## 5 Simulation Models as a Substitute  
### Simulation Models  
[PERSON] and [PERSON] (2018) pointed out that uncertainty treatment is needed in the risk analysis applications for maritime transportation, and also pointed out that simulation models are able to propagate the uncertainty of the input variables into the outputs for further consideration ([PERSON] and [PERSON], 2018). In most cases, simulation programs are performed in the risk analysis. It is very possible that simulation models have the potential to better reflect the influence of the various risk elements (listed in Table 1). There are two different simulation approaches for risk analysis: individual ship simulation and ship traffic simulation. This \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Risk Factors** & **Risk Elements** & **AASHTO Model** & **Kunz’s Model** & **Eurocode Model** & **Pedersen’s Model** & **Drift Model** & **Three Random Variables Model** \\ \hline \multirow{4}{*}{Structure Factor} & Pier/Object Positions & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \cline{2-7}  & Span of Bridge & \(\surd\) & \(\surd\) & - & \(\surd\) & \(\surd\) \\ \cline{2-7}  & Pier/Object Dimensions & \(\surd\) & \(\surd\) & - & \(\surd\) & \(\surd\) \\ \hline \multirow{4}{*}{Navigational Circumstances} & Wind & - & - & - & - & \(\surd\) & - \\ \cline{2-7}  & Current & \(\surd\) & - & - & - & \(\surd\) & - \\ \cline{2-7}  & Tide & - & - & - & - & \(\surd\) & - \\ \cline{2-7}  & Water Depth & \(\surd\) & - & - & \(\surd\) & \(\surd\) & \(\surd\) \\ \cline{2-7}  & Visibility & - & - & - & - & - & - \\ \cline{2-7}  & Channel Bends & \(\surd\) & - & \(\surd\) & - & - & - \\ \cline{2-7}  & Ship Traffic Density & \(\surd\) & - & \(\surd\) & \(\surd\) & - & - \\ \hline \multirow{4}{*}{Ship Direction} & Ship Dimension & \(\surd\) & - & - & \(\surd\) & \(\surd\) & \(\surd\) \\ \cline{2-7}  & Probability of & & & & \(\surd\) & \(\surd\) & - & - \\ \cline{2-7}  & Vesed Aberancy & \(\surd\) & - & \(\surd\) & \(\surd\) & - & - \\ \cline{2-7}  & Distribution of Vessel & & & & & & \\ \cline{2-7}  & Position Perpendicular to & \(\surd\) & - & \(\surd\) & \(\surd\) & - & \(\surd\) \\ \cline{2-7}  & Normal Route & & & & & & \\ \cline{2-7}  & Ship Deviation Angle & - & \(\surd\) & - & - & \(\surd\) & \(\surd\) \\ \cline{2-7}  & Distribution of & & & & & & \\ \cline{2-7}  & Stopping Distance & - & \(\surd\) & - & - & \(\surd\) & \(\surd\) \\ \cline{2-7}  & Failure Rate Per Travel Unit & - & \(\surd\) & \(\surd\) & - & - & \(\surd\) \\ \cline{2-7}  & Speed of The Ships & - & - & \(\surd\) & \(\surd\) & \(\surd\) & - \\ \cline{2-7}  & Ship Classification & \(\surd\) & - & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline Human Factor & Human Error & - & - & \(\surd\) & \(\surd\) & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the factors considered in the models. section tries to explain the advantages as well as the limitations of the existing simulations and gives insights regarding the future models for probabilistic risk assessments. For individual ships, the interaction with other ships and the role of human interventions are important. Dynamic ship movements can be simulated with manned ship-handling simulators (e.g., the Mermaid 500 at MARIN). One of the drawbacks of this is that normally only scenarios with certain extreme circumstances are simulated using the system. This relies too much on expert judgments. Another disadvantage is that different traffic patterns and uncertainties in the waterway are difficult reflected using this system. Different cases of ship encounters should be performed, and a single case of a ship-handling simulation is time consuming and the equipment is expensive [36]. Other cheaper options are the simulation of ship movements based on Fuzzy Logic [37], Bayesian Networks [38], and Neural Networks [39]. Nevertheless, these models remain dependent on expert opinions or other human interventions, otherwise proper vessel behavior in different situations is still missing [40].