Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A no...Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A novel class of correctors based on feedback-accelerated Picard iteration(FAPI)is proposed to further enhance computational performance.With optimal feedback terms that do not require inversion of matrices,significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts;however,the computational complexities are comparably low.These advantages enable nonlinear engineering problems to be solved quickly and accurately,even with rough initial guesses from elementary predictors.The proposed method offers flexibility,enabling the use of the generated correctors for either bulk processing of collocation nodes in a domain or successive corrections of a single node in a finite difference approach.In our method,the functional formulas of FAPI are discretized into numerical forms using the collocation approach.These collocated iteration formulas can directly solve nonlinear problems,but they may require significant computational resources because of the manipulation of high-dimensionalmatrices.To address this,the collocated iteration formulas are further converted into finite difference forms,enabling the design of lightweight predictor-corrector algorithms for real-time computation.The generality of the proposed method is illustrated by deriving new correctors for three commonly employed finite-difference approaches:the modified Euler approach,the Adams-Bashforth-Moulton approach,and the implicit Runge-Kutta approach.Subsequently,the updated approaches are tested in solving strongly nonlinear problems,including the Matthieu equation,the Duffing equation,and the low-earth-orbit tracking problem.The numerical findings confirm the computational accuracy and efficiency of the derived predictor-corrector algorithms.展开更多
Mathematical physics equations are often utilized to describe physical phenomena in various fields of science and engineering.One such equation is the Fourier equation,which is a commonly used and effective method for...Mathematical physics equations are often utilized to describe physical phenomena in various fields of science and engineering.One such equation is the Fourier equation,which is a commonly used and effective method for evaluating the effectiveness of temperature control measures for mass concrete.One important measure for temperature control in mass concrete is the use of cooling water pipes.However,the mismatch of grids between large-scale concrete models and small-scale cooling pipe models can result in a significant waste of calculation time when using the finite element method.Moreover,the temperature of the water in the cooling pipe needs to be iteratively calculated during the thermal transfer process.The substructure method can effectively solve this problem,and it has been validated by scholars.The Abaqus/Python secondary development technology provides engineers with enough flexibility to combine the substructure method with an iteration algorithm,which enables the creation of a parametric modeling calculation for cooling water pipes.This paper proposes such a method,which involves iterating the water pipe boundary and establishing the water pipe unit substructure to numerically simulate the concrete temperature field that contains a cooling water pipe.To verify the feasibility and accuracy of the proposed method,two classic numerical examples were analyzed.The results showed that this method has good applicability in cooling pipe calculations.When the value of the iteration parameterαis 0.4,the boundary temperature of the cooling water pipes can meet the accuracy requirements after 4∼5 iterations,effectively improving the computational efficiency.Overall,this approach provides a useful tool for engineers to analyze the temperature control measures accurately and efficiently for mass concrete,such as cooling water pipes,using Abaqus/Python secondary development.展开更多
This paper presents a novel cooperative value iteration(VI)-based adaptive dynamic programming method for multi-player differential game models with a convergence proof.The players are divided into two groups in the l...This paper presents a novel cooperative value iteration(VI)-based adaptive dynamic programming method for multi-player differential game models with a convergence proof.The players are divided into two groups in the learning process and adapt their policies sequentially.Our method removes the dependence of admissible initial policies,which is one of the main drawbacks of the PI-based frameworks.Furthermore,this algorithm enables the players to adapt their control policies without full knowledge of others’ system parameters or control laws.The efficacy of our method is illustrated by three examples.展开更多
Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyc...Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.展开更多
The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this ...The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.展开更多
Aimed at infinite horizon optimal control problems of discrete time-varying nonlinear systems,in this paper,a new iterative adaptive dynamic programming algorithm,which is the discrete-time time-varying policy iterati...Aimed at infinite horizon optimal control problems of discrete time-varying nonlinear systems,in this paper,a new iterative adaptive dynamic programming algorithm,which is the discrete-time time-varying policy iteration(DTTV)algorithm,is developed.The iterative control law is designed to update the iterative value function which approximates the index function of optimal performance.The admissibility of the iterative control law is analyzed.The results show that the iterative value function is non-increasingly convergent to the Bellman-equation optimal solution.To implement the algorithm,neural networks are employed and a new implementation structure is established,which avoids solving the generalized Bellman equation in each iteration.Finally,the optimal control laws for torsional pendulum and inverted pendulum systems are obtained by using the DTTV policy iteration algorithm,where the mass and pendulum bar length are permitted to be time-varying parameters.The effectiveness of the developed method is illustrated by numerical results and comparisons.展开更多
For linear time varying(LTV)multiple input multiple output(MIMO)systems with vector relative degree,an open‐closed‐loop iterative learning control(ILC)strategy is developed in this article,where the time interval of...For linear time varying(LTV)multiple input multiple output(MIMO)systems with vector relative degree,an open‐closed‐loop iterative learning control(ILC)strategy is developed in this article,where the time interval of operation is iteration dependent.To compensate the missing tracking signal caused by iteration dependent interval,the feedback control is introduced in ILC design.As the tracking signal of many continuous iterations is lost in a certain interval,the feedback control part can employ the tracking signal of current iteration for compensation.Under the assumption that the initial state vibrates around the desired initial state uniformly in mathematical expectation sense,the expectation of ILC tracking error can converge to zero as the number of iteration tends to infinity.Under the circumstance that the initial state varies around the desired initial state with a bound,as the number of iteration tends to infinity,the expectation of ILC tracking error can be driven to a bounded range,whose upper bound is proportional to the fluctuation.It is revealed that the convergence condition is dependent on the feed-forward control gains,while the feedback control can accelerate convergence speed by selecting appropriate feedback control gains.As a special case,the controlled system with integrated high relative degree is also addressed by proposing a simplified iteration dependent interval based open‐closed‐loop ILC method.Finally,the effectiveness of the developed iteration dependent interval based open‐closed‐loop ILC is illustrated by a simulation example with two cases on initial state.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
In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the inte...In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.展开更多
基金work is supported by the Fundamental Research Funds for the Central Universities(No.3102019HTQD014)of Northwestern Polytechnical UniversityFunding of National Key Laboratory of Astronautical Flight DynamicsYoung Talent Support Project of Shaanxi State.
文摘Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A novel class of correctors based on feedback-accelerated Picard iteration(FAPI)is proposed to further enhance computational performance.With optimal feedback terms that do not require inversion of matrices,significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts;however,the computational complexities are comparably low.These advantages enable nonlinear engineering problems to be solved quickly and accurately,even with rough initial guesses from elementary predictors.The proposed method offers flexibility,enabling the use of the generated correctors for either bulk processing of collocation nodes in a domain or successive corrections of a single node in a finite difference approach.In our method,the functional formulas of FAPI are discretized into numerical forms using the collocation approach.These collocated iteration formulas can directly solve nonlinear problems,but they may require significant computational resources because of the manipulation of high-dimensionalmatrices.To address this,the collocated iteration formulas are further converted into finite difference forms,enabling the design of lightweight predictor-corrector algorithms for real-time computation.The generality of the proposed method is illustrated by deriving new correctors for three commonly employed finite-difference approaches:the modified Euler approach,the Adams-Bashforth-Moulton approach,and the implicit Runge-Kutta approach.Subsequently,the updated approaches are tested in solving strongly nonlinear problems,including the Matthieu equation,the Duffing equation,and the low-earth-orbit tracking problem.The numerical findings confirm the computational accuracy and efficiency of the derived predictor-corrector algorithms.
文摘Mathematical physics equations are often utilized to describe physical phenomena in various fields of science and engineering.One such equation is the Fourier equation,which is a commonly used and effective method for evaluating the effectiveness of temperature control measures for mass concrete.One important measure for temperature control in mass concrete is the use of cooling water pipes.However,the mismatch of grids between large-scale concrete models and small-scale cooling pipe models can result in a significant waste of calculation time when using the finite element method.Moreover,the temperature of the water in the cooling pipe needs to be iteratively calculated during the thermal transfer process.The substructure method can effectively solve this problem,and it has been validated by scholars.The Abaqus/Python secondary development technology provides engineers with enough flexibility to combine the substructure method with an iteration algorithm,which enables the creation of a parametric modeling calculation for cooling water pipes.This paper proposes such a method,which involves iterating the water pipe boundary and establishing the water pipe unit substructure to numerically simulate the concrete temperature field that contains a cooling water pipe.To verify the feasibility and accuracy of the proposed method,two classic numerical examples were analyzed.The results showed that this method has good applicability in cooling pipe calculations.When the value of the iteration parameterαis 0.4,the boundary temperature of the cooling water pipes can meet the accuracy requirements after 4∼5 iterations,effectively improving the computational efficiency.Overall,this approach provides a useful tool for engineers to analyze the temperature control measures accurately and efficiently for mass concrete,such as cooling water pipes,using Abaqus/Python secondary development.
基金supported by the Industry-University-Research Cooperation Fund Project of the Eighth Research Institute of China Aerospace Science and Technology Corporation (USCAST2022-11)Aeronautical Science Foundation of China (20220001057001)。
文摘This paper presents a novel cooperative value iteration(VI)-based adaptive dynamic programming method for multi-player differential game models with a convergence proof.The players are divided into two groups in the learning process and adapt their policies sequentially.Our method removes the dependence of admissible initial policies,which is one of the main drawbacks of the PI-based frameworks.Furthermore,this algorithm enables the players to adapt their control policies without full knowledge of others’ system parameters or control laws.The efficacy of our method is illustrated by three examples.
文摘Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.
文摘The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.
基金supported in part by Fundamental Research Funds for the Central Universities(2022JBZX024)in part by the National Natural Science Foundation of China(61872037,61273167)。
文摘Aimed at infinite horizon optimal control problems of discrete time-varying nonlinear systems,in this paper,a new iterative adaptive dynamic programming algorithm,which is the discrete-time time-varying policy iteration(DTTV)algorithm,is developed.The iterative control law is designed to update the iterative value function which approximates the index function of optimal performance.The admissibility of the iterative control law is analyzed.The results show that the iterative value function is non-increasingly convergent to the Bellman-equation optimal solution.To implement the algorithm,neural networks are employed and a new implementation structure is established,which avoids solving the generalized Bellman equation in each iteration.Finally,the optimal control laws for torsional pendulum and inverted pendulum systems are obtained by using the DTTV policy iteration algorithm,where the mass and pendulum bar length are permitted to be time-varying parameters.The effectiveness of the developed method is illustrated by numerical results and comparisons.
基金supported in part by the National Natural Science Foundation of China of No.61903096Guangzhou Key Laboratory of Software‐Defined Low Latency Network of No.202102100006Guangdong Basic and Applied Basic Research Foundation of No.2020A1515110414.
文摘For linear time varying(LTV)multiple input multiple output(MIMO)systems with vector relative degree,an open‐closed‐loop iterative learning control(ILC)strategy is developed in this article,where the time interval of operation is iteration dependent.To compensate the missing tracking signal caused by iteration dependent interval,the feedback control is introduced in ILC design.As the tracking signal of many continuous iterations is lost in a certain interval,the feedback control part can employ the tracking signal of current iteration for compensation.Under the assumption that the initial state vibrates around the desired initial state uniformly in mathematical expectation sense,the expectation of ILC tracking error can converge to zero as the number of iteration tends to infinity.Under the circumstance that the initial state varies around the desired initial state with a bound,as the number of iteration tends to infinity,the expectation of ILC tracking error can be driven to a bounded range,whose upper bound is proportional to the fluctuation.It is revealed that the convergence condition is dependent on the feed-forward control gains,while the feedback control can accelerate convergence speed by selecting appropriate feedback control gains.As a special case,the controlled system with integrated high relative degree is also addressed by proposing a simplified iteration dependent interval based open‐closed‐loop ILC method.Finally,the effectiveness of the developed iteration dependent interval based open‐closed‐loop ILC is illustrated by a simulation example with two cases on initial state.
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In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.
