Stochastic Design of Flood Control Systems; Uncertainty Propagation and Results Representation

The design and operation of flood control systems are always subjected to different uncertainties. In general, uncertainty occurs due to the inherent randomness of natural events (aleatory) or the lack of information (epistemic). In this paper, the optimal design of flood control levees was considered with respect to different types of uncertainties. For this purpose, a stochastic model was developed in which the hydrologic, hydraulic, geotechnical, and economic uncertainties were considered. The probability theory and the evidence theory were utilized along with the Monte Carlo simulation for quantifying the uncertainties. A computational strategy was developed based on the Latin hypercube sampling and Cholesky decomposition to propagate the uncertainties using the real and site-specific data of the Leaf River in Hattiesburg city, Mississippi, USA. Optimization models were solved using a differential evolutionary algorithm. While the deterministic case resulted from the single value for each output such as the total cost (10.36 × 105 $) and height of the levees (2.46 and 3.28 m, for left and right levees, respectively), the stochastic case results from multiple values or an interval for each output variable as a probability distribution such as CCDF or quantile curves and decision-makers could select the system layout based on their desire risk; for example, with 50% epistemic risk, the total cost of system with a 90% confidence interval falls within [12.09 × 105, 28.62 × 105] $, and a corresponding height of the left and right levees falls within [4.23, 4.73] m, and [4.12, 4.75] m, respectively. On the other hand, the belief and plausibility curves (CCBF and CCPF) in evidence theory provide lower and upper bounds of probabilities or equivalently lower and upper bounds of an output value with a given risk. For example, results showed that with 90% confidence interval, the total cost falls within [0.325 × 105, 3.75 × 105] $ and [14.13 × 105, 24.47 × 105] $ based on CCBF and CCPF, respectively. Several codes were developed for calculating the probability quantiles, PDF, CCDF, CCBF, and CCPF curves, and proper tables and charts to summarize the results. This study is an attempt to involve the several uncertainties in the design and analysis of flood control systems and it seems if appropriate methods and tools are used, this purpose can be achieved.