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Abstract Under proper loading conditions, micro‐to‐nanoscale heterogeneities (ie, the bond system) that are commonly found within the materials of a system can coalesce until causing macroscopic alterations of the system properties. The bond system is responsible for atypical and invariant‐scale nonlinear elastic processes in granular media, from laboratory‐tested materials (mm) to the Earth's crust (km). The unusual observed behavior involves slow recovery, or relaxation, of the elastic properties after dynamic loading. Several models have been designed to explain non‐linear elasticity, although their physics is still partially unknown. Here, we show that recovery processes are also observed at intermediary scales (m) in civil engineering structures, and that they might be related to structural health due to the healing of cracks. For Japanese buildings subjected to earthquakes, we observe rapid co‐seismic reductions of their resonance frequency, followed by fascinating recoveries over different time scales. For the first time, slow recovery is presented in buildings over short times (ie, seconds) for a single earthquake; over intermediate times (ie, months) for a sequence of aftershocks; and over long times (ie, years) for a series of earthquakes. This study focuses on the analysis of long‐term recovery and recovery during aftershocks, in order to detect permanent damage. By comparing two buildings with different damage levels after the 2011 Tohoku earthquake, we show how relaxation models can characterize the level of cracking caused by damaging events. Our results demonstrate that nonlinear elasticity, combined with existing monitoring techniques, can be a powerful approach for damage detection and damage characterization.

The real-time analysis of a structure’s integrity associated with a process to estimate damage levels improves the safety of people and assets and reduces the economic losses associated with interrupted production or operation of the structure. The appearance of damage in a building changes its dynamic response (frequency, damping, and/or modal shape), and one of the most effective methods for the continuous assessment of integrity is based on the use of ambient vibrations. However, although resonance frequency can be used as an indicator of change, misinterpretation is possible since frequency is affected not only by the occurrence of damage but also by certain operating conditions and particularly certain atmospheric conditions. In this study, after analyzing the correlation of resonance frequency values with temperature for one building, we use the data mining method called “association rule learning” (ARL) to predict future frequencies according to temperature measurements. We then propose an anomaly interpretation strategy using the “traffic light” method.