Calibration modeling of wind tunnel balance based on multivariate orthogonal functions

Yan Wanfang; Wei Wei; Jiang Kun; Wei Zhongwu; Zhang Jiang

doi:10.7638/kqdlxxb-2024.0078

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Calibration modeling of wind tunnel balance based on multivariate orthogonal functions

更新时间：2026-05-28

- Calibration modeling of wind tunnel balance based on multivariate orthogonal functions
- Vol. 44, Issue 1, Pages: 39-47(2026)
- 作者机构：
  
  中国航天空气动力技术研究院,北京,100074
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2024.0078
  CLC： V221.7
- Published：2026
- 稿件说明：
移动端阅览
闫万方, 魏巍, 蒋坤, 等. 基于多元正交函数的风洞天平校准建模方法[J]. 空气动力学学报, 2026, 44(1): 39−47.

Yan Wanfang, Wei Wei, Jiang Kun, et al. Calibration modeling of wind tunnel balance based on multivariate orthogonal functions[J]. 2026, 44(1): 39-47.
闫万方, 魏巍, 蒋坤, 等. 基于多元正交函数的风洞天平校准建模方法[J]. 空气动力学学报, 2026, 44(1): 39−47. DOI： 10.7638/kqdlxxb-2024.0078

Yan Wanfang, Wei Wei, Jiang Kun, et al. Calibration modeling of wind tunnel balance based on multivariate orthogonal functions[J]. 2026, 44(1): 39-47. DOI： 10.7638/kqdlxxb-2024.0078.

摘要

针对载荷极不匹配天平校准建模时，因模型结构确定困难、参数估计不准而导致建模误差较大的问题，发展了基于多元正交函数的风洞天平校准建模方法。采用多元正交函数建模，并利用预测均方误差准则对模型项进行筛选，使模型结构选取与参数估计过程解耦。为验证模型的有效性，针对某载荷极不匹配“多体式”焊接天平，开展了滚转力矩

的高精度测量建模。结果表明，相比于传统全回归和逐步回归方法，采用正交函数法建模可获得拟合适用性更优的回归模型，拟合误差带内较大误差点的误差抑制效果较好；验证集均方误差与之相比分别降低28.6%和16.2%。针对焊接型天平的“双向特性”测量问题，利用本文建模方法引入绝对值项后，验证集均方误差进一步降低，建模效果显著。

Abstract

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

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.

关键词

Keywords

references

He Dexin. Wind tunnel balance[M]. Beijing: National Defense Industry Press, 2001(in Chinese).

Cahill D, Steinle F, Richardson S. Evaluation of wind tunnel internal force balances from multiple vendors[C]//42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada. AIAA, 2004: 1292. doi: 10.2514/6.2004-1292

Ulbrich N M, Volden T. Wind tunnel strain-gage balance calibration data analysis using a weighted least squares approach[C]//33rd AIAA Aerodynamic Measurement Technology and Ground Testing Conference, Denver, Colorado. Reston, Virginia: AIAA, 2017: 4426. doi: 10.2514/6.2017-4426

Yan Wanfang, Jiang Kun, Zhang Jiang. Development of a six-component wind tunnel balance with lower interference on axial force measurement[J]. Journal of Experiments in Fluid Mechanics, 2018, 32(6): 61−67(in Chinese). doi: 10.11729/syltlx20180082

AIAA. Calibration and use of internal strain-gage balances with application to wind tunnel testing: AIAA R-091A-2020[R]. 2020. doi: 10.2514/4.106019

Ulbrich N. Optimization of regression models of experimental data using confirmation points[C]//48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida. Reston, Virginia: AIAA, 2010: 930. doi: 10.2514/6.2010-930

Ulbrich N, Volden T. Strain-gage balance calibration analysis using automatically selected math models[C]//41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference Exhibit, Tucson, Arizona. Reston, Virginia: AIAA, 2005: 4084. doi: 10.2514/6.2005-4084

Ulbrich N, Volden T. Regression analysis of experimental data using an improved math model search algorithm[C]//Proc of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada. Reston, Virginia: AIAA, 2008: 833. doi: 10.2514/6.2008-833

Ulbrich N. Regression model optimization for the analysis of experimental data[C]//Proc of the 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, Orlando, Florida. Reston, Virginia: AIAA, 2009: 1344. doi: 10.2514/6.2009-1344

Che Binghui, Yin Xinfan, PENG Xianmin, et al. Research on data processing method of balance calibration based on BP neural network[J]. Computer Measurement Control, 2020, 28(10): 165−169(in Chinese).

Wang Yunpeng, Nie Shaojun, Wang Yue, et al. Application of convolutional neural network in static calibration of wind tunnel balance[J]. Acta Aerodynamica Sinica, 2023, 41(3): 25−32(in Chinese). doi: 10.7638/kqdlxxb-2022.0096

Danilov M N, Bardaev P P. Finite element and neural network approximations to measure forces using six-component wind tunnel balance[J]. High-Energy Processes in Condensed Matter (Hepcm 2019): Proceedings of the XXVI Conference on High-Energy Processes in Condensed Matter, Dedicated to the 150th Anniversary of the Birth of S A Chaplygin, 2019, 2125: 030091. doi: 10.1063/1.5117473

Bergmann R, Philipsen I. An experimental comparison of different load tables for balance calibration [C]//27th AIAA Aerodynamic Measurement Technology and Ground Testing Conference, Chicago, Illinois. Reston, Virginia: AIAA, 2010: 4544. doi: 10.2514/6.2010-4544

Philipsen I, Zhai Junnai. Comparative study of strain-gauge balance calibration procedures using the balance calibration machine[C]//45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada. AIAA, 2007: 143. doi: 10.2514/6.2007-143

Morelli E. Nonlinear aerodynamic modeling using multivariate orthogonal functions[C]//Proc of the Flight Simulation and Technologies, Monterey, CA, USA. AIAA, 1993: 3636. doi: 10.2514/6.1993-3636

Barron A R. Predicted squared error: A criterion for automatic model selection[M]. Farlow S J. ed. Self-organizing mehtods in modeling, Boca Raton: CRC Press, 1984.

Yang Yingchen. Development of small rolling moment measurement technique[J]. Experiments and Measurements in Fluid Mechanics, 1999, 13(1): 73−76(in Chinese). doi: 10.3969/j.issn.1672-9897.1999.01.012

Ulbrich N. Detection of bi-directionality in strain-gage balance calibration data[C]//28th Aerodynamic Measurement Technology, Ground Testing, and Flight Testing Conference, New Orleans, Louisiana. AIAA, 2012: 3320. doi: 10.2514/6.2012-3320

Kammeyer M, Ulbrich N M. The use of absolute-value terms in regression modeling of multi-piece force balances [C]//31st AIAA Aerodynamic Measurement Technology and Ground Testing Conference, Dallas, TX. AIAA, 2015: 3382. doi: 10.2514/6.2015-3382

Wei Wei, Yan Wanfang, Jiang Kun. Research on nonlinear characteristics and physical mechanism of non-matching balance[C]//2nd China Aerodynamics Conference, Tianjin, 2022(in Chinese).

Johnson T H, Parker P A, Landman D. Calibration modeling of nonmonolithic wind-tunnel force balances[J]. Journal of Aircraft, 2010, 47(6): 1860−1866. doi: 10.2514/1.46356

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