Characterizations of unknown groundwater pollution sources in terms of source location, source flux release history and sources activity initiation times, from sparse observation concentration measurements are a chall...Characterizations of unknown groundwater pollution sources in terms of source location, source flux release history and sources activity initiation times, from sparse observation concentration measurements are a challenging task. Optimization-based methods are often applied to solve groundwater pollution source characterization problem. These methods are effective only when the starting times of activity of the sources are precisely known, or the possible time window within which the sources activity actually start is known with a fair degree of certainty. However, in real life scenarios, the starting time of the activity of the sources is either unknown or can lie anywhere within a time window of years or decades. Absence of any prior information about the span of time window, within which the sources become active, makes existing source identification methodologies inefficient. As an alternative, an optimization-based source identification model is proposed, to simultaneously estimate source flux release history and sources activity initiation times. The method considers source flux release history and sources activity initiation times as explicit decision variables, optimally estimated by the decision model. Performance of the developed methodology is evaluated for an illustrative study area having multiple sources with different source activity initiation times, missing observation data and transient flow conditions. These evaluation results demonstrate the potential applicability of the proposed methodology and its capability to correctly estimate the unknown source flux releasing history and sources activity initiation times.展开更多
In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The centr...In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.展开更多
文摘Characterizations of unknown groundwater pollution sources in terms of source location, source flux release history and sources activity initiation times, from sparse observation concentration measurements are a challenging task. Optimization-based methods are often applied to solve groundwater pollution source characterization problem. These methods are effective only when the starting times of activity of the sources are precisely known, or the possible time window within which the sources activity actually start is known with a fair degree of certainty. However, in real life scenarios, the starting time of the activity of the sources is either unknown or can lie anywhere within a time window of years or decades. Absence of any prior information about the span of time window, within which the sources become active, makes existing source identification methodologies inefficient. As an alternative, an optimization-based source identification model is proposed, to simultaneously estimate source flux release history and sources activity initiation times. The method considers source flux release history and sources activity initiation times as explicit decision variables, optimally estimated by the decision model. Performance of the developed methodology is evaluated for an illustrative study area having multiple sources with different source activity initiation times, missing observation data and transient flow conditions. These evaluation results demonstrate the potential applicability of the proposed methodology and its capability to correctly estimate the unknown source flux releasing history and sources activity initiation times.
基金supported by National Natural Science Foundation of China (Grant Nos. 10731010, 10971012 and 11071015)
文摘In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.
