Deviation Metrics Calculations

The Sprague-Geers method is a robust way to gauge the similarity between two sets of curves.

A value close to 1.0 indicates a very close similarity between the curves and 0.0 indicates much dissimilarity between them. The measure takes into consideration all available data points and therefore represents the behavior of the entire set of data. The measure however is abstract, and visualizing the Sprague-Geers metric is difficult. For instance, what does a metric of 0.75 mean? You can only gauge this by plotting the curves.

Deviation Metric

In order to address the challenges of the Sprague-Geers method, you have to understand the deviation metric. This metric is very simple to compute and visualize.

You can use two deviation metrics, one for dynamic stiffness, and another for loss angle, which you calculate differently.

The deviation metric for dynamic stiffness is simply the maximum deviation between two sets of dynamic stiffness curves, A(xk) and B(xk), expressed as a percentage.
The deviation metric for loss angle is the absolute value of the maximum absolute deviation between two sets of loss angle curves, A(xk) and B(xk), expressed in degrees

The following table explains the metrics in more detail:

Table 1.
Deviation Metric	Description
Dynamic Stiffness	Let A(xk), k=0…N-1 be a set of data points measured experimentally. Let B(xk), k=0…N-1 be the corresponding set of data points from the analytical model. Let the deviation metric for Dynamic Stiffness be DK. The pseudo-code for calculating D_K is:
Loss Angle	Let A(xk), k=0…N-1 be a set of data points measured experimentally. Let B(xk), k=0…N-1 be the corresponding set of data points from the analytical model. Let the deviation metric for Dynamic Stiffness be D_LA. The pseudocode for calculating D_LA is: