## 2 Materials and Methods
### Damage-Sensitive Features  
DSFs are derived from vibration data and, when defined for a sensor pair that covers the entire structure, can be defined as metrics that characterize the condition (state) of a structure and allow for differentiation at succinct damage levels (see Figure 1). In the context of vibration-based monitoring, which forms the most realistic instance of seismic monitoring, DFSs can be extracted from measured acceleration time-series, possibly in near-real time, which is a feature that conveys their particular potential for rapid loss assessment [11]. As aforementioned, several vibration-based damage detection approaches have been applied and tested on slender or flexible structures, for instance high-rise buildings or bridges [61; 62; 63; 66; 67], for which higher vibration modes can be extracted from measurement data. The dynamic response of typical low-to-mid-rise buildings, on the other hand, is often governed by a single dominant mode in each direction, undermining the use of some of the most common existing approaches to damage detection. In addition, while some buildings such as steel or modern reinforced concrete structures offer significant ductility, others, such as masonry buildings, exhibit more sudden and possibly reversible stiffness changes (for instance, rocking motion of slender masonry walls), which may cause a rather brittle behavior and thus requires the use of DSFs that can pick up small variations in the dynamic behavior in short time windows. Therefore, the capacity of DSFs to pick up nonlinearity and/or residual damage will be evaluated in Section 3. In addition, when DSFs are derived for multiple sensor pairs that define substructures of the monitored building, information about the damage location can be inferred (see Figure 1).  
In what follows, we present DSFs that are constructed to reveal such variations in the response, mostly corresponding to signs of nonlinear structural responses, which can be associated with damage. The overviewed DSFs are formulated on the basis of five primary quantities, as briefly reviewed in the following sections prior to comparatively assessing their potential in Section 3:  
1. The first class contains DSFs, whose primary ingredient is the characteristic quantity of transmissibility, which operates in the frequency domain (see Section 2.1.1). Thus, stiffness changes, which may be provoked by nonlinear behavior, are revealed by transmissibility-based DSFs through changes in the (amplitude of the) frequency response function of an input-output signal pair.
2. The second class of DSFs derives from correlation and coherence as primary quantity (see Section 2.1.2). These DSFs track the similarity in behavior of two time-series in the time domain (correlation) and frequency domain (coherence). The onset of nonlinear behavior typically appears as loss of correlation/coherence for specific frequency bandwidths.
3. Energy-based DSFs (see Section 2.1.3) rely on the time-frequency representation offered by the wavelet decomposition in order to detect changes in energy distribution in the frequency domain and potentially reveal shifts linked to stiffness and damping.
4. DSFs that approximate the relationship between input accelerations and output displacements directly (see Section 2.1.4) are used as a representation of the stiffness that links the restoring force to displacement.
5. In addition, DSFs that derive from OMA (see Section 2.1.5) can be used to indicate permanent (residual) damage, which alters modal properties, such as natural frequencies and mode shapes.