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The Signature of a Signal: A New Approach to Model Validation for Toroidal Confinement Systems
| Author: | Barmish B.R. |
| Coauthor: | J.L. Shohet |
| Institution : | University of Wisconsin-Madison |
| Abstract text: | Given a hypothesized model for a toroidal confinement system, its validation via data acquisition is often hampered by two problems: First, from run to run, parameters of the system such as density, magnetic field and temperature may vary dramatically. Second, if the model is not rigorously derived from underlying equations of physics, a good “match” between the model prediction and the measured signals may be a manifestation of “over-parameterization” as opposed to quality of the model; i.e., with enough adjustable parameters, a good fit with experimental data is often attainable. With this background as motivation, the main objective of this work is to describe a framework for model validation based on a new concept: the “signature” obtained using an experimentally observed signal and a hypothesized model class.
While our framework applies to large classes of systems, to demonstrate the efficacy of signature theory, in this work we focus on traveling wave phenomena and, in particular, the reversed-field pinch slinky mode as observed in the MST experiment. To this end, we proceed as follows: We use the sine-Gordon equation as the generator for the hypothesized signal class and then demonstrate the use of signatures in the analysis of experimental data obtained from the magnetic pickup coils in MST.
With zeta denoting the traveling wave variable and phi(zeta) being the measured signal from the pickup coils, our approach involves generation of a signature function S_phi(zeta) using the hypothesized model class and the observed data. Subsequently, by comparing the observed signal phi(zeta) with the theoretical signature S_phi(zeta), we obtain a measure which is indicative of the quality of the model. Using the sine-Gordon equation in conjunction with MST data, this comparison discriminates between signals consistent with the hypothesized model class and others
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