Traditional procedures to treat vibrations of gyroscopic continua involve direct application of perturbation methods to a system with both a strong gyroscopic term and other weakly coupled terms.In this study,a gyrosc...Traditional procedures to treat vibrations of gyroscopic continua involve direct application of perturbation methods to a system with both a strong gyroscopic term and other weakly coupled terms.In this study,a gyroscopic modes decoupling method is used to obtain an equivalent system with decoupled gyroscopic modes having only weak couplings.Taking the axially moving string as an example,the instability boundaries in the vicinity of parametric resonances are detected using both the traditional coupled gyroscopic system and our system with decoupled gyroscopic modes,and the results are compared to show the advantages and disadvantages of each method.展开更多
Elasto-plastic consolidation is one of the classic coupling questions in geomechanics. To solve this problem, an elasto-plastic constitutive model is derived based on the numerical modeling method. The model is applie...Elasto-plastic consolidation is one of the classic coupling questions in geomechanics. To solve this problem, an elasto-plastic constitutive model is derived based on the numerical modeling method. The model is applied to Blot＇s consolidation theory. Incremental governing partial differential equations are established using this method. According to the stress path, the decoupling condition of these equations is discussed. Based on these conditions, an incremental diffusion equation and uncoupling governing equations are presented. The method is then applied to numerical analyses of three examples. The results show that （1） the effect of the stress path should be taken into account in the simulation of the soil consolidation question; （2） this decoupling method can predict the evolvement of pore water pressure; （3） the settlement using cam-clay model is less than that using numerical model because of dilatancy.展开更多
The mathematical model of hydraulic drive unit of quadruped robot was built in this paper. According to the coupling characteristics between position control system and force control system, the decoupling control str...The mathematical model of hydraulic drive unit of quadruped robot was built in this paper. According to the coupling characteristics between position control system and force control system, the decoupling control strategy was realized based on diagonal matrix method in AMESim?. The results of simulation show that using diagonal matrix method can achieve the decoupling control effectively and it can achieve the decoupling control more effectively with the method of not offset pole-zero in the S coordinate. This research can provide theoretical basis for the application of test system of hydraulic drive unit.展开更多
Exploring the factors driving the decoupling of China’s sulfur dioxide(SO_(2))emissions from economic growth(DEI)is crucial for achieving sustainable development.By analyzing the decoupling indicators and driving fac...Exploring the factors driving the decoupling of China’s sulfur dioxide(SO_(2))emissions from economic growth(DEI)is crucial for achieving sustainable development.By analyzing the decoupling indicators and driving factors at both the generation and treatment stages of SO_(2),more effective targeted mitigation strategies can be developed.We employ the Tapio decoupling model and propose a two-stage method to examine the decoupling issues related to SO_(2).Our findings indicate that:①DEI shows a steady and significant improvement,with SO_(2)emission intensity identified as the primary driver.②for the decoupling of economic growth and SO_(2)generation,energy scale serves as the largest stimulator,while the effect of energy intensity changes from negative to positive,and pollution intensity is first positive and then negative.③For the decoupling of SO_(2)generation and SO_(2)removal,treatment efficiency leads as the largest promoter,followed by treatment intensity.Based on these results,this study recommends that China focuses more on enhancing clean energy utilization and the effectiveness of treatment processes.展开更多
A tunable dual-band stop-band THz spectrum can be realized in a hybrid structure, which consists of metal nanoribbon arrays clad by graphene nanoribbons. Dual-band spectra can be controlled separately by the nanoribbo...A tunable dual-band stop-band THz spectrum can be realized in a hybrid structure, which consists of metal nanoribbon arrays clad by graphene nanoribbons. Dual-band spectra can be controlled separately by the nanoribbon width ω and graphene chemical potential μ_c. We explain that two local plasmonic modes excited at graphene ribbons belong to different gratings, which uncouple with each other by electro-magnetic shielding of the metal ribbons. Furthermore, plasmonic induced transparent(PIT) effects can also be realized by making the two transmission notches close to each other, with better performance than the PIT system based on plasmonic coupling,such as with a larger extinction radio and a tunable transparency window.展开更多
In actual power systems,most of the high-voltage buses of the transformers are zero injection buses without load or generation.Power injections into these buses are strictly 0,so based on Kirchhoff's current law(K...In actual power systems,most of the high-voltage buses of the transformers are zero injection buses without load or generation.Power injections into these buses are strictly 0,so based on Kirchhoff's current law(KCL),equality constraints should be used to handle these buses in a state estimation model.It is a challenge to ensure that these zero injection constraints can be strictly satisfied without losing computational efficiency.展开更多
The potential for mitigating climate change is growing worldwide,with an increasing emphasis on reducing CO_(2)emissions and minimising the impact on the environment.African continent is faced with the unique challeng...The potential for mitigating climate change is growing worldwide,with an increasing emphasis on reducing CO_(2)emissions and minimising the impact on the environment.African continent is faced with the unique challenge of climate change whilst coping with extreme poverty,explosive population growth and economic difficulties.CO_(2)emission patterns in Africa are analysed in this study to understand primary CO_(2)sources and underlying driving forces further.Data are examined using gravity model,logarithmic mean divisia index and Tapio's decoupling indicator of CO_(2)emissions from economic development in 20 selected African countries during 1984-2014.Results reveal that CO_(2)emissions increased by 2.11%(453.73 million ton)over the research period.Gravity centre for African CO_(2)emissions had shifted towards the northeast direction.Population and economic growth were primary driving forces of CO_(2)emissions.Industrial structure and emission efficiency effects partially offset the growth of CO_(2)emissions.The economic growth effect was an offset factor in central African countries and Zimbabwe due to political instability and economic mismanagement.Industrial structure and emission efficiency were insufficient to decouple economic development from CO_(2)emissions and relieve the pressure of population explosion on CO_(2)emissions in Africa.Thus,future efforts in reducing CO_(2)emissions should focus on scaleup energy-efficient technologies,renewable energy update,emission pricing and long-term green development towards sustainable development goals by 2030.展开更多
This paper attempts to explore the decoupling relationship and its drivers between industrial economic increase and energy-related CO_(2) emissions(ICE). Firstly, the decoupling relationship was evaluated by Tapio ind...This paper attempts to explore the decoupling relationship and its drivers between industrial economic increase and energy-related CO_(2) emissions(ICE). Firstly, the decoupling relationship was evaluated by Tapio index. Then, based on the DEA meta-frontier theory framework which taking into account the regional and industrial heterogeneity and index decomposition method, the driving factors of decoupling process were explored mainly from the view of technology and efficiency. The results show that during2000-2019, weak decoupling was the primary state. Investment scale expansion was the largest reason hindering decoupling process of industrial increase from ICE. Both energy saving and production technology achieved significant progress, which facilitated the decoupling process. Simultaneously, the energy technology gap and production technology gap among regions have been narrowed, and played a role in promoting decoupling process. On the contrary, both scale economy efficiency and pure technical efficiency have inhibiting effects on decoupling process. The former indicates that the scale economy of China's industry was not conducive to improve energy efficiency and production efficiency, while the latter indicates that resource misallocation problem may exist in both energy market and product market.展开更多
In this paper, we apply the two-time Green's function method, and provide a simple way to study themagnetic properties of one-dimensional spin-(S, s) Heisenberg ferromagnets.The magnetic susceptibility and correla...In this paper, we apply the two-time Green's function method, and provide a simple way to study themagnetic properties of one-dimensional spin-(S, s) Heisenberg ferromagnets.The magnetic susceptibility and correlationfunctions are obtained by using the Tyablikov decoupling approximation.Our results show that the magnetic susceptibilityand correlation length are a monotonically decreasing function of temperature regardless of the mixed spins.It isfound that in the case of S = s, our results of one-dimensional mixed-spin model is reduced to be those of the isotropicferromagnetic Heisenberg chain in the whole temperature region.Our results for the susceptibility are in agreement withthose obtained by other theoretical approaches.展开更多
Three-dimensional Information Decoupling System Based on PSD were designed based on LabVIEW, in order to achieve precision, timeliness, reliability require-ments of the PSD used in the ATP system of Satellite Earth qu...Three-dimensional Information Decoupling System Based on PSD were designed based on LabVIEW, in order to achieve precision, timeliness, reliability require-ments of the PSD used in the ATP system of Satellite Earth quantum communication. Firstly, the laser light source was driven by a stepper motor to scan on the PSD photosensitive surface, and the voltage value was collected and calculated to get the spot position. Analyzing the cause of nonlinear, a mathematical model was built between the actual value and the measured value by using binary quadratic polynomial method, PSD nonlinear correction function would be got. Then, the object micro displacement and angle offset were measured by combining optical triangulation method, and the error of the measurement results was corrected. Experimental results showed that, after the correction, the measuring deviation could be significantly reduced, the PSD performance calibration requirements was achieved, the efficiency of the system was developed greatly by using LabVIEW.展开更多
Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static...Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static problems;however,the simultaneous enforcement of I/BCs in dynamic problems remains challenging.To overcome this limitation,a novel approach called decoupled physics-informed neural network(d PINN)is proposed in this work.The d PINN operates based on the core idea of converting a partial differential equation(PDE)to a system of ordinary differential equations(ODEs)via the space-time decoupled formulation.To this end,the latent solution is expressed in the form of a linear combination of approximation functions and coefficients,where approximation functions are admissible and coefficients are unknowns of time that must be solved.Subsequently,the system of ODEs is obtained by implementing the weighted-residual form of the original PDE over the spatial domain.A multi-network structure is used to parameterize the set of coefficient functions,and the loss function of d PINN is established based on minimizing the residuals of the gained ODEs.In this scheme,the decoupled formulation leads to the independent handling of I/BCs.Accordingly,the BCs are automatically satisfied based on suitable selections of admissible functions.Meanwhile,the original ICs are replaced by the Galerkin form of the ICs concerning unknown coefficients,and the neural network(NN)outputs are modified to satisfy the gained ICs.Several benchmark problems involving different types of PDEs and I/BCs are used to demonstrate the superior performance of d PINN compared with regular PINN in terms of solution accuracy and computational cost.展开更多
In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled...In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled two-dimensional eigenvalue problem by cylindrical coordinate transformation and Fourier series expansion, and deduce the crucial essential pole conditions. Secondly, we define a kind of weighted Sobolev spaces, and establish a suitable variational formula and its discrete form for each two-dimensional eigenvalue problem. Furthermore, we derive the equivalent operator formulas and obtain some prior error estimates of spectral theory of compact operators. More importantly, we further obtained error estimates for approximating eigenvalues and eigenfunctions by using two newly constructed projection operators. Finally,some numerical experiments are performed to validate our theoretical results and algorithm.展开更多
It is widely used for the rotational parallel mechanism in the field of spatial orientation.While owing to the existence of coupling,the forward kinematic solution and the control of the general rotational parallel me...It is widely used for the rotational parallel mechanism in the field of spatial orientation.While owing to the existence of coupling,the forward kinematic solution and the control of the general rotational parallel mechanism are especially difficult.If decoupling can be realized,the kinematic analysis of the mechanism will be very simple.Presently,the research of the parallel mechanism is focused on the inverse solution and structure optimization,and there is a lack of rotation decoupled parallel mechanisms(DPMs).So this paper proposes a family of 2 degree of freedom(DOF)rotational DPMs based on the four-bar linkage mechanism,and performs a characteristic analysis.This family of DPMs is composed of a moving platform,a fixed base and three limbs.Taking U_RRU SPU DPM as an example,the motion feature of this DPM is analyzed with the constraint screw method,and its mobility is calculated by using the Modified Kutzbach-Grtibler criterion.The inverse and forward displacement problems of the proposed parallel mechanism are solved.The decoupled feature of the proposed parallel mechanism is validated by the deduction of the expression of the Jaeobian matrix.Three kinds of singularity conditions of this DPM are discussed,and the atlases of the output parameter concerning different geometric parameters are plotted with the theory of the physical model of the solution space.The proposition and characteristic analysis of the novel rotational DPMs in this paper should be useful for further research and application of the parallel mechanisms.展开更多
Fundamental principles from structural dynamics,random theory and perturbation methods are adopted to develop a new response spectrum combination rule for the seismic analysis of non-classically damped systems,such as...Fundamental principles from structural dynamics,random theory and perturbation methods are adopted to develop a new response spectrum combination rule for the seismic analysis of non-classically damped systems,such as structure-damper systems. The approach,which is named the perturbation spectrum method,can provide a more accurate evaluation of a non-classically damped system's mean peak response in terms of the ground response spectrum. To account for the effect of non-classical damping,all elements are included in the proposed method for seismic analysis of structure,which is usually ap-proximated by ignoring the off-diagonal elements of the modal damping matrix. Moreover,as has been adopted in the traditional Complete Quadratic Combination (CQC) method,the white noise model is also used to simplify the expressions of perturbation correlation coefficients. Finally,numerical work is performed to examine the accuracy of the proposed method by comparing the approximate results with exact ones and to demonstrate the importance of the neglected off-diagonal elements of the modal damping matrix. In the examined cases,the proposed method shows good agreement with direct time-history integration. Also,the perturbation spectrum method leads to a more efficient and economical calculation by avoiding the integral and complex operation.展开更多
By the modem time series analysis method, based on the autoregressive moving average （ARMA） innovation models and white noise estimation theory, using the optimal fusion rule weighted by diagonal matrices, a distrib...By the modem time series analysis method, based on the autoregressive moving average （ARMA） innovation models and white noise estimation theory, using the optimal fusion rule weighted by diagonal matrices, a distributed descriptor Wiener state fuser is presented by weighting the local Wiener state estimators for the linear discrete stochastic descriptor systems with multisensor. It realizes a decoupled fusion estimation for state components. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors are presented based on cross-covariances among the local innovation processes, input white noise, and measurement white noises. It can handle the fused filtering, smoothing, and prediction problems in a unified framework. Its accuracy is higher than that of each local estimator. A Monte Carlo simulation example shows its effectiveness and correctness.展开更多
Most of the important aspects of soliton propagation through optical fibers for transcontinental and transoceanic long distances can best be described using the nonlinear Schr?dinger equation.Optical solitons are elec...Most of the important aspects of soliton propagation through optical fibers for transcontinental and transoceanic long distances can best be described using the nonlinear Schr?dinger equation.Optical solitons are electromagnetic waves that span in nonlinear dispersive media and permit the stress and intensity to stay unaltered as a result of the delicate balance between dispersion and nonlinearity effects.However,this study exploited the Jacobi elliptic method and obtained different soliton solutions of the decoupled nonlinear Schr?dinger equation with ease.Discussions about the obtained solutions were made with the aid of some 3D graphs.展开更多
The invertible of the Large Air Dense Medium Fluidized Bed (ADMFB) were studied by introducing the concept of the inverse system theory of nonlinear systems. Then the ADMFB, which was a multivariable, nonlinear and co...The invertible of the Large Air Dense Medium Fluidized Bed (ADMFB) were studied by introducing the concept of the inverse system theory of nonlinear systems. Then the ADMFB, which was a multivariable, nonlinear and coupled strongly system, was decoupled into independent SISO pseudo-linear subsystems. Linear controllers were designed for each of subsystems based on linear systems theory. The practice output proves that this method improves the stability of the ADMFB obviously.展开更多
In this paper,a BDF2 modular grad-div algorithm for the Stokes/Darcy model is constructed.This method not only effectively avoids solver breakdown,but also increases computational efficiency for increasing parameter v...In this paper,a BDF2 modular grad-div algorithm for the Stokes/Darcy model is constructed.This method not only effectively avoids solver breakdown,but also increases computational efficiency for increasing parameter values.Herein,complete stability and error analysis are provided.Finally,some numerical tests are proposed to justify the theoretical analysis.展开更多
基金the National Natural Science Foundation of China(Grants 11772009,11672007)the Beijing Municipal Natural Science Foundation(Grant 3172003).
文摘Traditional procedures to treat vibrations of gyroscopic continua involve direct application of perturbation methods to a system with both a strong gyroscopic term and other weakly coupled terms.In this study,a gyroscopic modes decoupling method is used to obtain an equivalent system with decoupled gyroscopic modes having only weak couplings.Taking the axially moving string as an example,the instability boundaries in the vicinity of parametric resonances are detected using both the traditional coupled gyroscopic system and our system with decoupled gyroscopic modes,and the results are compared to show the advantages and disadvantages of each method.
文摘Elasto-plastic consolidation is one of the classic coupling questions in geomechanics. To solve this problem, an elasto-plastic constitutive model is derived based on the numerical modeling method. The model is applied to Blot＇s consolidation theory. Incremental governing partial differential equations are established using this method. According to the stress path, the decoupling condition of these equations is discussed. Based on these conditions, an incremental diffusion equation and uncoupling governing equations are presented. The method is then applied to numerical analyses of three examples. The results show that （1） the effect of the stress path should be taken into account in the simulation of the soil consolidation question; （2） this decoupling method can predict the evolvement of pore water pressure; （3） the settlement using cam-clay model is less than that using numerical model because of dilatancy.
文摘The mathematical model of hydraulic drive unit of quadruped robot was built in this paper. According to the coupling characteristics between position control system and force control system, the decoupling control strategy was realized based on diagonal matrix method in AMESim?. The results of simulation show that using diagonal matrix method can achieve the decoupling control effectively and it can achieve the decoupling control more effectively with the method of not offset pole-zero in the S coordinate. This research can provide theoretical basis for the application of test system of hydraulic drive unit.
基金the National Natural Science Foundation of China[Grant No.52270183].
文摘Exploring the factors driving the decoupling of China’s sulfur dioxide(SO_(2))emissions from economic growth(DEI)is crucial for achieving sustainable development.By analyzing the decoupling indicators and driving factors at both the generation and treatment stages of SO_(2),more effective targeted mitigation strategies can be developed.We employ the Tapio decoupling model and propose a two-stage method to examine the decoupling issues related to SO_(2).Our findings indicate that:①DEI shows a steady and significant improvement,with SO_(2)emission intensity identified as the primary driver.②for the decoupling of economic growth and SO_(2)generation,energy scale serves as the largest stimulator,while the effect of energy intensity changes from negative to positive,and pollution intensity is first positive and then negative.③For the decoupling of SO_(2)generation and SO_(2)removal,treatment efficiency leads as the largest promoter,followed by treatment intensity.Based on these results,this study recommends that China focuses more on enhancing clean energy utilization and the effectiveness of treatment processes.
基金Supported by the Key Disciplines of Physics of Guizhou Province under Grant No QXWB[2013]18the Major Research Projects for Innovation Groups of Guizhou Province under Grant No KY[2018]028+4 种基金the National Natural Science Foundation of China under Grant No 11464052the Science and Technology Foundation of Guizhou Province under Grant No J[2015]2149the Youth Foundation of the Education Department of Guizhou Province under Grant No KY[2017]248the Startup Foundation for Doctors of Zunyi Normal University under Grant No 40300326the Natural Science Foundation of Jiangxi Province under Grant No 20161BAB201002
文摘A tunable dual-band stop-band THz spectrum can be realized in a hybrid structure, which consists of metal nanoribbon arrays clad by graphene nanoribbons. Dual-band spectra can be controlled separately by the nanoribbon width ω and graphene chemical potential μ_c. We explain that two local plasmonic modes excited at graphene ribbons belong to different gratings, which uncouple with each other by electro-magnetic shielding of the metal ribbons. Furthermore, plasmonic induced transparent(PIT) effects can also be realized by making the two transmission notches close to each other, with better performance than the PIT system based on plasmonic coupling,such as with a larger extinction radio and a tunable transparency window.
文摘In actual power systems,most of the high-voltage buses of the transformers are zero injection buses without load or generation.Power injections into these buses are strictly 0,so based on Kirchhoff's current law(KCL),equality constraints should be used to handle these buses in a state estimation model.It is a challenge to ensure that these zero injection constraints can be strictly satisfied without losing computational efficiency.
基金supported by the National Water Pollution Control and Treatment Science and Technology Major Project(No.2017ZX07101001)the National Natural Science Foundation of China(Nos.41690142 and 41371535)the Fundamental Research Funds for the Central Universities(No.SWU019047)。
文摘The potential for mitigating climate change is growing worldwide,with an increasing emphasis on reducing CO_(2)emissions and minimising the impact on the environment.African continent is faced with the unique challenge of climate change whilst coping with extreme poverty,explosive population growth and economic difficulties.CO_(2)emission patterns in Africa are analysed in this study to understand primary CO_(2)sources and underlying driving forces further.Data are examined using gravity model,logarithmic mean divisia index and Tapio's decoupling indicator of CO_(2)emissions from economic development in 20 selected African countries during 1984-2014.Results reveal that CO_(2)emissions increased by 2.11%(453.73 million ton)over the research period.Gravity centre for African CO_(2)emissions had shifted towards the northeast direction.Population and economic growth were primary driving forces of CO_(2)emissions.Industrial structure and emission efficiency effects partially offset the growth of CO_(2)emissions.The economic growth effect was an offset factor in central African countries and Zimbabwe due to political instability and economic mismanagement.Industrial structure and emission efficiency were insufficient to decouple economic development from CO_(2)emissions and relieve the pressure of population explosion on CO_(2)emissions in Africa.Thus,future efforts in reducing CO_(2)emissions should focus on scaleup energy-efficient technologies,renewable energy update,emission pricing and long-term green development towards sustainable development goals by 2030.
基金financial support from the China Postdoctoral Science Foundation project(No.2023M733253)。
文摘This paper attempts to explore the decoupling relationship and its drivers between industrial economic increase and energy-related CO_(2) emissions(ICE). Firstly, the decoupling relationship was evaluated by Tapio index. Then, based on the DEA meta-frontier theory framework which taking into account the regional and industrial heterogeneity and index decomposition method, the driving factors of decoupling process were explored mainly from the view of technology and efficiency. The results show that during2000-2019, weak decoupling was the primary state. Investment scale expansion was the largest reason hindering decoupling process of industrial increase from ICE. Both energy saving and production technology achieved significant progress, which facilitated the decoupling process. Simultaneously, the energy technology gap and production technology gap among regions have been narrowed, and played a role in promoting decoupling process. On the contrary, both scale economy efficiency and pure technical efficiency have inhibiting effects on decoupling process. The former indicates that the scale economy of China's industry was not conducive to improve energy efficiency and production efficiency, while the latter indicates that resource misallocation problem may exist in both energy market and product market.
基金Supported by the Natural Science Foundation of Guangdong Province under Grant No.8151009001000055
文摘In this paper, we apply the two-time Green's function method, and provide a simple way to study themagnetic properties of one-dimensional spin-(S, s) Heisenberg ferromagnets.The magnetic susceptibility and correlationfunctions are obtained by using the Tyablikov decoupling approximation.Our results show that the magnetic susceptibilityand correlation length are a monotonically decreasing function of temperature regardless of the mixed spins.It isfound that in the case of S = s, our results of one-dimensional mixed-spin model is reduced to be those of the isotropicferromagnetic Heisenberg chain in the whole temperature region.Our results for the susceptibility are in agreement withthose obtained by other theoretical approaches.
文摘Three-dimensional Information Decoupling System Based on PSD were designed based on LabVIEW, in order to achieve precision, timeliness, reliability require-ments of the PSD used in the ATP system of Satellite Earth quantum communication. Firstly, the laser light source was driven by a stepper motor to scan on the PSD photosensitive surface, and the voltage value was collected and calculated to get the spot position. Analyzing the cause of nonlinear, a mathematical model was built between the actual value and the measured value by using binary quadratic polynomial method, PSD nonlinear correction function would be got. Then, the object micro displacement and angle offset were measured by combining optical triangulation method, and the error of the measurement results was corrected. Experimental results showed that, after the correction, the measuring deviation could be significantly reduced, the PSD performance calibration requirements was achieved, the efficiency of the system was developed greatly by using LabVIEW.
基金Project supported by the Basic Science Research Program through the National Research Foundation(NRF)of Korea funded by the Ministry of Science and ICT(No.RS-2024-00337001)。
文摘Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static problems;however,the simultaneous enforcement of I/BCs in dynamic problems remains challenging.To overcome this limitation,a novel approach called decoupled physics-informed neural network(d PINN)is proposed in this work.The d PINN operates based on the core idea of converting a partial differential equation(PDE)to a system of ordinary differential equations(ODEs)via the space-time decoupled formulation.To this end,the latent solution is expressed in the form of a linear combination of approximation functions and coefficients,where approximation functions are admissible and coefficients are unknowns of time that must be solved.Subsequently,the system of ODEs is obtained by implementing the weighted-residual form of the original PDE over the spatial domain.A multi-network structure is used to parameterize the set of coefficient functions,and the loss function of d PINN is established based on minimizing the residuals of the gained ODEs.In this scheme,the decoupled formulation leads to the independent handling of I/BCs.Accordingly,the BCs are automatically satisfied based on suitable selections of admissible functions.Meanwhile,the original ICs are replaced by the Galerkin form of the ICs concerning unknown coefficients,and the neural network(NN)outputs are modified to satisfy the gained ICs.Several benchmark problems involving different types of PDEs and I/BCs are used to demonstrate the superior performance of d PINN compared with regular PINN in terms of solution accuracy and computational cost.
基金Supported by the National Natural Science Foundation of China(Grant No.12261017)the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022ZCZX077)。
文摘In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled two-dimensional eigenvalue problem by cylindrical coordinate transformation and Fourier series expansion, and deduce the crucial essential pole conditions. Secondly, we define a kind of weighted Sobolev spaces, and establish a suitable variational formula and its discrete form for each two-dimensional eigenvalue problem. Furthermore, we derive the equivalent operator formulas and obtain some prior error estimates of spectral theory of compact operators. More importantly, we further obtained error estimates for approximating eigenvalues and eigenfunctions by using two newly constructed projection operators. Finally,some numerical experiments are performed to validate our theoretical results and algorithm.
基金supported by National Natural Science Foundation of China(Grant No.50875227)
文摘It is widely used for the rotational parallel mechanism in the field of spatial orientation.While owing to the existence of coupling,the forward kinematic solution and the control of the general rotational parallel mechanism are especially difficult.If decoupling can be realized,the kinematic analysis of the mechanism will be very simple.Presently,the research of the parallel mechanism is focused on the inverse solution and structure optimization,and there is a lack of rotation decoupled parallel mechanisms(DPMs).So this paper proposes a family of 2 degree of freedom(DOF)rotational DPMs based on the four-bar linkage mechanism,and performs a characteristic analysis.This family of DPMs is composed of a moving platform,a fixed base and three limbs.Taking U_RRU SPU DPM as an example,the motion feature of this DPM is analyzed with the constraint screw method,and its mobility is calculated by using the Modified Kutzbach-Grtibler criterion.The inverse and forward displacement problems of the proposed parallel mechanism are solved.The decoupled feature of the proposed parallel mechanism is validated by the deduction of the expression of the Jaeobian matrix.Three kinds of singularity conditions of this DPM are discussed,and the atlases of the output parameter concerning different geometric parameters are plotted with the theory of the physical model of the solution space.The proposition and characteristic analysis of the novel rotational DPMs in this paper should be useful for further research and application of the parallel mechanisms.
基金Project supported by the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0518)the Program of Introducing Talents of Discipline to Universities (No. B08014), China
文摘Fundamental principles from structural dynamics,random theory and perturbation methods are adopted to develop a new response spectrum combination rule for the seismic analysis of non-classically damped systems,such as structure-damper systems. The approach,which is named the perturbation spectrum method,can provide a more accurate evaluation of a non-classically damped system's mean peak response in terms of the ground response spectrum. To account for the effect of non-classical damping,all elements are included in the proposed method for seismic analysis of structure,which is usually ap-proximated by ignoring the off-diagonal elements of the modal damping matrix. Moreover,as has been adopted in the traditional Complete Quadratic Combination (CQC) method,the white noise model is also used to simplify the expressions of perturbation correlation coefficients. Finally,numerical work is performed to examine the accuracy of the proposed method by comparing the approximate results with exact ones and to demonstrate the importance of the neglected off-diagonal elements of the modal damping matrix. In the examined cases,the proposed method shows good agreement with direct time-history integration. Also,the perturbation spectrum method leads to a more efficient and economical calculation by avoiding the integral and complex operation.
基金the National Natural Science Foundation of China (No.60874063)the Innonvation Scientific Research Fundation for Graduate Students of Heilongjiang Province (No.YJSCX2008-018HLJ).
文摘By the modem time series analysis method, based on the autoregressive moving average （ARMA） innovation models and white noise estimation theory, using the optimal fusion rule weighted by diagonal matrices, a distributed descriptor Wiener state fuser is presented by weighting the local Wiener state estimators for the linear discrete stochastic descriptor systems with multisensor. It realizes a decoupled fusion estimation for state components. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors are presented based on cross-covariances among the local innovation processes, input white noise, and measurement white noises. It can handle the fused filtering, smoothing, and prediction problems in a unified framework. Its accuracy is higher than that of each local estimator. A Monte Carlo simulation example shows its effectiveness and correctness.
文摘Most of the important aspects of soliton propagation through optical fibers for transcontinental and transoceanic long distances can best be described using the nonlinear Schr?dinger equation.Optical solitons are electromagnetic waves that span in nonlinear dispersive media and permit the stress and intensity to stay unaltered as a result of the delicate balance between dispersion and nonlinearity effects.However,this study exploited the Jacobi elliptic method and obtained different soliton solutions of the decoupled nonlinear Schr?dinger equation with ease.Discussions about the obtained solutions were made with the aid of some 3D graphs.
文摘The invertible of the Large Air Dense Medium Fluidized Bed (ADMFB) were studied by introducing the concept of the inverse system theory of nonlinear systems. Then the ADMFB, which was a multivariable, nonlinear and coupled strongly system, was decoupled into independent SISO pseudo-linear subsystems. Linear controllers were designed for each of subsystems based on linear systems theory. The practice output proves that this method improves the stability of the ADMFB obviously.
基金Supported by the Provincial Natural Science Foundation of Shanxi(201901D111123)Key Research and Development(R&D)Projects of Shanxi Province(201903D121038).
文摘In this paper,a BDF2 modular grad-div algorithm for the Stokes/Darcy model is constructed.This method not only effectively avoids solver breakdown,but also increases computational efficiency for increasing parameter values.Herein,complete stability and error analysis are provided.Finally,some numerical tests are proposed to justify the theoretical analysis.
