基于校准系数标准误差的天平测量不确定度评估

Evaluation of balance measurement uncertainty based on standard error of calibration coefficients

  • 摘要: 应变天平测量不确定度是飞行器风洞试验数据不确定度的重要来源之一。传统方法通过综合加载残差法获取天平校准公式,该方式引入的测量不确定度易导致风洞试验数据处理中天平小载荷量程段合成的测量不确定度偏大。为此,提出了一种基于天平校准原始数据的天平测量不确定度评估方法。该方法运用最小二乘法获取校准公式的系数标准误差及其残差标准差,进而计算由校准公式引入的测量不确定度。为验证该方法的有效性,以100E天平为对象开展了静态校准、综合加载、风洞试验前加载及风洞试验等研究工作。结果表明:1)在5组不同温度工况综合加载结果获取的标准差对比中,新方法相较传统方法,法向力FY、俯仰力矩Mz、轴向力FX三个分量分别相差–0.017%~0.029%、–0.018%~–0.002%和分量相差–0.006%~0.058%,两者吻合良好;2)风洞试验前加载测试中,在扩展不确定度因子k = 2时,新方法计算的扩展不确定度能够较为客观地量化地面准备加载结果的测量不确定度,而传统方法允许的测量不确定度则相对保守;3)风洞试验中,相较于以重复性标准差表征的天平测量不确定度,传统方法引入校准数学模型后,轴向力FX分量的合成标准不确定度增量为3.41~4.42 N,而新方法的增量仅为0~0.40 N。新方法不依赖综合加载数据,客观可靠,既能与校准过程中的综合加载结果互相印证,又能有效评估风洞试验前加载结果,为风洞试验数据处理中天平校准公式的不确定度来源提供了可靠依据,显著提升了飞行器气动数据评估的准确度,具有重要的工程应用价值。

     

    Abstract: The measurement uncertainty of strain gauge balance is one of the important sources of uncertainty in aircraft wind tunnel test data. The conventional methodology obtains the balance calibration formula through the comprehensive loading residual method. The measurement uncertainty introduced by this approach tends to cause an overestimation of the combined measurement uncertainty in the low-load range during wind tunnel test data processing. To this end, a new methodology for evaluating the measurement uncertainty of a balance was proposed. The core idea lay in leveraging the calibration raw data through least-squares regression analysis to quantify the mathematical modeling uncertainty. Specifically, the methodology derived both the standard error of the calibration formula coefficients and residual standard deviation of the calibration formula, thereby systematically assessing the propagated uncertainty components introduced by the mathematical modeling of the balance calibration formula. To verify the effectiveness of this methodology, static calibration, comprehensive loading, loading before wind tunnel testing, and wind tunnel testing were carried out on a 100E balance. The results are as follows: 1) The comprehensive loading results from five different temperature conditions show that the new methodology agrees with the conventional methodology, with a slight difference of –0.017%~0.029% for the normal force (FY ), –0.018%~–0.002% for the pitching moment ( Mz ), and –0.006%~0.058% for the axial force (FX); 2) The loading before wind tunnel testing results show that with the expanded uncertainty factor k = 2, the uncertainty calculated by the new methodology can objectively quantify the measurement uncertainty, while that by the conventional methodology is relatively conservative; 3) The measurement results of the axial force (FX ) of the balance during the wind tunnel test demonstrate that when compared to the measurement uncertainty characterized by the repeatability standard deviation of the balance, the conventional methodology introduces an additional 3.41 N to 4.42 N of synthetic standard uncertainty through its calibration mathematical model, whereas the proposed methodology exhibits a negligible increment of 0 N to 0.40 N. The proposed methodology evaluates the measurement uncertainty introduced by the mathematical model of the calibration formula, which is objectively reliable without relying on comprehensive loading. It can not only be used to verify the comprehensive loading during the calibration process, but also effectively evaluate loading results before wind tunnel testing. At the same time, it provides a reliable basis for the uncertainty source of the balance calibration mathematical model in wind tunnel test data processing, significantly improving the accuracy of aircraft aerodynamic data evaluation and having important engineering application value.

     

/

返回文章
返回