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Produktbild: Noise and Vibration Analysis

Noise and Vibration Analysis Signal Analysis and Experimental Procedures

118,99 €

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

31.08.2023

Verlag

John Wiley & Sons

Seitenzahl

704

Maße (L/B/H)

25,2/17,4/4,3 cm

Gewicht

1442 g

Auflage

2. Auflage

Sprache

Englisch

ISBN

978-1-118-96218-3

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

31.08.2023

Verlag

John Wiley & Sons

Seitenzahl

704

Maße (L/B/H)

25,2/17,4/4,3 cm

Gewicht

1442 g

Auflage

2. Auflage

Sprache

Englisch

ISBN

978-1-118-96218-3

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Noise and Vibration Analysis
  • About the authors Preface Acknowledgments List of Abbreviations 21 List of Symbols 23 1 Introduction 1 1.1 Noise and Vibration 1 1.2 Noise and Vibration Analysis 2 1.3 Application Areas 3 1.4 Analysis of Noise and Vibrations 4 1.4.1 Experimental Analysis 5 1.5 Standards 5 1.6 Becoming a Noise and Vibration Analysis Expert 5 1.6.1 The Virtue of Simulation 6 1.6.2 Learning Tools and the Format of This Book 6 2 Dynamic Signals and Systems 9 2.1 Introduction 9 2.2 Periodic Signals 11 2.2.1 Sine Waves 11 2.2.2 Complex Sines 11 2.2.3 Interacting Sines 13 2.2.4 Orthogonality of Sines 15 2.3 Random Signals 16 2.4 Transient Signals 17 2.5 RMS Value and Power 18 2.6 Linear Systems 19 2.6.1 The Laplace Transform 20 2.6.2 The Transfer Function 24 2.6.3 The Impulse Response 25 2.6.4 Convolution 26 2.7 The Continuous Fourier Transform 29 2.7.1 Characteristics of the Fourier Transform 32 2.7.2 The Frequency Response 34 2.7.3 Relationship Between the Laplace and Frequency Domains 35 2.7.4 Transient Versus Steady-State Response 35 2.8 Chapter Summary 37 2.9 Problems 38 References 39 3 Time Data Analysis 41 3.1 Introduction to Discrete Signals 41 3.1.1 Discrete Convolution 42 3.2 The Sampling Theorem 42 3.2.1 Aliasing 44 3.2.2 Discrete Representation of Analog Signals 45 3.2.3 Interpolation and Resampling 46 3.3 Filters 50 3.3.1 Analog Filters 51 3.3.2 Digital Filters 53 3.3.3 Smoothing Filters 55 3.3.4 Acoustic Octave Filters 55 3.3.5 Analog RMS Integration 57 3.3.6 Frequency Weighting Filters 58 3.4 Time Series Analysis 59 3.4.1 Min- and Max-analysis 60 3.4.2 Time Data Integration 60 3.4.3 Time Data Differentiation 65 3.4.4 FFT-based Processing 68 3.5 Chapter Summary 68 3.6 Problems 70 References 71 4 Statistics and Random Processes 73 4.1 Introduction to the Use of Statistics 73 4.1.1 Ensemble and Time Averages 74 4.1.2 Stationarity and Ergodicity 74 4.2 Random Theory 75 4.2.1 Expected Value 75 4.2.2 Errors in Estimates 75 4.2.3 Probability Distribution 76 4.2.4 Probability Density 77 4.2.5 Histogram 77 4.2.6 Sample Probability Density Estimate 78 4.2.7 Average Value and Variance 78 4.2.8 Central Moments 80 4.2.9 Skewness 80 4.2.10 Kurtosis 81 4.2.11 Crest Factor 81 4.2.12 Correlation Functions 82 4.2.13 The Gaussian Probability Distribution 83 4.3 Statistical Methods 85 4.3.1 Hypothesis Tests 85 4.3.2 Test of Normality 88 4.3.3 Test of Stationarity 89 Frame statistics 89 The reverse arrangements test 90 The runs test 93 4.4 Quality Assessment of Measured Signals 94 4.5 Chapter Summary 96 4.6 Problems 98 References 98 5 Fundamental Mechanics 99 5.1 Newton's Laws 99 5.2 The Single Degree-of-freedom System (SDOF) 100 5.2.1 The Transfer Function 101 5.2.2 The Impulse Response 102 5.2.3 The Frequency Response 104 5.2.4 The Q-factor 107 5.2.5 SDOF Forced Response 108 5.3 Alternative Quantities for Describing Motion 108 5.4 Frequency Response Plot Formats 109 5.4.1 Magnitude and Phase 111 5.4.2 Real and Imaginary Parts 114 5.4.3 The Nyquist Plot - Imaginary vs. Real Part 114 5.5 Determining Natural Frequency and Damping Ratio 117 5.5.1 Peak in the Magnitude of FRF 117 5.5.2 Peak in the Imaginary Part of FRF 117 5.5.3 Resonance Bandwidth (3 dB Bandwidth) 118 5.5.4 Circle in the Nyquist Plot 118 5.6 Rotating Mass 119 5.7 Some Comments on Damping 120 5.7.1 Hysteretic Damping 121 5.8 Models Based on SDOF Approximations 121 5.8.1 Vibration Isolation 122 5.8.2 Resonance Frequency and Stiffness Approximations 124 5.9 The Two-degree-of-freedom System (2DOF) 125 5.10 The Tuned Damper 128 5.11 Chapter Summary 129 5.12 Problems 131 References 132 6 Modal Analysis Theory 133 6.1 Waves on a String 133 6.2 Matrix Formulations 135 6.2.1 Degree-of-freedom 135 6.3 Eigenvalues and Eigenvectors 136 6.3.1 Undamped System 136 6.3.2 Mode Shape Orthogonality 140 6.3.3 Modal Coordinates 141 6.3.4 Proportional Damping 143 6.3.5 General Damping 145 6.4 Frequency Response of MDOF Systems 149 6.4.1 Frequency Response from [M], [C], [K] 149 6.4.2 Frequency Response from Modal Parameters 150 6.4.3 Frequency Response from [M], [K], and _ - Modal Damping 155 6.4.4 Mode Shape Scaling 155 6.4.5 The Effect of Node Lines on FRFs 157 6.4.6 Antiresonance 158 6.4.7 Impulse Response of MDOF Systems 158 6.5 Free Decays 158 6.6 Chapter Summary 159 6.7 Problems 161 References 162 7 Transducers for Noise and Vibration Analysis 163 7.1 The Piezoelectric Effect 163 7.2 The Charge Amplifier 164 7.3 Transducers with Built-In Impedance Converters, 'IEPE' 165 7.3.1 Low-frequency Characteristics 167 7.3.2 High-frequency Characteristics 168 7.3.3 Transducer Electronic Data Sheet, TEDS 168 7.4 The Piezoelectric Accelerometer 169 7.4.1 Frequency Characteristics 170 7.4.2 Mounting Accelerometers 172 7.4.3 Electrical Noise 172 7.4.4 Choosing an Accelerometer 173 7.5 The Piezoelectric Force Transducer 174 7.6 The Impedance Head 176 7.7 The Impulse Hammer 177 7.8 Accelerometer Calibration 177 7.9 Measurement Microphones 178 7.10 Microphone Calibration 180 7.11 The Geophone 180 7.12 MEMS-Based Sensors 181 7.13 Shakers for Structure Excitation 181 7.14 Some Comments on Measurement Procedures 183 7.15 Problems 184 References 185 8 Frequency Analysis Theory 187 8.1 Periodic Signals - The Fourier Series 187 8.2 Spectra of Periodic Signals 189 8.2.1 Frequency and Time 190 8.3 Random Processes 190 8.3.1 Spectra of Random Processes 191 8.4 Transient Signals 193 8.5 Interpretation of spectra 194 8.6 Chapter Summary 196 8.7 Problems 197 References 197 9 Experimental Frequency Analysis 199 9.1 Frequency Analysis Principles 199 9.1.1 Nonparametric Frequency Analysis 200 9.2 Octave and Third-octave Band Spectra 201 9.2.1 Time Constants 201 9.2.2 Real-time Versus Serial Measurements 202 9.3 The Discrete Fourier Transform (DFT) 202 9.3.1 The Fast Fourier Transform, FFT 204 9.3.2 The DFT in Short 205 9.3.3 The Basis of the DFT 205 9.3.4 Periodicity of the DFT 207 9.3.5 Properties of the DFT 209 9.3.6 Relation Between DFT and Continuous Spectrum 210 9.3.7 Leakage 211 9.3.8 The Picket-fence Effect 214 9.3.9 Time Windows for Periodic Signals 215 Amplitude correction of window effects 217 Power correction of window effects 217 Comparison of common windows 219 Frequency resolution 223 9.3.10 Time Windows for Random Signals 223 9.3.11 Oversampling in FFT Analysis 224 9.3.12 Circular Convolution and Aliasing 225 9.3.13 Zero Padding 226 9.3.14 Frequency Domain Processing 227 9.3.15 Zoom FFT 228 9.4 Chapter Summary 229 9.5 Problems 230 References 231 10 Spectrum and Correlation Estimates Using the DFT 233 10.1 Averaging 233 10.2 Spectrum Estimators for Periodic Signals 235 10.2.1 The Autopower Spectrum 235 10.2.2 Linear Spectrum 236 10.2.3 Phase Spectrum 237 10.3 Estimators for PSD and CSD 237 10.3.1 The Periodogram 238 10.3.2 Welch's Method 239 10.3.3 Window Correction for Welch Estimates 240 10.3.4 Bias Error in Welch Estimates 241 10.3.5 Random Error in Welch Estimates 246 10.3.6 The Smoothed Periodogram Estimator 252 10.3.7 Bias Error in Smoothed Periodogram Estimates 254 10.3.8 Random Error in Smoothed Periodogram Estimates 254 10.4 Estimators for Correlation Functions 255 10.4.1 Correlation Estimator By Long FFT 256 10.4.2 Correlation Estimator By Welch's Method 258 10.4.3 Variance of the Correlation Estimator 259 10.4.4 Effect of Measurement Noise on Correlation Function Estimates 261 10.5 Estimators for Transient Signals 263 10.5.1 Windows for Transient Signals 265 10.6 A Signal Processing Framework for Spectrum and Correlation Estimation 266 10.7 Spectrum Estimation in Practice 267 10.7.1 Linear Spectrum Versus PSD 268 10.7.2 Example of a Spectrum of a Periodic Signal 270 10.7.3 Practical PSD Estimation 271 10.7.4 Spectrum of Mixed Property Signal 272 10.7.5 Calculating RMS Values in Practice 274 10.7.6 RMS From Linear Spectrum of Periodic Signal 274 10.7.7 RMS from PSD 276 10.7.8 Weighted RMS Values 277 10.7.9 Integration and Differentiation in the Frequency Domain 278 10.8 Multi-channel Spectral and Correlation Analysis 279 10.8.1 Matrix Notation for MIMO Spectral Analysis 280 10.8.2 Arranging Spectral Matrices in MATLAB/Octave 281 10.8.3 Multi-channel Correlation Functions 282 10.9 Chapter Summary 282 10.10Problems 283 References 284 11 Measurement and Analysis Systems 287 11.1 Principal Design 288 11.2 Hardware for Noise and Vibration Analysis 289 11.2.1 Signal Conditioning 289 11.2.2 Analog-to-Digital Conversion, ADC 290 Quantization and Dynamic Range 290 Setting the Measurement Range 291 Sampling Accuracy 293 Anti-Alias Filters 294 Sigma-Delta ADCs 295 11.2.3 Practical Issues 297 11.2.4 Hardware Specifications 298 Absolute Amplitude Accuracy 299 Anti-Alias Protection 299 Simultaneous Sampling 299 Cross-Channel Match 299 Dynamic Range 300 Cross-Channel Talk 301 11.2.5 Transient (Shock) Recording 301 11.3 FFT Analysis Software 301 11.3.1 Block Processing 302 11.3.2 Data Scaling 303 11.3.3 Triggering 303 11.3.4 Averaging 304 11.3.5 FFT Setup Parameters 306 11.4 Chapter Summary 306 11.5 Problems 306 References 307 12 Rotating Machinery Analysis 309 12.1 Vibrations in Rotating Machines 309 12.2 Understanding Time-Frequency Analysis 310 12.3 Rotational Speed Signals (Tachometer Signals) 312 12.4 RPM Maps 314 12.4.1 The Waterfall Plot 315 12.4.2 The Color Map Plot 316 12.5 Smearing 316 12.6 Order Tracks 318 12.7 Synchronous Sampling 319 12.7.1 DFT Parameters after Resampling 323 12.8 Averaging Rotation-speed-dependent Signals 323 12.9 Adding Change in RMS with Time 325 12.10Parametric Methods 329 12.11Chapter Summary 330 12.12Problems 331 References 331 13 Single-input Frequency Response Measurements 333 13.1 Linear Systems 334 13.2 Determining Frequency Response Experimentally 334 13.2.1 Method 1 - the H1 Estimator 335 13.2.2 Method 2 - the H2 Estimator 337 13.2.3 Method 3 - the Hc Estimator 338 13.3 Important Relationships for Linear Systems 339 13.4 The Coherence Function 340 13.5 Errors in Determining the Frequency Response 341 13.5.1 Bias Error in FRF Estimates 341 13.5.2 Random Error in FRF Estimates 343 13.5.3 Bias and Random Error Trade-offs 345 13.6 Coherent Output Power 345 13.7 The Coherence Function in Practice 346 13.7.1 Non-random Excitation 348 13.8 Impact Excitation 348 13.8.1 The Force Signal 349 13.8.2 The Response Signal and Exponential Window 352 13.8.3 Impact Testing Software 352 13.8.4 Compensating for the Influence of the Exponential Window 354 13.8.5 Sources of Error 356 13.8.6 Improving Impact Testing by Alternative Processing 357 13.9 Shaker Excitation 358 13.9.1 Signal-to-noise Ratio Comparison 359 13.9.2 Pure Random Noise 359 13.9.3 Burst Random Noise 361 13.9.4 Pseudo-random Noise 362 13.9.5 Periodic Chirp 363 13.9.6 Stepped-sine Excitation 363 13.10Examples of FRF Estimation - No Extraneous Noise 364 13.10.1 Pure Random Excitation 364 13.10.2 Burst Random Excitation 365 13.10.3 Periodic Excitation 367 13.11Example of FRF Estimation - with Output Noise 367 13.12Examples of FRF Estimation - with Input and Output Noise 369 13.12.1 Sources of Error during Shaker Excitation 371 13.12.2 Checking the Shaker Attachment 371 13.12.3 Other Sources of Error 372 13.13Chapter Summary 373 13.14Problems 374 References 375 14 Multiple-input Frequency Response Measurement 377 14.1 Multiple-input Systems 377 14.1.1 The 2-input/1-output System 378 14.1.2 The 2-input/1-output System - matrix notation 379 14.1.3 The H1 Estimator for MIMO 380 14.1.4 Multiple Coherence 382 14.1.5 Computation Considerations for Multiple-input System 384 14.1.6 The Hv Estimator 384 14.1.7 Other MIMO FRF Estimators 385 14.2 Conditioned Input Signals 386 14.2.1 Conditioned Output Signals 388 14.2.2 Partial Coherence 389 14.2.3 Ordering Signals Prior to Conditioning 390 14.2.4 Partial Coherent Output Power Spectra 391 14.2.5 Backtracking the H-systems 391 14.2.6 General Conditioned Systems 391 14.3 Bias and Random Errors for Multiple-input Systems 392 14.4 Excitation Signals for MIMO Analysis 393 14.4.1 Pure Random Noise 394 14.4.2 Burst Random Noise 394 14.4.3 Periodic Random Noise 395 14.4.4 The Multiphase Stepped-sine Method (MPSS) 395 14.5 Data Synthesis and Simulation Examples 396 14.5.1 Burst Random - Output Noise 396 14.5.2 Burst and Periodic Random - Input Noise 399 14.5.3 Periodic Random - Input and Output Noise 399 14.6 Real MIMO Data Case 403 14.7 Chapter Summary 406 14.8 Problems 407 References 408 15 Orthogonalization of Signals 409 15.1 Principal Components 409 15.1.1 Principal Components Used to Find Number of Sources 411 15.1.2 Data Reduction 413 15.2 Virtual Signals 416 15.2.1 Virtual Input Coherence 419 15.2.2 Virtual Input/Output Coherence 421 15.2.3 Virtual Coherent Output Power 422 15.3 Noise Source Identification (NSI) 426 15.3.1 Multiple Source Example 426 15.3.2 Automotive Example 429 15.4 Chapter Summary 429 15.5 Problems 432 References 432 16 Experimental Modal Analysis 433 16.1 Introduction to Experimental Modal Analysis 433 16.1.1 Main Steps in EMA 434 16.2 Experimental Setup 435 16.2.1 Points and DOFs 436 16.2.2 Selecting Measurement DOFs 436 16.2.3 Measurement System 437 16.2.4 Sensor Considerations 438 16.2.5 Data Acquisition Strategies 438 16.2.6 Suspension 439 16.2.7 Measurement Checks 440 16.2.8 Calibration 442 16.2.9 Data Acquisition 442 16.2.10 Mode Indicator Functions 442 16.2.11 Data Quality Assessment 445 16.2.12 Checklist 445 16.3 Introduction to Modal Parameter Extraction 445 16.4 SDOF Parameter Extraction 448 16.4.1 The Least Squares Local Method 448 16.4.2 The Least Squares Global Method 449 16.4.3 The Least Squares (Local) Polynomial Method 450 16.5 The Unified Matrix Polynomial Approach, UMPA 451 16.5.1 Mathematical Framework 451 16.5.2 Choosing Model Order 454 16.5.3 Matrix Coefficient Normalization 455 16.5.4 Data Compression 457 16.6 Time Versus Frequency Domain Parameter Extraction for EMA 459 16.7 Time Domain Parameter Extraction Methods 462 16.7.1 Converting Bandpass Filtered FRFs Into IRFs 463 16.7.2 The Ibrahim Time Domain Method 464 16.7.3 The Multiple-reference Ibrahim Time Domain Method (MITD) 467 16.7.4 Prony's Method 471 16.7.5 The Least Squares Complex Exponential Method 472 16.7.6 Polyreference Time Domain 473 16.7.7 The Modified Multiple-reference Ibrahim Time Domain Method (MMITD) 477 16.8 Frequency Domain Parameter Extraction Methods 479 16.8.1 The Least squares complex frequency domain method 480 16.8.2 The Frequency Domain Direct Parameter Identification Method (FDPI)483 16.8.3 The Frequency Z-Domain Direct Parameter Method, FDPIz 487 16.8.4 The Complex Mode indicator Function Method, CMIF 487 16.9 Methods for mode shape estimation and scaling 489 16.9.1 Least Squares Frequency Domain - Single Reference Case 489 16.9.2 Least Squares Frequency Domain - Multiple Reference Case 491 16.9.3 Least Squares Frequency Domain - Multiple Reference Without MPFs 493 16.9.4 Least Squares Time Domain 494 16.9.5 Scaling Modal Model When Poles and Mode Shapes are Known 495 16.10Evaluating the extracted parameters 495 16.10.1 Synthesized FRFs 496 16.10.2 The MAC matrix 496 16.11Chapter Summary 498 16.12Problems 499 References 500 17 Operational Modal Analysis (OMA) 503 17.1 Principles for OMA 504 17.2 Data Acquisition Principles 505 17.3 OMA Modal Parameter Extraction for OMA 506 17.3.1 Spectral Functions for OMA Parameter Extraction 506 17.3.2 Correlation Functions for OMA Parameter Extraction 510 17.3.3 Half spectra 512 17.3.4 Time versus Frequency Domain Parameter Extraction for OMA 513 17.3.5 Modal Parameter Estimation Methods for OMA 513 17.3.6 Least Squares Frequency Domain, OMA Versions 514 17.4 Scaling OMA modal models 516 17.4.1 Scaling an OMA Model Using the Mass Matrix 517 17.4.2 The OMAH method 517 17.5 Chapter Summary 520 17.6 Problems 521 References 522 18 Advanced Analysis Methods 525 18.1 Shock Response Spectrum 525 18.2 The Hilbert Transform 528 18.2.1 Computation of the Hilbert Transform 529 18.2.2 Envelope Detection by the Hilbert Transform 530 18.2.3 Relating Real and Imaginary Parts of Frequency Response Functions 531 18.3 Cepstrum Analysis 535 18.3.1 Power Cepstrum 536 18.3.2 Complex Cepstrum 537 18.3.3 The Real Cepstrum 539 18.3.4 Inverse Cepstrum 539 18.4 The Envelope Spectrum 539 18.5 Creating Random Signals with Known Spectral Density 542 18.6 Identifying Harmonics In Noise 543 18.6.1 The Three-parameter Sine Fit Method 544 18.6.2 Periodogram Ratio Detection, PRD 545 18.7 Harmonic Removal 548 18.7.1 Frequency Domain Editing, FDE 548 18.7.2 Cepstrum Based Harmonic Removal Methods 549 18.8 Chapter Summary 550 18.9 Problems 552 References 552 19 Practical Vibration Measurements and Analysis 555 19.1 Introduction to a Plexiglas Plate 555 19.2 Forced Response Simulation 556 19.2.1 Frequency Domain Forced Response for Periodic Inputs 557 19.2.2 Frequency Domain Forced Response for Random Inputs 559 19.2.3 Time Domain Computation of Forced Response for Any Inputs 559 Time Domain Response By Frequency Domain Computation 559 Time Domain Response By Digital Filters 560 19.2.4 Plexiglas Plate Forced Response Example 563 19.3 Spectra of periodic signals 564 19.4 Spectra of random signals 565 19.5 Data With Random and Periodic Content 568 19.5.1 Car Idling Sound 569 19.5.2 Container Ship Measurement 573 19.6 Operational Deflection Shapes - ODS 574 19.6.1 Plexiglas Plate ODS Example - Single Reference 577 19.6.2 Plexiglas Plate ODS Example - Multiple-Reference 578 19.7 Impact Excitation and FRF Estimation 581 19.8 Plexiglas EMA Example 585 19.8.1 FRF Quality Assessment 585 19.8.2 EMA Modal Parameter Extraction, MPE 590 19.9 Methods for EMA Modal Parameter Estimation, MPE 595 19.9.1 Time Domain Variable Settings 595 19.9.2 High Order Methods for EMA MPE 598 19.9.3 Low Order methods for EMA MPE 600 19.9.4 The Complex Mode Indicator Function, CMIF 604 19.9.5 Calculating Scaled Mode Shapes 604 19.10Conclusions of EMA MPE 609 19.11OMA examples 610 19.11.1 OMA Using Synthesized Data for Plexiglas Plate 610 19.11.2 OMA on Measured Data of Plexiglas Plate 618 19.11.3 OMA of a Supension Bridge 622 19.11.4 OMA On Container Ship 628 References 632 A Appendix A: Complex Numbers 635 B Appendix B: Logarithmic Diagrams 639 C Appendix C: Decibels 643 D Appendix D: Some Elementary Matrix Algebra 645 E Appendix E: Eigenvalues and the SVD 649 E.1 Eigenvalues and Complex Matrices 649 E.2 The Singular Value Decomposition (SVD) 650 F Appendix F: Organizations and Resources 653 G Appendix G: Checklist for Experimental Modal Analysis Testing 655 Reference 657 Index 665