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Sprague-Geers Metric for Data Similarity

Sprague-Geers Metric for Data Similarity

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Sprague-Geers Metric for Data Similarity

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This section defines and provides examples of the Sprague-Geers Metric for Data Similarity.

 

Definition

Consider two signals a(xk) and b(xk), k=1…N. You are interested in computing a metric that shows the similarity of these signals. Use the following steps to compute the Sprague-Geers metric:

 

1.Calculate the metric M for magnitude difference and P for phase difference as follows:

sprague1_eq_zoom50

(Click to enlarge)

 

2.Calculate the combined metric C as follows:

sprague2_eq_pdf_zoom70

C=1 is a perfect match. Metric C is what we want to show.

Note:sprague3_eq_zoom70 is known as the Sprague-Geers Combined Metric.

 

 

Examples

This section provides four plots showing the Sprague-Geers Metric:

 

Example 1: Signals with the same overall magnitude, but drastically different slopes

Sprague1_plot

Ψaa= 143.50,  Ψbb= 143.50, Ψab= 77.00, M=0.00, P=0.319714, C=0.680286

 

Example 2: Two very similar signals displaced in the y direction by 5%

Sprague2_plot

Ψaa= 0.50,  Ψbb= 0.51, Ψab= 0.50, M=-0.009852, P=0.044719, C=0.954208

 

Example 3: A synthesized MIT example for Dynamic Stiffness

Sprague3_plot

Ψaa= 3.39E+5,  Ψbb= 3.77E+5, Ψab= 3.57E+5, M=-0.051164, P=0.026831, C=0.942227

 

Example 4: A synthesized MIT example for Loss Angle

Sprague4_plot

Ψaa= 1.39628E+1,  Ψbb= 6.67958, Ψab= 9.59216, M=0.445811, P=0.037025, C=0.552654