卡尔曼滤波方法在地下水污染源反演中的应用

Application of Kalman filter to identify the groundwater contaminant sources

采用卡尔曼滤波方法反演识别地下水污染源的个数和大概位置.借助一个假想算例,建立地下水系统水流和溶质运移模拟模型,利用灵敏度分析方法筛选出对模拟结果影响最大的参数作为随机变量,对该参数进行抽样,运用蒙特卡罗方法将抽样结果输入模拟模型,生成污染质浓度场.采用卡尔曼滤波方法构造迭代过程,逐个利用采样点处浓度的实测值不断更新综合浓度场.引入模糊集理论表示污染羽,对比综合污染羽和单个污染羽的模糊集来更新各潜在污染源的权重,根据潜在污染源权重大小和综合污染羽收敛形状判断真实污染源的个数和大概位置.算例结果表明:采用卡尔曼滤波方法可以成功反演识别出地下水污染中真实污染源的准确个数和大概位置;引入模糊集理论表示污染羽,通过对比综合污染羽和单个污染羽的模糊集,可以确定各潜在污染源的权重.

Kalman filter was used to identify the number and approximate location of groundwater contaminant sources.Based on a hypothetical example,a groundwater flow and transport simulation model was established.The parameter that had the greatest impact on the simulation results was selected as a random variable by sensitivity analysis method.Then it was sampled and the sampling results were input into the simulation model by Monte Carlo method to generate the contaminant concentration field.Kalman filter method was used to update the composite concentration field one by one by using the measured concentration values at the sampling point.The fuzzy set theory was introduced to represent the pollution plume,and the weight of each potential contaminant source was updated by comparing the fuzzy sets of composite plume and individual plume.The number and approximate location of the real contaminant sources were judged according to the weight of potential contaminant sources and the convergence shape of composite plume.The results showed that the Kalman filter method can successfully identify the exact number and approximate location of the real contaminant sources in groundwater pollution;the fuzzy set theory was introduced to represent the pollution plume,and the weight of each potential contaminant source can be determined by comparing the fuzzy sets of the composite plume and the individual plume.