Vibration Data Analysis

Daniel R. Kiracofe, Ph. D.

• Contents
• Preface
• Filtering
  • Quick start: how to filter in matlab
  • Some filter concepts
    • Bandpass filters
    • filtfilt. Causal versus non-causal filters
  • Standard Analog Filter topologies
    • Butterworth
    • Chebyshev
    • Elliptic (Cauer)
    • Bessel
  • Digital Filters
    • IIR Filters
    • FIR Filters
  • Implementation of Digital Filters
  
  
• The analog to digital conversion process
  • Aliasing and the Nyquist frequency
  • The delta-sigma ADC
  • oversampling
  
  
• Instrumentation
  • .
  • Tachometers / Frequency Detection
    • Introduction to tachometers
    • Some simple algorithms
    • Tooth-to-tooth counting
    • Real-world problems with the tooth-to-tooth algorithm. The tooth-to-next-revolution algorithm
    • Using a Hilbert transform to estimate frequency
  
  
• Time domain analysis
  • Time domain differentiation (e.g. convert velocity to acceleration)
  • Time domain integration
  • Enveloping
  • Generating a signal from a frequency vector
  • Using cross-correlation to line up two periodic signals
  
  
• Frequency domain analysis
  • The Discrete Fourier Transform and Fast Fourier Transform
  • Making matlab's fft() function useful
  • Zero-Padding of FFTs
  • The windowed DFT
    • Motivation and theoretical background
    • More on spectral leakge: The picket fence effect
    • Frequency response of windows
    • Application: distinguish two equal strength signals that are very close in frequency - high resolution windows
    • Application: distinguish a small signal that is near a large signal - high dynamic range windows
    • Application: general purpose signal processing
    • Application: impact (modal) testing
    • Application: accurately determine amplitude / order tracking / avoid picket fence effect - the flat top window
  • Zoom FFTs
  • Enveloped FFT
  • Total Harmonic Distortion
  • Inverse DFT
  • Reference
  
  
• Random vibrations
  • Introduction to power spectral density
    • Power spectrums
    • Power spectral density
    • Barlett's method / Welch's method
    • Variance of PSD estimates
    • Bias of PSD estimates
    • operations
    • Rookie mistakes to avoid
    • other links
    • Sample matlab code for periodogram
    • Blackman-Tukey method
  • Amplitude metrics
  • Simulating random sequences
    • Generating white gaussian noise
    • Generating non-white noise
  • Impulsive noise
  
  
• Time-Spectral Analysis
  • Short time Fourier transform
  • Gabor Transform
  • The reassignment method
  • Order tracking
    • Resample method
    • STFT methods
    • Frequency shift methods
    • Vold-Kalman filtering
    • Time Variant discrete fourier transform order tracking
  • Wavelet analysis
  • The Wigner distribution (aka the Wigner-Ville distribution)
  
  
• Experimental Modal Analysis
• AC units Conversion
• Useful formulas
  • Euler-Bernoulli Beam formulas
  
  
• Misc
  • Noise
  
  
• Bibliography
• About this document ...