A load forecasting scene construction method considering extreme learning machine parameter optimization

Abstract

The application discloses a load prediction scene construction method considering limit learning machine parameter optimization, collects historical load data and weather data sets, screens data according to date type, week type and correlation coefficient after data preprocessing, and constitutes a load data training set; a genetic algorithm is used to optimize hidden layer input weight and bias of a prediction model, a quantile regression optimization model is used to optimize hidden layer input weight, and a limit learning machine model available for load prediction is determined; load prediction results are calculated according to the optimized model, and interval coverage rate and interval average width are used to measure prediction effect; and a K-means clustering algorithm is used to generate load prediction typical scenes, thereby providing references for power grid planning and operation. The application can realize relatively accurate load probability prediction, generate corresponding load typical scenes, and has practical application value.

Description

Technical Field

[0001] This invention relates to the field of power system forecasting and typical scenario generation technology, and in particular to a method for constructing load forecasting scenarios that considers extreme learning machine parameter optimization. Background Technology

[0002] With the increasing variety of load types and the growing penetration of renewable energy sources such as distributed photovoltaic power, the uncertainty of power grid load is gradually increasing, posing greater challenges to the safe and stable operation of the power grid. Therefore, load forecasting while ensuring high accuracy is of great significance for power grid planning.

[0003] Currently, load forecasting includes two forms: point forecasting and probabilistic forecasting. Point forecasting methods generally include regression analysis, support vector machine (SVM), and neural network (NN) methods. Using point forecasting methods, load forecasting can obtain values ​​that are relatively close to the variables to be predicted. The accuracy of the forecast is judged by calculating the difference between the predicted and actual values. However, this method can only obtain the exact value for a certain future period and does not consider the uncertainty and randomness of the load.

[0004] Unlike point-based forecasting methods, probabilistic forecasting effectively characterizes load uncertainty and provides more information. Based on the different forms of output expression, probabilistic forecasts can be categorized into probability density forecasting, quantile forecasting, and interval forecasting. Furthermore, some studies have not considered meteorological factors when performing load forecasting, and the computational efficiency and accuracy of current load forecasting methods need improvement. Based on existing research, it is clear that load forecasting methods require further refinement. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for constructing load prediction scenarios that considers the optimization of Extreme Learning Machine parameters. This method optimizes the input weights and biases of the Extreme Learning Machine model through a genetic algorithm, optimizes the output weights of the model through quantile regression, improves the accuracy of load probability prediction, and uses the K-means method to cluster and generate typical load scenarios.

[0006] One technical solution to achieve the above objective is: a method for constructing load prediction scenarios considering extreme learning machine parameter optimization, comprising the following steps:

[0007] Step 1: Collect historical load data and weather datasets, perform data preprocessing and normalization, and filter data according to date type and weekday type to form the model training set;

[0008] Step 2: Optimize the hidden layer input weights and bias parameters of the extreme learning machine using a genetic algorithm;

[0009] Step 3: Optimize the hidden layer output weights of ELM using quantile regression;

[0010] Step 4: Determine the optimized and improved ELM model, calculate the load probability prediction results, and characterize the prediction effect based on the interval coverage rate and the average width of the interval.

[0011] Step 5: Cluster the load prediction data using the K-means algorithm to construct typical load scenarios.

[0012] Furthermore, the method for collecting historical load data and weather datasets in step 1 is to collect the load data to be predicted and weather data such as daily average temperature, daily maximum temperature, daily minimum temperature, relative humidity, and rainfall at specific time intervals to form an initial dataset.

[0013] Furthermore, the data filtering method described in step 1 is as follows: the data dates are divided into working days and non-working days. If the date to be predicted has the same date characteristics as the previous day, the weather data of that day and the maximum load of the previous day are used as input variables for the prediction model; otherwise, the weather data of that day is used as input variables for the prediction model. The data corresponding to the dates with the same week type as that day are used as the training set, and the data correlation coefficient is calculated. Data with a correlation coefficient of less than 0.9 with the load of other dates are removed.

[0014] Furthermore, the specific model of the Extreme Learning Machine in step 2 is as follows:

[0015] The input quantity X of the i-th sample i There are n, and the actual output quantity is t. i There are m samples. After the input of these samples is trained by the Extreme Learning Machine model, the output y is obtained. i It can be represented as: y i =βg(w·X) i +b); where: w is the weight matrix between the input layer and the hidden layer of the extreme learning machine, which is a D×n matrix, where D is the number of nodes in the hidden layer; b is the bias matrix of the hidden layer; β is the weight matrix between the hidden layer and the output layer; g(·) is the activation function;

[0016] Choose g(·) such that y i With t i Approximately equal, t i It can be represented as: t i ≈βg(w·X i +b);

[0017] The actual outputs of N samples are T = [y1, y2, ..., y N ] T ∈R N×mIt can be expressed as: T≈Hβ; where: H is the matrix of N sample inputs after processing by ELM's w, b and g(·);

[0018] When w and b are determined, optimize β to make the difference between T and Hβ close to zero; this is the optimal β. * β can be obtained by finding the least squares solution to the above equation. * =H ◇ T;

[0019] Where: H ◇ The generalized inverse of the processed matrix H can be represented as H ◇ =H ◇ (HH T ) -1 .

[0020] Furthermore, the parameter optimization process using a genetic algorithm in step 2 is as follows:

[0021] First, generate N. ga An initial population is formed by combining w and b, and then the fitness values ​​of the individuals are calculated for evaluation. The individual fitness is calculated as follows:

[0022]

[0023] In the formula: η is a maximum number;

[0024] Next, 50 individuals with high fitness values ​​are selected as parents and mothers; the w and b values ​​corresponding to the best individual are used as the w and b values ​​corresponding to the parents, and the w and b values ​​corresponding to the remaining selected individuals are used as the w and b values ​​corresponding to the mothers; the w and b values ​​of the parents and mothers are randomly swapped to form offspring; then, the w and b values ​​in the offspring are mutated; the best individual needs to be retained in the next generation to prevent its performance from deteriorating after a series of processes; the loop can be exited when the fitness function value changes little or when the number of iterations reaches a certain value.

[0025] Furthermore, the parameter optimization process for quantile regression in step 3 is as follows:

[0026] The τ-th quantile of the predictor variable y can be expressed as: τ=inf{y:F(y)≥τ},0<τ<1; where: inf{·} is the infimum function; F(y) is the distribution function of y;

[0027] The upper bound of the prediction interval for the j-th predictor is... It is the αth of the predicted quantity up Quantiles, lower bound of the prediction interval is It is the αth of the predicted quantity low Quantiles; to simplify calculations, the following assumptions are made:

[0028] The output weights of the hidden layers of an ELM are calculated using a combination of extreme learning machine and quantile regression. The specific calculation method is as follows:

[0029]

[0030] In the formula: ρ(·) is the test function; t i Q(x) j ,β up ) and Q(x j ,β low ) are the actual value corresponding to the predicted value, the normalized value of the upper and lower bounds of the prediction interval, respectively;

[0031] The test function can be expressed as: ρ τ (μ)=μ(τ-I(μ)); where, if μ is less than zero, then I(μ) equals 1, otherwise I(μ) equals 0.

[0032] Furthermore, the methods for determining the interval coverage and average width of the prediction interval evaluation indicators in step 4 are as follows:

[0033] PICP refers to the ratio of the number of actual values ​​falling within the prediction interval to the total number of samples. The calculation formula is: In the formula: n is the total number of samples, K i (α) K is a Boolean value. If the actual value is greater than the upper bound of the prediction interval or less than the lower bound of the prediction interval, then K... i (α) It is 0 if it is not 1 otherwise;

[0034] PINAW is used to measure the width of the prediction interval, and its calculation method is as follows: In the formula: R is the maximum value of the predicted actual value, U i (α) L is the upper bound of the prediction interval. i (α) This is the lower bound of the prediction interval.

[0035] Furthermore, the specific method for K-means clustering in step 5 is as follows:

[0036] Step 5.1: Randomly select K groups of data that need to be clustered as clustering centers;

[0037] Step 5.2: Select data for each class, which includes data to be clustered that are close to the cluster center;

[0038] Step 5.3: The cluster centers are replaced by the mean of each class of data;

[0039] Step 5.4: If the change in cluster centers is less than the set value, then clustering is complete;

[0040] Using CH (+) The indicators are evaluated as follows:

[0041]

[0042] In the formula: n is the total number of data points, n i Let v be the total amount of data in the i-th class. i Let i be the cluster center of the i-th class. x is the mean of the data. j This represents the j-th data set.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] (1) This invention applies genetic algorithms and quantile regression to optimize the parameters of an extreme learning machine (ELM) model, thereby improving the model's prediction accuracy. Using an ELM for load forecasting avoids the shortcomings of traditional neural network models, such as overfitting and low efficiency, thus improving load forecasting efficiency and model versatility. The typical scenario generation method for the load forecasting model designed in this invention has high prediction accuracy and practical application value.

[0045] (2) This invention generates typical load scenarios based on the K-means method, ensuring that the typical load scenarios summarize the original information, intuitively reflecting the load forecast results, and assisting the power grid planning process. Attached Figure Description

[0046] Figure 1 This is a distribution diagram of load prediction indicators under different confidence levels according to an embodiment of the present invention;

[0047] Figure 2 The load forecast curve for March 12, 2014, is shown in this embodiment of the invention.

[0048] Figure 3 The results are generated for typical load scenarios in embodiments of the present invention. Detailed Implementation

[0049] To better understand the technical solution of the present invention, detailed descriptions are provided below through specific embodiments:

[0050] The present invention provides a method for load prediction and typical scenario construction considering extreme learning machine parameter optimization, comprising the following steps:

[0051] Step 1: Collect historical load data and weather datasets, perform data preprocessing and normalization, and filter data according to date type and weekday type to form the model training set;

[0052] Step 2: Use a genetic algorithm (GA) to optimize the hidden layer input weights and bias parameters of the Extreme Learning Machine (ELM);

[0053] Step 3: Optimize the hidden layer output weights of ELM using the quantile regression (QR) method;

[0054] Step 4: Determine the optimized and improved ELM model, and calculate the load probability prediction results. The prediction effect is characterized by the Prediction Interval Coverage Probability (PICP) and the Prediction Interval Nominal Average Width (PINAW).

[0055] Step 5: Cluster the load prediction data using the K-means algorithm to construct typical load scenarios.

[0056] In step 1, the historical load data and weather dataset refer to the collection of the load data to be predicted and the weather data of daily average temperature, daily maximum temperature, daily minimum temperature, relative humidity and rainfall at specific time intervals to form the initial dataset.

[0057] In step 1, data filtering refers to dividing the data dates into weekdays and non-weekdays. If the date to be predicted has the same characteristics as the previous day, then the weather data for that day and the maximum load of the previous day are used as input variables for the prediction model; otherwise, the weather data for that day is used as the input variables for the prediction model. Data corresponding to dates with the same weekday type as that day are used as the training set, and the data correlation coefficient is calculated. Data with a correlation coefficient less than 0.9 with the load of other dates are removed.

[0058] In step 2, the ELM model refers to a model where traditional neural networks suffer from large computational demands, numerous iterations, and lengthy processing times to achieve satisfactory results. In contrast, ELM offers advantages such as fast computation, the ability to maintain a relatively ideal output even with varying input samples, and the capacity to characterize the nonlinear relationship between input and output. Therefore, the ELM model is chosen for load probability prediction. Here, the input quantity X for the i-th sample... i There are n, and the actual output quantity is t. i There are m samples. After the input of this sample is trained by the ELM model, the output y is obtained. i It can be represented as: y i =βg(w·X) i+b). In the formula: w is the weight matrix between the input layer and the hidden layer of the ELM, which is a D×n matrix, where D is the number of nodes in the hidden layer; b is the bias matrix of the hidden layer; β is the weight matrix between the hidden layer and the output layer; g(·) is the activation function.

[0059] Choosing an appropriate g(·) can make y i With t i Approximately equal, t i It can be represented as: t i ≈βg(w·X i +b).

[0060] The actual outputs of N samples are T = [y1, y2, ..., y N ] T ∈R N×m It can be expressed as: T≈Hβ. Where: H is the matrix of N sample inputs after processing by ELM's w, b, and g(·).

[0061] When w and b are determined, β can be optimized to make the difference between T and Hβ infinitely close to zero. According to the generalized inverse theory, the optimal β... * β can be obtained by finding the least squares solution to equation (3-6). * =H ◇ T.

[0062] Where: H ◇ The generalized inverse of the processed matrix H can be represented as H ◇ =H ◇ (HH T ) -1 .

[0063] In step 2, the parameter optimization process using GA refers to: to ensure the accuracy of the hidden layer input matrices w and b, a genetic algorithm is used to search and optimize the values ​​of w and b. First, N is generated. ga An initial population is formed by combining w and b, and then the fitness values ​​of the individuals are calculated for evaluation. The individual fitness is calculated as follows:

[0064]

[0065] In the formula: η is a maximum number.

[0066] Ideally, the prediction interval PICP(w,b) should be as large as possible compared to PINC, while PINAW should be as small as possible. The closer the fitness value is to zero, the better the w and b values ​​for that individual. Given an individual's w and b, the corresponding β can be calculated using quantile regression. * This allows us to obtain the prediction interval, and then calculate the individual fitness value.

[0067] Next, 50 individuals with high fitness values ​​are selected as parents and mothers. The w and b values ​​corresponding to the best individual are used as the w and b values ​​for the parents, and the w and b values ​​corresponding to the remaining selected individuals are used as the w and b values ​​for the mothers. The w and b values ​​of the parents and mothers are randomly swapped to form the offspring. Then, the w and b values ​​in the offspring are mutated. The best individual needs to be retained in the next generation to prevent its performance from deteriorating after a series of processes. The loop can be exited when the fitness function value changes little or when the number of iterations reaches a certain value.

[0068] In step 3, the parameter optimization process using QR refers to the following: In the ELM model, generally, the number of training samples is greater than the number of hidden layer nodes D, which will lead to HH T Strange, unable to find a suitable β * Simply increasing the number of hidden layer nodes will lead to increased computation and overtraining, resulting in inaccurate training results. Considering these factors, the optimal weight matrix β is calculated using the QR method. * The τ-th quantile of the predictor variable y can be expressed as: τ=inf{y:F(y)≥τ},0<τ<1. Where: inf{·} is the infimum function; F(y) is the distribution function of y.

[0069] The upper bound of the prediction interval for the j-th predictor is... It is the αth of the predicted quantity up Quantiles, lower bound of the prediction interval is It is the αth of the predicted quantity low Quantiles. To simplify calculations, the following assumptions are made:

[0070] QR is mainly used to solve linear problems, while the "source load" prediction problem itself is a complex nonlinear problem. Therefore, a method combining ELM and QR is used to calculate the output weights of the ELM hidden layer. The specific calculation method is as follows:

[0071]

[0072] In the formula: ρ(·) is the test function; t i Q(x) j ,β up ) and Q(x j ,β low ) represent the actual value corresponding to the predicted value, the normalized value of the upper and lower bounds of the prediction interval, respectively.

[0073] The test function can be expressed as: ρ τ (μ)=μ(τ-I(μ)). In this formula, if μ is less than zero, then I(μ) equals 1, otherwise I(μ) equals 0.

[0074] In step 4, the prediction interval evaluation metrics PICP and PINAW refer to: PICP is the ratio of the number of actual values ​​within the prediction interval to the total number of samples, calculated using the following formula: In the formula: n is the total number of samples, K i (α) K is a Boolean value. If the actual value is greater than the upper bound of the prediction interval or less than the lower bound of the prediction interval, then K... i (α) It is 0 if it is not 0, otherwise it is 1.

[0075] Ideally, the PICP should be as large as possible to ensure that the prediction interval encompasses the actual value as much as possible. If the preset PINC is much larger than the PICP of the prediction interval, it indicates that the accuracy of the prediction interval is low, and the prediction model needs to be adjusted.

[0076] Besides the number of actual values ​​within the interval, the interval width is also an important metric for measuring the accuracy of the prediction results. PINAW is used to measure the width of the prediction interval, and its calculation method is as follows: In the formula: R is the maximum value of the predicted actual value, U i (α) L is the upper bound of the prediction interval. i (α) This is the lower bound of the prediction interval.

[0077] A lower PINAW value indicates less fluctuation in the predicted value and a more ideal prediction result. In actual forecasting, a balance should be sought between a higher PICP and a lower PINAW, that is, to maintain a balance between reliability and clarity in order to obtain a forecast range that meets the requirements.

[0078] Specifically, step 5 involves using the K-means clustering algorithm to obtain typical load scenarios. To cluster the data into K clusters, appropriate cluster centers need to be selected, as follows:

[0079] Step 5.1: Randomly select K groups of data that need to be clustered as clustering centers;

[0080] Step 5.2: Select data for each class, which includes data to be clustered that are close to the cluster center;

[0081] Step 5.3: The cluster centers are replaced by the mean of each class of data;

[0082] Step 5.4: If the change in cluster centers is less than the set value, then clustering is complete.

[0083] Choosing an appropriate number of clusters can improve clustering results; therefore, it is necessary to test clustering performance. This can be done using CH (Cluster Numbers). (+) The indicators are evaluated as follows:

[0084]

[0085] In the formula: n is the total number of data points, n i Let v be the total amount of data in the i-th class. i Let i be the cluster center of the i-th class. x is the mean of the data. j This represents the j-th data set.

[0086] In this embodiment, weather data and load data from a certain region from 2012 to 2014 are used to perform load probability prediction as a test case. The included weather data are daily average temperature, daily maximum temperature, daily minimum temperature, relative humidity, and rainfall, and the load data time interval is 15 minutes. This case performs load interval prediction with a time step of 15 minutes for the date to be predicted. Similar to distributed photovoltaic power probability prediction, the data after data filtering needs to be normalized before prediction.

[0087] Dates are divided into weekdays and non-weekdays. If the date to be predicted has the same date type as the previous day, then the weather data for that day and the maximum load of the previous day are used as model input variables; otherwise, the weather data for that day are used as model input variables. Data corresponding to dates with the same week type as the predicted date are used as the training set, and data with a correlation coefficient of less than 0.9 with the load of other dates are removed.

[0088] This example performs a probabilistic load forecast for March 12, 2014, with confidence levels set at 95% and 90%, and evaluates the results. The distributions of the PICP and PINAW indices for the load forecast interval at different significance levels are shown below. Figure 1 As shown, the PICP values ​​are all high and the PINAW values ​​are all less than 10%.

[0089] The load forecast curve for March 12 is as follows: Figure 2 As shown in the figure, the trend of the load forecast curve is basically consistent with the trend of the actual load curve. Under the test case, the model can obtain relatively accurate results and can describe the fluctuation of the power grid load. When the confidence level decreases, the coverage of the forecast interval to the actual load value remains the same or decreases, but the PINAW value decreases. In addition, it can be seen that the width of the forecast interval is narrower during periods of rapid load increase or decrease compared to other periods. Regarding the load peak, March 12th is a Wednesday in spring, and its load peak (per unit value) is close to 0.7, which is a basic characteristic of seasonal load.

[0090] Historical data was used to cluster the weather data for weekdays and non-weekdays in the region during the spring of 2014. After CH... (+)For indicator validation, weather data was clustered into four scenarios, with two typical scenarios each for weekdays and non-weekdays. Based on load forecasting results, the K-means algorithm was used for clustering to obtain typical load scenarios, as follows: Figure 3 As shown in the figure, scenarios one and two represent typical weekday load scenarios, while scenarios three and four represent typical non-weekday load scenarios. Analysis reveals that the constructed typical load scenarios are relatively accurate, conforming to the basic load trends of the season, and providing key characteristics of weekday and non-weekday loads, thus offering a reference for power grid planning.

[0091] Those skilled in the art should recognize that the above embodiments are merely illustrative of the present invention and are not intended to limit the present invention. Any variations or modifications to the above embodiments that are within the spirit and essence of the present invention will fall within the scope of the claims of the present invention.

Claims

1. A method for constructing load forecasting scenarios considering extreme learning machine parameter optimization, characterized in that, Includes the following steps: Step 1: Collect historical load data and weather datasets, perform data preprocessing and normalization, and filter data according to date type and weekday type to form the model training set; Step 2: Optimize the hidden layer input weights and bias parameters of the extreme learning machine using a genetic algorithm; Step 3: Optimize the hidden layer output weights of ELM using quantile regression; Step 4: Determine the optimized and improved ELM model, calculate the load probability prediction results, and characterize the prediction effect based on the interval coverage rate and the average width of the interval. Step 5: Cluster the load prediction data using the K-means algorithm to construct typical load scenarios. The data filtering method described in Step 1 is as follows: divide the data dates into weekdays and non-weekdays. If the date to be predicted has the same characteristics as the previous day, then use the weather data of that day and the maximum load of the previous day as input variables for the prediction model; otherwise, use the weather data of that day as input variables for the prediction model. Use the data corresponding to dates with the same weekday type as that day as the training set, calculate the data correlation coefficient, and remove data whose correlation coefficient with the load of other dates is less than 0.

9. The specific method for K-means clustering in step 5 is as follows: Step 5.1, select arbitrarily K Groups need clustered data as agglomeration centers; Step 5.2: Select data for each class, which includes data to be clustered that are close to the cluster center; Step 5.3: The cluster centers are replaced by the mean of each class of data; Step 5.4: If the change in cluster centers is less than the set value, then clustering is complete; use The indicators are evaluated as follows: In the formula: n For the total number of data points, For the first i Total amount of data of each class For the first i Cluster centers of classes The mean of the data. For the first j Group data, The method for collecting historical load data and weather datasets in step 1 is to collect the load data to be predicted and weather data such as daily average temperature, daily maximum temperature, daily minimum temperature, relative humidity and rainfall at specific time intervals to form an initial dataset; The parameter optimization process for quantile regression in step 3 is as follows: Predictor variables The Quantiles can be expressed as: In the formula: Infim function; for The distribution function; No. j The upper bound of the prediction interval for each predictor is: It is the first of the predicted quantities. Quantiles, lower bound of the prediction interval is It is the first of the predicted quantities. Quantiles; to simplify calculations, the following assumptions are made: ; The output weights of the hidden layers of an ELM are calculated using a combination of extreme learning machine and quantile regression. The specific calculation method is as follows: In the formula: For the test function; , and These are the actual value corresponding to the predicted value, and the normalized values ​​of the upper and lower bounds of the prediction interval, respectively. The test function can be expressed as: In the formula, if If less than zero, then It equals 1, otherwise It equals 0.

2. The method for constructing a load prediction scenario considering extreme learning machine parameter optimization according to claim 1, characterized in that, The specific model of the Extreme Learning Machine in step 2 is as follows: No. i Input quantity per sample have n One, actual output have m The input data of this sample is trained by the Extreme Learning Machine model, and the output data is obtained. It can be represented as: In the formula: Let be the weight matrix between the input layer and the hidden layer of the extreme learning machine, which is . 1-th order matrix, D This represents the number of hidden layer nodes. Here is the bias matrix of the hidden layer; This is the weight matrix between the hidden layer and the output layer; Let be the excitation function; Select make and Approximately equal It can be represented as: ; N The actual output of each sample is , can be represented as: In the formula: H for N The input of each sample is processed by ELM. , as well as The processed matrix; when and When determined, for Optimization, making T and The difference between them is close to zero, which is optimal. The following can be obtained by taking the least squares solution of the above equation: ; In the formula: The processed matrix The generalized inverse matrix can be represented as .

3. The method for constructing a load forecasting scenario considering extreme learning machine parameter optimization according to claim 1, characterized in that, The parameter optimization process using a genetic algorithm in step 2 is as follows: First generate indivual and An initial population is formed, and then the fitness values ​​of individuals are calculated for evaluation. The individual fitness is calculated as follows: In the formula: It is a maximum number; Then, 50 individuals with high fitness values ​​were selected as parents and mothers; the best individual's corresponding... and As the father's corresponding and The remaining selected individuals correspond to and As the corresponding mother and Randomly swap the parent's , with maternal side , Each row of data constitutes a child generation; then, within the child generation... and Mutation is performed; the best individual needs to be retained in the next generation of the population to prevent the performance of the best individual from deteriorating after a series of processes; the loop can be exited when the fitness function value changes little or when the number of iterations reaches a certain value.

4. The method for constructing a load forecasting scenario considering extreme learning machine parameter optimization according to claim 1, characterized in that, The methods for determining the interval coverage and average width of the prediction interval evaluation indicators in step 4 are as follows: PICP refers to the ratio of the number of actual values ​​falling within the prediction interval to the total number of samples. The calculation formula is: In the formula: n The total number of samples, This is a Boolean value. If the actual value is greater than the upper bound of the prediction interval or less than the lower bound of the prediction interval, then... It is 0 if it is not 1 otherwise; PINAW is used to measure the width of the prediction interval, and its calculation method is as follows: In the formula: R To predict the maximum value of the actual value, This is the upper bound of the prediction interval. This is the lower bound of the prediction interval.

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