Hilbert transform applications in mechanical vibration / / Michael Feldman

• Record Nr.: UNINA9910824251703321
• Autore: Feldman Michael <1951->
• Pubbl/distr/stampa: Chichester, : Wiley, 2011
• ISBN: 1-119-99165-X; 1-283-40537-7; 1-119-99164-1; 9786613405371; 1-119-99152-8
• Edizione: [1st ed.]
• Descrizione fisica: xxvii, 292 p. : ill
• Classificazione: SCI041000
• Disciplina: 620.301/515723
• Soggetti: Vibration - Mathematical models; Hilbert transform
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Hilbert Transform Applications in Mechanical Vibration -- List of Figures -- List of Tables -- Preface -- 1 Introduction -- 1.1 Brief history of the Hilbert transform -- 1.2 Hilbert transform in vibration analysis -- 1.3 Organization of the book -- PART I HILBERT TRANSFORM AND ANALYTIC SIGNAL -- 2 Analytic signal representation -- 2.1 Local versus global estimations -- 2.2 The Hilbert transform notation -- 2.3 Main properties of the Hilbert transform -- 2.4 The Hilbert transform of multiplication -- 2.5 Analytic signal representation -- 2.6 Polar notation -- 2.7 Angular position and speed -- 2.8 Signal waveform and envelope -- 2.9 Instantaneous phase -- 2.10 Instantaneous frequency -- 2.11 Envelope versus instantaneous frequency plot -- 2.12 Distribution functions of the instantaneous characteristics -- 2.12.1 Envelope distribution and average values -- 2.12.2 Instantaneous frequency average values -- 2.13 Signal bandwidth -- 2.14 Instantaneous frequency distribution and negative values -- 2.15 Conclusions -- 3 Signal demodulation -- 3.1 Envelope and instantaneous frequency extraction -- 3.2 Hilbert transform and synchronous detection -- 3.3 Digital Hilbert transformers -- 3.3.1 ; Frequency domain -- 3.3.2 Time domain -- 3.4 Instantaneous characteristics distortions -- 3.4.1 Total harmonic distortion and noise -- 3.4.2 End effect of the Hilbert transform -- 3.5 Conclusions -- PART II HILBERT TRANSFORM AND VIBRATION SIGNALS -- 4 Typical examples and description of vibration data -- 4.1 Random signal -- 4.2 Decay vibration waveform -- 4.3 Slow linear sweeping frequency signal -- 4.4 Harmonic frequency modulation -- 4.5 Harmonic amplitude modulation -- 4.5.1 Envelope and instantaneous frequency of AM signal -- 4.5.2 Low modulation index -- 4.5.3 High modulation index -- 4.6 Product of two harmonics -- 4.7 Single harmonic with DC offset.; 4.8 Composition of two harmonics -- 4.9 Derivative and integral of the analytic signal -- 4.10 Signal level -- 4.10.1 Amplitude overall level -- 4.10.2 Amplitude local level -- 4.10.3 Points of contact between envelope and signal -- 4.10.4 Local extrema points -- 4.10.5 Deviation of local extrema from envelope -- 4.10.6 Local extrema sampling -- 4.11 Frequency contents -- 4.12 Narrowband and wideband signals -- 4.13 Conclusions -- 5 Actual signal contents -- 5.1 Monocomponent signal -- 5.2 Multicomponent signal -- 5.3 Types of multicomponent signal -- 5.4 Averaging envelope and instantaneous frequency -- 5.5 Smoothing and approximation of the instantaneous frequency -- 5.6 Congruent envelope -- 5.7 Congruent instantaneous frequency -- 5.8 Conclusions -- 6 Local and global vibration decompositions -- 6.1 Empirical mode decomposition -- 6.2 Analytical basics of the EMD -- 6.2.1 Decomposition of a harmonic plus DC offset -- 6.2.2 Decomposition of two harmonics -- 6.2.3 Distance between envelope and extrema -- 6.2.4 Mean value between the local maxima and minima Curves -- 6.2.5 EMD as a nonstationary and nonlinear filter -- 6.2.6 Frequency resolution of the EMD -- 6.2.7 Frequency limit of distinguishing closest harmonics -- 6.3 Global Hilbert Vibration Decomposition -- 6.4 Instantaneous frequency of the largest energy component -- 6.5 Envelope of the largest energy component -- 6.6 Subtraction of the synchronous largest component -- 6.7 Hilbert Vibration Decomposition scheme -- 6.7.1 Frequency resolution of the HVD -- 6.7.2 Suggested types of signals for decomposition -- 6.8 Examples of Hilbert Vibration Decomposition -- 6.8.1 Nonstationary single-sine amplitude modulated signals -- 6.8.2 Nonstationary overmodulated signals -- 6.8.3 Nonstationary waveform presentation -- 6.8.4 Forced and free vibration separation -- 6.8.5 Asymmetric signal analysis.; 6.9 Comparison of the Hilbert transform decomposition methods -- 6.10 Common properties of the Hilbert transform decompositions -- 6.11 The differences between the Hilbert transform decompositions -- 6.12 Amplitude-frequency resolution of HT decompositions -- 6.12.1 The EMD method -- 6.12.2 The HVD method -- 6.13 Limiting number of valued oscillating components -- 6.13.1 The EMD method -- 6.13.2 The HVD method -- 6.14 Decompositions of typical nonstationary vibration signals -- 6.14.1 Examples of nonstationarity vibration signals -- 6.15 Main results and recommendations -- 6.16 Conclusions -- 7 Experience in the practice of signal analysis and industrial application -- 7.1 Structural health monitoring -- 7.1.1 The envelope and IF as a structure condition indicator -- 7.1.2 Bearing diagnostics -- 7.1.3 Gears diagnosis -- 7.1.4 Motion trajectory analysis -- 7.2 Standing and traveling wave separation -- 7.3 Echo signal estimation -- 7.4 Synchronization description -- 7.5 Fatigue estimation -- 7.6 Multichannel vibration generation -- 7.7 Conclusions -- PART III HILBERT TRANSFORM AND VIBRATION SYSTEMS -- 8 Vibration system characteristics -- 8.1 Kramers-Kronig relations -- 8.2 Detection of nonlinearities in frequency domain -- 8.3 Typical nonlinear elasticity ; characteristics -- 8.3.1 Large amplitude nonlinear behavior. polynomial model -- 8.3.2 Vibro-impact model -- 8.3.3 Restoring force saturation (limiter) -- 8.3.4 Small amplitude nonlinear behavior backlash spring -- 8.3.5 Preloaded (precompressed) spring -- 8.3.6 Piecewise linear spring bilinear model -- 8.3.7 Combination of different elastic elements -- 8.4 Phase plane representation of elastic nonlinearities in vibration systems -- 8.5 Complex plane representation -- 8.6 Approximate primary solution of a conservative nonlinear system -- 8.7 Hilbert transform and hysteretic damping.; 8.8 Nonlinear damping characteristics in a SDOF vibration system -- 8.9 Typical nonlinear damping in a vibration system -- 8.10 Velocity-dependent nonlinear damping -- 8.10.1 Velocity squared (quadratic, turbulent) damping -- 8.10.2 Dry friction -- 8.11 Velocity-independent damping -- 8.12 Combination of different damping elements -- 8.13 Conclusions -- 9 Identification of the primary solution -- 9.1 Theoretical bases of the Hilbert transform system identification -- 9.2 Free vibration modal characteristics -- 9.3 Forced vibration modal characteristics -- 9.4 Backbone (skeleton curve) -- 9.5 Damping curve -- 9.6 Frequency response -- 9.7 Force static characteristics -- 9.7.1 Averaging of the instantaneous modal parameters -- 9.7.2 Polynomial scaling technique -- 9.7.3 Selecting extrema and scaling technique -- 9.7.4 Decomposition technique -- 9.8 Conclusions -- 10 The FREEVIB and FORCEVIB methods -- 10.1 FREEVIB identification examples -- 10.2 FORCEVIB identification examples -- 10.3 System identification with biharmonic excitation -- 10.3.1 Linear system model -- 10.3.2 Nonlinear hardening system -- 10.3.3 Nonlinear softening system -- 10.4 Identification of nonlinear time-varying system -- 10.4.1 Model 1. Modulated elasticity -- 10.4.2 Model 2. Modulated elasticity + Quadratic damping + Swept excitation -- 10.4.3 Model 3. Parametric excitation -- 10.4.4 Model 4. Van-der-Pol + Duffing -- 10.4.5 Model 5. Van-der-Pol + Biharmonic excitation -- 10.4.6 Model 6. Van-der-Pol + Swept excitation -- 10.5 Experimental Identification of nonlinear vibration system -- 10.5.1 The structure under test -- 10.5.2 Free vibration identification -- 10.5.3 Forced vibration identification -- 10.6 Conclusions -- 11 Considering high-order superharmonics. Identification of asymmetric and MDOF systems -- 11.1 Description of the precise method scheme.; 11.2 Identification of the instantaneous modal parameters -- 11.3 Congruent modal parameters -- 11.3.1 Congruent envelope of the displacement -- 11.3.2 Congruent modal frequency -- 11.3.3 Congruent modal damping -- 11.3.4 Congruent envelope of the velocity -- 11.4 Congruent nonlinear elastic and damping forces -- 11.5 Examples of precise free vibration identification -- 11.5.1 Nonlinear spring identification -- 11.5.2 Nonlinear damping identification -- 11.5.3 Combined nonlinear spring and damping identification -- 11.6 Forced vibration identification considering high-order superharmonics -- 11.7 Identification of asymmetric nonlinear system -- 11.7.1 Asymmetric nonlinear system representation -- 11.7.2 The Hilbert transform identification technique -- 11.7.3 Asymmetric nonlinear system examples -- 11.8 Experimental identification of a crack -- 11.9 Identification of MDOF vibration system -- 11.9.1 Identification of linear coupled oscillators -- 11.9.2 Spring coupling -- 11.9.3 Reconstruction of coupling coefficients -- 11.10 Identification of weakly nonlinear coupled oscillators -- 11.10.1 Coupled nonlinear oscillators with linear coupling -- 11.10.2 Coupled linear oscillators with nonlinear coupling -- 11.10.3 HT decomposition and analysis -- 11.10.4 Modal skeleton curve estimation -- 11.10.5 Mode shape estimation -- 11.10.6 Description of the identification ; scheme -- 11.10.7 Simulation examples -- 11.11 Conclusions -- 12 Experience in the practice of system analysis and industrial application -- 12.1 Non-parametric identification of nonlinear mechanical vibration systems -- 12.2 Parametric identification of nonlinear mechanical vibrating systems -- 12.3 Structural health monitoring and damage detection -- 12.3.1 Damage detection in structures and buildings -- 12.3.2 Detecting anomalies in beams and plates.; 12.3.3 Health monitoring in power systems and rotors.
• Sommario/riassunto: "Hilbert Transform Applications in Mechanical Vibration addresses recent advances in research and applications of the modern Hilbert transform to vibration engineering, through which laboratory dynamic tests can be produced more quickly and accurately. The author integrates important pioneering developments in signal processing and mathematical models with typical properties of mechanical constructions such as resonance, dynamic stiffness and damping. This unique merger of technical properties and digital signal processing allows the instant solution of a variety of engineering problems and in-depth exploration of the physics of vibration by analysis, identification and simulation. Hilbert Transform Applications in Mechanical Vibration employs the author's pioneering applications of the Hilbert Vibration Decomposition method characterized by high frequency resolution, and provides a comprehensive account of the main applications, covering dynamic testing and extraction of the modal parameters of nonlinear vibration systems including the initial elastic and damping force characteristics."--; "The Hilbert transform allows identification of linear and non-linear elastic and damping characteristics including the instantaneous modal parameters and the initial force characteristics under free and forced vibration regimes"--