## 3 Resilience  
Resilience has recently emerged as a theoretical framework for examining and assessing an infrastructure's performance prior to, during, and following the occurrence of a disturbance. Such disturbances could arise from natural hazards or mechanical and technical failures. Moreover, resilience is being increasingly recognized as a proactive approach aimed at bolstering the robustness of infrastructures to enhance their preventative, mitigative, and recovery capabilities in the face of disruptive events [26]. Resilience is a concept defined in various ways, often contingent on the context of the analysis, whether it is an asset, a facility, a system, or a system-of-systems. In this discussion,we concentrate on definitions that pertain to the system-of-system or interdependent systems. One such definition posits resilience as \"the capacity of a system to absorb disturbance, undergo change, and retain essentially the same function, structure, identity, and feedback\" [27]. This perspective primarily focuses on resilience in the aftermath of a disruptive event. A contrasting definition proposed by the US government encompasses resilience both prior to and following an event, as depicted in Figure 1. It defines resilience as \"the ability to adapt to changing conditions and withstand and rapidly recover from disruption due to emergencies\" [28]. The Department of Homeland Security (DHS) offers a more specific definition of resilience in the context of critical infrastructures: \"the ability to reduce the magnitude, impact, or duration of a disruption. Resilience is the ability to absorb, adapt to, and rapidly recuperate from a potentially disruptive event\" [29]. Furthermore, a smart city can be considered resilient to a certain degree if it has enhanced capabilities to absorb anticipated shocks and strains to its social and technical network and infrastructures while maintaining the necessary level of functions, structures, and identification. Resilience has become a central concept for identifying and evaluating the performance of infrastructures before, during, and after a disturbance. These disturbances could be the result of natural calamities or mechanical or technological failures. As a forward-thinking strategy, resilience has garnered a great deal of attention for its potential to fortify infrastructure and improve its prevention, mitigation, and recovery capabilities during an event. There are numerous definitions of resilience, the particulars of which are frequently dependent on the context of analysis, such as whether it pertains to an asset, facility, system, or system-of-systems. The concentration of this article is on definitions pertinent to interdependent systems or system-of-systems. According to [27], resilience is \"the capacity of a system to absorb disturbance, undergo change, and retain essentially the same function, structure, identity, and feedback\". This explanation emphasizes the resilience following a disruptive event. In contrast, the US government's proposed definition includes resilience both before and after an event. It defines resilience as \"the ability to adapt to changing conditions and endure and recover quickly from disruptions caused by emergencies\" [28]. The Department of Homeland Security (DHS) offers a more detailed definition of resilience in relation to critical infrastructures. According to them, resilience is \"the capacity to lessen the extent, impact, or duration of a disturbance [29]\". Resilience is the capacity to absorb, adapt to, and swiftly recover from a potentially disruptive event. The American Society of Civil Engineers (ASCE) FEMA P-58 code [30], known as the Seismic Performance Assessment of Buildings, provides a vital framework for evaluating a building's potential seismic performance. This robust methodology is integral to the design for resilience, providing a performance-based approach that allows for detailed estimations of potential losses due to seismic events.