## 1 Introduction  
The main reason for excessive human losses and material damage during a seismic event is the insufficient seismic resistance of buildings. The assessment of seismic performance of buildings in an existing urban area is a demanding task for civil engineers, especially in old cities that have been gradually growing and expanding over the course of centuries. The heterogeneous distribution of buildings with different architectural, material and structural characteristics, accompanied by different ages of buildings, material degradation over time, various structural and non-structural interventions and, generally, the lack of knowledge about the performance of the structure, lead to numerous uncertainties in the analysis of such structures. Given the complexity of the problem, the assessment of seismic vulnerability and the risk to large areas is usually performed by simplified methods. The approaches for the evaluation of structural vulnerability can be generally classified as empirical, analytical, or hybrid. Among them, empirical methods are often used for the first screening of buildings and vulnerability classification. The vulnerability index method [1, 2] and the damage probability index method [3] are the most common approaches to assess a building's vulnerability at the urban scale. Different versions of the vulnerability index method have been derived from the approach developed by the Italian Defense National Group against Earthquakes (GNDT) for the seismic vulnerability assessment of masonry and RC buildings located in historical centers [2] by calibrating the weights of vulnerability parameters using information about the damage induced from past earthquakes [4; 5; 6]. The damage probability index method predicts the damage pattern caused by the given intensity of an earthquake using different macroseismic scales [7; 8; 9]. The advantage of empirical methods is primarily to reduce the computational efforts in comparison with more complex detailed approaches. Empirical methods are based on qualitative evaluations and can be used for setting priorities in reconstruction or undertaking measures of prevention, mitigation, preparedness, and response as part of a seismic risk management. Analytical methods aim to represent seismic vulnerability through the analysis of the mechanical behavior of the structure. These methods result in the quantitative evaluation of the seismic performance of buildings based on models of different complexity. Among them, the most detailed are the models based on non-linear methods such as non-linear static (pushover) [10] or incremental dynamic analysis [11], which are very demanding even for a single building and cannot be exploited to assess seismic vulnerability on a wider, urban scale. However, these methods can be used to derive fragility curves for certain typologies of buildings, whichcan, in turn, be used as starting points to subsequently proceed with the evaluation of seismic vulnerability and damage scenarios at the urban scale [12; 13; 14; 15; 16; 17; 18; 19; 20]. Finally, seismic vulnerability at the urban scale can be assessed by hybrid methods, namely methods combining empirical approaches with detailed analytical ones, and leading to the quantitative representation of the behavior of buildings under certain seismic actions. In this regard, most state-of-the-art contributions containing assessment methodologies, and their related case studies, rely upon the concept that the levels of vulnerability and damage shall depend on the earthquake intensity [21; 22; 23]. In particular, a reference can be performed by the study [24] for a thorough discussion of the most relevant vulnerability assessment methods applicable at different scales. Essentially, the choice of the approach should depend on a series of aspects. In addition to the area of study, as settlements will require methods that cannot be used to analyse cities or entire regions, a discriminant comes from data availability about the building stock.