CN107301475A - Load forecast optimization method based on continuous power analysis of spectrum - Google Patents

Abstract

The invention discloses a power load forecasting optimization method based on continuous power spectrum analysis. The continuous power spectrum analysis method is used to extract the hidden significant periodic sequence in the power load time series and separate to obtain the residual sequence. The optimization method is based on particle swarm optimization. The BP neural network predicts the significant periodic sequence and obtains the prediction results of each significant periodic sequence; the RBF neural network optimized by the particle swarm optimization algorithm is used to predict the first-order difference sequence of the residual sequence, and then the residual sequence is obtained by differential inverse operation Finally, the average value of the average power load time series is added to the prediction results of each significant period sequence and the prediction result of the residual sequence to obtain the final prediction result. Aiming at the periodic characteristics of electric load data, the present invention establishes a forecasting model, which can greatly improve the accuracy of short-term electric load forecasting.

Description

Optimal Method for Power Load Forecasting Based on Continuous Power Spectrum Analysis

technical field

The invention belongs to the technical field of electric power systems, and in particular relates to an electric load forecasting optimization method based on continuous power spectrum analysis.

Background technique

The power system load refers to the sum of the power consumption of all electrical equipment in the system, also known as the comprehensive power load of the power system. The comprehensive power load plus the loss in the power grid and the factory power of the power plant is the total power that all generators in the system should generate, also known as the power system power generation load. Power load is an important factor affecting the safe and stable operation of the system. Power load forecasting refers to the analysis and research on the historical records of power load, comprehensive consideration of various factors that affect power load changes, such as social development planning, economic conditions, meteorological change factors and holidays, etc., to predict the future development of power load. estimate. Power load forecasting is the basis for power system planning, planning, scheduling, and power consumption. Improving the technical level of power load forecasting is conducive to formulating a reasonable power supply construction plan, to rationally arranging the operation mode of the power grid and the maintenance plan of the unit, to saving coal, oil and power generation costs, to planning power consumption management, and to improving Economic and social benefits of power systems. Therefore, power load forecasting is one of the important contents to realize the modernization of power system management. Due to the influence of factors such as weather conditions and people's social activities, there are a large number of random and nonlinear relationships in the power load data. The factors affecting the power load time series can be divided into internal random factors and external random factors. The external factors include Meteorology, society, economy, etc., while the internal factors are the result of the nonlinear factors inside the power system, and the power load is the result of the joint action of the internal and external random factors of the system. The reason for the inaccurate prediction is not only external The influence of random factors is more importantly determined by the inherent dynamic characteristics of the system.

To this end, a variety of forecasting methods have emerged, ranging from general statistical models, such as ARIMA time series models, gray models, etc., to various intelligent models, such as neural network models, support vector machine models, etc. The improvement of algorithms is expected to improve the forecasting of power load. Accuracy, but most fundamentally lies in the learning and generalization performance of the prediction method used for the data. The power load is affected by human production and life with obvious regularity, but there is a lot of randomness in this regularity, which affects the learning and generalization ability of the model.

Contents of the invention

In order to solve the above technical problems, the present invention aims to provide a power load forecasting optimization method based on continuous power spectrum analysis. Through continuous power spectrum analysis, the hidden significant periodic sequence in the original power load time series is extracted and separated to obtain the residual sequence , because the significant periodic sequence accounts for a large proportion of the original sequence and has strong regularity, it can be predicted with high precision, while the residual sequence has a limited error due to its small proportion of the original sequence, thus ensuring that the accuracy of power load forecasting can be effectively improved.

Realize above-mentioned technical purpose, reach above-mentioned technical effect, the present invention realizes through the following technical solutions:

A power load forecasting optimization method based on continuous power spectrum analysis, including

Read in the original sampled power load time series, convert it into an average power load time series according to the forecast interval requirements, and then calculate the anomaly series of the average power load time series;

The continuous power spectrum analysis method is used to extract the hidden significant periodic sequence in the anomaly sequence of the average power load time series, and separate the residual sequence;

The BP neural network optimized by the particle swarm optimization algorithm is used to predict the significant periodic sequence, and the prediction results of each significant periodic sequence are obtained;

The RBF neural network optimized by the particle swarm optimization algorithm is used to predict the first-order difference sequence of the residual sequence, and then the prediction result of the residual sequence is obtained through the reverse operation of the difference;

The final prediction result is obtained by adding the average value of the average power load time series to the prediction results of each significant period series and the prediction results of the residual series.

Further, the original sampled power load time series is p={p(i), i=1,2,...,N}, where N is the number of original power load sampling points;

The average power load time series is p'={p'(j),j=1,2,...,M}, where M is the number of sampling points of the average power load sequence converted according to the forecast interval requirements , the average value of p' is make

The anomaly sequence of the average power load time series is

Further, the significant periodic sequence is {P ₁ , P ₂ ,...,P _k ,...,P _K }, where K is the number of significant periodic sequences implied in P, P _k ={P _k (1 ), P _k (2),…,P _k (M)}, where P _k (1), P _k (2),…, P _k (M) are the values of the significant periodic sequence P _k respectively; the residual The difference sequence is R=PP ₁ -P ₂ -...-P _K .

Further, using the continuous power spectrum analysis method to extract the hidden significant periodic sequence in the anomaly sequence of the average power load time series is specifically: using the continuous power spectrum method to analyze the anomaly sequence of the average power load time series Significant periodic bands, and use the frequency domain filtering method of fast Fourier transform to extract the time series corresponding to each significant periodic band, so as to obtain the significant periodic series.

Further, the specific process of predicting the significant periodic sequence by using the BP neural network optimized based on the particle swarm optimization algorithm is as follows:

(1) According to the Kolmogorov theorem, set up 3 layers of BP neural network models, set the number of input layer neurons as 1,

The number of hidden layer neurons is H, and the number of output layer neurons is O; wherein, H=2*I+1, O=1;

(2) Determine the parameters that need to be optimized, including: the input layer neuron number I of BP neural network and the length of the training set

L, also includes: W=(w(1),w(2),...,w(q)), q=I*H+H*O+H+O, wherein, w(1)～w (I*H) is the connection weight from the input layer to the hidden layer neurons of the BP neural network, w(I*H+1)～w(I*H+H*O) is the hidden layer of the BP neural network The connection weight to the neurons in the output layer, w(I*H+H*O+1)~w(I*H+H*O+H) is the threshold value of the neurons in the hidden layer of the BP neural network, w(I *H+H*O+H+1)～w(I*H+H*O+H+O) is the threshold value of neurons in the output layer of BP neural network;

(3) Initialize the population X=(X ₁ ,X ₂ ,...,X _Q1 ), where Q ₁ is the total number of particles, the i-th particle is X _i =(I _i ,W _i ,L _i ), the particle The speed is V _i = (v _Ii , v _Wi , v _Li ), where I _i , W _i , L _i are a set of alternative solutions for parameters I, W, and L;

(4) According to the parameters determined by each particle Xi = (I _i , W _i , L _{i )} in the population, construct the input and output matrices of the BP neural network training set, where the significant periodic sequence P _k and the BP neural network The number of neurons I _i in the input layer first establishes matrices Z ₁ and Z ₂ , where:

For the length L of the neural network training set to be optimized, the last L _i column in Z ₁ is used as the input matrix I _train of the training set, and the last L _i column in Z ₂ is used as the output matrix O _train of the training set; the prediction step size l is used as Test step size, the last _l column in Z1 is used as the input matrix Itest of the _test set, and the last _l column in Z2 is used as the output matrix Otest of the _test set; The sum of squared errors is taken as its fitness value, and the minimum fitness value is used as the optimization direction as the evaluation standard to judge the quality of each particle. The current individual extreme value of the particle X _i is recorded as P _best (i), and P _best (i) in the group is taken The best individual is taken as the overall extremum G _best ;

(5) For each particle _Xi in the group, its position and velocity are updated respectively;

In the formula: ω is the inertia weight, c ₁ and c ₂ are acceleration factors, g is the current iteration number, r ₁ and r ₂ are random numbers distributed in [0,1];

(6) recalculate the objective function value of each particle at this moment, update P _best (i) and G _best ;

(7) Determine whether the maximum number of iterations is reached, and if so, end the optimization process, and obtain the optimal value of the parameters optimized by the particle swarm optimization algorithm (I _best , W _best (w _best (1), w _best (2),. ..,w _best (q)),L _best ), otherwise return to step (4);

(8) According to I _best , W _best (w _best (1), w _best (2),...,w _best (q)), L _best constructs BP neural network training set Z ₃ and test set Z ₄ and initializes them BP neural network connects weights and thresholds, where:

w _best (1)～w _best (I*H) is the initial value of the connection weights from the input layer to the hidden layer neurons of the BP neural network, w _best (I*H+1)～w _best (I*H +H*O) is the initial value of the connection weights from the hidden layer to the output layer neurons of the BP neural network, w _best (I*H+H*O+1)～w _best (I*H+H*O +H) is the initial value of the threshold of the hidden layer neurons of the BP neural network, w _best (I*H+H*O+H+1)～w _best (I*H+H*O+H+O) is The initial value of the threshold of the neurons in the output layer of the BP neural network is established, and the BP neural network model is established. After training, iterative l-step prediction is performed, and the corresponding prediction results are obtained.

Further, the RBF neural network using particle swarm optimization is used to predict the primary difference sequence of the residual sequence, and the specific process is:

(1) Determine the parameters to be optimized, including: RBF neural network input layer neuron number I and the length L of the training set;

(2) Initialize the population Where Q ₂ is the total number of particles, the i- _{th particle is Xi = (I i , L i ) ,} and the particle speed is Among them, I _i and L _i are a group of alternative solutions for parameters I and L;

(3) According to each particle in the group Determined parameters, constructing the input and output matrices of the RBF neural network training set, wherein the matrix Z ₅ and Z ₆ are first established for the residual sequence R and the number of neurons I _i of the input layer of the RBF neural network, wherein:

For the length L of the neural network training set to be optimized, the last L _i column in Z ₅ is used as the input matrix I _train of the training set, and the last L _i column in Z ₆ is used as the output matrix O _train of the training set; the forecast step size l is used as Test step size, the last l column in Z ₅ is used as the input matrix I _test of the test set, and the last l column in Z ₆ is used as the output matrix O _test of the test set; the RBF neural network constructed according to the training set is to the simulation result of the test set The sum of squared errors is taken as its fitness value, and the minimum fitness value is used as the optimization direction as the evaluation standard to judge the quality of each particle. The current individual extreme value of the particle X _i is recorded as P _best (i), and P _best (i) in the group is taken The best individual is taken as the overall extremum G _best ;

(4) For each particle _Xi in the group, its position and velocity are updated respectively;

In the formula: ω is the inertia weight, c ₁ and c ₂ are acceleration factors, g is the current iteration number, and r ₁ and r ₂ are random numbers distributed in [0,1];

(5) recalculate the objective function value of each particle at this moment, update P _best (i) and G _best ;

(6) Determine whether the maximum number of iterations is reached, and if so, end the optimization process and obtain the optimal value of the parameters optimized by the particle swarm optimization algorithm (I _best , L _best ), otherwise return to step (3).

(7) construct RBF neural network training set Z ₇ and test set Z ₈ by I _best and L _best , wherein:

In this regard, the RBF neural network model is established, and after training, iterative l-step prediction is performed, and the corresponding prediction results are obtained.

Further, the inertia weight ω=0.5, and the acceleration factor c ₁ =c ₂ =1.49445.

Beneficial effects of the present invention:

(1) The significant periodic sequence of power load extracted by continuous power spectrum analysis can be predicted with high precision due to its strong regularity, and the significant periodic sequence accounts for a large proportion in the original power load sequence, thus establishing a high-precision forecast On the one hand, the residual sequence after removing the periodic signal has a small proportion in the overall power load sequence, and on the other hand, it becomes stable due to a difference operation in the process of processing, and its prediction error is relatively limited , so the method proposed by the present invention decomposes the power load sequence into multiple significant periodic sequences and a single residual sequence through continuous power spectrum analysis, and then predicts each significant periodic sequence and residual sequence respectively, which can greatly improve the overall forecast Effect.

(2) Aiming at the influence of different selections of neural network structure on forecasting performance, the present invention aims at the characteristics of the significant periodic sequence and residual sequence separated from the electric load sequence, adopts BP neural network and RBF neural network respectively, and for the neural network The structural parameters and the size of the training set are optimized using the particle swarm optimization algorithm, which significantly improves the generalization performance of the neural network and ultimately improves the prediction accuracy.

Description of drawings

Fig. 1 is the flow chart of the electric load forecast optimization method based on continuous power spectrum analysis of the present invention;

Figure 2 is a sequence diagram of the original power load;

Fig. 3 is the continuous power spectrum analysis result diagram of the anomaly sequence of the average power load time series;

Figure 4 is a diagram of the significant periodic sequence and the separated residual sequence extracted from the anomaly sequence of the average power load time series;

Fig. 5 (a) is the one-step prediction result figure of the inventive method;

Fig. 5 (b) is the two-step prediction result figure of the inventive method;

Fig. 5 (c) is the three-step prediction result figure of the inventive method;

Fig. 6(a) is a one-step prediction result diagram of particle swarm optimization RBF neural network for the original power load sequence;

Fig. 6(b) is a two-step prediction result diagram of particle swarm optimization RBF neural network for the original power load sequence;

Figure 6(c) is the three-step prediction result of the particle swarm optimization RBF neural network established for the original power load sequence

Figure 7(a) is a one-step prediction result diagram of the ARIMA time series model established for the original power load sequence;

Fig. 7(b) is the two-step prediction results of the ARIMA time series model established for the original power load sequence;

Figure 7(c) is the three-step forecasting result of the ARIMA time series model established for the original power load series.

detailed description

In order to make the object, technical solution and advantages of the present invention more clear, the present invention will be further described in detail below in conjunction with the examples. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

The application principle of the present invention will be described in detail below in conjunction with the accompanying drawings.

A power load forecasting optimization method based on continuous power spectrum analysis of the present invention adopts continuous power spectrum analysis method to extract the hidden significant periodic sequence in the power load time series and separates to obtain the residual sequence, and adopts the optimization method based on particle swarm optimization The BP neural network predicts the significant periodic sequence and obtains the prediction results of each significant periodic sequence. The RBF neural network optimized by the particle swarm optimization algorithm is used to predict the first-order difference sequence of the residual sequence, and then the residual sequence is obtained by the reverse operation of the difference. Finally, the average value of the average power load time series is added to the prediction results of each significant period sequence and the prediction result of the residual sequence to obtain the final prediction result.

As shown in Figure 1, specifically, the following steps are included:

S1, read in the original sampled power load time series, and convert it into the average power load time series according to the forecast interval requirements, and then calculate the anomaly series of the average power load time series;

The original sampled power load time series is p={p(i), i=1,2,...,N}, where N is the number of original power load sampling points;

The average power load sequence is p'={p'(j),j=1,2,...,M}, wherein M is the number of sampling points of the average power load sequence converted according to the forecast interval requirements, The average value of p' is make

The anomaly sequence of the average power load time series is

S2, using the continuous power spectrum analysis method to extract the significant periodic sequence hidden in the anomaly sequence of the average power load time series, and separate the residual sequence;

The significant periodic sequence is {P ₁ , P ₂ ,...,P _k ,...,P _K }, where K is the number of significant periodic sequences implied in P, P _k ={P _k (1),P _k (2),…,P _k (M)}, where P _k (1), P _k (2),…,P _k (M) are the values of the significant periodic sequence P _k respectively; the residual sequence is R=PP ₁ -P ₂ -...-P _K ; therefore, P=P ₁ +P ₂ +...+P _K +R.

The above extraction process is as follows:

Suppose a discrete time series is x _t , where t=0,1,...,N-1, a total of N sampling points, time interval δ _t =1, apply continuous power spectrum estimation method to analyze the discrete time series Significant periodic bands, and use the frequency domain filtering method of Fourier transform FFT to extract the time series corresponding to each significant periodic band, specifically including the following steps:

(1) Determine the continuous power spectrum value

First calculate the rough spectrum estimate of _xt continuous power spectrum:

in: is the rough spectrum estimation value of continuous power spectrum corresponding to h wavenumber, h is the wavenumber, h=0,1,...m, m=N/8, r(τ) is the autocorrelation of time series x _t with a lag time length of τ coefficient:

in, and s are the mean and standard deviation of the discrete time series x _t , respectively.

In order to eliminate small fluctuations in the rough spectrum estimate, Hanning smoothing is performed on formula (1), and the continuous power spectrum value after smoothing (as shown by the solid line in Figure 3) is:

S ₀ is the continuous power spectrum value corresponding to 0 wavenumber; Sh is the continuous power spectrum value corresponding to _h wavenumber, and S _m is the continuous power spectrum value corresponding to m wavenumber.

(2) Determine the analysis cycle

The period corresponding to the h wave number is: (that is, the period point corresponding to the abscissa in Figure 3), considering m=N8 in the embodiment of the present invention, then

(3) Continuous power spectrum reliability test

Compare the continuous power spectrum value obtained by formula (3) with the red noise spectrum value to judge its significance.

Assuming that the continuous power spectrum value obtained by formula (3) is a certain aperiodic process spectrum value, the continuous power spectrum value S _h corresponding to the wave number h and the average red noise spectrum value ^The ratio of follows a χ2 distribution divided by its degree of freedom ν:

where the average red noise spectrum value for:

In the formula, is the average value of the continuous power spectrum values of all wavenumbers calculated in formula (3), r(1) is the autocorrelation coefficient with the lagging time length of x _t being 1, and the degree of freedom ν is:

The embodiment of the present invention is selected at the 0.05 significance level, when When , the spectral value of this wave number is significant, then the periodic fluctuation is significant, It is the dotted line in Fig. 3.

(4) Extract the time series corresponding to the periodic band

Determination of the periodic band: Take the first periodic point lower than the red noise detection line on the left and right sides of the significant continuous power spectrum value selected in step (3) to form a periodic band, which is a significant periodic band, where in Figure 3 The first point on the left side lower than the red noise detection line is defined as the upper boundary of the periodic band, and the first point on the right side lower than the red noise detection line in Figure 3 is defined as the lower bound of the periodic band.

The extraction of the time series corresponding to the periodic band: the embodiment of the present invention adopts the geoscience data processing program library WHIGG F90LIB (WFL) developed by the Institute of Surveying and Geophysics, Chinese Academy of Sciences, and by applying the frequency domain filtering subroutine of the Fourier transform FFT of the software, To extract the time series corresponding to the period band, the subroutine is:

CALL FFT_FILTER(N,X,DT,PER1,PER2,FIL_METHOD,XOUT)

Among them, N is the total number of sampling points, X is x _t , DT is the sampling time interval δt, PER1 is the lower bound of the extraction period band, PER2 is the upper bound of the extraction period band, and FIL_METHOD is the filter type. Here, "BAND" is used to refer to Band period, XOUT is the time series corresponding to the extracted significant period band.

S3, using the BP neural network based on particle swarm optimization to predict the significant periodic sequence, the specific process is as follows;

(1) According to Kolmogorov's theorem, a 3-layer BP neural network can realize approximating any nonlinear function, therefore, the embodiment of the present invention sets up 3-layer BP neural network model, suppose input layer neuron number is 1, hidden layer The number of neurons is H, and the number of output layer neurons is O; wherein, H=2*I+1, O=1;

(2) Determine the parameters that need to be optimized, including: the input layer neuron number I of the BP neural network and the length L of the training set, and also include: W=(w(1),w(2),...,w (q)), q=I*H+H*O+H+O, wherein, w(1)～w(I*H) is the connection weight value of the input layer of BP neural network to hidden layer neuron, w(I*H+1)～w(I*H+H*O) is the connection weight from hidden layer to output layer neuron of BP neural network, w(I*H+H*O+1)～ w(I*H+H*O+H) is the threshold value of neurons in the hidden layer of BP neural network, w(I*H+H*O+H+1)～w(I*H+H*O+H +0) is the threshold of BP neural network output layer neuron;

(3) Initialize the population X=(X ₁ ,X ₂ ,...,X _Q1 ), where Q ₁ is the total number of particles, the i-th particle is X _i =(I _i ,W _i ,L _i ), the particle The speed is V _i = (v _Ii , v _Wi , v _Li ), where I _i , W _i , L _i are a set of alternative solutions for parameters I, W, and L;

(4) According to the parameters determined by each particle Xi = (I _i , W _i , L _{i )} in the population, construct the input and output matrices of the BP neural network training set, where the significant periodic sequence P _k and the BP neural network The number of neurons I _i in the input layer first establishes matrices Z ₁ and Z ₂ , where:

For the length L of the neural network training set to be optimized, the last L _i column in Z ₁ is used as the input matrix I _train of the training set, and the last L _i column in Z ₂ is used as the output matrix O _train of the training set; the prediction step size l is used as Test step size, the last _l column in Z1 is used as the input matrix Itest of the _test set, and the last _l column in Z2 is used as the output matrix Otest of the _test set; The sum of squared errors is taken as its fitness value, and the minimum fitness value is used as the optimization direction as the evaluation standard to judge the quality of each particle. The current individual extreme value of the particle X _i is recorded as P _best (i), and P _best (i) in the group is taken The best individual is taken as the overall extremum G _best ;

(5) For each particle _Xi in the group, its position and velocity are updated respectively;

In the formula: ω is the inertia weight, c ₁ and c ₂ are acceleration factors, g is the current iteration number, r ₁ and r ₂ are random numbers distributed in [0,1];

(6) recalculate the objective function value of each particle at this moment, update P _best (i) and G _best ;

(7) Determine whether the maximum number of iterations is reached, and if so, end the optimization process, and obtain the optimal value of the parameters optimized by the particle swarm optimization algorithm (I _best , W _best (w _best (1), w _best (2),. ..,w _best (q)),L _best ), otherwise return to step (4);

(8) According to I _best , W _best (w _best (1), w _best (2),...,w _best (q)), L _best constructs BP neural network training set Z ₃ and test set Z ₄ and initializes them BP neural network connects weights and thresholds, where:

w _best (1)～w _best (I*H) is the initial value of the connection weights from the input layer to the hidden layer neurons of the BP neural network, w _best (I*H+1)～w _best (I*H +H*O) is the initial value of the connection weights from the hidden layer to the output layer neurons of the BP neural network, w _best (I*H+H*O+1)～w _best (I*H+H*O +H) is the initial value of the threshold of the hidden layer neurons of the BP neural network, w _best (I*H+H*O+H+1)～w _best (I*H+H*O+H+O) is The initial value of the threshold of the neurons in the output layer of the BP neural network is established, and the BP neural network model is established. After training, iterative l-step prediction is performed, and the corresponding prediction results are obtained.

S4, using the particle swarm optimized RBF neural network to predict the first-order difference sequence of the residual sequence, the specific process is:

(1) Determine the parameters to be optimized, including: RBF neural network input layer neuron number I and the length L of the training set;

(2) Initialize the population Where Q ₂ is the total number of particles, the i- _{th particle is Xi = (I i , L i ) ,} and the particle speed is Among them, I _i and L _i are a group of alternative solutions for parameters I and L;

(3) According to the parameters determined by each particle Xi (I _i , L _{i )} in the population, construct the input and output matrices of the RBF neural network training set, in which for the residual sequence R and RBF neural network input layer neurons The number I _i first establishes matrices Z ₅ and Z ₆ , where:

For the length L of the neural network training set to be optimized, the last L _i column in Z ₅ is used as the input matrix I _train of the training set, and the last L _i column in Z ₆ is used as the output matrix O _train of the training set; the forecast step size l is used as Test step size, the last l column in Z ₅ is used as the input matrix I _test of the test set, and the last l column in Z ₆ is used as the output matrix O _test of the test set; the RBF neural network constructed according to the training set is to the simulation result of the test set The sum of squared errors is taken as its fitness value, and the minimum fitness value is used as the optimization direction as the evaluation standard to judge the quality of each particle. The current individual extreme value of the particle X _i is recorded as P _best (i), and P _best (i) in the group is taken The best individual is taken as the overall extremum G _best ;

(4) For each particle _Xi in the group, its position and velocity are updated respectively;

In the formula: ω is the inertia weight, c ₁ and c ₂ are acceleration factors, g is the current iteration number, and r ₁ and r ₂ are random numbers distributed in [0,1];

(5) recalculate the objective function value of each particle at this moment, update P _best (i) and G _best ;

(6) Determine whether the maximum number of iterations is reached, and if so, end the optimization process and obtain the optimal value of the parameters optimized by the particle swarm optimization algorithm (I _best , L _best ), otherwise return to step (3).

(7) construct RBF neural network training set Z ₇ and test set Z ₈ by I _best and L _best , wherein:

In this regard, the RBF neural network model is established, and after training, iterative l-step prediction is performed, and the corresponding prediction results are obtained.

S5, adding the average value of the average power load time series to the prediction results of each significant period sequence and the prediction result of the residual sequence to obtain the final prediction result.

Embodiment two

According to the steps S1-S5 in the first embodiment, the hour-level original power load time series collected by a certain power grid is taken, specifically referring to Fig. 2, since the purpose of the example of the present invention is the short-term forecast of the hour level, there is no need to analyze the original power load data It can be used directly after any adjustment, that is, p'(i)=p(i), i=1,2,...,N. In this embodiment, the first 1680 points of p'(i) are taken as training data, and the subsequent 50 points are predicted, and the effectiveness of the algorithm is checked with the relative percentage error MAPE as an index, namely:

Among them, Y(i) and p'(i) are the power load prediction value and sampling value respectively, and l is the prediction step size.

Figure 3 shows the continuous power spectrum analysis results of the anomaly sequence P of the average power load time series. It is found that the power load sequence of the power grid has two significant periodic bands with 12 and 24 hours as extreme points, which are taken around the extreme points Each of the first periodic points below the detection line on both sides forms a periodic band, and this periodic band is a significant periodic band. The detection line is the dotted line in Figure 3. In this embodiment, the 2 significant periodic bands are respectively For [21.8, 26.7] and [11.4, 12.6], the frequency domain filtering method of Fourier transform FFT is used to extract the time series corresponding to the two periodic bands, which are P ₁ and P ₂ respectively, and the corresponding residual sequence is obtained R, thus P=P ₁ +P ₂ +R, see FIG. 4 . It can be seen that the regularity of the two significant periodic sequences is very strong, and they can be predicted with higher precision; on the other hand, although the prediction error for the residual is inevitable, the energy (variance) of the residual R accounts for P The energy (variance) is 28.56%, which is a significant drop. Therefore, the prediction error for the residual is much smaller than the error for directly predicting P.

Although the neural network has strong nonlinear fitting ability and fast learning ability, how to choose the appropriate neural network model, determine the structure of the neural network, training set and test set still mainly depends on manual experience or trial and error, its universality poor. Through the analysis of the extracted significant periodic sequence, it is found that although it has obvious periodic variation characteristics and the sequence is smooth and smooth, the amplitude and phase of the sequence change slightly over time, which is more suitable for the BP neural network with strong fault tolerance. The sequence fluctuates around the 0 axis after the first-order difference, which is more suitable for the RBF neural network. Therefore, the embodiment of the present invention adopts the BP neural network model optimized based on the particle swarm optimization algorithm for the extracted significant periodic sequences P ₁ and P ₂ , while for the residual The difference sequence R adopts the RBF neural network optimized based on the particle swarm algorithm.

For P ₁ and P ₂ , the BP neural network model based on the particle swarm optimization algorithm is adopted, the range of the number of neurons in the input layer is [5,14], the length of the training set is [50,1650], the weight of the neural network and The range of the threshold is [-3,3], the particle swarm population size is 50, and the iteration is 30 times. For R, the RBF neural network optimized based on the particle swarm optimization algorithm is used. The range of the number of neurons in the input layer is [5,20], the length of the training set is [50,1650], the population size of the particle swarm is 50, and the iteration is 30. Second-rate. Table 1 shows the optimization results of the two parameters of input layer neuron number I and training set length L for significant periodic sequences P ₁ , P ₂ and residual R when performing 3-step prediction. For P ₁ , P ₂ The optimization results of the established BP neural network weights and thresholds are not listed one by one due to too many parameters.

Table 1

In this embodiment, 1-step, 2-step and 3-step prediction experiments with a total prediction step length of 50 are carried out. The prediction results are shown in Figure 5(a)-(c), and Table 2 shows the prediction error statistics. It can be seen that with the increase of the prediction step size, the overall prediction accuracy decreases, but the overall error is less than 5%, and the prediction results are relatively satisfactory.

Table 2

1 step forecast 2-step forecast 3 step forecast MAPE 0.0399 0.0436 0.0434

Comparative experiment 1

In order to verify the influence of the optimization strategy proposed by the present invention on the experimental results, comparative experiment 1 directly performs a differential operation on the original power load sequence p', and then establishes the RBF neural network optimized by the particle swarm optimization algorithm, and takes the range of the number of neurons in the input layer is [5,25], the length of the training set is [50,1650], the particle swarm population size is 50, and the iteration is 30 times. Table 3 shows the optimization results of RBF neural network parameters established for the original power load sequence p' when performing three-step forecasting.

table 3

Similarly, comparative experiment 1 carried out 1-step, 2-step and 3-step prediction experiments with a total prediction step size of 50. The prediction results are shown in Figure 6(a)-(c). Table 4 shows the statistics of prediction errors. The comparison table 2 It can be seen that the average error of its 1-3 step prediction has increased by 60.44% compared with Table 2.

Table 4

1 step forecast 2-step forecast 3 step forecast MAPE 0.0395 0.0708 0.0933

If p' is not subjected to a differential operation, the number I of neurons in the input layer of the RBF neural network and the length L of the training set are randomly selected, the final prediction error will be very different. In the embodiment of the present invention, two groups of different I and L pairs are selected The impact of the prediction error is illustrated, as shown in Table 5.

table 5

Compared with Table 2, the average error of the 1-3 step prediction of two groups of contrast experiments with different parameters increased by 47.68% and 170.61%. The poor effect of this group of comparative experiments shows that the selection of neural network parameters has a huge impact on the learning ability and generalization of the neural network, making the effect of directly using neural network modeling not good.

Comparative experiment 2

A differential autoregressive moving average model (Autoregressive Integrated Moving Average Model, ARIMA) model is established for the original power load sequence. Select the first 100 sampling data points of the prediction point, and determine the structure of the ARIMA model through the AIC criterion order determination method. Similarly, comparative experiment 2 carried out 1-step, 2-step and 3-step prediction experiments with a total prediction step length of 50. The prediction results As shown in Figure 7(a)-(c), Table 6 shows the prediction error statistics. Compared with Table 2, it can be seen that the average error of the 1-3 step prediction has increased by 136.25% compared with Table 2.

Table 6

1 step forecast 2-step forecast 3 step forecast MAPE 0.0169 0.1486 0.1343

In summary:

The significant periodic sequence of power load extracted by continuous power spectrum analysis has strong regularity, so it can be predicted with high precision, and the significant periodic sequence accounts for a large proportion in the original sequence, thus laying the foundation for higher precision prediction; Since the residual sequence after the periodic sequence has a small proportion in the original sequence, the prediction error is relatively limited. The method proposed by the present invention decomposes the power load sequence into multiple significant periodic sequences and a single residual sequence through continuous power spectrum analysis, and then separately predicts each significant periodic sequence and residual sequence, which can greatly improve the overall prediction effect.

The basic principles and main features of the present invention and the advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above-mentioned embodiments. What are described in the above-mentioned embodiments and the description only illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have Variations and improvements are possible, which fall within the scope of the claimed invention. The protection scope of the present invention is defined by the appended claims and their equivalents.

Claims (7)

1. A power load prediction optimization method based on continuous power spectrum analysis is characterized by comprising the following steps: comprises that

Reading in an original sampling power load time sequence, converting the original sampling power load time sequence into an average power load time sequence according to a forecast interval requirement, and then calculating a distance sequence of the average power load time sequence;

extracting a significant periodic sequence implied in a distance sequence of an average power load time sequence by adopting a continuous power spectrum analysis method, and separating to obtain a residual sequence;

predicting the significant periodic sequences by adopting a BP neural network optimized by a particle swarm algorithm to obtain the prediction result of each significant periodic sequence;

predicting a first-order difference sequence of the residual sequence by using a particle swarm optimization RBF neural network, and then obtaining a prediction result of the residual sequence through a difference inverse operation;

and adding the average value of the average power load time sequence, the prediction result of each significant period sequence and the prediction result of the residual sequence to obtain a final prediction result.

2. The method according to claim 1, wherein the method comprises the following steps:

the time sequence of the original sampling power load is p ═ { p (i) ═ 1, 2.., N }, wherein N is the number of original power load sampling points;

the average power load time sequence is p ' ═ { p ' (j), j is 1,2, as, M }, wherein M is the number of sampling points of the average power load sequence after conversion according to the forecast interval requirement, and the average value of p ' is p ' ═ p ' (j), j is 1,2Order to

The distance sequence of the average power load time sequence is

3. The method according to claim 2, wherein the method comprises the following steps:

the significant period sequence is { P }₁,P₂,…,P_k,…,P_KWhere K is the number of significant periodic sequences implied in P, P_k＝{P_k(1),P_k(2),…,P_k(M)}，Wherein P is_k(1),P_k(2),…,P_k(M) are respectively a significant periodic sequence P_kA value of (d);

the residual sequence is R ═ P-P₁-P₂-…-P_K。

4. The method for power load prediction optimization based on continuous power spectrum analysis according to any one of claims 1-3, wherein: the method for extracting the significant period sequence from the flat sequence of the average power load time sequence by adopting the continuous power spectrum analysis method specifically comprises the following steps: and analyzing the significant periodic bands of the average power load time sequence from the flat sequence by using a continuous power spectrum method, and extracting the time sequences corresponding to the significant periodic bands by using a frequency domain filtering method of fast Fourier transform so as to obtain the significant periodic sequences.

5. The method according to claim 3, wherein the method comprises the following steps: the specific process of predicting the significant periodic sequence by adopting the BP neural network optimized based on the particle swarm optimization is as follows:

(1) establishing a 3-layer BP neural network model according to Kolmogorov theorem, and setting the number of neurons in an input layer as I, the number of neurons in a hidden layer as H and the number of neurons in an output layer as O; wherein, H2I +1, O1;

(2) determining parameters needing optimization, including: the number I of neurons in the input layer of the BP neural network and the length L of the training set further comprise: w (1), W (2),. once, W (q)), q ═ H + O, where W (1) -W (I × H) are the connection weights from the input layer to the hidden layer neurons of the BP neural network, W (I × H +1) -W (I × H + O) are the connection weights from the hidden layer to the output layer neurons of the BP neural network, W (I × H + O + H) are the thresholds from the hidden layer to the output layer neurons of the BP neural network, and W (I × H + O + H +1) -W (I × H + O) are the thresholds from the hidden layer neurons of the BP neural network;

(3) initializing a populationWherein Q₁Is the total number of particles, the ith particle is X_i＝(I_i,W_i,L_i) The particle velocity isWherein I_i、W_i、L_iA set of alternative solutions for parameter I, W, L;

(4) according to each particle X in the population_i＝(I_i,W_i,L_i) Constructing input and output matrices of a training set of the BP neural network for the determined parameters, wherein the significant period sequence P is_kAnd BP neural network input layer neuron number I_iFirst, a matrix Z is established₁And Z₂Wherein:

<mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>...</mn> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mn>...</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mrow> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>*</mo> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </msub> </mrow>

<mrow> <msub> <mi>Z</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow>

training set length L, Z for neural network to be optimized₁Middle last L_iInput matrix I with columns as training set_train，Z₂Middle last L_iOutput matrix O with columns as training set_train(ii) a Taking the forecast step length l as the test step length, Z₁The last column in the test set is used as an input matrix I of the test set_test，Z₂The last column in the test set is used as the output matrix O of the test set_test(ii) a Taking the sum of the squares of errors of the simulation results of the BP neural network constructed according to the training set as the fitness value of the test set, taking the minimum fitness value as the optimization direction as the evaluation standard to judge the advantages and disadvantages of each particle, and recording the particle X_iCurrent individual extremum is P_best(i) Taking P in the population_best(i) Most preferably oneVolume as a whole extreme G_best；

(5) Each particle X in the population_iUpdating the position and the speed of the mobile terminal respectively;

<mrow> <msubsup> <mi>V</mi> <mi>i</mi> <mrow> <mi>g</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;omega;V</mi> <mi>i</mi> <mi>g</mi> </msubsup> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mi>g</mi> </msubsup> <mo>)</mo> <mo>+</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mi>g</mi> </msubsup> <mo>)</mo> </mrow> <mo>,</mo> </mrow>

<mrow> <msubsup> <mi>X</mi> <mi>i</mi> <mrow> <mi>g</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mi>g</mi> </msubsup> <mo>+</mo> <msubsup> <mi>V</mi> <mi>i</mi> <mrow> <mi>g</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow>

in the formula: omega is the inertial weight, c₁、c₂Is an acceleration factor, g is the current iteration number, r₁、r₂Is distributed in [0,1 ]]The random number of (2);

(6) recalculating the objective function value of each particle at the moment, and updating P_best(i) And G_best；

(7) Judging whether the maximum iteration times is reached, if so, ending the optimization process, and obtaining a parameter optimal value (I) obtained by the particle swarm optimization_best,W_best(w_best(1),w_best(2),...,w_best(q)),L_best) Otherwise, returning to the step (4);

(8) according to I_best、W_best(w_best(1),w_best(2),...,w_best(q))、L_bestConstructing BP neural network training set Z₃And test set Z₄And initializing a BP neural network connection weight and a threshold, wherein:

<mrow> <msub> <mi>Z</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>...</mn> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mn>...</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mrow> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>*</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>

<mrow> <msub> <mi>Z</mi> <mn>4</mn> </msub> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </msub> </mrow>

w_best(1)～w_best(I × H) is the initial value of the link weights from the input layer to the hidden layer neurons of the BP neural network, w_best(I*H+1)～w_best(I H + H O) is the initial value of the link weights from hidden layer to output layer neurons of the BP neural network, w_best(I*H+H*O+1)～w_best(I H + H O + H) is the initial value of the threshold of hidden layer neuron of BP neural network, w_best(I*H+H*O+H+1)～w_bestAnd (I H + H O + H + O) is an initial value of the threshold value of the neuron of the output layer of the BP neural network, so that a BP neural network model is established, iterative prediction is carried out in one step after training, and a corresponding prediction result is obtained.

6. The method according to claim 3, wherein the method comprises the following steps: the method adopts the RBF neural network optimized by the particle swarm to predict the primary difference sequence of the residual sequence, and comprises the following specific processes:

(1) determining parameters to be optimized, including: the number I of neurons in an input layer of the RBF neural network and the length L of a training set are calculated;

(2) initializing a populationWherein Q₂Is the total number of particles, the ith particle is X_i＝(I_i,L_i) The particle velocity isWherein I_i,L_iA set of alternative solutions for parameter I, L;

(3) according to each particle X in the population_i(I_i,L_i) Constructing input and output matrixes of a training set of the RBF neural network according to the determined parameters, wherein the input and output matrixes are used for the residual sequence R and the number I of neurons in the input layer of the RBF neural network_iFirst, a matrix Z is established₅And Z₆Wherein:

<mrow> <msub> <mi>Z</mi> <mn>5</mn> </msub> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>...</mo> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mo>...</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>M</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mrow> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>*</mo> <mrow> <mo>(</mo> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </msub> </mrow>

<mrow> <msub> <mi>Z</mi> <mn>6</mn> </msub> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow>

training set length L, Z for neural network to be optimized₅Middle last L_iInput matrix I with columns as training set_train，Z₆Middle last L_iOutput matrix O with columns as training set_train(ii) a Taking the forecast step length l as the test step length, Z₅The last column in the test set is used as an input matrix I of the test set_test，Z₆The last column in the test set is used as the output matrix O of the test set_test(ii) a The sum of the squares of errors of the simulation results of the test set by the RBF neural network constructed according to the training set is used as the fitness value of the test set, the minimum fitness value is used as the optimization direction to be used as the evaluation standard to judge the quality of each particle, and the particle X is recorded_iCurrent individual extremum is P_best(i) Taking P in the population_best(i) Optimal individual as global extremum G_best；

(4) Each particle X in the population_iUpdating the position and the speed of the mobile terminal respectively;

<mrow> <msubsup> <mi>V</mi> <mi>i</mi> <mrow> <mi>g</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;omega;V</mi> <mi>i</mi> <mi>g</mi> </msubsup> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mi>g</mi> </msubsup> <mo>)</mo> <mo>+</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>G</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mi>g</mi> </msubsup> <mo>)</mo> </mrow> <mo>,</mo> </mrow>

<mrow> <msubsup> <mi>X</mi> <mi>i</mi> <mrow> <mi>g</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mi>g</mi> </msubsup> <mo>+</mo> <msubsup> <mi>V</mi> <mi>i</mi> <mrow> <mi>g</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow>

in the formula: omega is the inertial weight, c₁、c₂For the acceleration factor, g is the current iteration number, and r₁、r₂Is distributed in [0,1 ]]The random number of (2);

(5) recalculating the objective function value of each particle at the moment, and updating P_best(i) And G_best；

(6) Judging whether the maximum iteration times is reached, if so, ending the optimizationObtaining the optimal value of the parameter (I) obtained by the optimization of the particle swarm optimization_best,L_best) Otherwise, returning to the step (3).

(7) According to I_bestAnd L_bestConstructing RBF neural network training set Z₇And test set Z₈Wherein:

<mrow> <msub> <mi>Z</mi> <mn>7</mn> </msub> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>...</mn> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mn>...</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mrow> <msub> <mi>I</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>*</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>

<mrow> <msub> <mi>Z</mi> <mn>8</mn> </msub> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>M</mi> <mo>-</mo> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </msub> </mrow>

and establishing an RBF neural network model, training, performing iterative prediction in one step, and obtaining a corresponding prediction result.

7. The method according to claim 5 or 6, wherein the method comprises the following steps: the inertia weight ω is 0.5, and the acceleration factor c₁＝c₂＝1.49445。