| The detection of gravitational waves has opened up a new window for human understanding of the universe.Compared to ground-based gravitational wave detection devices,space-based laser interferometric gravitational wave detectors operate at a lower frequency range(10-4 to 10Hz),with detection satellite formations working at distances on the order of millions of kilometers,capable of detecting wave sources such as binary neutron star systems and binary black hole rotation systems.Inertial sensors are the core scientific payloads for space-based gravitational wave detection satellite formations.To achieve high-precision laser interferometric measurements,the test masses in the inertial sensors need to be kept in a free-suspended state.However,the level of free-suspension of test masses in orbit is limited by various interfering forces,including self-gravity.The gravitational force between the satellite platform and test mass is called self-gravity.This paper summarizes the research status of self-gravity simulation methods for space-based gravitational wave missions,and calculates the linear acceleration,angular acceleration,gravitational gradient matrix,and torque gradient matrix of self-gravity based on the gravitational and gravitational potential derivatives between the upright hexahedron and point mass.A method combining analytical calculation and discrete summation is used to solve the combined gravitational force of the mass bodies around the test mass.Self-gravity simulation first requires the external mass sources to be meshed,and all the meshed elements are approximated as point masses,which inevitably introduces errors.The usual method is to refine the elements to reduce the error,but this refinement increases the total number of elements and reduces computational efficiency.To balance the computational efficiency and accuracy of the self-gravity simulation process,this paper conducts research on a distance-controlled mesh refinement algorithm.By selecting an appropriate mesh refinement scale factor and refining the mesh elements to different degrees based on their distance from the test mass,the distance-controlled mesh refinement algorithm generates smaller elements near the test mass and gradually larger elements as the distance increases compared to global refinement.When the partitioned element is a hexahedron,the self-gravity simulation with distance-controlled refinement has improved efficiency and accuracy to some extent.Self-gravity simulation is the main means to evaluate and optimize the self-gravity balance scheme.This paper analyzes the self-gravity balance problem from the perspective of optimization problem solving,taking the size and installation position of the balance mass block as the optimization parameters and using the self-gravity acceleration and gradient components as optimization objectives,while imposing constraints on the total mass of the balance mass block.Intelligent optimization algorithms（genetic algorithm and particle swarm algorithm）are used to solve the balance installation scheme.Assuming the compensating mass is spherical and installed in the gap between the electrode cage and the inner wall of the inertial sensor or the outer wall of the inertial sensor,both genetic algorithm and particle swarm algorithm provide preliminary installation schemes,providing references for optimizing the shape of the balance mass block and determining the installation position. |
