Abstract:Combining the grey model GM (1,1) with the bootstrap method and the uncertainty evaluation theory, a grey bootstrap evaluation model GBM (1,1) for dynamic measurement uncertainty of the explosion temperature in confined space was constructed by. A 300s temperature data in an explosion test were selected as the analysis data. Parameters such as the estimated true value, the estimated interval, and the mean uncertainty were used to characterize the estimation results. The results of this study indicate that the GBM (1,1) model, which combines the strengths of the GM (1,1) grey model and bootstrap method, can accurately model the probability distribution of the dynamic measurement data and track the variation trends of the measured instantaneous values in real time. Compared with the grey model GM (1,1) and bootstrap method, the grey bootstrap model has higher truth estimation accuracy and interval estimation reliability. The estimated error distribution range is [-12.62, 13.58], the standard deviation is 8.69℃, and the maximum relative error is 1.2%. Its interval estimation reliability exceeded 90%, and the estimated intervals fully enveloped the dynamic fluctuation range of the measured quantity. It proves that the GBM (1,1) model can evaluate the dynamic measurement uncertainty of the explosion temperature in confined space.
[1]王长利, 王惠, 刘晓新, 等. 小比距离爆炸的瞬时温度测量 [J]. 爆炸与冲击, 2013, 33(S1): 72-77.
Wang C L, Wang H, Liu X X, et al. Measurements of Transient Temperatures for Explosions at Small-scaled Distances [J]. [WTBX][STBX]Explosion and Shock Waves[STBZ][WTBZ], 2013, 33(S1): 72-77.
[2]马 红, 徐继东, 朱长春, 等. 密封容器内爆炸实验瞬态温度测试技术 [J]. 太赫兹科学与电子信息学报, 2014, 12(5): 750-756.
Ma H, Xu J D, Zhu C C, et al. Transient Temperature Testing Technology of Explosion Experiment in Airtight Container [J]. [WTBX][STBX]Journal of Terahertz Science and Electronic Information Technology[STBZ][WTBZ], 2014, 12(5): 750-756.
[3]Engel R, Baade H J. Quantifying Impacts on the Measurement Uncertainty in Flow Calibration Arising from Dynamic Flow Effects [J]. [WTBX][STBX]Flow Measurement & Instrumentation[STBZ][WTBZ], 2014, 44: 51-60.
[4]Mitchell M R, Link R E, Ge L, et al. Novel Uncertainty-Evaluation Method of Virtual Instrument Small Sample Size [J]. [WTBX][STBX]Journal of Testing & Evaluation[STBZ][WTBZ], 2008, 36(3): 273-279.
[5]Xia X T, Meng Y Y, Shi B J, et al. Bootstrap Forecasting Method of Uncertainty for Rolling Bearing Vibration Performance Based on GM(1, 1) [J]. [WTBX][STBX]Journal of Grey System[STBZ][WTBZ], 2015, 27(2): 78-92.
[6]Xia X T, Chen X Y, Zhang Y Z, et al. Grey Bootstrap Method of Evaluation of Uncertainty in Dynamic Measurement [J]. [WTBX][STBX]Measurement[STBZ][WTBZ], 2008, 41(6): 687-696.
[7]汪启跃, 王中宇, 王岩庆, 等. 乏信息空间机械臂随机振动信号的灰自助评估 [J]. 北京航空航天大学学报, 2016, 42(4): 858-864.
Wang Q Y, Wang Z Y, Wang Y Q, et al. Estimation of Space Manipulator Random Vibration Signals with Poor Information Based on Grey Bootstrap Method [J]. [WTBX][STBX]Journal of Beijing University of Aeronautics & Astronautics[STBZ][WTBZ], 2016, 42(4): 858-864.
[8]Wang Y Q, Wang Z Y, Sun J Y, et al. Dynamic Uncertainty Analysis for Random Vibration Signals in Flight Test [J]. [WTBX][STBX]Journal of Aircraft[STBZ][WTBZ], 2014, 51(6): 1966-1972.
[9]Hirsch R M, Archfield S A, Cicco L A D. A Bootstrap Method for Estimating Uncertainty of Water Quality Trends [J]. [WTBX][STBX]Environmental Modelling & Software[STBZ][WTBZ], 2015, 73: 148-166.
[10]张龙, 叶松, 王晓蕾, 等. 基于灰自助模型的气压动态测量结果评估方法 [J]. 仪器仪表学报, 2017, 38(7): 1645-1652.
Zhang L, Ye S, Wang X L, et al. Evaluation method for dynamic measurement result of atmospheric pressure based on grey bootstrap model [J]. [WTBX][STBX]Chinese Journal of Scientific Instrument[STBZ][WTBZ], 2017, 38(7): 1645-1652.
[11]Reeves J J. Bootstrap Prediction Intervals for ARCH Models [J]. [WTBX][STBX]International Journal of Forecasting[STBZ][WTBZ], 2005, 21(2): 237-248.
[12]Paparoditis E, Politis D N. Bootstrap Hypothesis Testing in Regression Models [J]. [WTBX][STBX]Statistics and Probability Letters[STBZ][WTBZ], 2005, 74(4): 356-365.
[13]费业泰. 误差理论与数据处理 [M]. 北京:机械工业出版社, 2004.
[14]姚悦,丁永红,裴东兴,等. 空气中爆炸冲击波曲线重建方法[J]. 计量学报, 2019,40(4): 636-641.
Yao Y,Ding Y H, Pei D X, et al. Reconstruction Method on Curve of Explosive Shock Wave in the Air[J]. Acta Metrologica Sinica, 2019, 40(4): 636-641.