A major challenge of any optimization problem is to find the global optimum solution. In a multi-dimensional solution space which is highly non-linear, often the optimization algorithm gets trapped around some local o...A major challenge of any optimization problem is to find the global optimum solution. In a multi-dimensional solution space which is highly non-linear, often the optimization algorithm gets trapped around some local optima. Optimal Identification of unknown groundwater pollution sources poses similar challenges. Optimization based methodology is often applied to identify the unknown source characteristics such as location and flux release history over time, in a polluted aquifer. Optimization based models for identification of these characteristics of unknown ground-water pollution sources rely on comparing the simulated effects of candidate solutions to the observed effects in terms of pollutant concentration at specified sparse spatiotemporal locations. The optimization model minimizes the difference between the observed pollutant concentration measurements and simulated pollutant concentration measurements. This essentially constitutes the objective function of the optimization model. However, the mathematical formulation of the objective function can significantly affect the accuracy of the results by altering the response contour of the solution space. In this study, two separate mathematical formulations of the objective function are compared for accuracy, by incorporating different scenarios of unknown groundwater pollution source identification problem. Simulated Annealing (SA) is used as the solution algorithm for the optimization model. Different mathematical formulations of the objective function for minimizing the difference between the observed and simulated pollutant concentration measurements show different levels of accuracy in source identification results. These evaluation results demonstrate the impact of objective function formulation on the optimal identification, and provide a basis for choosing an appropriate mathematical formulation for unknown pollution source identification in contaminated aquifers.展开更多
An inverse problem of determining magnitude of groundwater pollution in a hydrologic region is investigated. By applying integral identity methods, a conditional stability for the inverse problem here is constructed w...An inverse problem of determining magnitude of groundwater pollution in a hydrologic region is investigated. By applying integral identity methods, a conditional stability for the inverse problem here is constructed with aids of an optimal adjoint problem and a suitable topology.展开更多
Source term identification is very important for the contaminant gas emission event. Thus, it is necessary to study the source parameter estimation method with high computation efficiency, high estimation accuracy and...Source term identification is very important for the contaminant gas emission event. Thus, it is necessary to study the source parameter estimation method with high computation efficiency, high estimation accuracy and reasonable confidence interval. Tikhonov regularization method is a potential good tool to identify the source parameters. However, it is invalid for nonlinear inverse problem like gas emission process. 2-step nonlinear and linear PSO （partial swarm optimization）-Tikhonov regularization method proposed previously have estimated the emission source parameters successfully. But there are still some problems in computation efficiency and confidence interval. Hence, a new 1-step nonlinear method combined Tikhonov regularizafion and PSO algorithm with nonlinear forward dispersion model was proposed. First, the method was tested with simulation and experiment cases. The test results showed that 1-step nonlinear hybrid method is able to estimate multiple source parameters with reasonable confidence interval. Then, the estimation performances of different methods were compared with different cases. The estimation values with 1-step nonlinear method were close to that with 2-step nonlinear and linear PSO-Tikhonov regularization method, 1-step nonlinear method even performs better than other two methods in some cases, especially for source strength and downwind distance estimation. Compared with 2-step nonlinear method, 1-step method has higher computation efficiency. On the other hand, the confidence intervals with the method proposed in this paper seem more reasonable than that with other two methods. Finally, single PSO algorithm was compared with 1-step nonlinear PSO-Tikhonov hybrid regularization method. The results showed that the skill scores of 1-step nonlinear hybrid method to estimate source parameters were close to that of single PSO method and even better in some cases. One more important property of 1-step nonlinear PSO-Tikhonov regularization method is its reasonable confidence interval, which is not obtained by single PSO algorithm. Therefore, 1-step nonlinear hybrid regularization method proposed in this paper is a potential good method to estimate contaminant gas emission source term.展开更多
Identification of the location and intensity of groundwater pollution source contributes to the effect of pollution remediation,and is called groundwater contaminant source identification.This is a kind of typical gro...Identification of the location and intensity of groundwater pollution source contributes to the effect of pollution remediation,and is called groundwater contaminant source identification.This is a kind of typical groundwater inverse problem,and the solution is usually ill-posed.Especially considering the spatial variability of hydraulic conductivity field,the identification process is more challenging.In this paper,the solution framework of groundwater contaminant source identification is composed with groundwater pollutant transport model(MT3DMS)and a data assimilation method(Iterative local update ensemble smoother,ILUES).In addition,Karhunen-Loève expansion technique is adopted as a PCA method to realize dimension reduction.In practical problems,the geostatistical method is usually used to characterize the hydraulic conductivity field,and only the contaminant source information is inversely calculated in the identification process.In this study,the identification of contaminant source information under Kriging K-field is compared with simultaneous identification of source information and K-field.The results indicate that it is necessary to carry out simultaneous identification under heterogeneous site,and ILUES has good performance in solving high-dimensional parameter inversion problems.展开更多
An inverse problem of determining the source term of the non-stationary transport equation was considered.The extra lateral boundary condition was chosen as the observation data.Based on a Carleman estimate on the non...An inverse problem of determining the source term of the non-stationary transport equation was considered.The extra lateral boundary condition was chosen as the observation data.Based on a Carleman estimate on the non-stationary transport equation,a global Lipschitz stability for the inverse problem was proved.展开更多
环境水力学系统存在诸多不确定性,如测量数据的不确定性等,这导致水体中污染源识别这一类反问题具有不适定性,尤其表现为反演结果的非唯一性。经典的正则化方法和最优化方法由于只能获得参数的"点估计",因而在求解不确定性较...环境水力学系统存在诸多不确定性,如测量数据的不确定性等,这导致水体中污染源识别这一类反问题具有不适定性,尤其表现为反演结果的非唯一性。经典的正则化方法和最优化方法由于只能获得参数的"点估计",因而在求解不确定性较强的问题时存在较大的困难。此外水质模型和流场控制方程(Navier-Stokes方程)耦合,使得正问题的解具有较强的非线性特征。为解决上述问题,针对水动力-水质耦合模型,建立了基于贝叶斯推理的污染物点源识别的数学模型,通过马尔科夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)后验抽样获得了污染源位置和强度的后验概率分布和估计量,较好地处理了模型的不确定性和非线性。算例结果表明,结合MCMC抽样的贝叶斯推理方法能很好地描述及求解水动力-水质耦合场条件下的污染源识别反问题。展开更多
文摘A major challenge of any optimization problem is to find the global optimum solution. In a multi-dimensional solution space which is highly non-linear, often the optimization algorithm gets trapped around some local optima. Optimal Identification of unknown groundwater pollution sources poses similar challenges. Optimization based methodology is often applied to identify the unknown source characteristics such as location and flux release history over time, in a polluted aquifer. Optimization based models for identification of these characteristics of unknown ground-water pollution sources rely on comparing the simulated effects of candidate solutions to the observed effects in terms of pollutant concentration at specified sparse spatiotemporal locations. The optimization model minimizes the difference between the observed pollutant concentration measurements and simulated pollutant concentration measurements. This essentially constitutes the objective function of the optimization model. However, the mathematical formulation of the objective function can significantly affect the accuracy of the results by altering the response contour of the solution space. In this study, two separate mathematical formulations of the objective function are compared for accuracy, by incorporating different scenarios of unknown groundwater pollution source identification problem. Simulated Annealing (SA) is used as the solution algorithm for the optimization model. Different mathematical formulations of the objective function for minimizing the difference between the observed and simulated pollutant concentration measurements show different levels of accuracy in source identification results. These evaluation results demonstrate the impact of objective function formulation on the optimal identification, and provide a basis for choosing an appropriate mathematical formulation for unknown pollution source identification in contaminated aquifers.
基金National Natural Science Foundation of China No. 10471080.
文摘An inverse problem of determining magnitude of groundwater pollution in a hydrologic region is investigated. By applying integral identity methods, a conditional stability for the inverse problem here is constructed with aids of an optimal adjoint problem and a suitable topology.
基金Supported by the National Natural Science Foundation of China(21676216)China Postdoctoral Science Foundation(2015M582667)+2 种基金Natural Science Basic Research Plan in Shaanxi Province of China(2016JQ5079)Key Research Project of Shaanxi Province(2015ZDXM-GY-115)the Fundamental Research Funds for the Central Universities(xjj2017124)
文摘Source term identification is very important for the contaminant gas emission event. Thus, it is necessary to study the source parameter estimation method with high computation efficiency, high estimation accuracy and reasonable confidence interval. Tikhonov regularization method is a potential good tool to identify the source parameters. However, it is invalid for nonlinear inverse problem like gas emission process. 2-step nonlinear and linear PSO （partial swarm optimization）-Tikhonov regularization method proposed previously have estimated the emission source parameters successfully. But there are still some problems in computation efficiency and confidence interval. Hence, a new 1-step nonlinear method combined Tikhonov regularizafion and PSO algorithm with nonlinear forward dispersion model was proposed. First, the method was tested with simulation and experiment cases. The test results showed that 1-step nonlinear hybrid method is able to estimate multiple source parameters with reasonable confidence interval. Then, the estimation performances of different methods were compared with different cases. The estimation values with 1-step nonlinear method were close to that with 2-step nonlinear and linear PSO-Tikhonov regularization method, 1-step nonlinear method even performs better than other two methods in some cases, especially for source strength and downwind distance estimation. Compared with 2-step nonlinear method, 1-step method has higher computation efficiency. On the other hand, the confidence intervals with the method proposed in this paper seem more reasonable than that with other two methods. Finally, single PSO algorithm was compared with 1-step nonlinear PSO-Tikhonov hybrid regularization method. The results showed that the skill scores of 1-step nonlinear hybrid method to estimate source parameters were close to that of single PSO method and even better in some cases. One more important property of 1-step nonlinear PSO-Tikhonov regularization method is its reasonable confidence interval, which is not obtained by single PSO algorithm. Therefore, 1-step nonlinear hybrid regularization method proposed in this paper is a potential good method to estimate contaminant gas emission source term.
基金supported by the Fundamental Research Funds for the Central Universities(No.22120190013)National Natural Science Foundation of China(No.41807187)
文摘Identification of the location and intensity of groundwater pollution source contributes to the effect of pollution remediation,and is called groundwater contaminant source identification.This is a kind of typical groundwater inverse problem,and the solution is usually ill-posed.Especially considering the spatial variability of hydraulic conductivity field,the identification process is more challenging.In this paper,the solution framework of groundwater contaminant source identification is composed with groundwater pollutant transport model(MT3DMS)and a data assimilation method(Iterative local update ensemble smoother,ILUES).In addition,Karhunen-Loève expansion technique is adopted as a PCA method to realize dimension reduction.In practical problems,the geostatistical method is usually used to characterize the hydraulic conductivity field,and only the contaminant source information is inversely calculated in the identification process.In this study,the identification of contaminant source information under Kriging K-field is compared with simultaneous identification of source information and K-field.The results indicate that it is necessary to carry out simultaneous identification under heterogeneous site,and ILUES has good performance in solving high-dimensional parameter inversion problems.
文摘An inverse problem of determining the source term of the non-stationary transport equation was considered.The extra lateral boundary condition was chosen as the observation data.Based on a Carleman estimate on the non-stationary transport equation,a global Lipschitz stability for the inverse problem was proved.
文摘环境水力学系统存在诸多不确定性,如测量数据的不确定性等,这导致水体中污染源识别这一类反问题具有不适定性,尤其表现为反演结果的非唯一性。经典的正则化方法和最优化方法由于只能获得参数的"点估计",因而在求解不确定性较强的问题时存在较大的困难。此外水质模型和流场控制方程(Navier-Stokes方程)耦合,使得正问题的解具有较强的非线性特征。为解决上述问题,针对水动力-水质耦合模型,建立了基于贝叶斯推理的污染物点源识别的数学模型,通过马尔科夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)后验抽样获得了污染源位置和强度的后验概率分布和估计量,较好地处理了模型的不确定性和非线性。算例结果表明,结合MCMC抽样的贝叶斯推理方法能很好地描述及求解水动力-水质耦合场条件下的污染源识别反问题。
