基于蒙特卡罗法的五孔探针测量不确定度评定

Evaluation of measurement uncertainties for five-hole probes based on Monte Carlo method

为对五孔探针的测量精度进行评定,发展了基于统计学的蒙特卡罗法(MCM)评定五孔探针测量不确定度的流程和方法,并对比了最大误差限法和不确定度传播律法(GUM),同时研究了抽样数M对MCM评定结果的影响。该方法适用于无数学表达式的测量模型中,能考虑模型非线性的影响,概率密度函数(PDF)能更科学地表征输入量的分布,而不局限于正态分布。为了验证该方法,将五孔探针在校准风洞中进行了校准和验证。结果显示,对于风洞实验某测量点的静压,MCM提供的95%最短包含区间较GUM区间长度小11.1%,该差值占标准偏差的33.3%,表明利用MCM评估测量不确定度能引入复杂数据处理过程中非线性的影响,相比GUM评定方法具有一定的优势。将MCM应用于叶栅栅后流场五孔探针测量结果不确定度评定,发现各参数的不确定度在整个测量截面内分布情况与误差分布类似,在叶顶泄漏涡区域内测量不确定度较大,能避免相对静压无法表示的困境,同时能去除粗大误差的影响。MCM本身的统计误差可通过适当增加M来解决,需要综合考虑计算机性能和时间成本。

To evaluate the measurement accuracy of five-hole probes, the method of evaluating measurement uncertainties based on statistical Monte Carlo method(MCM) was developed and compared with the maximum error limit method and the guide to the expression of uncertainty method(GUM). At the same time, the influence of sampling numbers M on the evaluation result of MCM was studied. The method was applicable to measurement models without mathematical expressions, and the influence of nonlinearity of the model can be considered. The probability density function(PDF) can more scientifically characterize the distribution of the input quantity, instead of being limited to the normal distribution. To verify the method, a five-hole probes was calibrated and used in a standard wind tunnel.The results showed that for the static pressure, the shortest 95% coverage interval provided by MCM was11.1% smaller than the GUM. The difference accounted for 33.3% of the standard deviation. Furthermore,using MCM, the non-linear influence in data processing procedure can be considered compared with GUM. The MCM was applied to evaluate the measurement results of the flow field behind the cascade using the five-hole probes. The results showed that the uncertainty distribution of each parameter was similar to the error distribution in the whole measured cross section. The uncertainty was larger in blade tip leakage vortex area. However, it can avoid the trouble that the relative static pressure can not be expressed,and the influence of gross error can be removed. The statistical error of MCM itself can be solved by appropriately increasing M while considering the computer performance and time cost.