An improved arnn-based user-side power load data processing method

Abstract

The application provides a user side power load data processing method based on an improved ARNN, and belongs to the technical field of data processing.S1: based on a K-means clustering algorithm, load data is classified;S2: based on an EPPS, an artificial neural network node number optimization model is solved, and an optimal matching node number scheme of each type of load curve is obtained;S3: based on a dynamic identification algorithm, a data type identification model is established, an input matrix is reconstructed, and a corresponding optimal node number is selected;S4: based on an improved ARNN, a short-term high-dimensional load dynamic prediction model is established.The application can accurately and effectively realize multi-step prediction for short-term high-dimensional load data, simultaneously considers clustering dynamic identification characteristics, can eliminate variables irrelevant to target variables, and optimizes neural network node numbers suitable for respective classes by using an EPPS, so that input data is predicted in the belonging class, and the application is suitable for solving short-term high-dimensional park load prediction problems.

Description

Technical Field

[0001] A user-side power load data processing method based on an improved ARNN belongs to the field of power load data processing technology. Background Technology

[0002] With the rapid development of the social economy and the continuous increase in the power load of the industrial park, the risk of overload on the distribution transformer equipment in the park is becoming increasingly serious, posing a hidden danger to the safe operation of the power grid. Due to the difficulty of energy storage, accurate and robust short-term load forecasting methods have become an indispensable part of the industrial park power system. The accuracy of short-term load forecasting is the foundation of the planning and operation of the industrial park power system, such as unit commitment, maintenance scheduling, pricing strategy formulation, combined heat and power, reserve extraction, and safety assessment. A related study shows that for every 1% reduction in forecasting error, a 10GW power plant can save $1.6 million annually. Therefore, accurate short-term power load forecasting not only ensures the reliable operation of the industrial park power system but also prevents the waste of power generation costs, making it crucial for the operation of the industrial park power grid.

[0003] Currently, the main methods for short-term load forecasting in industrial parks include: time series analysis, neural networks, support vector machines, regression analysis, and fuzzy forecasting. Time series analysis requires a high degree of stability in the known load sequence and performs poorly on load data with large fluctuations. Neural network algorithms are currently the most advanced load forecasting method, but they often require a large amount of data for training, necessitating long training times and significant computational resources. Support vector machine methods often involve manually selecting parameters and kernel functions based on experience in practical problems, introducing a degree of randomness. Regression analysis has a simple structure but struggles to describe various factors affecting load. Fuzzy forecasting requires a large amount of historical data in practical applications and has relatively low accuracy in short-term load forecasting.

[0004] Furthermore, short-term power load forecasting relies on existing historical data to build predictive models and forecast load values ​​for future moments or time periods. Short-term high-dimensional data is rich in information due to its high-dimensional variables; therefore, recent load data typically contains more information about near-term future evolution than older time series, making it more valuable for short-term load forecasting. However, due to the lack of sufficient data, conventional forecasting methods struggle to achieve satisfactory accuracy. Additionally, short-term high-dimensional data may contain interference information unrelated to the target variable, making multi-step forecasting based on only a short data series a challenging task. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a user-side power load data processing method based on an improved ARNN that can accurately predict short-term high-dimensional data in a class.

[0006] The technical solution adopted by this invention to solve its technical problem is: a user-side power load data processing method based on an improved ARNN, ​​characterized by including the following steps:

[0007] S1 classifies the load data based on the K-means clustering algorithm;

[0008] S2 solves the artificial neural network node number optimization model based on EPPS to obtain the optimal matching node number scheme for each type of load curve;

[0009] S3 establishes a data type identification model based on a dynamic identification algorithm, reconstructs the input matrix, and selects the corresponding optimal number of nodes;

[0010] S4 establishes a short-term high-dimensional load dynamic prediction model based on an improved ARNN.

[0011] Preferably, the method for classifying the load data based on the K-means clustering algorithm in step S1 includes the following steps:

[0012] S1.1 Randomly select K points from the data sample as the initial cluster centers for K clusters;

[0013] S1.2 Calculate the distance from each data sample to the K cluster centers, and divide the data into K clusters based on the closest distance;

[0014] S1.3 Find the average vector of the K clusters, and use the K average vectors as the new cluster centers for each cluster;

[0015] S1.4 Repeat S1.2 and S1.3 until the cluster centers no longer change.

[0016] Preferably, the method further includes solving the K-type load prediction model based on the evolutionary predator-prey intelligent optimization algorithm to obtain the optimal number of nodes for the ARNN with a 4-layer structure for the K-type load curve.

[0017] Preferably, the method for establishing a data category identification model based on a dynamic identification algorithm and reconstructing the input matrix in step S3 includes the following steps:

[0018] S3.1 Compare the input data with the K-type load data at the corresponding time to determine whether the input data is between the maximum and minimum values ​​of the corresponding time for that type. Find the category that meets the numerical value condition. If only one cluster center meets the condition, the input data belongs to that category; otherwise, proceed to step S3.2.

[0019] S3.2 Compare the slope similarity of the input data with the cluster centers obtained in the first step within the same time period to find the category that meets the slope condition. If only one cluster center meets the condition, the input data belongs to that category; otherwise, proceed to step S3.3.

[0020] S3.3 Compare the power similarity of the input data with the cluster centers obtained in the second step at the same time to find the category that meets the power condition. If only one cluster center meets the condition, the input data belongs to that category; otherwise, proceed to step S3.4.

[0021] S3.4 Compare the similarity of the input data with the cluster centers obtained in step 3 within the same time period to find the category that meets the step size condition. If only one cluster center meets the condition, the input data belongs to that category. Otherwise, increase the similarity coefficient and execute S3.2 again until the loop is exited.

[0022] Preferably, the method further includes the slope direction of the input data. The slope direction of the Kth type of load cluster center They are respectively:

[0023] ;

[0024] ;

[0025] in, The slope of the input load sequence. Let be the slope of the Kth type of load cluster center.

[0026] Preferably, the method further includes binary variables. and binary variables and They are respectively:

[0027] ;

[0028] ;

[0029] in, T represents time.

[0030] Slope condition is ,in For similarity.

[0031] Preferably, the method further includes the difference between the input load sequence and the cluster center power of the Kth type of load. for:

[0032] .

[0033] Preferably, the method further includes binary variables. and binary variables and They are respectively:

[0034] ;

[0035] ;

[0036] in, The minimum power difference between the input load sequence and the cluster center power of the Kth type of load;

[0037] The power condition is: .

[0038] Preferably, the method further includes the step distance between two points in the input load sequence. Step distance between the cluster centers of the Kth type of load and the cluster center They are respectively:

[0039] ;

[0040] ;

[0041] in, For adjacent time intervals;

[0042] Step distance between two points in the input load sequence Step distance between the cluster centers of the Kth type of load and the cluster center difference for:

[0043] ;

[0044] binary variables and binary variables and for:

[0045] ;

[0046] ;

[0047] in, Step distance between two points in the input load sequence Step distance between the cluster centers of the Kth type of load and the cluster center The minimum step size distance difference;

[0048] Step size condition is .

[0049] Preferably, establishing a short-term high-dimensional load dynamic prediction model based on an improved ARNN includes the following steps:

[0050] S4.1 Construct the ARNN-based STI equation based on the input data matrix:

[0051] ;

[0052] in, , for The weight matrix, for The weight matrix, for The identity matrix, To predict the step size, For dimension, for The reconstructed input data matrix, T=M, is given by F, which is a feedforward neural network. = ;

[0053] S4.2 Update Matrix, in Randomly select k-dimensional variables from the data. for:

[0054] ;

[0055] in, It is a weight matrix Part of It is a weight matrix Part of;

[0056] S4.3 Update Matrices U and R:

[0057] ;

[0058] in, For the input data matrix, and The unknown part in the solution is solved as follows:

[0059] ;

[0060] in, and All are augmented matrices;

[0061] S4.4 Check convergence;

[0062] The convergence condition is:

[0063] ;

[0064] in, , For any natural number, For the number of iterations, It is the Euclidean norm;

[0065] If the convergence condition is not met, proceed to step S4.2; if the convergence condition is met, determine the matrix. and The unknown part in the code is determined, and the target variable is output by S4.5;

[0066] S4.5 outputs the predicted values; the target variable is obtained from the convergence results of S4.3. future value of position .

[0067] Compared with the prior art, the beneficial effects of this invention are:

[0068] This paper proposes an improved ARNN-based user-side power load data processing method, which constructs a short-term campus load forecasting model based on clustering and dynamic recognition ARNN. This model can accurately and effectively perform multi-step forecasting for short-term high-dimensional load data. It also considers the dynamic recognition characteristics of clustering, which can eliminate variables that are irrelevant to the target variable. Furthermore, it uses EPPS to optimize the number of neural network nodes suitable for each class, enabling the input data to be predicted within its respective class. This approach is suitable for solving the problem of short-term high-dimensional campus load forecasting. Attached Figure Description

[0069] Figure 1 This is a flowchart of a user-side power load data processing method based on an improved ARNN. Detailed Implementation

[0070] The present invention will be further described below with reference to specific embodiments. However, those skilled in the art should understand that the detailed description given here with reference to the accompanying drawings is for better explanation. The structure of the present invention necessarily exceeds the limited embodiments described herein. Some equivalent alternatives or common means will not be described in detail here, but still fall within the protection scope of this application.

[0071] Figure 1 This is the preferred embodiment of the present invention, which is described below in conjunction with the accompanying drawings. Figure 1 The present invention will be further described below.

[0072] like Figure 1 As shown: A user-side power load data processing method based on an improved ARNN includes the following steps:

[0073] S1 classifies the load data based on the K-means clustering algorithm;

[0074] S2 solves the artificial neural network node number optimization model based on EPPS to obtain the optimal matching node number scheme for each type of load curve;

[0075] S3 establishes a data type identification model based on a dynamic identification algorithm, reconstructs the input matrix, and selects the corresponding optimal number of nodes;

[0076] S4 establishes a short-term high-dimensional load dynamic prediction model based on an improved ARNN.

[0077] This invention constructs an improved ARNN short-term load forecasting model that considers the similarity between input data and historical data, enabling accurate and effective short-term load forecasting even when data is insufficient.

[0078] As one possible implementation of this embodiment, the method for classifying load data based on the K-means clustering algorithm includes the following steps:

[0079] S1.1 Randomly select K points from the data sample as the initial cluster centers for K clusters;

[0080] S1.2 Calculate the distance from each data sample to the K cluster centers, and divide the data into K clusters based on the closest distance;

[0081] S1.3 Find the average vector of the K clusters, and use the K average vectors as the new cluster centers for each cluster;

[0082] S1.4 Repeat S1.2 and S1.3 until the cluster centers no longer change.

[0083] As one implementation of this embodiment, the process of solving the artificial neural network node number optimization model based on EPPS to obtain the optimal matching node number scheme for each type of load curve is as follows: The K-type load prediction models are solved respectively based on the evolutionary predator-prey intelligent optimization algorithm to obtain the optimal node number scheme for a 4-layer ARNN structure for the K-type load curves. For details on the evolutionary predator-prey intelligent optimization algorithm, please refer to the article titled "Evolutionary predator and prey strategy for global optimization" in Volume 327, pages 217-232 of the journal *Information Sciences*.

[0084] As one implementation of this embodiment, the method for establishing a data category identification model based on a dynamic identification algorithm and reconstructing the input matrix includes the following steps:

[0085] S2.1 The input data is compared with the values ​​of K-type load data at the corresponding time points to determine the range between the maximum and minimum values ​​of the input data for that type of load at the corresponding time.

[0086] ;

[0087] in, , For all load curves of type K, The input load sequence.

[0088] Find the categories that meet the conditions. If only one cluster center meets the conditions, the input data belongs to that category; otherwise, proceed to the next step.

[0089] S2.2 Compare the slope similarity of the input data with the cluster centers obtained in the first step within the same time period;

[0090] Slope direction of input data The slope and slope direction of the Kth type load cluster center They are respectively:

[0091] ;

[0092] ;

[0093] in, The slope of the input load sequence. Let be the slope of the Kth type of load cluster center.

[0094] Assumption These are binary variables. Within each adjacent time interval, which class's slope direction is the same as the slope direction of the input load sequence, and which class corresponds to... The value is 1, and the rest are 0. Summation yields .

[0095] ;

[0096] ;

[0097] in, T is the number of input data;

[0098] Slope condition is ,in For similarity.

[0099] Find the conditions The categories, among which For similarity, if only one cluster center satisfies the condition, the input data belongs to that class; otherwise, proceed to step S2.3.

[0100] S2.3 The input data is compared with the cluster centers obtained in step two at the same time:

[0101] ;

[0102] in, This is the difference between the power of the cluster centers of the input load sequence and the power of the Kth type of load.

[0103] Assumption It is a binary variable. At a certain time t, the minimum power difference... Corresponding category The value for each category is 1, and the value for all other categories is 0. Summation yields .

[0104] ;

[0105] ;

[0106] in, The minimum power difference between the input load sequence and the cluster center power of the Kth type of load;

[0107] The power condition is: .

[0108] Find the conditions If only one cluster center satisfies the criteria, the input data belongs to that category; otherwise, proceed to S2.4.

[0109] S2.4 The input data is compared with the cluster centers obtained in step 3 within the same time period:

[0110] ;

[0111] ;

[0112] in, For adjacent time intervals, The step distance between two points in the input load sequence. Let be the step distance between the two cluster centers of the Kth type of load. It is the difference between the two.

[0113] Assumption It is a binary variable. At a certain time t, the minimum step size distance difference... Corresponding category The value for each category is 1, and the value for all other categories is 0. Summation yields .

[0114] ;

[0115] ;

[0116] in, Step distance between two points in the input load sequence Step distance between the cluster centers of the Kth type of load and the cluster center The minimum step size distance difference;

[0117] Step size condition is ;

[0118] Find the conditions If only one cluster center satisfies the category, the input data belongs to that category; otherwise, the similarity coefficient is increased, and step S2.2 is executed until the loop is exited.

[0119] Based on the results of the dynamic recognition algorithm, the input data and all data of the corresponding category form a new input matrix, and the optimal number of nodes for that category is selected.

[0120] As one possible implementation of this embodiment, the method for establishing a short-term high-dimensional load dynamic prediction model based on an improved ARNN includes the following steps:

[0121] Based on the aforementioned clustering, identification, and node optimization results, the input data matrix is ​​reconstructed, and it is determined which class of nodes the ARNN should use. The ARNN process is essentially an iterative solution. The process of inputting a data matrix of That is, the target predictor variable. , Reconstruct the input matrix, where Given the input sequence, The load is the category to which the input sequence belongs.

[0122] ;

[0123] ;

[0124] S4.1 Construct an ARNN-based STI (spatiotemporal information) equation based on the input data matrix:

[0125] ;

[0126] in, , for The weight matrix, for The weight matrix, for The identity matrix, To predict the step size, Let be the dimension, and in this case, the number of days. for The reconstructed input data matrix is ​​given by T, where T is time T=M, and F is a feedforward neural network. After being converted by F Dimensional variables , and Given that U, V and The values ​​to be predicted included It is unknown. Furthermore, the weights of the neural network F are randomly assigned and fixed. and It was initially set to an empty matrix and updated in S5.2 and S5.3. Initialize to 0.

[0127] S4.2 Update Matrix, in Randomly select k-dimensional variables ( ), for:

[0128] ;

[0129] in, It is a weight matrix Part of It is a weight matrix Part of;

[0130] S4.3 Update Matrices U and R:

[0131] ;

[0132] and The unknown part in the solution is solved as follows:

[0133] ;

[0134] in, and All are augmented matrices;

[0135] S4.4 Check convergence: The convergence condition of this algorithm is:

[0136] ;

[0137] in, , For any natural number, For the number of iterations, It is the Euclidean norm;

[0138] If the convergence condition is not met, proceed to step S4.2 and update the V matrix. After a sufficient number of such iterations, if the convergence condition is met, then determine the matrix. and The unknown part in the code is determined, and the target variable is output by S4.5;

[0139] S4.5 outputs the predicted values; the target variable is obtained from the convergence results of S4.3. future value of position .

[0140] This invention effectively addresses the problem of short-term high-dimensional campus load forecasting by employing a clustering and dynamic recognition ARNN strategy. It enables short-term high-dimensional load forecasting within classes, thereby improving the accuracy of short-term load forecasting.

[0141] The following example illustrates the user-side power load data processing method based on the improved ARNN of this invention. In this example, 232 days of load data from a certain industrial park are used as the research object, with one load value taken every minute, totaling 1440 data points per day. First, the data from day 1 to day 231 are clustered according to the number of days, into three categories: the first category contains 65 days, the second contains 121 days, and the third contains 45 days. EPPS is used to determine the optimal number of nodes for the neural network F corresponding to each of the three datasets. Next, the input length is set to 30, and the data from the first 30 moments of day 232 is input. Clustering identification is used to compare the data with the three categories to determine which category it belongs to, and the data from the same time period in the same category is then used to construct a cluster. As input to the ARNN, ​​the data from time 31 to 33 is predicted. The next time step, the data from time 2 to 31 is input, and so on, to predict the data from time 32 to 34, thus establishing a rolling prediction model.

[0142] After clustering and dynamic identification, the input sequence and similar loads form an input matrix. In the improved ARNN framework, the reservoir component contains a multi-layer neural network F with randomly fixed weights but an optimal number of nodes, which has time-varying inputs. Based on delayed embedding theory, predict the target vector. This structure is formed through the processing of two weight matrices U and V and a neural network F. With preprocessing for clustering and dynamic recognition, this structure overcomes the shortcomings of traditional ARNNs in accurately predicting short-term load changes under data mutation conditions, enhancing robustness and enabling accurate prediction of future information of the target variable r even in short-term time series.

[0143] Table 1. Performance evaluation of different prediction models on the 232-day dataset of Zibo Industrial Park.

[0144]

[0145] Table 1 compares the prediction accuracy of different prediction models. This invention uses four commonly used metrics to evaluate prediction error: Normalized Mean Absolute Error (NMAE), Normalized Root Mean Square Error (NRMSE), Mean Absolute Percentage Error (MAPE), and Willmott Index of Agreement (IA). The calculation formulas are as follows:

[0146] ;

[0147] ;

[0148] ;

[0149] .

[0150] Where NUM=1440, For the true value, For predicted values, The average of the true values. The maximum value is the true value. Among these four indicators, the smaller the value of NMAE, NRMSE, or MAPE, the more accurate or stable the prediction result is. IA is a standardized measure of the degree of model prediction error, which fluctuates in the range of 0 to 1. The closer its value is to 1, the better the predicted value matches the actual value and the smaller the prediction error.

[0151] As shown in Table 1, the NMAE, NRMSE, and MAPE values ​​of the ARNN based on clustering and dynamic recognition are the smallest. Compared with Elman neural network, back-propagation neural network (BP) and generalized regression neural network (GRNN), the error is reduced by more than half, and the IA value is as high as 0.9666, which is closest to 1, indicating that the ARNN based on clustering and dynamic recognition has the most accurate prediction results. Among them, GRNN uses a four-fold cross-validation method to train the neural network and uses loops to find the optimal SPREAD value, but the effect is still not as ideal as the method of this invention. Elman and BP rely on different training and test set partitions, and need to train the network with the training set first, and then use the trained network for prediction. The prediction results are unstable and prone to overfitting, with many uncertainties. In contrast, ARNN does not require training and essentially has no training process. Relying on the combination of STI and reservoir calculation, once the input data is input, it can predict the load value at the next moment after clustering and dynamic recognition. In terms of both effect and application, the prediction performance of this invention is better than other algorithms.

[0152] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A user-side power load data processing method based on an improved ARNN, ​​characterized in that: Includes the following steps: S1 classifies the load data based on the K-means clustering algorithm; S2 solves the artificial neural network node number optimization model based on EPPS to obtain the optimal matching node number scheme for each type of load curve; S3 establishes a data type identification model based on a dynamic identification algorithm, reconstructs the input matrix, and selects the corresponding optimal number of nodes; S4 establishes a short-term high-dimensional load dynamic prediction model based on an improved ARNN; Step S3, which involves establishing a data category identification model based on a dynamic identification algorithm and reconstructing the input matrix, includes the following steps: S3.1 Compare the input data with the K-type load data at the corresponding time to determine whether the input data is between the maximum and minimum values ​​of the corresponding time for that class. Find the class that meets the numerical value condition. If only one cluster center meets the condition, then the input data belongs to that class. Otherwise, proceed to step S3.2; S3.2 Compare the slope similarity of the input data with the cluster centers obtained in the first step within the same time period to find the category that meets the slope condition. If only one cluster center meets the condition, the input data belongs to that category. Otherwise, proceed to step S3.3; S3.3 The input data is compared with the cluster centers obtained in the second step at the same time to find the category that meets the power condition. If only one cluster center meets the condition, the input data belongs to that category. Otherwise, proceed to step S3.4; S3.4 Compare the similarity of the input data with the cluster centers obtained in step 3 within the same time period to find the category that meets the step size condition. If only one cluster center meets the condition, the input data belongs to that category. Otherwise, increase the similarity coefficient and execute S3.2 again until the loop is exited.

2. The user-side power load data processing method based on improved ARNN according to claim 1, characterized in that: The method for classifying the load data based on the K-means clustering algorithm in step S1 includes the following steps: S1.1 Randomly select K points from the data sample as the initial cluster centers for K clusters; S1.2 Calculate the distance from each data sample to the K cluster centers, and divide the data into K clusters based on the closest distance; S1.3 Find the average vector of the K clusters, and use the K average vectors as the new cluster centers for each cluster; S1.4 Repeat S1.2 and S1.3 until the cluster centers no longer change.

3. The user-side power load data processing method based on improved ARNN according to claim 1, characterized in that: The method also includes solving the K-type load prediction model based on the evolutionary predator-prey intelligent optimization algorithm to obtain the optimal number of nodes for the ARNN with a 4-layer structure for the K-type load curve.

4. The user-side power load data processing method based on improved ARNN according to claim 1, characterized in that: The method also includes the slope direction of the input data. The slope direction of the Kth type of load cluster center They are respectively: ； ； in, The slope of the input load sequence. Let be the slope of the Kth type of load cluster center.

5. The user-side power load data processing method based on improved ARNN according to claim 4, characterized in that: The method also includes binary variables. and binary variables and They are respectively: ； ； in, T represents time. Slope condition is ,in For similarity.

6. The user-side power load data processing method based on improved ARNN according to claim 1, characterized in that: The method further includes the difference between the input load sequence and the cluster center power of the Kth type of load. for: ； in, For all load curves of type K, The input load sequence.

7. The user-side power load data processing method based on improved ARNN according to claim 6, characterized in that: The method also includes binary variables. and binary variables and They are respectively: ； ； in, The minimum power difference between the input load sequence and the cluster center power of the Kth type of load; The power condition is: .

8. The user-side power load data processing method based on improved ARNN according to claim 1, characterized in that: The method also includes a step distance between two points in the input load sequence. Step distance between the cluster centers of the Kth type of load and the cluster center They are respectively: ； ； in, For adjacent time intervals; Step distance between two points in the input load sequence Step distance between the cluster centers of the Kth type of load and the cluster center difference for: ； binary variables and binary variables and for: ； ； in, Step distance between two points in the input load sequence Step distance between the cluster centers of the Kth type of load and the cluster center The minimum step size distance difference, For all load curves of type K, For the input load sequence, Step size condition is , For similarity.

9. The user-side power load data processing method based on improved ARNN according to claim 1, characterized in that: The steps for establishing a short-term high-dimensional load dynamic prediction model based on an improved ARNN are as follows: S4.1 Construct the ARNN-based STI equation based on the input data matrix: ； in, , for The weight matrix, for The weight matrix, for The identity matrix, To predict the step size, For dimension, for The reconstructed input data matrix, T=M, is given by F, which is a feedforward neural network. = ; S4.2 Update Matrix, in Randomly select k-dimensional variables from the data. for: ； in, It is a weight matrix Part of It is a weight matrix Part of; S4.3 Update Matrices U and R: ； in, Let T be the input data matrix, and T be the time interval. After being converted by F Dimensional variables , and The unknown part in the solution is solved as follows: ； in, and All are augmented matrices; S4.4 Check convergence; The convergence condition is: ； in, , For any natural number, For the number of iterations, It is the Euclidean norm; If the convergence condition is not met, proceed to step S4.2; if the convergence condition is met, determine the matrix. and The unknown part in the code is determined, and the target variable is output by S4.5; S4.5 outputs the predicted values; the target variable is obtained from the convergence results of S4.

3. future value of position .

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