With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Ya...With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.展开更多
To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregress...To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.展开更多
In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ...In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.展开更多
This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2<sup>nd</sup>-BERRU-PMD. The attribute “2<sup>nd</sup>” indicates that this met...This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2<sup>nd</sup>-BERRU-PMD. The attribute “2<sup>nd</sup>” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2<sup>nd</sup>-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2<sup>nd</sup>-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.展开更多
This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and par...This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and parameters. This methodology is designated by the acronym 2<sup>nd</sup>-BERRU-PMP, where the attribute “2<sup>nd</sup>” indicates that this methodology incorporates second- order uncertainties (means and covariances) and second (and higher) order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best-Estimate Results with Reduced Uncertainties” and the last letter (“P”) in the acronym indicates “probabilistic,” referring to the MaxEnt probabilistic inclusion of the computational model responses. This is in contradistinction to the 2<sup>nd</sup>-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as presented in the accompanying work (Part I). Although both the 2<sup>nd</sup>-BERRU-PMP and the 2<sup>nd</sup>-BERRU-PMD methodologies yield expressions that include second (and higher) order sensitivities of responses to model parameters, the respective expressions for the predicted responses, for the calibrated predicted parameters and for their predicted uncertainties (covariances), are not identical to each other. Nevertheless, the results predicted by both the 2<sup>nd</sup>-BERRU-PMP and the 2<sup>nd</sup>-BERRU-PMD methodologies encompass, as particular cases, the results produced by the extant data assimilation and data adjustment procedures, which rely on the minimization, in a least-square sense, of a user-defined functional meant to represent the discrepancies between measured and computed model responses.展开更多
This work illustrates the innovative results obtained by applying the recently developed the 2<sup>nd</sup>-order predictive modeling methodology called “2<sup>nd</sup>- BERRU-PM”, where the ...This work illustrates the innovative results obtained by applying the recently developed the 2<sup>nd</sup>-order predictive modeling methodology called “2<sup>nd</sup>- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2<sup>nd</sup>-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2<sup>nd</sup>-order response sensitivities must always be included to quantify the need for including (or not) the 3<sup>rd</sup>- and/or 4<sup>th</sup>-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1<sup>st</sup>- and 2<sup>nd</sup>-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3<sup>rd</sup>- and even 4<sup>th</sup>-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1<sup>st</sup>-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2<sup>nd</sup>-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis).展开更多
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ...Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.展开更多
Target tracking control for wheeled mobile robot (WMR) need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control sy...Target tracking control for wheeled mobile robot (WMR) need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.展开更多
A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using...A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application.展开更多
To address the low accuracy and stability when applying classical control theory in distribution networks with distributed generation,a control method involving flexible multistate switches(FMSs)is proposed in this st...To address the low accuracy and stability when applying classical control theory in distribution networks with distributed generation,a control method involving flexible multistate switches(FMSs)is proposed in this study.This approach is based on an improved double-loop recursive fuzzy neural network(DRFNN)sliding mode,which is intended to stably achieve multiterminal power interaction and adaptive arc suppression for single-phase ground faults.First,an improved DRFNN sliding mode control(SMC)method is proposed to overcome the chattering and transient overshoot inherent in the classical SMC and reduce the reliance on a precise mathematical model of the control system.To improve the robustness of the system,an adaptive parameter-adjustment strategy for the DRFNN is designed,where its dynamic mapping capabilities are leveraged to improve the transient compensation control.Additionally,a quasi-continuous second-order sliding mode controller with a calculus-driven sliding mode surface is developed to improve the current monitoring accuracy and enhance the system stability.The stability of the proposed method and the convergence of the network parameters are verified using the Lyapunov theorem.A simulation model of the three-port FMS with its control system is constructed in MATLAB/Simulink.The simulation result confirms the feasibility and effectiveness of the proposed control strategy based on a comparative analysis.展开更多
This paper investigates the consensus problem of second-order nonlinear multi-agent systems (MASs) via the sliding mode control (SMC) approach. The velocity of each agent is assumed to be unmeasurable. A second-order ...This paper investigates the consensus problem of second-order nonlinear multi-agent systems (MASs) via the sliding mode control (SMC) approach. The velocity of each agent is assumed to be unmeasurable. A second-order sliding mode observer is designed to estimate the velocity. Then a distributed discontinuous control law based on first-order SMC is presented to solve the consensus problem. Moreover, to overcome the chatting problem, two controllers based on the boundary layer method and the super-twisting algorithm respectively are presented. It is shown that the MASs will achieve consensus under some given conditions. Some examples are provided to demonstrate the effectiveness of the proposed control laws.展开更多
In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a gene...In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.展开更多
This paper deals with the consensus problem of multi-agent systems with second-order dynamics. The objective is to design algorithms such that all agents will have same positions and velocities. First, a reference mod...This paper deals with the consensus problem of multi-agent systems with second-order dynamics. The objective is to design algorithms such that all agents will have same positions and velocities. First, a reference model based consensus algorithm is proposed. It is proved that the consensus can be achieved if the communication graph has a spanning tree. Different from most of the consensus algorithms proposed in the literature, the parameters of the control laws are different among agents. Therefore, each agent can design its control law independently. Secondly, it gives a consensus algorithm for the case that the velocities of the agents are not available. Thirdly, the effectiveness of the input delay and the communication delay is considered. It shows that consensus can be achieved if the input delay of every agent is smaller than a bound related to parameters in its control law. Finally, some numerical examples are given to illustrate the proposed results.展开更多
A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale flu...A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the sin- gle-scale second-order moment two-phase turbulence model superposed with a particle collision model (USM-θ model) in most regions.展开更多
This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is...This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.展开更多
The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman's path integral theory. It is concluded that whether the sec...The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman's path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra.展开更多
The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equation...The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.展开更多
基金supported by the National Natural Science Foundation of China (10872192)
文摘With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.
基金The National Key Research and Development Program of China under contract No.2023YFC3107701the National Natural Science Foundation of China under contract No.42375143.
文摘To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.
文摘In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
文摘This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2<sup>nd</sup>-BERRU-PMD. The attribute “2<sup>nd</sup>” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2<sup>nd</sup>-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2<sup>nd</sup>-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.
文摘This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and parameters. This methodology is designated by the acronym 2<sup>nd</sup>-BERRU-PMP, where the attribute “2<sup>nd</sup>” indicates that this methodology incorporates second- order uncertainties (means and covariances) and second (and higher) order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best-Estimate Results with Reduced Uncertainties” and the last letter (“P”) in the acronym indicates “probabilistic,” referring to the MaxEnt probabilistic inclusion of the computational model responses. This is in contradistinction to the 2<sup>nd</sup>-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as presented in the accompanying work (Part I). Although both the 2<sup>nd</sup>-BERRU-PMP and the 2<sup>nd</sup>-BERRU-PMD methodologies yield expressions that include second (and higher) order sensitivities of responses to model parameters, the respective expressions for the predicted responses, for the calibrated predicted parameters and for their predicted uncertainties (covariances), are not identical to each other. Nevertheless, the results predicted by both the 2<sup>nd</sup>-BERRU-PMP and the 2<sup>nd</sup>-BERRU-PMD methodologies encompass, as particular cases, the results produced by the extant data assimilation and data adjustment procedures, which rely on the minimization, in a least-square sense, of a user-defined functional meant to represent the discrepancies between measured and computed model responses.
文摘This work illustrates the innovative results obtained by applying the recently developed the 2<sup>nd</sup>-order predictive modeling methodology called “2<sup>nd</sup>- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2<sup>nd</sup>-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2<sup>nd</sup>-order response sensitivities must always be included to quantify the need for including (or not) the 3<sup>rd</sup>- and/or 4<sup>th</sup>-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1<sup>st</sup>- and 2<sup>nd</sup>-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3<sup>rd</sup>- and even 4<sup>th</sup>-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1<sup>st</sup>-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2<sup>nd</sup>-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis).
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.
基金supported by National Natural Science Foundation of China (Grant No. 61075081)State Key Laboratory of Robotics Technique and System Foundation,Harbin Institute of Technology,China(Grant No. SKIRS200802A02)
文摘Target tracking control for wheeled mobile robot (WMR) need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.
基金The project sponsored by the Foundation for Doctorate Thesis of Tsinghua Universitythe National Key Project in 1999-2004 sponsored by the Ministry of Science and Technology of China
文摘A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application.
基金the Natural Science Foundation of Fujian,China(No.2021J01633).
文摘To address the low accuracy and stability when applying classical control theory in distribution networks with distributed generation,a control method involving flexible multistate switches(FMSs)is proposed in this study.This approach is based on an improved double-loop recursive fuzzy neural network(DRFNN)sliding mode,which is intended to stably achieve multiterminal power interaction and adaptive arc suppression for single-phase ground faults.First,an improved DRFNN sliding mode control(SMC)method is proposed to overcome the chattering and transient overshoot inherent in the classical SMC and reduce the reliance on a precise mathematical model of the control system.To improve the robustness of the system,an adaptive parameter-adjustment strategy for the DRFNN is designed,where its dynamic mapping capabilities are leveraged to improve the transient compensation control.Additionally,a quasi-continuous second-order sliding mode controller with a calculus-driven sliding mode surface is developed to improve the current monitoring accuracy and enhance the system stability.The stability of the proposed method and the convergence of the network parameters are verified using the Lyapunov theorem.A simulation model of the three-port FMS with its control system is constructed in MATLAB/Simulink.The simulation result confirms the feasibility and effectiveness of the proposed control strategy based on a comparative analysis.
基金supported by the National Natural Science Foundation of China(6137510561403334)
文摘This paper investigates the consensus problem of second-order nonlinear multi-agent systems (MASs) via the sliding mode control (SMC) approach. The velocity of each agent is assumed to be unmeasurable. A second-order sliding mode observer is designed to estimate the velocity. Then a distributed discontinuous control law based on first-order SMC is presented to solve the consensus problem. Moreover, to overcome the chatting problem, two controllers based on the boundary layer method and the super-twisting algorithm respectively are presented. It is shown that the MASs will achieve consensus under some given conditions. Some examples are provided to demonstrate the effectiveness of the proposed control laws.
基金supported by the Swiss National Science Foundation(Grant No.189882)the National Natural Science Foundation of China(Grant No.41961134032)support provided by the New Investigator Award grant from the UK Engineering and Physical Sciences Research Council(Grant No.EP/V012169/1).
文摘In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.
基金supported by the National Natural Science Foundation of China (Grant No. 60904022)
文摘This paper deals with the consensus problem of multi-agent systems with second-order dynamics. The objective is to design algorithms such that all agents will have same positions and velocities. First, a reference model based consensus algorithm is proposed. It is proved that the consensus can be achieved if the communication graph has a spanning tree. Different from most of the consensus algorithms proposed in the literature, the parameters of the control laws are different among agents. Therefore, each agent can design its control law independently. Secondly, it gives a consensus algorithm for the case that the velocities of the agents are not available. Thirdly, the effectiveness of the input delay and the communication delay is considered. It shows that consensus can be achieved if the input delay of every agent is smaller than a bound related to parameters in its control law. Finally, some numerical examples are given to illustrate the proposed results.
基金The project supported by the Special Funds for Major State Basic Research,China(G-1999-0222-08)the Postdoctoral Science Foundation(2004036239)
文摘A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the sin- gle-scale second-order moment two-phase turbulence model superposed with a particle collision model (USM-θ model) in most regions.
基金Project supported by the Executive Agency for Higher Education Research Development and Innovation Funding of Romania(No.PN-III-P4-PCE-2021-0993)。
文摘This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.
基金Project supported by the National Natural Science Foundation of China(Grant No.11404255)the Doctor Foundation of Education Ministry of China(Grant No.20130201120013)
文摘The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman's path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra.
文摘The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.