# Analytical Modeling for Underground Risk Assessment in Smart Cities
## 2 Related Work
PipeDiver is a small robot designed by Pure Technologies that can freely swim inside a pipe using flexible fins [13]. This device has three main modules: (a) tracking module; (b) battery module; and (c) sensing module. PipeDiver sends and receive radio signals to detect distortion to identify stress point. In many settings, specialized cameras are used to take pictures of underground facilities that are later processed and analyzed for cracks detection. [PERSON] et al. [14] developed a Raspberry Pi based system to detect cracks in structures using image processing and computer vision algorithms. To monitor civil structure surface from outside, real time images were collected by Unmanned Air Vehicle (UAV) and integrated with data collected from other sources for analysis in [15]. [PERSON] et al. [16] proposed a real time image processing based scheme for displacement monitoring during excavation works using camera attached to sensors. Similarly, [PERSON] and [PERSON] [17] constructed a 3D scene from 2D images to perform improved assessment of the structure. [PERSON] et al. [18] presented an image processing based algorithm for crack detection in underground tunnel sub-way. Defects in heavy industrial pipelines are usually detected through manual inspection, which is time consuming and expensive. [PERSON] et al. [19] presented a three step image processing based algorithm to automate process of damage hole and crack detection. Underground structure diversity and varying spatial and lighting conditions requires different image and video stream processing algorithms to detect anomaly and risk. Various approaches are described in [20] to address underlying complexity by complementing with augmented reality based solutions for faster and accurate risk assessment in underground facilities. Indirect method is based on water auditing, flow testing and conducting soil test to identify risk. Metal pipe corrosion can be estimated by measuring polarization resistance with weak potential difference. Similarly, different kinds of tests can be conducted on soil surrounding the buried pipelines to estimate the risk index. Some example tests include soil resistivity; pH value; chloride and moisture content; sulfates; shrinking, swelling or buffering capacity; LPR; redox potential; contaminants; soil compaction; etc. For continuous monitoring and inspection, the idea of \"smart pipes\" is coined, i.e., pipes equipped with range of sensors [21]. Smart pipe based project was initiated in Europe for installation of deep-sea pipelines in 2006. Several robotic platforms are developed that can swim and move inside the pipe to collect data regarding pipe status and condition [22]. Risk identification and quantification is a challenging task due to underlying nonlinear and complex relationship among the risk contributing factors. A model for estimating underground pipe failure risk is proposed in [23] based on four sub-models, i.e., pipe-segment corrosion model, pipe stress model, pipe wrap protection model and stress model. Failure probabilities estimated from Monte Carlo simulation reveals that improving accuracy and acquiring knowledge can make the model more reliable. Several models found in the literature are empirical in nature based on data fitting [24; 25; 26; 27; 28], such as the famous two-parameter corrosion model (given below) initially proposed by [PERSON] in 1957 using historical data [24]. \[w=k\times T^{n} \tag{1}\]  
where w is resultant loss in pipe thickness with exposure time T (years), k is proportionality constant and n is exponential constant. Values of k and n depend on location and pipe material. Fault tree analysis based model [29] is a famous scheme for risk analysis that uses top-down approach to analyze related hazards in a sequence to estimate occurrence probability of each and system capability to avoid the same.