CN-122021042-A - Method and system for predicting long-term stability of gravitational wave detection formation configuration based on Fourier series

CN122021042ACN 122021042 ACN122021042 ACN 122021042ACN-122021042-A

Abstract

The invention discloses a method and a system for predicting long-term stability of a gravitational wave detection formation configuration based on Fourier series, and belongs to the technical field of aerospace science and technology. The method comprises the steps of firstly obtaining initial values and predicted time lengths of orbit elements of all spacecrafts in formation, extracting long-term item data of the orbit elements by solving an orbit element perturbation differential equation set and utilizing a double-average method, establishing a Fourier series model of the long-term items of the orbit elements of the spacecrafts, further combining space geometrical relations among the spacecrafts, constructing a semi-analytical model describing the change rate of the long-term items of arm lengths, respiratory angles and pointing angles of configuration stability, and comprising a linear part and a nonlinear part, wherein the nonlinear part comprises a composite function representing the perturbation effect of lunar attraction, and establishing a semi-analytical prediction relation between the semi-analytical model and the initial orbit elements and the predicted duration of the spacecraft. The method and the system realize quick and direct prediction of the long-term stability of the formation configuration.

Inventors

SHI PENG
ZHANG JIAN
CHEN JIAYANG
WU DI
GONG SHENGPING

Assignees

北京航空航天大学

Dates

Publication Date: 20260512
Application Date: 20260209

Claims (10)

1. A method for predicting long-term stability of gravitational wave detection formation configuration based on Fourier series is characterized by comprising the following steps: step 1, obtaining long term time-varying data of orbit elements based on initial values of orbit elements and predicted time lengths of all spacecrafts in formation; step 2, based on the long term time-varying data of the track element, combining nominal initial value data of the track element, and constructing a Fourier series model of the long term of the track element; Step 3, calculating configuration stability index long term time-varying data based on the rail element long term time-varying data and combining formation configuration space geometrical relationship; And 4, constructing a configuration stability index long term item semi-analytical model according to the orbit element long term item Fourier series model and configuration stability index long term item time-varying data so as to directly calculate the configuration stability index long term item change rate at the target moment.
2. The method for predicting long-term stability of a gravitational wave detection formation configuration based on a Fourier series according to claim 1, wherein said step 1 comprises, Taking initial values of orbit elements of all the spacecrafts in the formation as starting points, and numerically solving an orbit element differential equation set containing the gravitational perturbation of the moon to obtain orbit element time-varying data of all the spacecrafts in a predicted time period; And processing the orbit element time-varying data by using a double-average method, filtering short-period and long-period fluctuation in the orbit motion, and extracting orbit element long-term time-varying data representing the long-term evolution trend.
3. The method for predicting long-term stability of a gravitational wave detection formation based on a Fourier series of claim 1, wherein said step2 comprises, And constructing an orbit element long term Fourier series model of a single spacecraft based on the orbit element long term time-varying data, wherein the model decouples the orbit element long term into a function of an initial value and time.
4. The method for predicting long-term stability of a gravitational wave detection formation based on a Fourier series of claim 1, wherein said step 3 comprises, Calculating space position coordinate time-varying data of each spacecraft in a predicted time period based on the orbit element time-varying data; calculating time-varying data of a configuration stability index according to the space geometric relation of the formation configuration, wherein the stability index comprises arm length, respiratory angle and pointing angle; and (3) re-applying a double-average method to the time-varying data of the stability index, and extracting the time-varying data of the long term of the time-varying data as a direct evaluation basis of the long-term stability of the configuration.
5. The method for predicting the long-term stability of the formation configuration of the gravitational wave detection based on the Fourier series, which is disclosed in claim 1, is characterized in that the long-term semi-analytical model of the formation stability index constructed in the step 4 comprises a linear part and a nonlinear part, wherein the linear part is a linear function of initial values of a formation reference perigee amplitude angle and an orbit inclination angle, and the nonlinear part is a composite function of initial values of orbit elements of a spacecraft and prediction time, and comprises a nonlinear function for representing the perturbation effect of the gravitational attraction of the moon.
6. The method for predicting the long-term stability of the gravitational wave detection formation configuration based on the Fourier series is characterized in that the nonlinear part is decoupled into a first function term and a second function term, the first function term is used for establishing a relation between a long-term of the configuration stability index and an initial value and a latitude amplitude angle difference of orbit elements of a spacecraft, and the second function term is specifically a combination term of trigonometric functions comprising the initial value of the orbit inclination angle, the initial value of the perigee amplitude angle and the latitude amplitude angle difference of the single spacecraft and is used for accurately representing the periodic influence of gravitational perturbation of the moon.
7. The method for predicting the long-term stability of the gravitational wave detection formation configuration based on the Fourier series is characterized in that a first function item in the nonlinear part is divided into a plurality of groups of function items according to linear combination forms of different spacecraft numbers and latitude angles, each group comprises a plurality of items, the coupling influence of the sum and difference combinations of the latitude angles between different spacecraft pairs on the configuration stability is respectively described, a second function item in the nonlinear part is divided into a plurality of groups according to different spacecraft numbers, each group comprises a plurality of items, and the influence of the gravitational perturbation of the moon on the long-term item of the orbit element of a single spacecraft is respectively described.
8. A fourier series-based gravitational wave detection formation long-term stability prediction system, comprising: the spacecraft orbit element time-varying value calculation module is used for acquiring orbit element long-term time-varying data based on orbit element initial values and predicted time lengths of all the spacecraft in the formation; the spacecraft orbit element long term item prediction module is used for constructing an orbit element long term item semi-analytical model based on the orbit element long term item time-varying data and combined with orbit element nominal initial value data; the formation configuration stability index time-varying value calculation module is used for calculating configuration stability index long-term time-varying data based on the rail element long-term time-varying data and combining formation configuration space geometric relations; And the formation configuration stability index long term prediction module is used for constructing a configuration stability index long term semi-analytical model according to the track element long term Fourier series model and the configuration stability index long term time-varying data so as to directly calculate the configuration stability index long term change rate at the target moment.
9. An electronic device, comprising: one or more processors; A memory for storing one or more programs; wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of fourier series-based gravitational wave detection formation configuration long-term stability prediction of any of claims 1-7.
10. A computer readable storage medium having stored thereon executable instructions which when executed by a processor enable the processor to implement a fourier series-based gravitational wave detection formation configuration long-term stability prediction method as recited in any one of claims 1-7.

Description

Method and system for predicting long-term stability of gravitational wave detection formation configuration based on Fourier series Technical Field The invention belongs to the technical field of aerospace science and technology, and particularly relates to a method and a system for predicting long-term stability of a gravitational wave detection formation configuration based on Fourier series. Background Gravitational wave detection is an important means for verifying generalized relativity and exploring cosmic mystery. With the success of ground detection devices such as LIGO, the detection focus is gradually turning into space to avoid ground noise interference and expand the low frequency detection capability. Space gravitational wave detection generally adopts a spacecraft formation form, wherein an equilateral triangle configuration with the earth as the center and the side length of the equilateral triangle can reach the order of hundred thousand kilometers is one of the main schemes. In this configuration, three spacecraft measure the change of optical path length caused by gravitational wave by high-precision laser interferometry, so maintaining stability of formation configuration in long-term task is a precondition of successful detection. Stability of formation configuration mainly includes three aspects, namely arm length (space between spacecrafts), breathing angle (opening angle between spacecrafts) and pointing angle (included angle between normal vector of configuration plane and direction of wave source). The drift of these indicators over a period of years of a mission must be tightly controlled to within a very small range. However, achieving long-term stability predictions presents serious challenges. The on-orbit operation of the spacecraft is subjected to complex coupling actions of various ingeniously-driven forces such as the earth aspheric gravitation, the solar-lunar gravitation, the solar pressure and the like, and the force fields have the characteristics of space non-uniformity and time variation and are difficult to describe by uniform analysis. Currently, research methods rely primarily on numerical simulations to search for initial trajectory elements by optimization algorithms to minimize configuration drift over a particular period of time. Although numerical methods are effective within a range, they have inherent limitations. For tasks of up to several years, the numerical integral calculation amount is huge, the trade-off problem between the calculation efficiency and the numerical precision is faced, the quick evaluation of a single design scheme is difficult to realize, and the instant comparison and optimization of a large number of candidate schemes cannot be supported. Therefore, developing an analytical or semi-analytical model that can establish a direct and rapid correlation between the configuration stability and the initial orbit element becomes a key technical problem to be broken through in the field. Disclosure of Invention In order to solve the technical problems, the invention provides a method and a system for predicting the long-term stability of a formation configuration based on the Fourier series gravitational wave detection, which realize the rapid and direct prediction of the long-term stability of the formation configuration, avoid the problems of low calculation efficiency and dependence on the previous step data of the traditional numerical integration method, and are suitable for the long-term stability assessment and the optimal design of the formation configuration in the space gravitational wave detection task. In order to achieve the above purpose, the invention adopts the following technical scheme: a method for predicting long-term stability of gravitational wave detection formation configuration based on Fourier series comprises the following steps: step 1, obtaining long term time-varying data of orbit elements based on initial values of orbit elements and predicted time lengths of all spacecrafts in formation; Step 2, based on the long term item time-varying data of the track element, combining nominal initial value data of the track element, and constructing a Fourier series model of the long term item of the track element; Step 3, calculating configuration stability index long term time-varying data based on the rail element long term time-varying data and combining formation configuration space geometrical relationship; And 4, constructing a configuration stability index long term item semi-analytical model according to the orbit element long term item Fourier series model and configuration stability index long term item time-varying data so as to directly calculate the configuration stability index long term item change rate at the target moment. Further, the step 1 includes, Taking initial values of orbit elements of all the spacecrafts in the formation as starting points, and numerically solving an orbit element differential equ