Planetary and Asteroid Motion Simulation Analysis System

Abstract

The present invention relates to the technical field of motion simulation, specifically a system for simulating and analyzing the motion of planets and asteroids. The system includes a data collection module, a dynamic weight adjustment module, a trajectory correction module, and a result comprehensive evaluation module. The data collection module collects real-time position and velocity information of planets and asteroids based on astronomical telescopes and space probes. In the present invention, through the random forest and gradient boosting tree algorithms, the accuracy and response speed of the motion simulation of planets and asteroids are improved. When processing celestial body motion data, not only the weight adjustment process is optimized, but also through the dynamic update of the real-time data set, the system is allowed to continuously adapt to new observation inputs. Especially for the immediate update of the position and velocity of celestial bodies, it can reduce the delay of data processing, improve the real-time performance of trajectory prediction, enhance the immediate feedback and adaptive adjustment ability of the model, and ensure the accuracy of prediction in the ever-changing celestial environment.

Description

Technical Field

[0001] The present invention relates to the technical field of motion simulation, and particularly to a system for simulating and analyzing the motion of planets and asteroids. Background Art

[0002] Motion simulation technology is a technology widely used in scientific research, engineering design, and the entertainment industry. By using high-performance computers to simulate the dynamic behavior of objects, this technology uses complex mathematical models and algorithms to predict and reproduce the motion of objects in real or virtual environments, including the simulation of planetary motion, aircraft navigation, car collisions, and sports. Its core lies in using physical laws for accurate prediction and analysis.

[0003] Among them, the system for simulating and analyzing the motion of planets and asteroids focuses on motion simulation in the field of astrophysics, aiming to study and analyze the motion trajectories and dynamic behaviors of planets and asteroids in space through computer simulation. The system is usually used in astronomical research and space mission planning, such as orbit design, impact risk assessment, and spacecraft navigation. By accurately simulating the motion of celestial bodies, it is possible to better understand the dynamic structure of the solar system, predict the future positions of celestial bodies, and evaluate asteroids that pose a threat to the Earth. In addition, it can also help people learn and understand the basic principles and complexities of celestial body motion.

[0004] Traditional systems mainly rely on fixed algorithms and models with long-period updates in celestial body motion simulation, which appear inflexible and untimely when dealing with sudden celestial events or rapidly changing orbits. Although they can perform basic trajectory predictions, in the case of rapid adjustments, their prediction models lack an effective adaptive mechanism, resulting in a deviation between the prediction results and actual observation data. This lag is likely to lead to inaccurate judgments when making emergency judgments or impact risk assessments. Summary of the Invention

[0005] The purpose of the present invention is to solve the disadvantages existing in the prior art and propose a system for simulating and analyzing the motion of planets and asteroids.

[0006] To achieve the above purpose, the present invention adopts the following technical solution: A system for simulating and analyzing the motion of planets and asteroids, the system comprising:

[0007] The data collection module collects real-time position and velocity information of planets and asteroids based on astronomical telescopes and space probes, calculates the current orbital elements of celestial bodies, organizes orbital data, converts the organized data into a simulation format, and obtains a real-time celestial body dataset;

[0008] The dynamic weight adjustment module performs preliminary adjustment of weights and parameters based on the real-time celestial body dataset, refines the learning rate and weight decay parameters according to the historical gradient squares of the parameters, updates the model parameter weights, and uses the random forest algorithm to evaluate the parameters to generate a weight adjustment parameter set;

[0009] The trajectory correction module uses the weight adjustment parameter set, combines new observation data, and gradually corrects the trajectory prediction error through the gradient boosting tree algorithm, and calculates the negative gradient of the loss function to generate a corrected trajectory prediction model;

[0010] The result comprehensive evaluation module analyzes the corrected trajectory prediction model, compares the deviations between the trajectory predictions and the observation data at different time points, evaluates the accuracy and response speed of the prediction model, and generates an overview of the prediction performance evaluation.

[0011] The improvements of the present invention are that the specific steps for collecting the real-time position and velocity information are as follows:

[0012] Use astronomical telescopes and space probes for continuous monitoring to collect optical data of target planets and asteroids, and the data includes timestamps and optical images;

[0013] Perform data processing on the collected image data, automatically identify celestial body features, and extract the celestial coordinate positions;

[0014] Based on the coordinate data of two consecutive observations, use the formula:

[0015]

[0016] Calculate the velocity vector of the celestial body, combine with the position information, and standardize it into real-time position and velocity information. Among them, Δx is the position change amount, representing the displacement of the planet or asteroid within the time Δt, Δt is the time interval, which is the time difference between two observations, β and γ are deviation coefficients used to adjust the deviations caused by the environment and equipment, ω is the correction frequency, t is the observation time point, and α is the fine-tuning coefficient of the time interval, which is used to control the influence of the time difference in velocity calculation.

[0017] The improvements of the present invention are that the specific steps for calculating the current orbital elements of the celestial body are as follows:

[0018] Calculate according to the collected real-time position and velocity information using Kepler's laws and Newton's laws of motion;

[0019] Combine the celestial body mass, gravitational constant, orbital period, and current time to calculate the key parameters of the orbit, using the formula:

[0020]

[0021] and

[0022]

[0023] Calculate the semi-major axis and eccentricity, and output the calculation results as the current orbital elements of the celestial body. Among them, G is the gravitational constant, which represents the physical constant of the interaction between celestial bodies, m is the mass of the celestial body, which is a key factor in calculating the orbital elements, T is the orbital period, which refers to the time required for the celestial body to complete one full orbital motion, a is the semi-major axis, which represents half of the length of the major axis of the orbital ellipse, and e is the eccentricity, which represents the shape of the orbital ellipse.

[0024] The improvement of the present invention is that the specific steps for the preliminary adjustment of the weights and parameters are as follows:

[0025] Based on the real-time celestial body data set, collect the information of the celestial body position and velocity parameters;

[0026] Use historical data to calculate the average value of the square of the historical gradient of the parameters, using the formula:

[0027]

[0028] Adjust the sensitivity of the learning rate, and combine the historical gradient of the parameters to adjust the weights and parameters. Among them, η represents the adjusted learning rate, η 0 is the initially set learning rate, g is the average value of the square of the historical gradient of the parameters, ∈ is a small positive number to avoid the denominator being zero, λ is the weight adjustment factor, which is used to adjust the change rate of the learning rate according to the maximum value of the gradient, g max is the maximum value in the square of the historical gradient, which is used to reflect the additional influence of the gradient extreme value on the learning rate.

[0029] The improvement of the present invention is that the specific steps for the evaluation of the parameters are as follows:

[0030] Collect the adjusted model parameters and weights, and input the parameter weights;

[0031] Apply the random forest algorithm to evaluate the parameters, using the formula:

[0032]

[0033] Calculate the feature criticality score, and generate a weight adjustment parameter set according to the evaluation results of the random forest algorithm. Among them, I represents the criticality of the feature, Δi represents the change in the model accuracy after removing the feature, w i is the feature weight coefficient, N is the number of decision trees, S i is the number of samples of the feature, S total is the total number of samples of the feature, which is used to standardize the proportional influence.

[0034] The improvement of the present invention is that the specific steps for calculating the negative gradient of the loss function are as follows:

[0035] Collect new observation data, where the data includes current trajectory information, use the set of weight adjustment parameters to update the weights of the gradient boosting tree model, and match the new observation data;

[0036] Apply the current model parameters, calculate the error between the predicted trajectory and the observed trajectory, and determine the loss function;

[0037] And calculate the negative gradient of the loss function with respect to each parameter, using the formula:

[0038]

[0039] Obtain a corrected trajectory prediction model, where L is the loss calculated based on the difference between the current model prediction and the observation, p represents the parameters in the model, α is an adjustment coefficient used to optimize the influence of the second derivative, β is another adjustment coefficient used to adjust the weight of the first derivative, and k is an error decay constant used to smooth the error contribution, is the negative gradient of the calculated loss function, which is used to guide parameter adjustment and minimize the loss.

[0040] The improvement of the present invention is that the step of comparing the deviation between the trajectory prediction and the observation data is specifically:

[0041] Extract the trajectory prediction data of the corrected trajectory prediction model at the target time point, and collect the observation data at the corresponding time point;

[0042] Compare the trajectory prediction data and the observation data at each difference time point, using the formula:

[0043] D t =(p t -o t )+λ(p t-1 -o t-1 )×k

[0044] Calculate the deviation between the two, where D t is the deviation at the target time point t, p t is the predicted value of the model at time point t, o t is the observed value at time point t, λ is a decay factor used to adjust the influence of the deviation at the previous time point, k is an adjustment coefficient used to balance the deviation weight at the previous time point, p t-1 and o t-1 are the predicted and observed values at the previous time point, which are used to calculate the influence of time continuity on the current deviation.

[0045] The improvement of the present invention is that the step of evaluating the accuracy and response speed of the prediction model is specifically:

[0046] Collect deviation data, using the formula:

[0047]

[0048] and

[0049]

[0050] Calculate the mean and standard deviation of the deviation, and analyze the response speed. Use the rate calculation formula:

[0051]

[0052] Calculate the rate of change of the deviation. Combine the mean and standard deviation to generate an overview of the predictive performance evaluation of the prediction model. Among them, D t is the total deviation at time point t, μ D is the mean of the deviation, adjusted to incorporate the influence of the deviation at the previous time point on the current value. σ D is the standard deviation of the deviation, calculated by incorporating the deviation at the previous time point. α is the weight coefficient of the deviation at the previous time point, used to balance the influence of historical data on the current calculation. R is the rate of change of the deviation, combined with the weighted deviations at two consecutive time points. Δt is the time interval, used to calculate the rate of change of the deviation.

[0053] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0054] In the present invention, through the random forest and gradient boosting tree algorithms, the accuracy and response speed of the simulation of the motion of planets and asteroids are improved. When processing celestial motion data, not only the weight adjustment process is optimized, but also through the dynamic update of the real-time data set, the system is allowed to continuously adapt to new observation inputs. Especially for the immediate update of the celestial position and velocity, it can reduce the delay of data processing, improve the real-time performance of trajectory prediction, enhance the immediate feedback and adaptive adjustment ability of the model, ensure the accuracy of prediction in the ever-changing celestial environment, and thus optimize the research quality of celestial motion and the safety planning of space missions. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a module diagram of the planetary and asteroid motion simulation analysis system proposed by the present invention;

[0056] Figure 2 is a flowchart for collecting real-time position and velocity information in the planetary and asteroid motion simulation analysis system proposed by the present invention;

[0057] Figure 3 is a flowchart for calculating the current orbital elements of celestial bodies in the planetary and asteroid motion simulation analysis system proposed by the present invention;

[0058] Figure 4This is the flowchart for the preliminary adjustment of weights and parameters in the planetary and asteroid motion simulation analysis system proposed by the present invention;

[0059] Figure 5 This is the flowchart for the evaluation of parameters in the planetary and asteroid motion simulation analysis system proposed by the present invention;

[0060] Figure 6 This is the flowchart for the calculation of the negative gradient of the loss function in the planetary and asteroid motion simulation analysis system proposed by the present invention;

[0061] Figure 7 This is the flowchart for the deviation comparison between the trajectory prediction and the observation data in the planetary and asteroid motion simulation analysis system proposed by the present invention;

[0062] Figure 8 This is the flowchart for evaluating the accuracy and response speed of the prediction model in the planetary and asteroid motion simulation analysis system proposed by the present invention. Detailed implementation manners

[0063] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present 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 only used to explain the present invention and are not used to limit the present invention.

[0064] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings. These are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the present invention. In addition, in the description of the present invention, the meaning of "plurality" is two or more unless otherwise specifically defined.

[0065] Embodiment

[0066] Please refer to Figure 1 , the present invention provides a technical solution: The planetary and asteroid motion simulation analysis system includes:

[0067] The data collection module collects the real-time position and velocity information of planets and asteroids based on astronomical telescopes and space probes, calculates the current orbital elements of celestial bodies, conducts orbital data collation, converts the collated data into a simulation format, and obtains a real-time celestial body dataset;

[0068] The dynamic weight adjustment module performs preliminary adjustments of weights and parameters based on the real-time celestial body dataset, refines the learning rate and weight decay parameters according to the historical gradient squares of the parameters, updates the model parameter weights, and uses the random forest algorithm to evaluate the parameters to generate a weight adjustment parameter set;

[0069] The trajectory correction module uses the weight adjustment parameter set, combines new observation data, and gradually corrects the trajectory prediction error through the gradient boosting tree algorithm, and calculates the negative gradient of the loss function to generate a corrected trajectory prediction model;

[0070] The result comprehensive evaluation module analyzes the corrected trajectory prediction model, compares the deviations between the trajectory predictions and the observation data at different time points, evaluates the accuracy and response speed of the prediction model, and generates an overview of the prediction performance evaluation.

[0071] The real-time celestial body dataset includes the orbital period, eccentricity, and semi-major axis. The weight adjustment parameter set includes the parameter update frequency, adjustment amplitude, and weight initial value. The corrected trajectory prediction model includes the prediction error range, trajectory adjustment accuracy, and model iteration times. The overview of the prediction performance evaluation includes evaluation accuracy, model stability, and prediction deviation information.

[0072] Please refer to Figure 2 , and the specific steps for collecting real-time position and velocity information are as follows:

[0073] Use astronomical telescopes and space probes for continuous monitoring to collect optical data of target planets and asteroids. The data includes timestamps and optical images;

[0074] Perform data processing on the collected image data, automatically identify celestial body features, and extract the celestial body coordinate positions;

[0075] Based on the coordinate data of two consecutive observations, use the formula:

[0076]

[0077] Calculate the velocity vector of the celestial body, combine the position information, and standardize it into real-time position and velocity information. Among them, Δx is the position change amount, representing the displacement of the planet or asteroid within the time Δt. Δt is the time interval, which is the time difference between two observations. β and γ are deviation coefficients used to adjust the deviations caused by the environment and equipment. ω is the correction frequency, t is the observation time point, and α is the fine-tuning coefficient of the time interval, which is used to control the influence of the time difference in velocity calculation.

[0078] Suppose there are the following parameters:

[0079] The position of the planet x at the first observation 1 = 100 units;

[0080] The position of the planet x at the second observation2 = 150 units;

[0081] Observation time interval t 1 = 0 seconds, t 2 = 10 seconds;

[0082] Adjustment parameters β = 0.5, γ = 0.3;

[0083] Calibration frequency ω = π (radians per second),

[0084] Time interval fine-tuning coefficient α = 0.1 second.

[0085] Calculate the position change Δx:

[0086] Δx = x 2 - x 1 = 150 - 100 = 50 units

[0087] Calculate the time interval Δt

[0088] Δt = t 2 - t 1 = 10 - 0 = 10 seconds

[0089] Calculate the sine and cosine adjustments:

[0090] sin(ω·t 2 ) = sin(π·10) = 0 (since sin(10π) is an integer multiple of the periodic function at t = 10 seconds)

[0091] cos(ω·t 2 ) = cos(π·10) = 1 (similarly, an integer multiple of the periodic function)

[0092] Apply the adjustment parameters:

[0093] The adjusted position change Δx' = Δx + β·sin(ω·t 2 ) + γ·cos(ω·t 2 )

[0094] Δx' = 50 + 0.5·0 + 0.3·1 = 50.3 units

[0095] Calculate the adjusted time interval:

[0096] Δt' = Δt + α = 10 + 0.1 = 10.1 seconds

[0097] Final calculation of velocity V

[0098]

[0099] Please refer to Figure 3, the calculation steps for the current orbital elements of the celestial body are specifically as follows:

[0100] Based on the collected real-time position and velocity information, calculations are performed using Kepler's laws and Newton's laws of motion;

[0101] Combined with the celestial body mass, gravitational constant, orbital period, and current time, calculate the key parameters of the orbit using the formulas:

[0102]

[0103] and

[0104]

[0105] Calculate the semi-major axis and eccentricity, and output the calculation results as the current orbital elements of the celestial body. Among them, G is the gravitational constant, representing the physical constant of the interaction between celestial bodies, m is the celestial body mass, which is a key factor in calculating orbital elements, T is the orbital period, referring to the time required for the celestial body to complete one full orbital motion, a is the semi-major axis, representing half the length of the major axis of the orbital ellipse, and e is the eccentricity, indicating the shape of the orbital ellipse.

[0106] Suppose there are the following parameters:

[0107] The mass of the celestial body m = 5.972×10 24 kg (the mass of the Earth);

[0108] The gravitational constant G = 6.674×10 -11 m 3 / kg / s 2 ;

[0109] The orbital period T = 365.25 days, converted to seconds as T = 31557600 seconds.

[0110] Calculation of the semi-major axis a:

[0111] Substitute the parameters into the formula:

[0112]

[0113] a = 1.496×10 11 meters (approximately the average distance from the Earth to the Sun)

[0114] Calculation of the eccentricity e:

[0115] Assume a is known (obtained from the above calculation),

[0116] Substitute the known a, G, m, and T for calculation to obtain the specific value of e,

[0117]

[0118] e ≈ 0.0167 (approximate value of the Earth's orbital eccentricity)

[0119] Thus, accurately calculate the orbital elements of celestial bodies, such as the semi-major axis and eccentricity.

[0120] Please refer to Figure 4 , the specific steps for the preliminary adjustment of weights and parameters are as follows:

[0121] Based on the real-time celestial body dataset, collect information on the positions and velocity parameters of celestial bodies;

[0122] Using historical data, calculate the average value of the squared historical gradients of the parameters, using the formula:

[0123]

[0124] Adjust the sensitivity of the learning rate, and adjust the weights and parameters in combination with the historical gradients of the parameters. Among them, η represents the adjusted learning rate, η 0 is the initially set learning rate, g is the average value of the squared historical gradients of the parameters, ∈ is a small positive number to avoid the denominator being zero, λ is the weight adjustment factor used to adjust the change rate of the learning rate according to the maximum value of the gradient, g max is the maximum value in the squared historical gradients, used to reflect the additional influence of the gradient extreme value on the learning rate.

[0125] Suppose there is the following data:

[0126] Initial learning rate η 0 = 0.1;

[0127] Small positive number ∈ to prevent zero = 1×10 -8 ;

[0128] Adjustment factor λ = 0.1;

[0129] Squared historical gradient g = 0.02;

[0130] Maximum value g of all squared historical gradients max = 0.05.

[0131] Calculate the average value of the squared historical gradients g:

[0132] Obtain g = 0.02 from historical data, indicating the average squared gradient of each parameter.

[0133] Calculate the maximum squared historical gradient g max :

[0134] Suppose that among all the recorded historical gradient data, the largest squared gradient value is g max = 0.05.

[0135] Apply the learning rate adjustment formula to calculate the new learning rate, and substitute specific values:

[0136]

[0137]

[0138] η≈0.63246

[0139] The calculation process ensures that the learning rate adjustment combines the historical changes of the gradient and can adaptively adjust the learning rate according to the update history of different parameters to optimize the performance and response of the model.

[0140] Please refer to Figure 5 , and the evaluation steps of the parameters are specifically as follows:

[0141] Collect the adjusted model parameters and weights and perform the input of parameter weights;

[0142] Apply the random forest algorithm to evaluate the parameters, using the formula:

[0143]

[0144] Calculate the feature criticality score, and generate a weight adjustment parameter set according to the evaluation result of the random forest algorithm, where I represents the criticality of the feature, Δi represents the change in the model accuracy after removing the feature, w i is the feature weight coefficient, N is the number of decision trees, S i is the sample number of the feature, S total is the total sample number of the feature, which is used to standardize the proportional impact.

[0145] Suppose there is the following data:

[0146] N = 100 (the number of decision trees).

[0147] For a certain target feature i:

[0148] Δi = 0.02 (the average change in the model accuracy after removing this feature);

[0149] w i = 1.5 (the weight coefficient of this feature in the model);

[0150] S i = 300 (the sample number of this feature);

[0151] S total = 5000 (the total sample number of all features).

[0152] Calculate the importance score of a single feature:

[0153] Substitute the parameters into the formula for calculation:

[0154]

[0155] Score = 0.03 × 0.06

[0156] Score = 0.0018

[0157] Summarize the importance scores of all features:

[0158] If it is assumed that the calculations of other features follow the same pattern, the final I can be calculated by summing up the scores of all features:

[0159] Assume that the average scores of the other 99 features are the same as in the above example

[0160]

[0161] I = 0.0018

[0162] The importance score of each feature is calculated, taking into account the influence of the feature (through weights) and representativeness (through the number of samples), thus making the model evaluation more accurate and comprehensive.

[0163] Please refer to Figure 6 , and the specific calculation steps of the negative gradient of the loss function are as follows:

[0164] Collect new observation data, which includes current trajectory information, adjust the parameter set using weights, update the weights of the gradient boosting tree model, and match the new observation data;

[0165] Apply the current model parameters, calculate the error between the predicted trajectory and the observed trajectory, and determine the loss function;

[0166] And calculate the negative gradient of the loss function with respect to each parameter, using the formula:

[0167]

[0168] Obtain the corrected trajectory prediction model, where L is the loss calculated based on the difference between the current model prediction and the observation, p represents the parameters in the model, α is an adjustment coefficient used to optimize the influence of the second derivative, β is another adjustment coefficient used to adjust the weight of the first derivative, k is an error decay constant used to smooth the error contribution, is the calculated negative gradient of the loss function, which is used to guide parameter adjustment and minimize the loss.

[0169] Assume that in practical applications, there are the following parameter values:

[0170] The loss function L is expressed as where y is the actual observed value, is the model predicted value;

[0171] The actual observed value y = 100;

[0172] Predicted value

[0173] The current value of the model parameter p is 5;

[0174] The adjustment coefficients are α = 0.1 and β = 0.05;

[0175] The error decay constant k = 0.9.

[0176] Calculate the loss function L:

[0177] L=(100 - 95) 2 = 25

[0178] Calculate the first derivative of the loss function with respect to the parameter p

[0179] Since depends on p, assume

[0180]

[0181] Calculate the second derivative of the loss function with respect to the parameter p

[0182]

[0183] Apply the negative gradient formula:

[0184]

[0185] Please refer to Figure 7 , the specific steps for comparing the deviation between the trajectory prediction and the observed data are as follows:

[0186] Extract the trajectory prediction data of the corrected trajectory prediction model at the target time point and collect the observed data at the corresponding time point;

[0187] Compare the trajectory prediction data and the observed data at each difference time point, using the formula:

[0188] D t =(p t - o t )+λ(p t-1 - o t-1 )×k

[0189] Calculate the deviation between the two, where D t is the deviation at the target time point t, p t is the predicted value of the model at time point t, ot is the observed value at time point t, λ is the decay factor used to adjust the influence of the previous time point deviation, k is the adjustment coefficient used to balance the deviation weight of the previous time point, p t-1 and o t-1 are the predicted and observed values of the previous time point, used to calculate the impact of time continuity on the current deviation.

[0190] Suppose there are the following data and parameter values:

[0191] The predicted value p at the current time point t t = 150;

[0192] The observed value o at the current time point t t = 145;

[0193] The predicted value p at the previous time point t - 1 t-1 = 148;

[0194] The observed value o at the previous time point t - 1 t-1 = 147;

[0195] The decay factor λ = 0.5;

[0196] The adjustment coefficient k = 2.

[0197] Calculate the deviation D at the current time point t :

[0198] First, calculate the direct deviation:

[0199] p t - o t = 150 - 145 = 5

[0200] Then, calculate the adjusted deviation of the previous time point:

[0201] (p t-1 - o t-1 ) = 148 - 147 = 1

[0202] Apply the decay factor and adjustment coefficient:

[0203] λ(p t-1 - o t-1 )×k = 0.5×1×2 = 1

[0204] Sum up the calculation results:

[0205] Add up the deviations of the two parts:

[0206] D t = 5 + 1 = 6

[0207] Through this method, not only the direct deviation between individual time points is calculated, but also the continuity of the time series is considered, making the deviation calculation more refined and sensitive.

[0208] Please refer to Figure 8 , the steps to evaluate the accuracy and response speed of the prediction model are specifically as follows:

[0209] Collect deviation data and use the formula:

[0210]

[0211] and

[0212]

[0213] Calculate the average value and standard deviation of the deviation, and analyze the response speed. Adopt the rate calculation formula:

[0214]

[0215] Calculate the rate of change of the deviation. Combine the average value and the standard deviation to generate an overview of the prediction performance evaluation of the prediction model. Among them, D t is the total deviation at time point t, μ D is the average value of the deviation, and after adjustment, it combines the influence of the deviation at the previous time point on the current value. σ D is the standard deviation of the deviation, and the deviation at the previous time point is combined in the calculation. α is the weight coefficient of the deviation at the previous time point, which is used to balance the influence of historical data on the current calculation. R is the rate of change of the deviation, which combines the weighted deviations of two consecutive time points. Δt is the time interval, which is used to calculate the rate of change of the deviation.

[0216] Suppose there is the following deviation data (D t ):

[0217] D 1 = 10, D 2 = 8, D 3 = 5;

[0218] The weight coefficient α of the deviation at the previous time point = 0.5;

[0219] The time interval Δt = 1 (for example, the interval between each time point is 1 hour).

[0220] Calculate the weighted deviation average value μ D :

[0221] D 1 When there is no previous time point, so D' 1 = D 1 = 10

[0222] D' 2= D 2 + α·D 1 = 8 + 0.5 × 10 = 13

[0223] D′ 3 = D 3 + α·D 2 = 5 + 0.5 × 8 = 9

[0224]

[0225] Calculate the standard deviation σ of the weighted deviation D :

[0226]

[0227] Calculate the rate of change of deviation R:

[0228] Only D 2 and D 3 can be calculated:

[0229]

[0230] Through this calculation method, not only the deviation at a single time point is considered, but also a more dynamic and sensitive error analysis is provided by weighting historical deviations, so as to more accurately evaluate the performance of the model.

[0231] The above is only a preferred embodiment of the present invention, and it is not intended to limit the present invention in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes and apply them to other fields. However, as long as it does not depart from the technical solution content of the present invention, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. Planet and asteroid motion simulation and analysis system, characterized in that: The system comprises: The data collection module is based on astronomical telescopes and space probes to collect real-time position and velocity information of planets and asteroids, calculate the current orbital elements of celestial bodies, organize orbital data, convert the organized data into analog format, and obtain real-time celestial body data sets; The dynamic weight adjustment module performs preliminary adjustment of weights and parameters based on the real-time celestial data set, refines the learning rate and weight decay parameters according to the square of the historical gradient of the parameters, updates the model parameter weights, and evaluates the parameters using the random forest algorithm to generate a weight adjustment parameter set; The initial adjustment steps of the weights and parameters are specifically as follows: Based on the real-time celestial data set, collecting celestial body position and velocity parameter information; Using historical data, calculate the historical gradient square average of the parameter using the formula: Adjust the sensitivity of the learning rate and adjust the weights and parameters in combination with the historical gradient of the parameters, where η represents the adjusted learning rate, η0 is the initial learning rate, g is the average square of the historical gradient of the parameter, ∈ is a small positive number to avoid the denominator being zero, λ is the weight adjustment factor, which is used to adjust the rate of change of the learning rate according to the maximum value of the gradient, and g max It is the maximum value of the historical gradient square, which is used to reflect the additional impact of the gradient extreme value on the learning rate; The trajectory correction module uses the weight adjustment parameter set, combined with the new observation data, to gradually correct the trajectory prediction error through the gradient boosting tree algorithm, and calculates the negative gradient of the loss function to generate a corrected trajectory prediction model; The calculation steps of the negative gradient of the loss function are specifically as follows: Collect new observation data, the data including current trajectory information, use the weight adjustment parameter set to update the weight of the gradient boosting tree model, and match the new observation data; Apply the current model parameters, calculate the error between the predicted trajectory and the observed trajectory, and determine the loss function; And calculate the negative gradient of the loss function for each parameter using the formula: Get the corrected trajectory prediction model, where L is the loss calculated based on the difference between the current model prediction and the observation, p represents the parameters in the model, α is an adjustment coefficient used to optimize the influence of the second-order derivative, β is another adjustment coefficient used to adjust the weight of the first-order derivative, k is the error attenuation constant used to smooth the error contribution, is the calculated negative gradient of the loss function, which is used to guide parameter adjustment and minimize the loss; The result comprehensive evaluation module analyzes the modified trajectory prediction model, compares the deviation between the trajectory prediction and the observed data at the difference time point, evaluates the accuracy and response speed of the prediction model, and generates an overview of the prediction performance evaluation.

2. The planet and asteroid motion simulation and analysis system according to claim 1, characterized in that: The steps for collecting the real-time position and speed information are specifically as follows: Use astronomical telescopes and space probes to continuously monitor and collect optical data of target planets and asteroids, including timestamps and optical images; Process the collected image data, automatically identify celestial features, and extract celestial coordinate positions; Based on the coordinate data of two consecutive observations, use the formula: Calculate the velocity vector of the celestial body, combine it with the position information, and standardize it into real-time position and velocity information, where Δx is the position change, which represents the displacement of the planet or asteroid within time Δt, Δt is the time interval, which is the time difference between two observations, and β z and γ are used to adjust the deviation coefficient caused by the environment and equipment, ω is the correction frequency, t is the observation time point, α z It is a fine-tuning coefficient of the time interval, which is used to control the influence of time difference in speed calculation.

3. The planet and asteroid motion simulation and analysis system according to claim 1, characterized in that: The specific steps for calculating the current orbital element of the celestial body are: Calculate using Kepler's laws and Newton's laws of motion based on the real-time position and velocity information collected; The key parameters of the orbit are calculated by combining the mass of the celestial body, the gravitational constant, the orbital period and the current time, using the formula: and Calculate the semi-major axis and eccentricity, and output the calculation results as the current orbital elements of the celestial body, where G is the gravitational constant, which represents the physical constant of the interaction between celestial bodies; m is the mass of the celestial body, which is the key factor in calculating the orbital elements; T is the orbital period, which refers to the time required for the celestial body to complete a complete orbital motion; a is the semi-major axis, which represents half the length of the major axis of the orbital ellipse; and e is the eccentricity, which represents the shape of the orbital ellipse.

4. The planet and asteroid motion simulation and analysis system according to claim 1, characterized in that: The parameter evaluation steps are specifically as follows: Collect the adjusted model parameters and weights, and input the parameter weights; The random forest algorithm is applied to evaluate the parameters using the formula: Calculate the feature criticality score and generate a weight adjustment parameter set based on the evaluation results of the random forest algorithm, where I represents the criticality of the feature, Δi represents the change in model accuracy after removing the feature, and w i is the feature weight coefficient, N is the number of decision trees, S i is the number of samples of the feature, S total is the total number of samples of the feature, used to normalize the proportional effect.

5. The planet and asteroid motion simulation and analysis system according to claim 1, characterized in that: The step of comparing the deviation between the trajectory prediction and the observed data is specifically as follows: Extracting trajectory prediction data of the modified trajectory prediction model at a target time point, and collecting observation data at a corresponding time point; Compare the trajectory prediction data and observation data at each difference time point using the formula: D t (p t -the t )+λ v ( p t-1 -the t-1 ) × k v Calculate the deviation between the two, where D t is the deviation at the target time point t, p t is the predicted value of the model at time point t, o t is the observed value at time point t, λ v is the attenuation factor used to adjust the impact of the deviation at the previous time point, k v is the adjustment coefficient used to balance the deviation weight at the previous time point, p t-1 and t-1 are the forecasts and observations at the previous time point, which are used to calculate the impact of time continuity on the current deviation.

6. The planet and asteroid motion simulation and analysis system according to claim 1, characterized in that: The steps of evaluating the accuracy and response speed of the prediction model are specifically as follows: Collect deviation data using the formula: and Calculate the mean and standard deviation of the deviation and analyze the response speed using the rate calculation formula: The rate of change of the deviation is calculated and combined with the mean and standard deviation to generate an overview of the prediction performance evaluation of the prediction model, where D t is the total deviation at time t, μ D is the mean of the deviations, σ D is the standard deviation of the deviation, α u is the weight coefficient of the deviation at the previous time point, which is used to balance the impact of historical data on the current calculation. R is the deviation change rate, which combines the weighted deviations of two consecutive time points. Δt is the time interval used to calculate the deviation change rate.

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