This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either...This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.展开更多
The low-field nuclear magnetic resonance(NMR)technique has been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields.However,the speed and accuracy of the ex...The low-field nuclear magnetic resonance(NMR)technique has been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields.However,the speed and accuracy of the existing numerical inversion methods are still challenging due to the ill-posed nature of the first kind Fredholm integral equation and the contamination of the noises.This paper proposes a novel inversion algorithmto accelerate the convergence and enhance the precision using empirical truncated singular value decompositions(TSVD)and the linearized Bregman iteration.The L1 penalty term is applied to construct the objective function,and then the linearized Bregman iteration is utilized to obtain fast convergence.To reduce the complexity of the computation,empirical TSVD is proposed to compress the kernel matrix and determine the appropriate truncated position.This novel inversion method is validated using numerical simulations.The results indicate that the proposed novel method is significantly efficient and can achieve quick and effective data solutions with low signal-to-noise ratios.展开更多
The electronic density of states and band structures of doped and un-doped anatase TiO2 were studied by the Linearized Augmented Plane Wave method based on the density functional theory. The calculation shows that the...The electronic density of states and band structures of doped and un-doped anatase TiO2 were studied by the Linearized Augmented Plane Wave method based on the density functional theory. The calculation shows that the band structures of TiO2 crystals doped with transition metal atoms become narrower. Interesting, an excursion towards high energy level with increasing atomic number in the same element period could be observed after doping with transition metal atoms.展开更多
A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretizatio...A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming (P1)2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.展开更多
In order to design linear controller for nonlinear systems,a simple but efficient method of modeling a nonlinear system was proposed by means of multiple linearized models at different operating points in the entire r...In order to design linear controller for nonlinear systems,a simple but efficient method of modeling a nonlinear system was proposed by means of multiple linearized models at different operating points in the entire range of the expected changes of the operating points.The original nonlinear system was described by linear combination of these multiple linearized models,with the linear combination parameters being identified on line based on least squares method.Model Predictive Control,an optimization based technique,was used to design the linear controller.A sufficient condition for ensuring the existence of a linear controller for the original nonlinear system was also given.Good performance indicated by two simulated examples confirms the usefulness of the proposed method.展开更多
In this paper a linearized and unified yield crierion of metals is presented, which is in a form of a set of linear functions with two pararneters. The parameters are ex- pressed in terms of tension yield stress and ...In this paper a linearized and unified yield crierion of metals is presented, which is in a form of a set of linear functions with two pararneters. The parameters are ex- pressed in terms of tension yield stress and so-called “shear-stretch ratio” and can bereadily determined from experimental data. It is shown that in stress space the set of yield functions is a set of polygons with twelve edges located between the Tresca’s hexagon and twin-shear-stress hexagon ̄[1]. In this paper the present yield function isused to analyse the prestressiap loose running fit cylinders.展开更多
The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.
Steel catenary risers, (SCR) usually installed between seabed wellhead and floating platform are subjected to vortex shedding. These impose direct forces, hence cyclic stresses, and fatigue damage on the SCR. Riser fa...Steel catenary risers, (SCR) usually installed between seabed wellhead and floating platform are subjected to vortex shedding. These impose direct forces, hence cyclic stresses, and fatigue damage on the SCR. Riser failure has both economic and environmental consequences;hence the design life is usually greater than the field life, which is significantly reduced by vortex induced vibration (VIV). In this study, SCR and metOcean data from a field in Offshore Nigeria were substituted into linearized hydrodynamic models for simulations. The results showed that the hang off and touchdown regions were most susceptible to fatigue failure. Further analysis using Miner-Palm green models revealed that the fatigue life reduced from a design value of 20-years to 17.04-years, shortened by 2.96-years due to VIV. Furthermore, a maximum wave load of 5.154 kN was observed. The wave loads results corroborated with those obtained from finite element Orca Flex software, yielding a correlation coefficient of 0.975.展开更多
The Alternating Direction Multiplier Method (ADMM) is widely used in various fields, and different variables are customized in the literature for different application scenarios [1] [2] [3] [4]. Among them, the linear...The Alternating Direction Multiplier Method (ADMM) is widely used in various fields, and different variables are customized in the literature for different application scenarios [1] [2] [3] [4]. Among them, the linearized alternating direction multiplier method (LADMM) has received extensive attention because of its effectiveness and ease of implementation. This paper mainly discusses the application of ADMM in dictionary learning (non-convex problem). Many numerical experiments show that to achieve higher convergence accuracy, the convergence speed of ADMM is slower, especially near the optimal solution. Therefore, we introduce the linearized alternating direction multiplier method (LADMM) to accelerate the convergence speed of ADMM. Specifically, the problem is solved by linearizing the quadratic term of the subproblem, and the convergence of the algorithm is proved. Finally, there is a brief summary of the full text.展开更多
The paper is concerned with the problem of reduction of the general relativity theory to the Newton gravitation theory for a gravitation field with relatively low intensity. This problem is traditionally solved on the...The paper is concerned with the problem of reduction of the general relativity theory to the Newton gravitation theory for a gravitation field with relatively low intensity. This problem is traditionally solved on the basis of linearized equations of general relativity which, being matched to the Newton theory equations, allow us to link the classical gravitation constant with the constant entering the general relativity equations. Analysis of the linearized general relativity equations shows that it can be done only for empty space in which the energy tensor is zero. In solids, the set of linearized general relativity equations is not consistent and is not reduced to the Newton theory equations. Specific features of the problem are demonstrated with the spherically symmetric static problem of general relativity which has the closed-form solution.展开更多
A linearized rock physics inversion method is proposed to deal with two important issues, rock physical model and inversion algorithm, which restrict the accuracy of rock physics inversion. In this method, first, the ...A linearized rock physics inversion method is proposed to deal with two important issues, rock physical model and inversion algorithm, which restrict the accuracy of rock physics inversion. In this method, first, the complex rock physics model is expanded into Taylor series to get the first-order approximate expression of the inverse problem of rock physics;then the damped least square method is used to solve the linearized rock physics inverse problem directly to get the analytical solution of the rock physics inverse problem. This method does not need global optimization or random sampling, but directly calculates the inverse operation, with high computational efficiency. The theoretical model analysis shows that the linearized rock physical model can be used to approximate the complex rock physics model. The application of actual logging data and seismic data shows that the linearized rock physics inversion method can obtain accurate physical parameters. This method is suitable for linear or slightly non-linear rock physics model, but may not be suitable for highly non-linear rock physics model.展开更多
The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real applications.In the cases where subproblems do not have closed-for...The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real applications.In the cases where subproblems do not have closed-form solutions,e.g.,due to complex constraints,infeasible subsolvers are indispensable,giving rise to an infeasible inexact PALM(PALM-I).Numerous efforts have been devoted to analyzing the feasible PALM,while little attention has been paid to the PALM-I.The usage of the PALM-I thus lacks a theoretical guarantee.The essential difficulty of analysis consists in the objective value nonmonotonicity induced by the infeasibility.We study in the present work the convergence properties of the PALM-I.In particular,we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact criterion.Based upon these,we manage to establish the stationarity of any accumulation point,and moreover,show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz property.The prominent advantages of the PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3-dimensional anisotropic frictional contact.展开更多
We experimentally demonstrated the use of intelligent impairment equalization(IIE)for microwave downconversion link linearization in noncooperative systems.Such an equalizer is realized based on an artificial neural n...We experimentally demonstrated the use of intelligent impairment equalization(IIE)for microwave downconversion link linearization in noncooperative systems.Such an equalizer is realized based on an artificial neural network(ANN).Once the training process is completed,the inverse link transfer function can be determined.With the inverse transformation for the detected signal after transmission,the third-order intermodulation distortion components are suppressed significantly without requiring any prior information from an input RF signal.Furthermore,fast training speed is achieved,since the configuration of ANN-based equalizer is simple.Experimental results show that the spurious-free dynamic range of the proposed link is improved to 106.5 dB·Hz^(2/3),which is 11.3 dB higher than that of a link without IIE.Meanwhile,the training epochs reduce to only five,which has the potential to meet the practical engineering requirement.展开更多
When urban distribution systems are gradually modernized,the overhead lines are replaced by underground cables,whose shunt admittances can not be ignored.Traditional power flow(PF)model withπequivalent circuit shows ...When urban distribution systems are gradually modernized,the overhead lines are replaced by underground cables,whose shunt admittances can not be ignored.Traditional power flow(PF)model withπequivalent circuit shows non-convexity and long computing time,and most recently proposed linear PF models assume zero shunt elements.All of them are not suitable for fast calculation and optimization problems of modern distribution systems with non-negligible line shunts.Therefore,this paper proposes a linearized branch flow model considering line shunt(LBFS).The strength of LBFS lies in maintaining the linear structure and the convex nature after appropriately modeling theπequivalent circuit for network equipment like transformers.Simulation results show that the calculation accuracy in nodal voltage and branch current magnitudes is improved by considering shunt admittances.We show the application scope of LBFS by controlling the network voltages through a two-stage stochastic Volt/VAr control(VVC)problem with the uncertain active power output from renewable energy sources(RESs).Since LBFS results in a linear VVC program,the global solution is guaranteed.Case study exhibits that VVC framework can optimally dispatch the discrete control devices,viz.substation transformers and shunt capacitors,and also optimize the decision rules for real-time reactive power control of RES.Moreover,the computing efficiency is significantly improved compared with that of traditional VVC methods.展开更多
In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining ...In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining the Tweedie regression model involves training on a centralized dataset,when the data is provided by multiple parties,training a privacy-preserving Tweedie regression model without exchanging raw data becomes a challenge.To address this issue,this study introduces a novel vertical federated learning-based Tweedie regression algorithm for multi-party auto insurance rate setting in data silos.The algorithm can keep sensitive data locally and uses privacy-preserving techniques to achieve intersection operations between the two parties holding the data.After determining which entities are shared,the participants train the model locally using the shared entity data to obtain the local generalized linear model intermediate parameters.The homomorphic encryption algorithms are introduced to interact with and update the model intermediate parameters to collaboratively complete the joint training of the car insurance rate-setting model.Performance tests on two publicly available datasets show that the proposed federated Tweedie regression algorithm can effectively generate Tweedie regression models that leverage the value of data fromboth partieswithout exchanging data.The assessment results of the scheme approach those of the Tweedie regressionmodel learned fromcentralized data,and outperformthe Tweedie regressionmodel learned independently by a single party.展开更多
A 28/56 Gb/s NRZ/PAM-4 dual-mode transceiver(TRx)designed in a 28-nm complementary metal-oxide-semiconduc-tor(CMOS)process is presented in this article.A voltage-mode(VM)driver featuring a 4-tap reconfigurable feed-fo...A 28/56 Gb/s NRZ/PAM-4 dual-mode transceiver(TRx)designed in a 28-nm complementary metal-oxide-semiconduc-tor(CMOS)process is presented in this article.A voltage-mode(VM)driver featuring a 4-tap reconfigurable feed-forward equal-izer(FFE)is employed in the quarter-rate transmitter(TX).The half-rate receiver(RX)incorporates a continuous-time linear equal-izer(CTLE),a 3-stage high-speed slicer with multi-clock-phase sampling,and a clock and data recovery(CDR).The experimen-tal results show that the TRx operates at a maximum speed of 56 Gb/s with chip-on board(COB)assembly.The 28 Gb/s NRZ eye diagram shows a far-end vertical eye opening of 210 mV with an output amplitude of 351 mV single-ended and the 56 Gb/s PAM-4 eye diagram exhibits far-end eye opening of 33 mV(upper-eye),31 mV(mid-eye),and 28 mV(lower-eye)with an output amplitude of 353 mV single-ended.The recovered 14 GHz clock from the RX exhibits random jitter(RJ)of 469 fs and deterministic jitter(DJ)of 8.76 ps.The 875 Mb/s de-multiplexed data features 593 ps horizontal eye opening with 32.02 ps RJ,at bit-error rate(BER)of 10-5(0.53 UI).The power dissipation of TX and RX are 125 and 181.4 mW,respectively,from a 0.9-V sup-ply.展开更多
We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have...We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have demonstrated their superiority over their convex counterparts. The computational challenge lies in the fact that the proximal mapping associated with non-convex regularization is not easily obtained due to the imposed linear composition. Fortunately, the problem structure allows one to introduce an auxiliary variable and reformulate it as an optimization problem with linear constraints, which can be solved using the Linearized Alternating Direction Method of Multipliers (LADMM). Despite the success of LADMM in practice, it remains unknown whether LADMM is convergent in solving such non-convex compositely regularized optimizations. In this research, we first present a detailed convergence analysis of the LADMM algorithm for solving a non-convex compositely regularized optimization problem with a large class of non-convex penalties. Furthermore, we propose an Adaptive LADMM (AdaLADMM) algorithm with a line-search criterion. Experimental results on different genres of datasets validate the efficacy of the proposed algorithm.展开更多
Recently,many variational models involving high order derivatives have been widely used in image processing,because they can reduce staircase effects during noise elimination.However,it is very challenging to construc...Recently,many variational models involving high order derivatives have been widely used in image processing,because they can reduce staircase effects during noise elimination.However,it is very challenging to construct efficient algo-rithms to obtain the minimizers of original high order functionals.In this paper,we propose a new linearized augmented Lagrangian method for Euler’s elastica image denoising model.We detail the procedures of finding the saddle-points of the aug-mented Lagrangian functional.Instead of solving associated linear systems by FFTor linear iterative methods(e.g.,the Gauss-Seidel method),we adopt a linearized strat-egy to get an iteration sequence so as to reduce computational cost.In addition,we give some simple complexity analysis for the proposed method.Experimental results with comparison to the previous method are supplied to demonstrate the efficiency of the proposed method,and indicate that such a linearized augmented Lagrangian method is more suitable to deal with large-sized images.展开更多
The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representat...The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.展开更多
Many macroscopic equations are proposed to describe the rarefied gas dynamics beyond the Navier-Stokes level,either from the mesoscopic Boltzmann equation or some physical arguments,including(i)Burnett,Woods,super-Bur...Many macroscopic equations are proposed to describe the rarefied gas dynamics beyond the Navier-Stokes level,either from the mesoscopic Boltzmann equation or some physical arguments,including(i)Burnett,Woods,super-Burnett,augmented Burnett equations derived from the Chapman-Enskog expansion of the Boltzmann equation,(ii)Grad 13,regularized 13/26 moment equations,rational extended thermodynamics equations,and generalized hydrodynamic equations,where the velocity distribution function is expressed in terms of low-order moments and Hermite polynomials,and(iii)bi-velocity equations and“thermo-mechanically consistent"Burnett equations based on the argument of“volume diffusion”.This paper is dedicated to assess the accuracy of these macroscopic equations.We first consider the RayleighBrillouin scattering,where light is scattered by the density fluctuation in gas.In this specific problem macroscopic equations can be linearized and solutions can always be obtained,no matter whether they are stable or not.Moreover,the accuracy assessment is not contaminated by the gas-wall boundary condition in this periodic problem.Rayleigh-Brillouin spectra of the scattered light are calculated by solving the linearized macroscopic equations and compared to those from the linearized Boltzmann equation.We find that(i)the accuracy of Chapman-Enskog expansion does not always increase with the order of expansion,(ii)for the moment method,the more moments are included,the more accurate the results are,and(iii)macroscopic equations based on“volume diffusion"do not work well even when the Knudsen number is very small.Therefore,among about a dozen tested equations,the regularized 26 moment equations are the most accurate.However,for moderate and highly rarefied gas flows,huge number of moments should be included,as the convergence to true solutions is rather slow.The same conclusion is drawn from the problem of sound propagation between the transducer and receiver.This slow convergence of moment equations is due to the incapability of Hermite polynomials in the capturing of large discontinuities and rapid variations of the velocity distribution function.This study sheds some light on how to choose/develop macroscopic equations for rarefied gas dynamics.展开更多
基金supported by the NSF under Grant DMS-2208391sponsored by the NSF under Grant DMS-1753581.
文摘This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.
基金support by the National Nature Science Foundation of China(42174142)CNPC Innovation Found(2021DQ02-0402)National Key Foundation for Exploring Scientific Instrument of China(2013YQ170463).
文摘The low-field nuclear magnetic resonance(NMR)technique has been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields.However,the speed and accuracy of the existing numerical inversion methods are still challenging due to the ill-posed nature of the first kind Fredholm integral equation and the contamination of the noises.This paper proposes a novel inversion algorithmto accelerate the convergence and enhance the precision using empirical truncated singular value decompositions(TSVD)and the linearized Bregman iteration.The L1 penalty term is applied to construct the objective function,and then the linearized Bregman iteration is utilized to obtain fast convergence.To reduce the complexity of the computation,empirical TSVD is proposed to compress the kernel matrix and determine the appropriate truncated position.This novel inversion method is validated using numerical simulations.The results indicate that the proposed novel method is significantly efficient and can achieve quick and effective data solutions with low signal-to-noise ratios.
文摘The electronic density of states and band structures of doped and un-doped anatase TiO2 were studied by the Linearized Augmented Plane Wave method based on the density functional theory. The calculation shows that the band structures of TiO2 crystals doped with transition metal atoms become narrower. Interesting, an excursion towards high energy level with increasing atomic number in the same element period could be observed after doping with transition metal atoms.
基金supported by the National Natural Science Foundation of China(No.10771150)the National Basic Research Program of China(No.2005CB321701)+1 种基金the Program for New Century Excellent Talents in University(No.NCET-07-0584)the Natural Science Foundation of Sichuan Province(No.07ZB087)
文摘A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming (P1)2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.
文摘In order to design linear controller for nonlinear systems,a simple but efficient method of modeling a nonlinear system was proposed by means of multiple linearized models at different operating points in the entire range of the expected changes of the operating points.The original nonlinear system was described by linear combination of these multiple linearized models,with the linear combination parameters being identified on line based on least squares method.Model Predictive Control,an optimization based technique,was used to design the linear controller.A sufficient condition for ensuring the existence of a linear controller for the original nonlinear system was also given.Good performance indicated by two simulated examples confirms the usefulness of the proposed method.
文摘In this paper a linearized and unified yield crierion of metals is presented, which is in a form of a set of linear functions with two pararneters. The parameters are ex- pressed in terms of tension yield stress and so-called “shear-stretch ratio” and can bereadily determined from experimental data. It is shown that in stress space the set of yield functions is a set of polygons with twelve edges located between the Tresca’s hexagon and twin-shear-stress hexagon ̄[1]. In this paper the present yield function isused to analyse the prestressiap loose running fit cylinders.
文摘The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.
文摘Steel catenary risers, (SCR) usually installed between seabed wellhead and floating platform are subjected to vortex shedding. These impose direct forces, hence cyclic stresses, and fatigue damage on the SCR. Riser failure has both economic and environmental consequences;hence the design life is usually greater than the field life, which is significantly reduced by vortex induced vibration (VIV). In this study, SCR and metOcean data from a field in Offshore Nigeria were substituted into linearized hydrodynamic models for simulations. The results showed that the hang off and touchdown regions were most susceptible to fatigue failure. Further analysis using Miner-Palm green models revealed that the fatigue life reduced from a design value of 20-years to 17.04-years, shortened by 2.96-years due to VIV. Furthermore, a maximum wave load of 5.154 kN was observed. The wave loads results corroborated with those obtained from finite element Orca Flex software, yielding a correlation coefficient of 0.975.
文摘The Alternating Direction Multiplier Method (ADMM) is widely used in various fields, and different variables are customized in the literature for different application scenarios [1] [2] [3] [4]. Among them, the linearized alternating direction multiplier method (LADMM) has received extensive attention because of its effectiveness and ease of implementation. This paper mainly discusses the application of ADMM in dictionary learning (non-convex problem). Many numerical experiments show that to achieve higher convergence accuracy, the convergence speed of ADMM is slower, especially near the optimal solution. Therefore, we introduce the linearized alternating direction multiplier method (LADMM) to accelerate the convergence speed of ADMM. Specifically, the problem is solved by linearizing the quadratic term of the subproblem, and the convergence of the algorithm is proved. Finally, there is a brief summary of the full text.
文摘The paper is concerned with the problem of reduction of the general relativity theory to the Newton gravitation theory for a gravitation field with relatively low intensity. This problem is traditionally solved on the basis of linearized equations of general relativity which, being matched to the Newton theory equations, allow us to link the classical gravitation constant with the constant entering the general relativity equations. Analysis of the linearized general relativity equations shows that it can be done only for empty space in which the energy tensor is zero. In solids, the set of linearized general relativity equations is not consistent and is not reduced to the Newton theory equations. Specific features of the problem are demonstrated with the spherically symmetric static problem of general relativity which has the closed-form solution.
基金Supported by the China National Science and Technology Major Project(2017ZX05049-002,2016ZX05027004-001)the National Natural Science Foundation of China(41874146,41674130)+2 种基金Fundamental Research Funds for the Central University(18CX02061A)Innovative Fund Project of China National Petroleum Corporation(2016D-5007-0301)Scientific Research&Technology Development Project of China National Petroleum Corporation(2017D-3504).
文摘A linearized rock physics inversion method is proposed to deal with two important issues, rock physical model and inversion algorithm, which restrict the accuracy of rock physics inversion. In this method, first, the complex rock physics model is expanded into Taylor series to get the first-order approximate expression of the inverse problem of rock physics;then the damped least square method is used to solve the linearized rock physics inverse problem directly to get the analytical solution of the rock physics inverse problem. This method does not need global optimization or random sampling, but directly calculates the inverse operation, with high computational efficiency. The theoretical model analysis shows that the linearized rock physical model can be used to approximate the complex rock physics model. The application of actual logging data and seismic data shows that the linearized rock physics inversion method can obtain accurate physical parameters. This method is suitable for linear or slightly non-linear rock physics model, but may not be suitable for highly non-linear rock physics model.
基金supported by National Natural Science Foundation of China(Grant Nos.12125108,11971466,11991021,11991020,12021001 and 12288201)Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.ZDBS-LY-7022)CAS(the Chinese Academy of Sciences)AMSS(Academy of Mathematics and Systems Science)-PolyU(The Hong Kong Polytechnic University)Joint Laboratory of Applied Mathematics.
文摘The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real applications.In the cases where subproblems do not have closed-form solutions,e.g.,due to complex constraints,infeasible subsolvers are indispensable,giving rise to an infeasible inexact PALM(PALM-I).Numerous efforts have been devoted to analyzing the feasible PALM,while little attention has been paid to the PALM-I.The usage of the PALM-I thus lacks a theoretical guarantee.The essential difficulty of analysis consists in the objective value nonmonotonicity induced by the infeasibility.We study in the present work the convergence properties of the PALM-I.In particular,we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact criterion.Based upon these,we manage to establish the stationarity of any accumulation point,and moreover,show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz property.The prominent advantages of the PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3-dimensional anisotropic frictional contact.
基金supported in part by the National Key Research and Development Program of China(No.2018YFB2201702)the National Natural Science Foundation of China(Nos.U21A20507 and 62005228)the Fundamental Research Funds for the Central Universities(No.2682021CX050)。
文摘We experimentally demonstrated the use of intelligent impairment equalization(IIE)for microwave downconversion link linearization in noncooperative systems.Such an equalizer is realized based on an artificial neural network(ANN).Once the training process is completed,the inverse link transfer function can be determined.With the inverse transformation for the detected signal after transmission,the third-order intermodulation distortion components are suppressed significantly without requiring any prior information from an input RF signal.Furthermore,fast training speed is achieved,since the configuration of ANN-based equalizer is simple.Experimental results show that the spurious-free dynamic range of the proposed link is improved to 106.5 dB·Hz^(2/3),which is 11.3 dB higher than that of a link without IIE.Meanwhile,the training epochs reduce to only five,which has the potential to meet the practical engineering requirement.
基金supported in part by the National Natural Science Foundation of China(No.51977115)。
文摘When urban distribution systems are gradually modernized,the overhead lines are replaced by underground cables,whose shunt admittances can not be ignored.Traditional power flow(PF)model withπequivalent circuit shows non-convexity and long computing time,and most recently proposed linear PF models assume zero shunt elements.All of them are not suitable for fast calculation and optimization problems of modern distribution systems with non-negligible line shunts.Therefore,this paper proposes a linearized branch flow model considering line shunt(LBFS).The strength of LBFS lies in maintaining the linear structure and the convex nature after appropriately modeling theπequivalent circuit for network equipment like transformers.Simulation results show that the calculation accuracy in nodal voltage and branch current magnitudes is improved by considering shunt admittances.We show the application scope of LBFS by controlling the network voltages through a two-stage stochastic Volt/VAr control(VVC)problem with the uncertain active power output from renewable energy sources(RESs).Since LBFS results in a linear VVC program,the global solution is guaranteed.Case study exhibits that VVC framework can optimally dispatch the discrete control devices,viz.substation transformers and shunt capacitors,and also optimize the decision rules for real-time reactive power control of RES.Moreover,the computing efficiency is significantly improved compared with that of traditional VVC methods.
基金This research was funded by the National Natural Science Foundation of China(No.62272124)the National Key Research and Development Program of China(No.2022YFB2701401)+3 种基金Guizhou Province Science and Technology Plan Project(Grant Nos.Qiankehe Paltform Talent[2020]5017)The Research Project of Guizhou University for Talent Introduction(No.[2020]61)the Cultivation Project of Guizhou University(No.[2019]56)the Open Fund of Key Laboratory of Advanced Manufacturing Technology,Ministry of Education(GZUAMT2021KF[01]).
文摘In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining the Tweedie regression model involves training on a centralized dataset,when the data is provided by multiple parties,training a privacy-preserving Tweedie regression model without exchanging raw data becomes a challenge.To address this issue,this study introduces a novel vertical federated learning-based Tweedie regression algorithm for multi-party auto insurance rate setting in data silos.The algorithm can keep sensitive data locally and uses privacy-preserving techniques to achieve intersection operations between the two parties holding the data.After determining which entities are shared,the participants train the model locally using the shared entity data to obtain the local generalized linear model intermediate parameters.The homomorphic encryption algorithms are introduced to interact with and update the model intermediate parameters to collaboratively complete the joint training of the car insurance rate-setting model.Performance tests on two publicly available datasets show that the proposed federated Tweedie regression algorithm can effectively generate Tweedie regression models that leverage the value of data fromboth partieswithout exchanging data.The assessment results of the scheme approach those of the Tweedie regressionmodel learned fromcentralized data,and outperformthe Tweedie regressionmodel learned independently by a single party.
基金supported by National Natural Science Foundation of China under Grant 62174132the Fundamental Research Funds for Central Universities under Grant xzy022022060.
文摘A 28/56 Gb/s NRZ/PAM-4 dual-mode transceiver(TRx)designed in a 28-nm complementary metal-oxide-semiconduc-tor(CMOS)process is presented in this article.A voltage-mode(VM)driver featuring a 4-tap reconfigurable feed-forward equal-izer(FFE)is employed in the quarter-rate transmitter(TX).The half-rate receiver(RX)incorporates a continuous-time linear equal-izer(CTLE),a 3-stage high-speed slicer with multi-clock-phase sampling,and a clock and data recovery(CDR).The experimen-tal results show that the TRx operates at a maximum speed of 56 Gb/s with chip-on board(COB)assembly.The 28 Gb/s NRZ eye diagram shows a far-end vertical eye opening of 210 mV with an output amplitude of 351 mV single-ended and the 56 Gb/s PAM-4 eye diagram exhibits far-end eye opening of 33 mV(upper-eye),31 mV(mid-eye),and 28 mV(lower-eye)with an output amplitude of 353 mV single-ended.The recovered 14 GHz clock from the RX exhibits random jitter(RJ)of 469 fs and deterministic jitter(DJ)of 8.76 ps.The 875 Mb/s de-multiplexed data features 593 ps horizontal eye opening with 32.02 ps RJ,at bit-error rate(BER)of 10-5(0.53 UI).The power dissipation of TX and RX are 125 and 181.4 mW,respectively,from a 0.9-V sup-ply.
基金supported by the National Natural Science Foundation of China(Nos.61303264,61202482,and 61202488)Guangxi Cooperative Innovation Center of Cloud Computing and Big Data(No.YD16505)Distinguished Young Scientist Promotion of National University of Defense Technology
文摘We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have demonstrated their superiority over their convex counterparts. The computational challenge lies in the fact that the proximal mapping associated with non-convex regularization is not easily obtained due to the imposed linear composition. Fortunately, the problem structure allows one to introduce an auxiliary variable and reformulate it as an optimization problem with linear constraints, which can be solved using the Linearized Alternating Direction Method of Multipliers (LADMM). Despite the success of LADMM in practice, it remains unknown whether LADMM is convergent in solving such non-convex compositely regularized optimizations. In this research, we first present a detailed convergence analysis of the LADMM algorithm for solving a non-convex compositely regularized optimization problem with a large class of non-convex penalties. Furthermore, we propose an Adaptive LADMM (AdaLADMM) algorithm with a line-search criterion. Experimental results on different genres of datasets validate the efficacy of the proposed algorithm.
基金supported by the NNSF of China grants 11526110,11271069,61362036 and 61461032,the 863 Program of China grant 2015AA01A302the Open Research Fund of Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing(2016WICSIP013)the Youth Foundation of Nanchang Institute of Technology(2014KJ021).
文摘Recently,many variational models involving high order derivatives have been widely used in image processing,because they can reduce staircase effects during noise elimination.However,it is very challenging to construct efficient algo-rithms to obtain the minimizers of original high order functionals.In this paper,we propose a new linearized augmented Lagrangian method for Euler’s elastica image denoising model.We detail the procedures of finding the saddle-points of the aug-mented Lagrangian functional.Instead of solving associated linear systems by FFTor linear iterative methods(e.g.,the Gauss-Seidel method),we adopt a linearized strat-egy to get an iteration sequence so as to reduce computational cost.In addition,we give some simple complexity analysis for the proposed method.Experimental results with comparison to the previous method are supplied to demonstrate the efficiency of the proposed method,and indicate that such a linearized augmented Lagrangian method is more suitable to deal with large-sized images.
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.GRANT3862].
文摘The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.
文摘Many macroscopic equations are proposed to describe the rarefied gas dynamics beyond the Navier-Stokes level,either from the mesoscopic Boltzmann equation or some physical arguments,including(i)Burnett,Woods,super-Burnett,augmented Burnett equations derived from the Chapman-Enskog expansion of the Boltzmann equation,(ii)Grad 13,regularized 13/26 moment equations,rational extended thermodynamics equations,and generalized hydrodynamic equations,where the velocity distribution function is expressed in terms of low-order moments and Hermite polynomials,and(iii)bi-velocity equations and“thermo-mechanically consistent"Burnett equations based on the argument of“volume diffusion”.This paper is dedicated to assess the accuracy of these macroscopic equations.We first consider the RayleighBrillouin scattering,where light is scattered by the density fluctuation in gas.In this specific problem macroscopic equations can be linearized and solutions can always be obtained,no matter whether they are stable or not.Moreover,the accuracy assessment is not contaminated by the gas-wall boundary condition in this periodic problem.Rayleigh-Brillouin spectra of the scattered light are calculated by solving the linearized macroscopic equations and compared to those from the linearized Boltzmann equation.We find that(i)the accuracy of Chapman-Enskog expansion does not always increase with the order of expansion,(ii)for the moment method,the more moments are included,the more accurate the results are,and(iii)macroscopic equations based on“volume diffusion"do not work well even when the Knudsen number is very small.Therefore,among about a dozen tested equations,the regularized 26 moment equations are the most accurate.However,for moderate and highly rarefied gas flows,huge number of moments should be included,as the convergence to true solutions is rather slow.The same conclusion is drawn from the problem of sound propagation between the transducer and receiver.This slow convergence of moment equations is due to the incapability of Hermite polynomials in the capturing of large discontinuities and rapid variations of the velocity distribution function.This study sheds some light on how to choose/develop macroscopic equations for rarefied gas dynamics.