To assess the groundwater vulnerability due to leaching of chemicals, the groundwater system in the unsaturated zone is characterized by conceptual models that are further extended and refined with more detailed mathe...To assess the groundwater vulnerability due to leaching of chemicals, the groundwater system in the unsaturated zone is characterized by conceptual models that are further extended and refined with more detailed mathematical models to understand the governing physical processes in detail. However, due to lack of data and uncertainty level, an intermediate transition through index based models is researched. The attenuation factor (AF) approach, which works under the assumption that the chemicals degrade following a first-order kinetics and determines the fraction of the chemicals that goes to groundwater table, is one of the index based models that has been widely used due to its simplicity. Therefore, the objective of this paper is to review the research works done using the AF approach, to outline the future research needs. Furthermore, the mathematical implementation of the AF approach and the associated uncertainty levels is explained through an example and MATLAB source code.展开更多
An improved method using kernel density estimation (KDE) and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only smal...An improved method using kernel density estimation (KDE) and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only small samples can be used due to the high costs of experimental measurements. However, model validation provides more confidence for decision makers when improving prediction accuracy at the same time. The confidence level method is introduced and the optimum sample variance is determined using a new method in kernel density estimation to increase the credibility of model validation. As a numerical example, the static frame model validation challenge problem presented by Sandia National Laboratories has been chosen. The optimum bandwidth is selected in kernel density estimation in order to build the probability model based on the calibration data. The model assessment is achieved using validation and accreditation experimental data respectively based on the probability model. Finally, the target structure prediction is performed using validated model, which are consistent with the results obtained by other researchers. The results demonstrate that the method using the improved confidence level and kernel density estimation is an effective approach to solve the model validation problem with small samples.展开更多
文摘To assess the groundwater vulnerability due to leaching of chemicals, the groundwater system in the unsaturated zone is characterized by conceptual models that are further extended and refined with more detailed mathematical models to understand the governing physical processes in detail. However, due to lack of data and uncertainty level, an intermediate transition through index based models is researched. The attenuation factor (AF) approach, which works under the assumption that the chemicals degrade following a first-order kinetics and determines the fraction of the chemicals that goes to groundwater table, is one of the index based models that has been widely used due to its simplicity. Therefore, the objective of this paper is to review the research works done using the AF approach, to outline the future research needs. Furthermore, the mathematical implementation of the AF approach and the associated uncertainty levels is explained through an example and MATLAB source code.
基金Funding of Jiangsu Innovation Program for Graduate Education (CXZZ11_0193)NUAA Research Funding (NJ2010009)
文摘An improved method using kernel density estimation (KDE) and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only small samples can be used due to the high costs of experimental measurements. However, model validation provides more confidence for decision makers when improving prediction accuracy at the same time. The confidence level method is introduced and the optimum sample variance is determined using a new method in kernel density estimation to increase the credibility of model validation. As a numerical example, the static frame model validation challenge problem presented by Sandia National Laboratories has been chosen. The optimum bandwidth is selected in kernel density estimation in order to build the probability model based on the calibration data. The model assessment is achieved using validation and accreditation experimental data respectively based on the probability model. Finally, the target structure prediction is performed using validated model, which are consistent with the results obtained by other researchers. The results demonstrate that the method using the improved confidence level and kernel density estimation is an effective approach to solve the model validation problem with small samples.