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Sunspot research based on predictive models
Summary
Because sunspots are related to other types of solar activity, sunspots can be used to help predict space weather, the state of the ionosphere, and conditions related to shortwave radio propagation or satellite communications. Therefore, this article will collect sunspot related data to establish a prediction model for research and analysis.
First, in order to find relevant data, we used python data crawlers and self-search methods to collect historical data on sunspots using SILSO, NASA, and ESA. First, identify and process missing values and outliers in the data, use the 3σ principle and box plots to identify and process outliers, and eliminate the outliers. The linear interpolation method of Newton interpolation is used to fill missing values.
For question one, predict the start and end of the current and next solar cycle. The duration of each solar cycle is collected, and this indicator is used as an independent variable to build a prediction model for prediction. Use the ARIMA (Autoregressive Integrated Moving Average) model to process time series data. First, use autocorrelation plots, partial autocorrelation plots, and unit root tests to determine stability. After introducing the Barrett test to determine randomness, an ARIMA model was established to more accurately identify and predict changes in the solar cycle.
For question two, predict the start time and duration of solar maximum for the next solar cycle. Taking the solar maximum as the independent variable, a gray prediction model is used for univariate prediction. For the duration, the time length is calculated using the start and end time of each maximum value, and the time length is used as the independent variable, and the gray prediction model is used for univariate prediction.
For question three, predict the number and area of sunspots during the current and next solar cycle. We introduce the LSTM prediction model and combine ARIMA, gray and LSTM (long short-term memory) network models to establish a weighted average prediction model. Taking the minimum error as the objective function and the weight coefficient sum as 1 as the constraint condition, an optimization model is constructed, and the particle swarm algorithm is introduced for algorithm optimization. Use historical data to analyze the relationship between quantity and area, and introduce correlation analysis for judgment. Finally, the matlab fitting toolbox is used to construct the nonlinear fitting relationship. Use the predicted quantities and nonlinear functional relationships to solve and calculate the area. Finally, evaluation indicators such as MAPE and MAE are introduced to evaluate the prediction results, and cross-checking is performed to verify the stability of the model.
Finally, based on ARIMA, gray and LSTM prediction models, related transformations of various indicators of the current and next solar cycle are implemented. Not only can sunspot activity be predicted more accurately, but it can also provide a deeper understanding of the complex interactions between solar activity and the Earth's environment. This method combines the advantages of traditional statistics and modern data science to provide a solid foundation for solving complex astronomical prediction problems.
Keywords: correlation model, data preprocessing, prediction model, optimization model,
Table of contents
Sunspot research based on predictive models
Summary
1. Restatement of the problem
1.1 Problem background
1.2 Problem review
2. Problem analysis
1.1 Data analysis
1.2 Analysis of Problem 1
1.3 Analysis of Problem 2
1.4 Analysis of Question 3
3. Model Assumptions
4. Symbol description
5. Model establishment and solution
5.1 Data preprocessing
5.1.1 Data collection
5.1.2 Outlier processing
5.1.3 Missing value processing
5.2 Problem 1: Establishment and solution of prediction model
5.2.1 Variable selection
1. Data inspection and processing
2. Establish a model
5.3 Establishment and solution of problem 2 prediction model
5.3.1 Correlation analysis
5.3.2 Maximum duration nonlinear fitting
5.3.4 Maximum nonlinear fitting
5.3.5 Minimum value prediction
6.3.3 Establishment of seasonal ARIMA sequence model
5.3.6 Maximum prediction
5.4 Establishment and solution of the prediction model for question 3
5.4.1 Construction of LSTM prediction model
5.4.2 SVM prediction model
5.4.3 Random Forest
5.4.4 Weighted Optimization Forecast
5.4.6 Evaluation indicators
The evaluation index results are as follows
5.4.6 Relationship determination
6. Model summary
6.1 Model advantages
6.2 Model Disadvantages
6.3 Model promotion
7. References
8. Appendix
5.1 Data preprocessing
5.1.1 Data collection
In order to find relevant data, we use python data crawlers and self-search methods, and use SILSO, NASA and ESA to collect historical sunspot data. Here is the process of data collected using SILSO,
For this website, the data is downloaded into txt files and the data are merged together. Therefore, we use python to convert the file type and combine the data and indicators. The pseudo code is as follows
Table 1: Pseudocode
| Import the pandas library as pd |
| # Read text file |
| Set file_path to '/mnt/data/g1874.txt' |
| # Use pandas to read files into DataFrame |
| # Use the 'read_fwf' method to read fixed-width format data |
| df = read fixed-width format file (file_path, column specification=[(0, 4), (4, 6), ..., (69, 74)], header=None) |