Online flatness detection of aircraft rudder surfaces serves as a pivotal core procedure for ensuring the manufacturing precision, aerodynamic performance and operational safety of aeronautical components. Traditional plane fitting-based detection approaches are constrained by low detection efficiency, susceptibility to local optimal solutions, weak anti-noise robustness and limited automation capability, which fail to satisfy the micron-level high-precision online detection requirements for curved composite rudder surfaces in batch manufacturing scenarios. To address the aforementioned technical bottlenecks, this study proposes a bidirectionally coupled PSO-SA hybrid optimization algorithm for non-convex minimum zone flatness evaluation of curved rudder surfaces, which overcomes the unidirectional open-loop iteration limitation inherent in conventional serial PSO-SA composite frameworks. Two targeted algorithmic improvements are elaborated in this work: a residual-adaptive nonlinear inertia weight strategy, which dynamically balances global exploration and local exploitation capabilities based on the fluctuation characteristics of free-form surface measurement residuals; and a measurement noise-modified Metropolis acceptance criterion, which substantially enhances the algorithm’s anti-interference performance against on-machine trigger sampling noise. Integrating with the trigger-type on-machine detection hardware of computer numerical control (CNC) machine tools, an integrated online detection system is established to realize the full-process functions of point cloud data acquisition, error compensation, intelligent plane fitting and flatness error evaluation. Meanwhile, the complete technical workflow involving measurement path planning, probe calibration and algorithm iterative solution is systematically illustrated. Comparative simulation experiments implemented on the MATLAB platform demonstrate that the proposed algorithm exhibits superior performance in convergence speed, fitting accuracy and optimization stability over five mainstream algorithms, including standard particle swarm optimization (PSO), standard simulated annealing (SA), comprehensive learning PSO (CLPSO), adaptive cooling SA and conventional serial PSO-SA. On-machine physical measurement experiments are conducted on 24 aircraft rudder workpieces covering aluminum alloy skins and assembled riveted components. After multi-dimensional systematic calibration, the overall detection error of the developed system is controlled within 1 μm. The experimental results indicate that the average flatness error calculated by the proposed bidirectionally coupled PSO-SA algorithm is 29.7 μm, which is 30.1% and 38.5% lower than that of standard PSO and standard SA, respectively, fully complying with the aviation flatness tolerance specification of 0.1–0.3 mm. Moreover, the full detection cycle for a single workpiece is only 2.1 min, achieving a 34.4% reduction in detection time compared with standard PSO and effectively improving the efficiency of online in-process inspection. One-way analysis of variance (ANOVA) combined with Tukey’s posthoc test further verifies that the accuracy superiority of the proposed algorithm is statistically significant. This research provides a targeted theoretical basis and complete engineering implementation scheme for intelligent flatness detection of aerospace curved thin-walled parts, and offers a valuable technical reference for form and position error evaluation of irregular industrial components under noisy measurement conditions.
Yang et al. (Mon,) studied this question.