A robust quantitative comparison criterion of two signals based on the Sobolev norm of their difference
Abstract
We present a method for the quantitative comparison of two surfaces, applicable to temporal and/or spatial extent in one or two dimensions. Often surface comparisons are simply overlaid graphs of results from different methodologies that are qualitative at best; it is the purpose of this work to facilitate quantitative evaluation. The surfaces can be analytical, numerical, and/or experimental, and the result returned by the method, termed surface similarity parameter or normalized error, has been normalized so that its value lies between zero and one. When the parameter has a value of zero, the surfaces are in perfect agreement, whereas a value of one is indicative of perfect disagreement. To provide insight regarding the magnitude of the parameter, several canonical cases are presented, followed by results from breaking water wave experimental measurements with numerical simulations, and by a comparison of a prescribed, periodic, square-wave surface profile with the subsequent manufactured surface.
- Publication:
-
Journal of Engineering Mathematics
- Pub Date:
- December 2016
- DOI:
- 10.1007/s10665-016-9849-7
- arXiv:
- arXiv:1412.6977
- Bibcode:
- 2016JEnMa.101..115P
- Keywords:
-
- Canonical surfaces comparison;
- Normalized error;
- Quantitative surfaces comparison;
- Sobolev norm;
- Surface similarity parameter;
- 94A17;
- 65Z05;
- 62K99;
- 62B15;
- Physics - Fluid Dynamics;
- Physics - Atmospheric and Oceanic Physics;
- Physics - Data Analysis;
- Statistics and Probability
- E-Print:
- J Eng Math 101, 115-124 (2016)