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Averaging types: What’s the difference?

Siemens Experimenter Siemens Experimenter
Siemens Experimenter

In LMS Test.Lab Signature Acquisition, there are five different averaging types to choose from when doing a stationary measurement:

  • Energy average
  • Linear average
  • Energy exponential average
  • Minimum Value
  • Maximum Value

What is the difference between these averaging types? When is an averaging type appropriate for a particular application?

Figure 1: Test.Lab has five options in the “Averaging type” drop-down menu.Figure 1: Test.Lab has five options in the “Averaging type” drop-down menu.

 Example:

 

In LMS Test.Lab, the “stationary” measurement mode creates a single averaged autopower at the end of an acquisition.

 

Suppose, for example, that three individual blocks/averages of data are acquired. These three individual autopowers will be averaged together to create the end result. Normally, more averages are acquired; three averages is just for illustration purposes.

 

Suppose, at the 10Hz spectral line, the three different amplitude values from the three different autopowers are 3g, 5g, and 10g.

 

Let’s take a look at how the different averaging types change the way the three values are averaged to obtain the final value at the 10Hz spectral line.

 

Energy average:

 

The energy average is the default average type for stationary measurements.

 

The energy average calculates the averages of the squared values of all values. For this reason, sometimes the term RMS (root mean square) average is used in lieu of energy average.

 

Equation 1: The energy average equation.Equation 1: The energy average equation.

Equation 2: The energy average equation with our example values.Equation 2: The energy average equation with our example values.

The value at the 10Hz spectral line would be 6.68g.

 

Due to the nature of the energy average equation, this averaging type results in the higher amplitude values getting more weight in the final average.

 

It is common for energy averaging to be used in acoustic applications. For example, a sound power average of several sound pressure microphones uses energy averaging. 

 

Energy averaging does not use phase in the averaging process.  The squaring process removes the phase.

 

Linear Average:

 

The linear average calculates the arithmetic mean of all the values.

Equation 3: The linear average equation.Equation 3: The linear average equation.

Equation 4: The linear average equation with our example values.Equation 4: The linear average equation with our example values.

 

The value at the 10Hz spectral line would be 6g.

 

The linear average gives the same weight to each amplitude value in the average.

 

A linear average does include phase in the averaging process if it is available.  For example, using Time or Spectrum as the measurement type includes phase, while Autopower does not. If phasing effects are important, Linear averaging should be used in conjuction with Spectrums.

 

 

Energy Exponential Average:

 

The energy exponential averages the values and weights the acquisitions taken later in time more heavily than the earlier acquisitions.

 

Equation 5: The energy exponential average equation. The exponential weighting factor (EWF) is a value between 0% and 100%.Equation 5: The energy exponential average equation. The exponential weighting factor (EWF) is a value between 0% and 100%.

The user inputs a value for the exponential weighting factor (EWF) between 0% and 100%.

 

If the weighting factor is 0%, the average is equal to the last measured block of data (in this case, 10g).

 

If the weighting factor is 100%, the average is equal to the first measured block of data (in this case, 3g).

 

For this example, the EWF is set at 50%.

 

Figure 2: The energy exponential average equation with our example values.Figure 2: The energy exponential average equation with our example values.

For the three values of 3g, 5g, and 10g, the exponential averaged value would be 7 g at the 10Hz spectral line.

 

If the three values occurred in a different sequence, for example 5 g, 10g and 3g, the exponential averaged value would be 5.25g at the 10Hz spectral line.

 

Unlike the other averaging methods, the sequence in which the averages occur affects the final averaged value when using exponential averaging.

 

Maximum Value:

 

The maximum value average takes the maximum value at the spectral line.

Often this is referred to as peak hold averaging.

 

For the three values of 3g, 5g, and 10g in this example, the value at the 10Hz spectral line would be 10g.

 

The maximum value average is useful for measuring the worst case vibration.

 

Minimum Value:

 

The minimum value average takes the minimum value at the spectral line.

 

For the three values of 3g, 5g, and 10g in this example, the value at the 10Hz spectral line would be 3g.

 

The minimum value may be used in conjunction with the max value averaging type to get an envelope or range of values for the spectrum.

 

Conclusion:

 

The averaging type can greatly affect the amplitude of the data in the resulting spectrum. Figure 3 shows the amplitude of the 10Hz spectral line using the different averaging methods from the above example. Observe the large differences in amplitude.

 

Figure 3: Results of five different averaging methods.Figure 3: Results of five different averaging methods.

 

Have fun experimenting with the different averaging types!

 

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