CN110929611A - Modeling method of power transmission line icing thickness prediction model based on PR-KELM - Google Patents
Modeling method of power transmission line icing thickness prediction model based on PR-KELM Download PDFInfo
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Abstract
The invention provides a PR-KELM-based modeling method for a power transmission line icing thickness prediction model, which comprises a first stage of: converting the image data into LBP image data, reducing dimensions by using a PCA algorithm, and calculating a gray level histogram cascade to obtain extracted image data characteristics; performing feature screening on the meteorological data and the mechanical data by adopting a Relieff algorithm, and removing highly-related redundant features to obtain extracted meteorological and mechanical feature data; and a second stage: and forming sample data by using the characteristic data obtained in the first stage and the icing grade in the original image data, training the PR-KELM model by using the training data, testing the trained PR-KELM model by using the test data, and finally obtaining the power transmission line icing thickness prediction model. The invention has the beneficial effects that: the PR-KELM model is adopted for ice coating thickness prediction, so that the selection of the learning rate is not very sensitive, and the ice coating thickness prediction method is not easy to fall into a local optimal solution, and the accuracy of the prediction model is improved.
Description
Technical Field
The invention relates to the technical field of power system disaster early warning, in particular to a PR-KELM-based modeling method for a power transmission line icing thickness prediction model.
Background
At present, algorithms commonly used for the icing thickness prediction model of the power transmission line comprise a neural network, a support vector machine, a decision tree and improved versions of the models, but the algorithms only consider a single type of monitoring data, that is, feature extraction from image data is not considered. In fact, picture data is often rich in information, but the level and scale of use in the current common model are very low. In addition, the mechanical data and the meteorological data have the characteristics of high dimensionality, nonlinearity, heterogeneity and the like, and the characteristics are not well considered when the characteristics are extracted by the existing power transmission line icing thickness prediction model, so that the accuracy of the final prediction model is low.
Disclosure of Invention
In view of the above, the invention provides a modeling method of a power transmission line icing thickness prediction model based on PR-KELM, which comprises the steps of firstly processing original image data by adopting an LBP algorithm, reducing dimensions by utilizing a PCA algorithm, and calculating a gray level histogram cascade to obtain extracted image data characteristics; then, performing feature extraction on meteorological data and mechanical data by adopting a Relieff algorithm, further reducing data dimensions and eliminating a common linear relation; and finally, establishing a prediction model of the icing thickness of the power transmission line by using the extracted characteristic data and an extreme learning machine (PR-KELM) of a radial basis kernel function.
The invention provides a PR-KELM based modeling method of a power transmission line icing thickness prediction model, which comprises a first stage of carrying out feature extraction on image data, meteorological data and mechanical data and a second stage of establishing the power transmission line icing thickness prediction model by adopting a PR-KELM model, wherein:
the first stage comprises: for image Data, by converting the image Data into local binary pattern image Datan×mAnd using principal component analysis algorithm to the image Datan×mPerforming dimensionality reduction to obtain low-dimensionality feature data, and processing a local binary pattern image according to the low-dimensionality feature data to obtain a dimensionality-reduced image; dividing the image after dimensionality reduction into a plurality of small blocks, calculating a gray histogram of each small block image, and further calculating the gray histogram cascade of the whole image to obtain extracted image data characteristics;
for meteorological data and mechanical data, performing feature screening by adopting a Relieff algorithm, removing high-degree related redundant features, and obtaining extracted meteorological and mechanical feature data;
the second stage comprises: forming feature data by using image data features, meteorological feature data and mechanical feature data extracted in the first stage, taking the icing grade in original image data as label data to form sample data together, and dividing the sample data into training data and test data according to a certain proportion; the second phase comprises a training process and a testing process: and training the PR-KELM model by using the training data, testing the trained PR-KELM model by using the test data, and finally obtaining the power transmission line icing thickness prediction model.
Further, in the feature extraction of the image Data in the first stage, the local binary pattern image Datan×mThe method is an n x m dimensional characteristic matrix, sub-elements in the matrix represent the number of pixel points with the gray value of m-1 in corresponding image samples, n represents the number of original image samples, and m represents the number of gray values in an LBP image.
Further, the image Data is analyzed by principal component analysis algorithmn×mThe specific process of carrying out the dimensionality reduction is as follows:
calculating the LBP image Datan×mAverage value corresponding to each dimension
Calculating the difference between each dimension data and the average value to obtain new value data DataAdjustn×m：
DataAdjustn×m(j,i)＝Datan×m(j,i)-mean(i)；
Computing new value data DataAdjustn×mThe covariance matrix of (a);
obtaining an eigenvalue and an eigenvector of a covariance matrix based on the covariance matrix;
for the LBP image Data by maximum likelihood estimationn×mPerforming dimension estimation, selecting the first k eigenvalues in descending order according to the estimation result, and performing eigenvector matrixes Eigenvectors corresponding to the k eigenvaluesn×kAs a base of the mapping space;
data DataAdjust the new valuen×mMapping to a base space to obtain new low-dimensional feature data Fn×k：
Fn×k＝DataAdjustn×m·EigenVectorsm×k，
Wherein k represents the dimension number of the obtained low-dimension feature data, and the low-dimension feature data F is utilizedn×kAnd processing the LBP image to obtain a dimension-reduced image.
Furthermore, in the first stage, in the feature extraction of the image data, the number of pixel points corresponding to each gray value in each small image is counted by using a histogram to obtain a gray histogram of each small image; the gray level histogram of each small image together forms the gray level histogram cascade of the whole image.
Further, in the first stage of feature extraction on meteorological and mechanical data, a specific process of performing feature screening by using a ReliefF algorithm is as follows:
sampling a data set formed by meteorological data and mechanical data, wherein the sampling frequency is m, and determining k nearest neighbor samples H from a similar sample set B of any sampling sample Rj(j ═ 1,2, L, k), the same number of nearest neighbor samples M are determined from the heterogeneous sample set Cj(C) (j ═ 1,2, L, k), then the feature weights are updated:
wherein W (A) represents the weight corresponding to any feature A, P (. + -.) represents the probability, and the formula diff (A, R) is calculated1,R2) Represents a sample R1、R2The difference in characteristic a is specifically:
and setting a characteristic weight threshold delta, and removing the characteristics of which the calculated characteristic weight is smaller than the threshold delta to achieve the purpose of reducing the dimensions of the meteorological data and the mechanical data to obtain the meteorological and mechanical characteristic data.
Further, the specific process of the training process of the second stage is as follows:
determining the number of the neural units of an input layer, a hidden layer and an output layer of the PR-KELM model according to training data, wherein the training characteristic data XtrainTraining label data Y for MxQ dimensional matrix datatrainFor Mx 1 dimensional matrix data, test feature data XtestFor NxQ dimensional matrix data, test tag data YtestThe data is Nx 1 dimensional matrix data, M represents the number of training data samples, N represents the number of test data samples, and Q represents the total number of all features extracted in the first stage; using the training data Xtrain、YtrainTraining a PR-KELM model, and enabling (n, l and M) to respectively correspond to the number of nerve units of an input layer, a hidden layer and an output layer, wherein n is Q, l is M, and M is 1;
introducing a radial basis kernel function k (x)i,xj) Determining the output function of the PR-KELM model:
wherein omegaELM＝HHTH is a random feature mapping matrix, I represents a unit matrix, C is a regularization coefficient, and a radial basis kernel function k (x)i,xj) The calculation formula of (A) is as follows:
wherein i is 1, L, M, j is 1, L, M, xi、xjRepresenting training feature data Xtrainσ is the width reference of the radial basis kernel function; by training the tag data T ═ YtrainDetermining omegaELMAnd training to obtain a power transmission line icing thickness prediction model based on PR-KELM.
Further, the specific process of the test process at the second stage is as follows: test feature data XtestSubstituting the model into PR-KELM model obtained by training in the form of two-dimensional matrix, and obtaining a prediction result Y through matrix operationpreFurther constructing an evaluation index function by using the root mean square error, the average absolute error and the average absolute percentage error, wherein the predicted result Y ispreAnd test tag data YtestAnd obtaining an evaluation result of the extreme learning machine model based on the evaluation index function as an input parameter of the evaluation index function, and completing construction of the power transmission line icing thickness prediction model.
The technical scheme provided by the invention has the beneficial effects that:
(1) carrying out feature extraction on multi-source heterogeneous data by using different feature extraction methods, converting picture data into a local binary pattern, and carrying out feature extraction on the processed image data by adopting principal component analysis to obtain low-dimensional data features; for meteorological and mechanical data, a Relieff method is adopted for feature extraction, and the purpose of reducing dimensions is achieved while denoising is carried out;
(2) the extreme learning machine based on the radial basis kernel function is adopted for ice coating thickness prediction, the selection of the learning rate is not very sensitive, and the local optimal solution is not easy to fall into, so that the accuracy of the prediction model is improved.
Drawings
FIG. 1 is a flow chart of a modeling method of a PR-KELM based power transmission line icing thickness prediction model provided by the embodiment of the invention;
FIG. 2 is a schematic diagram of a feature extraction process for image data provided by an embodiment of the invention;
FIG. 3 is a block diagram of a PR-KELM model according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be further described with reference to the accompanying drawings.
Referring to fig. 1, an embodiment of the present invention provides a modeling method for a PR-KELM-based power transmission line icing thickness prediction model, including a first stage: namely, extracting the characteristics of the original data; further comprising a second stage: namely, the characteristics extracted in the first stage are utilized, and an extreme learning machine is adopted to establish a power transmission line icing thickness prediction model.
The original data come from a data set obtained by monitoring a power grid company online monitoring system terminal within a period of time, the data set comprises basic information data, image data, meteorological data and mechanical data, wherein the basic information data comprise a terminal name and a recording time date, and the basic information data cannot be used in the modeling process; the image data is an icing picture of the power transmission line; the meteorological data comprises temperature, humidity, rainfall, illumination intensity and the like; the mechanical data comprises the maximum and minimum tension, the pulling force, the wind deflection angle and the like of the wire. It should be noted that each image data sample further includes a corresponding icing level, and the levels are totally 6 states and respectively correspond to states 0 to 5, where the state 0 indicates that the power transmission line is not iced, and the states 1 to 5 sequentially indicate that the icing level of the power transmission line is increasingly severe.
The first stage performs feature extraction on image data, meteorological data and mechanical data, wherein:
for image data, converting the image data into Local Binary Pattern (LBP) image data, then performing dimensionality reduction by using a Principal Component Analysis (PCA) algorithm, dividing the image subjected to dimensionality reduction into a plurality of small blocks, and calculating gray level histogram cascade to obtain extracted image data characteristics. The specific process comprises the following steps:
s101, converting original image data into LBP image Datan×mReferring to fig. 2, for the original image of the power transmission line insulator shown in fig. (a), the converted LBP image is shown in fig. (b), the gray value range of the LBP image is 0-255, and the LBP image Data has 256 dimensions, that is, m is 256n×mIs an n x m dimensional feature matrix, and the sub-elements in the matrix represent the number of pixel points with the gray value of m-1 in the corresponding image sample.
S102, adopting PCA algorithm to carry out Data alignment on the LBP image Datan×mAnd reducing the dimension to obtain low-dimension feature data, and processing the LBP image by using the low-dimension feature data to obtain the image after dimension reduction. The LBP image Data obtained in step S101n×mThe dimensionality is high, and some dimensionalities may have linear correlation with each other, which may negatively affect the model prediction stage, so the present embodiment adopts PCA to perform dimensionality reduction. The PCA is a simple nonparametric method for extracting relevant information from LBP characteristic image data, is used for reducing data dimensionality and obtaining a brand new orthogonal vector, and has the main idea that a brand new orthogonal vector with a lower dimension is constructed through a mapping method, and relevant influences among indexes are eliminated. The method specifically comprises the following steps:
s1021, calculating LBP image Datan×mAverage value corresponding to each dimension
Then calculating the difference between each dimension data and the average value to obtain a new value data DataAdjustn×m：
DataAdjustn×m(j,i)＝Datan×m(j,i)-mean(i)；
S1022, calculating the new value data DataAdjust in the step S1021n×mThe covariance matrix of (a);
s1023, obtaining an eigenvalue and an eigenvector of a covariance matrix based on the covariance matrix;
s1024, performing maximum likelihood estimation on the LBP image Datan×mMaking dimension estimation according to the estimation resultSelecting the first k characteristic values in descending order, and selecting characteristic vector matrixes Eigenvectors corresponding to the k characteristic valuesn×kAs a base of the mapping space;
s1025, DataAdjust new value data obtained in the step S1021n×mMapping to a base space to obtain new low-dimensional feature data Fn×k：
Fn×k＝DataAdjustn×m·EigenVectorsm×k，
Wherein k represents the dimension number of the obtained low-dimension feature data, and the low-dimension feature data F is utilizedn×kAnd processing the LBP image to obtain a dimension-reduced image. Referring to fig. 2, fig. (c) shows an image obtained after PCA dimension reduction, where k is 59 in this embodiment.
S103, dividing the image after the dimension reduction obtained in step S102 into a plurality of small blocks, and using the histogram to count the number of pixels corresponding to each gray value in each small block image sample, to obtain a gray histogram of each small block, where the gray histograms of each small block together form a histogram cascade of the image after the dimension reduction, as shown in fig. 2(d), in this embodiment, the image after the dimension reduction in fig. c is divided into 9 small blocks, an abscissa represents a 59-dimensional gray value in the 9 small blocks, that is, a total 59 × 9-dimensional feature, and an ordinate represents the number of pixels corresponding to each gray value in each small block.
And (3) for the meteorological data and the mechanical data, performing feature screening on the meteorological data and the mechanical data by adopting a Relieff algorithm, and removing highly-related redundant features to obtain extracted meteorological and mechanical feature data. The Relieff algorithm idea is that a characteristic weight threshold delta is set, the weight value of the characteristic is calculated according to the correlation among the characteristics, the characteristic smaller than the threshold delta is removed, and the purpose of reducing the dimension is achieved. The specific process of the Relieff algorithm is as follows:
sampling a data set formed by meteorological data and mechanical data, wherein the sampling frequency is m, and determining k nearest neighbor samples H from a similar sample set B of any sampling sample Rj(j ═ 1,2, L, k), the same number of nearest neighbor samples M are determined from the heterogeneous sample set Cj(C) (j ═ 1,2, L, k), thenUpdating the feature weight:
wherein W (A) represents the weight corresponding to any feature A, P (. + -.) represents the probability, and the formula diff (A, R) is calculated1,R2) Represents a sample R1、R2The difference in characteristic a is specifically:
and eliminating the features with the feature weight smaller than the threshold value delta to achieve the purpose of reducing the dimension of the meteorological data and the mechanical data.
The characteristics shown in table 1 were obtained in this example through the first stage.
Table 1 feature extraction table of this embodiment
In the second stage, a power transmission line icing thickness prediction model is established by adopting a radial basis function-based extreme learning machine (PR-KELM), the extreme learning machine is a new algorithm for optimizing and improving a single hidden layer feedforward neural network (SLFNs), the structure of the extreme learning machine is shown in figure 3 and comprises an input layer, a hidden layer and an output layer, and a full-connection structure is adopted between adjacent layers. Specifically, the second phase includes a training process and a testing process:
the training process comprises:
s201, determining a model structure according to training data, namely determining the number of neural units of an input layer, a hidden layer and an output layer of the extreme learning machine. In order to ensure the generalization performance of the model, in this embodiment, the feature data samples obtained in the first stage are divided into training data and test data according to a ratio of 2:1, assuming that the training data includes M data samples, the test data includes N data samples, and the feature source and the feature dimension distribution in each data sample are as followsAs shown in table 1, the 531-dimensional image feature, the 12-dimensional meteorological feature and the 24-dimensional mechanical feature connection structure in each data sample form 567-dimensional feature data, and the 1-dimensional ice coating level feature is used as label data, wherein the training feature data XtrainTraining label data Y for MxQ dimensional matrix datatrainFor Mx 1 dimensional matrix data, test feature data XtestFor NxQ dimensional matrix data, test tag data YtestIs N x 1 dimensional matrix data; in the embodiment, M is 1295, N is 647, and Q is 567. Using the training data Xtrain、YtrainTraining the extreme learning machine, and enabling (n, l, M) to respectively correspond to the number of the neural units of the input layer, the hidden layer and the output layer, wherein n is Q, l is M, and M is 1.
S202, solving an optimization problem
A closed-form solution of the weight matrix β between the hidden layer and the output layer can be obtained
Where T represents the desired output, i.e. T ═ Ytrain，H+A Moore-Penrose generalized inverse of the random eigen-mapping matrix H representing the ELM, whereby the output function of the ELM can be expressed as:
where h (x) represents the output matrix of the hidden layer.
The traditional ELM model utilizes the weight, the bias matrix and the activation function between an input layer and a hidden layer to determine an output matrix h (x) of the hidden layer, which easily causes the instability of the algorithm; the embodiment adopts a PR-KELM model and introduces a radial basis kernel function k (x)i,xj) Instead of the eigenmatrix operation H (x) HTThus, the output function is as follows:
wherein omegaELM＝HHTWhere I denotes a unit matrix, C is a regularization coefficient, and k (x) is a radial basis functioni,xj) The calculation formula of (A) is as follows:
wherein i is 1, L, M, j is 1, L, M, xi、xjRepresenting training feature data Xtrainσ is a width reference of the radial basis kernel function, for controlling its radial range of action; by training the tag data T ═ YtrainDetermining omegaELMAnd therefore, the power transmission line icing thickness prediction model based on PR-KELM is obtained through training.
The test phase utilizes test data Xtest、YtestTesting the extreme learning machine model obtained by training, substituting the test characteristic data into the extreme learning machine model in a two-dimensional matrix form, and obtaining a prediction result Y through matrix operationpreFurther constructing an evaluation index function by utilizing a Root Mean Square Error (RMSE), a Mean Absolute Error (MAE), a Mean Absolute Percentage Error (MAPE) and the like, and predicting a result YpreAnd test tag data YtestAnd obtaining an evaluation result of the limit learning machine model as an input parameter of the evaluation index function, and completing construction of the power transmission line icing thickness prediction model.
In order to evaluate the performance of the power transmission line icing thickness prediction model based on PR-KELM, which is finally obtained in the embodiment, the model is compared with other power transmission line icing thickness prediction models based on Random Forest (RF), Support Vector Machine (SVM), BP neural network, Elman neural network and deep learning (BN), and five performance indexes of Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), correlation coefficient value (R) and Nash efficiency coefficient (NSEC) are adopted for evaluation, and the result is shown in Table 2.
TABLE 2 evaluation index values for the respective models
The RMSE index is used for evaluating the dispersion degree of the overall predicted value of the model, the RMSE value of the PR-KELM model of the embodiment is 0.6764 and is smaller than that of the RF, SVM, Elman and BN models, and the PR-KELM model has a lower error rate compared with the models; the values of MAE and MAPE of the PR-KELM model in the table are obviously smaller than those of other models, and the smaller the values of MAE and MAPE are, the more ideal the prediction effect of the model is; for NSEC, the PR-KELM model is higher than RF and BN, and the effect is better compared with the two models, but the NSEC values of SVM, BP and Elman are higher; the R coefficient value of PR-KELM is higher than the other models. In an overall view, the PR-KELM based power transmission line icing prediction model is superior to other models.
In this document, the terms front, back, upper and lower are used to define the components in the drawings and the positions of the components relative to each other, and are used for clarity and convenience of the technical solution. It is to be understood that the use of the directional terms should not be taken to limit the scope of the claims.
The features of the embodiments and embodiments described herein above may be combined with each other without conflict.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (7)
1. A modeling method of a power transmission line icing thickness prediction model based on PR-KELM is characterized by comprising a first stage of carrying out feature extraction on image data, meteorological data and mechanical data and a second stage of establishing the power transmission line icing thickness prediction model by adopting the PR-KELM, wherein:
the first stage comprises: for image Data, by converting the image Data into local binary pattern image Datan×mAnd using principal component analysis algorithm to the image Datan×mReducing the vitamin content to obtainProcessing a local binary pattern image according to the low-dimensional feature data to obtain a dimension-reduced image; dividing the image after dimensionality reduction into a plurality of small blocks, calculating a gray level histogram of each small block image, and further calculating the gray level histogram cascade of the whole image to obtain extracted image data characteristics;
for meteorological data and mechanical data, performing feature screening by adopting a Relieff algorithm, removing highly-related redundant features, and obtaining extracted meteorological and mechanical feature data;
the second stage comprises: forming feature data by using image data features, meteorological feature data and mechanical feature data extracted in the first stage, taking the icing grade in original image data as label data to jointly form sample data, and dividing the sample data into training data and test data according to a certain proportion; the second phase comprises a training process and a testing process: and training the PR-KELM model by using the training data, testing the trained PR-KELM model by using the test data, and finally obtaining the power transmission line icing thickness prediction model.
2. The modeling method of PR-KELM based power transmission line icing thickness prediction model according to claim 1, wherein in the first stage for feature extraction of image Data, the local binary pattern image Datan×mThe image is an n x m dimensional characteristic matrix, the sub-elements in the matrix represent the number of pixel points with the gray value of m-1 in the corresponding image sample, n represents the number of original image samples, and m represents the number of gray values in an LBP image.
3. The PR-KELM based power transmission line icing thickness prediction model modeling method according to claim 1, characterized in that the image Data is subjected to principal component analysis algorithmn×mThe specific process of carrying out the dimensionality reduction is as follows:
calculating the LBP image Datan×mAverage value corresponding to each dimension
Calculating the difference between each dimension data and the average value to obtain new value data DataAdjustn×m：
DataAdjustn×m(j,i)＝Datan×m(j,i)-mean(i)；
Computing new value data DataAdjustn×mThe covariance matrix of (a);
obtaining an eigenvalue and an eigenvector of a covariance matrix based on the covariance matrix;
for the LBP image Data by maximum likelihood estimationn×mPerforming dimension estimation, selecting the first k eigenvalues in descending order according to the estimation result, and performing eigenvector matrix EigenVectors corresponding to the k eigenvaluesn×kAs a base of the mapping space;
data DataAdjust the new valuen×mMapping to a base space to obtain new low-dimensional feature data Fn×k：
Fn×k＝DataAdjustn×m·EigenVectorsm×k，
Wherein k represents the dimension number of the obtained low-dimension feature data, and the low-dimension feature data F is utilizedn×kAnd processing the LBP image to obtain a dimension-reduced image.
4. The PR-KELM based modeling method for the electric transmission line icing thickness prediction model according to claim 1, wherein in the first stage of feature extraction of image data, a histogram is used for counting the number of pixel points corresponding to each gray value in each small image to obtain a gray histogram of each small image; the gray level histogram of each small image together forms the gray level histogram cascade of the whole image.
5. The modeling method of the power transmission line icing thickness prediction model based on the PR-KELM as claimed in claim 1, wherein in the first stage of the feature extraction of meteorological and mechanical data, the specific process of adopting the Relieff algorithm to carry out feature screening is as follows:
sampling a data set formed by meteorological data and mechanical data, wherein the sampling frequency is m, and determining k nearest neighbor samples H from a similar sample set B of any sampling sample Rj(j ═ 1,2, L, k), the same number of nearest neighbor samples M are determined from the heterogeneous sample set Cj(C) (j ═ 1,2, L, k), then the feature weights are updated:
wherein W (A) represents the weight corresponding to any feature A, P (. + -.) represents the probability, and the formula diff (A, R) is calculated1,R2) Represents a sample R1、R2The difference in characteristic a is specifically:
and setting a characteristic weight threshold delta, and removing the characteristics of which the calculated characteristic weight is smaller than the threshold delta to achieve the purpose of reducing the dimensions of the meteorological data and the mechanical data to obtain the meteorological and mechanical characteristic data.
6. The PR-KELM based modeling method for the power transmission line icing thickness prediction model according to claim 1, wherein the training process of the second stage comprises the following specific processes:
determining the number of neural units of an input layer, a hidden layer and an output layer of the PR-KELM model according to training data, wherein the training characteristic data XtrainTraining label data Y for MxQ dimensional matrix datatrainFor Mx 1 dimensional matrix data, test feature data XtestFor NxQ dimensional matrix data, test tag data YtestThe data is Nx 1 dimensional matrix data, M represents the number of training data samples, N represents the number of test data samples, and Q represents the total number of all features extracted in the first stage; using the training data Xtrain、YtrainTraining PR-KELM model to make (n, l, m) correspond to input layer, hidden layer and output layer respectivelyThe number of the neural units in the layer is determined, wherein n is Q, l is M, and M is 1;
introducing a radial basis kernel function k (x)i,xj) Determining the output function of the PR-KELM model:
wherein omegaELM＝HHTH is a random feature mapping matrix, I is a unit matrix, C is a regularization coefficient, and a radial basis kernel function k (x)i,xj) The calculation formula of (A) is as follows:
wherein i is 1, L, M, j is 1, L, M, xi、xjRepresenting training feature data Xtrainσ is the width reference of the radial basis kernel function; by training the tag data T ═ YtrainDetermining omegaELMAnd training to obtain a power transmission line icing thickness prediction model based on PR-KELM.
7. The modeling method of the PR-KELM based power transmission line icing thickness prediction model according to claim 1 or 6, wherein the specific process of the second stage test process is as follows: test feature data XtestSubstituting the model into PR-KELM model obtained by training in the form of two-dimensional matrix, and obtaining a prediction result Y through matrix operationpreFurther constructing an evaluation index function by utilizing the root mean square error, the average absolute error and the average absolute percentage error, wherein the predicted result Y ispreAnd test tag data YtestAnd obtaining an evaluation result of the limit learning machine model based on the evaluation index function as an input parameter of the evaluation index function, and completing construction of the power transmission line icing thickness prediction model.
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