| Summary: | 博士 === 國立臺灣大學 === 機械工程研究所 === 79 === A new concept for solving the failure detection and isolation
(FDI)problems in a linear system, which is called Parity-Cost algorithm,
has been develope. A parity function is used to generate the residual of
the measurement system by projecting the redundancy data from the
measurement domain into an orthogonal subspace, which is called parity
domain. The basic property of the parity fuction is a least square error
estimator, the format is so general that it can deal with both direct
redundancy and analytical redundancy problems.
The decision process of the FDI problem is done by using the model cost
analysis through the energy concept. The model cost method developed is a
quadratic form of the parity function. A residual which is generated by
the parity function will be treated as the external source toexcite the
analytical model. By definition, if there are no residual leakage from the
model, the the energy quantity is at minimum or zero level. Using the
decomposition property of the model cost method, the total model cost is
treated as a linear combination of the component cost. The fractuation of
the level of the component cost shows the possibility of the occurance of
failure. To decide when and where the failure occur, the method can
directly detect it by the comparison of the presetted threshold and the
level of the component cost.
To demonstrate the application and merit of the above method, the FDI
process of dirct redundancy measurement system and the analytical
redundancy system combined with sensors and actuators have been presented.
Also, a comparison of the detection time for the target tracking problem
of a dual-bandwidth Kalman filter and the Parity-Cost method is done.
The method developed in this thesis has following five merits: 1) Handle
the FDI problems for both the direct and the analytical redudancy systems
easily. 2) Solve the FDI problems combined with sensors and actuators
simultaneously. 3) Have the capability to detect the abrupt change of
target tracking problems. 4) Simplify the parity function generation
process, without using the voting system. 5) Quantify the failure events,
without lossing the stochastic property.
本文提出一種新的概念以解決處理系統失效偵測與鑑識之問題，同位函數技巧被用於
系統失效偵測及殘餘值產生器。其運作之基本觀念為複置量測儀器功能正常與否，可
經由一轉換矩陣，將其投射至所謂同位空間上，則在量測空間上之失效訊息將清楚的
以向量顯現於同位空間上。這些外顯之量，恰如同最小平方誤差估測法所得之殘餘值
。模式成本分析法將得來之殘餘值再行處理，以能量之計量觀點，將表示於同位空間
上之殘餘向量轉換為能量表示式。利用來自模式成本分析之特性，可得其單獨各元件
之成本變化量，藉以進行失效之鑑識工作。此種結合同位函數暨模式成本分析以處理
系統失效偵測與鑑識之方法，於本文稱為同位──模式成本分析法。
引用本法去處理直接複置量測系統和解析複置量測系統中感知器和（或）致動器失效
偵測與鑑識之研究，得知其為一種深具彈性變化之解答工具，能隨機轉換而不失其一
般性。應用於線上處置，將可同時兼顧感知器和致動器之失效偵測與鑑識工作；對於
多重失效偵測與鑑識工作亦可勝任。其另一特色為數量化的顯示失效發生的確實時機
，因而加速檢驗過速。本文中亦嘗試應用解決火控系統中雙頻卡爾曼濾波器追蹤目標
物之逃逸切換時機，以簡化其運算判定過程，而不失其精確性。
總結本法可獲致之效用為：1 ）能將解答直接複置系統及解析複置系統之失效偵測與
鑑識問題單純化；2 ）能同時處理系統中感知器和致動器失效之偵測與鑑識工作；3
）能應用於目標逃逸之追蹤偵測問題上；4 ）簡化同位函數之製造過程，可不必再倚
賴選舉系之協助，便能執行；5 ）將數量化觀念應用於系統之失效偵測，可使其更易
於辨識，而不背離其系統之隨機特性。
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