**4.3 Bayesian network approach**

Instead of solving Eq. (10) or Eq. (11) analytically or numerically, the BN in **Figure 5** can be used to model the tank flotation and estimate its probability. Knowing that *S* and *h* are the only random variables that contribute to the flotation, the BN should consist of two root nodes "S" and "h", and a leaf node, "Floatation".

*S* and *h* in Eq. (11) are continuous variables, but their corresponding nodes in the BN are discrete nodes. As such, *S* and *h* need to be discretized into a finite set of states. The probabilities of the states can then be calculated using the probability

**Figure 5.** *BN for modeling and assessing the probability of tank floatation.*

### *Vulnerability Assessment of Process Vessels in the Event of Hurricanes DOI: http://dx.doi.org/10.5772/intechopen.109430*

distributions of *S* and *h*, that is, *f <sup>S</sup>*ð Þ*S* and *f <sup>h</sup>*ð Þ *h* . Subsequently, the conditional probability table for node "Floatation" can readily be populated with 1s and 0s given Eq. (7), that is, 1 if S > ah + b, and 0 otherwise. Given the BN in **Figure 5**, the probability of floatation is estimated as 0.62, sufficiently close to the results obtained by solving the integrals analytically (Section 4.1) or numerically (Section 4.2).

While by increasing the resolution of nodes h and S (increasing their states) the calculated probability for the node Floatation can further be improved, such refinement comes at a substantially increased modeling time and effort. It is because the size of the conditional probability table for the node Floatation increases exponentially with the size of the probability tables (number of states) for nodes h and S.

Following the same procedure for the other failure modes, the final BN for assessing the combined failure probability can be developed as in **Figure 6**. In **Figure 6**, the nodes "V\_wind" and "V\_flood" denote the speed of wind and flood, respectively; "H\_ac" is the height of accumulated rainfall on the roof of storage tank; "Wind\_buckle" and "Flood\_buckle" represent shell buckling failure mode due to lateral forces of wind and flood, respectively; "Slide" denotes rigid sliding of the tank

#### **Figure 6.**

*Final BN for assessing the total failure probability considering all the failure modes [12].*


#### **Table 5.**

*A comparison between the discussed methodologies.*

due to lateral force of flood, and "Roof-sinking" denotes the failure mode due to accumulation of rainfall on the top.
