## 4 Current Approaches to Measure Resilience in Smart ICI
### Empirical Approach  
The empirical approach is a prevalent method for evaluating resilience in smart Interdependent Critical Infrastructures (ICIs). This approach emphasizes data collection directly from the infrastructure to determine overall resilience, relying on historical reports  
Figure 10: System composed of two subsystems with mutual functional dependency [47].  
Figure 9: Interconnections of four systems [47].  
to assess the total resilience of the ICI. In [49], the authors propose an empirically based tool that examines ICI connectivity measurements derived from news, articles, and other reports on severe ICI impacts. Recently, databases dedicated to collecting empirical data have been established to monitor and report ICI events. However, these databases primarily focus on individual smart infrastructures rather than ICIs as a whole.  
Many incidents, such as terrorist attacks on energy infrastructure, serve as examples of such databases. One notable example can be found in [49], a database containing public reports of ICI disruptions. Data in this database are gathered from open sources, including newspapers, articles, and news, and only high-impact events are recorded, e.g., those affecting at least 10,000 customers. Regularly occurring, limited, and planned operational disruptions are not included. Each event is characterized by various attributes, such as ICI sector and context, event start time, duration, affected geographical area, type of failure, losses and impact, recovery methods, and recommendations.  
Another framework using a similar data type is presented in [50], where the authors develop an analytical structure with practical applications for understanding ICI failures. They utilize significant power outages as primary data to demonstrate how major problems in power infrastructure can cause issues in interconnected (interdependent) infrastructures. Their analysis is based on three real examples: the August 2003 northeastern North American blackout, the 1998 Quebec ice storm, and a series of three 2004 Florida hurricanes. Data were collected through news and internet reports, and measures were developed to efficiently identify possible outcomes based on the type of failures and affected regions. A comparison between all events is provided as a basis for considering the advantages of risk mitigation. In [51], a knowledge-based learning method for ICI is employed to acquire reports of common patterns of ICI failure following external disturbances. The knowledge-based discovery process combines ICI failure reports and demonstrates the procedure for transforming them into new data frames for data mining purposes. A data mining algorithm known as a generalized sequential pattern (GSP) is then applied to identify common patterns in ICI failure records. Figure 11 illustrates the five main steps of this approach, which helps clarify the most frequent failure events.  
_Limitations:_ The collection of empirical data often focuses on specific failure types, such as cascading failures. However, there are numerous reasons why failures may propagate beyond CI sector boundaries and may not be captured in this type of data. Additionally, this data may lack accuracy since many failures are not reported in the news or at a technical level. Aside from the absence of accurate data, the database itself presents another limitation of the empirical approach, as no databases have been identified that concentrate on critical disturbances across all ICIs and cascading consequences using an \"all-hazards\" approach.