Robust spline decomposition and extreme value extraction method for solar wind speed time sequence

Abstract

The invention discloses a robust spline decomposition and extreme value extraction method for a solar wind speed time sequence, and the method comprises the steps: selecting n node positions in a generated time index according to a preset spline node number n through employing a quantile position method, constructing a cubic B-spline primary function, and forming a spline primary function; then, adopting a Huber loss function to realize robust fitting, dynamically reducing the weight of an abnormal point through iterative optimization, extracting a stable trend term, and setting an extreme value judgment threshold value by utilizing the absolute median difference of a residual error to accurately recognize abnormal fluctuation; the finally output decomposition result comprises a smooth trend item, an extreme fluctuation item and a weight vector; the above decomposition result can effectively distinguish the long-term trend and extreme events in the solar wind speed time sequence, improves the recognition capability of solar wind background analysis and space extreme weather, and is suitable for space weather forecast and disaster risk assessment.

Description

Technical Field

[0001] The present invention belongs to the field of space weather, and specifically relates to a solar wind speed time series trend analysis and extreme event identification method based on a robust spline decomposition mechanism, which is particularly suitable for separating and identifying abnormal disturbances and extreme fluctuation events in solar wind observation data. Background Art

[0002] Solar wind speed is a key observational indicator in space weather research. Its variations directly impact the Earth's magnetosphere and ionosphere, as well as the safety of space missions. Solar wind speed time series typically exhibit significant nonstationary characteristics, including periodic variations, trend fluctuations, and dramatic transient disturbances and extreme events. These disturbances are often closely associated with extreme space weather events such as solar flares, coronal mass ejection (CME) shock waves, and interplanetary shock waves.

[0003] Traditional time series decomposition methods (such as moving average, exponential smoothing, STL decomposition, etc.) are mostly suitable for extracting trends and periodicities in stable environments or under weak fluctuation conditions. In high-noise and strong-disturbance scenarios such as solar wind speed, extreme events or short-term abnormal fluctuations often lead to serious distortion of trend estimates, thereby reducing the accuracy of analysis of long-term changes in the solar wind.

[0004] Furthermore, existing methods generally lack explicit identification and modeling mechanisms for solar wind extremes, making it difficult to effectively distinguish between background trends and short-term, intense disturbances in solar wind speed time series. This confusion between trends and anomalous disturbances can severely impact the accuracy of forecast models and the effectiveness of space disaster risk assessments, particularly during subsequent space weather event forecasting or catastrophic event analysis.

[0005] Therefore, how to achieve the precise separation of trend information and extreme fluctuations in the solar wind speed series and accurately identify and capture extreme space weather events has become an important technical issue that needs to be urgently solved in the current space weather field.

[0006] [References]

[0007] [1] Castillo, Y., Pais, MA, Fernandes, J., Ribeiro, P., Morozova, AL, & Pinheiro, FJ (2021). Relating 27-day averages of solar, interplanetary medium parameters, and geomagnetic activity proxies in solar cycle 24. Solar Physics, 296(7),115.

[0008] [2]Temmer, M., Reiss, MA, Nikolic, L., Hofmeister, SJ, & Veronig, AM (2017). Preconditioning of interplanetary space due to transient CMEdisturbances. The Astrophysical Journal, 835(2),141.

[0009] [3]Hudson,MK,Elkington,SR,Li,Z.,Patel,M.,Pham,K.,Sorathia,K.,...&Leali,A.(2021).MHD-test particle simulations of moderate CME and CIR-driven geomagnetic storms at solar minimum.Space Weather, 19(12),e2021SW002882. Summary of the Invention

[0010] To address the problems of unstable trend extraction and difficulty in effectively identifying extreme events in traditional time series decomposition methods under the influence of abnormal solar wind speed disturbances, this paper proposes a robust spline decomposition and extreme value extraction method for solar wind speed time series. First, a cubic B-spline basis function matrix based on quantile nodes is used to construct an initial trend fitting framework, and the Huber loss function is introduced to construct a robust regression model. Through multiple rounds of iterative optimization, dynamic down-weighting of abnormal disturbance points is achieved, significantly improving the stability of solar wind speed trend term estimation. Secondly, in each iteration, the extreme event identification threshold is dynamically set based on the median absolute difference (MAD) of the residuals, accurately capturing and extracting the severe disturbance information corresponding to space extreme weather events in the solar wind speed time series. The final decomposition result can effectively distinguish the long-term trend of the solar wind speed series from short-term extreme fluctuation events, significantly improving the accuracy of space weather analysis and extreme event prediction. The present invention does not require manual labeling and has the advantages of automation, strong robustness and wide applicability. It is particularly suitable for key mission scenarios such as space weather monitoring and forecasting, and space disaster risk assessment.

[0011] In order to solve the above technical problems, the present invention proposes a robust spline decomposition and extreme value extraction method for solar wind speed time series, comprising the following steps:

[0012] Step 1) Input of solar wind speed time series: Obtain the solar wind speed time series y, which is a sequence of observations at equal time intervals; generate the corresponding time index t = [0, 1, 2, ..., N-1] for the input data length T ;

[0013] Step 2) constructing a spline basis function: according to a predetermined number of spline nodes n, using a quantile position method, selecting n node positions in the time index t generated in step 1), constructing a cubic B-spline basis function, and forming a spline basis function;

[0014] Step 3) Initialize the weight vector: construct a weight vector w with the same length as the solar wind speed time series y, and the initial value of each point in the weight vector w is all 1;

[0015] Step 4) Robust spline fitting and extreme value feedback iteration: Set the number of iterations to N and loop through the following sub-processes 4-1) to 4-3), including:

[0016] 4-1) Fitting the smooth trend term: Based on the current weight vector w, the robust regression model of the Huber loss function is used to perform weighted fitting on the spline basis function matrix formed in step 2) and the solar wind speed time series y to obtain the smooth trend term ^;

[0017] 4-2) Calculate the extreme fluctuation term: Calculate the extreme fluctuation term based on the solar wind speed time series y and the smooth trend term, and find the absolute median difference of the extreme fluctuation term. Set the extreme value discrimination threshold T based on the absolute median difference to measure the degree of abnormality of the fluctuation.

[0018] 4-3) Update the weight vector w. Dynamically adjust the value of each point in the weight vector w according to the extreme fluctuation term and the threshold T. Calculate the updated weight vector. At this point, the weight vector is updated once.

[0019] Step 5) After completing the number of iterations N, the final output includes a smooth trend term, an extreme fluctuation term, and a weight vector w; where:

[0020] 5-1) The smooth trend term output represents the combination of long-term structure and periodic pattern after removing extreme fluctuations in the solar wind speed time series, which helps to identify the basic pattern of solar activity.

[0021] 5-2) The extreme fluctuation term output retains the extreme value component centered at zero in the solar wind speed time series, reflecting the abnormal event characteristics of severe disturbances in the solar wind speed.

[0022] The weight vector w outputted by 5-3) represents a quantitative indicator of the degree of anomaly of the solar wind speed time series at each time point, which is used to determine the extreme degree of anomaly of the data point and assist in the subsequent classification of space weather events, location of anomaly points, and further anomaly diagnosis and analysis.

[0023] Furthermore, the robust spline decomposition and extreme value extraction method of the solar wind speed time series described in the present invention comprises:

[0024] The specific content of the step 2) constructing the spline basis function includes:

[0025] 2-1) The principle for setting the size of the spline node number n is: setting the number of spline nodes n based on the complexity of the solar wind speed time series. People in the industry know how to master this principle.

[0026] 2-2) After sorting the data values of the solar wind speed time series y using the quantile position method, divide it into n+1 intervals with equal probability according to the quantile position, and select nodes at the boundaries of these intervals;

[0027] 2-3) Construct a cubic B-spline basis function, where the set of cubic B-spline basis functions is expressed as:

[0028] X=[Φ1(t),Φ2(t),…,Φ m (t)] (1)

[0029] In formula (1), Φ m (t) represents the mth cubic B-spline basis function, and m represents the dimension of the spline basis function family;

[0030] 2-4) Apply the constructed cubic B-spline basis function to each time point in the time index t to obtain the corresponding spline basis function matrix X spline , whose dimension is N×m, and each row corresponds to the spline basis function vector at a specific time point.

[0031] The step 3) initializing the weight vector includes: for the time series data y=[y1, y2, ..., y n ] T , construct a weight vector w=[w1,w2,...,w n ] T ; In the initial state, the weights of all time points are set to 1, that is, w i =1.

[0032] The step 4-1) fitting the smooth trend term includes: based on the spline basis function matrix X constructed in step 2-4) spline, the time series data y in step 1), and the current weight vector w defined in step 3), construct a robust regression model based on the Huber loss function; the estimated regression coefficient in the robust regression model is:

[0033]

[0034] In formula (2), w i is the weight of the corresponding time point in the weight vector, X spline (i,:) represents the matrix X spline The i-th row vector of L, β represents the regression coefficient; δ (·) is the Huber loss function used in the robust regression model, which has the following mathematical expression:

[0035]

[0036] In formula (3), the residual term δ represents the threshold parameter of the Huber function, which is used to adjust the sensitivity of the model to extreme values;

[0037] Based on the estimated regression coefficients Calculate the smooth trend term

[0038]

[0039] The step 4-2) calculating the extreme fluctuation term includes:

[0040] 4-2-1) Subtract the smooth trend term from step 4-1) from the time series data y in step 1) Get the extreme fluctuation term The specific expression is:

[0041]

[0042] 4-2-2) Calculate the extreme fluctuation term obtained in step 4-2-1) The absolute median difference of:

[0043]

[0044] In formula (6), median(·) represents the median;

[0045] 4-2-3) Based on the absolute median difference obtained in step 4-2-2), set the extreme value identification threshold T to identify data points with abnormal fluctuations. The expression is as follows:

[0046] T = 1.5 × MAD (7).

[0047] The step 4-3) updates the weight vector w, including: the extreme fluctuation term obtained in step 4-2) And the extreme value discrimination threshold T calculates the updated weight vector:

[0048]

[0049] In formula (8), Represents the updated weight value of the i-th data point, Indicates the weight value of the i-th data point before updating, w min is the preset lower limit constant of weight, which is 0.2, and T is the extreme value discrimination threshold obtained in step 4-2). is the absolute value of the extreme fluctuation term corresponding to the i-th data point, ε is a positive constant with a value of 1×10 -8 , used to ensure the stability of numerical calculations.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] First, by introducing the Huber loss function and the extreme value feedback iteration mechanism, the present invention realizes the dynamic down-weighting of abnormal disturbance points in the solar wind speed time series, significantly enhances the robustness of the smooth trend term to abnormal events in the solar wind speed series, overcomes the problem of severe distortion of the trend term under abnormal disturbances in traditional methods, and improves the accuracy and reliability of trend estimation.

[0052] Secondly, by explicitly constructing the extreme fluctuation residual term, the present invention can not only accurately extract the long-term smooth trend in the solar wind speed time series, but also retain the short-term severe disturbance information in the solar wind speed, which facilitates the independent analysis and modeling of space extreme weather events in the solar wind speed, and effectively improves the interpretability of the solar wind speed time series and the accuracy of space weather forecasts.

[0053] Finally, the present invention adopts an automated extreme value feedback iterative weight update strategy, which does not require manual pre-labeling of abnormal events or pre-definition of fixed abnormality discrimination rules. It can adaptively identify extreme abnormal disturbances in solar wind speed during the data decomposition process, realizing the intelligence and automation of the method, and greatly expanding the scope of application and convenience of space weather data analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flow chart of the method of the present invention;

[0055] Figure 2 It is the decomposition result of the solar wind speed sequence in the research material of the present invention. DETAILED DESCRIPTION

[0056] This paper proposes a robust spline decomposition and extreme value extraction method for solar wind speed time series, aiming to accurately separate trend structure from extreme value disturbances in solar wind speed time series, thereby improving the accuracy of space weather forecasts and the ability to identify extreme events. Specifically, this method constructs a cubic B-spline basis function matrix based on quantile nodes, employs the Huber loss function for robust regression modeling, and incorporates an extreme value feedback iterative update mechanism. This method effectively extracts a smooth trend structure and clearly identified extreme fluctuation terms from the raw solar wind speed series, significantly enhancing the method's robustness and adaptability to anomalous solar wind disturbances.

[0057] For ease of explanation, the solar wind speed time series data is defined as follows:

[0058] Assume that the observed solar wind speed time series is y=[y1,y2,...,y n ] T , where n represents the length of the time series and y represents the observation value at the i-th time step. The corresponding time index is t = [0, 1, 2, ..., N-1] T The decomposition goal is to decompose the original sequence y into a smooth trend term ^ and an extreme volatility term ^, that is,

[0059] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the embodiments do not limit the scope of application of the present invention in any way.

[0060] Taking the actual observed solar wind speed time series as an example, the specific steps of the solar wind speed trend analysis and extreme event identification method proposed in the present invention are described as follows: Figure 1 As shown, the method includes the following steps:

[0061] Step 1) Input of solar wind speed time series. This step aims to complete the preparation and basic processing of the original solar wind speed series data.

[0062] Step 1) Input of solar wind speed time series. This step aims to complete the preparation and basic processing of the original solar wind speed series data. First, obtain the solar wind speed time series y observation data and express it as a one-dimensional vector y = [y1, y2, ..., y n ] T , where n is the total number of observation data points. The time intervals must be uniform to ensure the accuracy of subsequent fitting. For the length of the input data, the corresponding time index t = [0, 1, 2, ..., N-1] is generated. T , the time index will be used as the independent variable input to construct the spline basis function, ensuring that the fitting process strictly follows the time order.

[0063] After completing the above steps, the solar wind speed series data and its time index are ready, providing basic input for subsequent spline basis function construction and robust regression fitting.

[0064] Step 2) Constructing the spline basis function. After completing the input of the solar wind speed time series data, this step aims to construct a spline basis function for robust fitting by presetting the number of nodes.

[0065] First, the number of nodes required in the spline decomposition is set to n. This parameter determines the local fitting ability and smoothness of the B-spline basis function. The more nodes there are, the higher the flexibility of the fitting is, but the smoothness decreases. Conversely, the smoothness of the fitting is improved, but it may lead to insufficient fitting. Therefore, the principle of setting the size of the spline node number n is: based on the comprehensive consideration of the complexity of the time series data, the fitting accuracy requirements and the computational efficiency, and industry insiders know how to master this principle.

[0066] Then, according to the set number of spline nodes n, based on the constructed time index sequence t=[0,1,2,...,N-1] T , using a quantile partitioning strategy to determine node positions. Specifically, the quantile partitioning strategy evenly divides the time series data index into n+1 intervals based on the quantile positions of the data length, and selects nodes at the boundaries of these intervals. Compared to the traditional equidistant node partitioning strategy, this method can more effectively adapt to the non-uniform density distribution of time series, significantly improving the adaptability and expressiveness of spline fitting. Unlike traditional equidistant partitioning, the quantile selection method can better adapt to the uneven distribution of observation points in the time series, thereby improving the ability of the subsequent fitted curve to capture local features.

[0067] According to the selected node set, the spline basis function is constructed with the cubic B-spline as the basis function, where the cubic B-spline basis function set is expressed as:

[0068] X=[Φ1(t),Φ2(t),…,Φ m (t)]

[0069] Where, Φ m (t) represents the mth cubic B-spline basis function, and m represents the dimension of the spline basis function family;

[0070] Then, the constructed cubic B-spline basis function is applied to each time point in the time index t, that is, each time point in the time index t is substituted into all B-spline basis functions, and the corresponding response value is calculated to finally form the spline basis function X spline , whose dimension is N×m, and each row corresponds to the spline basis function vector at a specific time point. spline It will be used as the input feature matrix of the subsequent robust regression model to support the fitting process of the trend term.

[0071] Step 3) Initialize the weight vector. In order to effectively deal with outliers in the robust regression process, this step initializes the weight vector corresponding to each data point. Specifically, for the time series data y=[y1,y2,...,y n ] T , construct a weight vector w=[w1,w2,...,w n ] T , used to identify the degree of influence of each observation point on the fitting process. Initially, all weight elements are assigned a value of 1, that is, w i = 1 indicates that in the initial stage, all data points are considered equally important and participate equally in the trend fitting calculation, which is used to downweight outliers in the subsequent robust fitting process. As the iterative process progresses, the weight vector w will be dynamically updated based on the residual size, gradually reducing the interference of abnormal fluctuation points on the trend fitting results and improving the model's robustness to abnormal situations.

[0072] Step 4) Robust spline fitting and extreme value feedback iteration: After completing the construction of the spline basis function and weight initialization, this step sets the number of iterations N to cyclically optimize the robust fitting and extreme value feedback process to improve the ability to adapt to abnormal fluctuations. Specifically, each iteration includes the following sub-steps:

[0073] 4-3) Update the weight vector w. Dynamically adjust the value of each point in the weight vector w according to the extreme fluctuation term and the threshold T. Calculate the updated weight vector. At this point, the weight vector is updated once.

[0074] First, based on the current weight vector w, the Huber loss function is used to build a robust regression model. spline Perform weighted fitting with the solar wind speed time series y to solve the optimal regression coefficient and obtain the fitted smooth trend term The Huber loss function combines the accuracy advantage of squared error when the residual is small and the robustness of absolute error when the residual is large, thereby effectively reducing the impact of extreme values on the overall trend estimation.

[0075] The estimated regression coefficients in the robust regression model are:

[0076]

[0077] Where w i is the weight of the corresponding time point in the weight vector, X spline (i,:) represents the matrix X spline The i-th row vector of L, β represents the regression coefficient; δ(·) is the Huber loss function used in the robust regression model, which has the following mathematical expression:

[0078]

[0079] In the formula, the residual term δ represents the threshold parameter of the Huber function, which is used to adjust the sensitivity of the model to extreme values;

[0080] Based on the estimated regression coefficients Calculate the smooth trend term

[0081]

[0082] Then, the extreme fluctuation term is calculated based on the solar wind speed time series y and the smooth trend term, and the absolute median difference of the extreme fluctuation term is obtained; the extreme value discrimination threshold T is set according to the absolute median difference to measure the abnormal degree of fluctuation, that is, the original sequence y is subtracted from the smooth trend term obtained by fitting the current round. Get the extreme fluctuation term

[0083] Based on this extreme fluctuation term, the median and absolute median difference of the residuals are calculated.

[0084]

[0085] In the formula, median(·) represents the median. The extreme value discrimination threshold T = 1.5 × MAD is set according to the following formula to identify data points with abnormal fluctuations. MAD is a robust measure of residual distribution and effectively prevents the amplification effect of the mean square error on extreme outliers. The extreme value discrimination threshold T can distinguish between normal fluctuations and extreme fluctuations, determining the degree of abnormality at each time point.

[0086] Finally, the weight of each sample point is dynamically updated based on the residual size and the extreme value discrimination threshold T. The specific update rule is to compare the ratio of the current weight to the residual normalization threshold, and use the clipping operation to limit the weight update range.

[0087] According to the extreme fluctuation term And the extreme value discrimination threshold T calculates the updated weight vector:

[0088]

[0089] Where, Represents the updated weight value of the i-th data point, Indicates the weight value of the i-th data point before updating, w minis the preset lower limit constant of weight, which is set to 0.2 to avoid the weight being too small or invalid. T is the obtained extreme value discrimination threshold. is the absolute value of the extreme fluctuation term corresponding to the i-th data point, ε is a positive constant with a value of 1×10 -8 , which is used to ensure the stability of numerical calculations. Through the above extreme value feedback mechanism, the impact of extreme fluctuation points can be gradually reduced in multiple rounds of iterations, making the fitting results more robust.

[0090] The above steps are repeated within the set number of iterations N until the iteration termination condition is met.

[0091] Step 5) Output the results. After completing the set number of iterations N, this step outputs the final results of the solar wind speed time series decomposition process.

[0092] First, output the smooth trend term It represents the long-term trend structure and periodic variation pattern of the solar wind speed time series after multiple rounds of robust iterative fitting and the elimination of extreme fluctuation interference. This helps to identify the basic pattern of solar activity and can effectively reveal the background evolution trend of solar wind speed on the scale of solar activity cycle, providing a reliable basis for the analysis of space weather background state. Specifically, it reveals the long-term variation law of solar wind speed on the scale of solar activity cycle, such as the smooth evolution trend between slow wind and fast wind. This trend term is suitable for long-term trend analysis of solar wind speed, space weather background modeling, space weather forecasting and space mission orbital dynamics simulation research. Studies have shown that parameters such as solar wind speed, density and magnetic field strength show a 27-day periodic variation throughout the solar cycle, especially during the maximum and decline phases of solar activity [1]. Therefore, the periodicity makes solar wind speed one of the most predictable solar wind plasma characteristics.

[0093] Secondly, output extreme fluctuation terms It is defined as the difference between the solar wind speed time series and the smooth trend term. This extreme fluctuation term clearly retains the abnormal disturbance information in the solar wind speed series, and clearly shows the abnormal event characteristics of the solar wind speed violent disturbance in the short term, which usually corresponds to space weather extreme events such as solar flares, coronal mass ejection shock waves and interplanetary shock waves. This extreme fluctuation term is suitable for the automatic identification of solar wind extreme events, rapid response analysis of space weather disaster events, research on the statistical laws of extreme events and space weather disaster risk assessment; such as the signal characteristics of space extreme events such as solar flares, coronal mass ejection (CME) shock waves and interplanetary shock waves, it can be directly applied to the rapid identification, early warning and disaster risk analysis tasks of space extreme weather. For example: the output extreme fluctuation term retains the extreme value component centered at zero in the solar wind speed time series, reflecting the abnormal event characteristics of the solar wind speed violent disturbance. Studies have shown that CME events will cause the solar wind speed to increase by 18% to 32% during the event, and will still maintain an increase of 9% to 24% within two days after the event, indicating that the disturbance of CME to interstellar space may last for 3 to 6 days [2]. In contrast, CIR / HSS events usually originate from coronal holes near the solar equator, and their effects can last from several days to more than a week [3]. Therefore, by analyzing the abnormal disturbances in the solar wind speed, it is possible to effectively distinguish between CMEs and CIR / HSS events.

[0094] Finally, the final iteration results in a weight vector, w, which reflects the degree of anomaly in the solar wind speed time series at each time point during the trend term fitting process. Smaller weights indicate stronger anomaly fluctuations at that time point. The weight vector can be used as a quantitative indicator of anomaly severity to assist in the location analysis of subsequent space weather anomalies and subsequent outlier detection and diagnosis.

[0095] Research Materials

[0096] This study uses solar wind speed time series as the research object and proposes a robust spline decomposition and extreme value extraction method for this series. This method addresses the severe disturbances, nonstationary fluctuations, and local extreme values present in solar wind observational data by combining the Huber loss function with a spline fitting model to construct a robust time series decomposition framework. By dynamically adjusting sample point weights through an iterative feedback mechanism, it effectively suppresses the interference of extreme outliers on trend extraction.

[0097] Figure 2This paper demonstrates the decomposition results of this method on a solar wind speed dataset collected by NASA. Subfigure (a) shows the solar wind speed time series and the smoothed trend term. The red curve represents the solar wind speed time series in this dataset, and the black curve represents the extracted trend component, which clearly removes spike interference caused by explosive disturbances. Subfigure (b) shows the extreme fluctuation term component. The black curve represents the extracted extreme fluctuation term, and red dots indicate moments identified as strong fluctuation points. These locations often correspond to solar wind mutation events or instrument errors. Subfigure (c) shows the weight vector obtained from the final iteration. The lower the weight, the more likely the time point is an abnormal fluctuation point. The overall results reflect the advantages of the model's interpretability and stability.

[0098] This method can not only extract the main trend changes in the solar wind speed series for prediction and long-term evolution analysis, but also explicitly identify and quantify extreme points. It has practical technical value in application scenarios such as anomaly detection, data cleaning, and space weather warning.

[0099] Although the present invention has been described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments. The above-mentioned specific embodiments are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can make many improvements and changes without departing from the purpose of the present invention, which are all protected by the present invention.

Claims

1. A robust spline decomposition and extreme value extraction method for solar wind speed time series, characterized by: The method comprises the following steps: Step 1) Input of solar wind speed time series: Obtain the solar wind speed time series y, which is a sequence of observations at equal time intervals; generate the corresponding time index t = [0, 1, 2, ..., N-1] for the input data length T ; Step 2) constructing a spline basis function: according to a predetermined number of spline nodes n, using a quantile position method, selecting n node positions in the time index t generated in step 1), constructing a cubic B-spline basis function, and forming a spline basis function; Step 3) Initialize the weight vector: construct a weight vector w with the same length as the solar wind speed time series y, and the initial value of each point in the weight vector w is all 1; Step 4) Robust spline fitting and extreme value feedback iteration: Set the number of iterations to N and loop through the following sub-processes 4-1) to 4-3), including: 4-1) Fitting the smooth trend term: Based on the current weight vector w, the robust regression model of the Huber loss function is used to fit the spline basis function matrix X formed in step 2) spline Perform weighted fitting with the solar wind speed time series y to obtain a smooth trend term ^; 4-2) Calculate the extreme fluctuation term: Calculate the extreme fluctuation term based on the solar wind speed time series y and the smooth trend term, and find the absolute median difference of the extreme fluctuation term. Set the extreme value discrimination threshold T based on the absolute median difference to measure the degree of abnormality of the fluctuation. 4-3) Update the weight vector w. Dynamically adjust the value of each point in the weight vector w according to the extreme fluctuation term and the threshold T. Calculate the updated weight vector. At this point, the weight vector is updated once. Step 5) After completing the number of iterations N, the final output includes a smooth trend term, an extreme fluctuation term, and a weight vector w; where: The smoothed trend term of the output represents the combination of long-term structure and periodic pattern after removing extreme fluctuations in the solar wind speed time series, which helps to identify the basic pattern of solar activity; The extreme fluctuation term of the output retains the extreme value component centered at zero in the solar wind speed time series, reflecting the abnormal event characteristics of severe disturbances in the solar wind speed; The output weight vector w represents a quantitative indicator of the degree of anomaly of the solar wind speed time series at each time point. It is used to determine the extreme degree of anomaly of the data point and assist in subsequent space weather event classification, anomaly point location, and further anomaly diagnosis and analysis.

2. The robust spline decomposition and extreme value extraction method for solar wind speed time series according to claim 1, characterized in that: The step 2) comprises: 2-1) The principle for setting the number of spline nodes n is: setting the number of spline nodes n based on the complexity of the solar wind speed time series; 2-2) After sorting the data values of the solar wind speed time series y using the quantile position method, divide it into n+1 intervals with equal probability according to the quantile position, and select nodes at the boundaries of these intervals; 2-3) Construct a cubic B-spline basis function, where the set of cubic B-spline basis functions is expressed as: X=[Φ1(t),Φ2(t),…,Φ m (t)] (1) In formula (1), Φ m (t) represents the mth cubic B-spline basis function, and m represents the dimension of the spline basis function family; 2-4) Apply the constructed cubic B-spline basis function to each time point in the time index t to obtain the corresponding spline basis function matrix X spline , whose dimension is N×m, and each row corresponds to the spline basis function vector at a specific time point.

3. The robust spline decomposition and extreme value extraction method for solar wind speed time series according to claim 1, characterized in that: The step 3) comprises: For the time series data y=[y1,y2,...,y n ] T , construct a weight vector w=[w1,w2,...,w n ] T ; In the initial state, the weights of all time points are set to 1, that is, w i =1.

4. The robust spline decomposition and extreme value extraction method for solar wind speed time series according to claim 1, characterized in that: Step 4-1) includes: Based on the spline basis function matrix X constructed in steps 2-4) spline , the time series data y in step 1), and the current weight vector w defined in step 3), construct a robust regression model based on the Huber loss function; the estimated regression coefficient in the robust regression model is: In formula (2), w i is the weight of the corresponding time point in the weight vector, X spline (i,:) represents the matrix X spline The i-th row vector of L, β represents the regression coefficient; δ (·) is the Huber loss function used in the robust regression model, which has the following mathematical expression: In formula (3), the residual term δ represents the threshold parameter of the Huber function, which is used to adjust the sensitivity of the model to extreme values; Based on the estimated regression coefficients Calculate the smooth trend term 5. The robust spline decomposition and extreme value extraction method for solar wind speed time series according to claim 1, characterized in that: Step 4-2) includes: 4-2-1) Subtract the smooth trend term from step 4-1) from the time series data y in step 1) Get the extreme fluctuation term The specific expression is: 4-2-2) Calculate the extreme fluctuation term obtained in step 4-2-1) The absolute median difference of: In formula (6), median(·) represents the median; 4-2-3) Based on the absolute median difference obtained in step 4-2-2), set the extreme value identification threshold T to identify data points with abnormal fluctuations. The expression is as follows: T = 1.5 × MAD (7).

6. The robust spline decomposition and extreme value extraction method for solar wind speed time series according to claim 1, characterized in that: Step 4-3) includes: According to the extreme fluctuation term obtained in step 4-2) And the extreme value discrimination threshold T calculates the updated weight vector: In formula (8), Represents the updated weight value of the i-th data point, Indicates the weight value of the i-th data point before updating, w min is the preset lower limit constant of weight, which is 0.2, and T is the extreme value discrimination threshold obtained in step 4-2). is the absolute value of the extreme fluctuation term corresponding to the i-th data point, ε is a positive constant with a value of 1×10 -8 , used to ensure the stability of numerical calculations.

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