# Analytical Modeling for Underground Risk Assessment in Smart Cities
## 1 Introduction  
Globally, urbanization is taking place in many countries. More job opportunities, better healthcare, education and entertainment facilities along with other privileges, attracts people living in rural areas for permanent migration. Rapid population growth in urban areas puts more pressure on available resources in city areas which results in pollution, traffic congestion and environmental degradation. In every big city, land is one of most precious resource and, to overcome this challenge, underground facilities are increasing day-by-day, as it is considered an improved utilization of available space in smart cities. Typical facilities include underground railway lines, parking lots, electric and water supply, sewerage lines, etc. Besides its utility, these facilities also pose serious threats to citizens and property. Despite care and precautions, many severe and unfortunate incidents have happened in underground facilities around the globe. Besides natural disasters, technical faults and human mistakes, there are other silent factors which pose constant and serious threats, e.g., continuous leakage of water and sewage supply lines, structure fault and underground soil deformation. In most cases, the damage does not happen at once, rather the hazard builds up slowly and gradually behind the scene as many underground facilities are invisible and inaccessible. This is mainly attributed to poorconstruction and the slow degradation process in underground facility structures and materials due to continuous deterioration effects of weathering, aging, chemicals processes, corrosion, etc. [1; 2]. To avoid any accidental loss, a sensor based real time monitoring system is highly desirable to conduct automated and continuous risk assessment to report any abnormality before it happens. Risk at any location, at any point in time, depends on various associated factors, e.g., ground status, pipeline leakage, structure health, etc. These individual risk factors are referred to here as risk contributing factors (RCFs). Each RCF contributes towards final risk index (FRI) at that particular location. For underground risk analysis and assessment, the first step is to collect data about parameters of interest (i.e., RCF) via sensors deployed at selected locations. Risk index value of each individual factor is calculated by fusion and aggregation of relevant sensors data after necessary processing. Figure 1 shows the conceptual design for risk assessment of underground facilities. In a given geographical area, sensors are installed at selected locations for monitoring and risk assessment. Every RCF demands its own set of sensors. For example, water supply pipeline leakage is a risk contributing factor and its risk index is estimated by pressure sensors, flow sensors, and leakage sensors, as shown in Figure 1.  
Several risk contributing factors are involved in underground risk assessment, each having its own risk index values. We need a single risk index value for a given location that is somehow representative of risk index values of all risk contributing factors. There is no known formulation to get final risk index from associated risk contributing factors and the actual relationship can be very complex in reality. Several approaches are adopted in the literature to address this problem. A brief summary of some related techniques is presented in next section. Normally, subjective risk assessment can be done by experts by visiting the site and observing the risk point. Besides subjectivity, manual risk assessment is very time consuming and costly. Nonlinear and complex nature of relationship between risk score and risk rating contributing factors and corresponding final risk index demands an analytical modeling of the system.