A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and...A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.展开更多
This study introduces the lattice spring model(LSM)to investigate the incline angle of a non-uniform three-segment towed array under steady-state conditions.A numerical model was established,and parametric analysis wa...This study introduces the lattice spring model(LSM)to investigate the incline angle of a non-uniform three-segment towed array under steady-state conditions.A numerical model was established,and parametric analysis was conducted to examine the effects of towing speed and cable density on the incline angle.The numerical simulations demonstrate that for a conventional three-segment towed array with heavy vibration-isolation cable and density exceeding that of seawater,the towing speed must exceed 4 kn to maintain the acoustic cable's average incline angle below 10°.To validate the proposed LSM,a 100-meter-long towed array with variable densities was fabricated and tested through lake trials.The experimental results align closely with simulations,confirming LSM as a reliable model for predicting towed array position and posture.The study concludes by analyzing the parallel computing capabilities of LSM and its application in Fluid-Structure Interaction(FSI)problems.The model's precision and parallel computing capabilities make LSM an efficient,reliable tool for analyzing the steady-state behavior of towed systems.展开更多
Data-driven reduced-order modeling opens new avenues of understanding,predicting,controlling,and optimizing system behavior.Simple systems may have state spaces in which sparse human-interpretable dynamical systems ca...Data-driven reduced-order modeling opens new avenues of understanding,predicting,controlling,and optimizing system behavior.Simple systems may have state spaces in which sparse human-interpretable dynamical systems can be identified.This approach has been pioneered by Brunton et al.(2016,PNAS)with sparse identification of nonlinear dynamics.Complex systems,however,cannot be expected to benefit from such simple analytical descriptions.Yet,smoothness may be exploited by analytical local descriptions.In this paper,we identify a clusterwise polynomial dynamics from time-resolved snapshot data.The full state space is partitioned into clusters with a reduced-order polynomial description for each cluster and a global patching strategy.The resulting clusterwise modeling is entirely data-driven and requires no prior knowledge of the system dynamics.We illustrate the approach on the well-known chaotic Lorenz and Rössler systems,on the more challenging chaotic fluid flow dynamics of higher state-space dimensions,on a noisy electrocardiogram signal,and finally on the time evolution of the monthly sunspot number.Clusterwise modeling offers a powerful and interpretable paradigm for dynamical modeling.Nonlinear dynamics can be approximated by assembling many simple local models of different resolutions,opening new paths to understand and control intricate nonlinearities.展开更多
An optimal fuzzy tracking synthesis for nonlinear discrete-time descriptor systems is discussed through the Parallel Distributed Compensation(PDC)approach and the Proportional-Difference(P-D)feedback framework.Based o...An optimal fuzzy tracking synthesis for nonlinear discrete-time descriptor systems is discussed through the Parallel Distributed Compensation(PDC)approach and the Proportional-Difference(P-D)feedback framework.Based on the Takagi-Sugeno Fuzzy Descriptor Model(T-SFDM),a nonlinear discrete-time descriptor system is represented as several linear fuzzy subsystems,which facilitates the linear P-D feedback technique and streamlines the fuzzy controller design process.Leveraging the P-D feedback fuzzy controller,the closed-loop T-SFDM can be transformed into a standard system that guarantees non-impulsiveness and causality for the nonlinear discrete-time descriptor system.In view of the disturbance problems,a passive performance constraint is incorporated into the fuzzy tracking synthesis to achieve dissipativity of disturbance energy.To achieve a better balance between state and control responses,the H2 performance requirement is considered and a minimization constraint is applied to optimize the H2 index.It is observed that there is a lack of research focusing on both disturbance and control input issues in nonlinear descriptor systems.Extending the Lyapunov theory,a stability analysis method is proposed for the tracking purpose with the combination of the free-weighting matrix to relax the analysis process while complying multiple performance constraints.Finally,two simulation examples are presented to demonstrate the feasibility and applicability of the proposed approach in practical control scenarios for nonlinear descriptor systems.展开更多
In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a ge...In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields.Secondly,a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically.Thirdly,existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically.Lastly,numerical tests are given to verify the theoretical results.展开更多
We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method...We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method are exact in the thermodynamic limit.We present the single-site reduced densityρ^((1))(z),averages such as(z^(2)),<|z^(n)|>,and<(z_(1)-z_(2))^(2)>,the specific heat C_(v),and the static correlation functions.We analyze the scaling behavior of these quantities and obtain the exact scaling powers at the low and high temperatures.Using these results,we gauge the accuracy of the projective truncation approximation for theφ^(4)lattice model.展开更多
During strike-slip fault dislocation,multiple fault planes are commonly observed.The resulting permanent ground deformation can lead to profound structural damage to tunnels.However,existing analytical models do not c...During strike-slip fault dislocation,multiple fault planes are commonly observed.The resulting permanent ground deformation can lead to profound structural damage to tunnels.However,existing analytical models do not consider multiple fault planes.Instead,they concentrate the entire fault displacement onto a single fault plane for analysis,thereby giving rise to notable errors in the calculated results.To address this issue,a refined nonlinear theoretical model was established to analyze the mechanical responses of the tunnels subjected to multiple strike-slip fault dislocations.The analytical model considers the number of fault planes,nonlinear soil‒tunnel interactions,geometric nonlinearity,and fault zone width,leading to a significant improvement in its range of applicability and calculation accuracy.The results of the analytical model are in agreement,both qualitatively and quantitatively,with the model test and numerical results.Then,based on the proposed theoretical model,a sensitivity analysis of parameters was conducted,focusing on the variables such as the number of fault planes,fault plane distance(d),fault displacement ratio(η),burial depth(C),crossing angle(β),tunnel diameter(D),fault zone width(Wf),and strike-slip fault displacement(Δfs).The results show that the peak shear force(Vmax),bending moment(Mmax),and axial force(Nmax)decrease with increasing d.The Vmax of the tunnel is found at the fault plane with the largest fault displacement.C,D,andΔfs contribute to the increases in Vmax,Mmax,and Nmax.Additionally,increasing the number of fault planes reduces Vmax and Mmax,whereas the variation in Nmax remains minimal.展开更多
Dear Editor,Aiming at the consensus tracking problem of a class of unknown heterogeneous nonlinear multiagent systems(MASs)with input constraints,a novel data-driven iterative learning consensus control(ILCC)protocol ...Dear Editor,Aiming at the consensus tracking problem of a class of unknown heterogeneous nonlinear multiagent systems(MASs)with input constraints,a novel data-driven iterative learning consensus control(ILCC)protocol based on zeroing neural networks(ZNNs)is proposed.First,a dynamic linearization data model(DLDM)is acquired via dynamic linearization technology(DLT).展开更多
Nonlinear spring characteristics of the tense torsion bar in the gap-closing type electrostatic micromirror are examined. The macro model is introduced for the experimental study. The tension applied in the torsion ba...Nonlinear spring characteristics of the tense torsion bar in the gap-closing type electrostatic micromirror are examined. The macro model is introduced for the experimental study. The tension applied in the torsion bar is well controlled using the electromagnetic attraction. This controllability is suited for clearing the nonlinear nature. The tension is confirmed to have the effect to widen the controllable angle range of the mirror suppressing the pull-in. The pull-in angle is observed to increases to about 74% of the mechanical limit angle at the tension of 0,96 N. This is significantly larger than 44% of the case with the linear spring. The larger resonant frequency is maintained. The hardening of the spring can keep the balance with the electrostatic force over the limit of the linear spring. The observed features are explained reasonably with the combination of twisting and bending displacements of the torsion bar.展开更多
This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic p...This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic processes occur. Isothermal and isentropic compression and expansion of the air within the spring chambers are the two scenarios that are taken into consideration. In these situations, the air inside the spring chambers compresses and expands, resulting in nonlinear spring restoring forces. The MATLAB/Simulink software environment is used to build a numerical simulation model for the dynamic behavior of the air spring. To quantify the values of the stiffnesses of the proposed models, a numerical solution is run over time for various values of the design parameters. The isentropic process case has a higher dynamic air spring stiffness than the isothermal process case, according to the results. The size of the air spring chamber and the area of the air spring piston influence the air spring stiffness in both situations. It is demonstrated that the stiffness of the air spring increases linearly with increasing piston area and decreases nonlinearly with increasing air chamber length. As long as the ratio of the vibration’s amplitude to the air spring’s chamber length is small, there is good agreement in both scenarios between the linearized model and the full nonlinear model. This implies that linear modeling is a reasonable approximation of the complete nonlinear model in this particular scenario.展开更多
The authors constructed a simplified model of spring wheat (Triticum aestivum L.) carbon assimilation and dry matter accumulation (DMA) process which consisted of two independent variables, day length (L) and total...The authors constructed a simplified model of spring wheat (Triticum aestivum L.) carbon assimilation and dry matter accumulation (DMA) process which consisted of two independent variables, day length (L) and total daily radiation (TDR). Leaf water potential (Ψ) was incorporated into the simplified growth model based on the assumption that both light use efficiency (α) and CO 2 conductance of assimilation (g c) were depressed by water limitation. Finally,Ψ was estimated from a regression equation in which the independent variables were relative soil water content in the upper 80 cm (θ R,80 ), ambient temperature (T a), vapor pressure deficit (VPD), the cumulative leaf water potential below thresholds of -1.5 MPa (Ψ c,1.5 ). Some applications in research program of field experiment of atmosphere_land surface processes in Heihe River region were tested. The simulated data agreed well with the data observed at Linze oasis in 1989 for various levels of water supply and at Zhangye oasis in 1992 in the field. The analysis and simulation using the model demonstrated that the simplified growth model could describe very well the DMA process of spring wheat with and without water limitation in the region of HEIFE (Heihe field experiment).展开更多
[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According...[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According to dynamics,mathematical modeling and optimization theory,linear and nonlinear models were respectively set up by taking an absorption peak of 1 550 cm-1 as characteristic absorption peak. [Result] The correlation coefficient of nonlinear model was 0.922 7 and the recovery was 96%,which showed that the nonlinear model was more accurate than linearity model with correlation coefficient of 0.904 9 and recovery of 557%. [Conclusion] It is feasible to determine melamine content by using the nonlinear model quantitatively.展开更多
A wavelet collocation method with nonlinear auto companding is proposed for behavioral modeling of switched current circuits.The companding function is automatically constructed according to the initial error distri...A wavelet collocation method with nonlinear auto companding is proposed for behavioral modeling of switched current circuits.The companding function is automatically constructed according to the initial error distribution obtained through approximating the input output function of the SI circuit by conventional wavelet collocation method.In practical applications,the proposed method is a general purpose approach,by which both the small signal effect and the large signal effect are modeled in a unified formulation to ease the process of modeling and simulation.Compared with the published modeling approaches,the proposed nonlinear auto companding method works more efficiently not only in controlling the error distribution but also in reducing the modeling errors.To demonstrate the promising features of the proposed method,several SI circuits are employed as examples to be modeled and simulated.展开更多
A classic hysteretic model, Preisach-Mayergoyz model （P-M model）, was used to calculate the nonlinear elastic deformation of magnesium （Mg） and cobalt （Co）. Mg and Co samples in cylinder shape were compressively...A classic hysteretic model, Preisach-Mayergoyz model （P-M model）, was used to calculate the nonlinear elastic deformation of magnesium （Mg） and cobalt （Co）. Mg and Co samples in cylinder shape were compressively tested by uniaxial test machine to obtain their stress—strain curves with hysteretic loops. The hysteretic loops do have two properties of P-M hysteretic systems： wiping out and congruency. It is proved that P-M model is applicable for the analysis of these two metals’ hysteresis. This model was applied on Mg at room temperature and Co at 300 ℃. By the P-M model, Co and Mg nonlinear elastic deformation can be calculated based on the stress history. The simulated stress—strain curves agree well with the experimental results. Therefore, the mechanical hysteresis of these two metals can be easily predicted by the classic P-M hysteretic model.展开更多
A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are p...A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.展开更多
In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood e...In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.展开更多
In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wi...In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wings containing geometric nonlinearities.A structural modeling approach presented herein describes the stiffness nonlinearities with a modal formulation.Two orthogonal spanwise modes describe the foreshortening effects of the wing.Dynamic linearization of the ROM under nonlinear equilibrium states is applied to a nonlinear flutter analysis,and the fully nonlinear ROM coupled with the non-planar Unsteady Vortex Lattice Method(UVLM)is applied to gust response analysis.Furthermore,extended Precise Integration Method(PIM)ensures accuracy of the dynamic equation solutions.To demonstrate applicability and accuracy of the method presented,a wind tunnel test is conducted and good agreements between theoretical and test results of nonlinear flutter speed and gust response deflection are reached.The method described in this paper is suitable for predicting the nonlinear flutter speed and calculating the gust responses of a large-aspect-ratio wing in time domain.Meanwhile,the results derived highlight the effects of geometric nonlinearities obviously.展开更多
Increasing basic farmland soil productivity has significance in reducing fertilizer application and maintaining high yield of crops. In this study, we defined that the basic soil productivity （BSP） is the production...Increasing basic farmland soil productivity has significance in reducing fertilizer application and maintaining high yield of crops. In this study, we defined that the basic soil productivity （BSP） is the production capacity of a farmland soil with its own physical and chemical properties for a specific crop season under local environment and field management. Based on 22-yr （1990-2011） long-term experimental data on black soil （Typic hapludoll） in Gongzhuling, Jilin Province, Northeast China, the decision support system for an agro-technology transfer （DSSAT）-CERES-Maize model was applied to simulate the yield by BSP of spring maize （Zea mays L.） to examine the effects of long-term fertilization on changes of BSP and explore the mechanisms of BSP increasing. Five treatments were examined： （1） no-fertilization control （control）; （2） chemical nitrogen, phosphorus, and potassium （NPK）; （3） NPK plus farmyard manure （NPKM）; （4） 1.5 time of NPKM （1.5NPKM） and （5） NPK plus straw （NPKS）. Results showed that after 22-yr fertilization, the yield by BSP of spring maize significantly increased 78.0, 101.2, and 69.4% under the NPKM, 1.5NPKM and NPKS, respectively, compared to the initial value （in 1992）, but not significant under NPK （26.9% increase） and the control （8.9% decrease）. The contribution percentage of BSP showed a significant rising trend （P〈0.05） under 1.5NPKM. The average contribution percentage of BSP among fertilizations ranged from 74.4 to 84.7%, and ranked as 1.5NPKM〉NPKM〉NPK〉NPKS, indicating that organic manure combined with chemical fertilizers （I.5NPKM and NPKM） could more effectively increase BSP compared with the inorganic fertilizer application alone （NPK） in the black soil. This study showed that soil organic matter （SOM） was the key factor among various fertility factors that could affect BSP in the black soil, and total N, total P and/or available P also played important role in BSP increasing. Compared with the chemical fertilization, a balanced chemical plus manure or straw fertilization （NPKM or NPKS） not only increased the concentrations of soil nutrient, but also improved the soil physical properties, and structure and diversity of soil microbial population, resulting in an iincrease of BSP. We recommend that a balanced chemical plus manure or straw fertilization （NPKM or NPKS） should be the fertilization practices to enhance spring maize yield and improve BSP in the black soil of Northeast China.展开更多
Solving the nonlinear model of an aeroengine is converted to an optimization problem, and thus some optimization search methods can be used. An approach to solving the nonlinear model of an aeroengine by use of the g...Solving the nonlinear model of an aeroengine is converted to an optimization problem, and thus some optimization search methods can be used. An approach to solving the nonlinear model of an aeroengine by use of the genetic algorithm (GA) is developed. By comparison with N R algorithm, the accuracy of the values of initial guesses is not required for GA. Especially, the approach developed can be used when no priori knowledges of the values of initial guesses are availabe, and the convergence is improved significantly. GA properly combined with N R algorithm can increase the convergence speed.展开更多
High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of ...High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.42150204 and 2288101)supported by the China National Postdoctoral Program for Innovative Talents(BX20230045)the China Postdoctoral Science Foundation(2023M730279)。
文摘A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.
基金supported by the Key Research Project of Zhejiang Lab(Grant No.K2022MEOAC01)。
文摘This study introduces the lattice spring model(LSM)to investigate the incline angle of a non-uniform three-segment towed array under steady-state conditions.A numerical model was established,and parametric analysis was conducted to examine the effects of towing speed and cable density on the incline angle.The numerical simulations demonstrate that for a conventional three-segment towed array with heavy vibration-isolation cable and density exceeding that of seawater,the towing speed must exceed 4 kn to maintain the acoustic cable's average incline angle below 10°.To validate the proposed LSM,a 100-meter-long towed array with variable densities was fabricated and tested through lake trials.The experimental results align closely with simulations,confirming LSM as a reliable model for predicting towed array position and posture.The study concludes by analyzing the parallel computing capabilities of LSM and its application in Fluid-Structure Interaction(FSI)problems.The model's precision and parallel computing capabilities make LSM an efficient,reliable tool for analyzing the steady-state behavior of towed systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.12172109,12202121,and 12302293)the China Postdoctoral Science Foundation(Grant Nos.2023M730866 and 2023T160166)+1 种基金the Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515011492)the Shenzhen Science and Technology Program(Grant Nos.JCYJ20220531095605012,KJZD20230923115210021,and 29853MKCJ202300205).
文摘Data-driven reduced-order modeling opens new avenues of understanding,predicting,controlling,and optimizing system behavior.Simple systems may have state spaces in which sparse human-interpretable dynamical systems can be identified.This approach has been pioneered by Brunton et al.(2016,PNAS)with sparse identification of nonlinear dynamics.Complex systems,however,cannot be expected to benefit from such simple analytical descriptions.Yet,smoothness may be exploited by analytical local descriptions.In this paper,we identify a clusterwise polynomial dynamics from time-resolved snapshot data.The full state space is partitioned into clusters with a reduced-order polynomial description for each cluster and a global patching strategy.The resulting clusterwise modeling is entirely data-driven and requires no prior knowledge of the system dynamics.We illustrate the approach on the well-known chaotic Lorenz and Rössler systems,on the more challenging chaotic fluid flow dynamics of higher state-space dimensions,on a noisy electrocardiogram signal,and finally on the time evolution of the monthly sunspot number.Clusterwise modeling offers a powerful and interpretable paradigm for dynamical modeling.Nonlinear dynamics can be approximated by assembling many simple local models of different resolutions,opening new paths to understand and control intricate nonlinearities.
基金founded by the National Science and Technology Council(Taiwan)under contract NSTC113-2221-E-019-032.
文摘An optimal fuzzy tracking synthesis for nonlinear discrete-time descriptor systems is discussed through the Parallel Distributed Compensation(PDC)approach and the Proportional-Difference(P-D)feedback framework.Based on the Takagi-Sugeno Fuzzy Descriptor Model(T-SFDM),a nonlinear discrete-time descriptor system is represented as several linear fuzzy subsystems,which facilitates the linear P-D feedback technique and streamlines the fuzzy controller design process.Leveraging the P-D feedback fuzzy controller,the closed-loop T-SFDM can be transformed into a standard system that guarantees non-impulsiveness and causality for the nonlinear discrete-time descriptor system.In view of the disturbance problems,a passive performance constraint is incorporated into the fuzzy tracking synthesis to achieve dissipativity of disturbance energy.To achieve a better balance between state and control responses,the H2 performance requirement is considered and a minimization constraint is applied to optimize the H2 index.It is observed that there is a lack of research focusing on both disturbance and control input issues in nonlinear descriptor systems.Extending the Lyapunov theory,a stability analysis method is proposed for the tracking purpose with the combination of the free-weighting matrix to relax the analysis process while complying multiple performance constraints.Finally,two simulation examples are presented to demonstrate the feasibility and applicability of the proposed approach in practical control scenarios for nonlinear descriptor systems.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12371393,11971150 and 11801143)Natural Science Foundation of Henan Province(Grant No.242300421047).
文摘In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields.Secondly,a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically.Thirdly,existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically.Lastly,numerical tests are given to verify the theoretical results.
基金supported by the National Natural Science Foundation of China(Grant No.11974420).
文摘We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method are exact in the thermodynamic limit.We present the single-site reduced densityρ^((1))(z),averages such as(z^(2)),<|z^(n)|>,and<(z_(1)-z_(2))^(2)>,the specific heat C_(v),and the static correlation functions.We analyze the scaling behavior of these quantities and obtain the exact scaling powers at the low and high temperatures.Using these results,we gauge the accuracy of the projective truncation approximation for theφ^(4)lattice model.
基金support from the National Natural Science Foundation of China(Grant Nos.52378411,52208404)China National Railway Group Limited Science and Technology Research and Development Program(Grant No.K2023G041).
文摘During strike-slip fault dislocation,multiple fault planes are commonly observed.The resulting permanent ground deformation can lead to profound structural damage to tunnels.However,existing analytical models do not consider multiple fault planes.Instead,they concentrate the entire fault displacement onto a single fault plane for analysis,thereby giving rise to notable errors in the calculated results.To address this issue,a refined nonlinear theoretical model was established to analyze the mechanical responses of the tunnels subjected to multiple strike-slip fault dislocations.The analytical model considers the number of fault planes,nonlinear soil‒tunnel interactions,geometric nonlinearity,and fault zone width,leading to a significant improvement in its range of applicability and calculation accuracy.The results of the analytical model are in agreement,both qualitatively and quantitatively,with the model test and numerical results.Then,based on the proposed theoretical model,a sensitivity analysis of parameters was conducted,focusing on the variables such as the number of fault planes,fault plane distance(d),fault displacement ratio(η),burial depth(C),crossing angle(β),tunnel diameter(D),fault zone width(Wf),and strike-slip fault displacement(Δfs).The results show that the peak shear force(Vmax),bending moment(Mmax),and axial force(Nmax)decrease with increasing d.The Vmax of the tunnel is found at the fault plane with the largest fault displacement.C,D,andΔfs contribute to the increases in Vmax,Mmax,and Nmax.Additionally,increasing the number of fault planes reduces Vmax and Mmax,whereas the variation in Nmax remains minimal.
基金supported by the National Nature Science Foundation of China(U21A20166)the Science and Technology Development Foundation of Jilin Province(20230508095RC)+2 种基金the Major Science and Technology Projects of Jilin Province and Changchun City(20220301033GX)the Development and Reform Commission Foundation of Jilin Province(2023C034-3)the Interdisciplinary Integration and Innovation Project of JLU(JLUXKJC2020202).
文摘Dear Editor,Aiming at the consensus tracking problem of a class of unknown heterogeneous nonlinear multiagent systems(MASs)with input constraints,a novel data-driven iterative learning consensus control(ILCC)protocol based on zeroing neural networks(ZNNs)is proposed.First,a dynamic linearization data model(DLDM)is acquired via dynamic linearization technology(DLT).
文摘Nonlinear spring characteristics of the tense torsion bar in the gap-closing type electrostatic micromirror are examined. The macro model is introduced for the experimental study. The tension applied in the torsion bar is well controlled using the electromagnetic attraction. This controllability is suited for clearing the nonlinear nature. The tension is confirmed to have the effect to widen the controllable angle range of the mirror suppressing the pull-in. The pull-in angle is observed to increases to about 74% of the mechanical limit angle at the tension of 0,96 N. This is significantly larger than 44% of the case with the linear spring. The larger resonant frequency is maintained. The hardening of the spring can keep the balance with the electrostatic force over the limit of the linear spring. The observed features are explained reasonably with the combination of twisting and bending displacements of the torsion bar.
文摘This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic processes occur. Isothermal and isentropic compression and expansion of the air within the spring chambers are the two scenarios that are taken into consideration. In these situations, the air inside the spring chambers compresses and expands, resulting in nonlinear spring restoring forces. The MATLAB/Simulink software environment is used to build a numerical simulation model for the dynamic behavior of the air spring. To quantify the values of the stiffnesses of the proposed models, a numerical solution is run over time for various values of the design parameters. The isentropic process case has a higher dynamic air spring stiffness than the isothermal process case, according to the results. The size of the air spring chamber and the area of the air spring piston influence the air spring stiffness in both situations. It is demonstrated that the stiffness of the air spring increases linearly with increasing piston area and decreases nonlinearly with increasing air chamber length. As long as the ratio of the vibration’s amplitude to the air spring’s chamber length is small, there is good agreement in both scenarios between the linearized model and the full nonlinear model. This implies that linear modeling is a reasonable approximation of the complete nonlinear model in this particular scenario.
文摘The authors constructed a simplified model of spring wheat (Triticum aestivum L.) carbon assimilation and dry matter accumulation (DMA) process which consisted of two independent variables, day length (L) and total daily radiation (TDR). Leaf water potential (Ψ) was incorporated into the simplified growth model based on the assumption that both light use efficiency (α) and CO 2 conductance of assimilation (g c) were depressed by water limitation. Finally,Ψ was estimated from a regression equation in which the independent variables were relative soil water content in the upper 80 cm (θ R,80 ), ambient temperature (T a), vapor pressure deficit (VPD), the cumulative leaf water potential below thresholds of -1.5 MPa (Ψ c,1.5 ). Some applications in research program of field experiment of atmosphere_land surface processes in Heihe River region were tested. The simulated data agreed well with the data observed at Linze oasis in 1989 for various levels of water supply and at Zhangye oasis in 1992 in the field. The analysis and simulation using the model demonstrated that the simplified growth model could describe very well the DMA process of spring wheat with and without water limitation in the region of HEIFE (Heihe field experiment).
基金Supported by Promoting Projects of the Industrialization of University Research of Jiangsu Province (JHZD09-35)Natural Science Research Project of Universities in Jiangsu Province (09KJD210001)Research Foundation of Huaiyin Institute of Technology(HGA0908)~~
文摘[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According to dynamics,mathematical modeling and optimization theory,linear and nonlinear models were respectively set up by taking an absorption peak of 1 550 cm-1 as characteristic absorption peak. [Result] The correlation coefficient of nonlinear model was 0.922 7 and the recovery was 96%,which showed that the nonlinear model was more accurate than linearity model with correlation coefficient of 0.904 9 and recovery of 557%. [Conclusion] It is feasible to determine melamine content by using the nonlinear model quantitatively.
文摘A wavelet collocation method with nonlinear auto companding is proposed for behavioral modeling of switched current circuits.The companding function is automatically constructed according to the initial error distribution obtained through approximating the input output function of the SI circuit by conventional wavelet collocation method.In practical applications,the proposed method is a general purpose approach,by which both the small signal effect and the large signal effect are modeled in a unified formulation to ease the process of modeling and simulation.Compared with the published modeling approaches,the proposed nonlinear auto companding method works more efficiently not only in controlling the error distribution but also in reducing the modeling errors.To demonstrate the promising features of the proposed method,several SI circuits are employed as examples to be modeled and simulated.
基金Projects (51002045, 10947105) supported by the National Natural Science Foundation of ChinaProject (2010B430016) supported by the Nature Science Research Project of Education Department of Henan Province, ChinaProject (2012IRTSTHN007) supported by Program for Innovative Research Team (in Science and Technology) in the University of Henan Province, China
文摘A classic hysteretic model, Preisach-Mayergoyz model （P-M model）, was used to calculate the nonlinear elastic deformation of magnesium （Mg） and cobalt （Co）. Mg and Co samples in cylinder shape were compressively tested by uniaxial test machine to obtain their stress—strain curves with hysteretic loops. The hysteretic loops do have two properties of P-M hysteretic systems： wiping out and congruency. It is proved that P-M model is applicable for the analysis of these two metals’ hysteresis. This model was applied on Mg at room temperature and Co at 300 ℃. By the P-M model, Co and Mg nonlinear elastic deformation can be calculated based on the stress history. The simulated stress—strain curves agree well with the experimental results. Therefore, the mechanical hysteresis of these two metals can be easily predicted by the classic P-M hysteretic model.
文摘A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.
基金The National Natural Science Foundation of China(No.11171065)the Natural Science Foundation of Jiangsu Province(No.BK2011058)
文摘In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.
基金supported by the National Key Research and Development Program of China(No.2016YFB 0200703).
文摘In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wings containing geometric nonlinearities.A structural modeling approach presented herein describes the stiffness nonlinearities with a modal formulation.Two orthogonal spanwise modes describe the foreshortening effects of the wing.Dynamic linearization of the ROM under nonlinear equilibrium states is applied to a nonlinear flutter analysis,and the fully nonlinear ROM coupled with the non-planar Unsteady Vortex Lattice Method(UVLM)is applied to gust response analysis.Furthermore,extended Precise Integration Method(PIM)ensures accuracy of the dynamic equation solutions.To demonstrate applicability and accuracy of the method presented,a wind tunnel test is conducted and good agreements between theoretical and test results of nonlinear flutter speed and gust response deflection are reached.The method described in this paper is suitable for predicting the nonlinear flutter speed and calculating the gust responses of a large-aspect-ratio wing in time domain.Meanwhile,the results derived highlight the effects of geometric nonlinearities obviously.
基金supported by the National 973 Program of China (2011CB100501)the National 863 Program of China(2013AA102901)+1 种基金the Special Fund for Agro-Scientific Research in the Public Interest, China (201203077)the Science and Technology Project for Grain Production, China (2011BAD16B15)
文摘Increasing basic farmland soil productivity has significance in reducing fertilizer application and maintaining high yield of crops. In this study, we defined that the basic soil productivity （BSP） is the production capacity of a farmland soil with its own physical and chemical properties for a specific crop season under local environment and field management. Based on 22-yr （1990-2011） long-term experimental data on black soil （Typic hapludoll） in Gongzhuling, Jilin Province, Northeast China, the decision support system for an agro-technology transfer （DSSAT）-CERES-Maize model was applied to simulate the yield by BSP of spring maize （Zea mays L.） to examine the effects of long-term fertilization on changes of BSP and explore the mechanisms of BSP increasing. Five treatments were examined： （1） no-fertilization control （control）; （2） chemical nitrogen, phosphorus, and potassium （NPK）; （3） NPK plus farmyard manure （NPKM）; （4） 1.5 time of NPKM （1.5NPKM） and （5） NPK plus straw （NPKS）. Results showed that after 22-yr fertilization, the yield by BSP of spring maize significantly increased 78.0, 101.2, and 69.4% under the NPKM, 1.5NPKM and NPKS, respectively, compared to the initial value （in 1992）, but not significant under NPK （26.9% increase） and the control （8.9% decrease）. The contribution percentage of BSP showed a significant rising trend （P〈0.05） under 1.5NPKM. The average contribution percentage of BSP among fertilizations ranged from 74.4 to 84.7%, and ranked as 1.5NPKM〉NPKM〉NPK〉NPKS, indicating that organic manure combined with chemical fertilizers （I.5NPKM and NPKM） could more effectively increase BSP compared with the inorganic fertilizer application alone （NPK） in the black soil. This study showed that soil organic matter （SOM） was the key factor among various fertility factors that could affect BSP in the black soil, and total N, total P and/or available P also played important role in BSP increasing. Compared with the chemical fertilization, a balanced chemical plus manure or straw fertilization （NPKM or NPKS） not only increased the concentrations of soil nutrient, but also improved the soil physical properties, and structure and diversity of soil microbial population, resulting in an iincrease of BSP. We recommend that a balanced chemical plus manure or straw fertilization （NPKM or NPKS） should be the fertilization practices to enhance spring maize yield and improve BSP in the black soil of Northeast China.
基金Aeronautic Science Foundation of China ( 0 0 C5 2 0 3 0 ) and National Doctoral Education Foundation ( 2 0 0 0 0 2 870 1)
文摘Solving the nonlinear model of an aeroengine is converted to an optimization problem, and thus some optimization search methods can be used. An approach to solving the nonlinear model of an aeroengine by use of the genetic algorithm (GA) is developed. By comparison with N R algorithm, the accuracy of the values of initial guesses is not required for GA. Especially, the approach developed can be used when no priori knowledges of the values of initial guesses are availabe, and the convergence is improved significantly. GA properly combined with N R algorithm can increase the convergence speed.
文摘High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).
