Mathematical modeling of interdependent infrastructure: An object-oriented approach for generalized network-system analysis

Selection of the modeling resolution of infrastructure

“…Following Sharma and Gardoni (2022), let 𝐂 [𝑘] (𝑡) and 𝐃 [𝑘] (𝑡) epresent the vectors of the capacity and demand estimates for the components of 𝐺 [𝑘] at time t. Given 𝐂 [𝑘] (𝑡) and 𝐃 [𝑘] (𝑡), we can write the supply measure for 𝐺 [𝑘] , 𝐒 [𝑘] (𝑡) as a measure of the functional state of the network components as 𝐒 [𝑘] (𝑡) = 𝐒 [𝑘] [ 𝐱 [𝑘] (𝑡) , 𝐂 [𝑘] (𝑡) , 𝐃 [𝑘] (𝑡) , 𝚯…”

“…For example, in the case of water infrastructure, such interdependencies would capture the dependencies of the water flow network on the structural network. Following Sharma and Gardoni (2022)…”

“…Following Sharma and Gardoni (2022), we model the water infrastructure as a collection of two networks, the structural network, $${G^{[ 1 ]}}$$, and the water flow network, $${G^{[ 2 ]}}$$. The structural network describes the connectivity and physical damage of the water infrastructure.…”

“…Past research focused on developing the engineering tools needed to model the performance of individual infrastructure components like bridges, electric substations, and water and gas pipelines (e.g., Gardoni et al., 2002; Lanzano et al., 2013; Paolucci et al., 2010) and individual infrastructure like transportation, power, water, and gas distribution infrastructure (e.g., Bocchini & Frangopol, 2011; Cavalieri et al., 2014; Esposito et al., 2015; Nocera, Tabandeh, et al., 2019; Pudasaini & Shahandashti, 2020; Sharma & Gardoni, 2022). Past research also focused on additional important factors like the effects of aging and deterioration (e.g., Adeli, 2001; Kumar et al., 2015; Sanchez‐Silva et al., 2011), and the interdependencies among critical infrastructure (e.g., Argyroudis et al., 2015; Galbusera et al., 2018; Ouyang, 2014; Thacker et al., 2017) and among infrastructure and social systems (e.g., Franchin & Cavalieri, 2015; Guidotti et al., 2019).…”

“…This paper proposes a mathematical formulation to address these two challenges. The proposed formulation builds upon the available mathematical formulations for modeling the time‐varying performance of infrastructure (Sharma & Gardoni, 2022; Sharma et al., 2021). First, we propose a formulation to define equivalent simplified infrastructure models at different levels of resolution.…”