Uncertainty-decomposed robust design optimization via calibrated causal inference for multi-bolt assembly process in gantry machine tools

Large-scale gantry machine tools are highly sensitive to uncertainties arising from preload variation, contact conditions, and assembly errors. These uncertainties complicate assembly parameter design and reduce the reliability of deterministic optimization methods. Existing studies mainly rely on deterministic predictive models, which makes it difficult to separate different uncertainty sources and limits robust parameter design under varying operating conditions. This paper proposes an uncertainty-aware causal optimization framework for robust preload design in multi-bolt assembly systems. A hypernetwork-based uncertainty decomposition method is developed to explicitly separate aleatoric and epistemic uncertainty. The decomposed uncertainty is then integrated into a calibrated causal inference model to improve causal effect estimation between preload settings and assembly performance. Based on the learned causal relationships, a risk-aware optimization strategy is introduced to identify stable preload intervals instead of single-point solutions. Extensive experiments on a high-fidelity FE-based Bolt dataset and a controlled Toy benchmark show that the proposed framework reduces optimal-point deviation by 46% compared with the strongest baseline on the Bolt dataset and achieves the best causal estimation accuracy on the Toy dataset ( R 2 = 0.970 , MAE = 0.118 ). The proposed method provides a systematic solution for robust assembly parameter design under uncertainty and enables practical uncertainty-aware optimization in precision manufacturing systems.