Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, WB, 721302, India.
Deparment of Civil Engineering, Ramgarh Engineering College, Ramgarh, 825101, Jharkhand, India.
Environ Monit Assess. 2019 Apr 27;191(5):310. doi: 10.1007/s10661-019-7467-3.
In the present work, uncertainty-based dynamic sampling frameworks were tested for a sampling horizon with multiple time steps. Future concentration values were assumed as fuzzy numbers. Multiple realization-based simulations were used for generation of fuzzy numbers. The first framework considers fuzzy variance reduction. The second framework considers mass estimation error reduction with maximization of spatial coverage of the dynamic sampling network. It is a multi-objective optimization problem with a large number of objectives. In Dhar and Patil (2012), uncertainty-based optimal sampling design model was suggested using Nondominated Sorting Genetic Algorithm-II (NSGA-II) as its optimization algorithm. However, NSGA-II becomes computationally expensive while handling more than three objectives. We extend the previously suggested algorithm for multi-objective sampling network design problems based on NSGA-III framework. Two design frameworks were proposed: one incorporating a simulation model and a fuzzy covariance for minimizing the total contaminant-concentration variance and the other incorporating a simulation model and a fuzzy kriging model in conjunction with an optimization model to minimize the fuzzy mass estimation error and spatial coverage of spatiotemporal sampling locations. NSGA-III was used for solving the sampling network design model. Performances of the proposed frameworks were evaluated for two hypothetical illustrative examples. The results indicate that the proposed design frameworks perform satisfactorily under uncertain system conditions.
在本工作中，针对具有多个时间步长的采样范围，测试了基于不确定性的动态采样框架。未来的浓度值被假定为模糊数。基于多次实现的模拟用于生成模糊数。第一个框架考虑模糊方差减少。第二个框架考虑减少质量估计误差，并最大化动态采样网络的空间覆盖范围。这是一个具有大量目标的多目标优化问题。在 Dhar 和 Patil（2012）中，使用非支配排序遗传算法 II（NSGA-II）作为优化算法，提出了基于不确定性的最优采样设计模型。然而，当处理超过三个目标时，NSGA-II 的计算成本变得很高。我们扩展了之前基于 NSGA-III 框架提出的用于多目标采样网络设计问题的算法。提出了两种设计框架：一种结合了模拟模型和模糊协方差，以最小化总污染物浓度方差；另一种结合了模拟模型和模糊克里金模型以及优化模型，以最小化模糊质量估计误差和时空采样位置的空间覆盖范围。使用 NSGA-III 来求解采样网络设计模型。针对两个假设的示例对所提出的框架进行了性能评估。结果表明，在所提出的框架下，在不确定的系统条件下表现令人满意。
