Uncertainty evaluation of surface profile measurement error based on adaptive sparse grid polynomial chaos expansion

• Published in: Advances in mechanical engineering Vol. 17; no. 6
• Main Authors: Zhang, Ke, Zheng, Xinya, Zhang, Ruiyu
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.06.2025; Sage Publications Ltd; SAGE Publishing
• Subjects: Computational efficiency; Errors; Free form; Maximum entropy method; Polynomials; Profile measurement; Uncertainty; uncertainty evaluation; sparse grid quadrature; polynomial chaos expansion; surface profile error
• ISSN: 1687-8132; 1687-8140
• DOI: 10.1177/16878132251349043

To address the challenge of balancing accuracy and computational efficiency in evaluating the measurement error and uncertainty of surface profile errors on complex free-form surfaces, this paper proposes an evaluation method combining adaptive sparse grids and polynomial chaos expansion. First, the surface profile error of the car door outer surface is initially evaluated using a NURBS surface fitting and segmentation approximation algorithm. Next, based on the error evaluation results, a polynomial chaos expansion model for the surface profile error is established. This model is optimized using Cholesky decomposition to handle variable correlations, sparse grid integration for efficient generation of multidimensional integration points, and maximum entropy method for direct reconstruction of probability distributions, thereby achieving efficient evaluation of the measurement error and uncertainty of surface profile. Numerical and experimental validations based on the car door outer surface demonstrate that compared to the ISO standard method, this method achieves a mean prediction error of less than 0.3% and a standard deviation relative error of less than 0.5% with a reduction of 99.6% in the number of sample calculation points. The evaluation results are accurate, and the computational efficiency is improved by 96.4%.