Abstract:

In high-precision manufacturing domains such as aerospace, the assembly accuracy of complex products fundamentally determines their core performance and operational reliability. Traditional assemblyerror modeling methods exhibit significant limitations in capturing the nonlinear behaviors associated with “geometry-mechanics” coupling—particularly in accurately describing contact deformation and dynamic coupling effects, which are critical for high-precision applications. To address these challenges, an innovative Jacobian-Torsor Embedded Neural Network (JENN) approach was proposed. Physical constraints derived from Jacobian-Torsor theory were embedded into the neural network architecture, establishing a joint optimization mechanism that simultaneously minimized the “Jacobian-Torsor loss function” and the network’s prediction error, enabling precise modeling of complex nonlinear mechanisms such as contact deformation and dynamic coupling. The proposed method leveraged the multilayer nonlinear mapping capability of neural networks to capture latent physical correlations, while using kinematic constraints from Jacobian-Torsor theory to regularize network training. As a result, the model’s generalization ability and physical interpretability were significantly enhanced, particularly in small-sample scenarios. Experimental validation on a dual-axis turntable used azimuth and elevation angles as inputs to predict spatial pointing errors, demonstrating substantial improvements: compared with conventional networks without Jacobian embedding, prediction accuracy improved by 46.51%, 37.44%, and 50.86% in the x, y, and z directions, respectively. Five-fold cross-validation further showed that the proposed method consistently outperformed the conventional approach across four key metrics (MSE, RMSE, MAE, and R2), yielding lower prediction errors as well as markedly enhanced stability and generalization. This cross-domain fusion framework, integrating physics-based mechanism constraints with data-driven fitting, provided a novel pathway for addressing nonlinear transfer challenges in high-precision assembly applications.

Key words: assembly error, Jacobian-Torsor model, nonlinear error, neural network, data-physics fusion