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Simulated output (blue) vs. original observation (green) 

Simulated output (blue) vs. original observation (green) 

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Conference Paper
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Engineers are often faced with attempting to characterize data from an experiment without having complete knowledge of the experiment itself or the complete physics of the problem. There may also be limited access to data due to proprietary and/or classification issues. In such cases, developing a physics-based, first-principle model may not be pos...

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... Figure 2 demonstrates visually that the simulated output — in blue — compares favorably with the original observation — in green. This qualitative comparison must also be quantified to be of value in forecasting. The purely forecasted values lay from samples 1200 to 1500. Despite the favorable visual comparison, a quantitative measure of the goodness of fit is desirable to validate this method. The Captain Toolbox authors use a version of the Coefficient of Determination, , to compare simulations with observed data for time series data. This measure is defined by: In the definition above, y is the observation data set and fit is the simulated data [Captain Toolbox Handbook]. When tf , the simulation from the previous example is compared with the observed data, y , the result is also ...

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