Objectives The ship shafting alignment system, as a core equipment in ship manufacturing, relies heavily on parallel mechanisms for high-precision pose adjustment of shaft segments. However, in practical engineering scenarios, multiple error sources—including coordinate system deviations caused by uneven foundation surfaces, manufacturing and assembly errors of the mechanism, driving quantity errors of linear guides, angular errors of each axis of the actuators, contact position errors between the actuator ends and the shaft segments, and distance errors between parallel branches—couple together. This coupling leads to deviations between the theoretical kinematic model and the actual operational performance, resulting in reduced positioning accuracy of the shaft segments and affecting the overall quality and efficiency of ship assembly. Therefore, the purpose of this study is to identify various error parameters of the ship shafting alignment system, quantitatively correct the kinematic model to reduce the residual error of the shaft segment adjustment pose, and establish a dedicated kinematic calibration algorithm for the ship shafting docking system, thereby providing technical support for improving the alignment accuracy and operational reliability of the system in practical environments.

Methods Firstly, aiming at the structural characteristics of the ship shafting alignment system composed of two parallel actuators with five degrees of freedom, a spatial closed-loop vector equation of the system was established based on the vector method. By performing differentiation and linearization processing on this equation, the mapping relationship between various error sources (such as driving quantity errors, angular errors, contact position errors, and inter-actuator distance errors) and pose deviations was clarified, and a linearized error model was constructed. Secondly, considering that the established linearized error model is based on the small error assumption and will fail when errors exceed a certain range, the Bayesian inferential framework was adopted to estimate the identifiable interval of the model parameters. Through Monte Carlo simulation generating a large number of pose data, effective samples were screened, and the posterior distribution of error parameters was calculated to determine the reliable application boundary of the model, ensuring that subsequent parameter identification and pose compensation are carried out within a valid range. Finally, the Levenberg-Marquardt (LM) algorithm was selected as the parameter identification algorithm. To further optimize the iteration efficiency and convergence performance, a dynamic damping factor adjustment strategy was introduced. The iteration step size was optimized according to the convergence state of the pose residual error: if the pose residual error decreases after iteration, the current damping value is retained; otherwise, the damping factor is updated at a specific growth rate for re-iteration, thereby realizing accurate identification of error parameters and effective correction of the kinematic model.

Results Numerical simulation results show that the proposed kinematic calibration method achieves excellent performance in error parameter identification and model correction. The average accuracy of error parameter identification reaches 91.83%, among which 15 error parameters have an identification accuracy of over 99% and 23 error parameters have an accuracy of over 80%, demonstrating high reliability of the identification results. After applying the identified error parameters to the kinematic model correction, the pose accuracy of the shaft segment is significantly improved: the position errors in the Y and Z directions are reduced by an average of 80.2% and 59.7% respectively, and the error of the rotation attitude angle around the Z axis is reduced by an average of 72.9%. Although the error of the rotation attitude angle around the Y axis remains basically stable, this is mainly due to the random selection of pose configurations which affects the identification accuracy of key geometric parameters. In addition, under the condition of introducing measurement noise (0.001 mm for position measurement and 0.0001° for attitude measurement), 19 parameters still maintain an identification accuracy of over 90% and 21 parameters over 80%, indicating that the algorithm has good anti-noise performance and robustness.

Conclusions The research results verify the accuracy of the established linearized error model and the effectiveness of the improved L-M algorithm. The proposed kinematic calibration method can effectively identify various error parameters of the ship shafting alignment system, significantly reduce the pose residual error of the shaft segment after model correction, and maintain high identification accuracy even under low measurement noise disturbance. This study fills the gap in the dedicated kinematic calibration method for the ship shafting alignment system, provides a reliable technical reference for positioning compensation in practical engineering environments, and has important practical significance for improving the assembly precision and efficiency of ship shafting, as well as promoting the intelligent development of ship manufacturing equipment.