Keywords: premeditated destructive events, vulnerability, fuzzy set, fuzzy pair-wise comparison matrix, water treatment plant components, software.

The world in general and the engineering society in particular has realized the level of impact that a planned destructive event could cause. With recent events, the threat due to Premeditated Destructive Events (PDEs) has increased. Although the direct impact of these destructive events result in the loss of human lives, injuries and loss in infrastructure, the indirect impacts are equally appalling. They result in a dip in the country's economy, and have an everlasting psychological impact on the population. Evaluation of this impact aids the allocation of resources to the critical components to avoid or reduce the losses [1]. This paper is a study to evaluate the vulnerability of infrastructure systems to PDEs, with a focus on water treatment plants.

The choice of a water treatment plant to evaluate the impact of PDEs was based on a number of reasons. In the first place most of the water treatment plants in the United States were built at a time when such destructive events were unknown. Consequently they were not designed to resist such attacks. Secondly, water is a daily necessity to people. If the supply is disrupted it could at the very least, disrupt the daily routine of people, and could possibly result in widespread illness. This scenario excludes the possible loss of lives and destruction of the infrastructure. The possibility of occurrence of PDEs has necessitated the need for a model to evaluate the vulnerability of water treatment plant elements and to prioritize effective counter measures.

A fuzzy logic model using a fuzzy pair-wise comparison matrix based on fuzzy set theory has been developed and implemented as a software program to solve this problem. The model is based on gathering knowledge in the form of expert opinion from professionals as well as those involved in the design, construction and maintenance of water treatment plants. The objective of this study is to identify the vulnerable elements in a water treatment plant and automate the process of assessing their relative vulnerability. The authors have identified six such components namely, pre-treatment storage, water intake, primary treatment, chemical purification, post-treatment storage, and water distribution systems [2]. The model is limited in the sense that it does not consider the size of the population that the treatment plant is serving.

Fuzzy logic was used as it lends flexibility to the solution and provides a broader outlook to the end-user, and does not restrict his expertise to be stated in binary logic. Moreover, fuzzy logic can be used to extract information in the form of human knowledge which can then be converted to a form that can be electronically processed. Human knowledge implemented in this way is not limited by binary logic, and the intermediate values of significance can be implemented [2]. The construction of the fuzzy elements used in this project is based on Zadeh's fuzzy set concept. Relational words such as "much more", "more", "equally", "less" and "much less" were used, which were then quantified to produce practical results.

The model considers the severity of an undesired event resulting from a PDE and the likelihood that such an event might occur, the failure mode most likely to produce the undesired event, the component most likely to fail, and the relative cost of protecting components in a water treatment plant. These factors were developed as Fuzzy Pair Wise Comparison Matrices and the process of calculating their vulnerability and the ranking index values was automated using Visual Basic. The program prompts the user to enter the relative vulnerability of the water treatment plant components considered and gives the output in graphical format.

Based on the results of this research, suggestions could be made and incorporated in any new water treatment plant design. The model as well as the software developed can be extended to have application on any infrastructure system.

1

C.C. Hinds, W. Poteet, J.W. Duane, F.C. Hadipriono, P. Maughan, R. Nelson, "Failure of a Municipal Water Treatment Facility due to a Premeditated Destructive Event", Proceedings of the Seventh International Conference on the Application of Artificial Intelligence to Civil and Structural Engineering, Civil-Comp Press, Stirling, UK, 2003.

2

J.W. Duane, C.C. Tseng, F.C. Hadipriono, C.C. Hinds, T.I. Stewart, N.S. Al-Kaabi, "A Method for Capturing Knowledge of Vulnerability to Destructive Events", Proceedings of the Seventh International Conference on the Application of Artificial Intelligence to Civil and Structural Engineering, Civil-Comp Press, Stirling, UK, 2003. doi:10.4203/ccp.78.19

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