# Analytical Modeling for Underground Risk Assessment in Smart Cities
## 7 Results and Discussion  
For experimental purposes, we used synthetic data to evaluate accuracy and effectiveness of proposed models. Various input parameters are considered to estimate values of the four risk contributing factors for every location which serve as input data to our system. Length, depth, size and age (years of burial), leakage probability and pipeline ductability are the input parameters for water supply risk index (\(M_{1}\)) and sewage line risk index (\(M_{2}\)); age and degree of peripheral depression for \begin{table}
\begin{tabular}{c c c} \hline \hline
**Membership Function Name** & **Membership Function Labels** & **Range** \\ \hline Very Low & VL & (0.0 to 1.5) \\ Low & L & (0.5 to 4.0) \\ Medium & M & (3.0 to 7.0) \\ High & H & (6.0 to 9.5) \\ Very High & VH & (8.5 to 10) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Labels, ranges of input and output membership functions. metro structure risk index (\(M_{3}\)); and granularity, compaction and ground water level for ground state risk index (\(M_{4}\)). We have considered 100 different locations and values for each parameter are carefully selected from a valid range as given in Table 5 to have maximum diversity in the final dataset. Each parameter value is then scaled in range [0, 10]. Risk index for each factor is calculated by taking simple average of three schemes, i.e., simple average, weighted average and maximum based scheme. Finally, risk index values are also scaled in range [0, 10] where zero mean no risk and 10 means very high risk. To get estimated final risk index, data generated are first labeled for various selected parameters by assigning a descriptive label to express the corresponding parameters in a formal language such as very low, low, medium, high and very high. Descriptive data for each location with labeled parameters are then provided to three experts and they were asked to provide expected risk index for given locations based on their experience and expertise. Average values were taken to get estimated final risk for corresponding locations which is then used for comparative analysis with proposed method. First, we present results of linear approximation scheme. In this method, we estimate weights for all risk contributing factors using multiple linear regression analysis. As shown in Figure 9, linear approximation results match fairly well but are not fully aligned with estimated risk index as desired. This shows that final risk index cannot be estimated from simple linear combination of risk contributing factors. \begin{table}
\begin{tabular}{c r r r} \hline \hline
**Risk Contributing Factor** & **Parameter** & **Unit** & **Range** \\ \hline \multirow{4}{*}{Water supply risk index (M1)} & Length & [m] & (0–300) \\  & Depth & [mm] & (0–2500) \\  & Years of burial & [year] & (0–30) \\  & Leakage probability & [\%] & (0–100) \\  & Pipeline ductability & [cm] & (0–100) \\ \hline \multirow{4}{*}{Sewerage line risk index (M2)} & Length & [m] & (0–300) \\  & Depth & [mm] & (0–2500) \\  & Years of burial & [year] & (0–30) \\  & Leakage probability & [\%] & (0–100) \\  & Pipeline ductability & [cm] & (0–100) \\ \hline \multirow{4}{*}{Metro structure risk index (M3)} & Age & [year] & (0–30) \\  & Degree of peripheral depression & [\%] & (0–100) \\ \hline \multirow{2}{*}{Ground state risk index (M4)} & Granularity & [\%] & (0–100) \\  & Compaction & [\%] & (0–100) \\  & Ground water level & [m] & (0–10) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Selected parameters range and units for four risk contributing factors  
Figure 9: Final risk index results based on linear approximation. Next, we evaluate hierarchical FIS models. As discussed earlier, we have selected two different models for evaluating results of hierarchical FIS, as shown in Figures 6 and 7. Every model is separately evaluated for rules defined via both average based and maximum based schemes.