Expedited surrogate-based quantification of engineering tolerances using a modified polynomial regression

Statistical analysis is frequently used to determine how manufacturing tolerances or operating condition uncertainties affect system performance. Surrogate is one of the accelerating ways in engineering tolerance quantification to analyze uncertainty with an acceptable computational burden rather than costly traditional methods such as Monte Carlo simulation. Compared with more complicated surrogates such as the Gaussian process, or Radial Basis Function (RBF), the Polynomial Regression (PR) provides simpler formulations yet acceptable outcomes. However, PR with the common least-squares method needs to be more accurate and flexible for approximating nonlinear and nonconvex models. In this study, a new approach is proposed to enhance the accuracy and approximation power of PR in dealing with uncertainty quantification in engineering tolerances. For this purpose, first, by computing the differences between training sample points and a reference point (e.g., nominal design), we employ certain linear and exponential basis functions to transform an original variable design into new transformed variables. A second adjustment is made to calculate the bias between the true simulation model and the surrogate's approximated response. To demonstrate the effectiveness of the proposed PR approach, we provide comparison results between conventional and proposed surrogates employing four practical problems with geometric fabrication tolerances such as three-bar truss design, welded beam design, and trajectory planning of two-link and three-link (two and three degrees of freedom) robot manipulator. The obtained results prove the preference of the proposed approach over conventional PR by improving the approximation accuracy of the model with significantly lower prediction errors.