CN109636054A - Solar energy power generating amount prediction technique based on classification and error combination prediction - Google Patents

Abstract

The invention discloses a solar photovoltaic power generation forecasting method of classification and error combination forecasting, which includes S1, determining the forecast data according to time, and using KNN algorithm to determine the weather type according to the meteorological data and historical meteorological data of the forecast date; S2, After classification, the corresponding combined prediction model is used, and the MPSO-BP neural network and the gray model GM(1, 1) are used to predict respectively to obtain their respective prediction outputs; S3. Apply the error matrix obtained from the sample training data to obtain the respective combined predictions. Weight matrix; S4, combine the two parts of the predicted output values according to the weight matrix, and finally obtain the solar photovoltaic power generation. After the method is classified, the weight of each output point is obtained according to the error, so that the obtained prediction result is more reliable, and the reliable prediction of solar photovoltaic power generation is realized.

Description

Prediction method of solar photovoltaic power generation based on classification and error combination prediction

technical field

The invention belongs to the technical field of solar energy utilization, and in particular relates to a solar photovoltaic power generation amount prediction method based on classification and error combination prediction.

Background technique

Nowadays, traditional fossil fuel energy is increasingly depleted, and at the same time, it will cause great harm to the environment during its use. Renewable energy is an inexhaustible energy source. For the sustainable development of human society, countries around the world have turned their attention to renewable energy, and solar power is the main way to use renewable energy. The main components of the smart grid. A key goal of smart grid efforts is to greatly improve the utilization rate of environmentally friendly renewable energy, and microgrid technology is a key technology to achieve this goal. It is very important to find a suitable method to improve the reliability and effectiveness of the microgrid.

Current advances in some aspects of microgrid energy management have been significant, but efficient energy management requires accurate forecasting of grid loads and renewable energy generation. The existing forecasting methods for solar power generation are mainly statistical methods and artificial neural network methods. The neural network method takes the sample data as input and establishes a prediction model to predict the future power generation; the above two methods can achieve higher prediction accuracy for data information with strong regularity and periodicity, but solar energy has randomness , volatility and other characteristics, using these two methods, the prediction effect is very unsatisfactory, can not meet the needs of existing energy management, greatly limits the efficiency and reliability of microgrid energy management.

Therefore, it is important to find a method that can reliably predict solar photovoltaic power generation.

SUMMARY OF THE INVENTION

In view of the above deficiencies in the prior art, the solar photovoltaic power generation forecasting method based on classification and error combination prediction provided by the present invention solves the problems in the existing photovoltaic power generation forecasting method that the forecasting effect is not ideal, cannot meet the existing energy management, Issues that limit the efficiency and reliability of microgrid energy management.

In order to achieve the above purpose of the invention, the technical solution adopted in the present invention is: a solar photovoltaic power generation forecast method based on classification and error combination prediction, comprising the following steps:

S1. Obtain the meteorological data of the solar photovoltaic power generation forecast day from the meteorological station;

S2. Determine the weather type in the season to which the meteorological data belongs, input the meteorological data of the forecast day into the trained MPSO-BP neural network corresponding to the weather type, and obtain the first solar power output time series

At the same time, the meteorological data of the predicted day is input into the trained gray model GM(1,1) corresponding to the weather type, and the second solar power generation output time series is obtained.

S3. Output the first solar power generation time series Multiply with the combined prediction matrix W _BP in the corresponding trained MPSO-BP neural network to obtain the first solar power generation prediction quantity Y _BP ;

At the same time, the second solar power generation output time series Multiply with the combined prediction matrix W _GM in the corresponding trained grey model GM(1,1) to obtain the second solar power generation prediction quantity Y _GM ;

S4. Add the first predicted amount of solar power generation _YBP and the second predicted amount of solar power generation _YGM to obtain the predicted amount of power generation _YP on the predicted day of solar photovoltaic power generation.

Further, the meteorological data in the step S1 includes the highest temperature value, the lowest air temperature value, the temperature value every three hours, the difference between the highest temperature and the highest temperature on the previous day, and the difference between the lowest temperature and the lowest temperature on the previous day. value, relative humidity, and digitized UV intensity.

Further, the seasons to which the meteorological data in the step S2 belongs include spring, summer, autumn and winter; each season includes three weather types: sunny, cloudy and rainy;

Each weather type in each season has a corresponding trained MPSO-BP neural network and a trained gray model GM(1,1).

Further, the gray model GM(1,1) is:

In the formula, y ⁽¹⁾ (k _i+1j ) represents the accumulated sequence value of the i+1th output point of the jth sample obtained by prediction;

y ⁽¹⁾ (k _ij ) represents the accumulated sequence value of the ith output point of the jth sample;

m is the number of output points in the sample;

u, a model parameters to be found;

u and a are determined from the data entered into the grey model.

Further, the method for training the corresponding gray model GM(1,1) under one weather type in the step S2 is specifically:

A1. Obtain historical meteorological data of three weather types in different seasons from weather stations;

A2. Divide the historical meteorological data under the same weather type in the same season into one category;

A3. According to the date data in the similar historical meteorological data, obtain the actual solar photovoltaic power generation historical data in the corresponding date, and input it into the gray model GM(1,1) as a training sample;

A4. According to the data of the first j×m+i points of the training sample, calculate the accumulated sequence y ⁽¹⁾ of the gray model, and establish its corresponding calculation matrix;

A5. According to the calculation matrix, calculate u and a in the gray model by the least square method, and bring them into the accumulation sequence y ⁽¹⁾ to obtain y ⁽¹⁾ (ki _+1j ), and complete the gray model GM(1 , 1) of the training.

Further, in the step S2, the method for training a corresponding MPSO-BP neural network under a weather type is specifically:

B1. Obtain historical meteorological data of three weather types in different seasons from weather stations;

B2. Divide the historical meteorological data under the same weather type in the same season into one category;

B3. According to the date data in the similar historical meteorological data, obtain the actual solar photovoltaic power generation historical data in the corresponding date;

B4. The historical meteorological data is used as the sample input training data, and the solar photovoltaic power generation in the actual solar photovoltaic power generation historical data is used as the sample output training data every half an hour;

B5. Set the maximum training times of the MPSO-BP neural network as EP _max and the expected prediction convergence error ε _E ;

B6. Input the sample input training data into the MPSO-BP neural network, and train with the output sample output training data as the goal, until the training times reach the set maximum training times EP _max or the prediction error value ε _p during training is less than the set When the expected prediction error value _εE is determined, the training of the MPSO-BP neural network is completed.

Further, the method of determining the combined prediction matrix W _BP in the trained MPSO-BP neural network in the step S3 and determining the combined prediction matrix W _GM in the trained gray model GM(1,1) is specifically:

C1. When the training of the MPSO-BP neural network is completed, determine the error of the ith output point of the jth sample input training data as:

In the formula, The predicted solar photovoltaic power generation output of the ith output point of the input training data for the jth sample in the MPSO-BP neural network;

k _ij is the historical meteorological data corresponding to the ith output point of the jth sample input training data input into the MPSO-BP neural network;

y _real (k _ij ) is the actual historical data of solar photovoltaic power generation corresponding to the ith output point of the jth sample input training data;

At the same time, when the training of the gray model GM(1,1) is completed, it is determined that the error of the ith output point of the jth sample input training data is:

In the formula, is the predicted solar photovoltaic power generation output from the ith output point of the jth sample input training data in the gray model GM(1,1);

k _ij is the historical meteorological data corresponding to the ith output point of the jth sample input training data input to the gray model GM(1,1);

C2. According to the error of the output point corresponding to the input training data of each sample, the error matrix in the MPSO-BP neural network is obtained as:

In the formula, E ^t _BP is the error matrix in the neural network;

m is the number of output points;

At the same time, according to the error of the output point corresponding to the input training data of each sample, the error matrix in the gray model GM(1,1) is obtained as:

C3. Sum the errors of each output point in the error matrix to obtain the prediction error matrix in the MPSO-BP neural network as:

In the formula, a is the a-th training error sample;

At the same time, sum the errors of each output point corresponding to the output of the neural network in the error matrix, and obtain the prediction error matrix in the gray model GM(1,1) as:

C4. According to the prediction error matrix in the MPSO-BP neural network and the prediction error matrix in the gray model GM(1,1), respectively determine the weights W ^BP _k of the prediction error matrix of the MPSO-BP neural network and the gray model GM ( The weights W ^GM _k of the prediction error matrix of 1,1):

Among them, the weight of the prediction error matrix of MPSO-BP neural network is:

The weights of the prediction error matrix of the grey model GM(1,1) are:

C5. According to the weight of the prediction error matrix of the MPSO-BP neural network and the weight of the prediction error matrix of the grey model GM(1,1), respectively determine the combined prediction matrix W _BP and W BP in the trained MPSO-BP neural network The combined prediction matrix W _GM in the trained grey model GM(1,1);

Among them, the combined prediction matrix W _BP in the trained MPSO-BP neural network is:

The combined prediction matrix W _GM in the trained grey model GM(1,1) is:

The beneficial effects of the present invention are:

1. The present invention uses KNN to classify the data first, which ensures higher accuracy in different weather data, even in the case of few samples.

2. The present invention uses the error value based on each output point as the calculation parameter of the combined prediction weight of the corresponding point, which has higher precision and is more practical than the traditional method of unifying the combined weight of all output points. Happening.

3. The present invention uses the highest temperature, the lowest temperature, the temperature data every three hours apart, the difference from the highest temperature on the previous day, the difference from the low temperature on the previous day, and the numerical ultraviolet intensity as the prediction. The input parameters improve the accuracy of the predicted power generation.

Description of drawings

FIG. 1 is a flow chart of a method for predicting solar photovoltaic power generation based on classification and error combination prediction in the present invention.

Detailed ways

The specific embodiments of the present invention are described below to facilitate those skilled in the art to understand the present invention, but it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes Such changes are obvious within the spirit and scope of the present invention as defined and determined by the appended claims, and all inventions and creations utilizing the inventive concept are within the scope of protection.

As shown in Figure 1, the forecasting method of solar photovoltaic power generation based on classification and error combination forecasting includes the following steps:

S1. Obtain the meteorological data of the solar photovoltaic power generation forecast day from the meteorological station;

The meteorological data includes the highest temperature value, the lowest temperature value, the temperature value every three hours, the difference between the highest temperature and the highest temperature of the previous day, the difference between the lowest temperature and the lowest temperature of the previous day, relative humidity and numerical value UV intensity.

S2. Determine the weather type in the season to which the meteorological data belongs, input the meteorological data of the forecast day into the trained MPSO-BP neural network corresponding to the weather type, and obtain the first solar power output time series

At the same time, the meteorological data of the predicted day is input into the trained gray model GM(1,1) corresponding to the weather type, and the second solar power generation output time series is obtained.

The seasons to which the meteorological data in the above step S2 belongs include spring, summer, autumn and winter; each season includes three weather types: sunny, cloudy and rainy, and sunny, cloudy and rainy are three typical weather types. For the meteorological data of atypical weather (such as cloudy, showery and other weather types) under the season, the K-proximity algorithm (KNN) can be used to calculate the distance of the meteorological data corresponding to the typical weather type and classify it as the closest typical weather Type, to realize the classification of atypical weather into typical weather. The KNN algorithm can achieve more accurate classification even with fewer samples.

Each weather type in each season has a corresponding trained MPSO-BP neural network and a trained gray model GM(1,1).

S3. Output the first solar power generation time series Multiply with the combined prediction matrix W _BP in the corresponding trained MPSO-BP neural network to obtain the first solar power generation prediction quantity Y _BP ;

At the same time, the second solar power generation output time series Multiply with the combined prediction matrix W _GM in the corresponding trained grey model GM(1,1) to obtain the second solar power generation prediction quantity Y _GM ;

Among them, the predicted solar power generation Y _BP corresponding to the MPSO-BP neural network is:

The predicted solar power generation Y _GM corresponding to the gray model GM(1,1) is:

S4. Add the first predicted amount of solar power generation _YBP and the second predicted amount of solar power generation _YGM to obtain the predicted amount of power generation _YP on the predicted day of solar photovoltaic power generation.

Among them, the predicted power generation Y _P of the solar photovoltaic power generation forecast day is:

The gray model GM(1,1) in the above step S2 is:

In the formula, y ⁽¹⁾ (k _i+1j ) represents the accumulated sequence value of the i+1th output point of the jth sample obtained by prediction;

y ⁽¹⁾ (k _ij ) represents the accumulated sequence value of the ith output point of the jth sample;

m is the number of output points in the sample;

u, a are the parameters to be found in the model;

u and a are undetermined parameters determined according to the data input into the grey model;

The method for training the corresponding gray model GM(1,1) under one weather type in one season in the step S2 is specifically:

A1. Obtain historical meteorological data of three weather types in different seasons from weather stations;

A2. Divide the historical meteorological data under the same weather type in the same season into one category;

A3. According to the date data in the similar historical meteorological data, obtain the actual solar photovoltaic power generation historical data in the corresponding date, and input it into the gray model GM(1,1) as a training sample;

A4. According to the data of the first j×m+i points of the training sample, calculate the accumulated sequence y ⁽¹⁾ of the gray model, and establish its corresponding calculation matrix;

A5. According to the calculation matrix, calculate u and a in the gray model by the least square method, and bring them into the accumulation sequence y ⁽¹⁾ to obtain y ⁽¹⁾ (ki _+1j ), and complete the gray model GM(1 , 1) of the training.

In the above step A5, after obtaining y ⁽¹⁾ (k _i+1j ), the gray model is:

Let y ⁽¹⁾ (k ₁₁ )=y(k ₁₁ ), the predicted value of each historical data point of the training sample can be obtained.

In the above step S2, the method for training the MPSO-BP neural network corresponding to one weather type in one season is as follows:

B1. Obtain historical meteorological data of three weather types in different seasons from weather stations;

B2. Divide the historical meteorological data under the same weather type in the same season into one category;

B3. According to the date data in the similar historical meteorological data, obtain the actual solar photovoltaic power generation historical data in the corresponding date;

B4. The historical meteorological data is used as the sample input training data, and the solar photovoltaic power generation in the actual solar photovoltaic power generation historical data is used as the sample output training data every half an hour;

B5. Set the maximum training times of the MPSO-BP neural network as EP _max and the expected prediction convergence error ε _E ;

B6. Input the sample input training data into the MPSO-BP neural network, and train with the output sample output training data as the goal, until the training times reach the set maximum training times EP _max or the prediction error value ε _p during training is less than the set When the expected prediction error value _εE is set, the training of the MPSO-BP neural network is completed;

In the above step B6, the convergence error of the MPSO-BP neural network is set as ε _BP =0.5×ε _E ,

For each input set of sample input training data, MPSO-BP neural network outputs corresponding data, there is a prediction convergence error value ε _p , and in, For this reason, the predicted power generation is predicted according to the combination of the grey model GM(1,1) and the MPSO-BP neural network. Y _real is the actual historical data of solar photovoltaic power generation corresponding to the sample input training data. When ε _p ≤ ε _E When the MPSO-BP neural network prediction model converges, even if the MPSO-BP neural network does not meet the convergence error at this time, the MPSO-BP neural network will not continue to learn; on the contrary, the neural network will continue to input the sample input training data, Until the training times reaches the set maximum training times EP _max or the prediction error value ε _P during training is less than the set expected prediction error value ε _E , the training of the MPSO-BP neural network is completed.

The method of determining the combined prediction matrix W _BP in the trained MPSO-BP neural network and determining the combined prediction matrix W _GM in the trained gray model GM(1,1) in the above step S3 is specifically:

C1. When the training of the MPSO-BP neural network is completed, determine the error of the ith output point of the jth sample input training data as:

In the formula, The predicted solar photovoltaic power generation output of the ith output point of the input training data for the jth sample in the MPSO-BP neural network;

k _ij is the historical meteorological data corresponding to the ith output point of the jth sample input training data input into the MPSO-BP neural network;

y _real (k _ij ) is the actual historical data of solar photovoltaic power generation corresponding to the ith output point of the jth sample input training data;

At the same time, when the training of the gray model GM(1,1) is completed, it is determined that the error of the ith output point of the jth sample input training data is:

In the formula, is the predicted solar photovoltaic power generation output from the ith output point of the jth sample input training data in the gray model GM(1,1);

k _ij is the historical meteorological data corresponding to the ith output point of the jth sample input training data input to the gray model GM(1,1);

C2. According to the error of the output point corresponding to the input training data of each sample, the error matrix in the MPSO-BP neural network is obtained as:

In the formula, E ^t _BP is the error matrix in the neural network;

m is the number of output points;

At the same time, according to the error of the output point corresponding to the input training data of each sample, the error matrix in the gray model GM(1,1) is obtained as:

C3. Sum the errors of each output point in the error matrix to obtain the prediction error matrix in the MPSO-BP neural network as:

In the formula, a is the a-th training error sample;

At the same time, sum the errors of each output point corresponding to the output of the neural network in the error matrix, and obtain the prediction error matrix in the gray model GM(1,1) as:

C4. According to the prediction error matrix in the MPSO-BP neural network and the prediction error matrix in the gray model GM(1,1), respectively determine the weights W ^BP _k of the prediction error matrix of the MPSO-BP neural network and the gray model GM ( The weights W ^GM _k of the prediction error matrix of 1,1):

Among them, the weight of the prediction error matrix of MPSO-BP neural network is:

The weights of the prediction error matrix of the grey model GM(1,1) are:

C5. According to the weight of the prediction error matrix of the MPSO-BP neural network and the weight of the prediction error matrix of the grey model GM(1,1), respectively determine the combined prediction matrix W _BP and W BP in the trained MPSO-BP neural network The combined prediction matrix W _GM in the trained grey model GM(1,1);

Among them, the combined prediction matrix W _BP in the trained MPSO-BP neural network is:

The combined prediction matrix W _GM in the trained grey model GM(1,1) is:

The beneficial effects of the present invention are:

1. The present invention uses KNN to classify the data first, which ensures higher accuracy in different weather data, even in the case of few samples.

2. The present invention uses the error value based on each output point as the calculation parameter of the combined prediction weight of the corresponding point, which has higher precision and is more practical than the traditional method of unifying the combined weight of all output points. Happening.

3. The present invention uses the highest temperature, the lowest temperature, the temperature data every three hours apart, the difference from the highest temperature on the previous day, the difference from the low temperature on the previous day, and the numerical ultraviolet intensity as the prediction. The input parameters improve the accuracy of the predicted power generation.

Claims (7)

1. The solar photovoltaic power generation capacity prediction method based on classification and error combination prediction is characterized by comprising the following steps of:

s1, acquiring meteorological data of a solar photovoltaic power generation amount prediction day from a meteorological station;

s2, determining the weather type in the season to which the weather data belongs, inputting the weather data of the predicted day into the trained MPSO-BP neural network corresponding to the weather type, and obtaining the first solar power generation output time sequence

Simultaneously inputting weather data of the predicted day into a trained gray model GM (1,1) corresponding to the weather type to obtain a second solar power generation output time sequence

S3, outputting the first solar energy power generation amount to a time sequenceWith a corresponding combined prediction matrix W in the trained MPSO-BP neural network_BPMultiplying to obtain a first solar power generation prediction quantity Y_BP；

Simultaneously outputting the second solar power generation output time seriesWith the combined prediction matrix W in the corresponding trained gray model GM (1,1)_GMMultiplying to obtain a second solar power generation prediction quantity Y_GM；

S4, measuring the first solar power generation prediction quantity Y_BPAnd a second solar power generation prediction amount Y_GMAdding to obtain the predicted power generation amount Y of the predicted day of the solar photovoltaic power generation amount_P。

2. The method for solar photovoltaic power generation amount prediction based on classification and error combined prediction as claimed in claim 1, wherein the meteorological data in the step S1 includes a maximum air temperature value, a minimum air temperature value, a temperature value every three hours, a difference between the maximum temperature and the previous day maximum temperature, a difference between the minimum temperature and the previous day minimum temperature, a relative humidity and a digitized ultraviolet intensity.

3. The solar photovoltaic power generation amount prediction method based on classification and error combined prediction as claimed in claim 1, wherein the seasons to which the meteorological data in step S2 belongs include spring, summer, fall and winter; each season comprises three weather types of sunny days, cloudy days and rainy days;

and a corresponding trained MPSO-BP neural network and a trained gray model GM (1,1) are arranged under each weather type in each season.

4. The method for solar photovoltaic power generation amount prediction based on classification and error combined prediction according to claim 3, characterized in that the gray model GM (1,1) is:

in the formula, y⁽¹⁾(k_{i+1 j}) The accumulated sequence value of the (i + 1) th output point of the j sample obtained by prediction is represented;

y⁽¹⁾(k_ij) An accumulated sequence value representing the ith output point of the jth sample;

m is the number of output points in the sample;

u, a model to be subjected to parameter calculation;

u and a are determined from the data input to the gray model.

5. The method for predicting solar photovoltaic power generation amount based on classification and error combined prediction as claimed in claim 4, wherein the method for training the corresponding gray model GM (1,1) in the step S2 is specifically as follows:

a1, acquiring historical meteorological data of three weather types in different seasons from a meteorological station;

a2, classifying historical meteorological data under the same weather type in the same season;

a3, acquiring actual solar photovoltaic power generation amount historical data in a corresponding date according to date data in similar historical meteorological data, and inputting the actual solar photovoltaic power generation amount historical data serving as a training sample into a gray model GM (1, 1);

a4, top j from training sampleData of x m + i points, calculating the accumulation sequence y of the gray model⁽¹⁾And establishing a corresponding calculation matrix;

a5, calculating u and a in the gray model by the least square method according to the calculation matrix and substituting the calculated u and a into the accumulation sequence y⁽¹⁾In (b) to obtain y⁽¹⁾(k_{i+1 j}) And finishing the training of the gray model GM (1, 1).

6. The method for predicting solar photovoltaic power generation amount based on classification and error combined prediction as claimed in claim 3, wherein in the step S2, the method for training the MPSO-BP neural network corresponding to a weather type is specifically as follows:

b1, acquiring historical meteorological data of three weather types in different seasons from a meteorological station;

b2, classifying the historical meteorological data under the same weather type in the same season;

b3, acquiring historical data of actual solar photovoltaic power generation amount in corresponding date according to date data in similar historical meteorological data;

b4, inputting historical meteorological data as sample input training data, and outputting solar photovoltaic power generation amount as sample output training data every half an hour in actual solar photovoltaic power generation amount historical data;

b5, setting the maximum training times of the MPSO-BP neural network as EP_maxAnd expected prediction convergence error ε_E；

B6, inputting the sample input training data into the MPSO-BP neural network, training by taking the output sample output training data as a target until the training times reach the set maximum training times EP_maxOr prediction error value epsilon during training_pLess than a set desired prediction error value epsilon_EAnd finishing the training of the MPSO-BP neural network.

7. The method for solar photovoltaic power generation prediction based on classification and error combined prediction as claimed in claim 6, wherein the determination of the trained MPSO-BP neural network in the step S3Combined prediction matrix W in a network_BPAnd determining a combined prediction matrix W in the trained gray model GM (1,1)_CMThe method comprises the following steps:

c1, when the training of the MPSO-BP neural network is completed, determining the error of the ith output point of the jth sample input training data as:

in the formula,inputting the predicted solar photovoltaic power generation output by the ith output point of training data for the jth sample in the MPSO-BP neural network;

k_ijinputting historical meteorological data corresponding to an ith output point of training data for a jth sample input into the MPSO-BP neural network;

y_real(k_ij) Inputting actual solar photovoltaic power generation amount historical data corresponding to the ith output point of training data for the jth sample;

meanwhile, when the training of the gray model GM (1,1) is completed, the error of the ith output point of the jth sample input training data is determined as:

in the formula,inputting the predicted solar photovoltaic power generation output by the ith output point of training data for the jth sample in the gray model GM (1, 1);

k_ijinputting historical meteorological data corresponding to the ith output point of the training data for the jth sample input into the gray model GM (1, 1);

c2, according to the error of the output point corresponding to each sample input training data, obtaining an error matrix in the MPSO-BP neural network as follows:

in the formula, E^t _BPIs an error matrix in the neural network;

m is the number of output points;

meanwhile, according to the error of the output point corresponding to each sample input training data, the error matrix in the gray model GM (1,1) is obtained as follows:

c3, summing the error of each output point in the error matrix to obtain a prediction error matrix in the MPSO-BP neural network, wherein the prediction error matrix is as follows:

in the formula, a is an a-th training error sample;

meanwhile, summing the error of each output point corresponding to the output of the neural network in the error matrix to obtain a prediction error matrix in a gray model GM (1,1) as follows:

c4, respectively determining the weight W of the prediction error matrix of the MPSO-BP neural network according to the prediction error matrix in the MPSO-BP neural network and the prediction error matrix in the gray model GM (1,1)^BP _kAnd the weight W of the prediction error matrix of the gray model GM (1,1)^GM _k：

Wherein, the weight of the prediction error matrix of the MPSO-BP neural network is as follows:

the weight of the prediction error matrix of the gray model GM (1,1) is:

c5, respectively determining a combined prediction matrix W in the trained MPSO-BP neural network according to the weight of the prediction error matrix of the MPSO-BP neural network and the weight of the prediction error matrix of the gray model GM (1,1)_BPAnd a combined prediction matrix W in a trained gray model GM (1,1)_GM；

Wherein the combined prediction matrix W in the trained MPSO-BP neural network_BPComprises the following steps:

combined prediction matrix W in trained gray model GM (1,1)_GMComprises the following steps: