故障诊断的单传感器检验关系方法及鲁棒设计

Method of Parity Relations and its Robust Design for Fault Diagnosis of Single Sensor

本文提出了一种诊断传感器故障的单传感器检验关系（ＳＳＰＲ）方法，给出了具有最小时间跨度的ＳＳＰＲ表达式；通过引入两个定理，提出了一种同时计算最小时间跨度和检验关系系数向量的反向稳定的计算方法；最后讨论了系统不确定参数对计算结果的影响。

The 1988 paper by Massoumnia et al 121 is the only paper known to the authors concerning SSPR (Single Sensor Parity Relations) method for sensor fault diagnosis. This paper is different from Re f. [2] in that the authors do two things not found in Ref.[2] : stable algorithm for computing SSPR coefficient vector under minimal time interval and robust design of SSPR in uncertain systems. Mathematical analysis gives two conclusions: (1) the minimal time interval of SSPR is really jUst the rank of the observability matrix; (2) the coefficient vector of SSPR with minimal time interval is uniquely determined from the characteristic polynomial of the minimal realization system. The proposed algorithm is based on orthogonal transformations and double oR decomposition of system matrices; thus it is backward stable. Consequently, the algorithm is better for practical applications to systems with uncertaintics in that the reliability of the obtained SSPR and also the influcnces of the model uncertainties can be evaluated by simply checking the condition number of the corresponding matrix cigenvalue problem, and that the robust design of SSPR is castly formulated as an optimizing process under system uncertaintics. Finally, an example illustrating the feasibility of this paper's method is given.