The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features becau...The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.展开更多
In high-resolution cone-beam computed tomography （CBCT） using the flat-panel detector, imperfect or defect detector elements cause ring artifacts due to the none-uniformity of their X-ray response. They often distur...In high-resolution cone-beam computed tomography （CBCT） using the flat-panel detector, imperfect or defect detector elements cause ring artifacts due to the none-uniformity of their X-ray response. They often disturb the image quality. A dedicated fitting correction method for high-resolution micro-CT is presented. The method converts each elementary X-ray response curve to an average one, and eliminates response inconsistency among pixels. Other factors of the method are discussed, such as the correction factor variability by different sampling frames and nonlinear factors over the whole spectrum. Results show that the noise and artifacts are both reduced in reconstructed images展开更多
With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion a...With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.展开更多
The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of t...The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.展开更多
Based on the structural characteristics of the double-differenced normal equation, a new method was proposed to resolve the ambiguity float solution through a selection of parameter weights to construct an appropriate...Based on the structural characteristics of the double-differenced normal equation, a new method was proposed to resolve the ambiguity float solution through a selection of parameter weights to construct an appropriate regularized matrix, and a singular decomposition method was used to generate regularization parameters. Numerical test results suggest that the regularized ambiguity float solution is more stable and reliable than the least-squares float solution. The mean square error matrix of the new method possesses a lower correlation than the variancecovariance matrix of the least-squares estimation. The size of the ambiguity search space is reduced and the search efficiency is improved. The success rate of the integer ambiguity searching process is improved significantly when the ambiguity resolution by using constraint equation method is used to determine the correct ambiguity integervector. The ambiguity resolution by using constraint equation method requires an initial input of the ambiguity float solution candidates which are obtained from the LAMBDA method in the new method. In addition, the observation time required to fix reliable integer ambiguities can he significantly reduced.展开更多
A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercriti...A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.展开更多
Principles of polynomial fitting zero offset profile are introduced, and a new polynomial fitting method, tbe time-amplitude dual fitting method, is developed. The method can be used to purify seismic waves and suppre...Principles of polynomial fitting zero offset profile are introduced, and a new polynomial fitting method, tbe time-amplitude dual fitting method, is developed. The method can be used to purify seismic waves and suppress multiples. The effect of suppressing multiples is compared with other multiple suppression methods.展开更多
Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of s...Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.展开更多
The optimal condition and its geometrical characters of the least square adjustment were proposed. Then the relation between the transformed surface and least squares was discussed. Based on the above, a non iterative...The optimal condition and its geometrical characters of the least square adjustment were proposed. Then the relation between the transformed surface and least squares was discussed. Based on the above, a non iterative method, called the fitting method of pseudo polynomial, was derived in detail. The final least squares solution can be determined with sufficient accuracy in a single step and is not attained by moving the initial point in the view of iteration. The accuracy of the solution relys wholly on the frequency of Taylor’s series. The example verifies the correctness and validness of the method. [展开更多
The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not...The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.展开更多
For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows....For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows.In this paper,a compact least-squares reconstruction method is proposed to calculate the gradients for the distribution of flow field variables approximation.The compactness of the new reconstruction method is reflected in the gradient calculation process.The geometries of the face-neighboring elements are no longer utilized,and the weighted average values at the centroid of the interfaces are used to calculate the gradients instead of the values at the centroid of the face-neighboring elements.Meanwhile,an exact Jacobian solving strategy is developed for implicit temporal discretization.The accurate processing of Jacobian matrix can extensively improve the invertibility of the Jacobian matrix and avoid introducing extra numerical errors.In addition,a modified Venkatakrishnan limiter is applied to deal with the shock which may appear in transonic flows and the applicability of the mentioned methods is enhanced further.The combination of the proposed methods makes the numerical simulations of turbulent flow converge rapidly and steadily with an adaptive increasing CFL number.The numerical results of several benchmarks indicate that the proposed methods perform well in terms of robustness,efficiency and accuracy,and have good application potential in turbulent flow simulations of complex configurations.展开更多
The Anjialing No. 1 Coal Mine in Shanxi Province, China, contains a complicated old goaf and an unknown water distribution that hold high potential for serious water hazards. Due to poor detection resolution, previous...The Anjialing No. 1 Coal Mine in Shanxi Province, China, contains a complicated old goaf and an unknown water distribution that hold high potential for serious water hazards. Due to poor detection resolution, previous attempts have failed to determine the scope of the old goal and the water distribution in the mine by separate use of various exploration methods such as seismic method, direct current resistivity, audio magnetotellurics, controlled-source audio-frequency magnetotellurics, and transient electromag-netics. To solve this difficult problem, a combination of the wide-field electromagnetic method and the flow field fitting method with three-dimensional resistivity data inversion was applied to determine the precise scope of the goal and the locations where water is present, and to identify the hydraulic con- nection between the water layers so as to provide reliable technical support for safe coal production. Reasonable results were achieved, with all these goals being met. As a result, a mining area of nearly 4 km^2 has been released for operation.展开更多
For physical ozone absorption without reaction,two parametric estimation methods,i.e.the common linear least square fitting and non-linear Simplex search methods,were applied,respectively,to determine the ozone mass t...For physical ozone absorption without reaction,two parametric estimation methods,i.e.the common linear least square fitting and non-linear Simplex search methods,were applied,respectively,to determine the ozone mass transfer coefficient during absorption and both methods give almost the same mass transfer coefficient.While for chemical absorption with ozone decomposition reaction,the common linear least square fitting method is not applicable for the evaluation of ozone mass transfer coefficient due to the difficulty of model linearization for describing ozone concentration dissolved in water.The nonlinear Simplex method obtains the mass transfer coefficient by minimizing the sum of the differences between the simulated and experimental ozone concentration during the whole absorption process,without the limitation of linear relationship between the dissolved ozone concentration and absorption time during the initial stage of absorption.Comparison of the ozone concentration profiles between the simulation and experimental data demonstrates that Simplex method may determine ozone mass transfer coefficient during absorption in an accurate and high efficiency way with wide applicability.展开更多
In order to rationally select the welding current of stainless steel during metal inert gas(MIG)welding,its welding current under different plate thicknesses was taken as the object of study.The scatter function provi...In order to rationally select the welding current of stainless steel during metal inert gas(MIG)welding,its welding current under different plate thicknesses was taken as the object of study.The scatter function provided by the data fitting software was used to draw scatter plots for the welding current data from two different sources,the polynomial fit(polyfit)function and the curve fitting toolbox were used to fit polynomial curves and perform optimality analysis on the fitted equations.Scatter plots and first-,second-,and third-order curve fitting equations for welding currents at different plate thicknesses were obtained,as well as curve equations for the optimum order of welding current data from two different sources.The results show that the optimization effect of the third-order curve is superior to that of the first-order and second-order curves.Finally,through the experiment,it is verified that the curve equation has some guiding significance in determining the welding current range of stainless steel MIG welding.展开更多
A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approxi...A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.展开更多
In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training ...In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training a Multilayer Perceptron(MLP)for generating reference sequence and Time of Flight(TOF)to the target,and deriving a system of linear algebraic equations for obtaining the initial costates.To overcome the challenge of generating training samples for the MLP,the backward generation method is proposed to obtain five different training databases.The training database and sample form are determined by analyzing the input and output correlation using the Pearson correlation coefficient.The best-performing MLP is obtained by analyzing the training results with various hyper-parameter combinations.A reference sequence starting from the initial states is obtained by integrating forward with the near-optimal control vector from the output of MLP.Finally,a system of linear algebraic equations for estimating the initial costates is derived using the reference sequence and the necessary conditions for optimality.Simulation results demonstrate that the proposed initial costates solver improves the convergence ratio and reduce the function calls of the shooting function.Furthermore,Monte-Carlo simulation illustrates that the initial costates solver is applicable to different initial velocities,demonstrating excellent generalization ability.展开更多
Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the mot...Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the motion, when a Lagrangian approach with the present curve-fitting method is applied, can be transformed into an easily solvable form of the system of nonlinear ordinary dif- ferential equations. The applicability of Bezier curves, B-spline, and Lagrange interpolating polyno- mials is investigated. Local Lagrange interpolating polynomials with a shift operator are proposed as the best selection for applications, since it provides superior system characteristics with minimum computing time, compared to other methods. In addition, the Gauss quadrature formula with local refinement strategy has been developed for an accurate prediction of the induced velocity computed with the line integration of the Biot-Savart law. Rotary-wing problems including a vortex ring problem are analyzed to show the efficiency, accuracy, and flexibility in the applications of the pro- posed method.展开更多
A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary ...A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.展开更多
In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the line...In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.展开更多
We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponent...We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.展开更多
基金This project is supported by Research Foundation for Doctoral Program of Higher Education, China (No.98033532)
文摘The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.
基金Supported by the National Basic Research Program of China ("973"Program)(2006CB601201)~~
文摘In high-resolution cone-beam computed tomography （CBCT） using the flat-panel detector, imperfect or defect detector elements cause ring artifacts due to the none-uniformity of their X-ray response. They often disturb the image quality. A dedicated fitting correction method for high-resolution micro-CT is presented. The method converts each elementary X-ray response curve to an average one, and eliminates response inconsistency among pixels. Other factors of the method are discussed, such as the correction factor variability by different sampling frames and nonlinear factors over the whole spectrum. Results show that the noise and artifacts are both reduced in reconstructed images
基金partially supported by the National Natural Science Foundation of China (No.41230318)
文摘With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.
文摘The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.
文摘Based on the structural characteristics of the double-differenced normal equation, a new method was proposed to resolve the ambiguity float solution through a selection of parameter weights to construct an appropriate regularized matrix, and a singular decomposition method was used to generate regularization parameters. Numerical test results suggest that the regularized ambiguity float solution is more stable and reliable than the least-squares float solution. The mean square error matrix of the new method possesses a lower correlation than the variancecovariance matrix of the least-squares estimation. The size of the ambiguity search space is reduced and the search efficiency is improved. The success rate of the integer ambiguity searching process is improved significantly when the ambiguity resolution by using constraint equation method is used to determine the correct ambiguity integervector. The ambiguity resolution by using constraint equation method requires an initial input of the ambiguity float solution candidates which are obtained from the LAMBDA method in the new method. In addition, the observation time required to fix reliable integer ambiguities can he significantly reduced.
基金the National Science Council ot Taiwan,China for funding this research(Project no.:NSC 94-2218-E-035-011)
文摘A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.
文摘Principles of polynomial fitting zero offset profile are introduced, and a new polynomial fitting method, tbe time-amplitude dual fitting method, is developed. The method can be used to purify seismic waves and suppress multiples. The effect of suppressing multiples is compared with other multiple suppression methods.
基金the National Science Council of Taiwan for funding this research (NSC 96-2221-E-019-061).
文摘Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.
文摘The optimal condition and its geometrical characters of the least square adjustment were proposed. Then the relation between the transformed surface and least squares was discussed. Based on the above, a non iterative method, called the fitting method of pseudo polynomial, was derived in detail. The final least squares solution can be determined with sufficient accuracy in a single step and is not attained by moving the initial point in the view of iteration. The accuracy of the solution relys wholly on the frequency of Taylor’s series. The example verifies the correctness and validness of the method. [
基金supported by the National Basic Research Program of China (2005CB321701)NSF of mathematics research special fund of Hebei Province(08M005)
文摘The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.
基金supported by the National Natural Science Foundation of China(Nos.11702329,12102247)the Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems,China(No.VATLAB-2021-01)。
文摘For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows.In this paper,a compact least-squares reconstruction method is proposed to calculate the gradients for the distribution of flow field variables approximation.The compactness of the new reconstruction method is reflected in the gradient calculation process.The geometries of the face-neighboring elements are no longer utilized,and the weighted average values at the centroid of the interfaces are used to calculate the gradients instead of the values at the centroid of the face-neighboring elements.Meanwhile,an exact Jacobian solving strategy is developed for implicit temporal discretization.The accurate processing of Jacobian matrix can extensively improve the invertibility of the Jacobian matrix and avoid introducing extra numerical errors.In addition,a modified Venkatakrishnan limiter is applied to deal with the shock which may appear in transonic flows and the applicability of the mentioned methods is enhanced further.The combination of the proposed methods makes the numerical simulations of turbulent flow converge rapidly and steadily with an adaptive increasing CFL number.The numerical results of several benchmarks indicate that the proposed methods perform well in terms of robustness,efficiency and accuracy,and have good application potential in turbulent flow simulations of complex configurations.
文摘The Anjialing No. 1 Coal Mine in Shanxi Province, China, contains a complicated old goaf and an unknown water distribution that hold high potential for serious water hazards. Due to poor detection resolution, previous attempts have failed to determine the scope of the old goal and the water distribution in the mine by separate use of various exploration methods such as seismic method, direct current resistivity, audio magnetotellurics, controlled-source audio-frequency magnetotellurics, and transient electromag-netics. To solve this difficult problem, a combination of the wide-field electromagnetic method and the flow field fitting method with three-dimensional resistivity data inversion was applied to determine the precise scope of the goal and the locations where water is present, and to identify the hydraulic con- nection between the water layers so as to provide reliable technical support for safe coal production. Reasonable results were achieved, with all these goals being met. As a result, a mining area of nearly 4 km^2 has been released for operation.
基金Project(2011467001)supported by the Ministry of Environment Protection of ChinaProject(2010DFB94130)supported by the Ministry of Science and Technology of China
文摘For physical ozone absorption without reaction,two parametric estimation methods,i.e.the common linear least square fitting and non-linear Simplex search methods,were applied,respectively,to determine the ozone mass transfer coefficient during absorption and both methods give almost the same mass transfer coefficient.While for chemical absorption with ozone decomposition reaction,the common linear least square fitting method is not applicable for the evaluation of ozone mass transfer coefficient due to the difficulty of model linearization for describing ozone concentration dissolved in water.The nonlinear Simplex method obtains the mass transfer coefficient by minimizing the sum of the differences between the simulated and experimental ozone concentration during the whole absorption process,without the limitation of linear relationship between the dissolved ozone concentration and absorption time during the initial stage of absorption.Comparison of the ozone concentration profiles between the simulation and experimental data demonstrates that Simplex method may determine ozone mass transfer coefficient during absorption in an accurate and high efficiency way with wide applicability.
基金supported by the National Natural Science Foundation of China(52301098)。
文摘In order to rationally select the welding current of stainless steel during metal inert gas(MIG)welding,its welding current under different plate thicknesses was taken as the object of study.The scatter function provided by the data fitting software was used to draw scatter plots for the welding current data from two different sources,the polynomial fit(polyfit)function and the curve fitting toolbox were used to fit polynomial curves and perform optimality analysis on the fitted equations.Scatter plots and first-,second-,and third-order curve fitting equations for welding currents at different plate thicknesses were obtained,as well as curve equations for the optimum order of welding current data from two different sources.The results show that the optimization effect of the third-order curve is superior to that of the first-order and second-order curves.Finally,through the experiment,it is verified that the curve equation has some guiding significance in determining the welding current range of stainless steel MIG welding.
文摘A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.
基金This study was funded by the National Natural Science Foundation of China(Nos.11972077 and 12272039).
文摘In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training a Multilayer Perceptron(MLP)for generating reference sequence and Time of Flight(TOF)to the target,and deriving a system of linear algebraic equations for obtaining the initial costates.To overcome the challenge of generating training samples for the MLP,the backward generation method is proposed to obtain five different training databases.The training database and sample form are determined by analyzing the input and output correlation using the Pearson correlation coefficient.The best-performing MLP is obtained by analyzing the training results with various hyper-parameter combinations.A reference sequence starting from the initial states is obtained by integrating forward with the near-optimal control vector from the output of MLP.Finally,a system of linear algebraic equations for estimating the initial costates is derived using the reference sequence and the necessary conditions for optimality.Simulation results demonstrate that the proposed initial costates solver improves the convergence ratio and reduce the function calls of the shooting function.Furthermore,Monte-Carlo simulation illustrates that the initial costates solver is applicable to different initial velocities,demonstrating excellent generalization ability.
基金supported by the EDISON Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Science,ICT and Future Planning(No.2011-0020560)
文摘Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the motion, when a Lagrangian approach with the present curve-fitting method is applied, can be transformed into an easily solvable form of the system of nonlinear ordinary dif- ferential equations. The applicability of Bezier curves, B-spline, and Lagrange interpolating polyno- mials is investigated. Local Lagrange interpolating polynomials with a shift operator are proposed as the best selection for applications, since it provides superior system characteristics with minimum computing time, compared to other methods. In addition, the Gauss quadrature formula with local refinement strategy has been developed for an accurate prediction of the induced velocity computed with the line integration of the Biot-Savart law. Rotary-wing problems including a vortex ring problem are analyzed to show the efficiency, accuracy, and flexibility in the applications of the pro- posed method.
文摘A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.
文摘In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.
基金The project supported by Liu Hui Applied Mathematics Center of Nankai University and 985 Education Development Plan of Tianjin University
文摘We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.
