A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, th...A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.展开更多
A newly-developed numerical algorithm, which is called the new Generalized-α （G-α） method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired ...A newly-developed numerical algorithm, which is called the new Generalized-α （G-α） method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zero- stable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.展开更多
We introduce a new dynamical evolutionary algorithm（DEA） based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The conver...We introduce a new dynamical evolutionary algorithm（DEA） based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The convergence of the algorithm is discussed. We make the numerical experiments and test our model using the two famous chaotic systems （mainly the Lorenz and Chen systems）. The results show the relatively accurate reconstruction of these chaotic systems based on observational data can be obtained. Therefore we may conclude that there are broad prospects using our method to model the nonlinear dynamical systems.展开更多
Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm （Chang, 2003） are presented. One extends the stability study from a given time step t...Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm （Chang, 2003） are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom （SDOF） system, can be applied to a nonlinear multiple degree of freedom （MDOF） system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing.展开更多
Blast furnace （BF） ironmaking process has complex and nonlinear dynamic characteristics. The molten iron temperature （MIT） as well as Si, P and S contents of molten iron is difficult to be directly measured online...Blast furnace （BF） ironmaking process has complex and nonlinear dynamic characteristics. The molten iron temperature （MIT） as well as Si, P and S contents of molten iron is difficult to be directly measured online, and large-time delay exists in offline analysis through laboratory sampling. A nonlinear multivariate intelligent modeling method was proposed for molten iron quality （MIQ） based on principal component analysis （PCA） and dynamic ge- netic neural network. The modeling method used the practical data processed by PCA dimension reduction as inputs of the dynamic artificial neural network （ANN）. A dynamic feedback link was introduced to produce a dynamic neu- ral network on the basis of traditional back propagation ANN. The proposed model improved the dynamic adaptabili- ty of networks and solved the strong fluctuation and resistance problem in a nonlinear dynamic system. Moreover, a new hybrid training method was presented where adaptive genetic algorithms （AGA） and ANN were integrated, which could improve network convergence speed and avoid network into local minima. The proposed method made it easier for operators to understand the inside status of blast furnace and offered real-time and reliable feedback infor- mation for realizing close-loop control for MIQ. Industrial experiments were made through the proposed model based on data collected from a practical steel company. The accuracy could meet the requirements of actual operation.展开更多
A variable mass tuned particle absorber is designed for the nonlinear vertical vibration control of the corrugated rolling mill in the composite plate rolling process.Considering the nonlinear damping and nonlinear st...A variable mass tuned particle absorber is designed for the nonlinear vertical vibration control of the corrugated rolling mill in the composite plate rolling process.Considering the nonlinear damping and nonlinear stiffness between the corrugated interface,a three-degree-of-freedom nonlinear vertical vibration mathematical model of corrugated rolling mill based on dynamic vibration absorber control is established.The multi-scale method is used to solve the amplitude–frequency characteristic curve equation of the installed dynamic vibration absorber(DVA)system.The effects of stiffness coefficient and damping coefficient on the amplitude–frequency characteristic curve are analyzed.The expressions of the dynamic developed factor of the corrugated roll are derived,and the influence laws of mass ratio,frequency ratio and damping ratio on the dynamic amplification factor are analyzed.The optimal parameters of the DVA are obtained by adaptive genetic algorithm.The control effect of the DVA on the nonlinear vertical vibration is studied by numerical simulation.The feasibility of the designed dynamic absorber is verified through experiments.The results show that the designed dynamic absorber can effectively suppress the vertical vibration of the corrugated roller.展开更多
Motion cueing algorithm plays a key role in simulator motion reproduction and improves the realism of movement sensation by combining with the human vestibular system.It is well established that scaling&limiting s...Motion cueing algorithm plays a key role in simulator motion reproduction and improves the realism of movement sensation by combining with the human vestibular system.It is well established that scaling&limiting should be used to decrease the amplitude of the acceleration and angular velocity signals for making full use of limited workspace of motion platform.A novel nonlinear scaling method based on a third-order polynomial and back propagation(BP)neural networks for the motion cueing algorithm is proposed in this paper.The third-order polynomial method is applied to the low amplitude segment of the input signal to minimize the trigger delay of the sensation acceleration;in the high amplitude segment,the BP neural network is used to adaptively adjust the scaling factor of the input signal,to avoid washout displacement and angular displacement beyond the boundary of the workspace.The simulation experiment is verified in the longitudinal/pitch direction for flight simulator,and the result implies that the proposed method not only can overcome the problem of constant scaling parameter and improve motion platform workspace utilization,but also reduce the false cues during the motion simulation process.展开更多
In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint me...In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.展开更多
Motion cueing algorithms(MCA)are often applied in the motion simulators.In this paper,a nonlinear optimal MCA,taking into account translational and rotational motions of a simulator within its physical limitation,is d...Motion cueing algorithms(MCA)are often applied in the motion simulators.In this paper,a nonlinear optimal MCA,taking into account translational and rotational motions of a simulator within its physical limitation,is designed for the motion platform aiming to minimize human’s perception error in order to provide a high degree of fidelity.Indeed,the movement sensation center of most MCA is placed at the center of the upper platform,which may cause a certain error.Pilot’s station should be paid full attention to in the MCA.Apart from this,the scaling and limiting module plays an important role in optimizing the motion platform workspace and reducing false cues during motion reproduction.It should be used along within the washout filter to decrease the amplitude of the translational and rotational motion signals uniformly across all frequencies through the MCA.A nonlinear scaling method is designed to accurately duplicate motions with high realistic behavior and use the platform more efficiently without violating its physical limitations.The simulation experiment is verified in the longitudinal/pitch direction for motion simulator.The result implies that the proposed method can not only overcome the problem of the workspace limitations in the simulator motion reproduction and improve the realism of movement sensation,but also reduce the false cues to improve dynamic fidelity during the motion simulation process.展开更多
A simplified model is proposed for an easy understanding of the coarse-grained technique and for achieving a first approximation to the behavior of gases. A mole of a gas substance, within a cubic container, is repres...A simplified model is proposed for an easy understanding of the coarse-grained technique and for achieving a first approximation to the behavior of gases. A mole of a gas substance, within a cubic container, is represented by six particles symmetrically moving. The impacts of particles on container walls, the inter-particle collisions, as well as the volume of particles and the inter-particle attractive forces, obeying a Lennard-Jones curve, are taken into account. Thanks to the symmetry, the problem is reduced to the nonlinear dynamic analysis of a SDOF oscillator, which is numerically solved by a step-by-step time integration algorithm. Five applications of proposed model, on Carbon Dioxide, are presented: 1) Ideal gas in STP conditions. 2) Real gas in STP conditions. 3) Condensation for small molar volume. 4) Critical point. 5) Iso-kinetic energy curves and iso-therms in the critical point region. Results of the proposed model are compared with test data and results of the Van der Waals model for real gases.展开更多
基金supported by the National Natural Science Foundation of China (60374063)the Natural Science Basic Research Plan Project in Shaanxi Province (2006A12)+1 种基金the Science and Technology Research Project of the Educational Department in Shaanxi Province (07JK180)the Emphasis Research Plan Project of Baoji University of Arts and Science (ZK0840)
文摘A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.
文摘A newly-developed numerical algorithm, which is called the new Generalized-α （G-α） method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zero- stable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.
基金Supported by the National Natural Science Foun-dation of China (60133010) the Natural Science Foundation ofHubei Province (2004ABA011)
文摘We introduce a new dynamical evolutionary algorithm（DEA） based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The convergence of the algorithm is discussed. We make the numerical experiments and test our model using the two famous chaotic systems （mainly the Lorenz and Chen systems）. The results show the relatively accurate reconstruction of these chaotic systems based on observational data can be obtained. Therefore we may conclude that there are broad prospects using our method to model the nonlinear dynamical systems.
基金NSC, Chinese Taipei Under Grant No. NSC-97-2221-E-027-036-MY2
文摘Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm （Chang, 2003） are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom （SDOF） system, can be applied to a nonlinear multiple degree of freedom （MDOF） system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing.
基金Sponsored by National Natural Science Foundation of China(61290323,61333007,614730646)IAPI Fundamental Research Funds(2013ZCX02-09)+1 种基金Fundamental Research Funds for the Central Universities of China(N130508002,N130108001)National High-tech Research and Development Program of China(2015AA043802)
文摘Blast furnace （BF） ironmaking process has complex and nonlinear dynamic characteristics. The molten iron temperature （MIT） as well as Si, P and S contents of molten iron is difficult to be directly measured online, and large-time delay exists in offline analysis through laboratory sampling. A nonlinear multivariate intelligent modeling method was proposed for molten iron quality （MIQ） based on principal component analysis （PCA） and dynamic ge- netic neural network. The modeling method used the practical data processed by PCA dimension reduction as inputs of the dynamic artificial neural network （ANN）. A dynamic feedback link was introduced to produce a dynamic neu- ral network on the basis of traditional back propagation ANN. The proposed model improved the dynamic adaptabili- ty of networks and solved the strong fluctuation and resistance problem in a nonlinear dynamic system. Moreover, a new hybrid training method was presented where adaptive genetic algorithms （AGA） and ANN were integrated, which could improve network convergence speed and avoid network into local minima. The proposed method made it easier for operators to understand the inside status of blast furnace and offered real-time and reliable feedback infor- mation for realizing close-loop control for MIQ. Industrial experiments were made through the proposed model based on data collected from a practical steel company. The accuracy could meet the requirements of actual operation.
基金National Key Research and Development Project(2018YFA0707300)National Natural Science Foundation of China(52205404)Fundamental Research Program of Shanxi Province(202203021212293).
文摘A variable mass tuned particle absorber is designed for the nonlinear vertical vibration control of the corrugated rolling mill in the composite plate rolling process.Considering the nonlinear damping and nonlinear stiffness between the corrugated interface,a three-degree-of-freedom nonlinear vertical vibration mathematical model of corrugated rolling mill based on dynamic vibration absorber control is established.The multi-scale method is used to solve the amplitude–frequency characteristic curve equation of the installed dynamic vibration absorber(DVA)system.The effects of stiffness coefficient and damping coefficient on the amplitude–frequency characteristic curve are analyzed.The expressions of the dynamic developed factor of the corrugated roll are derived,and the influence laws of mass ratio,frequency ratio and damping ratio on the dynamic amplification factor are analyzed.The optimal parameters of the DVA are obtained by adaptive genetic algorithm.The control effect of the DVA on the nonlinear vertical vibration is studied by numerical simulation.The feasibility of the designed dynamic absorber is verified through experiments.The results show that the designed dynamic absorber can effectively suppress the vertical vibration of the corrugated roller.
基金Wuhan Technical College of Communications Fund(Y2019006)Wuhan Technical College of Communications Innovation Team(CX2018A07)。
文摘Motion cueing algorithm plays a key role in simulator motion reproduction and improves the realism of movement sensation by combining with the human vestibular system.It is well established that scaling&limiting should be used to decrease the amplitude of the acceleration and angular velocity signals for making full use of limited workspace of motion platform.A novel nonlinear scaling method based on a third-order polynomial and back propagation(BP)neural networks for the motion cueing algorithm is proposed in this paper.The third-order polynomial method is applied to the low amplitude segment of the input signal to minimize the trigger delay of the sensation acceleration;in the high amplitude segment,the BP neural network is used to adaptively adjust the scaling factor of the input signal,to avoid washout displacement and angular displacement beyond the boundary of the workspace.The simulation experiment is verified in the longitudinal/pitch direction for flight simulator,and the result implies that the proposed method not only can overcome the problem of constant scaling parameter and improve motion platform workspace utilization,but also reduce the false cues during the motion simulation process.
基金Application investigation of conditional nonlinear optimal perturbation in typhoon adaptive observation (40830955)
文摘In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.
基金Supported by Natural Science Foundation of Hubei Province(2019CFB693)Scientific Research Guiding Project of Education Department of Hubei Province(B2020418)。
文摘Motion cueing algorithms(MCA)are often applied in the motion simulators.In this paper,a nonlinear optimal MCA,taking into account translational and rotational motions of a simulator within its physical limitation,is designed for the motion platform aiming to minimize human’s perception error in order to provide a high degree of fidelity.Indeed,the movement sensation center of most MCA is placed at the center of the upper platform,which may cause a certain error.Pilot’s station should be paid full attention to in the MCA.Apart from this,the scaling and limiting module plays an important role in optimizing the motion platform workspace and reducing false cues during motion reproduction.It should be used along within the washout filter to decrease the amplitude of the translational and rotational motion signals uniformly across all frequencies through the MCA.A nonlinear scaling method is designed to accurately duplicate motions with high realistic behavior and use the platform more efficiently without violating its physical limitations.The simulation experiment is verified in the longitudinal/pitch direction for motion simulator.The result implies that the proposed method can not only overcome the problem of the workspace limitations in the simulator motion reproduction and improve the realism of movement sensation,but also reduce the false cues to improve dynamic fidelity during the motion simulation process.
文摘A simplified model is proposed for an easy understanding of the coarse-grained technique and for achieving a first approximation to the behavior of gases. A mole of a gas substance, within a cubic container, is represented by six particles symmetrically moving. The impacts of particles on container walls, the inter-particle collisions, as well as the volume of particles and the inter-particle attractive forces, obeying a Lennard-Jones curve, are taken into account. Thanks to the symmetry, the problem is reduced to the nonlinear dynamic analysis of a SDOF oscillator, which is numerically solved by a step-by-step time integration algorithm. Five applications of proposed model, on Carbon Dioxide, are presented: 1) Ideal gas in STP conditions. 2) Real gas in STP conditions. 3) Condensation for small molar volume. 4) Critical point. 5) Iso-kinetic energy curves and iso-therms in the critical point region. Results of the proposed model are compared with test data and results of the Van der Waals model for real gases.
