Thermoelastic stability is a critical requirement for inertial sensors (ISs) in the space-based gravitational wave detection, with the relative distance stability between the IS and the optical bench being a key performance driver. In existing studies, systematic optimization strategy for the thermoelastic compensation support of the IS has yet to be developed. In this study, a unified design framework integrating parametric geometric modeling, thermoelastic simulation, and the optimization algorithms is established and applied to the optimization of a typical IS support structure. A set of practical design strategy is proposed: (i) steady temperature and heat sources have negligible coupling effects into the frequency-domain thermoelastic analysis; (ii) the level of the thermal noise should be treated as a constraint in the optimization design; (iii) the lowest frequency within the target frequency band may be selected as the representative for the full band. Following these strategy, the gain for the thermoelastic displacement reduces from 3.28 × 10−8 m/W@ 0.1 mHz to 5.81 × 10−9 m/W@ 0.1 mHz for an improved configuration. The gain for the temperature fluctuation reaches 0.94 × 10−4 K/W@ 0.1 mHz, which remains within the acceptable limits. This work provides systematic optimization methodology and design criteria for the future space ISs.
