Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studi...Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.展开更多
In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by ad...In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.展开更多
The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisi...The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisis(somemultipliers vanish identically). failing to achieve his aim. The crisis is caused by the fact that the Inultipliers are treatedas independent variables in the process of variatioll. but after identification they become functions of the originalindependent variables. To overcome it, a Inodified Lagrange multiplier method or semi-inverse method has beenproposed to deduce generalized varistional principles. Some e-camples are given to illustrate its convenience andeffectiveness of the novel method.展开更多
A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is refo...A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.展开更多
Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed ...Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.展开更多
In this paper, we consider the convergence of the generalized alternating direction method of multipliers（GADMM） for solving linearly constrained nonconvex minimization model whose objective contains coupled functio...In this paper, we consider the convergence of the generalized alternating direction method of multipliers（GADMM） for solving linearly constrained nonconvex minimization model whose objective contains coupled functions. Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality, we prove that the sequence generated by the GADMM converges to a critical point of the augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large. Moreover, we also present some sufficient conditions guaranteeing the sublinear and linear rate of convergence of the algorithm.展开更多
The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be ...The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.展开更多
The alternating direction method of multipliers(ADMM)is a widely used method for solving many convex minimization models arising in signal and image processing.In this paper,we propose an inertial ADMM for solving a t...The alternating direction method of multipliers(ADMM)is a widely used method for solving many convex minimization models arising in signal and image processing.In this paper,we propose an inertial ADMM for solving a two-block separable convex minimization problem with linear equality constraints.This algorithm is obtained by making use of the inertial Douglas-Rachford splitting algorithm to the corresponding dual of the primal problem.We study the convergence analysis of the proposed algorithm in infinite-dimensional Hilbert spaces.Furthermore,we apply the proposed algorithm on the robust principal component analysis problem and also compare it with other state-of-the-art algorithms.Numerical results demonstrate the advantage of the proposed algorithm.展开更多
This paper investigates the distributed model predictive control(MPC)problem of linear systems where the network topology is changeable by the way of inserting new subsystems,disconnecting existing subsystems,or merel...This paper investigates the distributed model predictive control(MPC)problem of linear systems where the network topology is changeable by the way of inserting new subsystems,disconnecting existing subsystems,or merely modifying the couplings between different subsystems.To equip live systems with a quick response ability when modifying network topology,while keeping a satisfactory dynamic performance,a novel reconfiguration control scheme based on the alternating direction method of multipliers(ADMM)is presented.In this scheme,the local controllers directly influenced by the structure realignment are redesigned in the reconfiguration control.Meanwhile,by employing the powerful ADMM algorithm,the iterative formulas for solving the reconfigured optimization problem are obtained,which significantly accelerate the computation speed and ensure a timely output of the reconfigured optimal control response.Ultimately,the presented reconfiguration scheme is applied to the level control of a benchmark four-tank plant to illustrate its effectiveness and main characteristics.展开更多
By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive...By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.展开更多
In this paper, a distributed algorithm is proposed to solve a kind of multi-objective optimization problem based on the alternating direction method of multipliers. Compared with the centralized algorithms, this algor...In this paper, a distributed algorithm is proposed to solve a kind of multi-objective optimization problem based on the alternating direction method of multipliers. Compared with the centralized algorithms, this algorithm does not need a central node. Therefore, it has the characteristics of low communication burden and high privacy. In addition, numerical experiments are provided to validate the effectiveness of the proposed algorithm.展开更多
This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the...This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the rigid structure is taken as ＂fictitious＂ fluid with zero strain rate. Both fluid and structure are described by velocity and pressure. The whole domain, including fluid region and structure region, is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh. However, to keep the structure＇ s rigid body shape and behavior, a rigid body constraint is enforced on the ＂fictitious＂ fluid domain by use of the Distributed Lagrange Multipher/Fictitious Domain （DLM/ FD） method which is originally introduced to solve particulate flow problems by Glowinski et al. For the verification of the model presented herein, a 2D numerical wave tank is established to simulate small amplitude wave propagations, and then numerical results are compared with analytical solutions. Finally, a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity.展开更多
In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although ...In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.展开更多
Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacemen...Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.展开更多
The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results.This situation occurs when the test modal model is incomplete,as is often the case in practi...The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results.This situation occurs when the test modal model is incomplete,as is often the case in practice.An improved optimal elemental method is presented that defines a new objective function,and as a byproduct,circumvents the need for mass normalized modal shapes,which are also not readily available in practice.To solve the group of nonlinear equations created by the improved optimal method,the Lagrange multiplier method and Matlab function fmincon are employed.To deal with actual complex structures, the float-encoding genetic algorithm(FGA)is introduced to enhance the capability of the improved method.Two examples,a 7- degree of freedom(DOF)mass-spring system and a 53-DOF planar frame,respectively,are updated using the improved method. The example results demonstrate the advantages of the improved method over existing optimal methods,and show that the genetic algorithm is an effective way to update the models used for actual complex structures.展开更多
This paper presents theoretical investigations of lattice Boltzmann method(LBM)to develop a completed LBM theory.Based on H-theorem with Lagrangian multiplier method,an amended theoretical equilibrium distribution fun...This paper presents theoretical investigations of lattice Boltzmann method(LBM)to develop a completed LBM theory.Based on H-theorem with Lagrangian multiplier method,an amended theoretical equilibrium distribution function(EDF)is derived,which modifies the current Maxwell–Boltzmann distribution(MBD)to include the total internal energy as its parameter.This modification allows the three conservation laws derived directly from lattice Boltzmann equation(LBE)without additional small-parameter expansions adopted in references.From this amended theoretical EDF,an improved LBM is developed,in which the total internal energy like the mass density and mean velocity is a new macroscopic variable to be updated for different times and cells during simulations.The developed method provides a means to consider external forces and energy generation sources as generalised forces in LBM simulations.The corresponding model and implementation process of the improved LBM are presented with its performance theoretically investigated.Analytically hand-workable examples are given to illustrate its applications and to confirm its validity.The paper will excite more researchers and scientists of this area to numerically practice the new theory and method dealing with complex physical problems,from which it is expected to further advance LBM benefiting science and engineering.展开更多
By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constra...By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.展开更多
This paper is a further study of two papers [1] and [2], which were related to Ill-Conditioned Load Flow Problems and were published by IEEE Trans. PAS. The authors of this paper have some different opinions, for exam...This paper is a further study of two papers [1] and [2], which were related to Ill-Conditioned Load Flow Problems and were published by IEEE Trans. PAS. The authors of this paper have some different opinions, for example, the 11-bus system is not an ill-conditioned system. In addition, a new approach to solve Load Flow Problems, E-ψtc, is introduced. It is an explicit method;solving linear equations is not needed. It can handle very tough and very large systems. The advantage of this method has been fully proved by two examples. The authors give this new method a detailed description of how to use it to solve Load Flow Problems and successfully apply it to the 43-bus and the 11-bus systems. The authors also propose a strategy to test the reliability, and by solving gradient equations, this new method can answer if the solution exists or not.展开更多
This paper aims to enhance the array Beamforming(BF) robustness by tackling issues related to BF weight state estimation encountered in Constant Modulus Blind Beamforming(CMBB). To achieve this, we introduce a novel a...This paper aims to enhance the array Beamforming(BF) robustness by tackling issues related to BF weight state estimation encountered in Constant Modulus Blind Beamforming(CMBB). To achieve this, we introduce a novel approach that incorporates an L1-regularizer term in BF weight state estimation. We start by explaining the CMBB formation mechanism under conditions where there is a mismatch in the far-field signal model. Subsequently, we reformulate the BF weight state estimation challenge using a method known as variable-splitting, turning it into a noise minimization problem. This problem combines both linear and nonlinear quadratic terms with an L1-regularizer that promotes the sparsity. The optimization strategy is based on a variable-splitting method, implemented using the Alternating Direction Method of Multipliers(ADMM). Furthermore, a variable-splitting framework is developed to enhance BF weight state estimation, employing a Kalman Smoother(KS) optimization algorithm. The approach integrates the Rauch-TungStriebel smoother to perform posterior-smoothing state estimation by leveraging prior data. We provide proof of convergence for both linear and nonlinear CMBB state estimation technology using the variable-splitting KS and the iterated extended Kalman smoother. Simulations corroborate our theoretical analysis, showing that the proposed method achieves robust stability and effective convergence, even when faced with signal model mismatches.展开更多
In this paper,we investigate the convergence of the generalized Bregman alternating direction method of multipliers(ADMM)for solving nonconvex separable problems with linear constraints.This algorithm relaxes the requ...In this paper,we investigate the convergence of the generalized Bregman alternating direction method of multipliers(ADMM)for solving nonconvex separable problems with linear constraints.This algorithm relaxes the requirement of global Lipschitz continuity of differentiable functions that is often seen in many researches,and it incorporates the acceleration technique of the proximal point algorithm(PPA).As a result,the scope of application of the algorithm is broadened and its performance is enhanced.Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality,we demonstrate that the iterative sequence generated by the algorithm converges to a critical point of its augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large.Finally,we analyze the convergence rate of the algorithm.展开更多
文摘Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.
基金Supported by National Natural Science Foundation of China (No.51275348)College Students Innovation and Entrepreneurship Training Program of Tianjin University (No.201210056339)
文摘In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.
文摘The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisis(somemultipliers vanish identically). failing to achieve his aim. The crisis is caused by the fact that the Inultipliers are treatedas independent variables in the process of variatioll. but after identification they become functions of the originalindependent variables. To overcome it, a Inodified Lagrange multiplier method or semi-inverse method has beenproposed to deduce generalized varistional principles. Some e-camples are given to illustrate its convenience andeffectiveness of the novel method.
基金The Scientific Research Foundation of Nanjing University of Posts and Telecommunications(No.NY210049)
文摘A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.
基金Supported by the National Natural Science Foundation of China(61203021)the Key Science and Technology Program of Liaoning Province(2011216011)+1 种基金the Natural Science Foundation of Liaoning Province(2013020024)the Program for Liaoning Excellent Talents in Universities(LJQ2015061)
文摘Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1157117811801455)the Fundamental Research Funds of China West Normal University(Grant No.17E084)
文摘In this paper, we consider the convergence of the generalized alternating direction method of multipliers（GADMM） for solving linearly constrained nonconvex minimization model whose objective contains coupled functions. Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality, we prove that the sequence generated by the GADMM converges to a critical point of the augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large. Moreover, we also present some sufficient conditions guaranteeing the sublinear and linear rate of convergence of the algorithm.
基金Supported by the National Natural Science Foundation of China(Grant No.11971149,11871381)Natural Science Foundation of Henan Province for Youth(Grant No.202300410146)。
文摘The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12061045,12061046,11661056,11771198,11771347,91730306,41390454,11401293)the China Postdoctoral Science Foundation(Grant No.2015M571989)the Jiangxi Province Postdoctoral Science Foundation(Grant No.2015KY51)。
文摘The alternating direction method of multipliers(ADMM)is a widely used method for solving many convex minimization models arising in signal and image processing.In this paper,we propose an inertial ADMM for solving a two-block separable convex minimization problem with linear equality constraints.This algorithm is obtained by making use of the inertial Douglas-Rachford splitting algorithm to the corresponding dual of the primal problem.We study the convergence analysis of the proposed algorithm in infinite-dimensional Hilbert spaces.Furthermore,we apply the proposed algorithm on the robust principal component analysis problem and also compare it with other state-of-the-art algorithms.Numerical results demonstrate the advantage of the proposed algorithm.
基金the National Natural Science Foundation of China(61833012,61773162,61590924)the Natural Science Foundation of Shanghai(18ZR1420000)。
文摘This paper investigates the distributed model predictive control(MPC)problem of linear systems where the network topology is changeable by the way of inserting new subsystems,disconnecting existing subsystems,or merely modifying the couplings between different subsystems.To equip live systems with a quick response ability when modifying network topology,while keeping a satisfactory dynamic performance,a novel reconfiguration control scheme based on the alternating direction method of multipliers(ADMM)is presented.In this scheme,the local controllers directly influenced by the structure realignment are redesigned in the reconfiguration control.Meanwhile,by employing the powerful ADMM algorithm,the iterative formulas for solving the reconfigured optimization problem are obtained,which significantly accelerate the computation speed and ensure a timely output of the reconfigured optimal control response.Ultimately,the presented reconfiguration scheme is applied to the level control of a benchmark four-tank plant to illustrate its effectiveness and main characteristics.
文摘By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.
文摘In this paper, a distributed algorithm is proposed to solve a kind of multi-objective optimization problem based on the alternating direction method of multipliers. Compared with the centralized algorithms, this algorithm does not need a central node. Therefore, it has the characteristics of low communication burden and high privacy. In addition, numerical experiments are provided to validate the effectiveness of the proposed algorithm.
基金This study is supported by the National Natural Science Foundation of China (Grant No50579046) the Science Foundation of Tianjin Municipal Commission of Science and Technology (Grant No043114711)
文摘This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the rigid structure is taken as ＂fictitious＂ fluid with zero strain rate. Both fluid and structure are described by velocity and pressure. The whole domain, including fluid region and structure region, is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh. However, to keep the structure＇ s rigid body shape and behavior, a rigid body constraint is enforced on the ＂fictitious＂ fluid domain by use of the Distributed Lagrange Multipher/Fictitious Domain （DLM/ FD） method which is originally introduced to solve particulate flow problems by Glowinski et al. For the verification of the model presented herein, a 2D numerical wave tank is established to simulate small amplitude wave propagations, and then numerical results are compared with analytical solutions. Finally, a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity.
基金Supported by National Natural Science Foundation of China (Grant Nos.52305127,52075414)China Postdoctoral Science Foundation (Grant No.2021M702595)。
文摘In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.
基金supported by the China Postdoctoral Science Foundation Funded Project (20080430038) the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (05004999200602)
文摘Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.
基金The China Hi-Tech R&D Program(863 Program) Project Number 2001AA602023
文摘The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results.This situation occurs when the test modal model is incomplete,as is often the case in practice.An improved optimal elemental method is presented that defines a new objective function,and as a byproduct,circumvents the need for mass normalized modal shapes,which are also not readily available in practice.To solve the group of nonlinear equations created by the improved optimal method,the Lagrange multiplier method and Matlab function fmincon are employed.To deal with actual complex structures, the float-encoding genetic algorithm(FGA)is introduced to enhance the capability of the improved method.Two examples,a 7- degree of freedom(DOF)mass-spring system and a 53-DOF planar frame,respectively,are updated using the improved method. The example results demonstrate the advantages of the improved method over existing optimal methods,and show that the genetic algorithm is an effective way to update the models used for actual complex structures.
基金The author acknowledges the School of Naval Architecture and Ocean Engineering,HUST,providing the finance support managed by Guoxiang Hou,enabling author to visit HUST to tackle LBM.Thanks also are given to Yuehong Qian of Soochow University for providing some references involved in the paper.
文摘This paper presents theoretical investigations of lattice Boltzmann method(LBM)to develop a completed LBM theory.Based on H-theorem with Lagrangian multiplier method,an amended theoretical equilibrium distribution function(EDF)is derived,which modifies the current Maxwell–Boltzmann distribution(MBD)to include the total internal energy as its parameter.This modification allows the three conservation laws derived directly from lattice Boltzmann equation(LBE)without additional small-parameter expansions adopted in references.From this amended theoretical EDF,an improved LBM is developed,in which the total internal energy like the mass density and mean velocity is a new macroscopic variable to be updated for different times and cells during simulations.The developed method provides a means to consider external forces and energy generation sources as generalised forces in LBM simulations.The corresponding model and implementation process of the improved LBM are presented with its performance theoretically investigated.Analytically hand-workable examples are given to illustrate its applications and to confirm its validity.The paper will excite more researchers and scientists of this area to numerically practice the new theory and method dealing with complex physical problems,from which it is expected to further advance LBM benefiting science and engineering.
文摘By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.
文摘This paper is a further study of two papers [1] and [2], which were related to Ill-Conditioned Load Flow Problems and were published by IEEE Trans. PAS. The authors of this paper have some different opinions, for example, the 11-bus system is not an ill-conditioned system. In addition, a new approach to solve Load Flow Problems, E-ψtc, is introduced. It is an explicit method;solving linear equations is not needed. It can handle very tough and very large systems. The advantage of this method has been fully proved by two examples. The authors give this new method a detailed description of how to use it to solve Load Flow Problems and successfully apply it to the 43-bus and the 11-bus systems. The authors also propose a strategy to test the reliability, and by solving gradient equations, this new method can answer if the solution exists or not.
基金supported in Natural Science Foundation of Shandong Province,China(ZR2013FM018)。
文摘This paper aims to enhance the array Beamforming(BF) robustness by tackling issues related to BF weight state estimation encountered in Constant Modulus Blind Beamforming(CMBB). To achieve this, we introduce a novel approach that incorporates an L1-regularizer term in BF weight state estimation. We start by explaining the CMBB formation mechanism under conditions where there is a mismatch in the far-field signal model. Subsequently, we reformulate the BF weight state estimation challenge using a method known as variable-splitting, turning it into a noise minimization problem. This problem combines both linear and nonlinear quadratic terms with an L1-regularizer that promotes the sparsity. The optimization strategy is based on a variable-splitting method, implemented using the Alternating Direction Method of Multipliers(ADMM). Furthermore, a variable-splitting framework is developed to enhance BF weight state estimation, employing a Kalman Smoother(KS) optimization algorithm. The approach integrates the Rauch-TungStriebel smoother to perform posterior-smoothing state estimation by leveraging prior data. We provide proof of convergence for both linear and nonlinear CMBB state estimation technology using the variable-splitting KS and the iterated extended Kalman smoother. Simulations corroborate our theoretical analysis, showing that the proposed method achieves robust stability and effective convergence, even when faced with signal model mismatches.
文摘In this paper,we investigate the convergence of the generalized Bregman alternating direction method of multipliers(ADMM)for solving nonconvex separable problems with linear constraints.This algorithm relaxes the requirement of global Lipschitz continuity of differentiable functions that is often seen in many researches,and it incorporates the acceleration technique of the proximal point algorithm(PPA).As a result,the scope of application of the algorithm is broadened and its performance is enhanced.Under the assumption that the augmented Lagrangian function satisfies the Kurdyka-Lojasiewicz inequality,we demonstrate that the iterative sequence generated by the algorithm converges to a critical point of its augmented Lagrangian function when the penalty parameter in the augmented Lagrangian function is sufficiently large.Finally,we analyze the convergence rate of the algorithm.
