Coherence-Based Damage Indicators for Story Stiffness Reduction from Seismic Building Responses

Coherence-based damage indicators enable story-level assessment of reinforced concrete buildings from response measurements alone. Four indicators, the mutual information (MI), the transmissibility modal assurance criterion (TMAC), the accumulated transmissibility coherence (ATC), and a normalized spectral L1 distance, are computed from the transmissibility coherence between floor pairs in the Welch and Morlet wavelet domains and validated against documented per-story stiffness reduction on three cases: a numerical pinching frame, a one-third-scale shake-table frame, and a full-scale five-story building through six damage states. The indicators are ordinal severity measures producing the same ranking under in-band noise to 10%, saturation thresholds of 0.995 and above, a 36% shorter analysis window, and displacement in place of acceleration. The normalized L1 distance is the most robust severity measure, +0.96 on the base-to-first-floor path of the numerical case; MI detects onset, falling to 3 to 15% of its estimator ceiling. A measured base channel is the most valuable instrument: the only channel whose removal degrades the severity correlation, and the only path on which the coherence formulation clearly outperforms an elementary amplitude index. Story-level localization requires a sequence of damage states; severity is recovered from base and roof alone.