A metric to quantify structural damage under seismic excitation is developed, leveraging system identification methods to predict the hypothetical serviceable response of structures. This metric measures the deviation between a dynamical system model trained on response data from a specific seismic event and a model trained on response data from other seismic or non-seismic events. The models are constructed using the System Realization using Information Matrix (SRIM) method, modified to constrain unstable modes and incorporate a computationally efficient output-error minimization algorithm. The proposed deviation metric exhibits increasing trends with seismic event intensity, mirroring observed period elongation trends, and serves as a meaningful indicator of structural damage. This tool offers a practical approach for structural health monitoring, facilitating regional-scale assessments of instrumented bridges based on predictive response modeling.