A fiducial-aided data fusion method for the measurement of multiscale complex surfaces

  • Shixiang Wang
  • Chi Fai CheungEmail author
  • Mingyu Liu


Multiscale complex surfaces, possessing high form accuracy and geometric complexity, are widely used for various applications in fields such as telecommunications and biomedicines. Despite the development of multi-sensor technology, the stringent requirements of form accuracy and surface finish still present many challenges in their measurement and characterization. This paper presents a fiducial-aided data fusion method (FADFM), which attempts to address the challenge in modeling and fusion of the datasets from multiscale complex surfaces. The FADFM firstly makes use of fiducials, such as standard spheres, as reference data to form a fiducial-aided computer-aided design (FA-CAD) of the multiscale complex surface so that the established intrinsic surface feature can be used to carry out the surface registration. A scatter searching algorithm is employed to solve the nonlinear optimization problem, which attempts to find the global minimum of the transformation parameters in the transforming positions of the fiducials. Hence, a fused surface model is developed which takes into account both fitted surface residuals and fitted fiducial residuals based on Gaussian process modeling. The results of the simulation and measurement experiments show that the uncertainty of the proposed method was up to 3.97 × 10−5 μm based on a surface with zero form error. In addition, there is a 72.5% decrease of the measurement uncertainty as compared with each individual sensor value and there is an improvement of more than 36.1% as compared with the Gaussian process-based data fusion technique in terms of root-mean-square (RMS) value. Moreover, the computation time of the fusion process is shortened by about 16.7%. The proposed method achieves final measuring results with better metrological quality than that obtained from each individual dataset, and it possesses the capability of reducing the measurement uncertainty and computational cost.


Multiscale complex surface Precision surface measurement Data fusion Fiducial Multi-sensor Ultra-precision machining 


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Funding information

The work described in this paper was fully supported by a grant from the Research Grants Council of the Government of the Hong Kong Special Administrative Region, China (Project No. PolyU 15202814). The authors would also like to express their sincere thanks to the Research Committee of The Hong Kong Polytechnic University for their financial support of the project through a PhD studentship (project account code: RUEN).


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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Partner State Key Laboratory of Ultraprecision Machining Technology, Department of Industrial and Systems EngineeringThe Hong Kong Polytechnic UniversityHong KongChina

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