A decoupling algorithm & its application for 3D scanning probes

The 3D scanning probe is the “eye” of precision measuring instruments, coupling errors among its axes remain an urgent problem; accurate decoupling is essential for improving probe data accuracy. This paper presents an improved algorithm that integrates Particle Swarm Optimization (PSO)、Latin Hypercube Sampling (LHS), and an Opposition-Based Learning (OBL) strategy. The inertia weight w is dynamically adjusted using a cycloidal schedule, ensuring both rapid initial convergence and refined exploration in later stages. Additionally, the cognitive and social coefficients c 1 and c 2 are linearly decreased to minimize the risk of the swarm becoming trapped in local optima. Compared with the standard PSO algorithm, the improved algorithm can obtain the global optimal solution, while the standard algorithm only achieves the local optimal solution and thus cannot be applied to probe decoupling. Compared with the LSM algorithm, the coupling matrices obtained by the two methods are basically consistent under the condition of outlier-free data. Nevertheless, when outliers exist in the dataset, the LO-PSO algorithm achieves superior robustness and decoupling accuracy relative to LSM. Tests were conducted on the original dataset, and the results show that decoupling improves the measurement accuracy of test data in the X, Y and Z directions. Compared with the pre-decoupling results, the four X-group datasets showed a maximum type-I error of 0.747%, corresponding to an average gain of 8.02%; the Y-group datasets showed a maximum type-I error of −0.956%, corresponding to an average gain of 10.82%; and the Z-group datasets showed a maximum type-I error of 1.658%, corresponding to an average gain of 8.86%. The results show that the improved algorithm significantly enhances the data accuracy of the 3D scanning probe. Under laboratory calibration test conditions, the LO-PSO algorithm achieves superior decoupling accuracy and outlier resistance robustness compared with the least squares method, and it has the engineering potential to be integrated into precision measurement software for on-site decoupling.