Weighting by Cross-Validation: A Calibration Method for Force Measurements via Transient Response Analysis

  • C. Luo
  • Y. Wang
  • Z. Hu
  • J. Li
  • Z. Jiang


Transient response analysis is an indirect method for the measurement of the aerodynamic force experienced by hypersonic vehicles in impulse wind-tunnel facilities; a transfer function is identified by a calibration experiment in advance and is then used to recover the target aerodynamic force. Theoretically, the transfer function is unique for a given measurement system. However, the calibration experiment may involve unpredictable factors and noise that are inevitable in practical applications, which will result in systematic errors. In this paper, a new calibration method, weighting by cross-validation (WCV), is proposed to reduce the systematic errors. In WCV, a series of on-site calibration experiments are carried out to obtain a set of transfer functions prior to the wind tunnel test. The transfer functions are cross-validated against each other to create a cross-validation table of relative measurement errors. The aerodynamic force is then calibrated using the average and standard deviation of the cross-validation errors. The working mechanism of the WCV method is demonstrated by analogy of measurements with a set of non-standard rulers. The effectiveness of the WCV method has been verified by tests in the JF-12 shock tunnel. Studies show that the WCV method improves the measurement accuracy significantly. In addition, the concept of the WCV method is general and can also be applied to other indirect measurement problems to reduce systematic errors, especially when no exact/standard measurement tools are available.


Aerodynamic force measurement Dynamic system Impact response Cross-validation System identification 



This work has been supported by the National Natural Science Foundation of China (Grant No. 11532014).


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© The Society for Experimental Mechanics, Inc 2018

Authors and Affiliations

  1. 1.State Key Laboratory of High Temperature Gas Dynamics, Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.School of Engineering SciencesUniversity of Chinese Academy of SciencesBeijingChina

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