Short‐term load forecasting based on a generalized regression neural network optimized by an improved sparrow search algorithm using the empirical wavelet decomposition method

With the development of the electric market, electric load forecasting has been increasingly pursued by many scholars. Because the electric load is affected by many factors, it is characterized by volatility and uncertainty, and it cannot be forecasted accurately only by a single model. In the research, a short‐term load forecasting integrated model is proposed to solve the problem of inaccurate forecasting of a single model. The key point of using the integrated model to forecast is to optimize the decomposed sequence to improve the accuracy of the forecast. empirical wavelet decomposition (EWT) is used to decompose the sequence into stationary sequences and avoid modal aliasing; the sparrow search algorithm (SSA) simulates the forecasting and anti‐forecasting behavior of the sparrow population, which is very similar to the electricity consumption behavior of various industries and has good optimization effect; generalized regression neural network (GRNN) is used for forecast and reconstruction; This is the EWT‐SSA‐GRNN model. This paper studies and analyzes the power load of a city in southern Australia. The results show that the integrated model reduces volatility through decomposition and optimization, and can improve forecast accuracy.


| INTRODUCTION
Since the second industrial revolution brought electricity to human society, it has been rapidly developing. At the same time, the arrival of the third technological revolution brought us a large-scale electricity system, which further promoted the development of the electric electricity industry. Therefore, the study of electricity has a profound impact on both the micro-unit and the whole of society. As an important material basis for economic growth, social development, science, and national security, electric electricity energy plays a vital role in the process of national construction and development. 1 The research on electricity is usually carried out from the supply and demand of two aspects. Only the balance of supply and demand can make the development of the electricity industry more stable. Electric load forecasting is the basis to ensure the balance of electricity supply and demand. Accurate load forecasting not only helps to alleviate the contradiction between electricity supply and demand but also can realize the stable and reliable operation of the electricity grid. 2 The redesign of electricity markets, which is necessary for the establishment of sustainable intelligent energy systems, has recently attracted much attention from researchers and policymakers. 3 Some behavioral characteristics of human beings are reflected in their daily consumption habits and recorded and preserved in the form of electric load. Therefore, the electric load is a description of human electricity consumption behavior and further reflects human social activities. Therefore, the potential information can be found by analyzing the electric load according to its characteristics of volatility and uncertainty. However, the mere forecasting of electric load cannot meet the development of the modern electric electricity industry. What the development of the electric electricity industry pursues is accurate and more accurate forecasting to make the future development of the industry more competitive. The electric industry plays an irreplaceable role in economic development. The growth of electric demand fluctuates with the continuous change in the economic period and the electric load is the best measure of electricity. Therefore, there is an inseparable relationship between the development of the electric industry and economic development. Accurate forecasting of electric load is the premise and basis for the development of the electric industry and on this basis. It will promote the development of the entire economy. With the development of the economy, the demand for electric energy is also increasing. In recent years, a lot of studies have made great efforts to propose an innovative deep-learning model 4,5 and conduct a theoretical analysis [6][7][8] to improve robustness and flexibility. 9 Technological innovation, especially the innovation and improvement of electric load forecasting technology, is particularly important for promoting the development of the electric industry.
1.1 | Short-term electric load forecasting method

| Traditional forecasting method
In the past decades, the development of mathematical theory and modern computing technology has promoted the continuous improvement of load forecasting methods. Including traditional forecasting methods and intelligent algorithms. The rapid development of neural networks benefits from the fetching of Big Data and the development of large-scale computing power, which consists of highly parallel processing units. However, the state-of-the-art neural network models progressively evolve at the cost of the model scale. That is, the excellent performance is followed by ever-increasing computation consumption and memory demand. 10 This is for traditional forecasting techniques such as time series, [11][12][13][14] regression analysis, [15][16][17][18] and gray analysis. [19][20][21][22] With the continuous development and progress of society, risk factors will follow. And the various risks faced by the electric electricity industry are constantly increasing. Therefore, the forecasting effect obtained by using the traditional forecasting method to forecast the electric load is weakened.

| Intelligent forecasting method
In recent years, with the continuous development of a mathematical theoretical basis and the continuous improvement of Internet technology. The technology and method of forecasting are also constantly improving. The improvement of theory and technology provides the basis for our research. To improve the forecasting accuracy of the electric load, we can use these advanced technical means and rich theoretical knowledge to forecast the electric load. With the continuous development of science and technology and the continuous improvement of theoretical knowledge, various intelligent forecasting algorithms are also constantly developing and innovating. The methods and comparison methods used in this paper. Such as generalized regression neural network (GRNN) model, short-term memory neural network LSTM, 23 support vector regression SVR, 24 cyclic neural network RNN, 25 RNN-CNN neural network fusion algorithm, 26 generative FAN ET AL. | 2445 adversarial networks (GAN) 27 Neural Architecture Search (NAS) 28 and other modern intelligent algorithms, are some of the most commonly used forecasting methods. These methods are based on more perfect theoretical knowledge and more developed science and technology innovation. It can solve the forecasting problems caused by more complex factors and further improve forecasting accuracy.
Based on Table 1, it is clear to learn about the advantages and disadvantages of each method. By comparing the advantages and disadvantages of each method, we can see that the GRNN method has many advantages. The electric load itself is nonlinear and the data is large. GRNN has the ability of nonlinear mapping, strong data learning ability, flexible network architecture, good fault-tolerant performance, and stability that can effectively solve the problems encountered in load forecasting. Next, it will further illustrate the advantages of this forecasting method through an example analysis.

| Electric load short-term forecasting method
In this paper, to forecast the electric load we study, we introduce a new modern intelligent forecasting algorithm, whose model is GRNN. Specht 29 introduced a probabilistic neural network method GRNN, a learning algorithm for function approximation. GRNN is a nonparametric one-way learning algorithm with a highly parallel structure. It does not make any assumptions about the form of the basic distribution. GRNN is simpler than other existing algorithms. The advantage of this algorithm is that its implementation is very simple, and it does not need experiments and error procedures, nor does it need prior knowledge about parameters. 30 Even if the number of samples is insufficient, the output results of GRNN can converge to the optimal regression. By reducing the risk of using local optima and improving the learning rate and generalization ability. This algorithm has been applied in many forecasting fields. 26,[31][32][33][34][35] For example, based on the results from Niu et al. 26 GRNN is the preferred of many soft computing techniques because of its ability to evaluate continuous variables through rapid training. Similarly, it can evaluate a function directly from the training data without repeating the training course and can estimate any random function between the input and the response. Few researchers have effectively applied GRNN to unconventional processing problems, 36,37 electric field, 38 medical field, 39 image processing field, 40 and other different fields. [41][42][43][44] Meanwhile, the GRNN has a nonlinear mapping ability and fast learning speed. And can converge to optimized regression through more sample aggregation. For GRNN, even if the training sample is small, the forecasting results can be satisfactory, 43 especially in the aspect of optimizing the smoothing factor of GRNN. 26,[45][46][47] GRNN also has its limitations, such as high computational complexity and spatial complexity, which will increase the difficulty of forecasting. At the same time, although the forecasting effect of GRNN has good accuracy compared with the above traditional forecasting methods. There are still certain limitations in the forecasting of data based on the single model of GRNN. 43 T A B L E 1 Comparison of advantages and disadvantages. For example, a single forecasting model cannot process the data, which will increase the forecasting error and weaken the forecasting effect due to the large fluctuation of the data or a large amount of data. The single forecasting model cannot describe the electricity consumption behavior. And the forecasting error will be increased due to the complexity of the electricity consumption behavior, so the forecasting effect is not significant. A single forecasting model can not take all kinds of complex factors into account, which will lead to an unsatisfactory forecasting effect. Based on this, we choose to build an integrated model to improve the accuracy of the forecasting.

| Research motivation and innovation
This paper is based on city data for short-term electric load forecasting, which belongs to the data form with relatively small training samples. Therefore, compared with other intelligent forecasting methods. This model algorithm is well suited to urban electric load data forecasting, which has a large amount of data and a small range of data fluctuations, and the forecasting accuracy is more accurate. The advantage of this forecasting method lies in the empirical wavelet decomposition (EWT), through which the nonstationary sequences become stationary, avoiding the problem of modal aliasing, reducing the complexity of calculation, and improving the accuracy of forecasting. EWT 48 is a data decomposition method superior to empirical decomposition (EMD). 49 EMD, EWT and variational mode decomposition (VMD) are commonly used signal decomposition methods. EMD has problems such as mode aliasing, sensitivity to noise data, and boundary effects. The signal decomposition effect of EMD is not as good as that of VMD and EWT. Compared with VMD, EWT can extract sub-signals with narrow bandwidth according to the Fourier spectrum of the signal. 50 EWT decomposes nonstationary original sequences to obtain several relatively stable new sequences. And then only needs to forecast several groups of data obtained after decomposition. The data volume is reduced by decomposition, which simplifies the computational complexity limitation of the GRNN forecasting method itself. Meanwhile, wavelet decomposition combines the EMD method and wavelet transform theory. 51 Therefore, compared with the EMD method, the EWT method overcomes the problem of mode mixing caused by signal time-frequency scale discontinuity and the problem of over-envelope and under-envelope. It can be found that the EWT method is superior to the EMD 49 method through theoretical and performance observations. EWT method reconstructs the decomposed data to obtain a set of amplitude modulation and frequency modulation components and adaptively extracts different frequency components of the signal. In terms of data decomposition, the trouble of finding different frequency components of the extracted signal can be avoided. Completely nonrecursive VMD. The idea of VMD is that the signal to be decomposed is composed of different IMF sub-signals. To avoid modal aliasing during signal decomposition, VMD abandons the idea of a recursive solution used by traditional signal decomposition algorithms when calculating IMF. VMD adopts completely nonrecursive modal decomposition. Compared with the traditional signal decomposition algorithm, VMD has the advantages of a nonrecursive solution and independent selection of the number of modes. The algorithm can decompose the transient zerosequence current signal of the jth line into K eigenmode functions with a central angular frequency of, where K is the number of artificially specified modal components. It can achieve simultaneous extraction of the decomposed models. The model looks for a set of models and their respective center frequencies so that the modes together reproduce the input signal, while each model is smooth after demodulation to the baseband. The essence of the algorithm is to extend the classical Wiener filter to multiple adaptive bands so that it has a solid theoretical basis and is easy to understand. The alternate direction multiplier method is used to optimize the variational model effectively, which makes the model more robust to the sampled noise. Completely nonrecursive VMD the spectral bands of long-term modes change dramatically over time and overlap on a global scale. By comparison, EWT is better than completely nonrecursive variational model decomposition in avoiding model aliasing. The decomposed data set obtained by EWT is random, and the decomposition makes the original nonstationary sequence randomly generate several stationary sequences. EWT adaptively decomposes the original sequence into multiple subsequences. 52 In this paper, we verify the effect of the decomposed data by regrouping the decomposed data and comparing it with the original data. Effective recombination of decomposed data can weaken the randomness of data decomposition and thus obtain a group of the most appropriate decomposed data. A group of appropriately decomposed arrays can provide a good basis for data forecasting and improve the accuracy of forecasting.
To better solve the optimization problem, various population intelligent optimization algorithms have been proposed. But these optimization algorithms have been widely used in many fields. 53 We propose a new optimization algorithm-the sparrow search algorithm (SSA). 54 The importance of population is inspired by the predation and anti-predation behavior of sparrows. To get the best factor. This method of SSA to find the best position to get the best factor is just suitable for finding the smoothing factor in GRNN, and the optimal smoothing factor is found by the sparrow optimization method. The output data and training sample errors of the GRNN neural network are mainly determined by the smoothing factor. Therefore, GRNN neural network has a very simple performance control mode, and better performance can be obtained only by adjusting the smoothing factor. The ability to forecast risk factors is relatively weak while that of smoothing factors is relatively strong. Seeking the best smoothing factor is equivalent to finding the risk factor with the least risk. Therefore, SSA can help find the optimal smoothing factor and then make the forecast. SSA is a new swarm intelligent optimization algorithm, which completes the code operation by simulating the foraging behavior and anti-predation behavior of sparrows. The EMD process first needs to determine the local extreme points of the signal, and then use the cubic spline to connect all the local maximum and minimum values to form the upper and lower envelopes, and then get the mean curve from the upper and lower envelopes. In the process of obtaining the envelope, when there is an abnormal event in the signal. It will inevitably affect the selection of the extreme points, making the distribution of the extreme points uneven, resulting in the combination of the local envelope of the abnormal event and the real signal envelope. The mean value calculated by the envelope and the IMF component filtered out contains the inherent patterns and abnormal events of the signal or the inherent patterns of the adjacent characteristic time scales, resulting in pattern aliasing. Compared with PSO 23 and other algorithms, SSA uses several adjustment parameters and has a relatively fast convergence speed and simple calculation. 55 According to the behavior of sparrows, the sparrows are divided into three groups, which are the discoverer, the joiner, and the forewarning. The predation and antipredation behaviors of sparrows contribute to effective inter-colony communication. The shortest path from start to finish in electricity usage is determined using SSA because SSA can quickly discover solutions in GRNN. 55 SSA is optimized by residual energy and distance to overcome the limitation of uncertain convergence time. The foraging behavior and antipredation behavior of sparrows are extremely complex group activities. The electricity data used in this paper are urban electricity data. The main contributors of which are all kinds of industrial and enterprise electricity consumption data, whose electricity consumption behavior is greatly influenced by external factors and the group behavior is relatively obvious. The predatory and anti-predatory behavior of sparrows is relatively complex and has obvious variability and uncertainty characteristics, which are very similar to the variability and uncertainty characteristics of urban electric load. Therefore, SSA can better simulate urban electric load through sparrows' predatory and antipredatory behavior and better deal with its variability and uncertainty characteristics. Thus further improving the forecasting accuracy through this optimization method. The electricity consumption behavior of urban industries is relatively complex, which is similar to the foraging behavior and anti-predation behavior of sparrows. Therefore, the SSA proposed in this paper can describe the electricity consumption behavior characteristics of urban industries well.
It is the goal of the current electricity analysis to constantly improve the forecasting accuracy of electric load forecasting. The influencing factors of power load are relatively complex. Through analyzing the load change and the degree of correlation between the influencing factors, find out the main influencing factors that affect the load change, to determine the law of load change with the influencing factors. The factors affecting the power load characteristics can be divided into time factors, electricity price factors, economic factors, meteorological factors, and so forth. According to the industry category, the load has significant cyclical and seasonal changes. At the same time, various problems faced by electric electricity are also increasing, and in some aspects. The problems are becoming more severe. Therefore, we need to constantly search for new forecasting methods to improve forecasting accuracy. Of course, the improvement of forecasting accuracy cannot be separated from the support of theories and the development and progress of science and technology in today's world. Therefore, we should have a sufficient theoretical basis and be good at combining with modern intelligent methods when making forecasting.
In this paper, based on the short-term load forecasting of urban electricity data, a forecasting algorithm of GRNN based on Sparrow Optimization (SSA) after EWT is proposed. EWT avoids modal aliasing and other problems, which is better for data decomposition. The cause of mode aliasing is a mainly intermittent phenomenon, which is often caused by abnormal events (such as intermittent signals, pulse interference, and noise). The GRNN model has higher accuracy than other modern intelligent algorithm forecasting models. The SSA optimizes the model by searching for smooth factors. Strong global search ability, fast search speed, and fast convergence are the advantages of SSA. 56,57 Because of its highperformance search ability, SSA can search the potential area of the global optimal well, and can effectively avoid falling into the local optimal problem. 58,59 It was found that the combination of the GRNN and SSA proposed in this paper is a relatively innovative method in electric load forecasting. And through continuous in-depth analysis and research, it is found that this method is more suitable for urban electric load data series with a large amount of data and a small fluctuation range of data. This ensemble model has been greatly improved in terms of forecasting accuracy, high-precision electric load forecasting can solve the contradiction between supply and demand in the electricity industry, provide an effective basis for the long-term stable development of the electricity grid, and provide a reference index for the state to formulate electricity policies and manage the electricity industry. Accurate forecasting can provide a basis for the production capacity of the electricity industry, to produce electric energy reasonably and allocate the generated electric energy reasonably to avoid the waste of resources. It provides a reference basis for the government to formulate an electric electricity policy and guarantees the reasonable and effective provisions of the system to promote the stable development of the social economy and social progress. This paper focuses on the study and analysis of different forecasting methods to find a suitable model for short-term electric load forecasting, and through real cases to prove the real availability of the forecasting method.
In the next part of this paper, we will conduct in-depth research and analysis of the following content. Section 2 briefly introduces the theoretical knowledge of the model used in this paper, including EWT, generalized regression neural network model, and SSA. At the same time, it briefly outlines how to use the integrated model to make short-term forecasting of electric load and presents it in the form of a flowchart. In Section 3, the forecasting process of the proposed EWT-SSA-GRNN integrated model is elaborated, and the electric load forecasting of a city in southern Australia is analyzed as an example. In Section 4, the forecasting effect of other models and that of the integrated model introduced by us are compared and analyzed by different metrics to evaluate the overall forecasting effect of the integrated model and point out the innovation points of the model. Section 5 draws conclusions and points out the shortcomings of the model and gives constructive suggestions.

| EWT model
The principle of the EWT method is to divide the Fourier spectrum of the signal into continuous intervals, and then construct wavelet filter banks on each interval for filtering. Finally, a group of amplitude-frequency modulation components is obtained through signal reconstruction. The proposed method can identify the location of feature information in the Fourier spectrum of the signal by using a wavelet filter structure with tight support characteristics and extracting different frequency components of the signal adaptively. An empirical wavelet is a band-pass filter bank defined on the interval Λ n , which is designed by using the idea of constructing (Littlewood-Paley) and (Meyer) wavelets with n > 0. The empirical wavelet function ψ ω ( ) n and empirical scale function φ ω ( ) n , are dressed by the following equation: (1) Using the idea of the classical wavelet transform for reference, the empirical wavelet coefficients constructed by Gilles 60 are generated by the inner product, and the details coefficients W n t ( , ) f e , are generated by the empirical wavelet function ψ n and signal f t ( ) inner product, which can be written as follows: The approximation coefficient W t (0, ) f e , generated by the empirical scaling function ψ n and the inner product of the signal f t ( ), can be written as follows: After EWT processing, the signal f t ( ) is decomposed to obtain the AM-FM single component whose frequency is low to high As can be seen from Equations (5) and (6), EWT is a method to deal with nonstationary signals. This method uses the Fourier transform in data forecasting and gets the normalized Fourier spectrum within a certain range. This method decomposes the data into components of different frequencies, avoids the problem of mode aliasing, reduces computational complexity, and improves the accuracy of forecasting.

| VMD model
VMD converts signal decomposition into variational decomposition mode, which is essentially multiple adaptive Wiener filter banks. VMD can realize adaptive segmentation of each component in the signal frequency domain, effectively overcome the pattern aliasing phenomenon caused by EMD decomposition, and has stronger noise robustness and weaker end effects than EMD. In the process of VMD decomposition, classical Wiener filter, Hilbert transforms and frequency mixing are involved. It is assumed that the multicomponent signal is composed of modal components with limited bandwidth, and the center frequency of each IMF is the constraint condition of decomposition, in which the sum of all modes is equal to the input signal. The following describes how to implement VMD. After Hilbert transformation, the analytical signal is obtained and the single side spectrum is calculated, and then multiplied by the center band modulated to the corresponding fundamental band. calculate the norm of the demodulation signal gradient above, and estimate the signal bandwidth of each mode.
In Equation (7), to obtain the optimal solution of the constrained variational problem, the Lagrange multiplication operator and quadratic penalty factor α are introduced to transform the constrained variational problem into an unconstrained variational problem α, guarantees the signal reconstruction accuracy in the presence of Gaussian noise.
Keep the constraints rigid. The augmented Lagrange expression is as follows: Then the multipliers alternate direction algorithm is used to solve the above problem, and each component and its central frequency are constantly updated. Finally, the saddle point of the unconstrained model is obtained, which is the optimal solution to the original problem.
VMD is a decomposition mode that converts the signal to be decomposed into nonrecursive and variational modes and can decompose the noise signal well. The overall framework of VMD is a variational problem. Assuming that each mode is a finite bandwidth with different center frequencies, each mode and its corresponding center frequencies are constantly updated by using the alternating direction method of the multiplication operator. After the noise signal is decomposed, each variable mode component and its center frequency can be obtained.

| Difference and connection between EWT and VMD
EWT is a new adaptive signal decomposition method, which combines the adaptive decomposition concept of the EMD method and the tight support framework of wavelet transform theory, and provides a new adaptive time-frequency analysis idea for signal processing. Compared with the EMD method, the EWT method can adaptively select the frequency band and overcome the mode aliasing problem caused by the discontinuity of the signal time-frequency scale. At the same time, it has a complete and reliable mathematical theoretical basis, low computational complexity, and can overcome the problem of over-envelope and under-envelope in the EMD method. The principle of the EWT method is to divide the Fourier spectrum of the signal into continuous intervals, then construct wavelet filter banks on each interval for filtering, and finally obtain a group of AM and FM components through signal reconstruction. This method can identify the position of the feature information in the Fourier spectrum of the signal using the wavelet filter bank with tight support characteristics, and adaptively extract the different frequency components of the signal.
VMD is a new time-frequency analysis method. This method can effectively process linear and stationary signals, but it also has the characteristics of being sensitive to noise. When there is noise, it may cause modal aliasing in the decomposition. VMD transfers the acquisition process of signal components to the variational framework, adopts a recursive processing strategy, and decomposes the original signal by constructing and solving the constrained variational problem, which can effectively avoid modal aliasing, over-envelope, overenvelope, boundary effect, and other problems. The decomposition process of VMD is the solution process of the variational problem. In this algorithm, the intrinsic mode function (IMF) is defined as a bandwidth-limited amplitude-frequency modulation function. The function of the VMD algorithm is to decompose the original signal into a specified number of IMF components by constructing and solving the constrained variational problem. The filter used in this process is the Wiener filter.
Both EWT and VMD methods can avoid modal aliasing, and over-envelope and under-envelope problems, but the VMD method may cause modal aliasing in decomposition when there is noise. At the same time, EWT constructs a wavelet filter according to the boundary frequency of components, while VMD constructs a Wiener filter according to the central frequency of components. The filters they construct are also different. The number of components obtained during decomposition will also be different. When the mode selection value is small because the VMD algorithm is equivalent to an adaptive filter bank, some important signals in the original signal will be filtered, affecting the accuracy of the subsequent forecast, so the EWT method has certain advantages to decompose.

| GRNN
GRNN is a radial basis function network based on mathematical statistics and its theoretical basis is nonlinear regression analysis. GRNN has strong nonlinear mapping ability and learning speed. At last, the network generally converges to the optimal regression with large sample size agglomeration. When the sample data is small, the forecasting effect is very good, and can also deal with unstable data. GRNN schematic diagram is shown in Figure 1.
The theoretical basis of GRNN is nonlinear regression analysis. Let the joint probability density function of random variables x and random variables y f x y ( , ), and the known x observations are X , then the relative regression y (the conditional mean) is X . Ŷ is the forecasted output of Y when the input is X . It is shown in the following equation: . It is shown in the following equation: where X Y , i i is the sample observation of random variables x, and y. n This is the sample size. p This is the dimension of a random variable x and σ is the width coefficient of the Gaussian function, that is smoothing factor.
The order of exchange integral and addition is taken into account. And the dependent variable corresponding to the sample point closest to the forecasting point is given greater weight, thus a better forecasting result is obtained.

| 2451
The errors of output data and training samples of the GRNN neural network are mainly determined by the smoothing factor. Therefore, GRNN neural network has a very simple performance control mode, and better performance can be obtained only by adjusting the smoothing factor.

| SSA
The SSA is a kind of swarm intelligence optimization algorithm, which is mainly inspired by the sparrow's foraging and back-feeding behavior. Its bionic principle is in the process of sparrow foraging, it is divided into discoverer, warning, and participator. Discoverer and early warning are responsible for finding food in the population and providing foraging areas and directions for the whole sparrow population, while the participator uses the discoverer to obtain food. The behavioral characteristics of the discoverer are expressed in the following equation: (1) For discoverers: where T represents the current number of iterations of the algorithm, and i represents the i-th sparrow in the population, which also refers to the ith discoverer in this formula. X i j T , represents the j-dimensional coordinate position of the current ith discoverer. The random value ∈ α (0, 1], Maxlter represents the maximum number of iterations, Q is a random value that obeys the normal distribution. L represents a column vector of the same dimension as the sparrow individual, and the constituent elements are all 1. The size of the early warning value ∈ R R ( [0,1]) 2 2 and the safety value ∈ ST ST ( [0.5, 1]) determines the location update mode of the discoverer. In this paper, R 2 is set to a random value, while ST is set to a quantitative value. And each iteration is compared with the resulting R 2 so that the discoverer is not fixed in a way of a location update.
(2) For participators: where i represents the ith sparrow in the population, in Equation (12) also refers to the ith participant. Xworst is the current worst foraging position. X P T is the best foraging location searched by the discoverer in the current Equation (12). X i j T , representing the coordinate location of the j dimension of the current ith participator.
Q and L play the same role in Equation (12); A represents a column vector with the same dimension as the sparrow individual. The internal element is composed of 1 and −1, and n represents the number of participators in the population. When  i n/2 the participant will actively follow the discoverer to move to a better foraging position. When  i n/2 the participant will get rid of the current poor foraging position combined with the characteristics of exp the function.
(3) For forewarning: where f i represents the adaptation value of the early warning person. f f , g w represents the current global optimal fitness value and the worst adaptation value, respectively. X X , best worst is the current global optimal foraging location, and the worst foraging location X i j T , represents the coordinate location of the j dimension of i warning.

| The EWT-SSA-GRNN
The forecast process of the short-term load forecast model based on EWT-SSA-GRNN is as follows: Firstly, the random nonstationary electric load is decomposed into different stationary components by the EWT method. Through the modal analysis of the different stationary sequences obtained by decomposition, it can be seen that they have different behavior characteristics in different modes. GRNN forecasts the load of each subsequence derived from EWT decomposition and then reconstructs the forecasted results of each subsequence to obtain the final forecast results. The forecasting results of the forecasting model are random, so the results are different each time for each component. Therefore, we obtained a new set of electric loads by cycle-forecasting the different components and comparing the selection from each set of different forecasting results, and finding out the appropriate components for reconstruction. This group of loads derived from the reconstruction is our forecast. To further improve the forecasting accuracy of the forecasting results based on the GRNN model, we use the SSA to optimize the relevant parameters. Further improving the forecasting accuracy of the electric load of the model The flowchart is shown in Figure 2.
The specific steps are as follows: Step 1: Data modal analysis. First of all, bring the raw data (n) into the formula, W n t f ψ is calculated, then, the original sequence is decomposed into multiple subsequences adaptively by formula, , and the decomposed multiple sequences are analyzed and studied as the original input variables.
Step 2: Data testing and verification. The data f t ( ) that has been processed in the first step is loaded into the algorithm, and the data is divided into the training set and test set according to a certain proportion, and the random subpackage function is used for cross-verification. Here the proportionally allocated training set is used as a marker for the fourfold observation sample. The tag contains the same or similar proportion of 1 murk, which divides the sample into K mutually exclusive subsets. In the cross-test, three data are used as training data(train), and the remaining one is used as test data(test). Finally, this practice is cycled, and a different fold is selected as the test set each time.
Step 3: Find the best smoothing factor. The proportion of the test set (test) and training set (train) that have been divided in the second step is substituted into The flowchart of the proposed method.

, then
. adders, when i n > /2, then  ( ) , + , and fore- warning, when . By changing the value before and after, comparing the value of MSE, then the smallest MSE population is the best smoothing factor (Best_pos) as the optimal parameter forecasted in the next step. If in the process of comparison, it does not meet the conditions of the judicial function, it will be re-brought into the second step to find it in a loop.
Step 4: GRNN forecasting. The optimal parameters obtained(Best_pose) in the third step are substituted into the algorithm. First, the data f t ( ) are normalized to forecast.
After outputting the forecasting results, the forecasting results are tested by the net p value test, and the forecasting results of the net p value test are output again. To get the optimal forecasting results, we add the t-test, and the output result through the t-test is the best forecasting result.

| The analysis of sequence by EWT
In this paper, a short-term load forecasting model is established, and the forecasting results are obtained by optimizing the electric load of a certain city. The electric load of a city from August 13, 2007, to August 19, 2007, is selected for 24-hour short-term load forecasting at an interval of half an hour. The electric load signal is input into the six components obtained by EMT model decomposition, and the decomposition result is shown in Figure 3: There are also some differences in the volatility between the stationary series obtained by the decomposition of the nonstationary series, and different frequencies of fluctuation will have different effects on the forecasting results. It can be seen from Figure 3 that the fluctuation frequencies of mode 3, mode 4, mode 5, and mode 6 are higher and belong to high frequency, while the fluctuation frequencies of mode 1 and mode 2 are relatively lower, especially the fluctuation frequencies of mode 1 are lower and seem to be stable and belong to low frequency. Based on Figure 3, WE can intuitively observe that the decomposed sequences are in sequence from low frequency to high frequency, and the decomposed sequences are more stable than the original data. Wavelet decomposition decomposes the nonstationary original sequences to obtain several relatively stable new sequences. From the sequence decomposition diagram of EWT, we can see that the adaptive decomposition diagram of EWT has been decomposed from high frequency to low frequency to the extent that it can no longer be decomposed. From the sequence decomposition diagram of VDM, it can be seen that it is also decomposed from high frequency to low frequency, and the corresponding spectrum diagram can also be seen. It can be seen from the figure that both decomposition methods can achieve good decomposition results. However, in the following forecast process, it can be seen that using EWT decomposition to forecast results will be better.

| Model forecasting and model optimization
This paper selects the electric load of a certain city and uses the generalized regression neural network (GRNN) model. Through the observation, it can be found that the model still obtains a good forecasting effect when forecasting relatively large and nonstable data sequences such as the urban electric load forecasting. However, with the emergence of more complex factors, the accuracy of the forecasting can not achieve the desired effect, and the simple forecasting methods can not meet people's forecasting needs, so we need to further explore ways to improve the forecasting accuracy. The development of science and technology and the improvement of theoretical knowledge provide a good foundation for the improvement of the forecasting method, among which the most prominent one is to optimize the model of the forecasting method to further improve the forecasting accuracy of the forecasting method.
Because different optimization models and forecasting models have different degrees of adaptability and different degrees of optimization effect, an optimization model called SSA is proposed in continuous comparison. The optimization model simulates the predation and antipredation behavior of sparrows, which is consistent with the electricity consumption behavior of the city, so the optimization model has good adaptability to optimize the forecasting model, and further improves the forecasting accuracy. As shown in Figure 4, we can see that the forecasting accuracy is significantly improved.
From the forecasting results of Figure 4, we can see that the forecasting effect of the forecasting model not optimized above is significantly lower than that obtained by the optimization of the forecasting model below. Therefore, we can further illustrate that the optimization method further improves the forecasting accuracy of the model.
In terms of the development of the electric electricity industry, what human beings pursue is the sustainable development of energy, especially in the serious waste of resources in recent years and the frequent mention of green energy, which makes human beings increasingly aware of the importance of sustainable energy development. Forecasting of electric load is from the source of electric electricity development to realize the sustainable F I G U R E 3 The EWT and VDM decomposition. FAN ET AL. development of energy, the forecasting of electric load first for the electricity industry electricity supply provides a strong guarantee to a certain extent to avoid excess capacity leading to waste of resources, secondly for the government to formulate feasible electricity policy provides a reference index can optimize the allocation of resources, the final reasonable use of resources to a certain extent reduce the destruction of ecological protection effect. It is these advantages that constantly promote the development of forecasting methods and optimization methods, and also put forward higher and higher requirements for the forecasting accuracy of electric load.

| parameter of the model
To verify the effectiveness of the forecasting models mentioned in this paper, the forecasting effects of EWT-SSA-GRNN, EWT-GRNN, GRNN, LSTM, SVR, CNN-RNN, and RNN forecasting models were selected to compare the forecasting effects. The parameter settings for the comparison model are shown in Table 2 Figure 5.
It can only be seen from Figure 5 that the trend of the forecasting results of each forecasting model is generally consistent with the trend of the real data. Figure 5 shows | 2457 that the methods we have chosen have their advantages so that the forecasted trend of the forecasting method in the chart is consistent with the fluctuation trend of the original series, and we illustrate the advantages of the method we chose through the method of local research. From the comparison of forecasting results of the second model in Figure 5, IT can be seen that the results forecasted by the integrated model of VDM-GRNN and VDM-EWT-GRNN are significantly different from those forecasted by the integrated model of EWT-SSA-GRNN. The EWT-SSA-GRNN integrated model is most consistent with the trend of the original data. Therefore, the integrated model of VDM-GRNN and VDM-EWT-GRNN cannot achieve a good forecasting effect. In conclusion, we can see that EWT-SSA-GRNN integrated model is the best method to forecast. Figure 6 shows the general trend of each forecasting method. What is shown in the figure is that the fluctuation trend of each forecast effect is generally the same, and it is difficult to get the result through intuitive observation. For this reason, we choose to perform a partial amplification analysis on the graph. The right side is the partial enlargement of the peaks and valleys in the fluctuation trend of the selected model. From the partial graph on the right side, we can intuitively see that the integration method we choose is more consistent with the real data in the fluctuation trend than other methods, so it has higher forecast accuracy. The main observation in Figure 6 is the fluctuation trend of electric load with time. Since the factors affecting the characteristics of electric load can be divided into time factors, electricity price factors, economic factors, meteorological factors, F I G U R E 6 Partial enlargement of the forecasting method comparison chart. and so forth, the fluctuation trend in the figure is affected by these factors.
The fluctuation of the image shown in Figure 6 is mainly caused by the complex electric consumption behavior of industrial electricity and commercial electricity consumption and other large electricity units, especially we can study the electricity consumption behavior of these large electricity units from the trough and peak and then have an overall grasp of the urban electric data. From the peak period of electricity consumption and the trough period we can roughly have an analysis of the city's electric data, in the peak period should be these large electricity units at the beginning of the day of electricity, in a variety of production workshops and enterprise buildings are consuming electricity, in the trough stage of these electricity units should be to the end of the work time of the electrical appliances in each workshop are turned off to reduce energy consumption into a small electricity unit of residential electricity, the electric supply industry should be based on these to choose the appropriate time to supply electric and how much electricity is provided. From the forecasting results in Figure 6, WE can see that the forecasting method has higher accuracy and more accurately forecasts the urban electric data, which provides a good theoretical basis for the electric supply industry. With the continuous development of the economy and the gradual expansion of energy demand, electric energy has become the key factor of economic development and the electric load is the best measure of electric energy, providing sufficient guarantee for the operation and production of various industries.
Through the observation of the first two graphs, we can not get the desired results, and then we conducted a more detailed analysis of the comparison graph, from Figure 6 we selected the most prominent two places and zoomed in, from the two enlarged plots on the right can observe that the optimized forecasting results are more relevant to the real data.
From the local amplification analysis of the second figure, we can see that there are many big differences between the results obtained by using the integrated model of VDM-GRNN and VDM-EWT-GRNN and those forecasted by the integrated model of EWT-SSA-GRNN. By observing the first local figure on the right, it can be seen that although the forecasting using the integrated model of VDM-GRNN and VDM-EWT-GRNN has the same trend as that using the integrated model of EWT-SSA-GRNN, there are huge differences between the data. The second local graph on the right shows that there is no consistency between the forecasted trends when the forecast analysis is performed. Therefore, it can be seen that EWT-SSA-GRNN integrated model is used to obtain the best forecasting effect.

| evaluating indicator
This paper uses the goodness of fit (R 2 ) in Equation (14), to test the forecasting model, Used to compare how well their forecasting match what happened; the average absolute error (MAE) expressed by Equation (15) can avoid the problem that errors offset each other, Therefore, it can accurately reflect the actual size of the forecasting error; Equation (16) is the mean square error (MSE), This indicator is a measure of the degree of difference between the estimator and the estimated quantity; Equation (17) is the root mean square error (RMSE), The index is the square root of the ratio of the deviation between the forecasted value and the true value to the number of observations n. In the actual measurements, The number of observations n is always finite, True values can only be replaced by reliable (best) values; Equation (18) is the average absolute percentage error (MAPE), The measure itself is often used as statistical measures of forecasting accuracy, Thus, the index can describe the accuracy. In summary, we used these five metrics to evaluate the effectiveness of the forecasting model. There are also slight differences in these five indicators, such as R 2 MAE, MSE, RMSE, and MAPE. The smaller the value of the forecasting electricity of different forecasting models, the closer the value is to 1, and the better the forecasting electricity of the model. The formula for these five metrics is as follows: Among them, are the number of observation data points, the actual value of t-time, the forecasted value of t-time, and the average value of t-time.
The measurement of forecasting error has its unique advantages in various fields. Accurate measurement of forecasting errors can help us solve many social life problems, such as in terms of electricity, we can modify the production of electricity through the forecasting of errors, which can eliminate the waste of more production of electricity as much as possible, and also avoid the economic losses caused by insufficient electric supply to people's lives.
From the above multiple error indicators, select two indicators with a small data span to make a stereo chart as shown in Figure 7, from the resulting phase we can observe that the two indicators have a consistent trend in the description of the data, their fluctuation trend has consistency, and from the figure, we can intuitively see that the EWT-SSA-GRNN forecasting residual is the smallest and the forecasting effect is the best. It also shows that the two indicators are consistent in describing how good the forecasting method is. Other indicators are relatively large in data span, so we will not conduct indepth research here, but from the data in the table, we can still clearly feel that these indicators are consistent in the test of error.

| KSPA test
The KSPA test is a complementary statistical test for the determination of forecasting accuracy in two sets. It is a nonparametric test of the Kolmogorov-Smirnov (KS) test principle. The advantage of the KSPA test is that it not only determines the forecasting distribution of the two models but also determines whether the model has a minimal random error. The test is not affected by any autocorrelation in the forecasting error.
First, a two-sample two-sided KSPA test (hereinafter a two-sided KSPA test) was used to determine whether there was a statistically significant difference between the two forecasting error distributions. The null hypothesis is that there is no significant difference between the two statistical forecastings, when the two-sided KSPA test produces test statistics below the significance level (usually 1%, 5%, or 10%), the null hypothesis is rejected, and the alternative hypothesis that the distribution of unit area of forecasting error is accepted. In this case, there are statistically significant differences in the forecasted distributions provided by the model and therefore statistically significant.
First, the statistically significant difference between the proposed forecasting model and the six comparison models was confirmed. A one-sided KSPA test was then used to identify the proposed model and to compare the low random error reported by the forecasting.
Based on the data from Australia, the forecastings obtained using the EWT-SSA-GRNN model outperformed the comparative models based on the computational error statistics. Thus, there are significant differences between the proposed model and the comparison model. The KSPA error distribution and the empirical cumulative distribution function are given in Figures 8 and 9. The proposed EWT-SSA-GRNN model describes the random bias well, with smaller errors and high forecasting accuracy.
From the data analysis in Table 3, it is known that the p value of each set of models is less than 0.05, so the error in each group of models is relatively small, and the forecasted data obtained is relatively accurate. However, in contrast, the EWT-SSA-GRNN model combination is more accurate the p value is below 0.01, so our data is more accurate under the p value correspondence of each set of models (Table 4).

| Model evaluation
In this paper, we adopt different metrics to demonstrate that our chosen ensemble model has more advantages in improving forecasting accuracy. We first map the integrated model we adopted with various other models. Figures 5 AND 6  the form of numbers, and the comparison of the errorindex result size of each forecasting model can further observe the forecasting effect of each forecasting model. Both of the above metrics prove that our selected ensemble model can improve the forecasting accuracy very well. Finally, the selected integration model was further tested and passed the consistency test, which further proves that our selected integration model is more advantageous.

| Model innovation
The different indicators show that our chosen integration model has more advantages in forecasting, so what are its advantages? First of all, through the EWT of electric load decomposition into a different stable sequence, the smooth sequence forecasting can partly avoid the forecasting error due to large fluctuations, and the decomposition model compared with other traditional decomposition models and has the advantages of can avoid modal aliasing, so it can improve the forecasting accuracy to a certain extent. Second, the SSA model is used to optimize the electric load, which seeks the smooth factor by simulating the sparrow predation and anti-predation behavior. The predation and antipredation behavior of the animals simulated in this optimization method is very irregular and uncertain, which is extremely similar to the uncertainty of the electricity consumption behavior of various enterprises and public institutions in the cities. Therefore, the optimization of this method has good results, which further improves the forecasting effect of the model and improves the forecasting accuracy of the electric load. Finally, the generalized regression neural network model is used to forecast the decomposed electric load according to the smooth factor found by the sparrow optimization. From the observation of the forecasting results, it can be seen that the forecasting model has more advantages in forecasting the electric load than the other forecasting models. The forecasting results obtained by using the generalized regression neural network model are random, and the results are different each time the decomposed sequence is tested by using this method, r. It is the stochastic nature of the forecasting model that provides us to further improve the forecasting accuracy. To obtain the optimal forecasting results, we use the method to forecast the decomposed sequence of the cycle F I G U R E 9 Experience-based cumulative distribution. and get different forecasting results, and then select different results of each forecasting result to reconstruct a set of new data, for each reconstructed data calculation of error index and through the comparison of error indicators to further select a set of good data, continuous cycle above work to find a set of optimal data. Using the forecasting method to reconstruct the data is our indepth research and analysis of the electric load, which has a certain theoretical basis and is further confirmed in the electric load forecasting. It is also the unique advantage of our method and an innovation point of our method. Each method has its limitations, which is an inevitable law, and our method is inevitably flawed. Although we selected the integration model to improve the accuracy of the forecasting and also inevitably increase the workload of data processing, especially in the data reconstruction, in addition, it forecasts the random different sequences to reconstruct and is the calculation of error indicators, which undoubtedly increases our workload.

| CONCLUSIONS
Aiming at the nonlinearity and randomness of electricity load sequence, a hybrid model combining EWT, SSA, and GRNN was established. First, the original load sequence is decomposed into multiple modes to weaken the volatility of the sequence affected by complex indicators. Then, SSA is used to optimize the smoothing factor in GRNN to obtain the optimal smoothing factor. Finally, GRNN forecasting was used to forecast the optimal result with the optimal smoothing factor, and EWT was used to reconstruct the forecasted data. The results show that the MAE, RMSE, MSE, and MAPE of the mixed model are the lowest, and the value R 2 is closest to 1. Therefore, the model is effective, efficient, and feasible in the electricity system.

This paper establishes a new short-term electric load
forecasting model-the EWT-SSA-GRNN model, which effectively solves the problems such as the volatility and uncertainty of electric load and further improves the forecasting accuracy. EWT model can decompose data to avoid the influence of modal aliasing. The predation and anti-predation behaviors of sparrows simulated by the SSA model have good commonality with human electricity consumption behaviors, that is, they are both characterized by uncertainty, and the electric load is further optimized. According to the randomness of the forecasting results, GRNN reconstructs the electric load forecasting process to further improve the forecasting effect. 2. Electricity is closely related to people's lives, electricity data can portray people's electricity behavior and can reflect people's demand for electricity, electricity data can reflect the economic development of a certain area to a certain extent, further reflect the living standards of residents in the area. Therefore, the forecasting of electricity load has a promoting effect on the economic development of a certain region, and we can make long-term or short-term planning for the future economic development of the region through the forecasting of electricity load. 3. The electricity industry plays a certain role in promoting the development of the national economy and social progress, so the improvement of the accuracy of electricity data forecasting can provide an effective basis for electricity production, which can avoid the waste of electricity to a certain extent and improve the utilization rate of resources. For the T A B L E 4 KSPA test results. | 2465 electricity production sector, the basis for effective electricity data forecasting can reduce production costs, which is of guiding significance for the longterm development of electricity enterprises. 4. For the enterprise sector, this increase in utilization rate not only greatly reduces the additional expenditure on electricity, but also reduces a lot of energy and financial expenditure in environmental protection, thereby promoting the sustainable development of enterprises. The state is vigorously advocating the protection and maintenance of a green ecological environment, and reasonable energy utilization is a favorable response to this aspect. 5. The development of the social economy cannot be separated from the supply and development of electric energy, and the electric load forecasting and analysis and the accuracy of forecasting for the development of the electric power industry can also promote the development of the economy. Under the current economic background, we need to continuously improve the forecasting accuracy of electric load. The improvement of forecasting accuracy requires us to select the most suitable forecasting method through continuous analysis. The EWT-SSA-GRNN used in this paper is the forecasting method suitable for the city's electric load.