本研究推導並實現一種新的弗德-卡曼濾波階次追蹤（Vold-Kalman Filtering Order Tracking, VKF_OT）方法，稱為適應性角速度VKF_OT(adaptive angular- velocity VKF_OT )，以改善原有角速度VKF_OT方法應用於旋轉機械狀態監測與故障診斷時之缺點，也就是運算時間長，並且無法線上即時運算。論文涵蓋了理論推導及數值模擬驗證，此外並對影響階次追蹤性能之權重因子以及結構方程式的相關函數(如參數 )進行討論。從處理三組不同之模擬訊號結果與工程應用得知，本文所提出之演算法可同時擷取並分離階次相近或交錯之旋轉訊號分量機械系統。由於適應性角速度VKF_OT是基於卡曼濾波器(Kalman Filter)之演算法，其具有即時運算的功能，因此可當作即時處理之工具。

The study presents and implements one advanced VKF_OT approaches, i.e. adaptive angular-velocity VKF_OT techniques, to overcome the deficiencies of original VKF_OT schemes for condition monitoring and diagnosis of rotary machinery. This thesis comprises the theoretical derivation, numerical implementation, and experimental justification. Comparisons of the improved VKF_OT schemes to the original ones are accomplished through processing three synthetic signals composed of different order/spectral components. Some parameters such as the weighting factor, the correlation matrix of process noise, and unwanted signatures/noise, which influence tracking performance, are investigated in the study. Additionally, three experimentations are designed to justify the effectiveness of applying the developed VKF_OT techniques in practical works. These proposed schemes can simultaneously extract multiple order/spectral components, and effectively decouple close or crossing orders associated with multi-axial reference rotating speeds. Furthermore, the adaptive angular-velocity VKF_OT scheme based on the Kalman filter can be calculated on-line and implemented as a real-time processing application.

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