A Gaussian Process Data Modelling and Maximum Likelihood Data Fusion Method for Multi-Sensor CMM Measurement of Freeform Surfaces

Nowadays, the use of freeform surfaces in various functional applications has become more widespread. Multi-sensor coordinate measuring machines (CMMs) are becoming popular and are produced by many CMM manufacturers since their measurement ability can be significantly improved with the help of different kinds of sensors. Moreover, the measurement accuracy after data fusion for multiple sensors can be improved. However, the improvement is affected by many issues in practice, especially when the measurement results have bias and there exists uncertainty regarding the data modelling method. This paper proposes a generic data modelling and data fusion method for the measurement of freeform surfaces using multi-sensor CMMs and attempts to study the factors which affect the fusion result. Based on the data modelling method for the original measurement datasets and the statistical Bayesian inference data fusion method, this paper presents a Gaussian process data modelling and maximum likelihood data fusion method for supporting multi-sensor CMM measurement of freeform surfaces. The datasets from different sensors are firstly modelled with the Gaussian process to obtain the mean surfaces and covariance surfaces, which represent the underlying surfaces and associated measurement uncertainties. Hence, the mean surfaces and the covariance surfaces are fused together with the maximum likelihood principle so as to obtain the statistically best estimated underlying surface and associated measurement uncertainty. With this fusion method, the overall measurement uncertainty after fusion is smaller than each of the single-sensor measurements. The capability of the proposed method is demonstrated through a series of simulations and real measurements of freeform surfaces on a multi-sensor CMM. The accuracy of the Gaussian process data modelling and the influence of the form error and measurement noise are also discussed and demonstrated in a series of experiments. The limitations and some special cases are also discussed, which should be carefully considered in practice.