CN112529268A - Medium-short term load prediction method and device based on manifold learning - Google Patents

Medium-short term load prediction method and device based on manifold learning Download PDF

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CN112529268A
CN112529268A CN202011367745.3A CN202011367745A CN112529268A CN 112529268 A CN112529268 A CN 112529268A CN 202011367745 A CN202011367745 A CN 202011367745A CN 112529268 A CN112529268 A CN 112529268A
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黎静华
韦善阳
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Abstract

The invention provides a method and a device for predicting medium and short term load based on manifold learning, belonging to the technical field of load prediction, wherein the method for predicting the load comprises the following steps: carrying out nonlinear dimensionality reduction on the historical load data set by adopting a local linear embedding method to obtain a low-dimensional manifold sequence; inputting the low-dimensional manifold sequence into the trained long-term and short-term memory neural network model to obtain a prediction sequence; and reconstructing the prediction sequence by adopting a manifold learning reconstruction method to obtain a load prediction value. The invention adopts the manifold learning method to reduce the dimension of the load data, and the manifold learning method can better dig out the nonlinear characteristics of the load. Meanwhile, the low-dimensional manifold sequence obtained after dimensionality reduction is predicted by a deep learning method, the self time sequence rule of the low-dimensional manifold sequence is better excavated, and the load prediction precision is favorably improved.

Description

Medium-short term load prediction method and device based on manifold learning
Technical Field
The invention belongs to the technical field of load prediction, and particularly relates to a medium-short term load prediction method and device based on manifold learning.
Background
Short-term load curve prediction (hours to days in advance) and medium-term load curve prediction (days to months in advance) are of great significance to the optimal planning and operation of power systems and power trading.
The change of the power load mainly depends on the regularity of production and life of people and is influenced by many external factors. The external factors include weather factors (such as temperature), economic factors (such as electricity price), seasonal factors, and historical electricity usage, etc. Under the influence of the above factors, the power load has complex characteristics of periodicity, uncertainty, multidimensional nonlinearity and the like, so that accurate load prediction becomes very difficult, especially for prediction of a longer time scale, such as medium-term load prediction. The key for improving the prediction precision is to deeply dig the relationship between the power load and the influencing factors and grasp the internal rule of the power load change.
The data dimension reduction method can extract key feature information from data, and is beneficial to improving prediction accuracy, so that the method is widely applied to load prediction. However, all the data dimension reduction methods adopted in the current load prediction are linear dimension reduction methods. For example, in a document "Short-term load forecasting with experientially weighted methods", a Singular Value Decomposition (SVD) method is adopted to perform linear dimension reduction on load data and extract a load mode within one week, so as to obtain main potential features of each time period within one week, and then realize load prediction one week ahead. In the document "a data-drive stream for short-term electric load for evaluating Dynamic Mode Decomposition (DMD)" a Dynamic Mode Decomposition (DMD) method is used to decompose and reduce the dimension of the load data, thereby performing short-term load prediction. DMD is an extension of Principal Component Analysis (PCA) and also belongs to a linear dimensionality reduction method. Because the nonlinear characteristics of the load data are difficult to excavate by the linear dimension reduction method, the prediction effect of the methods is limited. On the other hand, for the low-dimensional feature sequences after dimensionality reduction, the conventional statistical models such as ARIMA and shallow neural network models are adopted for prediction in the prior art. For example, patent "CN 202010072450.7" adopts an extreme learning machine to predict the data after dimension reduction. These conventional statistical methods and shallow network models have limited predictive effect on low-dimensional feature sequences.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method and a device for predicting a medium-short term load based on manifold learning, and aims to solve the problem that the linear dimension reduction method adopted by the existing load prediction method is low in prediction accuracy.
In order to achieve the above object, the present invention provides a method for predicting a medium-short term load based on manifold learning, comprising the following steps:
s1: carrying out nonlinear dimensionality reduction on the historical load data set by adopting a local linear embedding method in manifold learning to obtain a low-dimensional manifold sequence;
s2: acquiring a prediction sequence by adopting a low-dimensional manifold sequence and utilizing a trained long-term and short-term memory neural network model;
s3: and reconstructing the prediction sequence by adopting a manifold learning reconstruction method to obtain a load prediction value.
Preferably, step S1 specifically includes the following steps:
s1.1, abnormal data processing and logarithmic transformation are carried out on historical load data;
s1.2, selecting neighbor points of each historical load data according to Euclidean distance;
s1.3, calculating a first linear reconstruction coefficient of each historical load data and each neighboring point;
s1.4, calculating a low-dimensional manifold sequence by utilizing the linear reconstruction coefficient.
Preferably, the training method of the long-short term memory neural network model comprises the following steps:
dividing the low-dimensional manifold sequence into a training set and a test set according to a preset proportion;
determining parameters of the long-term and short-term memory neural network model by taking the minimum prediction error of the test set as a target; the parameters include hidden layer neuron number and learning rate.
Preferably, step S3 specifically includes the following steps:
acquiring a neighbor point set corresponding to each data in the prediction sequence according to the Euclidean distance;
calculating a second linear reconstruction coefficient between each data in the prediction sequence and the adjacent point;
calculating a load logarithm value according to the second linear reconstruction coefficient;
and carrying out inverse logarithmic transformation on the load logarithm value to obtain a load predicted value.
Based on the method for predicting the load of the medium and short term based on manifold learning, the invention provides a corresponding load prediction device, which comprises a nonlinear dimension reduction module, a prediction module and a data reconstruction module which are connected in sequence;
the nonlinear dimensionality reduction module is used for carrying out nonlinear dimensionality reduction on the historical load data set by adopting a local linear embedding method in manifold learning to obtain a low-dimensional manifold sequence;
the prediction module is used for acquiring a prediction sequence by adopting a low-dimensional manifold sequence and utilizing a trained long-term and short-term memory neural network model;
and the data reconstruction module is used for reconstructing the prediction sequence by adopting a manifold learning reconstruction method to obtain a load prediction value.
Preferably, the nonlinear dimensionality reduction module comprises a data preprocessing unit, a first neighbor point screening unit, a first computing unit and a low-dimensional manifold data acquisition unit;
the data preprocessing unit is used for performing abnormal data processing and logarithmic conversion on the historical load data;
the first neighbor screening unit is used for selecting neighbor points of each historical load data according to Euclidean distance;
the first calculation unit is used for calculating a first linear reconstruction coefficient of each historical load data and the neighboring point;
the low-dimensional manifold data acquisition unit is used for calculating a low-dimensional manifold sequence by utilizing the linear reconstruction coefficient.
Preferably, the training method of the long-short term memory neural network model comprises the following steps:
dividing the low-dimensional manifold sequence into a training set and a test set according to a preset proportion;
determining parameters of the long-term and short-term memory neural network model by taking the minimum prediction error of the test set as a target; the parameters include hidden layer neuron number and learning rate.
Preferably, the data reconstruction module comprises a second neighbor screening unit, a second computing unit and a predicted value obtaining unit;
the second neighbor point screening unit is used for acquiring a neighbor point set corresponding to each data in the prediction sequence according to the Euclidean distance;
the second calculation unit is used for calculating a second linear reconstruction coefficient between each data in the prediction sequence and a neighboring point;
and the predicted value obtaining unit is used for calculating the load logarithm according to the second linear reconstruction coefficient, and then carrying out logarithmic inverse transformation on the load logarithm to obtain the load predicted value.
The load prediction method based on manifold learning provided by the invention can be stored in a computer readable storage medium, and a computer program is stored on the computer readable storage medium, and when being executed by a processor, the computer program can realize the load prediction method based on manifold learning.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
the invention provides a load prediction method based on manifold learning, which takes historical load data as a high-dimensional data set, adopts a nonlinear manifold learning method to reduce the dimension of the load data set, and obtains a low-dimensional manifold sequence representing the main characteristics of a load. Further, the obtained low-dimensional manifold sequence is predicted by adopting a long-short term memory (LSTM) neural model. And finally, converting the low-dimensional manifold predicted value into a load predicted value in the original high-dimensional space by adopting a manifold reconstruction technology. The invention adopts the manifold learning method to reduce the dimension of the load data, and compared with the traditional linear dimension reduction method such as a principal component analysis method, the manifold learning method can better dig out the nonlinear characteristics of the load. Meanwhile, the low-dimensional manifold sequence obtained after dimensionality reduction is predicted by a deep learning method, the self time sequence rules of the low-dimensional manifold sequence and the mapping relation between the time sequence rules and load influence factors are better excavated, and the load prediction precision is favorably improved.
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FIG. 1 is a schematic diagram of a load prediction method based on manifold learning according to an embodiment of the present invention;
FIG. 2 is a schematic representation of manifold reconstruction error as a function of low dimensional dimensions provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of how manifold reconstruction errors vary with the number of neighboring points according to an embodiment of the present invention;
FIG. 4 is a diagram of a prediction sequence obtained by LSTM for a low-dimensional manifold sequence according to an embodiment of the present invention;
FIG. 5 is an internal structure diagram of an LSTM neural network model provided by an embodiment of the present invention;
FIG. 6 shows the predicted load at a location 1 week ahead of time according to an embodiment of the present invention;
FIG. 7 shows the prediction of load in a location 1 month ahead of time 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, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a medium and short term load prediction method based on manifold learning, which takes historical load data as a high-dimensional data set, adopts a nonlinear manifold learning method to reduce the dimension of the load data set, and obtains a low-dimensional manifold sequence representing the main characteristics of a load. And further, predicting the obtained low-dimensional manifold sequence by using an LSTM neural model. And finally, converting the low-dimensional manifold predicted value into a load predicted value in the original high-dimensional space by adopting a manifold reconstruction technology.
As shown in fig. 1, the invention provides a medium-short term load prediction method based on manifold learning, comprising the following steps:
s1: preprocessing load data, wherein the preprocessing comprises abnormal data processing and logarithmic conversion;
s2: performing nonlinear dimensionality reduction on the load data set by adopting a Local Linear Embedding (LLE) method in manifold learning;
specifically, a given high-dimensional historical load data set is X,
Figure BDA0002805373420000051
m is the data dimension, and n is the number of load samples; the LLE method aims at obtaining a corresponding low-dimensional manifold Y,
Figure BDA0002805373420000052
k<m, the specific process is as follows:
s2.1, selecting d neighbor points of each data point of X according to the Euclidean distance; set point xiIs Ni；
S2.2 passing through a first minimizing cost function E1(ω), calculate each point xiA first linear reconstruction coefficient with d neighboring points;
Figure BDA0002805373420000053
Figure BDA0002805373420000054
wherein, ω isijRepresenting a first linear reconstruction coefficient between point i and a neighboring point j.
S2.3 computing a low-dimensional manifold sequence yi,i∈[1,n]；
Figure BDA0002805373420000061
The above formula is further rewritten as:
Figure BDA0002805373420000062
Mij＝δij-ωij-ωji+∑kωkiωkj
wherein,
Figure BDA0002805373420000063
for each yiThere are the following constraints: sigmaiyi＝0，(1/n)∑iyiyT iI ═ I; the eigenvectors corresponding to the first k minimum eigenvalues of the matrix M are the low-dimensional manifold yi；
It should be pointed out that 2 parameters, namely the number d of neighboring points and the low-dimensional dimension k, need to be determined in the LLE dimension reduction process; the method of determining these two parameters is: and (5) drawing a curve of the manifold reconstruction error along with the change of the two parameters, and taking d and k at the inflection point of the curve. Suppose that
Figure BDA0002805373420000064
As a load reconstruction value, x0The real value of the load is used as the load,
Figure BDA0002805373420000065
is a load vector x0J is 1,2, … D, D is x0Of (c) is calculated. Then for point x0The manifold reconstruction error calculation formula is as follows:
Figure BDA0002805373420000066
the reconstruction error for the entire data set X is:
Figure BDA0002805373420000067
s3: predicting a low-dimensional manifold sequence by adopting a Long Short-Term Memory (LSTM) neural network model;
predicting the obtained k-dimensional low-dimensional manifold sequence by adopting LSTM for each dimension; for a certain low-dimensional sequence with n samples, dividing the low-dimensional manifold sequence into a training set and a test set; the proportion of the training set test set samples is set to be 7: 3; determining parameters of the LSTM network model including the number of neurons in a hidden layer and the learning rate by taking the minimum prediction error of the test set as a target; acquiring a low-dimensional manifold sequence by using the trained LSTM network model;
s4: reconstructing the prediction sequence to an original high-dimensional space by adopting a manifold learning reconstruction method to obtain a load prediction value in the high-dimensional space;
suppose y1,y2,...,ynLow-dimensional manifold vector obtained for LLE dimension reduction, for predictor y in low-dimensional space0The process of manifold reconstruction is as follows:
s4.1 at y according to Euclidean distance1,y2,...,ynIn (2) find y0D neighbor set N0；
S4.2 calculating y0And a second linear reconstruction coefficient between neighboring points;
Figure BDA0002805373420000071
Figure BDA0002805373420000072
wherein E is2(ω) is a second minimized cost function.
S4.3, calculating a load predicted value reconstructed into a high-dimensional space;
Figure BDA0002805373420000073
wherein,
Figure BDA0002805373420000074
and carrying out inverse logarithmic transformation on the load logarithm to obtain a load predicted value.
Based on the method for predicting the load of the medium and short term based on manifold learning, the invention provides a corresponding device for predicting the load of the medium and short term, which comprises a nonlinear dimension reduction module, a prediction module and a data reconstruction module which are connected in sequence;
the nonlinear dimensionality reduction module is used for carrying out nonlinear dimensionality reduction on the historical load data set by adopting a local linear embedding method in manifold learning to obtain a low-dimensional manifold sequence;
the prediction module is used for acquiring a prediction sequence by adopting a low-dimensional manifold sequence and utilizing a trained long-term and short-term memory neural network model;
and the data reconstruction module is used for reconstructing the prediction sequence to obtain a load prediction value.
Preferably, the nonlinear dimensionality reduction module comprises a data preprocessing unit, a first neighbor point screening unit, a first computing unit and a low-dimensional manifold data acquisition unit;
the data preprocessing unit is used for performing abnormal data processing and logarithmic conversion on the historical load data;
the first neighbor screening unit is used for selecting neighbor points of each historical load data according to Euclidean distance;
the first calculation unit is used for calculating a first linear reconstruction coefficient of each historical load data and the neighboring point;
the low-dimensional manifold data acquisition unit is used for calculating a low-dimensional manifold sequence by utilizing the linear reconstruction coefficient.
Preferably, the training method of the long-short term memory neural network model comprises the following steps:
dividing the low-dimensional manifold sequence into a training set and a test set according to a preset proportion;
determining parameters of the long-term and short-term memory neural network model by taking the minimum prediction error of the test set as a target; the parameters include hidden layer neuron number and learning rate.
Preferably, the data reconstruction module comprises a second neighbor screening unit, a second computing unit and a predicted value obtaining unit;
the second neighbor point screening unit is used for acquiring a neighbor point set corresponding to each data in the prediction sequence according to the Euclidean distance;
the second calculation unit is used for calculating a second linear reconstruction coefficient between each data in the prediction sequence and a neighboring point;
and the predicted value obtaining unit is used for calculating the load logarithm according to the second linear reconstruction coefficient, and then carrying out logarithmic inverse transformation on the load logarithm to obtain the load predicted value.
The load prediction method based on manifold learning provided by the invention can be stored in a computer readable storage medium, and a computer program is stored on the computer readable storage medium, and when being executed by a processor, the computer program can realize the load prediction method based on manifold learning.
Examples
The embodiment provides a medium-short term load prediction method based on manifold learning, which specifically comprises the following steps:
s1: carrying out prediction preprocessing on historical load data;
firstly, processing abnormal data, and then carrying out logarithmic transformation on a historical load data set;
and (3) exception data processing: for data points deviating from the normal range and missing data points, replacing the data points by the average value of the two points before and after the point;
logarithmic transformation: logarithmic conversion is carried out on the historical load data set, the load fluctuation range is smaller after the logarithmic conversion, the obtained low-dimensional manifold distribution is more uniform, and the prediction precision is favorably improved;
s2: performing nonlinear dimensionality reduction on the historical load data set by adopting an LLE method;
according to the assumption
Figure BDA0002805373420000081
As a load reconstruction value, x0The real value of the load is used as the load,
Figure BDA0002805373420000082
is a load vector x0The jth element, then for point x0The manifold reconstruction error calculation formula is as follows:
Figure BDA0002805373420000091
the reconstruction error for the entire data set X is:
Figure BDA0002805373420000092
when inflection points appear on a curve of which manifold reconstruction errors change along with the number d of adjacent points and the low-dimensional dimension k, determining the number d of the adjacent points and the low-dimensional dimension k;
as shown in fig. 2, when k is 4, the manifold reconstruction error of the entire data set is minimal, so the low dimension takes 4;
as shown in fig. 3, when d is 24, the manifold reconstruction error of the whole data set is minimum, so the number of neighboring points is 24;
s3: as shown in fig. 4, an LSTM neural network model is established for each low-dimensional manifold sequence, and each low-dimensional sequence is predicted by using the LSTM neural network model; s3 specifically includes the following steps:
s3.1, dividing a training set test set for each low-dimensional manifold sequence with n samples according to the ratio of 7: 3;
s3.2, constructing an LSTM neural network model; the internal structure of the LSTM neural network model is shown in FIG. 5; the LSTM neural network model comprises an input layer, a Dropout layer, a full connection layer and an output layer; in this embodiment, the number of neurons in the input layer is set to 7, that is, 1 point is predicted by using the first 7 points, the initial value of the number of neurons in the hidden layer is set to 50, and the number of neurons in the output layer is 1; the initial value of the LSTM network learning rate is set to 0.01;
s3.3, training parameters of the LSTM neural network model by using a training set, and evaluating the prediction effect of the LSTM in a prediction set by using a root mean square error (MAPE); according to the prediction result of the LSTM model in the prediction set, the number of neurons of the hidden layer and the learning rate parameter are adjusted; selecting the number of neurons in the hidden layer and learning rate parameters which enable the prediction effect to be optimal;
s3.4, after determining the parameters of the LSTM neural network model, training the LSTM neural network model by using all historical data (namely n samples);
s3.5, predicting a low-dimensional manifold sequence by using the trained LSTM neural network model;
for prediction h days ahead, h points of each low-dimensional sequence need to be predicted, a recursive prediction mode is adopted, namely when the t +1 point is predicted, the predicted value of the t point needs to be used as the input of a model;
s4: reconstructing the prediction sequence to an original high-dimensional space to obtain a prediction result in the high-dimensional space; carrying out logarithmic inversion on the prediction result to obtain a load prediction value;
taking the load data of a certain place as an example, the final load prediction result is shown in fig. 6 and 7, and the load prediction method based on manifold learning provided by the invention has higher precision than that of the load prediction method directly using the LSTM.
In summary, the invention adopts the manifold learning method to reduce the dimension of the load data. Compared with a traditional linear dimension reduction method such as a principal component analysis method, the manifold learning method can better excavate the nonlinear characteristics of the load. Meanwhile, the low-dimensional manifold sequence obtained after dimensionality reduction is predicted by a deep learning method, the self time sequence rules of the low-dimensional manifold sequence and the mapping relation between the time sequence rules and load influence factors are better excavated, and the load prediction precision is favorably improved.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (9)

1. A load prediction method based on manifold learning is characterized by comprising the following steps:
s1: carrying out nonlinear dimensionality reduction on the historical load data set by adopting a local linear embedding method to obtain a low-dimensional manifold sequence;
s2: inputting the low-dimensional manifold sequence into the trained long-term and short-term memory neural network model to obtain a prediction sequence;
s3: and reconstructing the prediction sequence by adopting a manifold learning reconstruction method to obtain a load prediction value.
2. The load prediction method according to claim 1, wherein the step S1 specifically includes the steps of:
s1.1, abnormal data processing and logarithmic transformation are carried out on historical load data;
s1.2, selecting neighbor points of each historical load data according to Euclidean distance;
s1.3, calculating a first linear reconstruction coefficient of each historical load data and each neighboring point;
s1.4, calculating a low-dimensional manifold sequence by utilizing the linear reconstruction coefficient.
3. The load prediction method according to claim 1 or 2, wherein the training method of the long-short term memory neural network model is:
dividing the low-dimensional manifold sequence into a training set and a test set according to a preset proportion;
determining parameters of the long-term and short-term memory neural network model by taking the minimum prediction error of the test set as a target; the parameters include hidden layer neuron number and learning rate.
4. The load prediction method according to claim 3, wherein the step S3 specifically includes the steps of:
acquiring a neighbor point set corresponding to each data in the prediction sequence according to the Euclidean distance;
calculating a second linear reconstruction coefficient between each data in the prediction sequence and the adjacent point;
calculating a predicted load logarithm value according to the second linear reconstruction coefficient;
and carrying out inverse logarithmic transformation on the logarithm value of the predicted load to obtain a predicted value of the load.
5. A load prediction device based on the load prediction method of claim 1, comprising a nonlinear dimensionality reduction module, a prediction module and a data reconstruction module which are connected in sequence;
the nonlinear dimensionality reduction module is used for carrying out nonlinear dimensionality reduction on the historical load data set by adopting a local linear embedding method to obtain a low-dimensional manifold sequence;
the prediction module is used for inputting the low-dimensional manifold sequence into the trained long and short term memory neural network model to obtain a prediction sequence;
and the data reconstruction module is used for reconstructing the prediction sequence by adopting a manifold learning reconstruction method to obtain a load prediction value.
6. The load prediction device according to claim 5, wherein the nonlinear dimensionality reduction module comprises a data preprocessing unit, a first neighbor point screening unit, a first computing unit and a low-dimensional manifold data acquisition unit;
the data preprocessing unit is used for performing abnormal data processing and logarithmic conversion on historical load data;
the first neighbor screening unit is used for selecting neighbor points of each historical load data according to Euclidean distance;
the first calculation unit is used for calculating a first linear reconstruction coefficient of each historical load data and the neighboring point;
the low-dimensional manifold data acquisition unit is used for calculating a low-dimensional manifold sequence by utilizing the linear reconstruction coefficient.
7. The load prediction device according to claim 5 or 6, wherein the training method of the long-short term memory neural network model comprises:
dividing the low-dimensional manifold sequence into a training set and a test set according to a preset proportion;
determining parameters of the long-term and short-term memory neural network model by taking the minimum prediction error of the test set as a target; the parameters include hidden layer neuron number and learning rate.
8. The load prediction device according to claim 6, wherein the data reconstruction module includes a second neighbor screening unit, a second calculation unit, and a predicted value acquisition unit;
the second neighbor point screening unit is used for acquiring a neighbor point set corresponding to each data in the prediction sequence according to the Euclidean distance;
the second calculation unit is used for calculating a second linear reconstruction coefficient between each data in the prediction sequence and a neighboring point;
the predicted value obtaining unit is used for calculating the predicted load logarithm according to the second linear reconstruction coefficient, and then carrying out logarithmic inverse transformation on the predicted load logarithm to obtain the load predicted value.
9. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 4.
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