基于不确定理论的退化数据分析方法

作为可靠性领域传统的数学工具，概率论难以解决现代可靠性工程面临的难题。本文以不确定理论在退化数据分析中的应用为切入点,阐述了不确定理论的基本公理、运算法则与不确定统计方法,给出了基于确信可靠性理论的可靠性建模思路,提出了不确定失效阈值情形下的退化数据分析与可靠性建模方法。利用时变不确定正态分布建立产品的退化方程,根据专家知识建立失效阈值的不确定分布进而构建裕量方程,最终根据度量方程推导出产品可靠性模型。使用不确定统计中的极大似然估计法与假设检验法解决参数估计与模型验证问题。案例分析说明如果不考虑失效阈值的不确定性,会造成可靠性评估结果较大偏差。研究表明不确定理论适合处理退化数据分析中的不确定性难题,具有广阔的应用前景。

Fault accommodation for a class of linear time-varying systems with parametric uncertainties

Based on the H_∞ control theorem,by introducing the H_∞ performance index,a novel roubst adaptive observer using Lyapunov approach is designed for a class of MIMO linear time-varying systems with parameter uncertainties.By designing two differenent adaptive fault estimation laws and comparing with each other,several factors influencing the performance of fault estimation for the class of adaptive observer are obtained.The designed adaptive observer is used to the problem of fault accommodation for a class of linear time-varying systems with parameter uncertainties,and the fault estimation error is ultimately bounded uniformly and satisfies the prescribed H_∞ performance index.The simulation result for a flight control system illustrates the effectiveness and feasibility of the proposed method.