Understanding Wavelet Analysis

1. Definition: What is Wavelet Analysis?

Wavelet Analysis is an advanced signal processing technique used to analyze vibration signals where the frequency content is changing over time. Unlike the traditional Fast Fourier Transform (FFT), which is best suited for stationary signals (signals with a constant frequency content), wavelet analysis can effectively capture and represent transient events, shocks, and other non-stationary behaviors.

It works by decomposing a signal into a set of basis functions called “wavelets.” Each wavelet is a short, oscillating wave-like packet that is localized in both time and frequency. This dual localization is what gives wavelet analysis its power.

2. Wavelet Analysis vs. the FFT

To understand the value of wavelet analysis, it’s important to understand the limitation of the FFT:

• FFT (Fast Fourier Transform): The FFT tells you *what* frequencies are present in a signal, but it gives you no information about *when* they occurred. It analyzes the entire signal at once, providing excellent frequency resolution but zero time resolution.
• Wavelet Analysis: Wavelet analysis tells you *what* frequencies are present and *when* they are present. It provides a “time-frequency” map of the signal, showing how the spectral content evolves over time.

Imagine a signal that contains a short “click” event from a cracked gear tooth. The FFT might show a slight increase in broadband energy, but the click would be averaged out over the entire signal. Wavelet analysis, however, would produce a plot clearly showing a burst of high-frequency energy at the exact moment in time the click occurred.

3. The Scalogram: A Time-Frequency Map

The most common output of wavelet analysis is a scalogram (or a similar time-frequency plot). This is a 2D color map where:

• The X-axis represents time.
• The Y-axis represents frequency (or scale).
• The color represents the amplitude or energy of the vibration at that specific time and frequency.

This visualization makes it easy to spot transient events that would be hidden in a standard FFT spectrum. For example, a vertical line of “hot” color on a scalogram indicates a broadband event (like an impact) that occurred at a specific instant in time.

4. Applications in Vibration Diagnostics

Wavelet analysis is not typically used for routine vibration monitoring but is a powerful tool for advanced diagnostics in specific situations:

• Gearbox Analysis: It is exceptionally good at detecting localized faults like a single cracked or broken tooth, which generates a distinct impact each revolution.
• Bearing Defect Analysis: It can be used to detect the individual impacts caused by a rolling element passing over a spall, especially in very slow-speed machinery where traditional envelope analysis can be challenging.
• Transient Event Analysis: It is ideal for analyzing signals from machine startup, shutdown, or other processes where the speed and vibration characteristics are constantly changing.
• Structural Analysis: It can be used to analyze the response of a structure to an impact (a bump test) to understand its damping and natural frequencies.

While computationally more intensive than the FFT, modern computer software has made wavelet analysis an accessible and valuable tool for the advanced vibration analyst dealing with complex, non-stationary signals.

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