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系統識別號 U0002-1409201209244200
中文論文名稱 利用現代希爾伯特-黃轉換及改進的序列比對法之飛行性能參數研究
英文論文名稱 An Investigation of Flight Vehicle Performance Parameters via the Modern Hilbert-Huang Transform and the Improved Sequence Alignment Methods
校院名稱 淡江大學
系所名稱(中) 航空太空工程學系碩士班
系所名稱(英) Department of Aerospace Engineering
學年度 100
學期 2
出版年 101
研究生中文姓名 鄭宇軒
研究生英文姓名 Norman Cheng
電子信箱 andantecheng@gmail.com
學號 600430077
學位類別 碩士
語文別 英文
口試日期 2012-07-17
論文頁數 187頁
口試委員 指導教授-宛同
委員-鄭育能
委員-官文霖
中文關鍵字 飛航操作品保系統  希爾伯特-黃轉換  改進的基因序列比對法  二維模擬拍撲翼空氣動力學  本質模態函數錯位現象  飛行資料分析  信號分析  ATR-72  生物資訊學 
英文關鍵字 Flight Operational Quality Assurance (FOQA)  Hilbert-Huang Transform (HHT)  Improved Sequence Alignment (ISA)  2-D Simulated Flapping Wing Aerodynamics  IMF Staggering Effect  Flight Data Analysis  Signal Processing  ATR-72  Bioinformatics 
學科別分類 學科別應用科學航空太空
中文摘要 本研究的主旨是利用希爾伯特-黃轉換(Hilbert-Huang Transform, HHT, 包含Empirical Mode Decomposition, EMD和Hilbert Spectral Analysis, HSA)及改進的基因序列比對法(Improved Sequence Alignment, ISA)分析飛行操作品質系統(Flight Operational Quality Assurance, FOQA)之飛行性能參數資料及二維模擬拍撲翼之空氣動力係數。本研究最初目的是利用HHT分析原始訊號,從隱藏且以頻率為基底的本質模態函數群(Intrinsic Mode Functions, IMF)
找出規律性的模式。盡管EMD作為一種濾波器,透過不同的頻率層級分解出具有數學意義的IMF,但不一定具有強健的物理意義。EMD的特性是將原始訊號分解出8~12個IMF,這增加分析問題的困難度,尤其是物理意義不顯明的函數群。於是本篇論文研發之改進的基因序列比對法(Improved Sequence Alignment, ISA)用於量化IMF函數群,以統計的方式記錄函數群的五個本質字母(5-Elemental Alphabets),並且存放置基因譜(Genetic Profile),用於實現兩個序列的序列比對。
本研究裡,使用二維模擬拍撲翼在固定風場下的升阻力訊號作為基準,以證明HHT和ISA整合的實用性,因為其結果是可預測的。實際的案例則以ATR-72班機的三把正常航班及一把異常航班為例,異常航班的引擎資料是一把No.1引擎在巡航階段空中熄火的狀況,以系統和方法分析之。IMF錯位現象(IMF Staggering Effect)被發現在拍撲翼的HHT分析結果,並且從ISA的排列方式得到證實。飛機扭力參數的序列排列資料說明潛在因子可被偵測的可能性,但是因子仍然不明顯。這個原因主要因為引擎參數變化通常發生在為秒之間,原始資料則是1Hz紀錄,造成資料先天不精準性。拍撲翼的分析為基準,證實了IMF錯位現象可被ISA排列出來,譬如Lift和Lift_2ms_h有著sequence A = (c0, c1, c2, c3, -, c4, c5, c6, c7, c8, c9, c10, c11, c12)和sequence B = (c0, -, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12)的排列。
另外,頻率相似度F是支配排列結果的重要因子,以拍撲翼為例,在升力排列的出現次數為37.10%,阻力為47.89%。飛行資料中找出相似模式的機率為55.13%。本研究的結論是證實HHT和ISA的可行性,未來展望期望加入更進階的經驗搜尋法則,從排列的結果中更快速找到相似模式,從排列的模式裡還另外找出資料同源的可能性(Homology)。
英文摘要 A set of Flight Operational Quality Assurance (FOQA) flight data and a set of flapping wings lift and drag computational fluid dynamics (CFD) results were examined by the aid of Hilbert-Huang Transform (HHT) and Improved Sequence Alignment (ISA) method. The purpose of applying HHT to data is to find the hidden frequency-based (Intrinsic Mode Functions) IMF patterns from the origin signal. Despite HHT works as a filter to extract the variability of signals with different frequency levels and has the ability to decompose original signals into several mathematical subcomponents, the results often being very hard to explain the physical meaning. It is often difficult to analyze a population of data when these data were recorded. Hence, the ISA method of quantizing all the signals to statistical measurements by statistical measurements was invented here, and was applied for data dimensionality reduction. The approach of this thesis study is to first apply HHT and ISA on flapping wing CFD data as the benchmark since the expected aligned results are explicit and then apply the system and methods on FOQA data. The flight data of three normal flights and one abnormal flight, a case of engine No.1 failure during cruise flight, was extracted from a specific ATR-72 twin-engine turboprop airliner. The IMF staggering effect was first found in flapping wings HHT results and was fully verified via ISA. Several important alignment results of different flight phases were found in the parameter Torque of ATR-72 flight data that indicates the existence of potential risk factors before the event flight. The alignment results of flapping wings are well as a very good benchmark case, but the alignment results of FOQA engine failure during operation in flight are vague. This reason is majorly because of the engine failure event usually appears to be a sudden change within milliseconds. The data time interval used in current work is 1 Hz. This is considered as the congenital missing of data that leads to a fundamental problem lacking of precise measures. Facts are found using HHT and ISA method. The benchmark case of aligning Lift and Lift_2ms_h as sequence A = (c0, c1, c2, c3, -, c4, c5, c6, c7, c8, c9, c10, c11, c12) and sequence B = (c0, -, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12). The case shows perfect alignment with staggering effect included. Another important fact is the F (degree of frequency measurement) of the 5-elemental alphabets is a dominating factor since HHT is frequency-based. The probability of formats containing alphabet F in Lift is 37.10% and Drag is 47.89%, indicating alphabet F is very common in alignments and in IMF as well. For FOQA data alignments, the pattern finding probability is approximately 55.13%. An empirical system and procedure for pattern searching is needed to handle a population of data. The hidden patterns were found in both cases and the concept of data homology was illustrated.
論文目次 TABLE OF CONTENTS
ACKNOWLEDGEMENTS I
ABSTRACT III
TABLE OF CONTENTS IX
LIST OF TABLES XII
LIST OF FIGURES XIV
NOMENCLATURE AND ABBREVIATIONS XVII
I. INTRODUCTION 1
I. A. INTRODUCTION 1
I. B. MOTIVATIONS & INSPIRATIONS 5
I. C. A BRIEF DESCRIPTION OF THE PROBLEM-SOLVING PROCESS 7
I. D. ORGANIZATION OF THE THESIS – DUEL PROBLEMS 9
II. BACKGROUND RESEARCH AND LITERATURE REVIEW 10
II. A. FLIGHT OPERATIONS QUALITY ASSURANCE (FOQA) 10
II. B. BRIEF INTRODUCTION TO THE HILBERT-HUANG TRANSFORMATION (HHT) 11
II. C. APPLICATION AND REALIZATION OF HHT – A LITERATURE REVIEW 12
II. D. HHT ON COMPUTATIONAL FLUID DYNAMICS – MAV FLAPPING WINGS 13
II. E. SEQUENCE ALIGNMENT IN BIOINFORMATICS 14
II. F. PROBABILISTIC SEQUENCE ALIGNMENT METHODS FOR ON-LINE SCORE FOLLOWING OF MUSIC PERFORMANCE – A LITERATURE REVIEW 14
II. F. 1. Concept 14
II. F. 2. Benefits 17
II. F. 3. Inspirations 18
III. THEORETICAL METHOD – THE HILBERT-HUANG TRANSFORM (HHT) 19
III. A. THE EMPIRICAL MODE DECOMPOSITION (EMD) 19
III. A. 1. The Empirical Mode Decomposition Methodology 20
III. A. 2. The Stopping Criteria 22
III. A. 3. Properties of EMD 23
III. B. HILBERT SPECTRAL ANALYSIS (HSA) 24
III. B. 1. Hilbert Transform and the Instantaneous Frequency 24
III. B. 2. Completeness of Hilbert Transform 26
III. B. 3. Comparison of Different Spectral Analysis 27
III. C. MATHEMATICAL PROBLEMS RELATED TO HHT 29
III. D. HHT VERIFICATIONS 30
III. D. 1. Simple Harmonic Data 30
III. D. 2. Decaying Signal 31
III. D. 3. Sunspot Data 34
IV. THEORETICAL METHOD – SEQUENCE ALIGNMENT 36
IV. A. INTRODUCTION 36
IV. B. THE SCORING SYSTEM 39
IV. C. GLOBAL SEQUENCE ALIGNMENT (NEDLEMAN AND WUNSCH ALGORITHM) 40
IV. D. LOCAL SEQUENCE ALIGNMENT (SMITH-WATERMAN ALGORITHM) 43
V. THE IMPLEMENTATION – SYSTEM AND METHODS 44
V. A. A BRIEF REVIEW 44
V. B. IMPROVED SEQUENCE ALIGNMENTS – A COMPREHENSIVE METHOD 45
V. B. 1. The Schema 45
V. B. 2. Procedure Details – Statistical Analysis 48
V. B. 3. Procedure Details – Generation of Genetic Profile 52
V. B. 4. Procedure Details – Classification of Statistical Measurements 53
V. B. 5. Procedure Details – Discussions on Defining Alphabets 54
V. B. 6. Procedure Details – Improved Scoring System (Comprehensive) 56
V. B. 7. Procedure Details – Improved Global Sequence Alignment Methods 60
V. B. 8. Procedure Details – An Example of Alignment Results 61
V. C. A SUMMARY OF CURRENT MODELS 64
V. C. 1. Comparisons of Sequence Alignments and Current Methods 64
V. C. 2. Improvements of Current Methods 65
V. C. 3. Program Structure 66
VI. RESULTS – FLAPPING WINGS 67
VI. A. RESULTS OF FLAPPING WING VIA HHT 67
VI. A. 1. Staggering Effects 72
VI. B. APPLICATIONS BY IMPROVED SEQUENCE ALIGNMENT METHODS 76
VI. B. 1. Lift & Lift_2ms_v 76
VI. B. 2. Lift & Lift_2ms_hv 79
VI. B. 3. Lift & Lift_5ms_h 81
VI. B. 4. Lift & Lift_5ms_v 83
VI. B. 5. Lift & Lift_5ms_hv 85
VI. B. 6. Drag & Drag_2ms_h 87
VI. B. 7. Drag & Drag_2ms_v 89
VI. B. 8. Drag & Drag_2ms_hv 91
VI. B. 9. Drag & Drag_5ms_h 93
VI. B. 10. Drag & Drag_5ms_v 95
VI. B. 11. Drag & Drag_5ms_hv 97
VI. C. DISCUSSIONS ON ALIGNMENTS 99
VII. RESULTS – FOQA DATA 107
VII. A. INTRODUCTION UNEXPECTED ENGINE EVENT INVESTIGATION 107
VII. B. RESULTS OF FOQA DATA VIA HHT 110
VII. C. ALIGNMENT RESULTS 111
VIII. OBSERVATIONS, DISCUSSIONS, AND STATEMENTS 119
VIII. A. OBSERVATIONS 119
VIII. B. DISCUSSIONS 122
VIII. B. 1. Discussions on HHT Method 122
VIII. B. 2. Discussions on the Improved Sequence Alignment 123
VIII. B. 3. Discussions by Case – FOQA Data 124
VIII. C. STATEMENTS 124
IX. CONCLUSIONS 126
IX. A. CONCLUSIONS 126
IX. B. FUTURE STUDIES 128
REFERENCES 129
APPENDIX A – FLAPPING WINGS DATA 132
APPENDIX A. 1. FLAPPING WINGS GENETIC PROFILE 132
APPENDIX A. 2. EMD RESULTS DB STRUCTURE 144
APPENDIX B – FOQA FLIGHT DATA 145
APPENDIX B. 1. FOQA HHT RESULTS 145
APPENDIX B. 2. FOQA ALIGNMENT FORMAT RESULTS (FOR EXAMPLE) 157
APPENDIX C – AIAA FORMAT CONFERENCE PAPER 173

LISTOFTABLES
TABLE 2.1: A COMPARISON OF PARDO’S METHOD AND CURRENT MODEL 18
TABLE 3.1 COMPARISON OF DIFFERENT SPECTRAL ANALYSIS METHODS (HUANG ET AL., 1998) 28
TABLE 3.2: EMD RESULTS OF SIMPLE HARMONIC DATA 31
TABLE 3.3: EEMD RESULTS OF SUNSPOT DATA 34
TABLE 5.1: LIST OF 7-FUNDAMENTAL MEASUREMENTS 49
TABLE 5.2: LIST OF 5-ELEMENTAL ALPHABETS 50
TABLE 5.3: EXAMPLE OF A GENETIC PROFILE 52
TABLE 5.4: A SUMMARY OF PROBLEMS ENCOUNTERED WHEN DEFINING ALPHABETS 55
TABLE 5.5: COMBINATIONS OF 5-ELEMENTAL ALPHABETS 57
TABLE 5.6: THE SUB-SCORING MATRIX 58
TABLE 5.7: THE OVERALL SCORING MATRIX 59
TABLE 5.8: THE FINAL ALIGNMENT OF THE EXAMPLE CASE 63
TABLE 5.9: COMPARISON OF TRADITIONAL AND CURRENT METHODS 64
TABLE 5.10: THE TERMINOLOGY TABLE 65
TABLE 6.1: THE COLLECTION OF RAW FLAPPING CFD RESULTS (HUANG, 2010) 69
TABLE 6.2: A LIST OF STAGGERING EFFECTS 72
TABLE 6.3: THE FINAL ALIGNMENT OF LIFT (SEQUENCE A) AND LIFT 2M/S VERTICAL (SEQUENCE B) 78
TABLE 6.4: THE FINAL ALIGNMENT OF LIFT (SEQUENCE A) AND LIFT 2M/S HORIZONTAL + VERTICAL (SEQUENCE B) 80
TABLE 6.5: THE FINAL ALIGNMENT OF LIFT (SEQUENCE A) AND LIFT 5M/S HORIZONTAL (SEQUENCE B) 82
TABLE 6.6: THE FINAL ALIGNMENT OF LIFT (SEQUENCE A) AND LIFT 5M/S VERTICAL (SEQUENCE B) 84
TABLE 6.7: THE FINAL ALIGNMENT OF LIFT (SEQUENCE A) AND LIFT 5M/S HORIZONTAL + VERTICAL (SEQUENCE B) 86
TABLE 6.8: THE FINAL ALIGNMENT OF DRAG (SEQUENCE A) AND DRAG 2M/S HORIZONTAL (SEQUENCE B) 88
TABLE 6.9: THE FINAL ALIGNMENT OF DRAG (SEQUENCE A) AND DRAG 2M/S VERTICAL (SEQUENCE B) 90
TABLE 6.10: THE FINAL ALIGNMENT OF DRAG (SEQUENCE A) AND DRAG 2M/S HORIZONTAL + VERTICAL (SEQUENCE B) 92
TABLE 6.11: THE FINAL ALIGNMENT OF DRAG (SEQUENCE A) AND DRAG 5M/S HORIZONTAL (SEQUENCE B) 94
TABLE 6.12: THE FINAL ALIGNMENT OF DRAG (SEQUENCE A) AND DRAG 5M/S VERTICAL (SEQUENCE B) 96
TABLE 6.13: THE FINAL ALIGNMENT OF DRAG (SEQUENCE A) AND DRAG 5M/S HORIZONTAL + VERTICAL (SEQUENCE B) 98
TABLE 6.14: THE ALIGNMENT COMPARISON OF LIFT 2M/S AND LIFT 5 M/S UNDER HORIZONTAL STEADY WIND CONDITION 100
TABLE 6.15: THE ALIGNMENT COMPARISON OF LIFT 2M/S AND LIFT 5 M/S UNDER VERTICAL STEADY WIND CONDITION 101
TABLE 6.16: THE ALIGNMENT COMPARISON OF LIFT 2M/S AND LIFT 5 M/S UNDER HORIZONTAL + VERTICAL STEADY WIND CONDITION 102
TABLE 6.17: THE ALIGNMENT COMPARISON OF DRAG 2M/S AND DRAG 5 M/S UNDER HORIZONTAL STEADY WIND CONDITION 103
TABLE 6.18: THE ALIGNMENT COMPARISON OF DRAG 2M/S AND DRAG 5 M/S UNDER VERTICAL STEADY WIND CONDITION 104
TABLE 6.19: THE ALIGNMENT COMPARISON OF DRAG 2M/S AND DRAG 5 M/S UNDER HORIZONTAL + VERTICAL STEADY WIND CONDITION 105
TABLE 7.1: ALL FLIGHT PHASES 108
TABLE 7.2: IMPORTANT ALIGNMENT RESULTS OF DIFFERENT FLIGHT PHASES (PARAMETER TQ1) 112
TABLE 7.3: PARAMETER TQ1, FLIGHT PHASE 1 113
TABLE 7.4: PARAMETER TQ1, FLIGHT PHASE 2 114
TABLE 7.5: PARAMETER TQ1, FLIGHT PHASE 3 115
TABLE 7.6: PARAMETER TQ1, FLIGHT PHASE 4 116
TABLE 7.7: PARAMETER TQ1, FLIGHT PHASE 5 117
TABLE 7.8: PARAMETER TQ1, FLIGHT PHASE 6 117
TABLE 7.9: PARAMETER TQ1, FLIGHT PHASE 8 118
TABLE 8.1: AN EXAMPLE OF CASE HOMOLOGY 121
TABLE 8.2: LIST OF 5-ELEMENTAL ALPHABETS (VERSION 2) 123

LIST OF FIGURES
FIGURE (2.1): SYSTEM AND METHODS OF THE TRANSCRIPTION OF MUSIC SCORES [23] 15
FIGURE (3.1): THE TYPICAL TYPE OF EMD PROCEDURE 22
FIGURE (3.2): THE UNIT CIRCLE ON Z-PLANE. SOURCE: [8] 26
FIGURE (3.3): THE HSA PROCEDURE OF HHT 27
FIGURE (3.4): THE COMPARISON OF DIFFERENT SPECTRAL ANALYSIS. SOURCE: [2] 28
FIGURE (3.5): EMD RESULTS OF A SIMPLE HARMONIC DATA 32
FIGURE (3.6): THE COMPLETENESS OF IMFS 32
FIGURE (3.7): THE EMD RESULT OF A DECAYING SIGNAL 33
FIGURE (3.8): THE COMPLETENESS OF DECAYING SIGNAL 33
FIGURE (3.9): THE EEMD RESULT OF HALF-YEAR SUNSPOT DATA 35
FIGURE (3.10): THE INSTANTANEOUS FREQUENCY OF HALF-YEAR SUNSPOT DATA 35
FIGURE (5.1): THE OVERALL PROGRAM SCHEME, TAKE FLAPPING WINGS CASE FOR EXAMPLE 47
FIGURE (5.2): 5-ELEMENTAL ALPHABETS C, M, AND D OF A COSINE WAVE 51
FIGURE (5.3): 5-ELEMENTAL ALPHABETS F AND V OF A COSINE WAVE 51
FIGURE (5.4): AN EXAMPLE SCORING TABLE (FLAPPING WINGS) OF IMPROVED SEQUENCE ALIGNMENT METHODS 61
FIGURE (5.5): THE EXAMPLE ALIGNMENT FORMAT CARD OF FLAPPING WINGS CASE 63
FIGURE (5.6): THE GENERAL SYSTEM STRUCTURE 66
FIGURE (6.1): THE MECHANIC CONFIGURATION OF 2-D FLAPPING WING [7] 68
FIGURE (6.2): EMD RESULT OF HUANG’S CASE 70
FIGURE (6.3): EMD RESULT OF WANG’S CASE 70
FIGURE (6.4): A COMPARISON OF IMF C0 INDICATES THE ORIGINAL SIGNAL 71
FIGURE (6.5): A COMPARISON OF IMF C3 71
FIGURE (6.6): THE STAGGERING EFFECT OF LIFT (SEQUENCE A) AND LIFT 2M/S HORIZONTAL (SEQUENCE B) 73
FIGURE (6.7): THE STAGGERING EFFECT OF LIFT (SEQUENCE A) AND LIFT 2M/S VERTICAL (SEQUENCE B) 74
FIGURE (6.8): THE STAGGERING EFFECT OF LIFT (SEQUENCE A) AND LIFT 2M/S HORIZONTAL + VERTICAL (SEQUENCE B) 75
FIGURE (6.9): THE SCORING TABLE OF ALIGNING LIFT (SEQUENCE A) AND LIFT 2M/S VERTICAL (SEQUENCE B) 77
FIGURE (6.10): THE FORMAT CARD OF ALIGNING LIFT (SEQUENCE A) AND LIFT 2M/S VERTICAL (SEQUENCE B) 78
FIGURE (6.11): THE SCORING TABLE OF ALIGNING LIFT (SEQUENCE A) AND LIFT 2M/S HORIZONTAL + VERTICAL (SEQUENCE B) 79
FIGURE (6.12): THE FORMAT CARD OF ALIGNING LIFT (SEQUENCE A) AND LIFT 2M/S HORIZONTAL + VERTICAL (SEQUENCE B) 80
FIGURE (6.13): THE SCORING TABLE OF ALIGNING LIFT (SEQUENCE A) AND LIFT 5M/S HORIZONTAL (SEQUENCE B) 81
FIGURE (6.14): THE FORMAT CARD OF ALIGNING LIFT (SEQUENCE A) AND LIFT 5M/S HORIZONTAL (SEQUENCE B) 82
FIGURE (6.15): THE SCORING TABLE OF ALIGNING LIFT (SEQUENCE A) AND LIFT 5M/S VERTICAL (SEQUENCE B) 83
FIGURE (6.16): THE FORMAT CARD OF ALIGNING LIFT (SEQUENCE A) AND LIFT 5M/S VERTICAL (SEQUENCE B) 84
FIGURE (6.17): THE SCORING TABLE OF ALIGNING LIFT (SEQUENCE A) AND LIFT 5M/S HORIZONTAL + VERTICAL (SEQUENCE B) 85
FIGURE (6.18): THE FORMAT CARD OF ALIGNING LIFT (SEQUENCE A) AND LIFT 5M/S HORIZONTAL + VERTICAL (SEQUENCE B) 86
FIGURE (6.19): THE SCORING TABLE OF ALIGNING DRAG (SEQUENCE A) AND DRAG 2M/S HORIZONTAL (SEQUENCE B) 87
FIGURE (6.20): THE FORMAT CARD OF ALIGNING DRAG (SEQUENCE A) AND DRAG 2M/S HORIZONTAL (SEQUENCE B) 88
FIGURE (6.21): THE SCORING TABLE OF ALIGNING DRAG (SEQUENCE A) AND DRAG 2M/S VERTICAL (SEQUENCE B) 89
FIGURE (6.22): THE FORMAT CARD OF ALIGNING DRAG (SEQUENCE A) AND DRAG 2M/S VERTICAL (SEQUENCE B) 90
FIGURE (6.23): THE SCORING TABLE OF ALIGNING DRAG (SEQUENCE A) AND DRAG 2M/S HORIZONTAL + VERTICAL (SEQUENCE B) 91
FIGURE (6.24): THE FORMAT CARD OF ALIGNING DRAG (SEQUENCE A) AND DRAG 2M/S HORIZONTAL + VERTICAL (SEQUENCE B) 92
FIGURE (6.25): THE SCORING TABLE OF ALIGNING DRAG (SEQUENCE A) AND DRAG 5M/S HORIZONTAL (SEQUENCE B) 93
FIGURE (6.26): THE FORMAT CARD OF ALIGNING DRAG (SEQUENCE A) AND DRAG 5M/S HORIZONTAL (SEQUENCE B) 94
FIGURE (6.27): THE SCORING TABLE OF ALIGNING DRAG (SEQUENCE A) AND DRAG 5M/S VERTICAL (SEQUENCE B) 95
FIGURE (6.28): THE FORMAT CARD OF ALIGNING DRAG (SEQUENCE A) AND DRAG 5M/S VERTICAL (SEQUENCE B) 96
FIGURE (6.29): THE SCORING TABLE OF ALIGNING DRAG (SEQUENCE A) AND DRAG 5M/S HORIZONTAL + VERTICAL (SEQUENCE B) 97
FIGURE (6.30): THE FORMAT CARD OF ALIGNING DRAG (SEQUENCE A) AND DRAG 5M/S HORIZONTAL + VERTICAL (SEQUENCE B) 98
FIGURE (6.31): FREQUENCY OF APPEARANCE OF ALIGNMENT TYPES/FORMAT OF LIFT CASES 106
FIGURE (6.32): FREQUENCY OF APPEARANCE OF ALIGNMENT TYPES/FORMAT OF DRAG CASES 106
FIGURE (7.1): ENGINE NO.1 MAIN PARAMETERS OF FLIGHT EF(0) 109
FIGURE B. (1.1): THE EEMD RESULT OF FLIGHT EF(0) ON PARAMETER TQ 145
FIGURE B. (1.2): THE IFS OF FLIGHT EF(0) ON PARAMETER TQ 145
FIGURE B. (1.3): THE EEMD RESULT OF FLIGHT EF(-1) ON PARAMETER TQ 146
FIGURE B. (1.4): THE IFS OF FLIGHT EF(-1) ON PARAMETER TQ 146
FIGURE B. (1.5): THE EEMD RESULT OF FLIGHT EF(-2) ON PARAMETER TQ 147
FIGURE B. (1.6): THE IFS OF FLIGHT EF(-2) ON PARAMETER TQ 147
FIGURE B. (1.7): THE EEMD RESULT OF FLIGHT EF(0) ON PARAMETER PROP_SPD_NP 148
FIGURE B. (1.8): THE IFS OF FLIGHT EF(0) ON PARAMETER PROP_SPD_NP 148
FIGURE B. (1.9): THE EEMD RESULT OF FLIGHT EF(-1) ON PARAMETER PROP_SPD_NP 149
FIGURE B. (1.10): THE IFS OF FLIGHT EF(-1) ON PARAMETER PROP_SPD_NP 149
FIGURE B. (1.11): THE EEMD RESULT OF FLIGHT EF(-2) ON PARAMETER PROP_SPD_NP 150
FIGURE B. (1.12): THE IFS OF FLIGHT EF(-2) ON PARAMETER PROP_SPD_NP 150
FIGURE B. (1.13): THE EEMD RESULT OF FLIGHT EF(0) ON PARAMETER ITT 151
FIGURE B. (1.14): THE IFS OF FLIGHT EF(0) ON PARAMETER ITT 151
FIGURE B. (1.15): THE EEMD RESULT OF FLIGHT EF(-1) ON PARAMETER ITT 152
FIGURE B. (1.16): THE IFS OF FLIGHT EF(-1) ON PARAMETER ITT 152
FIGURE B. (1.17): THE EEMD RESULT OF FLIGHT EF(-2) ON PARAMETER ITT 153
FIGURE B. (1.18): THE IFS OF FLIGHT EF(-2) ON PARAMETER ITT 153
FIGURE B. (1.19): THE EEMD RESULT OF FLIGHT EF(0) ON PARAMETER NH 154
FIGURE B. (1.20): THE IFS OF FLIGHT EF(0) ON PARAMETER NH 154
FIGURE B. (1.21): THE EEMD RESULT OF FLIGHT EF(-1) ON PARAMETER NH 155
FIGURE B. (1.22): THE IFS OF FLIGHT EF(-1) ON PARAMETER NH 155
FIGURE B. (1.23): THE EEMD RESULT OF FLIGHT EF(-2) ON PARAMETER NH 156
FIGURE B. (1.24): THE IFS OF FLIGHT EF(-2) ON PARAMETER NH 156
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[17] Meeson, R. N. “HHT sifting and filtering,” Hilbert–Huang Transform and its Applications, Hilbert–Huang Transform and its Applications, 1st eds., Covent Garden, London, 2005, pp. 75-104.

[18] Feldman, M. “Hilbert Transform Applications in Mechanical Vibration” Wiley, 2011.

[19] Morelli, E. A. and Smith, M. S., “Real-Time Dynamic Modeling: Data Information Requirements and Flight-Test Results,” Journal of Aircraft, Vol. 46, No.6, AIAA, 2009.

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[23] Pardo, B. A., “Probabilistic Sequence Alignment Methods for On-Line Score Following of Music Performances,” A PhD dissertation, University of Michigan, 2005.
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