Model Validation Criteria for System Identification in Time Domain

The fit ratio is one of the most commonly used criteria to evaluate a result of system identification in the time domain. This criterion is given by the root mean squared error (RMSE) divided by the standard deviation of the measured signal. However, the fit ratio has some problems. For example, it can take negative values because it is not normalized, and it is easy to obtain a better value for a low-amplitude signal than for a high-amplitude signal. In this paper, we introduce some normalized criteria from the field of physical geography and consider criteria that resolve these problems. We evaluated these criteria through two case studies. We found that the correlation coefficient was effective to evaluate the phase, and a criterion obtained from the triangle inequality was effective for evaluating the gain and phase.