Estimation of measurement results with poor information using the dynamic bootstrap grey method

Abstract Because of time, cost or safety restrictions, multi-sensor measurement results are commonly of poor information characterized by small data samples and an unknown data distribution. A dynamic bootstrap grey method is proposed to handle such problems considering that traditional statistical methods cannot. For small data samples, the proposed method has a lower relative estimation error of the measurement results compared to the grey bootstrap method and the Monte Carlo method. It is also superior to the Bessel method for large data samples. Based on two sets of experimental data, the estimation reliability of the dynamic bootstrap grey method is above 95% with a confidence level of 99.7% while providing a very low relative error of the estimated expected measured value and estimated measurement uncertainty. The presented results show that the dynamic bootstrap grey method can estimate the measurement results successfully without requiring data distribution information or a large sample size.

[1]  Cha'o-Kuang Chen,et al.  Application of grey prediction to inverse nonlinear heat conduction problem , 2008 .

[2]  A. Ferrero,et al.  Measurement Uncertainty - Part 8 in a series of tutorials in intsrumentation and measurement , 2006 .

[3]  G. Wübbeler,et al.  Evaluation of measurement uncertainty and its numerical calculation by a Monte Carlo method , 2008 .

[4]  Youmin Zhang,et al.  A novel variable‐length sliding window blockwise least‐squares algorithm for on‐line estimation of time‐varying parameters , 2004 .

[5]  Zhongyu Wang,et al.  Grey evaluation of non-statistical uncertainty in multidimensional precision measurement , 2006 .

[6]  Gabriele Moser,et al.  Automatic Parameter Optimization for Support Vector Regression for Land and Sea Surface Temperature Estimation From Remote Sensing Data , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[7]  Jun-Seok Lim,et al.  Noisy FIR parameter estimation by combining of total least mean squares estimation and least mean squares estimation , 2009, IEICE Electron. Express.

[8]  Jie Cui,et al.  A novel grey forecasting model and its optimization , 2013 .

[9]  Ignacio Lira,et al.  Bayesian evaluation of the standard uncertainty and coverage probability in a simple measurement model , 2001 .

[10]  Yanyan Meng,et al.  Evaluation of Variation Coefficient of Slewing Bearing Starting Torque Using Bootstrap Maximum-Entropy Method , 2013 .

[11]  Masatake Nagai,et al.  Prediction of relative dynamic elasticity modulus by extending a grey system theory , 2007 .

[12]  C. Manoj,et al.  The application of artificial neural networks to magnetotelluric time-series analysis , 2003 .

[13]  Wang Zhongyu,et al.  Novel Uncertainty-Evaluation Method of Virtual Instrument Small Sample Size , 2008 .

[14]  Zhongyu Wang,et al.  A seismic intensity estimation method based on the fuzzy-norm theory , 2012 .

[15]  Xintao Xia,et al.  Reliability Analysis of Zero‐Failure Data with Poor Information , 2012, Qual. Reliab. Eng. Int..

[16]  Stephen V. Crowder,et al.  A two-stage Monte Carlo approach to the expression of uncertainty with non-linear measurement equation and small sample size , 2006 .

[17]  Jianfeng Chen,et al.  Fuzzy Hypothesis Testing and Time Series Analysis of Rolling Bearing Quality , 2011 .

[18]  Chittaranjan Sahay,et al.  Uncertainty analysis of cylindricity measurements using bootstrap method , 2009 .

[19]  Chia-Yon Chen,et al.  Applications of improved grey prediction model for power demand forecasting , 2003 .

[20]  Le-Ren Chang-Chien,et al.  Online estimation of system parameters for artificial intelligence applications to load frequency control , 2011 .

[21]  Zhou Jing,et al.  Novel Error Prediction Method of Dynamic Measurement Lacking Information , 2012 .

[22]  Chong-Yu Xu,et al.  Development and comparison in uncertainty assessment based Bayesian modularization method in hydrological modeling , 2013 .

[23]  Mohammad Bagher Menhaj,et al.  A novel neuro-estimator and it’s application to parameter estimation in a remotely piloted vehicle , 2000 .

[24]  Okyay Kaynak,et al.  Grey system theory-based models in time series prediction , 2010, Expert Syst. Appl..