# A Modeling of Human Reliability Analysis on Dam Failure Caused by Extreme Weather
## 4 Bayesian Network Construction
### Sensitivity Analysis  
The model is validated and analyzed, and its results can help us to identify the main root causes of failures in dam engineering, to reduce the risk and prevent accidents. Validation models can use sensitivity analysis, response analysis, external validation, and other methods. In the Bayesian network approach employed in reliability analysis, the validation methods for hardware and structure reliability are based on real data, simulated data and comparative modeling, while the validation methods for software reliability are based on real data and based on contrastive modeling. In contrast, when studying human reliability, since obtaining real or even simulated data is very difficult, validation is performed only using contrast-based modeling [45]. Since the dam safety field does not have as many pre-existing HRA analysis models as the nuclear power plant and maritime fields, the three principles proposed in the literature [38] are considered, which are:  
1. a small increase/decrease in the a priori subjective probability of each parent node should be matched by a corresponding increase/decrease in the posterior probability of the child nodes;
2. the impact of subjective probability changes of each parent node on the child nodes should remain the same;
3. the total magnitude of the impact of changes in the probability of x needs to be always larger than the ensemble x - y (y\(\in\)x). It is verified that the model satisfies these three axioms. Taking the node \"Operator Physiological Ability\", for example, when the positive status of its parent node \"Operator Physiological Age\" changes from 95% to 100%, the positive status of the child node changes from 86.0% to 87.3%. When the positive state of \"Organization Task allocation Staff assign\" also changes from 95% to 100%, the positive state of the child node changes to 88.7%. Also, when the positive state of \"Environment Engineering\" becomes 100%, it increases to 90%. By increasing each influence node, the posterior probability of the corresponding child node also appears to grow. The impact of each parent node remains consistent and meets the requirement. Through this approach, the model was validated. Sensitivity analysis is the process of assuming inaccurate node data, introducing changes into each node, and observing changes in the remaining nodes to understand the importance and interdependence of each node. In the process of risk evaluation and analysis, it is important to focus on preventing and controlling the obtained critical nodes in order to efficiently improve the reliability and reduce the probability of failure. The Entropy Reduction in the Shannon's Mutual Information measure [46] is used for sensitivity analysis. Also known as mutual information between two variables, it is the decrease in the expectation of its child node \(Q\) due to a change in the node \(F\). The entropy reduction takes values in the interval [0, \(H(Q)\)], and is 0 when \(Q\) is independent of \(F\). The calculation formula is as follows, and the result is \"bits\":  
\[I(Q,F)=H(Q)-H(Q|F)=\sum_{f\in Dom(F)}\ \sum_{q\in Dom(Q)}\Pr(q,f)\cdot\log_{2} \Bigl{[}\frac{\Pr(q,f)}{\Pr(q)\cdot\Pr(f)}\Bigr{]}, \tag{9}\]  
In Equation (9), \(Q\) is the query variable; \(F\) is the varying variable; q, f is a particular state of \(Q\) and \(F\), respectively; \(H(Q)=-\sum_{q\in Dom(Q)}\Pr(q)\cdot\log_{2}\Pr(q)\) is the entropy of variable \(Q\); \(H(Q|F)\) is the entropy reduction in \(Q\) given the state of \(F\); \(I(Q,F)\) is the entropy reduction in \(Q\) relative to \(F\). The idea implied in the formula is that the greater the entropy reduction in a child node caused by a change in the parent node, the greater the contribution of the parent node to it, for modeling Bayesian networks for dam failure accidents; that is, the PSF nodes with the greater influence on the final probability.