Mixed-effects models,also called random-effects models,are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject,but also to describe the variation among ...Mixed-effects models,also called random-effects models,are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject,but also to describe the variation among different subjects.Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data.In this paper,nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies.By using this type of models,statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance.Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.展开更多
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
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
Korean larch(Larix olgensis)is one of the main tree species for aff orestation and timber production in northeast China.However,its timber quality and growth ability are largely infl uenced by crown size,structure and...Korean larch(Larix olgensis)is one of the main tree species for aff orestation and timber production in northeast China.However,its timber quality and growth ability are largely infl uenced by crown size,structure and shape.The majority of crown models are static models based on tree size and stand characteristics from temporary sample plots,but crown dynamic models has seldom been constructed.Therefore,this study aimed to develop height to crown base(HCB)and crown length(CL)dynamic models using the branch mortality technique for a Korean larch plantation.The nonlinear mixed-eff ects model with random eff ects,variance functions and correlation structures,was used to build HCB and CL dynamic models.The data were obtained from 95 sample trees of 19 plots in Meng JiaGang forest farm in Northeast China.The results showed that HCB progressively increases as tree age,tree height growth(HT growth)and diameter at breast height growth(DBH growth).The CL was increased with tree age in 20 years ago,and subsequently stabilized.HT growth,DBH growth stand basal area(BAS)and crown competition factor(CCF)signifi cantly infl uenced HCB and CL.The HCB was positively correlated with BAS,HT growth and DBH growth,but negatively correlated with CCF.The CL was positively correlated with BAS and CCF,but negatively correlated with DBH growth.Model fi tting and validation confi rmed that the mixed-eff ects model considering the stand and tree level random eff ects was accurate and reliable for predicting the HCB and CL dynamics.However,the models involving adding variance functions and time series correlation structure could not completely remove heterogeneity and autocorrelation,and the fi tting precision of the models was reduced.Therefore,from the point of view of application,we should take care to avoid setting up over-complex models.The HCB and CL dynamic models in our study may also be incorporated into stand growth and yield model systems in China.展开更多
Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as...Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as SAS and R/S-Plus are generally limited k) single-or multi-level NLME models that only allow nested random effects and are unable to cope with crossed random effects within the framework of NLME modeling.In t his study,wc propose a general formulation of NLME models that can accommodate both nested and crassed random effects,and then develop a computational algorit hm for parameter estimation based on normal assumptions.The maximum likelihood estimation is carried out using the first-order conditional expansion (FOCE) for NLME model linearization and sequential quadratic programming (SCJP) for computational optimization while ensuring positive-definiteness of the estimated variance-covariance matrices of both random effects and error terms.The FOCE-SQP algorithm is evaluated using the height and diameter data measured on trees from Korean larch (L.olgeiisis var,Chang-paienA.b) experimental plots aa well as simulation studies.We show that the FOCE-SQP method converges fast with high accuracy.Applications of the general formulation of NLME models are illustrated with an analysis of the Korean larch data.展开更多
Moistube irrigation is a new micro-irrigation technology.Accurately estimating its wetting pattern dimensions presents a challenge.Therefore,it is necessary to develop models for efficient assessment of the wetting tr...Moistube irrigation is a new micro-irrigation technology.Accurately estimating its wetting pattern dimensions presents a challenge.Therefore,it is necessary to develop models for efficient assessment of the wetting transport pattern in order to design a cost-effective moistube irrigation system.To achieve this goal,this study developed a multivariate nonlinear regression model and compared it with a dimensional model.HYDRUS-2D was used to perform numerical simulations of 56 irrigation scenarios with different factors.The experiments showed that the shape of the wetting soil body approximated a cylinder and was mainly affected by soil texture,pressure head,and matric potential.A multivariate nonlinear model using a power function relationship between wetting size and irrigation time was developed,with a determination coefficient greater than 0.99.The model was validated for cases with six soil texture types,with mean average absolute errors of 0.43-0.90 cm,root mean square errors of 0.51-0.95 cm,and mean deviation percentage values of 3.23%-6.27%.The multivariate nonlinear regression model outperformed the dimensional model.It can therefore provide a scientific foundation for the development of moistube irrigation systems.展开更多
For complex engineering problems,multi-fidelity modeling has been used to achieve efficient reliability analysis by leveraging multiple information sources.However,most methods require nested training samples to captu...For complex engineering problems,multi-fidelity modeling has been used to achieve efficient reliability analysis by leveraging multiple information sources.However,most methods require nested training samples to capture the correlation between different fidelity data,which may lead to a significant increase in low-fidelity samples.In addition,it is difficult to build accurate surrogate models because current methods do not fully consider the nonlinearity between different fidelity samples.To address these problems,a novel multi-fidelity modeling method with active learning is proposed in this paper.Firstly,a nonlinear autoregressive multi-fidelity Kriging(NAMK)model is used to build a surrogate model.To avoid introducing redundant samples in the process of NAMK model updating,a collective learning function is then developed by a combination of a U-learning function,the correlation between different fidelity samples,and the sampling cost.Furthermore,a residual model is constructed to automatically generate low-fidelity samples when high-fidelity samples are selected.The efficiency and accuracy of the proposed method are demonstrated using three numerical examples and an engineering case.展开更多
This paper presents a Nonlinear Model Predictive Controller(NMPC)for the path following of autonomous vehicles and an algorithm to adaptively adjust the preview distance.The prediction model includes vehicle dynamics,...This paper presents a Nonlinear Model Predictive Controller(NMPC)for the path following of autonomous vehicles and an algorithm to adaptively adjust the preview distance.The prediction model includes vehicle dynamics,path following dynamics,and system input dynamics.The single-track vehicle model considers the vehicle’s coupled lateral and longitudinal dynamics,as well as nonlinear tire forces.The tracking error dynamics are derived based on the curvilinear coordinates.The cost function is designed to minimize path tracking errors and control effort while considering constraints such as actuator bounds and tire grip limits.An algorithm that utilizes the optimal preview distance vector to query the corresponding reference curvature and reference speed.The length of the preview path is adaptively adjusted based on the vehicle speed,heading error,and path curvature.We validate the controller performance in a simulation environment with the autonomous racing scenario.The simulation results show that the vehicle accurately follows the highly dynamic path with small tracking errors.The maximum preview distance can be prior estimated and guidance the selection of the prediction horizon for NMPC.展开更多
The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.B...The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.By fitting the identified nonlinear coefficients under different excitation amplitudes,the nonlinear vibration responses of the system are predicted.The results show that the accuracy of the BWM is higher than that of the CSFM,especially in the non-resonant region.However,the optimization time of the BWM is longer than that of the CSFM.展开更多
The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can repr...The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.展开更多
Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. How...Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.展开更多
SiO_(2)-particle reinforced silicon rubber composite(SP-RSRC)is a widely utilized material that offers shock absorption protection to various engineering structures in impact environments.This paper presents a compreh...SiO_(2)-particle reinforced silicon rubber composite(SP-RSRC)is a widely utilized material that offers shock absorption protection to various engineering structures in impact environments.This paper presents a comprehensive investigation of the mechanical behavior of SP-RSRC under various strain rates,employing a combination of experimental,theoretical,and numerical analyses.Firstly,quasi-static and dynamic compression tests were performed on SP-RSRC utilizing a universal testing machine and split Hopkinson pressure bar(SHPB)apparatus.Nonlinear stress-strain relationships of SP-RSRC were obtained for strain rates ranging from 1×10^(−3) to 3065 s^(−1).The results indicated that the composite showed evident strain rate sensitivity,along with nonlinearity.Then,a nonlinear visco-hyperelastic constitutive model was developed,consisting of a hyperelastic component utilizing the 3rd-order Ogden energy function and a viscous component employing a rate-dependent relaxation time scheme.The model accurately characterized the dynamic mechanical response of SP-RSRC,effectively mitigating the challenge of calibrating an excessive number of material parameters inherent in conventional viscoelastic models.Furthermore,the simplified rubber material(SRM)model,integrated within the LS-DYNA software,was chosen to depict the mechanical properties of SP-RSRC in numerical simulations.The parameters of the SRM model were further calibrated based on the strain-stress relationships of SP-RSRC,as predicted by the developed nonlinear visco-hyperelastic constitutive model.Finally,an inverse ballistic experiment using a single-stage air gun was conducted for SP-RSRC.Numerical simulations of SHPB experiments and the inverse ballistic experiment were then performed,and the reliability of the calibrated SRM model was verified by comparing the results of experiments and numerical simulations.This study offers a valuable reference for the utilization of SP-RSRC in the realm of impact protection.展开更多
This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be converg...This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be convergent in L^(2).Then for any T≥0 the corresponding solutions for the quantum lattice Boltzmann scheme are shown to be convergent in C([0,T];L^(2)(R^(1)))to the strong solution to the nonlinear Dirac equations as the mesh sizes converge to zero.In the proof,at first a Glimm type functional is introduced to establish the stability estimates for the difference between two solutions for the corresponding quantum lattice Boltzmann scheme,which leads to the compactness of the set of the solutions for the quantum lattice Boltzmann scheme.Finally the limit of any convergent subsequence of the solutions for the quantum lattice Boltzmann scheme is shown to coincide with the strong solution to a Cauchy problem for the nonlinear Dirac equations.展开更多
Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid...Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.展开更多
This paper proposes a robust control scheme based on the sequential convex programming and learning-based model for nonlinear system subjected to additive uncertainties.For the problem of system nonlinearty and unknow...This paper proposes a robust control scheme based on the sequential convex programming and learning-based model for nonlinear system subjected to additive uncertainties.For the problem of system nonlinearty and unknown uncertainties,we study the tube-based model predictive control scheme that makes use of feedforward neural network.Based on the characteristics of the bounded limit of the average cost function while time approaching infinity,a min-max optimization problem(referred to as min-max OP)is formulated to design the controller.The feasibility of this optimization problem and the practical stability of the controlled system are ensured.To demonstrate the efficacy of the proposed approach,a numerical simulation on a double-tank system is conducted.The results of the simulation serve as verification of the effectualness of the proposed scheme.展开更多
How the state of living muscles modulates the features of nonlinear elastic waves generated by external dynamic loads remains unclear because of the challenge of directly observing and modeling nonlinear elastic waves...How the state of living muscles modulates the features of nonlinear elastic waves generated by external dynamic loads remains unclear because of the challenge of directly observing and modeling nonlinear elastic waves in skeletal muscles in vivo,considering their active deformation behavior.Here,this important issue is addressed by combining experiments performed with an ultrafast ultrasound imaging system to track nonlinear shear waves(shear shock waves)in muscles in vivo and finite element analysis relying on a physically motivated constitutive model to study the effect of muscle activation level.Skeletal muscle was loaded with a deep muscle stimulator to generate shear shock waves(SSWs).The particle velocities,second and third harmonics,and group velocities of the SSWs in living muscles under both passive and active states were measured in vivo.Our experimental results reveal,for the first time,that muscle states have a pronounced effect on wave features;a low level of activation may facilitate the occurrence of both the second and third harmonics,whereas a high level of activation may inhibit the third harmonic.Finite element analysis was further carried out to quantitatively explore the effect of active muscle deformation behavior on the generation and propagation of SSWs.The simulation results at different muscle activation levels confirmed the experimental findings.The ability to reveal the effects of muscle state on the features of SSWs may be helpful in elucidating the unique dynamic deformation mechanism of living skeletal muscles,quantitatively characterizing diverse shock wave-based therapy instruments,and guiding the design of muscle-mimicking soft materials.展开更多
This paper investigates the motion control of the heavy-duty Bionic Caterpillar-like Robot(BCR)for the maintenance of the China Fusion Engineering Test Reactor(CFETR).Initially,a comprehensive nonlinear mathematical m...This paper investigates the motion control of the heavy-duty Bionic Caterpillar-like Robot(BCR)for the maintenance of the China Fusion Engineering Test Reactor(CFETR).Initially,a comprehensive nonlinear mathematical model for the BCR system is formulated using a physics-based approach.The nonlinear components of the model are compensated through nonlinear feedback linearization.Subsequently,a fuzzy-based regulator is employed to enhance the receding horizon opti-mization process for achieving optimal results.A Deep Neural Network(DNN)is trained to address disturbances.Conse-quently,a novel hybrid controller incorporating Nonlinear Model Predictive Control(NMPC),the Fuzzy Regulator(FR),and Deep Neural Network Feedforward(DNNF),named NMPC-FRDNNF is developed.Finally,the efficacy of the control system is validated through simulations and experiments.The results indicate that the Root Mean Square Error(RMSE)of the controller with FR and DNNF decreases by 33.2 and 48.9%,respectively,compared to the controller without these enhancements.This research provides a theoretical foundation and practical insights for ensuring the future highly stable,safe,and efficient maintenance of blankets.展开更多
文摘Mixed-effects models,also called random-effects models,are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject,but also to describe the variation among different subjects.Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data.In this paper,nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies.By using this type of models,statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance.Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.
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 Key Research and Development Program of China(2017YFD0600401)the Fundamental Research Funds for the Central Universities(2572019CP08)
文摘Korean larch(Larix olgensis)is one of the main tree species for aff orestation and timber production in northeast China.However,its timber quality and growth ability are largely infl uenced by crown size,structure and shape.The majority of crown models are static models based on tree size and stand characteristics from temporary sample plots,but crown dynamic models has seldom been constructed.Therefore,this study aimed to develop height to crown base(HCB)and crown length(CL)dynamic models using the branch mortality technique for a Korean larch plantation.The nonlinear mixed-eff ects model with random eff ects,variance functions and correlation structures,was used to build HCB and CL dynamic models.The data were obtained from 95 sample trees of 19 plots in Meng JiaGang forest farm in Northeast China.The results showed that HCB progressively increases as tree age,tree height growth(HT growth)and diameter at breast height growth(DBH growth).The CL was increased with tree age in 20 years ago,and subsequently stabilized.HT growth,DBH growth stand basal area(BAS)and crown competition factor(CCF)signifi cantly infl uenced HCB and CL.The HCB was positively correlated with BAS,HT growth and DBH growth,but negatively correlated with CCF.The CL was positively correlated with BAS and CCF,but negatively correlated with DBH growth.Model fi tting and validation confi rmed that the mixed-eff ects model considering the stand and tree level random eff ects was accurate and reliable for predicting the HCB and CL dynamics.However,the models involving adding variance functions and time series correlation structure could not completely remove heterogeneity and autocorrelation,and the fi tting precision of the models was reduced.Therefore,from the point of view of application,we should take care to avoid setting up over-complex models.The HCB and CL dynamic models in our study may also be incorporated into stand growth and yield model systems in China.
基金The authors would like to thank the Thirteenth Five-year Plan Pioneering project of High Technology Plan of the National Department of Technology (No. 2017YFC0504101)the National Natural Science Foundations of China (Nos. 31470641, 31300534 and 31570628) for the financial support of this study.
文摘Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as SAS and R/S-Plus are generally limited k) single-or multi-level NLME models that only allow nested random effects and are unable to cope with crossed random effects within the framework of NLME modeling.In t his study,wc propose a general formulation of NLME models that can accommodate both nested and crassed random effects,and then develop a computational algorit hm for parameter estimation based on normal assumptions.The maximum likelihood estimation is carried out using the first-order conditional expansion (FOCE) for NLME model linearization and sequential quadratic programming (SCJP) for computational optimization while ensuring positive-definiteness of the estimated variance-covariance matrices of both random effects and error terms.The FOCE-SQP algorithm is evaluated using the height and diameter data measured on trees from Korean larch (L.olgeiisis var,Chang-paienA.b) experimental plots aa well as simulation studies.We show that the FOCE-SQP method converges fast with high accuracy.Applications of the general formulation of NLME models are illustrated with an analysis of the Korean larch data.
基金supported by the National Natural Science Foundation of China(Grant No.51969013)the Natural Science Foundation of Gansu Province(Grant No.21JR7RA225).
文摘Moistube irrigation is a new micro-irrigation technology.Accurately estimating its wetting pattern dimensions presents a challenge.Therefore,it is necessary to develop models for efficient assessment of the wetting transport pattern in order to design a cost-effective moistube irrigation system.To achieve this goal,this study developed a multivariate nonlinear regression model and compared it with a dimensional model.HYDRUS-2D was used to perform numerical simulations of 56 irrigation scenarios with different factors.The experiments showed that the shape of the wetting soil body approximated a cylinder and was mainly affected by soil texture,pressure head,and matric potential.A multivariate nonlinear model using a power function relationship between wetting size and irrigation time was developed,with a determination coefficient greater than 0.99.The model was validated for cases with six soil texture types,with mean average absolute errors of 0.43-0.90 cm,root mean square errors of 0.51-0.95 cm,and mean deviation percentage values of 3.23%-6.27%.The multivariate nonlinear regression model outperformed the dimensional model.It can therefore provide a scientific foundation for the development of moistube irrigation systems.
基金supported by the Major Projects of Zhejiang Provincial Natural Science Foundation of China(No.LD22E050009)the National Natural Science Foundation of China(No.51475425)the College Student’s Science and Technology Innovation Project of Zhejiang Province(No.2022R403B060),China.
文摘For complex engineering problems,multi-fidelity modeling has been used to achieve efficient reliability analysis by leveraging multiple information sources.However,most methods require nested training samples to capture the correlation between different fidelity data,which may lead to a significant increase in low-fidelity samples.In addition,it is difficult to build accurate surrogate models because current methods do not fully consider the nonlinearity between different fidelity samples.To address these problems,a novel multi-fidelity modeling method with active learning is proposed in this paper.Firstly,a nonlinear autoregressive multi-fidelity Kriging(NAMK)model is used to build a surrogate model.To avoid introducing redundant samples in the process of NAMK model updating,a collective learning function is then developed by a combination of a U-learning function,the correlation between different fidelity samples,and the sampling cost.Furthermore,a residual model is constructed to automatically generate low-fidelity samples when high-fidelity samples are selected.The efficiency and accuracy of the proposed method are demonstrated using three numerical examples and an engineering case.
基金“National Science and Technology Council”(NSTC 111-2221-E-027-088)。
文摘This paper presents a Nonlinear Model Predictive Controller(NMPC)for the path following of autonomous vehicles and an algorithm to adaptively adjust the preview distance.The prediction model includes vehicle dynamics,path following dynamics,and system input dynamics.The single-track vehicle model considers the vehicle’s coupled lateral and longitudinal dynamics,as well as nonlinear tire forces.The tracking error dynamics are derived based on the curvilinear coordinates.The cost function is designed to minimize path tracking errors and control effort while considering constraints such as actuator bounds and tire grip limits.An algorithm that utilizes the optimal preview distance vector to query the corresponding reference curvature and reference speed.The length of the preview path is adaptively adjusted based on the vehicle speed,heading error,and path curvature.We validate the controller performance in a simulation environment with the autonomous racing scenario.The simulation results show that the vehicle accurately follows the highly dynamic path with small tracking errors.The maximum preview distance can be prior estimated and guidance the selection of the prediction horizon for NMPC.
文摘The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.By fitting the identified nonlinear coefficients under different excitation amplitudes,the nonlinear vibration responses of the system are predicted.The results show that the accuracy of the BWM is higher than that of the CSFM,especially in the non-resonant region.However,the optimization time of the BWM is longer than that of the CSFM.
基金the support of Texas A&M University at Qatar for the 2022 Sixth Cycle Seed Grant Project。
文摘The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.
基金supported in part by the National Nature Science Foundation of China(Nos.62173091,62073082)in part by the Natural Science Foundation of Fujian Province(No.2023J01268)in part by the Taishan Scholar Program of Shandong Province.
文摘Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.
文摘SiO_(2)-particle reinforced silicon rubber composite(SP-RSRC)is a widely utilized material that offers shock absorption protection to various engineering structures in impact environments.This paper presents a comprehensive investigation of the mechanical behavior of SP-RSRC under various strain rates,employing a combination of experimental,theoretical,and numerical analyses.Firstly,quasi-static and dynamic compression tests were performed on SP-RSRC utilizing a universal testing machine and split Hopkinson pressure bar(SHPB)apparatus.Nonlinear stress-strain relationships of SP-RSRC were obtained for strain rates ranging from 1×10^(−3) to 3065 s^(−1).The results indicated that the composite showed evident strain rate sensitivity,along with nonlinearity.Then,a nonlinear visco-hyperelastic constitutive model was developed,consisting of a hyperelastic component utilizing the 3rd-order Ogden energy function and a viscous component employing a rate-dependent relaxation time scheme.The model accurately characterized the dynamic mechanical response of SP-RSRC,effectively mitigating the challenge of calibrating an excessive number of material parameters inherent in conventional viscoelastic models.Furthermore,the simplified rubber material(SRM)model,integrated within the LS-DYNA software,was chosen to depict the mechanical properties of SP-RSRC in numerical simulations.The parameters of the SRM model were further calibrated based on the strain-stress relationships of SP-RSRC,as predicted by the developed nonlinear visco-hyperelastic constitutive model.Finally,an inverse ballistic experiment using a single-stage air gun was conducted for SP-RSRC.Numerical simulations of SHPB experiments and the inverse ballistic experiment were then performed,and the reliability of the calibrated SRM model was verified by comparing the results of experiments and numerical simulations.This study offers a valuable reference for the utilization of SP-RSRC in the realm of impact protection.
基金partially supported by the NSFC(11421061,12271507)the Natural Science Foundation of Shanghai(15ZR1403900)。
文摘This paper studies the strong convergence of the quantum lattice Boltzmann(QLB)scheme for the nonlinear Dirac equations for Gross-Neveu model in 1+1 dimensions.The initial data for the scheme are assumed to be convergent in L^(2).Then for any T≥0 the corresponding solutions for the quantum lattice Boltzmann scheme are shown to be convergent in C([0,T];L^(2)(R^(1)))to the strong solution to the nonlinear Dirac equations as the mesh sizes converge to zero.In the proof,at first a Glimm type functional is introduced to establish the stability estimates for the difference between two solutions for the corresponding quantum lattice Boltzmann scheme,which leads to the compactness of the set of the solutions for the quantum lattice Boltzmann scheme.Finally the limit of any convergent subsequence of the solutions for the quantum lattice Boltzmann scheme is shown to coincide with the strong solution to a Cauchy problem for the nonlinear Dirac equations.
基金Project supported by the National Natural Science Foundation of China (Nos.12072119,12325201,and 52205594)the China National Postdoctoral Program for Innovative Talents (No.BX20220118)。
文摘Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.
文摘This paper proposes a robust control scheme based on the sequential convex programming and learning-based model for nonlinear system subjected to additive uncertainties.For the problem of system nonlinearty and unknown uncertainties,we study the tube-based model predictive control scheme that makes use of feedforward neural network.Based on the characteristics of the bounded limit of the average cost function while time approaching infinity,a min-max optimization problem(referred to as min-max OP)is formulated to design the controller.The feasibility of this optimization problem and the practical stability of the controlled system are ensured.To demonstrate the efficacy of the proposed approach,a numerical simulation on a double-tank system is conducted.The results of the simulation serve as verification of the effectualness of the proposed scheme.
基金supported by the National Students Training Program for Innovation(Grant No.202210007029)。
文摘How the state of living muscles modulates the features of nonlinear elastic waves generated by external dynamic loads remains unclear because of the challenge of directly observing and modeling nonlinear elastic waves in skeletal muscles in vivo,considering their active deformation behavior.Here,this important issue is addressed by combining experiments performed with an ultrafast ultrasound imaging system to track nonlinear shear waves(shear shock waves)in muscles in vivo and finite element analysis relying on a physically motivated constitutive model to study the effect of muscle activation level.Skeletal muscle was loaded with a deep muscle stimulator to generate shear shock waves(SSWs).The particle velocities,second and third harmonics,and group velocities of the SSWs in living muscles under both passive and active states were measured in vivo.Our experimental results reveal,for the first time,that muscle states have a pronounced effect on wave features;a low level of activation may facilitate the occurrence of both the second and third harmonics,whereas a high level of activation may inhibit the third harmonic.Finite element analysis was further carried out to quantitatively explore the effect of active muscle deformation behavior on the generation and propagation of SSWs.The simulation results at different muscle activation levels confirmed the experimental findings.The ability to reveal the effects of muscle state on the features of SSWs may be helpful in elucidating the unique dynamic deformation mechanism of living skeletal muscles,quantitatively characterizing diverse shock wave-based therapy instruments,and guiding the design of muscle-mimicking soft materials.
基金supported by Comprehensive Research Facility for Fusion Technology Program of China under Contract No.2018-000052-73-01-001228the China Scholarship Council with No.202206340050National Natural Science Foundation of China with Grant No.11905147.
文摘This paper investigates the motion control of the heavy-duty Bionic Caterpillar-like Robot(BCR)for the maintenance of the China Fusion Engineering Test Reactor(CFETR).Initially,a comprehensive nonlinear mathematical model for the BCR system is formulated using a physics-based approach.The nonlinear components of the model are compensated through nonlinear feedback linearization.Subsequently,a fuzzy-based regulator is employed to enhance the receding horizon opti-mization process for achieving optimal results.A Deep Neural Network(DNN)is trained to address disturbances.Conse-quently,a novel hybrid controller incorporating Nonlinear Model Predictive Control(NMPC),the Fuzzy Regulator(FR),and Deep Neural Network Feedforward(DNNF),named NMPC-FRDNNF is developed.Finally,the efficacy of the control system is validated through simulations and experiments.The results indicate that the Root Mean Square Error(RMSE)of the controller with FR and DNNF decreases by 33.2 and 48.9%,respectively,compared to the controller without these enhancements.This research provides a theoretical foundation and practical insights for ensuring the future highly stable,safe,and efficient maintenance of blankets.
