Nonlinear weighted feedback control of groundwater remediation under uncertainty
Nonlinear weighted feedback control of groundwater remediation under uncertainty
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不确定性下地下水修复的非线性加权反馈控制
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
C. Shoemaker
中科院分区：
文献类型：
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作者：
G. Whiffen;C. Shoemaker
利用微分动态规划方法计算了地下水修复中水泵的最优时变抽水策略和处理策略。由约束微分动态规划算法与惩罚函数产生的反馈法被用作反馈法的基础上测试的情况下，有不确定性的水力传导性。采用二维Galerkin隐式时间差分有限单元法模拟了承压含水层的非稳定渗流和输运。最优策略是使用给定的或“测量的”水力传导率和初始条件来计算的。使用具有第二组或“真实”电导率的相同有限元模型来应用最佳策略（有反馈和无反馈）。“真实”的电导率集随机产生的自相关对数正态分布的频谱方法。这里使用的方法比其他不确定性方法有优势，因为它是没有必要精确地指定哪些参数被认为是不确定的，哪些是确定的。也没有单一的概率分布需要假设每个不确定的参数。通过调整分配给每个罚函数的相对权重，得到了在9种不同假设误差分布下同样表现良好的鲁棒反馈律。在我们的示例中，精心设计的反馈策略的成本比在不使用反馈定律的情况下应用计算出的最佳策略的成本低4%到51%。
Differential dynamic programming is used to compute optimal time-varying pumping policies for a pump and treat strategy for groundwater remediation. The feedback law generated by a constrained differential dynamic programming algorithm with penalty functions is used as the basis of feedback laws tested in cases where there is uncertainty in the hydraulic conductivity. Confined transient aquifer flow and transport are modeled using a two-dimensional Galerkin finite element scheme with implicit time differencing. Optimal policies are calculated using a given or “measured” set of hydraulic conductivities and initial conditions. The optimal policies (with and without feedback) are applied using the same finite element model with a second or “true” set of conductivities. The “true” sets of conductivities are generated randomly from an autocorrelated lognormal distribution by the spectral method. The approach used here has an advantage over other uncertainty approaches because it is not necessary to specify precisely which parameters are considered uncertain and which are certain. Also no single probability distribution need be assumed for each uncertain parameter. By adjusting the relative weight assigned each penalty function, robust feedback laws were obtained that perform equally well under nine different assumed error distributions. In our examples, well-designed feedback policies cost between 4% and 51% less than the cost of applying the calculated optimal policies without using a feedback law.