A method and system for predicting solar radiation based on skew-normal distribution

Abstract

The application discloses a kind of based on the prediction method and system of solar radiation of skew normal distribution, belong to solar radiation prediction technical field.Method includes (1) in model establishment process, using skew normal distribution function to establish the relationship trend model of solar radiation and time.(2) in order to better handle solar radiation data, the application uses Pearson correlation coefficient and Granger causality test method to determine the index associated with solar radiation.(3) after completing data processing, the application uses improved adaptive genetic algorithm to optimize the solar fitting parameter of skew normal distribution.Finally, using the optimized results trains ANN neural network model, to predict the specific mathematical expression of solar radiation change with time in future one day.The application is characterized in that a variety of methods are comprehensively used, accurate prediction model is established, and strong support is provided for the practical application of photovoltaic power generation.

Description

Technical Field

[0001] This invention belongs to the field of solar radiation prediction technology, and more specifically, relates to a method and system for predicting solar radiation based on a skewed normal distribution. Background Technology

[0002] Solar energy, as a clean and renewable energy source, has been widely applied and developed globally. Under the current backdrop of environmental advocacy and sustainable development, the utilization of solar energy has become a trend and a pursuit. To better utilize solar energy, improve its efficiency, and reduce energy waste, it is necessary to predict and quantify solar radiation.

[0003] Solar radiation refers to the energy released by the sun onto the Earth's surface. It is a crucial component of solar energy and the foundation for the operation of solar panels. Accurate prediction and quantification of solar radiation are essential for the design and use of solar panels, enabling more informed decision-making. Currently, solar radiation prediction typically employs methods such as machine learning. However, these methods only provide numerical results, not concrete formulas. This presents challenges in both scientific research and practical applications. First, numerical results alone cannot meet the needs of scientific research and practical applications because they lack specific mathematical formulas. Second, using specific formulas to fit data and predict the accuracy of solar radiation predictions also presents limitations, as variations in solar radiation are influenced by numerous factors with complex relationships. Therefore, a new method is needed to better predict and quantify solar radiation, improving the accuracy and precision of predictions. Summary of the Invention

[0004] In response to the shortcomings and improvement needs of existing technologies, this invention provides a method and system for predicting solar radiation based on a partially normal distribution. It aims to solve the technical problem that although current solar radiation prediction models can provide high prediction accuracy, they often cannot provide specific mathematical expressions, thus limiting their application scope in scientific research and practical applications.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for predicting solar radiation based on a partially normal distribution is provided, comprising the following steps: S1, acquire historical meteorological characteristic data and corresponding historical solar radiation data; S2, the historical solar radiation data are fitted using a skewed normal distribution; random initialization is generated. N The fitting parameters are used as individuals in the initial population; wherein, the fitting parameters include the amplitude, mean, standard deviation and skewness parameters of the skewed normal distribution; S3, select several individuals with the highest fitness in the current population and perform replication, crossover, and mutation to obtain a new population; calculate the fitness value of all individuals in the new population, compare it with the current best individual, and take the best of the two; S4: Determine if the iteration stopping condition has been met. If yes, output the optimal fitting parameters; otherwise, return to execute S3. S5. Repeat S1 to S4 to obtain several sets of historical meteorological characteristic data and corresponding optimal fitting parameters as training sample sets; based on the training sample sets, train the neural network to obtain the fitting parameter prediction model. S6. Input the meteorological characteristic data to be predicted into the fitting parameter prediction model, and then obtain the relationship between solar radiation and time based on the prediction results.

[0006] Furthermore, in step S1, acquiring historical meteorological characteristic data includes: Meteorological characteristics affecting solar radiation data are used as candidate indicators, and the correlation coefficient between any two candidate indicators is calculated using the Pearson correlation coefficient. For two candidate indicators with a correlation coefficient greater than a preset threshold, the Granger causality test method is used to retain the indicator that is the cause and remove the indicator that is the result. Obtain historical meteorological characteristic data corresponding to the remaining candidate indicators.

[0007] Furthermore, in step S2, a skewed normal distribution is used to fit the historical solar radiation data, and the specific expression is as follows:

[0008] in, Represents solar radiation data, including random variables. Obtain the parameter as The skewed normal distribution The density function representing the standard normal distribution. It is the distribution function of the standard normal distribution. , , , These represent the amplitude, mean, standard deviation, and skewness parameter of a skewed normal distribution, respectively.

[0009] Furthermore, in S2, The value is set to be in Time's up Average solar radiation at any given time The formula is as follows:

[0010] in, express t The amount of solar radiation at any given time. It represents the time interval between two adjacent points in a single sampling.

[0011] Furthermore, in step S3, before performing crossover and mutation, it is necessary to determine whether the adaptive probabilities of crossover and mutation are satisfied; wherein,

[0012]

[0013] In the formula, and These represent the adaptive probabilities of crossover and mutation, respectively. and These are the first and second cross-adaptive factors, respectively. and These are the first and second variation adaptive factors, respectively; This represents the maximum fitness of the current population. This represents the average fitness of the current population. c This is a positive constant used to control the gradient magnitude of crossover mutations and prevent the algorithm from overfitting.

[0014] Furthermore, in step S4, before outputting the optimal fitting parameters, the following steps are also included: The optimal fitting parameters are determined; if a certain fitting parameter exists... s If the constraints are exceeded, they will be corrected in the following ways:

[0015]

[0016]

[0017]

[0018] in, This represents the corrected fitting parameters. They represent the fitting parameters respectively. s The maximum and minimum values, These represent the maximum and minimum fitness values ​​of the current population, respectively.

[0019] On the other hand, the present invention also provides a solar radiation prediction system based on a skewed normal distribution, comprising: a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the above-described method for predicting solar radiation based on a skewed normal distribution.

[0020] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects: (1) Unlike existing technologies, which acquire historical meteorological feature data and corresponding historical solar radiation data, and then directly use the historical meteorological feature data as input and the corresponding historical solar radiation data as output to train a solar radiation prediction model, this invention acquires historical meteorological feature data and corresponding historical solar radiation data, fits the historical solar radiation data using a skewed normal distribution, and optimizes the fitting parameters of the skewed normal distribution using a genetic algorithm. Then, using the historical meteorological feature data as input and the corresponding optimal fitting parameters as output, a neural network is trained to obtain a fitting parameter prediction model. This not only improves the accuracy of solar radiation prediction but also yields a specific mathematical expression, making the model more reliable and interpretable in practical applications.

[0021] (2) In the historical data acquisition stage, this invention uses Pearson correlation coefficient and Granger causality test to determine the indicators associated with solar radiation, thereby simplifying the model and reducing redundancy among variables.

[0022] (3) Based on practical experience, this invention considers incorporating the fitting parameters The value is set to be in Time's up Average solar radiation at any given time This multiplies the algorithm's performance and improves computational efficiency.

[0023] (4) Unlike traditional genetic algorithms where the crossover and mutation probabilities are fixed values, improper settings will affect the algorithm's performance, making it difficult to converge and only obtaining local solutions; this invention proposes a nonlinear adaptive adjustment algorithm to improve the algorithm's solution efficiency and accuracy.

[0024] (5) The genetic algorithm uses binary chromosome encoding for crossover and mutation operations, where every bit of the binary value may be modified. However, the decoded value may not meet the constraints of the fitting parameters. Therefore, this invention corrects the fitting parameters that do not meet the constraints, which is beneficial for establishing a more accurate prediction model. Attached Figure Description

[0025] Figure 1 A flowchart illustrating a method for predicting solar radiation based on a skewed normal distribution, provided as an embodiment of the present invention; Figure 2A flowchart of an improved adaptive genetic algorithm for fitting solar radiation parameters provided in an embodiment of the present invention; Figure 3 This is a diagram of the ANN model architecture provided in an embodiment of the present invention; Figure 4 A comparison chart of the fitting effects of the improved adaptive genetic algorithm and the traditional adaptive genetic algorithm provided in the embodiments of the present invention; Figure 5 The figure shows a comparison of the simulation results of solar radiation prediction based on skewed normal distribution and normal distribution, provided for embodiments of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0027] In this invention, the terms "first," "second," etc. (if present) in the invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0028] See Figure 1 , combined Figures 2 to 5 The present invention provides a method for predicting solar radiation based on a skewed normal distribution, comprising operations S1 to S6.

[0029] Operate S1 to obtain historical meteorological characteristic data and corresponding historical solar radiation data.

[0030] In this embodiment, solar radiation is influenced by various factors, including meteorological characteristics such as temperature, air pressure, humidity, oxygen concentration, ozone concentration, and PM2.5. However, some of the sub-indicators we selected may exhibit correlation. To simplify the model and reduce redundancy among variables, we need to merge highly correlated indicators. To study the relationships between these sub-indicators, we employ Pearson correlation coefficient analysis to better understand the correlations between the indicators, as shown in the following formula:

[0031] For two sets of strongly correlated indicators (i.e., two indicators with a correlation coefficient greater than a preset threshold), we need to merge them to eliminate redundant indicators. The merging principle is to determine the causal relationship between the two indicators and replace the indicator that can act as the cause with the indicator that acts as the result. To explore the causal relationship between these two indicators, this invention employs the Granger causality test method. This method helps reduce the influence of redundant indicators and improves the accuracy of the indicators. and indicators The Granger causality test is performed as follows: (1) Assumption As the dependent variable, As the independent variable, and Time series are divided into observation series and delayed series, where the observation series includes The delayed sequence contains [number] observations. There are several delay values. Next, two models are used to represent them. and The time series data is expressed by the following formula:

[0032] (2) Calculate the sum of squared residuals for the two models. and ,pass Judging by statistics Is it? The reason for Granger's effect is explained by the following mathematical formula:

[0033] Furthermore, it should be noted that the meteorological characteristic data and solar radiation data mentioned in this invention are all time-series data.

[0034] Operation S2 involves fitting the historical solar radiation data using a partially normal distribution; random initialization is then performed to generate... N The fitting parameters are used as individuals in the initial population; wherein, the fitting parameters include the amplitude, mean, standard deviation and skewness parameters of a skewed normal distribution.

[0035] Specifically, operation S2 includes: S21, a skewed normal distribution is used to fit the solar radiation data, and the specific expression is as follows:

[0036] in, Represents solar radiation data, including random variables. Obtain the parameter as The skewed normal distribution The density function representing the standard normal distribution. It is the distribution function of the standard normal distribution. , , , These represent the amplitude, mean, standard deviation, and skewness parameter of a skewed normal distribution, respectively.

[0037] S22, for the fitted parameters It is used to determine the maximum value of the skewed normal distribution. Based on practical experience, the most significant diurnal variations in solar radiation typically occur within a continuous timeframe, such as from 10 AM to 3 PM. Therefore, to improve algorithm performance and increase computational efficiency, The value can be set to be in Time's up Average solar radiation at any given time The formula is as follows:

[0038] in, express t The amount of solar radiation at any given time. It represents the time interval between two adjacent points in a single sampling.

[0039] S23, therefore use , and To replace parameters This is used to fit the parameters of a mathematical model of solar radiation. The specific expression is as follows:

[0040] Operation S3: Select several individuals with the highest fitness in the current population and perform replication, crossover, and mutation to obtain a new population; calculate the fitness value of all individuals in the new population, compare it with the current best individual, and take the best of the two.

[0041] Specifically, such as Figure 2 As shown, this embodiment of the invention provides a method for fitting solar radiation parameters based on an adaptive genetic algorithm, wherein: (1) The parameters in the mathematical formula of solar radiation are fitted using Gray code; (2) The root mean square error (RMSE) is used as the evaluation function for individual fitness, and its expression is as follows:

[0042] in, Representing the One chromosome, Indicates the number of experimental data groups. Indicates the first The group observed solar radiation data, while express The solar radiation fitting data.

[0043] (3) The selection operation of the genetic algorithm involves selecting parent individuals from the current population for reproduction to produce the next generation. We adopted an elite retention selection method. Specifically, elite retention selects the individuals with the highest fitness and retains them to add to the next generation population. The formula is as follows:

[0044] (4) In genetic algorithms, crossover is an important genetic operation. It generates better individuals by exchanging useful information from parent individuals, thus helping to avoid the algorithm getting trapped in local optima. We use position-based genetic algorithm crossover. Specifically, this operation first randomly selects several genes at different positions in parent individual 1, and then copies these genes to offspring individual 1. Next, the missing elements from offspring individual 1 in parent individual 2 are sequentially filled into offspring individual 1, and offspring individual 2 is generated in the same way, finally resulting in two offspring chromosomes. Compared with other types of genetic algorithm crossover operations, position-based crossover can explore the search space more effectively, thereby improving the algorithm's global search capability.

[0045] (5) The crossover and mutation probabilities in traditional genetic algorithms are fixed values. If these are not set properly, they will affect the algorithm's performance, making it difficult to converge and resulting in only local solutions. Although general adaptive genetic algorithms can adjust the crossover and mutation probabilities according to the degree of adaptivity, their changes are linear and lack intelligent adjustment methods. Therefore, we propose a nonlinear adaptive adjustment algorithm to improve the algorithm's solution efficiency and accuracy. The formula is as follows:

[0046]

[0047] In the formula, and These represent the adaptive probabilities of crossover and mutation, respectively. and These are the first and second cross-adaptive factors, which are empirically set to 1 and 2 respectively; and These are the first and second adaptive variation factors, respectively, which are empirically set to 0.02 and 0.05. This represents the maximum fitness of the current population. This represents the average fitness of the current population. c This is a positive constant used to control the gradient magnitude of crossover mutations and prevent overfitting of the algorithm; it is typically set to 1.

[0048] This invention uses Because with The increase, The rate of increase is faster. This function form can more accurately reflect the differences in population fitness, while providing richer information to describe the distribution and concentration of the population. We chose to use... The value is because .when When the average fitness is close to the maximum fitness, the fitness of individual populations generally increases, leading to a more concentrated fitness among individuals. As population fitness increases, the mutation probability should also increase accordingly to help the population escape the influence of extreme points. Therefore, we can... and To monitor changes in population fitness through comparison, by increasing the coefficient This is used to adjust the mutation probability in order to improve the evolutionary efficiency of the population.

[0049] Operation S4 determines whether the iteration stopping condition has been met. If yes, the optimal fitting parameters are output; otherwise, return to execute S3.

[0050] In this embodiment, the iteration stopping condition is, for example, reaching the maximum number of generations of the population, or other preset conditions.

[0051] Furthermore, because genetic algorithms use binary chromosome encoding for crossover and mutation operations, every bit of the binary value can be modified. However, the decoded value may not conform to the parameters. The defined limits necessitate the evaluation and correction of infeasible offspring. We utilize the Sigmoid function to map infeasible values ​​to a specified range, and then adjust the fitted parameters that exceed the constraints in the following way. s Make corrections:

[0052]

[0053]

[0054]

[0055] in, This represents the corrected fitting parameters. They represent the fitting parameters respectively. s The maximum and minimum values, These represent the maximum and minimum fitness values ​​of the current population, respectively.

[0056] After passing through S1 to S4, a set of historical meteorological characteristic data and the corresponding optimal fitting parameters can be obtained as a training sample.

[0057] Operation S5 repeats S1 to S4 to obtain several sets of historical meteorological characteristic data and corresponding optimal fitting parameters as training sample sets; based on the training sample sets, train the neural network to obtain the fitting parameter prediction model.

[0058] Specifically, such as Figure 3 As shown, this invention proposes an ANN training model, which includes the following steps: (1) The data for each indicator of the neural network are subjected to Sum Normalization, as shown in the following expression:

[0059] (2) During model training, we chose Mean Square Error (MSE) as the loss function and optimized the model parameters by minimizing the loss function. Simultaneously, we also chose to train the model using supervised learning, that is, using the true value as the metric to continuously adjust the model parameters so that its output is closer to the true value. The MSE expression is as follows:

[0060] in Represents the actual value. This represents the predicted value.

[0061] (3) For the neural network model of the ANN algorithm, considering the requirements of accuracy and training time, we chose to set the number of hidden layers of the neural network to 2. For the input layer of the neural network, we selected the four time-varying index data obtained from the index evaluation in the previous section, and used the various parameters in the solar radiation data model. , , , , , This serves as the output layer. The number of neurons in the hidden layer is designed using the following formula:

[0062] in This indicates the number of neurons in the hidden layer. This indicates the number of neurons in the input layer. This indicates the number of neurons in the output layer.

[0063] (4) For the activation function in the ANN model, we will use the logarithmic sigmoid function (logsig) as follows:

[0064] (5) To improve the accuracy of the neural network model's prediction of solar radiation, the training function is an essential component. The training function mainly evaluates the values ​​of each neuron in the neural network model, adjusts the weights in the network, and gradually reduces the error between the trained values ​​and the target values, thereby improving the model's generalization and prediction capabilities. Therefore, we adopt the Traingda training method. During model training, this algorithm uses an adaptive learning rate, which can converge faster and has higher robustness. Compared with the traditional backpropagation algorithm, Traingda adaptively adjusts the model's weights based on the weight gradient in each neuron and the direction of the gradient from the previous update. The weight update formula is as follows:

[0065] in Indicates the first layer to the first Layer connection weights Indicates the weight update amount. This represents the learning rate at the current moment. Represents the output neuron The error, Indicates input neurons The output value, Represents the output neuron The weighted average of the sum of squared gradients, The weighted average coefficients of the sum of squared gradients are represented. To represent the minimum value, avoid having a denominator of 0.

[0066] S6. Input the meteorological characteristic data to be predicted into the fitting parameter prediction model, and then obtain the relationship between solar radiation and time based on the prediction results.

[0067] like Figure 4The image shows a comparison of the root mean square error (RMSE) of fitting solar radiation data for a specific day in Wuhan City using an improved adaptive genetic algorithm (AGA) and a traditional adaptive genetic algorithm. It can be seen that the improved AGA performs better in fitting performance. Specifically, the improved AGA converges completely after approximately 180 iterations, while the traditional AGA requires approximately 270 iterations to converge. Furthermore, in the final fitting result, the RMSSE of the improved AGA is about 15% smaller than that of the traditional AGA. This is because the traditional AGA's adaptive adjustment is linear, unable to dynamically adjust the crossover and mutation parameter probabilities according to the actual situation, resulting in the need for more iterations to converge the adaptive function. Simultaneously, this also makes the traditional AGA prone to getting trapped in local optima, unable to efficiently and flexibly explore the optimal solution. Therefore, the improved AGA performs better in the solar radiation prediction model.

[0068] like Figure 5 The figure shows the results of fitting solar radiation data for a specific day in Wuhan, comparing two fitting models: a skewed normal distribution and a normal distribution. The figure reveals that actual solar radiation exhibits a right-skewed distribution, which the normal distribution cannot accurately fit. This is because the normal distribution is based on the mean... The data is symmetrically distributed around the center of symmetry, therefore it cannot well fit the right-skewed trend in the solar radiation curve. In contrast, the skewed normal distribution introduces a shift factor, which can better fit the individual points of solar radiation and accurately reflect the characteristics of the actual distribution.

[0069] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting solar radiation based on a partially normal distribution, characterized in that, Includes the following steps: S1, acquire historical meteorological characteristic data and corresponding historical solar radiation data; S2, the historical solar radiation data are fitted using a skewed normal distribution; random initialization is generated. N The fitting parameters are used as individuals in the initial population; wherein, the fitting parameters include the amplitude, mean, standard deviation and skewness parameters of a skewed normal distribution; S3, select several individuals with the highest fitness in the current population and perform replication, crossover, and mutation to obtain a new population; calculate the fitness value of all individuals in the new population, compare it with the current best individual, and take the best of the two; S4: Determine if the iteration stopping condition has been met. If yes, output the optimal fitting parameters; otherwise, return to execute S3. S5. Repeat S1 to S4 to obtain several sets of historical meteorological characteristic data and corresponding optimal fitting parameters as training sample sets; based on the training sample sets, train the neural network to obtain the fitting parameter prediction model. S6, input the meteorological characteristic data to be predicted into the fitting parameter prediction model, and then obtain the relationship between solar radiation and time based on the prediction results; In step S2, a skewed normal distribution is used to fit the historical solar radiation data, and the specific expression is as follows: in, Represents solar radiation data, including random variables. Obtain the parameter as The skewed normal distribution The density function representing the standard normal distribution. It is the distribution function of the standard normal distribution. , , , These represent the amplitude, mean, standard deviation, and skewness parameter of a skewed normal distribution, respectively. In S2, The value is set to be in Time's up Average solar radiation at any given time The formula is as follows: in, express t The amount of solar radiation at any given time. It represents the time interval between two adjacent points in a single sampling.

2. The method for predicting solar radiation based on a skewed normal distribution according to claim 1, characterized in that, In step S1, historical meteorological characteristic data is acquired, including: Meteorological characteristics affecting solar radiation data are used as candidate indicators, and the correlation coefficient between any two candidate indicators is calculated using the Pearson correlation coefficient. For two candidate indicators with a correlation coefficient greater than a preset threshold, the Granger causality test method is used to retain the indicator that is the cause and remove the indicator that is the result. Obtain historical meteorological characteristic data corresponding to the remaining candidate indicators.

3. The method for predicting solar radiation based on a skewed normal distribution according to claim 1, characterized in that, In step S3, before performing crossover and mutation, it is necessary to determine whether the adaptive probabilities of crossover and mutation are satisfied; where, In the formula, and These represent the adaptive probabilities of crossover and mutation, respectively. and These are the first and second cross-adaptive factors, respectively. and These are the first and second variation adaptive factors, respectively; This represents the maximum fitness of the current population. This represents the average fitness of the current population. c This is a positive constant used to control the gradient magnitude of crossover mutations and prevent the algorithm from overfitting.

4. A method for predicting solar radiation based on a skewed normal distribution according to claim 1 or 3, characterized in that, In step S4, before outputting the optimal fitting parameters, the following is also included: The optimal fitting parameters are determined; if a certain fitting parameter exists... s If the constraints are exceeded, they will be corrected in the following ways: in, This represents the corrected fitting parameters. They represent the fitting parameters respectively. s The maximum and minimum values, These represent the maximum and minimum fitness values ​​of the current population, respectively.

5. A solar radiation prediction system based on a partially normal distribution, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the solar radiation prediction method based on a skewed normal distribution as described in any one of claims 1-4.

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