Consideration of Total Cost Uncertainty in Risk-based Flood Defense System Design

Abstract eng:
Flood defense infrastructural systems (e.g., levees, storm sewers, and reservoirs) are installed in natural environments subject to random floods. The ability of the system with a design flow carrying capacity cannot be expected to handle floods of all magnitudes at all times during its intended service period. When flood magnitude exceeds the capacity of the system, damage would occur. Since flood damage is a function of system's flow carrying capacity and random flood magnitude, the damage itself is a random variable. In the conventional risk-based design of hydro-infrastructural systems, only the annual expected damage is considered in the trade-off analysis with the system installation cost. Engineering designs in general involve choosing an alternative that is expected to yield the optimal outcome. However, due to the presence of uncertainties from various sources, the outcome of the design cannot be certain. In other word, there is always a likelihood that the chosen alternative would perform worse than a non-chosen one. This study proposes a framework of risk-based flood defense system design and evaluation based on the regret theory and the minimax principle. The risk measure of the expected opportunity loss (EOL) can explicitly quantify the adverse consequences under uncertain state of nature. This quantitative risk measure is conceptually compatible with the acceptable risk, and can capture the full probability features and the correlation effect of multiple alternative outcomes under consideration. The proposed risk-based design criterion is demonstrated through an example of flood defense planning study involving three alternatives for flood damage reduction. This example shows that the explicit consideration of tradeoffs between risk and failure consequences is important. Furthermore, numerical results also show that the uncertainty and correlation of the project net benefit could have a significant impact on the ranking and feasibility of design alternatives.

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