11.2 Data acquisition and signal processing

Data acquisition and signal processing are crucial in vibration measurement. These techniques transform analog sensor signals into digital data for analysis. Understanding sampling rates, resolution, and conversion processes is key to accurately capturing vibration information.

Signal processing enhances vibration data quality and extracts meaningful insights. Filtering removes unwanted frequencies, while advanced techniques like FFT and wavelet transforms enable detailed analysis of vibration signals in both time and frequency domains.

Data acquisition and conversion

Analog-to-Digital Conversion Process

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• Data acquisition in vibration measurement captures analog signals from sensors and converts them into digital form for analysis and storage
• Analog-to-digital conversion (ADC) transforms continuous analog signals into discrete digital values at specific time intervals
• Nyquist-Shannon sampling theorem requires sampling rate to be at least twice the highest frequency component in the signal to avoid aliasing
• Resolution in ADC represents the number of discrete digital values used to represent the continuous analog signal (12-bit, 16-bit)
• Key components of a data acquisition system
  • Sensors
  • Signal conditioning circuits
  • Anti-aliasing filters
  • Sample-and-hold circuits
  • Analog-to-digital converters

ADC Limitations and Specifications

• Quantization error results from finite resolution of digital representation of continuous analog signals
• Dynamic range of an ADC system measures the ratio between largest and smallest signals it can accurately measure (expressed in dB)
• Signal-to-quantization-noise ratio (SQNR) measures quality of digitized signal
  • Improves by approximately 6 dB for each additional bit of resolution
• Quantization noise decreases with higher resolution ADCs

Signal processing techniques

Filtering and Windowing

• Filtering removes unwanted frequency components from vibration signals
  • Common types: low-pass, high-pass, band-pass, notch filters
• Digital filters implemented as Finite Impulse Response (FIR) or Infinite Impulse Response (IIR)
  • FIR filters provide linear phase response, stable operation
  • IIR filters offer computational efficiency, steeper roll-off characteristics
• Windowing reduces spectral leakage when performing Fourier transforms on finite-length signals
  • Common window functions: Hanning, Hamming, Blackman
  • Hanning window provides good frequency resolution and amplitude accuracy
  • Hamming window offers slightly better side-lobe suppression than Hanning
  • Blackman window provides excellent side-lobe suppression at the cost of frequency resolution

Advanced Signal Processing Techniques

• Signal averaging improves signal-to-noise ratio (SNR) by reducing random noise in repetitive measurements
  • SNR improvement proportional to square root of number of averages
• Fast Fourier Transform (FFT) efficiently converts time-domain signals to frequency domain
  • Essential for spectral analysis of vibration data
  • Radix-2 FFT algorithm requires number of samples to be power of 2
• Overlap processing in FFT analysis increases effective number of averages and improves frequency resolution
  • Common overlap percentages: 50%, 67%, 75%
• Time-frequency analysis techniques analyze non-stationary vibration signals
  • Short-Time Fourier Transform (STFT) provides time-localized frequency information
  • Wavelet transforms offer multi-resolution analysis, suitable for transient events

Sampling rate and resolution

Sampling Fundamentals

• Sampling rate measures number of samples taken per second from a continuous signal to create a discrete-time signal
• Nyquist frequency defined as half the sampling rate
  • Represents highest frequency accurately represented in a sampled signal
• Aliasing occurs when signal sampled at rate lower than twice its highest frequency component
  • Results in false lower-frequency components in reconstructed signal
• Anti-aliasing filters (low-pass filters) remove frequency components above Nyquist frequency
  • Prevent aliasing by attenuating high-frequency content before sampling
  • Butterworth filters provide maximally flat passband response
  • Chebyshev filters offer steeper roll-off at expense of passband ripple

Resolution and Quantization

• Signal resolution in digital systems determined by number of bits used to represent each sample
  • Higher bit depths provide finer amplitude resolution
  • Common resolutions: 12-bit (4096 levels), 16-bit (65,536 levels), 24-bit (16,777,216 levels)
• Quantization noise introduced by rounding analog values to nearest digital level
  • Decreases with higher resolution ADCs
  • Can be modeled as additive white noise for complex signals
• Dynamic range increases with higher resolution
  • 12-bit ADC provides approximately 72 dB dynamic range
  • 16-bit ADC provides approximately 96 dB dynamic range
• Oversampling technique improves effective resolution
  • Samples signal at higher rate than required, then digitally filters and downsamples
  • Each 4x increase in sampling rate adds 1 bit of effective resolution

Vibration data analysis

Time-Domain Analysis

• Time-domain analysis examines vibration signals as function of time
  • Peak-to-peak amplitude measures total excursion of waveform
  • RMS value represents effective energy content of signal
  • Crest factor (ratio of peak to RMS) indicates presence of impulsive events
• Statistical parameters characterize time-domain signals
  • Kurtosis measures "peakedness" of signal distribution
  • Skewness quantifies asymmetry of signal distribution
• Time synchronous averaging reduces non-synchronous components in rotating machinery analysis
  • Requires precise trigger signal synchronized with machine rotation

Frequency-Domain Analysis

• Frequency-domain analysis transforms time-domain signals into frequency domain using Fourier transform
  • Reveals frequency content of vibration signals
  • Identifies dominant frequency components and harmonics
• Power Spectral Density (PSD) characterizes random vibrations
  • Provides measure of signal power distribution across frequencies
  • Useful for comparing vibration levels in different frequency bands
• Order analysis normalizes frequency components to rotational speed
  • Particularly useful for analyzing variable-speed machinery
  • Allows tracking of speed-dependent vibration components
• Cepstrum analysis detects harmonics and sidebands in vibration signals
  • Inverse Fourier transform of logarithm of magnitude spectrum
  • Useful for gear and bearing fault diagnosis
• Coherence function analysis determines degree of linear relationship between input and output signals
  • Values range from 0 (no correlation) to 1 (perfect correlation)
  • Helps identify resonances and validate vibration measurements