Understanding Coherence

1. Definition: What is Coherence?

Coherence (also called the Coherence Function) is a signal processing tool used in vibration analysis to determine the quality and validity of a measurement. It is a value between 0 and 1 that indicates how much of the output signal at a given frequency is directly caused by the input signal.

• A coherence of 1.0 at a specific frequency means there is a perfect linear relationship between the two signals. 100% of the output at that frequency is being caused by the input.
• A coherence of 0.5 means that only 50% of the output signal’s energy at that frequency is linearly related to the input signal. The other 50% is due to other factors like noise, non-linearities, or other unmeasured inputs.
• A coherence of 0.0 means there is no linear relationship at all between the two signals at that frequency.

Coherence is calculated using cross-power spectral density and requires a multi-channel analyzer that can measure two signals simultaneously.

2. Primary Uses of Coherence

Coherence is primarily used in two key areas:

a) Validating Frequency Response Function (FRF) Measurements

This is the most common and critical use of coherence. When performing an impact test (or bump test) to measure an FRF, the coherence plot is essential for judging the quality of the data.

• Good Measurement: For a valid FRF, the coherence should be very close to 1.0 at the frequencies corresponding to the resonant peaks. If coherence is high (e.g., >0.95), it gives the analyst confidence that the measured response was indeed caused by the hammer impact and not by background vibration or measurement noise.
• Poor Measurement: If the coherence drops significantly at a resonant peak, it indicates a poor measurement. This could be due to a poor hammer strike, a noisy environment, or a non-linear structural response. The analyst should reject the data from that impact and try again. Coherence will naturally be low at anti-resonances (the “valleys” in the FRF), which is normal.

b) Source Identification

Coherence can be used to determine if the vibration from one machine is causing the vibration in another. For example, if you have a pump and a motor on a shared base and you suspect the motor is causing the pump to vibrate:

• Procedure: Place one accelerometer on the motor (the input) and a second accelerometer on the pump (the output). Measure both signals simultaneously and calculate the coherence.
• Interpretation: If the coherence is high at the motor’s running speed, it provides strong evidence that the vibration is being transmitted from the motor to the pump through their shared structure. If the coherence is low, the pump’s vibration is likely being caused by its own issues (e.g., pump unbalance, cavitation) and not by the motor.

3. Factors That Reduce Coherence

Several factors can cause the coherence value to be less than 1.0:

• Measurement Noise: Contamination of either the input or output signal by extraneous noise.
• Non-Linear Systems: Coherence only measures the *linear* relationship. If the system is non-linear (e.g., due to looseness, cracks, or fluid-structure interactions), the coherence will be low even if there is a causal relationship.
• Time Delays: A significant time delay between the input and output signals can reduce coherence.
• Other Unmeasured Inputs: If the output is being caused by more than one source, and you are only measuring one of them as the input, the coherence will be low.

In summary, the coherence function is a vital quality-control tool for advanced vibration measurements, providing confidence in the validity of FRF data and helping to identify vibration transmission paths.

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