An Improved Dual-Attention Transformer-LSTM for Small-Sample Prediction of Modal Frequency and Actual Anchor Radius in Micro Hemispherical Resonator Design

The high-temperature glassblowing-fabricated micro hemispherical resonator (MHR) exhibits high symmetry and high Q-value for precision inertial navigation. However, MHR design entails a comprehensive evaluation of multiple possible configurations and demands extremely time-consuming simulation of key parameters combination. To address this problem, this paper proposed a rapid prediction method of modal frequency and actual anchor radius of designed MHR using an improved Transformer-LSTM (Long Short-Term Memory) model for rapid design sizing. High-temperature-induced softening deformation at the anchor point reduces the actual anchor radius below the designed value. By varying key parameters such as resonator height, anchor radius and edge thickness, finite element glassblowing simulation and modal analyse were conducted to obtain the first six modal frequencies and actual anchor radius. To address regression prediction challenges with limited data, dual multi-head self-attention (MHSA) mechanisms replaced the transformer's standard Feed Forward Network, to improve hidden information capture for high-accuracy predictions of modal frequencies and anchor radius. By checking fabricating feasibility of anchor radius and allowing rapid modal characteristics evaluation without interference, ablation and comparative experiments validated the method's superiority, as an effective support of MHR design. Design optimization experiments demonstrate a prediction accuracy of 96.35%, with computational time reduced to 1/48,000 of traditional finite element methods, significantly improving design efficiency. This study offers a new paradigm for intelligent Micro-Electro-Mechanical System (MEMS) device design under complex process conditions.