Highly efficient Coordinate Measuring Machine error compensation via Greedy Randomized Kaczmarz algorithm and nongeometric error identification neural network

Abstract

Coordinate Measuring Machines (CMMs) are essential for high-precision measurements in modern manufacturing. However, their accuracy is often compromised by geometric and nongeometric errors. This paper presents a comprehensive error compensation method that integrates model-based and data-driven approaches. Geometric error compensation is achieved through the Product of Exponentials (POE) formula for modeling and the Greedy Randomized Kaczmarz (GRK) algorithm for efficient parameter identification. For nongeometric errors, a data-driven approach is employed using the High-Precision and Lightweight Nongeometric Error Identification Neural Network (NEINN). It introduces a novel network architecture, which incorporates compensation information from neighboring points to enhance robustness and prediction accuracy while mitigating overfitting. Experimental tests were conducted on a CMM with a nominal accuracy of 1.5 $\mu m+L\left[\mathrm{mm}\right]/400\mu m$, using a laser tracking interferometer as the high-precision calibration device. In the geometric error compensation experiment, a total of 738 unknown parameters were identified, and 567 calibration points were measured. The parameter identification process took 4.1 s, resulting in a 56% improvement in efficiency compared to the traditional Levenberg–Marquardt algorithm. For nongeometric error compensation, a dataset of 4,000 samples was collected for training and testing. The designed NEINN network outperforms existing methods in key evaluation metrics, including Root Mean Squared Error and Mean Absolute Error, significantly enhancing overall error compensation performance. Validation tests conducted using ISO 10360 standards show that the CMM compensated with our method achieves high measurement accuracy, with a length measurement error of 0.5 $\mu m+L\left[\mathrm{mm}\right]/400\mu m$, and a detection error $0.25\mu m$. Furthermore, tests across various CMMs and environmental conditions confirm the effectiveness and practical applicability of the proposed approach. The method significantly enhances CMM performance, improving both measurement precision and the efficiency of the error compensation process, thus providing a scalable solution for industrial applications. However, the proposed method assumes a rigid-body model for the CMM, which may limit its applicability in dynamic operational scenarios. Future work will aim to address this limitation, further enhancing the method’s robustness and expanding its range of practical applications.