关于有偏估计提高测量可靠性的探讨

doi:10.3969/j.issn.0438-1157.2013.09.027

化工学报 ›› 2013, Vol. 64 ›› Issue (9): 3270-3276.DOI: 10.3969/j.issn.0438-1157.2013.09.027

关于有偏估计提高测量可靠性的探讨

岳元龙, 左信, 罗雄麟

中国石油大学(北京)自动化系, 北京 102249

收稿日期:2012-01-04 修回日期:2012-04-23 出版日期:2013-09-05 发布日期:2013-09-05
通讯作者: 罗雄麟
作者简介:岳元龙(1984- ),男,博士研究生。
基金资助:
国家自然科学基金项目(21006127)。

Improving measurement reliability based on biased estimation

YUE Yuanlong, ZUO Xin, LUO Xionglin

Department of Automation, China University of Petroleum, Beijing 102249, China

Received:2012-01-04 Revised:2012-04-23 Online:2013-09-05 Published:2013-09-05
Supported by:
supported by the National Natural Science Foundation of China(21006127).

摘要/Abstract

摘要： 可靠性是评价化工过程测量数据优劣的重要指标。理论与实践中普遍采用的观测数据平均值或加权平均作为待测参数测量值方法的本质是最小二乘无偏估计,而无偏测量数据可靠性与方差一一对应,根据高斯-马尔科夫定理可知无偏测量方差有下界,所以无偏测量数据不一定具有高可靠性。提出采用有偏估计改善测量数据的可靠性,首先分析未知参数测量与参数估计过程之间的等价性;其次给出同时采用方差和偏差定量表示有偏测量数据可靠性的方法;最后研究偏参数对有偏测量数据可靠性的影响,并采用数值法求解了偏参数的最优值。仿真结果表明偏参数合理取值范围内有偏测量的可靠性总是优于无偏测量的可靠性。

关键词: 可靠性, 测量, 有偏估计, 岭估计, 偏差, 方差

Abstract: Reliability is an important index to evaluate the properties of chemical process measurement data.In practical application and theoretical analysis the method of taking average or weighted average of observed data as the measurement value of unknown parameter is the special case of least square unbiased estimation.The reliability of measurement data arising from unbiased measurement is corresponding to variance.Based on the Gauss-Markov theorem,the variance of unbiased measurement has a lower bound,so the reliability of unbiased measurement cannot be guaranteed.A method used to improve measurement reliability by biased estimation was proposed.Firstly,the equivalence between classical measurement process and LS was discussed.Secondly,a quantitative description method was proposed to evaluate the reliability of biased measurement data.Finally,the effect of biased parameter on reliability was studied.Numerical solution of optimal value of biased parameter was also given.Simulation results showed that the proposed method was always superior to unbiased measurement process in terms of reliability given the reasonable numerical range of biased parameters.

Key words: reliability, measurement, biased estimator, ridge estimator, bias, variance

中图分类号:

TB114.3
TB22

岳元龙, 左信, 罗雄麟. 关于有偏估计提高测量可靠性的探讨[J]. 化工学报, 2013, 64(9): 3270-3276.

YUE Yuanlong, ZUO Xin, LUO Xionglin. Improving measurement reliability based on biased estimation[J]. CIESC Journal, 2013, 64(9): 3270-3276.

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关于有偏估计提高测量可靠性的探讨

Improving measurement reliability based on biased estimation

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