進階弗德-卡曼階次追蹤濾波器

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姓名

吳承學(Cheng-Xue Wu) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

進階弗德-卡曼階次追蹤濾波器
(Advanced Vold-Kalman Filtering Order Tracking)

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摘要(中)

本研究提出並實現兩種新的弗德-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。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。文中藉由處理三組以不同階次所合成之模擬訊號，對所改良之方法與原先方法進行比較，並針對影響其階次追蹤性能之參數，如權重因子（weighting factor）、程序雜訊相關矩陣（correlation matrix of process noise）及免疫於環境雜訊干擾之影響等分別探討。在實際工程應用上，則以過去實驗室所設計進行之三組實驗量測訊號驗證所發展方法之有效性。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。此外適應性角位移VKF_OT為一基於卡曼濾波器（Kalman Filter），可進行線上（on-line）運算並實現即時（real-time）處理應用之階次追蹤演算法。

摘要(英)

The study presents and implements two advanced VKF_OT approaches, i.e. the extended angular-velocity and adaptive angular-displacement VKF_OT techniques, to overcome the deficiencies of two 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 two 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- displacement VKF_OT scheme based on the Kalman filter can be calculated on-line and implemented as a real-time processing application.

關鍵字(中)

★ 卡曼濾波器
★ 弗德-卡曼濾波器
★ 階次追蹤

關鍵字(英)

★ Kalman filter
★ Vold-Kalman tracking filter
★ order tracking

論文目次

ABSTRACT I
CONTENTS II
LIST OF FIGURES IV
LIST OF TABLES IX
CHAPTER 1 INTRODUCTION 1
1.1 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 Tracked order Components 7
2.1.4 Amplitude and Phase Evaluation 11
2.2 The Adaptive Angular-Displacement VKF Order Tracking 12
2.2.1 Structural Equation 13
2.2.2 Data Equation 15
2.2.3 The Kalman Filter Based on One-step Prediction 16
CHAPTER 3 NUMERICAL IMPLEMENTATION 22
3.1 Two Close Orders Distinguishing－Synthetic Signal 1 22
3.2 Multi-axle Crossing Orders Decoupling－Synthetic Signal 2 28
3.3 Varying Order Tracking－Synthetic Signal 3 33
3.4 Influence of the Designed Parameters and Noise Effect in the Adaptive
Angular- Displacement VKF_OT 37
CHAPTER 4 ENGINEERING APPLICATIONS 45
4.1 Separation of Two Close Orders 45
4.1.1 Transmission Component Test Bench 46
4.1.2 Experimental Results and Discussion 48
4.2 Decoupling of Crossing Orders 52
4.2.1 Electric Scooter with Planetary Gear Sets and Multi-stage Gear
Transmission 52
4.2.2 Experimental Results and Discussion 56
4.3 Ranking of Pass by Noise Components 64
4.3.1 Electric Scooter with CVT Transmission and Speed-reduction Gears 64
4.3.2 Experimental Results and Discussion 67
CHAPTER 5 CONCLUSIONS AND RESEARCH PROSPECTS 71
5.1 Concluding Remarks 71
5.2 Research Prospects 73
BIBLIOGRAPHY 74
APPENDIX 77
A. The Adaptive Angular-Displacement VKF Order Tracking 77
A.1 Structural equation 78
A.2 Data equation 78
A.3 Computation of the envelope 79
A.4 Conjugate gradient method 82

參考文獻

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指導教授

潘敏俊(Min-Chun Pan)

審核日期

2006-7-22

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