臺灣博碩士論文加值系統

本研究探討兩種新的弗德-卡曼濾波階次追蹤（Vold-Kalman Filtering Order Tracking, VKF_OT）方法，分別是 (1) 擴展型角速度與 (2) 適應性角位移VKF_OT技術，以改善原有兩種VKF_OT方法應用於旋轉機械狀態監測與故障診斷時之弱點。並將適應性角位移VKF_OT技術加以實現。論文涵蓋了理論推導、數值模擬與工程應用之實驗驗證三個部份。研究結果顯示本文所提出之二種演算法皆可同時擷取並分離階次相近或交錯之多軸轉速系統的階次訊號。適應性角位移VKF_OT為一基於卡曼濾波器（Kalman Filter），可藉由使用數位訊號處理器進行線上（on-line）運算並實現即時（real-time）處理應用之階次追蹤演算法。因此，文中藉由處理三組以不同階次所合成之模擬訊號及兩組實驗量測訊號驗證所發展方法於實際應用上之有效性。

This thesis comprises the theoretical derivation, numerical implementation, and experimental justification. To overcome the deficiencies of two original VKF_OT schemes for condition monitoring and diagnosis of rotary machinery, the study shows two advanced VKF_OT approaches, i.e. the extended angular-velocity and adaptive angular-displacement VKF_OT techniques and implement the latter technique in this thesis. These two proposed schemes can simultaneously extract multiple order/spectral components, and effectively decouple close or crossing orders associated with multi-axial reference rotating speeds. The adaptive angular- displacement VKF_OT scheme based on the Kalman filter can be calculated on-line and implemented as a real-time processing application through using a digital signal processor (DSP). Hence, three synthetic signals composed of different order/spectral components and two experimentations are designed to justify the effectiveness of applying the adaptive VKF_OT technique in practical works.

ABSTRACT..............................................................................................................................I
CONTENTS............................................................................................................................II
LIST OF FIGURES.................................................................................................................IV
LIST OF TABLES...................................................................................................................VI
CHAPTER 1 INTRODUCTION..................................................................................................................1
1.1 Background and Motivation............................................................................................1
1.2 Literature Survey.............................................................................................................2
1.3 Framework of the Thesis.................................................................................................4
CHAPTER 2 THEORETICAL BASIS........................................................................................................5
2.1 The Extended Angular-Velocity VKF Order Tracking....................................................5
2.1.1 Structural Equation.................................................................................................5
2.1.2 Data Equation.........................................................................................................7
2.1.3 Computation of the Tracked order Components....................................................7
2.1.4 Amplitude and Phase Evaluation..........................................................................12
2.2 The Adaptive Angular-Displacement VKF Order Tracking..........................................12
2.2.1 Structural Equation...............................................................................................14
2.2.2 Data Equation.......................................................................................................16
2.2.3 Kalman Filtering Based on One-step Prediction..................................................17
2.3 Conclusions...................................................................................................................26
CHAPTER 3 VKF ORDER TRACKING IMPLEMENTATION AND APPLICATIONS....................27
3.1 BCB Human-Machine Interface for VKF Order Tracking............................................27
3.2 Numerical Implementation............................................................................................29
3.2.1 Synthetic Signal 1－Distinguishing of Two Close Orders...................................29
3.2.2 Synthetic Signal 2－Crossing Orders and Multi-axle System.............................32
3.2.3 Synthetic Signal 3－Varying Order Tacking.......................................................35
3.3 Engineering Applications..............................................................................................38
3.3.1 Experimentation 1－Verification of Adaptive Angular-Displacement VKF-OT.39
3.3.2 Experimentation 2－Separation of Two Close Orders.........................................43
CHAPTER 4 CONCLUSIONS AND PROSPECTS.................................................................................49
4.1 Concluding Remarks.....................................................................................................49
4.2 Research Prospects........................................................................................................50
BIBLIOGRAPHY...................................................................................................................51
APPENDIX............................................................................................................................54
A. The Adaptive Angular-Displacement VKF Order Tracking...........................................54
A.1 Structural equation....................................................................................................55
A.2 Data equation............................................................................................................55
A.3 Computation of the envelope....................................................................................56
A.4 Conjugate gradient method.......................................................................................59

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