# An Alternative Procedure for the Description of Seismic Intensity Parameter-Based Damage Potential
## 1 Introduction  
Modern building codes provide a framework for analyzing, designing, and assessing structures, focusing on protecting human life. This human life protection is achieved by allowing structural deterioration in sufficiently strong seismic events and preventing partial or total collapse [1, 2]. Given the uniqueness and the stochastic nature of strong ground motions, the cause-effect relationship between earthquake excitation and structural response is highly complex [3]. Numerous studies have been conducted in the past decades to identify and quantify the characteristics that best describe the damaging potential of earthquake events, resulting in the realization of several Intensity Measures (IMs), as described in the works of [3, 4]. Each IM represents the damage potential of a given strong motion as a single numerical value. It becomes immediately apparent that a single IM is not able to capture the characteristics of an excitation [3] completely. On the other hand, this uniqueness of seismic events equally impacts the structural response, with significant implications for structural design and assessment [5]. DamageIndices (DIs) are employed to aid decision-makers (engineers and state authorities) both in working proactively for the design of new structures and in quantifying any damage sustained post-earthquake [6], providing damage grade approximations in the form of a single number, usually in the range [0, 1], where the former represents a healthy and the latter a collapsed structure, respectively [7,8]. Various DIs have been proposed in the literature [5,6], each derived from a different scientific standpoint and, therefore, measuring different response quantities. Several methods for damage identification, localization, and assessment have been proposed in the past decades, each catering to specific needs. Such needs arise, e.g., in Structural Health Monitoring (SHM), which deals with the compelling issue of real-time damage detection and localization [9, 10, 11, 12, 13]. In SHM, eigen perturbation techniques are commonly utilized to perform damage localization in real-time. Furthermore, Damage Indices based on eigen perturbation techniques are tasked to report sustained damage at a specific point of a structure (local damage). On the other hand, the present study does not focus on the time histories of local damages and their locations. The focus is on the interrelation between global Damage Indices, which lump the structural post-seismic status in a single numerical value, and the single-value seismic Intensity Measures. Furthermore, utilizing IMs in the form defined in the literature requires that the complete time-history record is already known. The interdependency between seismic excitation and structural response has been verified by previous academic work from recorded post-seismic data and computer simulations [4,14,15]. Regression models have been generated in the past [16] to assess the damage grade of a structure as a function of the IMs of a specific seismic event. In the present study, an alternative procedure is proposed to strengthen the relationship between highly correlated IMs with various DIs, in which the IMs are transformed, directly considering their rank correlation coefficient with their respective DI, to provide an accurate estimation of several Damage Indices. The proposed methodology aims to aid practitioners in performing rapid post-earthquake in situ assessments with only a limited amount of readily available data. This close relationship between IMs and DIs forms the basis for fragility analysis, primarily generating a probabilistic seismic demand model that minimizes the inherent epistemic uncertainty [17]. Statistical procedures and Machine Learning algorithms are usually employed to determine the resulting damage grade of a structure given a specific seismic event, as well as the optimal IM combination for the prediction of the sustained damage, e.g., [18, 19, 20, 21, 22, 23, 24].