Calibration modeling of wind tunnel balance based on multivariate orthogonal functions

The performance of wind tunnel balance, which largely depends on the calibration modeling, plays a decisive role in the wind tunnel test capabilities and force measurement accuracy. However, there are still challenges for the calibration modeling in extreme conditions, two of which are inaccurate model feature selection and parameter estimation. This paper proposes a novel wind tunnel balance modeling method based on multivariate orthogonal functions coupled with the predicted squared error criterion for selecting model terms so that the model feature selection and parameter estimation processes are decoupled. This innovative method has been rigorously validated by its application to a multi-piece welding balance. The measured high-precision M_x demonstrates that the regression model with better fitting applicability can be obtained using the orthogonal functions method, and the mean square error of the verification set can be reduced by 28.6% and 16.2%, respectively, when compared with the traditional total regression and stepwise regression methods. Moreover, for bidirectional welded balance, introducing the absolute value into the model can further reduce the mean squared error of the verification set, yielding a remarkably accurate model.