results show that the prediction accuracy of the present invention reaches more than 87%, which can realize the pump inspection cycle operation guidance of the pumping well. BRIEF DESCRIPTION OF THE DRAWINGS
[0041] Figure 1 Flow chart of the method of the present invention
[0042] Figure 2 This is the dynamic feature extraction flow chart of the present invention DETAILED DESCRIPTION
[0043] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.
[0044] The method for predicting the pump inspection cycle of a well pumping unit based on feature fusion of the present invention is shown in the flowchart of the method. Figure 1 As shown, the method includes the following steps:
[0045] 1. Collect sample data from a complete pump inspection cycle of an oilfield pumping well, and divide the data related to the pump inspection cycle of the pumping well into static data and dynamic data according to the degree of data change. Static data mainly includes parameters such as upstream current, downstream current, pump diameter, pump depth, stroke, stroke frequency, displacement, pump efficiency, maximum load, minimum load, etc. Dynamic data mainly includes parameters such as daily liquid production, daily oil production, daily water production, water cut, oil pressure, casing pressure, flow pressure, dynamic liquid level, wellhead temperature, etc.
[0046] 2. Use the correlation coefficient method to select parameters with strong correlation with the pump inspection cycle in the static and dynamic data;
[0047] 1) Use the Spearman rank correlation coefficient to screen the static parameters, and calculate the correlation coefficients of upstream current, downstream current, pump diameter, pump depth, stroke, stroke frequency, displacement, pump efficiency, maximum load, minimum load and pump inspection cycle. Take the upstream current as an example, and assume that the upstream current value is X={x1,x2,…x n}, where x i ={t1,t2,…,t d}, i∈[1,n] represents the uplink current value of each day in the i-th pump inspection cycle; let the number of days in the pump inspection cycle be Y={y1,y2,…y nThe Spearman rank correlation coefficient is a nonparametric indicator that measures the dependence of two variables. It uses a monotonic equation to evaluate the correlation between two statistical variables. The formula is as follows:
[0048]
[0049] Where, d i It represents the position difference of the paired variables after sorting the upstream current and the pump detection period, that is, the difference in the rank of X and Y. This method is used to calculate other parameters and screen ρ s Static parameters with values greater than 0.6 are used as input parameters of the model, including minimum load, pump efficiency, maximum load, stroke frequency, pump depth, and pump diameter.
[0050] 2) Use the Pearson correlation coefficient to screen the correlation parameters between dynamic parameters and pump inspection cycle. Take the pump inspection cycle of the pumping well as the feature vector, and use the Pearson correlation coefficient to analyze and calculate the absolute value of the linear relationship between daily liquid production, daily oil production, daily water production, water content, oil pressure, casing pressure, flow pressure, dynamic liquid level, wellhead temperature and the feature vector. The larger the absolute value of the output value, the stronger the linear relationship of the associated feature. Taking daily liquid production as an example, let the daily liquid production value be X={x1,x2,…x n}, where x i ={t1,t2,…,t d}, i∈[1,n] represents the daily liquid production value of each day in the i-th pump inspection cycle; let the number of days in the pump inspection cycle be Y={y1,y2,…y n}, Pearson correlation coefficient r xy Expressed as:
[0051]
[0052] From this, the Pearson correlation coefficient r value between the pump inspection cycle and each production parameter can be calculated, and production parameters with an r value greater than 0.6 can be selected as input features, including water content, daily liquid production, flow pressure, daily water production, and daily oil production.
[0053] 3. Based on the screened parameters, a static feature extraction model based on SVR and a dynamic feature extraction model based on convolutional neural network are established to extract the static and dynamic features of the parameters respectively;
[0054] 1) The steps to establish a static feature extraction model based on SVR are as follows:
[0055] ①Build training samples
[0056] Assume that the historical data of the pump inspection cycle is Y={Y1,Y2,…,Y n}, where n is the data length, Y iis the pump inspection period of the i-th group of data, i∈[1,n]; let the historical data of the static parameters be X N ={X1,X2,…,X n}, n = 6, X N is a vector composed of six groups of static characteristics: minimum load, pump efficiency, maximum load, stroke frequency, pump depth, and pump diameter. i ={x1,x2,…,x t}, i∈[1,6] is the data of the i-th static parameter in the time series t, and the training sample {X N ,Y}.
[0057] ② Obtain the optimal penalty factor and kernel function width
[0058] A radial basis kernel function was selected, and a grid search method was used to obtain the optimal penalty factor C and kernel width σ. The parameter C was set to a range of 0 to 100 with a search step of 1, and the parameter σ was set to a range of 0 to 1 with a search step of 0.01. Within the given range, the dataset was divided into 10 subsets of equal size, and a coarse 10×10 grid was obtained for the parameters. SVR was used to learn the samples within all (C, σ) combinations, and the cross-validation mean square error (MSE) was used to express it:
[0059]
[0060] where y i is the actual pump inspection period of the i-th point, y′ i is the predicted pump inspection period of the i-th point. Compare the MSE and select the parameter combination with the smallest MSE as the optimal (C, σ) parameter combination.
[0061] ③Establish feature extraction model
[0062] The essence of SVR is to map sample data that cannot be linearly regressed to high-dimensional linear regression through a nonlinear mapping. The function expression of the regression is:
[0063]
[0064] The training samples and the optimal (C, σ) parameter combination are brought into the SVR model for training, and the weight ω of each input feature is fitted according to the sample number N and the pump inspection cycle value.
[0065] 2) The flow chart of establishing a dynamic feature extraction model based on convolutional neural network is as follows Figure 2 As shown, the steps are as follows:
[0066] ① Parameter reconstruction
[0067] Before training the model, in order to prevent the presence of large values in the data from weakening or even invalidating the training effect due to smaller values, the data is generally standardized and normalized to eliminate the dimension and regularize the data to a uniform range. The formula is as follows:
[0068]
[0069] in is the characteristic parameter after normalization; x is the original characteristic parameter of the pumping well; X min Indicates the minimum value of the characteristic parameter; X max Indicates the maximum value among the characteristic parameters.
[0070] The input to a convolutional neural network is a matrix. Since there are relatively few types of dynamic parameters, the parameter structure must be reconstructed. For a single well, for example, 30 data points for five dynamic parameters are selected in chronological order as a group. These six data sets are then combined into a 30x30 matrix.
[0071] ②Training model
[0072] The reconstructed dynamic parameters are input into the convolutional neural network for training, and the feature extraction process is as follows: Figure 2 shown.
[0073] The feature extraction network consists of a convolutional layer, a maximum pooling layer, and a fully connected layer, and uses a rectified linear unit (ReLU). The convolutional layer is used to extract features, the maximum pooling layer is used to enhance the robustness of detection, and the fully connected layer is used to map the learned distributed features to the sample label space. ReLU is a nonlinear activation function used to prevent gradient disappearance. The loss function of the model training is defined as:
[0074]
[0075] Among them, P j Y represents the predicted pump detection cycle value output by the convolutional neural network; j It is the actual pump inspection cycle value.
[0076] 4. Input the extracted static features and dynamic features into the multimodal compression bilinear pooling model for feature fusion;
[0077] The static characteristics f1(S n ) and dynamic characteristics f2(D n ), input the Multimodal Compact Bilinear Pooling model for feature fusion. Since MCBP uses the outer product calculation method, it encodes f1(S n ) and f2(D n) The relationship between each element in the feature vector, the resulting multimodal fusion feature vector is more expressive than other feature fusion methods, such as splicing, bitwise multiplication, and bitwise addition; and MCBP converts f1(S n ) and f2(D n ) feature vectors are projected into the frequency domain, avoiding the direct calculation of the outer product, effectively solving the problems of the original bilinear pooling, such as high dimension, complex calculation, and easy overfitting.
[0078] MCBP uses the Count Sketch projection function ψ to transform the outer product of the static eigenvector and the dynamic eigenvector Projected into low-dimensional space, it is represented as:
[0079]
[0080] Where h and g are hash maps, and * represents the convolution operation. According to the convolution theorem, convolution in the time domain corresponds to multiplication in the frequency domain. The above formula can be expressed as:
[0081]
[0082] Among them, ⊙ represents the dot product operation, and the result is the fused feature vector.
[0083] 5. Use the mixed Gaussian model to relearn the fusion features and establish a pump inspection cycle prediction model;
[0084] 1) Determine the optimal number of clusters
[0085] To more accurately predict pump inspection cycles and narrow the range of days, based on actual production experience and data, the pump inspection cycle duration of 300 to 1200 days was grouped into 50-day and 100-day intervals, resulting in 18 and 9 clusters, respectively. The Bayesian Information Criterion (BIC) model selection theory was used to estimate the probability of clustering with 18 and 9 clusters. The formula is:
[0086] C BIC =-1ln(L)+n p ln(m)
[0087] Where C BIC is the BIC value, n p is the number of pump cycle parameters within the group, L is the maximum value of the estimated model likelihood function, and the model with a low BIC value is preferred.
[0088] 2) Cluster pump inspection cycle
[0089] The fused feature vector is input into the Gaussian mixture model for training to obtain the trained Gaussian mixture model. The expectation-maximization (EM) algorithm is used to fit the k mixed Gaussian distributions to obtain the mean μ of each distribution. j and covariance ε j (1≤j≤k). Using the calculated Gaussian parameters, we traverse all samples and assign them to the class with the highest probability.
[0090] 6. Based on the pump inspection cycle prediction model, the pump inspection cycle of the pumping well is actually predicted.
Claims
1. A method for predicting the pump inspection cycle of a well pumping unit based on feature fusion, comprising the following steps: 1) Collect sample data of a complete pump inspection cycle of an oilfield pumping well, and divide the data related to the pump inspection cycle of the pumping well into static data and dynamic data according to the degree of data change; 2) The correlation coefficient method is used to screen out parameters with strong correlation with the pump inspection cycle in the static and dynamic data; 3) Based on the filtered parameters, a static feature extraction model based on SVR and a dynamic feature extraction model based on convolutional neural network are established to extract the static and dynamic features of the parameters respectively; 4) Input the extracted static features and dynamic features into the multimodal compression bilinear pooling model for feature fusion; 5) Using the mixed Gaussian model to relearn the fusion features and establish a pump inspection cycle prediction model; 6) Based on the pump inspection cycle prediction model, the pump inspection cycle of the pumping well is actually predicted.
2. The method for predicting the pump inspection cycle of a well pumping unit based on feature fusion according to claim 1, characterized in that: The step 1) divides the data related to the pumping unit well inspection cycle into static data and dynamic data according to the degree of data change: the static data includes upstream current, downstream current, pump diameter, pump depth, stroke, stroke frequency, displacement, pump efficiency, maximum load, and minimum load parameters; the dynamic data includes daily liquid production, daily oil production, daily water production, water content, oil pressure, casing pressure, flow pressure, dynamic liquid level, and wellhead temperature parameters.
3. The method for predicting the pump inspection cycle of a well pumping unit based on feature fusion according to claim 1, characterized in that: In step 2), the Spearman rank correlation coefficient is used to screen the static parameters, and the correlation coefficient values ρ of the upstream current, downstream current, pump diameter, pump depth, stroke, stroke frequency, displacement, pump efficiency, maximum load, minimum load and pump inspection cycle are calculated respectively. s ; Screening ρ s Static parameters with values greater than 0.6 are used as input parameters of the model, including minimum load, pump efficiency, maximum load, stroke frequency, pump depth, and pump diameter.
4. The method for predicting the pump inspection cycle of a well pumping unit based on feature fusion according to claim 1, characterized in that: In the step 2), the Pearson correlation coefficient is used to screen the correlation parameters between the dynamic parameters and the pump inspection cycle; the pump inspection cycle of the pumping well is used as a feature vector, and the Pearson correlation coefficient is used to analyze and calculate the absolute value of the linear relationship between the daily liquid production, daily oil production, daily water production, water cut, oil pressure, casing pressure, flow pressure, dynamic liquid level, wellhead temperature and the feature vector. The larger the absolute value of the output value, the stronger the linear relationship of the associated feature; and production parameters with an r value greater than 0.6 are screened as input features, including water cut, daily liquid production, flow pressure, daily water production, and daily oil production.
5. The method for predicting the pump inspection cycle of a well pumping unit based on feature fusion according to claim 1, characterized in that: In step 3), the steps of establishing a static feature extraction model based on SVR are as follows: 1) Construct training samples Assume that the historical data of the pump inspection cycle is Y={Y1,Y2,…,Y n }, where n is the data length, Y i is the pump inspection period of the i-th group of data, i∈[1,n]; let the historical data of the static parameters be X N ={X1,X2,…,X n }, n = 6, X N is a vector composed of six groups of static characteristics: minimum load, pump efficiency, maximum load, stroke frequency, pump depth, and pump diameter. i ={x1,x2,…,x t }, i∈[1,6] is the data of the i-th static parameter in the time series t, and the training sample {X N ,Y}; 2) Obtain the optimal penalty factor and kernel function width A radial basis kernel function was selected, and a grid search method was used to obtain the optimal penalty factor C and kernel function width σ. The parameter C was set to a value range of 0 to 100 with a search step of 1, and the parameter σ was set to a value range of 0 to 1 with a search step of 0.
01. Within the given value range, the data set was divided into 10 subsets of equal size, and a coarse grid of 10×10 parameters was obtained. SVR was used to learn the samples in all (C, σ) combinations, and the cross-validation mean square error (MSE) was used to represent it. The MSE was compared, and the parameter combination with the smallest MSE was selected as the optimal (C, σ) parameter combination. 3) Establish feature extraction model The training samples and the optimal (C,σ) parameter combination are brought into the SVR model for training, and the weight ω of each input feature is fitted according to the number of samples and the pump inspection cycle value.
6. The method for predicting the pump inspection cycle of a well pumping unit based on feature fusion according to claim 1, characterized in that: In step 3), the steps of establishing a dynamic feature extraction model based on a convolutional neural network are as follows: 1) Parameter reconstruction Before training the model, the data was standardized and normalized to eliminate the dimension and regularize the data into a unified interval. The normalized parameters were then reconstructed. For a single well, 30 data points of five dynamic parameters were selected in chronological order as a group, and the six groups of data were merged into a 30*30 matrix. 2) Training the model The reconstructed dynamic parameters are input into the convolutional neural network for training. The loss function of the model training is defined as: Among them, P j Y represents the predicted pump detection cycle value output by the convolutional neural network; j It is the actual pump inspection cycle value.
7. The method for predicting the pump inspection cycle of a well pumping unit based on feature fusion according to claim 1, characterized in that: In step 4), the static characteristics f1 (S n ) and dynamic characteristics f2(D n ), input the multimodal compression bilinear pooling model for feature fusion.
8. The method for predicting the pump inspection cycle of a well pumping unit based on feature fusion according to claim 1, characterized in that: In step 5), the fusion features are relearned using a mixed Gaussian model to establish a pump inspection cycle prediction model for training as follows: 1) Determine the optimal number of clusters To more accurately predict the pump inspection cycle and narrow the range of days, based on actual production experience and data, the pump inspection cycle days of 300 to 1200 days were grouped into 18 and 9 categories at intervals of 50 and 100 days, respectively. The Bayesian Information Criterion (BIC) model selection theory was used to estimate the probability of grouping with 18 and 9 clusters, and the model with the lower BIC value was selected as the best. 2) Cluster pump inspection cycle The fused feature vector is input into the Gaussian mixture model for training to obtain the trained Gaussian mixture model; the maximum expectation EM algorithm is used to fit the k mixed Gaussian distributions to obtain the mean μ of each distribution j and covariance ε j , 1≤j≤k; use the calculated Gaussian parameters to traverse all samples and classify the samples into the category with the highest probability.
Citation Information
Patent Citations
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