The time delay estimation (TDE) of two different received signals from the same source has attracted many interests of researchers in the field of signal processing. A method described for precisely estimating time de...The time delay estimation (TDE) of two different received signals from the same source has attracted many interests of researchers in the field of signal processing. A method described for precisely estimating time delay in this paper is based on the assumption that little priori knowledge on statistical characteristics is available for the received signals. The variance of the estimate is derived . The basic architecture of this method is to use the adaptive noise canceller, in the steady state , and to interpolate the weight coefficients by using a generalized quadratic interpolation matrix. The formula of the time delay estimation is presented . The method proposed by F.A. Reed is a special case of this method . The hardware implementation is much easier than that of the conventional time delay estimation method . The results of the system simulation and the experimental results at sea show a good agreement with the theoretical analysis.展开更多
In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model f...In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.展开更多
This paper provides a finite-difference discretization for the one-and two-dimensional tempered fractional Laplacian and solves the tempered fractional Poisson equation with homogeneous Dirichlet boundary conditions.T...This paper provides a finite-difference discretization for the one-and two-dimensional tempered fractional Laplacian and solves the tempered fractional Poisson equation with homogeneous Dirichlet boundary conditions.The main ideas are to,respectively,use linear and quadratic interpolations to approximate the singularity and non-singularity of the one-dimensional tempered fractional Laplacian and bilinear and biquadratic interpolations to the two-dimensional tempered fractional Laplacian.Then,we give the truncation errors and prove the convergence.Numerical experiments verify the convergence rates of the order O(h^2−2s).展开更多
Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial val...Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.展开更多
For a given set of data points in the plane, a new method is presented for computing a parameter value（knot） for each data point. Associated with each data point, a quadratic polynomial curve passing through three a...For a given set of data points in the plane, a new method is presented for computing a parameter value（knot） for each data point. Associated with each data point, a quadratic polynomial curve passing through three adjacent consecutive data points is constructed. The curve has one degree of freedom which can be used to optimize the shape of the curve. To obtain a better shape of the curve, the degree of freedom is determined by optimizing the bending and stretching energies of the curve so that variation of the curve is as small as possible. Between each pair of adjacent data points, two local knot intervals are constructed, and the final knot interval corresponding to these two points is determined by a combination of the two local knot intervals. Experiments show that the curves constructed using the knots by the new method generally have better interpolation precision than the ones constructed using the knots by the existing local methods.展开更多
In the framework of finite volume method(FVM),two modified schemes of quadratic upstream interpolation for convective kinematics(QUICK),namely quasi-QUICK(Q-QUICK) and normal quasi-QUICK(NQ-QUICK),for improving the pr...In the framework of finite volume method(FVM),two modified schemes of quadratic upstream interpolation for convective kinematics(QUICK),namely quasi-QUICK(Q-QUICK) and normal quasi-QUICK(NQ-QUICK),for improving the precision of convective flux approximation are verified in 3D unsteady advectiondiffusion equation of pollutants on unstructured grids.The constructed auxiliary nodes for Q-QUICK or NQQUICK are composed of two neighboring nodes plus the next upwind node;the later node is generated from intersection of the line of current neighboring nodes and their corresponding interfaces.The numerical results show that Q-QUICK and NQ-QUICK overwhelm central differencing scheme(CDS) in computational accuracy and behave similar numerical stability to upwind difference scheme(UDS),hybrid differencing scheme(HDS) and power difference scheme(PDS) after applying the deferred correction method.Their corresponding CPU time is approximately equivalent to that of traditional difference schemes.In addition,their abilities for adapting high grid deformation are robust.It is so promising to apply the suggested schemes to simulate pollutant transportation on arbitrary 3D natural boundary in the hydraulic or environmental engineering.展开更多
The Calculation of area and volume of B-rep solid is discussed, and a numerical method is presented. The method is based on the integrand simplification of the double integral by quadratic triangular Bezier interpolat...The Calculation of area and volume of B-rep solid is discussed, and a numerical method is presented. The method is based on the integrand simplification of the double integral by quadratic triangular Bezier interpolation.展开更多
The evolution of the overland flow velocity along the distance downslope on smooth and granular beds in different cases is investigated by means of the electrolyte tracer via flume experiments. The results demonstrate...The evolution of the overland flow velocity along the distance downslope on smooth and granular beds in different cases is investigated by means of the electrolyte tracer via flume experiments. The results demonstrate that a non-uniform flow regime and a uniform flow regime exist in the development process of the overland flow. Owing to the different attributes of beds＇ roughness, the position of those zones with different flow regimes varies correspondingly：（1） the overland flow on granular beds enters into the uniform regime much sooner, additionally, the roll waves tend to appear because of the presence of the proper flow resistance impa-rted by the roughness （coarse sands）, and large slopes （20o and 25o） which makes the flow velocities and depths to undulate spatially. Furthermore, the flow resistance of the overland flows with different roughness elements, that is the non-sands, the fine sands and the coarse sands, is calculated. A quadratic interpolation method of the third order accuracy is employed in the calculation of the longitu-dinal flow resistance. The results show that it is rational to use the bed slope to approximate the hydraulic energy slope over a rela-tive small roughness （the present roughness）, however on the other hand, if the mean flow velocities and depths rather than the local parameters are used to calculate the flow resistance, a considerable error will be induced within the non-uniform regime of the over-land flows, including the acceleration zone and the roll-wave zone.展开更多
Parameter estimation of the 2 R-1 C model is usually performed using iterative methods that require high-performance processing units.Consequently,there is a strong motivation to develop less time-consuming and more p...Parameter estimation of the 2 R-1 C model is usually performed using iterative methods that require high-performance processing units.Consequently,there is a strong motivation to develop less time-consuming and more power-efficient parameter estimation methods.Such low-complexity algorithms would be suitable for implementation in portable microcontroller-based devices.In this study,we propose the quadratic interpolation non-iterative parameter estimation(QINIPE)method,based on quadratic interpolation of the imaginary part of the measured impedance,which enables more accurate estimation of the characteristic frequency.The 2 R-1 C model parameters are subsequently calculated from the real and imaginary parts of the measured impedance using a set of closed-form expressions.Comparative analysis conducted on the impedance data of the 2 R-1 C model obtained in both simulation and measurements shows that the proposed QINIPE method reduces the number of required measurement points by 80%in comparison with our previously reported non-iterative parameter estimation(NIPE)method,while keeping the relative estimation error to less than 1%for all estimated parameters.Both non-iterative methods are implemented on a microcontroller-based device;the estimation accuracy,RAM,flash memory usage,and execution time are monitored.Experiments show that the QINIPE method slightly increases the execution time by 0.576 ms(about 6.7%),and requires 24%(1.2 KB)more flash memory and just 2.4%(32 bytes)more RAM in comparison to the NIPE method.However,the impedance root mean square errors(RMSEs)of the QINIPE method are decreased to 42.8%(for the real part)and 64.5%(for the imaginary part)of the corresponding RMSEs obtained using the NIPE method.Moreover,we compared the QINIPE and the complex nonlinear least squares(CNLS)estimation of the 2 R-1 C model parameters.The results obtained show that although the estimation accuracy of the QINIPE is somewhat lower than the estimation accuracy of the CNLS,it is still satisfactory for many practical purposes and its execution time reduces to1/45–1/30.展开更多
文摘The time delay estimation (TDE) of two different received signals from the same source has attracted many interests of researchers in the field of signal processing. A method described for precisely estimating time delay in this paper is based on the assumption that little priori knowledge on statistical characteristics is available for the received signals. The variance of the estimate is derived . The basic architecture of this method is to use the adaptive noise canceller, in the steady state , and to interpolate the weight coefficients by using a generalized quadratic interpolation matrix. The formula of the time delay estimation is presented . The method proposed by F.A. Reed is a special case of this method . The hardware implementation is much easier than that of the conventional time delay estimation method . The results of the system simulation and the experimental results at sea show a good agreement with the theoretical analysis.
基金This work was supported by the National Natural Science Foundation of China(10071037)
文摘In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.
基金the National Natural Science Foundation of China under Grant No.11671182the Fundamental Research Funds for the Central Universities under Grant No.lzujbky-2018-ot03.
文摘This paper provides a finite-difference discretization for the one-and two-dimensional tempered fractional Laplacian and solves the tempered fractional Poisson equation with homogeneous Dirichlet boundary conditions.The main ideas are to,respectively,use linear and quadratic interpolations to approximate the singularity and non-singularity of the one-dimensional tempered fractional Laplacian and bilinear and biquadratic interpolations to the two-dimensional tempered fractional Laplacian.Then,we give the truncation errors and prove the convergence.Numerical experiments verify the convergence rates of the order O(h^2−2s).
基金Supported by National Natural Science Foundation of China (10771063)the Doctor Programme of the National Education Committee (20050542006)
文摘Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.
基金Supported by the National Natural Science Foundation of China(61602277,61672327,61472227)the Shandong Provincial Natural Science Foundation,China(ZR2016FQ12)
文摘For a given set of data points in the plane, a new method is presented for computing a parameter value（knot） for each data point. Associated with each data point, a quadratic polynomial curve passing through three adjacent consecutive data points is constructed. The curve has one degree of freedom which can be used to optimize the shape of the curve. To obtain a better shape of the curve, the degree of freedom is determined by optimizing the bending and stretching energies of the curve so that variation of the curve is as small as possible. Between each pair of adjacent data points, two local knot intervals are constructed, and the final knot interval corresponding to these two points is determined by a combination of the two local knot intervals. Experiments show that the curves constructed using the knots by the new method generally have better interpolation precision than the ones constructed using the knots by the existing local methods.
基金the National Public Research Institutes for Basic Research and Development Operating Expenses Special Project (Nos.CKSF2010014/SL,YWF0905,CKSF2010011 and CKSF2012008/SL)the National Basic Research Program (973) of China(No.2007CB714106)
文摘In the framework of finite volume method(FVM),two modified schemes of quadratic upstream interpolation for convective kinematics(QUICK),namely quasi-QUICK(Q-QUICK) and normal quasi-QUICK(NQ-QUICK),for improving the precision of convective flux approximation are verified in 3D unsteady advectiondiffusion equation of pollutants on unstructured grids.The constructed auxiliary nodes for Q-QUICK or NQQUICK are composed of two neighboring nodes plus the next upwind node;the later node is generated from intersection of the line of current neighboring nodes and their corresponding interfaces.The numerical results show that Q-QUICK and NQ-QUICK overwhelm central differencing scheme(CDS) in computational accuracy and behave similar numerical stability to upwind difference scheme(UDS),hybrid differencing scheme(HDS) and power difference scheme(PDS) after applying the deferred correction method.Their corresponding CPU time is approximately equivalent to that of traditional difference schemes.In addition,their abilities for adapting high grid deformation are robust.It is so promising to apply the suggested schemes to simulate pollutant transportation on arbitrary 3D natural boundary in the hydraulic or environmental engineering.
文摘The Calculation of area and volume of B-rep solid is discussed, and a numerical method is presented. The method is based on the integrand simplification of the double integral by quadratic triangular Bezier interpolation.
基金Project supported by the National Natural Science Foundation of China(Grant No.41171016)
文摘The evolution of the overland flow velocity along the distance downslope on smooth and granular beds in different cases is investigated by means of the electrolyte tracer via flume experiments. The results demonstrate that a non-uniform flow regime and a uniform flow regime exist in the development process of the overland flow. Owing to the different attributes of beds＇ roughness, the position of those zones with different flow regimes varies correspondingly：（1） the overland flow on granular beds enters into the uniform regime much sooner, additionally, the roll waves tend to appear because of the presence of the proper flow resistance impa-rted by the roughness （coarse sands）, and large slopes （20o and 25o） which makes the flow velocities and depths to undulate spatially. Furthermore, the flow resistance of the overland flows with different roughness elements, that is the non-sands, the fine sands and the coarse sands, is calculated. A quadratic interpolation method of the third order accuracy is employed in the calculation of the longitu-dinal flow resistance. The results show that it is rational to use the bed slope to approximate the hydraulic energy slope over a rela-tive small roughness （the present roughness）, however on the other hand, if the mean flow velocities and depths rather than the local parameters are used to calculate the flow resistance, a considerable error will be induced within the non-uniform regime of the over-land flows, including the acceleration zone and the roll-wave zone.
基金Project supported by the Ministry of Science and Technology of the Republic of Srpska(No.19/6-020/961-143/18)the EU’s H2020 MSCA MEDLEM(No.690876).
文摘Parameter estimation of the 2 R-1 C model is usually performed using iterative methods that require high-performance processing units.Consequently,there is a strong motivation to develop less time-consuming and more power-efficient parameter estimation methods.Such low-complexity algorithms would be suitable for implementation in portable microcontroller-based devices.In this study,we propose the quadratic interpolation non-iterative parameter estimation(QINIPE)method,based on quadratic interpolation of the imaginary part of the measured impedance,which enables more accurate estimation of the characteristic frequency.The 2 R-1 C model parameters are subsequently calculated from the real and imaginary parts of the measured impedance using a set of closed-form expressions.Comparative analysis conducted on the impedance data of the 2 R-1 C model obtained in both simulation and measurements shows that the proposed QINIPE method reduces the number of required measurement points by 80%in comparison with our previously reported non-iterative parameter estimation(NIPE)method,while keeping the relative estimation error to less than 1%for all estimated parameters.Both non-iterative methods are implemented on a microcontroller-based device;the estimation accuracy,RAM,flash memory usage,and execution time are monitored.Experiments show that the QINIPE method slightly increases the execution time by 0.576 ms(about 6.7%),and requires 24%(1.2 KB)more flash memory and just 2.4%(32 bytes)more RAM in comparison to the NIPE method.However,the impedance root mean square errors(RMSEs)of the QINIPE method are decreased to 42.8%(for the real part)and 64.5%(for the imaginary part)of the corresponding RMSEs obtained using the NIPE method.Moreover,we compared the QINIPE and the complex nonlinear least squares(CNLS)estimation of the 2 R-1 C model parameters.The results obtained show that although the estimation accuracy of the QINIPE is somewhat lower than the estimation accuracy of the CNLS,it is still satisfactory for many practical purposes and its execution time reduces to1/45–1/30.
