Integrated prediction method based on empirical mode decomposition algorithm and random configuration network

Abstract

The invention discloses an integrated prediction method based on an empirical mode decomposition algorithm and a random configuration network in the technical field of power load demand prediction. The method comprises the following steps: firstly, decomposing a load demand time sequence into several intrinsic mode functions (IMFs); the method comprises the following steps of: extracting IMFs from a load demand, then modeling each extracted IMF by using a data dependent stochastic configuration network (SCNs) so as to accurately predict the trend of the IMFs, and finally combining the prediction results of all IMFs through unbiased or weighted summation so as to obtain aggregate output of the load demand.

Description

Technical Field

[0001] The invention relates to the technical field of power load demand prediction, and in particular to an integrated prediction method based on an empirical mode decomposition algorithm and a random configuration network. Background Art

[0002] Electricity load demand forecasting is one of the most important tasks in modern power system management. Improving the accuracy and efficiency of load demand forecasting helps power companies to formulate reasonable grid construction plans, thereby improving the economic and social benefits of the system. In addition, high-precision forecasting results can also effectively predict potential faults in the power system, thereby providing a reliable and secure foundation for grid operation. In other words, the goal of load demand forecasting is to provide a reliable power supply while keeping operating costs as low as possible.

[0003] Since 1940, various statistical baseline linear time series forecasting methods have been proposed. The common goal of these linear models is to use time series analysis to infer future energy demand. In recent years, with the rapid development of computational intelligence, artificial neural networks (ANN), fuzzy comprehensive evaluation and support vector machine (SVM) methods, these methods have been widely used in short-term load forecasting. The existing technology uses a gradient descent neural network model, which has problems such as large number of network parameters, complex network structure and low training efficiency. Summary of the invention

[0004] The present invention aims to provide an integrated prediction method based on the empirical mode decomposition algorithm and the random configuration network to solve the problems of large number of network parameters, complex network structure and low training efficiency in the existing prediction methods.

[0005] In order to solve the above technical problems, the present invention provides the following technical solution: an integrated prediction method based on an empirical mode decomposition algorithm and a random configuration network, comprising the following steps: S1. Decompose the time series data into multiple IMFs and a residual through EMD; S2. For each IMF and residual, construct a training matrix as the input of SCN; S3. Train SCN to obtain prediction results for each extracted IMF and residual; S4. Combine all forecasts by summing or using a linear neural network to form an integrated output of the time series.

[0006] Further, the steps in the EMD algorithm in step S1 are as follows: Step 1. Given a time series signal x(t), calculate its upper and lower envelopes through spline interpolation of local extrema; Step 2. Calculate the average value m(t) of the upper envelope and the lower envelope; Step 3. Subtract the mean from the original time series to obtain the first component ; Step 4. By considering As new Repeat steps 1 to 3 until one of the following stopping criteria is met: The number of approaches to zero, zero crossings, and extrema is approximately equal or reaches a predetermined maximum number of iterations; Step 5. as the IMF and calculate the residual signal: ; Step 6. Use the remaining signal As new To obtain the next IMF, repeat steps 1 to 5 until all IMFs are obtained; Step 7. Finally, the original TS signal is decomposed into: .

[0007] Furthermore, the process of constructing the SCN network in S2 is as follows: Given training data ,in Represents the sample characteristics, ; represents the sample label, ; , N represents the number of samples; Step 1. Given the objective function , assuming that SCN The hidden layer nodes have been configured, so the current network output It can be calculated by formula (1): (1) In the formula, represents the output weight of node j; gj represents the activation function; and Represent the input weight and bias of node j, respectively, and their ranges are and , Represents the parameter range; ; Step 2: The current network residual vector can be calculated by formula (2): (2) Step 3: According to the preset error or the set maximum number of nodes, determine whether the preset conditions are met. If the preset conditions are not met, adaptively increase the number of nodes L and configure the node parameters according to formula (3): (3) (4) In the formula, Represents the output dimension; represents the output of node L, calculated by equation (4); and They represent the node L parameters to be determined respectively; Represents the number of candidate parameters; ; represents a sequence of non-negative real numbers, where , According to formula (3), The candidate node parameter with the maximum value is taken as the final parameter of node L; Step 4: Determine the SCN output weight according to the objective function of formula (5) : (5) In the formula, ; ; express The Moore-Penrose generalized inverse of ; Step 5: According to formula (6), calculate the final output of SCN f : (6) Beneficial effects of the present invention: 1. EMD-based hybrid methods are generally superior to corresponding single structure models for load demand time series forecasting. 2. The proposed EMD-based integrated deep learning method has the best performance according to statistical test results. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 It is a flow chart of the integrated prediction method based on the empirical mode decomposition algorithm and the random configuration network of the present invention; Figure 2 is an example of a decomposed load demand time series signal; Figure 3 Configure the network structure randomly. DETAILED DESCRIPTION

[0009] The following is further described in detail through specific implementation methods: The embodiment is basically as shown in the attached Figure 1 -Attached Figure 3As shown: 1. An integrated prediction method based on the empirical mode decomposition algorithm and the random configuration network includes the following steps: Step 1: Decompose the time series data into multiple IMFs and a residual through EMD EMD, also known as HHT, is a method to decompose a signal into several intrinsic mode functions (IMFs). EMD is a method to obtain instantaneous trends from non-stationary and nonlinear data sets. System load is a random non-stationary process composed of thousands of individual components. System load behavior is affected by many factors, which can be classified as economic factors, date, season, weather, and random effects. Therefore, the EMD algorithm is very effective in load demand forecasting. IMF is a function with only one extreme value between zero crossings and a mean value of zero.

[0010] The steps within the EMD algorithm are as follows: S1. Given a time series signal x(t), calculate its upper and lower envelopes through spline interpolation of local extreme values; S2. Calculate the average value m(t) of the upper envelope and the lower envelope; S3. Subtract the mean from the original time series to obtain the first component ; S4. By considering As new Repeat steps 1 to 3 until one of the following stopping criteria is met: The number of approaches to zero, zero crossings, and extrema is approximately equal or reaches a predetermined maximum number of iterations; S5. as the IMF and calculate the residual signal: ; S6. Using the residual signal As new To obtain the next IMF, repeat steps 1 to 5 until all IMFs are obtained; S7. Finally, the original TS signal is decomposed into: .

[0011] Step 2: For each IMF and residual, construct a training matrix as the input of SCN SCN was proposed by Professor Wang Dianhui in 2017. It is a type of randomized neural network model. Different from other single-hidden layer feedforward neural networks (SLFNs), SCN adopts an incremental learning method and uses inequality constraints to randomly configure the parameters of hidden layer nodes. The network structure gradually increases from one hidden layer node to complete the network construction.

[0012] The SCN network structure is as follows Figure 3 As shown, the construction process can be described as: Step 1. Given the objective function , assuming that SCN The hidden layer nodes have been configured, so the current network output It can be calculated by formula (1): (1) In the formula, represents the output weight of node j; gj represents the activation function; and Represent the input weight and bias of node j, respectively, and their ranges are and , Represents the parameter range; ; Step 2: The current network residual vector can be calculated by formula (2): (2) Step 3: According to the preset error or the set maximum number of nodes, determine whether the preset conditions are met. If the preset conditions are not met, adaptively increase the number of nodes L and configure the node parameters according to formula (3): (3) (4) In the formula, Represents the output dimension; represents the output of node L, calculated by equation (4); and They represent the node L parameters to be determined respectively; Represents the number of candidate parameters; ; represents a sequence of non-negative real numbers, where , According to formula (3), The candidate node parameter with the maximum value is taken as the final parameter of node L; Step 4: Determine the SCN output weight according to the objective function of formula (5) : (5) In the formula, ; ; express The Moore-Penrose generalized inverse of ; Step 5: According to formula (6), calculate the final output of SCNf : (6) Step 3: Train SCN to obtain prediction results for each extracted IMF and residual Step 4: Combine all forecasts by summing or using a linear neural network to form an integrated output of the time series 2. Methods and Experiments 2.1 Dataset The experimental data comes from the electricity load demand dataset of the Australian Energy Market Operator (AEMO). Data from New South Wales (NSW), Tasmania (TAS), Queensland (QLD), South Australia (SA) and Victoria (VIC) in 2013 were selected for training and testing.

[0013] 2.2 Data Characteristics The load demand data is sampled every half hour, which means there are 48 data points in each day. Since the information includes weather and social activities, the power load demand data shows significant periodicity: daily, weekly and annual. In order to identify periodic variables, Raza proposed a transition detection method based on exponentially weighted moving average (EWMA) for subset selection. Assuming that the given time series dataset is , where T is the index set. The autocorrelation coefficient of lag k is It can be calculated as follows:

[0014] in is the mean value of the time series X, Measures the linear correlation of the time series between times t and tk.

[0015] From the autocorrelation function (ACF) of the power load demand time series, we can identify the three most strongly dependent time-lag variables: data from half an hour ago , data from the same time of the previous week and the data from the same time the previous day Therefore, in the present invention, the input feature set for one-day-ahead load demand forecasting consists of the data points of the previous day arrive Data points from the same day of the previous week arrive These are the most informative time-lagged variables.

[0016] 2.3 Methodology For the power load demand dataset, all training and test values ​​are linearly scaled to [0, 1] using the following scaling formula:

[0017] In order to realize the simulation, SCN and RVFL are selected as comparative experiments. The method in this paper is referred to as EMD-SCN. The node parameters are selected between 25 and 200, and the average results of 100 times are selected as the final results.

[0018] 2.4 Performance Evaluation Two error metrics are used in this paper to examine the accuracy of the prediction model: root mean square error (RMSE) and mean absolute percentage error (MAPE).

[0019] They are defined as:

[0020]

[0021] in is corresponding where n is the number of data points in the test time series.

[0022] The endpoint data expansion problem is an important issue that should be considered in the EMD algorithm. In general, the endpoint is not a local extreme value, so it is necessary to expand the two maximum extreme values ​​and the two minimum extreme values ​​to obtain the extreme value envelope. The characteristic wave is used to obtain the maximum extreme value and the minimum extreme value. However, different characteristic waves will lead to different results, and it is difficult to select a suitable waveform for each iteration. In this work, the Matlab EMD package implemented by G. Rilling is used to decompose the time series signal. Figure 2 An example of a decomposed load demand time series signal is shown.

[0023] 3. Results and Comparison Use the one-day-in-advance (short-term) method.

[0024] The forecast results for one-day-ahead load forecasting are shown in Table 1. In this case, the time horizon is 24 hours, which means that we assume that the forecast value is the same as the value 24 hours ago.

[0025] The original load demand time series data is modeled by RVFL and SCN models to reveal the advantages of the EMD-based hybrid method. Comparing the prediction results listed in the table below, we can conclude that the EMD and SCN ensemble methods are generally better than single structure machine learning algorithms in most cases. The bold numbers in the table indicate the methods with the best performance for this dataset under this performance metric.

[0026] Table 1

[0027] The experimental data comes from the electricity load demand dataset of the Australian Energy Market Operator (AEMO). The first column represents the state and city data of New South Wales (NSW), Tasmania (TAS), Queensland (QLD), South Australia (SA) and Victoria (VIC). The second column represents the forecasts for different months, January, May, September and November. The third column is the evaluation index, which is used to indicate the prediction performance of the model. Columns 4-6 represent the test performance of the three models in different states and cities in different months. The smaller the value, the better the prediction performance.

Claims

1. An integrated prediction method based on the empirical mode decomposition algorithm and the random configuration network, characterized in that: The following steps are involved: S1. Decompose the time series data into multiple IMFs and a residual through EMD; S2. For each IMF and residual, construct a training matrix as the input of SCN; S3. Train SCN to obtain prediction results for each extracted IMF and residual; S4. Combine all forecast results by summing or using a linear neural network to form an integrated output of the time series.

2. The integrated prediction method based on the empirical mode decomposition algorithm and the random configuration network according to claim 1, characterized in that: The steps in the EMD algorithm in step S1 are as follows: Step 1. Given a time series signal x(t), calculate its upper and lower envelopes through spline interpolation of local extreme values; Step 2. Calculate the average value m(t) of the upper envelope and the lower envelope; Step 3. Subtract the mean from the original time series to obtain the first component h(t) = x(t) - m(t); Step 4. Repeat steps 1 to 3 by considering h(t) as the new x(t) until one of the following stopping criteria is met: m(t) is close to zero, the number of zero crossings and extrema is approximately equal, or a predetermined maximum number of iterations is reached; Step 5. Take h(t) as IMF and calculate the residual signal: r(t) = x(t) - h(t); Step 6. Use the residual signal r(t) as the new x(t) to obtain the next IMF, and repeat steps 1 to 5 until all IMFs are obtained; Step 7. Finally, the original TS signal is decomposed into:

3. The integrated prediction method based on the empirical mode decomposition algorithm and the random configuration network according to claim 2, characterized in that: The process of constructing the SCN network in S2 is as follows: Given training data {X,Y}, where X = {x1,x2,…,x N } represents the sample characteristics, Y={y1,y2,…,y N } represents the sample label, N represents the sample size; Step 1. Given the objective function f: Assuming that the L-1 hidden layer nodes of SCN have been configured, the current network output f L-1 (X) can be calculated by formula (1): In the formula, β j =[β j,1 ,β j,2 ,...,β j,m ] T represents the output weight of node j; gj represents the activation function; w j and b j Represent the input weight and bias of node j, respectively, and their ranges are [-λ,λ] d and [-λ,λ], λ represents the parameter range; j=1,2,...,L max ; Step 2: The current network residual vector can be calculated by formula (2): Step 3: According to the preset error or the set maximum number of nodes, determine whether the preset conditions are met. If the preset conditions are not met, adaptively increase the number of nodes L and configure the node parameters according to formula (3): Where q=1,2,...,m represents the output dimension; h L represents the output of node L, calculated by equation (4); w L and b L Respectively represent the node L parameters to be determined; T max represents the number of candidate parameters; r∈(0,1); {μ L } represents a sequence of non-negative real numbers, where μ L ≤1-r,lim L→+∞ μ L =0; According to formula (3), it satisfies The candidate node parameter with the maximum value is used as the final parameter of node L; Step 4: According to the objective function of formula (5), determine the SCN output weight β: Where, β=[β1,β2,...,β L ]; H = [h1,h2,…,h L ]; H L + Indicates H L The Moore-Penrose generalized inverse of Step 5: According to formula (6), calculate the final output f of SCN: f=Hβ (6).

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