This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation.Taking the finite dement pair Q11/Q01×Q10 as an example, a new mixed finite element method (FEM)i...This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation.Taking the finite dement pair Q11/Q01×Q10 as an example, a new mixed finite element method (FEM)is established and the r-independent superclose results of the original variable u in Hi-norm and the flux variable q=-a(u)■u in L^2- norm are deduced (τ is the temporal partition parameter).A key to our analysis is all error splitting technique,with which the time-discrete and the spatial-discrete systems are constructed,respectively.For the first system,tile boundedness of the temporal errors are obtained.For the second system,the spatial superclose results are presented unconditionally.while the previous literature always only obtain the convergent estimates or require certain time step conditions.Finally,some numerical results are provided to confirm the theoretical analysis,and show the efficiency of the proposed method.展开更多
Based on the output-voltage error function, a novel time discrete modulation technique is proposed for matrix converters （MCs） and time-discrete difference equations of a MC circuit are derived. Switch states of MC ...Based on the output-voltage error function, a novel time discrete modulation technique is proposed for matrix converters （MCs） and time-discrete difference equations of a MC circuit are derived. Switch states of MC are obtained when the output voltage error function is minimized, thus the optimum combination of switch states is derived for the closed-loop control of MC. Meanwhile, advantages of the least calculation workload, the simple process, and the convenient for implementation are brought while switch states are described as space vectors in the α-β coordination system. Simulation and experimental results demonstrate the validity of the time-discrete modulation technique and the feasibility of the control approach.展开更多
In this paper,the unconditional error estimates are presented for the time-dependent Navier-Stokes equations by the bilinear-constant scheme.The corresponding optimal error estimates for the velocity and the pressure ...In this paper,the unconditional error estimates are presented for the time-dependent Navier-Stokes equations by the bilinear-constant scheme.The corresponding optimal error estimates for the velocity and the pressure are derived unconditionally,while the previous works require certain time-step restrictions.The analysis is based on an iterated time-discrete system,with which the error function is split into a temporal error and a spatial error.The τ-independent(τ is the time stepsize)error estimate between the numerical solution and the solution of the time-discrete system is proven by a rigorous analysis,which implies that the numerical solution in L^(∞)-norm is bounded.Thus optimal error estimates can be obtained in a traditional way.Numerical results are provided to confirm the theoretical analysis.展开更多
Recent advances in intelligent transportation system allow traffic safety studies to extend from historic data-based analyses to real-time applications. The study presents a new method to predict crash likelihood with...Recent advances in intelligent transportation system allow traffic safety studies to extend from historic data-based analyses to real-time applications. The study presents a new method to predict crash likelihood with traffic data collected by discrete loop detectors as well as the web-crawl weather data. Matched case-control method and support vector machines （SVMs） technique were employed to identify the risk status. The adaptive synthetic over-sampling technique was applied to solve the imbalanced dataset issues. Random forest technique was applied to select the contributing factors and avoid the over-fitting issues. The results indicate that the SVMs classifier could successfully classify 76.32% of the crashes on the test dataset and 87.52% of the crashes on the overall dataset, which were relatively satisfactory compared with the results of the previous studies. Compared with the SVMs classifier without the data, the SVMs classifier with the web-crawl weather data increased the crash prediction accuracy by 1.32% and decreased the false alarm rate by 1.72%, showing the potential value of the massive web weather data. Mean impact value method was employed to evaluate the variable effects, and the results are identical with the results of most of previous studies. The emerging technique based on the discrete traffic data and web weather data proves to be more applicable on real- time safety management on freeways.展开更多
This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an e...This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.展开更多
This paper deals with the initial-value problem of nonlinear evolution inclusions of the form dB（u）/dt ＋ A（u） f, v0 ∈ B（u）（0）, where the operator B is induced by a subgradient and A is pseudomonotone. Existe...This paper deals with the initial-value problem of nonlinear evolution inclusions of the form dB（u）/dt ＋ A（u） f, v0 ∈ B（u）（0）, where the operator B is induced by a subgradient and A is pseudomonotone. Existence theorem is established via the time discretization technique and the regularization method. In contrast to the previous results, here we impose a weaker coerciveness condition on A and remove the strong monotonicity from B.展开更多
基金Natural Science Foundation of China (Grant Nos.11671369,11271340).
文摘This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation.Taking the finite dement pair Q11/Q01×Q10 as an example, a new mixed finite element method (FEM)is established and the r-independent superclose results of the original variable u in Hi-norm and the flux variable q=-a(u)■u in L^2- norm are deduced (τ is the temporal partition parameter).A key to our analysis is all error splitting technique,with which the time-discrete and the spatial-discrete systems are constructed,respectively.For the first system,tile boundedness of the temporal errors are obtained.For the second system,the spatial superclose results are presented unconditionally.while the previous literature always only obtain the convergent estimates or require certain time step conditions.Finally,some numerical results are provided to confirm the theoretical analysis,and show the efficiency of the proposed method.
文摘Based on the output-voltage error function, a novel time discrete modulation technique is proposed for matrix converters （MCs） and time-discrete difference equations of a MC circuit are derived. Switch states of MC are obtained when the output voltage error function is minimized, thus the optimum combination of switch states is derived for the closed-loop control of MC. Meanwhile, advantages of the least calculation workload, the simple process, and the convenient for implementation are brought while switch states are described as space vectors in the α-β coordination system. Simulation and experimental results demonstrate the validity of the time-discrete modulation technique and the feasibility of the control approach.
基金supported by National Natural Science Foundation of China(No.11671369)the Doctoral Starting Foundation of Zhengzhou University of Aeronautics(No.63020390).
文摘In this paper,the unconditional error estimates are presented for the time-dependent Navier-Stokes equations by the bilinear-constant scheme.The corresponding optimal error estimates for the velocity and the pressure are derived unconditionally,while the previous works require certain time-step restrictions.The analysis is based on an iterated time-discrete system,with which the error function is split into a temporal error and a spatial error.The τ-independent(τ is the time stepsize)error estimate between the numerical solution and the solution of the time-discrete system is proven by a rigorous analysis,which implies that the numerical solution in L^(∞)-norm is bounded.Thus optimal error estimates can be obtained in a traditional way.Numerical results are provided to confirm the theoretical analysis.
基金supported by the National Natural Science Foundation (71301119)the Shanghai Natural Science Foundation (12ZR1434100)
文摘Recent advances in intelligent transportation system allow traffic safety studies to extend from historic data-based analyses to real-time applications. The study presents a new method to predict crash likelihood with traffic data collected by discrete loop detectors as well as the web-crawl weather data. Matched case-control method and support vector machines （SVMs） technique were employed to identify the risk status. The adaptive synthetic over-sampling technique was applied to solve the imbalanced dataset issues. Random forest technique was applied to select the contributing factors and avoid the over-fitting issues. The results indicate that the SVMs classifier could successfully classify 76.32% of the crashes on the test dataset and 87.52% of the crashes on the overall dataset, which were relatively satisfactory compared with the results of the previous studies. Compared with the SVMs classifier without the data, the SVMs classifier with the web-crawl weather data increased the crash prediction accuracy by 1.32% and decreased the false alarm rate by 1.72%, showing the potential value of the massive web weather data. Mean impact value method was employed to evaluate the variable effects, and the results are identical with the results of most of previous studies. The emerging technique based on the discrete traffic data and web weather data proves to be more applicable on real- time safety management on freeways.
文摘This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.
基金supported by NSFC (10971019)Scientific Research Fund of Guangxi Education Department (201012MS067)Hunan Provincial Innovation Foundation For Postgraduate (CX2010B117)
文摘This paper deals with the initial-value problem of nonlinear evolution inclusions of the form dB（u）/dt ＋ A（u） f, v0 ∈ B（u）（0）, where the operator B is induced by a subgradient and A is pseudomonotone. Existence theorem is established via the time discretization technique and the regularization method. In contrast to the previous results, here we impose a weaker coerciveness condition on A and remove the strong monotonicity from B.
