Extension of Common Seismic Risk Evaluation Equations to be Applicable for Complex and Wise Systems

In this article, a uniform framework is presented that has the capability to be used in multi hazard risk evaluation, specifically seismic hazards and hazards related to wise threats. In this stream, first, common equations for seismic risk evaluation are completed in a more general pattern. The main novelty of this phase was providing the direct connection between every two parameters without any intervening third parameter. To show the performance of such re-derived equations, they are implemented on a sample case selected from petrochemical industry, where a vessel mounted on skirt is falling on a pipe rack. It is illustrated that traditional equations cannot predict complex risks like overturning of one equipment on another one. In spite of that, new proposed equations can simply include such irregular happenings and hence would provide more accurate risk estimates. In the next step, the state and wiseness parameters are added to the revised equations, introduced above, which adds the capability of applying these equations against wise threats. The wiseness parameters implemented in these equations are the knowledge of the owner about the asset, the knowledge of the owner about threats, the capability of owner to process the available knowledge and take preventive actions, the knowledge of wise threat about target asset, the knowledge of wise threat about attacking capabilities and at the wise threat ability to process the available knowledge and take offensive actions. In this part, again, the high flexibility and performance of new proposed equations is shown for different states of owner-attacker knowledge through several examples. These examples cover blind attack, wise attack, wise attacker against owner with restricted knowledge, wise attacker against owner with restricted processing and acting capabilities and, at last, attacker with restricted knowledge against wise owner. In the final step, the applicability of proposed equations for cases with dynamic variable states and dynamic owner-attacker knowledge levels are illustrated in an example. It is expressed that how dynamic parameters can be included, through revising probability distribution functions, in the proposed framework. It should be confirmed that the presented equations can be reduced to the traditional form which is common in current seismic risk evaluation practice. Also it should be mentioned that the above equations just form the basic framework in risk evaluation and in order to implement them in real cases, each term would need to be expanded to several new parts. Besides, the required probability distribution equations should be provided for every specific problem distinctly.