The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect t...The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect the unsaturated soil strength; meanwhile, the relationship between the unsaturated soil strength and matric suction is nonlinear. This work is to present closed-form equations of critical embedment depth for a rigid retaining wall against overturning by means of moment equilibrium. Matric suction is considered to be distributed uniformly and linearly with depth. The unified shear strength formulation for unsaturated soils under the plane strain condition is adopted to characterize the intermediate principal stress effect, and strength nonlinearity is described by a hyperbolic model of suction angle. The result obtained is orderly series solutions rather than one specific answer; thus, it has wide theoretical significance and good applicability. The validity of this present work is demonstrated by comparing it with a lower bound solution. The traditional overturning designs for rigid retaining walls, in which the saturated soil mechanics neglecting matric suction or the unsaturated soil mechanics based on the Mohr-Coulomb criterion are employed, are special cases of the proposed result. Parametric studies about the intermediate principal stress, matric suction and its distributions along with two strength nonlinearity methods on a new defined critical buried coefficient are discussed.展开更多
The identification of nonlinear systems with multiple sampled rates is a difficult task.The motivation of our paper is to study the parameter estimation problem of Hammerstein systems with dead-zone characteristics by...The identification of nonlinear systems with multiple sampled rates is a difficult task.The motivation of our paper is to study the parameter estimation problem of Hammerstein systems with dead-zone characteristics by using the dual-rate sampled data.Firstly,the auxiliary model identification principle is used to estimate the unmeasurable variables,and the recursive estimation algorithm is proposed to identify the parameters of the static nonlinear model with the dead-zone function and the parameters of the dynamic linear system model.Then,the convergence of the proposed identification algorithm is analyzed by using the martingale convergence theorem.It is proved theoretically that the estimated parameters can converge to the real values under the condition of continuous excitation.Finally,the validity of the proposed algorithm is proved by the identification of the dual-rate sampled nonlinear systems.展开更多
Measurement of nonlinearity parameter using the second-harmonic reflective model is studied. A new kind of compound transducer is designed and fabricated for this purpose. With this transducer and the finite amplitude...Measurement of nonlinearity parameter using the second-harmonic reflective model is studied. A new kind of compound transducer is designed and fabricated for this purpose. With this transducer and the finite amplitude insert-substitution method, an experimental system to measure the nonlinearity parameter using reflective model is developed. B/A values of some liquids and biological tissues are obtained and results coincide well with those presented in the literatures.展开更多
This paper studies the global fixed time synchronization of complex dynamical network,including non-identical nodes with disturbances and uncertainties as well as input nonlinearity.First,a novel fixed time sliding ma...This paper studies the global fixed time synchronization of complex dynamical network,including non-identical nodes with disturbances and uncertainties as well as input nonlinearity.First,a novel fixed time sliding manifold is constructed to achieve the fixed time synchronization of complex dynamical network with disturbances and uncertainties.Second,a novel sliding mode controller is proposed to realize the global fixed time reachability of sliding surfaces.The outstanding feature of the designed control is that the fixed convergence time of both reaching and sliding modes can be adjusted to the desired values in advance by choosing the explicit parameters in the controller,which does not rest upon the initial conditions and the topology of the network.Finally,the effectiveness and validity of the obtained results are demonstrated by corresponding numerical simulations.展开更多
The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule.The stability factors of slopes were calculated using vertical slice method based on limit analysis.The pote...The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule.The stability factors of slopes were calculated using vertical slice method based on limit analysis.The potential sliding mass was divided into a series of vertical slices as well as the traditional slice technique.Equating the external work rate to the internal energy dissipation,the optimum solutions to stability factors were determined by the nonlinear programming algorithm.From the numerical results,it is found that the present solutions agree well with previous results when the nonlinear criterion reduces to the linear criterion,and the nonassociated flow rule reduces to the associated flow rule.The stability factors decrease by 39.7%with nonlinear parameter varying from 1.0 to 3.0.Dilation and nonlinearity have significant effects on the slope stability factors.展开更多
The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soi...The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule.The multipoint tangent(multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion.A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique,and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming.The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule,which demonstrates the rationality of the presented method.Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique.The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis.The combined effect of nonlinearity and dilation on slope stability was analyzed,and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.展开更多
In order to enhance the control performance of piezo-positioning system,the influence of hysteresis characteristics and its compensation method are studied.Hammerstein model is used to represent the dynamic hysteresis...In order to enhance the control performance of piezo-positioning system,the influence of hysteresis characteristics and its compensation method are studied.Hammerstein model is used to represent the dynamic hysteresis nonlinear characteristics of piezo-positioning actuator.The static nonlinear part and dynamic linear part of the Hammerstein model are represented by models obtained through the Prandtl-Ishlinskii(PI)model and Hankel matrix system identification method,respectively.This model demonstrates good generalization capability for typical input frequencies below 200 Hz.A sliding mode inverse compensation tracking control strategy based on P-I inverse model and integral augmentation is proposed.Experimental results show that compared with PID inverse compensation control and sliding mode control without inverse compensation,the sliding mode inverse compensation control has a more ideal step response and no overshoot,moreover,the settling time is only 6.2 ms.In the frequency domain,the system closed-loop tracking bandwidth reaches 119.9 Hz,and the disturbance rejection bandwidth reaches 86.2 Hz.The proposed control strategy can effectively compensate the hysteresis nonlinearity,and improve the tracking accuracy and antidisturbance capability of piezo-positioning system.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
Herein,we report the synthesis and third-order nonlinear optical(NLO)properties of a novel cage-based 2D metal-organic framework constructed from Ti_(4)L_(6)(L4-=embonate)cage combined with Mg^(2+)and tris[4-(1H-imida...Herein,we report the synthesis and third-order nonlinear optical(NLO)properties of a novel cage-based 2D metal-organic framework constructed from Ti_(4)L_(6)(L4-=embonate)cage combined with Mg^(2+)and tris[4-(1H-imidazol-1-yl)phenyl]amine(tipa)ligand,whose molecular formula is(Me_(2)CH_(2))_(2)[Mg_(3)(Ti_(4)L_(6))(tipa)(H_(2)O)_(12)](PTC‑378).The Ti_(4)L_(6)tetrahedral cages serve as robust building units,while the Mg^(2+)ions and tipa ligands provide structural stability and tunable optical properties.The resulting PTC‑378 film exhibited intriguing third-order NLO property,which was systematically investigated using Z-scan techniques.Our results demonstrate that the synergistic interaction between Ti_(4)L_(6)cages andπ-conjugated ligands significantly enhances the NLO performance of the materials.CCDC:2453909.展开更多
With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixe...With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.展开更多
In this paper a fully parametrized finite element simulation model of the stator bar end is created using the COMSOL Multiphysics.The model allows conducting the comparison of different corona protection structures’d...In this paper a fully parametrized finite element simulation model of the stator bar end is created using the COMSOL Multiphysics.The model allows conducting the comparison of different corona protection structures’design,various materials properties,and finally optimizing the corona protection system.Several samples of SiC based nonlinear conductivity materials for corona protection were fabricated in laboratory and then investigated.The conductivity dependencies on electric field(0.05 to 1 kV/mm)and temperature(20 to 155℃)were measured.By comparing the heat-resistant grades of the corona protection material and the insulating material,the maximum working temperature of the corona protection material corresponds to the heat-resistant grade F of the insulating material.As the temperature increases,the nonlinear characteristics of the corona protection material in the experiment decrease dramatically,reducing the heat-resistant grade of the corona protection material.The decrease in the nonlinear characteristics of the corona protection material at the maximum operating temperature causes the maximum electric field strength at the end of the HV rotating machines end corona protection(ECP)exceeding the corona discharge electric field strength,resulting in corona phenomenon.展开更多
An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solutio...An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.展开更多
The generation of optical vortices from nonlinear photonic crystals(NPCs)with spatially modulated second-order nonlinearity offers a promising approach to extend the working wavelength and topological charge of vortex...The generation of optical vortices from nonlinear photonic crystals(NPCs)with spatially modulated second-order nonlinearity offers a promising approach to extend the working wavelength and topological charge of vortex beams for various applications.In this work,the second harmonic(SH)optical vortex beams generated from nonlinear fork gratings under Gaussian beam illumination are numerically investigated.The far-field intensity and phase distributions,as well as the orbital angular momentum(OAM)spectra of the SH beams,are analyzed for different structural topological charges and diffraction orders.Results reveal that higher-order diffraction and larger structural topological charges lead to angular interference patterns and non-uniform intensity distributions,deviating from the standard vortex profile.To optimize the SH vortex quality,the effects of the fundamental wave beam waist,crystal thickness,and grating duty cycle are explored.It is shown that increasing the beam waist can effectively suppress diffraction order interference and improve the beam’s quality.This study provides theoretical guidance for enhancing the performance of nonlinear optical devices based on NPCs.展开更多
In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introduc...In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.展开更多
This study involved a comprehensive investigation aimed at achieving efficient multi-millijoule THz wave generation by exploiting the unique properties of cylindrical GaAs waveguides as effective mediators of the conv...This study involved a comprehensive investigation aimed at achieving efficient multi-millijoule THz wave generation by exploiting the unique properties of cylindrical GaAs waveguides as effective mediators of the conversion of laser energy into THz waves.Through meticulous investigation,valuable insights into optimizing THz generation processes for practical applications were unearthed.By investigating Hertz potentials,an eigen-value equation for the solutions of the guided modes(i.e.,eigenvalues)was found.The effects of various param-eters,including the effective mode index and the laser pulse power,on the electric field components of THz radia-tion,including the fundamental TE(transverse electric)and TM(transverse magnetic)modes,were evaluated.By analyzing these factors,this research elucidated the nuanced mechanisms governing THz wave generation within cylindrical GaAs waveguides,paving the way for refined methodologies and enhanced efficiency.The sig-nificance of cylindrical GaAs waveguides extends beyond their roles as mere facilitators of THz generation;their design and fabrication hold the key to unlocking the potential for compact and portable THz systems.This trans-formative capability not only amplifies the efficiency of THz generation but also broadens the horizons of practical applications.展开更多
When the proton exchange membrane fuel cell(PEMFC)system is running,there will be a condition that does not require power output for a short time.In order to achieve zero power output under low power consumption,it is...When the proton exchange membrane fuel cell(PEMFC)system is running,there will be a condition that does not require power output for a short time.In order to achieve zero power output under low power consumption,it is necessary to consider the diversity of control targets and the complexity of dynamic models,which brings the challenge of high-precision tracking control of the stack output power and cathode intake flow.For system idle speed control,a modelbased nonlinear control framework is constructed in this paper.Firstly,the nonlinear dynamic model of output power and cathode intake flow is derived.Secondly,a control scheme combining nonlinear extended Kalman filter observer and state feedback controller is designed.Finally,the control scheme is verified on the PEMFC experimental platform and compared with the proportion-integration-differentiation(PID)controller.The experimental results show that the control strategy proposed in this paper can realize the idle speed control of the fuel cell system and achieve the purpose of zero power output.Compared with PID controller,it has faster response speed and better system dynamics.展开更多
In order to get rid of the dependence on high-precision centrifuges in accelerometer nonlinear coefficients calibration,this paper proposes a system-level calibration method for field condition.Firstly,a 42-dimension ...In order to get rid of the dependence on high-precision centrifuges in accelerometer nonlinear coefficients calibration,this paper proposes a system-level calibration method for field condition.Firstly,a 42-dimension Kalman filter is constructed to reduce impact brought by turntable.Then,a biaxial rotation path is designed based on the accelerometer output model,including orthogonal 22 positions and tilt 12 positions,which enhances gravity excitation on nonlinear coefficients of accelerometer.Finally,sampling is carried out for calibration and further experiments.The results of static inertial navigation experiments lasting 4000 s show that compared with the traditional method,the proposed method reduces the position error by about 390 m.展开更多
The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The n...The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The normal vector used to calculate the first-type limit function is determined in the natural frame without the aid of the curvature parameter of worm helicoid.The first-type limit line is ascertained via solving the nonlinear equations iteratively.It is discovered that one first-type limit line exists on the tooth surface of worm wheel by numerical simulation,and such a line is normally located out of the meshing zone.Only one intersection point exists between the first and second-types of limit lines,and this point is a lubrication weak point.The undercutting mechanism is essentially that a part of the meshing zone near the conjugated line of worm tooth crest will come into the undercutting area and will be cut off during machining the worm wheel.The machining simulation verifies the correctness of undercutting mechanism.Moreover,a convenient and practical characteristic quantity is proposed to judge whether the undercutting exists in the whole meshing zone via computing the first-type limit function values on the worm tooth crest.展开更多
Intercepting high-maneuverability hypersonic targets in near-space environments poses significant challenges due to their extreme speeds and evasive capabilities.To address these challenges,this study presents an inte...Intercepting high-maneuverability hypersonic targets in near-space environments poses significant challenges due to their extreme speeds and evasive capabilities.To address these challenges,this study presents an integrated approach that combines a Three-Dimensional Finite-Time Optimal Cooperative Guidance Law(FTOC)with an Information Fusion Anti-saturation Predefined-time Observer(IFAPO).The proposed FTOC guidance law employs a nonlinear,non-quadratic finite-time optimal control strategy designed for rapid convergence within the limited timeframes of near-space interceptions,avoiding the need for remaining flight time estimation or linear decoupling inherent in traditional methods.To complement the guidance strategy,the IFAPO leverages multi-source information fusion theory and incorporates anti-saturation mechanisms to enhance target maneuver estimation.This method ensures accurate and real-time prediction of target acceleration while maintaining predefined convergence performance,even under complex interception conditions.By integrating the FTOC guidance law and IFAPO,the approach optimizes cooperative missile positioning,improves interception success rates,and minimizes fuel consumption,addressing practical constraints in military applications.Simulation results and comparative analyses confirm the effectiveness of the integrated approach,demonstrating its capability to achieve cooperative interception of highly maneuvering targets with enhanced efficiency and reduced economic costs,aligning with realistic combat scenarios.展开更多
Piezo actuators are widely used in ultra-precision fields because of their high response and nano-scale step length.However,their hysteresis characteristics seriously affect the accuracy and stability of piezo actuato...Piezo actuators are widely used in ultra-precision fields because of their high response and nano-scale step length.However,their hysteresis characteristics seriously affect the accuracy and stability of piezo actuators.Existing methods for fitting hysteresis loops include operator class,differential equation class,and machine learning class.The modeling cost of operator class and differential equation class methods is high,the model complexity is high,and the process of machine learning,such as neural network calculation,is opaque.The physical model framework cannot be directly extracted.Therefore,the sparse identification of nonlinear dynamics(SINDy)algorithm is proposed to fit hysteresis loops.Furthermore,the SINDy algorithm is improved.While the SINDy algorithm builds an orthogonal candidate database for modeling,the sparse regression model is simplified,and the Relay operator is introduced for piecewise fitting to solve the distortion problem of the SINDy algorithm fitting singularities.The Relay-SINDy algorithm proposed in this paper is applied to fitting hysteresis loops.Good performance is obtained with the experimental results of open and closed loops.Compared with the existing methods,the modeling cost and model complexity are reduced,and the modeling accuracy of the hysteresis loop is improved.展开更多
基金Project(41202191)supported by the National Natural Science Foundation of ChinaProject(2015JM4146)supported by the Natural Science Foundation of Shaanxi Province,ChinaProject(2015)supported by the Postdoctoral Research Project of Shaanxi Province,China
文摘The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect the unsaturated soil strength; meanwhile, the relationship between the unsaturated soil strength and matric suction is nonlinear. This work is to present closed-form equations of critical embedment depth for a rigid retaining wall against overturning by means of moment equilibrium. Matric suction is considered to be distributed uniformly and linearly with depth. The unified shear strength formulation for unsaturated soils under the plane strain condition is adopted to characterize the intermediate principal stress effect, and strength nonlinearity is described by a hyperbolic model of suction angle. The result obtained is orderly series solutions rather than one specific answer; thus, it has wide theoretical significance and good applicability. The validity of this present work is demonstrated by comparing it with a lower bound solution. The traditional overturning designs for rigid retaining walls, in which the saturated soil mechanics neglecting matric suction or the unsaturated soil mechanics based on the Mohr-Coulomb criterion are employed, are special cases of the proposed result. Parametric studies about the intermediate principal stress, matric suction and its distributions along with two strength nonlinearity methods on a new defined critical buried coefficient are discussed.
基金supported by the National Natural Science Foundation of China(61863034)
文摘The identification of nonlinear systems with multiple sampled rates is a difficult task.The motivation of our paper is to study the parameter estimation problem of Hammerstein systems with dead-zone characteristics by using the dual-rate sampled data.Firstly,the auxiliary model identification principle is used to estimate the unmeasurable variables,and the recursive estimation algorithm is proposed to identify the parameters of the static nonlinear model with the dead-zone function and the parameters of the dynamic linear system model.Then,the convergence of the proposed identification algorithm is analyzed by using the martingale convergence theorem.It is proved theoretically that the estimated parameters can converge to the real values under the condition of continuous excitation.Finally,the validity of the proposed algorithm is proved by the identification of the dual-rate sampled nonlinear systems.
文摘Measurement of nonlinearity parameter using the second-harmonic reflective model is studied. A new kind of compound transducer is designed and fabricated for this purpose. With this transducer and the finite amplitude insert-substitution method, an experimental system to measure the nonlinearity parameter using reflective model is developed. B/A values of some liquids and biological tissues are obtained and results coincide well with those presented in the literatures.
文摘This paper studies the global fixed time synchronization of complex dynamical network,including non-identical nodes with disturbances and uncertainties as well as input nonlinearity.First,a novel fixed time sliding manifold is constructed to achieve the fixed time synchronization of complex dynamical network with disturbances and uncertainties.Second,a novel sliding mode controller is proposed to realize the global fixed time reachability of sliding surfaces.The outstanding feature of the designed control is that the fixed convergence time of both reaching and sliding modes can be adjusted to the desired values in advance by choosing the explicit parameters in the controller,which does not rest upon the initial conditions and the topology of the network.Finally,the effectiveness and validity of the obtained results are demonstrated by corresponding numerical simulations.
基金Project(200550)supported by the Foundation for the Author of National Excellent Doctoral Dissertation of ChinaProject(200631878557)supported by West Traffic of Science and Technology of China
文摘The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule.The stability factors of slopes were calculated using vertical slice method based on limit analysis.The potential sliding mass was divided into a series of vertical slices as well as the traditional slice technique.Equating the external work rate to the internal energy dissipation,the optimum solutions to stability factors were determined by the nonlinear programming algorithm.From the numerical results,it is found that the present solutions agree well with previous results when the nonlinear criterion reduces to the linear criterion,and the nonassociated flow rule reduces to the associated flow rule.The stability factors decrease by 39.7%with nonlinear parameter varying from 1.0 to 3.0.Dilation and nonlinearity have significant effects on the slope stability factors.
基金Projects(51208522,51478477)supported by the National Natural Science Foundation of ChinaProject(2012122033)supported by the Guizhou Provincial Department of Transportation Foundation,ChinaProject(CX2015B049)supported by the Scientific Research Innovation Project of Hunan Province,China
文摘The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule.The multipoint tangent(multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion.A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique,and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming.The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule,which demonstrates the rationality of the presented method.Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique.The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis.The combined effect of nonlinearity and dilation on slope stability was analyzed,and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.
文摘In order to enhance the control performance of piezo-positioning system,the influence of hysteresis characteristics and its compensation method are studied.Hammerstein model is used to represent the dynamic hysteresis nonlinear characteristics of piezo-positioning actuator.The static nonlinear part and dynamic linear part of the Hammerstein model are represented by models obtained through the Prandtl-Ishlinskii(PI)model and Hankel matrix system identification method,respectively.This model demonstrates good generalization capability for typical input frequencies below 200 Hz.A sliding mode inverse compensation tracking control strategy based on P-I inverse model and integral augmentation is proposed.Experimental results show that compared with PID inverse compensation control and sliding mode control without inverse compensation,the sliding mode inverse compensation control has a more ideal step response and no overshoot,moreover,the settling time is only 6.2 ms.In the frequency domain,the system closed-loop tracking bandwidth reaches 119.9 Hz,and the disturbance rejection bandwidth reaches 86.2 Hz.The proposed control strategy can effectively compensate the hysteresis nonlinearity,and improve the tracking accuracy and antidisturbance capability of piezo-positioning system.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
文摘Herein,we report the synthesis and third-order nonlinear optical(NLO)properties of a novel cage-based 2D metal-organic framework constructed from Ti_(4)L_(6)(L4-=embonate)cage combined with Mg^(2+)and tris[4-(1H-imidazol-1-yl)phenyl]amine(tipa)ligand,whose molecular formula is(Me_(2)CH_(2))_(2)[Mg_(3)(Ti_(4)L_(6))(tipa)(H_(2)O)_(12)](PTC‑378).The Ti_(4)L_(6)tetrahedral cages serve as robust building units,while the Mg^(2+)ions and tipa ligands provide structural stability and tunable optical properties.The resulting PTC‑378 film exhibited intriguing third-order NLO property,which was systematically investigated using Z-scan techniques.Our results demonstrate that the synergistic interaction between Ti_(4)L_(6)cages andπ-conjugated ligands significantly enhances the NLO performance of the materials.CCDC:2453909.
基金Supported by the National Natural Science Foundation of China(12201368,62376252)Key Project of Natural Science Foundation of Zhejiang Province(LZ22F030003)Zhejiang Province Leading Geese Plan(2024C02G1123882,2024C01SA100795).
文摘With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.
文摘In this paper a fully parametrized finite element simulation model of the stator bar end is created using the COMSOL Multiphysics.The model allows conducting the comparison of different corona protection structures’design,various materials properties,and finally optimizing the corona protection system.Several samples of SiC based nonlinear conductivity materials for corona protection were fabricated in laboratory and then investigated.The conductivity dependencies on electric field(0.05 to 1 kV/mm)and temperature(20 to 155℃)were measured.By comparing the heat-resistant grades of the corona protection material and the insulating material,the maximum working temperature of the corona protection material corresponds to the heat-resistant grade F of the insulating material.As the temperature increases,the nonlinear characteristics of the corona protection material in the experiment decrease dramatically,reducing the heat-resistant grade of the corona protection material.The decrease in the nonlinear characteristics of the corona protection material at the maximum operating temperature causes the maximum electric field strength at the end of the HV rotating machines end corona protection(ECP)exceeding the corona discharge electric field strength,resulting in corona phenomenon.
基金Supported by Scientific Research Fund of Hunan Provincial Education Departmen(t23A0361)。
文摘An evolution inequality of Sobolev type involving a nonlinear convolution term is considered.By using the nonlinear capacity method and the contradiction argument,the non-existence of the nontrivial local weak solution is proved.
基金supported by the National Nat-ural Science Foundation of China(Nos.12192251,12174185,92163216,and 62288101).
文摘The generation of optical vortices from nonlinear photonic crystals(NPCs)with spatially modulated second-order nonlinearity offers a promising approach to extend the working wavelength and topological charge of vortex beams for various applications.In this work,the second harmonic(SH)optical vortex beams generated from nonlinear fork gratings under Gaussian beam illumination are numerically investigated.The far-field intensity and phase distributions,as well as the orbital angular momentum(OAM)spectra of the SH beams,are analyzed for different structural topological charges and diffraction orders.Results reveal that higher-order diffraction and larger structural topological charges lead to angular interference patterns and non-uniform intensity distributions,deviating from the standard vortex profile.To optimize the SH vortex quality,the effects of the fundamental wave beam waist,crystal thickness,and grating duty cycle are explored.It is shown that increasing the beam waist can effectively suppress diffraction order interference and improve the beam’s quality.This study provides theoretical guidance for enhancing the performance of nonlinear optical devices based on NPCs.
基金Supported by the National Natural Science Foundation of China(12061048)NSF of Jiangxi Province(20232BAB201026,20232BAB201018)。
文摘In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.
文摘This study involved a comprehensive investigation aimed at achieving efficient multi-millijoule THz wave generation by exploiting the unique properties of cylindrical GaAs waveguides as effective mediators of the conversion of laser energy into THz waves.Through meticulous investigation,valuable insights into optimizing THz generation processes for practical applications were unearthed.By investigating Hertz potentials,an eigen-value equation for the solutions of the guided modes(i.e.,eigenvalues)was found.The effects of various param-eters,including the effective mode index and the laser pulse power,on the electric field components of THz radia-tion,including the fundamental TE(transverse electric)and TM(transverse magnetic)modes,were evaluated.By analyzing these factors,this research elucidated the nuanced mechanisms governing THz wave generation within cylindrical GaAs waveguides,paving the way for refined methodologies and enhanced efficiency.The sig-nificance of cylindrical GaAs waveguides extends beyond their roles as mere facilitators of THz generation;their design and fabrication hold the key to unlocking the potential for compact and portable THz systems.This trans-formative capability not only amplifies the efficiency of THz generation but also broadens the horizons of practical applications.
基金Supported by the Major Science and Technology Projects in Jilin Province and Changchun City(20220301010GX).
文摘When the proton exchange membrane fuel cell(PEMFC)system is running,there will be a condition that does not require power output for a short time.In order to achieve zero power output under low power consumption,it is necessary to consider the diversity of control targets and the complexity of dynamic models,which brings the challenge of high-precision tracking control of the stack output power and cathode intake flow.For system idle speed control,a modelbased nonlinear control framework is constructed in this paper.Firstly,the nonlinear dynamic model of output power and cathode intake flow is derived.Secondly,a control scheme combining nonlinear extended Kalman filter observer and state feedback controller is designed.Finally,the control scheme is verified on the PEMFC experimental platform and compared with the proportion-integration-differentiation(PID)controller.The experimental results show that the control strategy proposed in this paper can realize the idle speed control of the fuel cell system and achieve the purpose of zero power output.Compared with PID controller,it has faster response speed and better system dynamics.
基金supported by the National Natural Science Foundation of China(42276199).
文摘In order to get rid of the dependence on high-precision centrifuges in accelerometer nonlinear coefficients calibration,this paper proposes a system-level calibration method for field condition.Firstly,a 42-dimension Kalman filter is constructed to reduce impact brought by turntable.Then,a biaxial rotation path is designed based on the accelerometer output model,including orthogonal 22 positions and tilt 12 positions,which enhances gravity excitation on nonlinear coefficients of accelerometer.Finally,sampling is carried out for calibration and further experiments.The results of static inertial navigation experiments lasting 4000 s show that compared with the traditional method,the proposed method reduces the position error by about 390 m.
基金Projects(52205069,52075083,52304049)supported by the National Natural Science Foundation of ChinaProject(2021-BS-164)supported by the Liaoning Province Doctoral Research Startup Fund,China+2 种基金Project(LJKZ0264)supported by the Science and Technology Research Projects of Education Department of Liaoning Province,ChinaProject(G2022003010L)supported by the High-end Foreign Experts Recruitment Plan of ChinaProject(E2021203095)supported by the Natural Science Foundation for Young Scholars of Hebei Province,China。
文摘The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The normal vector used to calculate the first-type limit function is determined in the natural frame without the aid of the curvature parameter of worm helicoid.The first-type limit line is ascertained via solving the nonlinear equations iteratively.It is discovered that one first-type limit line exists on the tooth surface of worm wheel by numerical simulation,and such a line is normally located out of the meshing zone.Only one intersection point exists between the first and second-types of limit lines,and this point is a lubrication weak point.The undercutting mechanism is essentially that a part of the meshing zone near the conjugated line of worm tooth crest will come into the undercutting area and will be cut off during machining the worm wheel.The machining simulation verifies the correctness of undercutting mechanism.Moreover,a convenient and practical characteristic quantity is proposed to judge whether the undercutting exists in the whole meshing zone via computing the first-type limit function values on the worm tooth crest.
基金supported by the National Natural Science Foundation of China(Grant No.61773142).
文摘Intercepting high-maneuverability hypersonic targets in near-space environments poses significant challenges due to their extreme speeds and evasive capabilities.To address these challenges,this study presents an integrated approach that combines a Three-Dimensional Finite-Time Optimal Cooperative Guidance Law(FTOC)with an Information Fusion Anti-saturation Predefined-time Observer(IFAPO).The proposed FTOC guidance law employs a nonlinear,non-quadratic finite-time optimal control strategy designed for rapid convergence within the limited timeframes of near-space interceptions,avoiding the need for remaining flight time estimation or linear decoupling inherent in traditional methods.To complement the guidance strategy,the IFAPO leverages multi-source information fusion theory and incorporates anti-saturation mechanisms to enhance target maneuver estimation.This method ensures accurate and real-time prediction of target acceleration while maintaining predefined convergence performance,even under complex interception conditions.By integrating the FTOC guidance law and IFAPO,the approach optimizes cooperative missile positioning,improves interception success rates,and minimizes fuel consumption,addressing practical constraints in military applications.Simulation results and comparative analyses confirm the effectiveness of the integrated approach,demonstrating its capability to achieve cooperative interception of highly maneuvering targets with enhanced efficiency and reduced economic costs,aligning with realistic combat scenarios.
基金National Natural Science Foundation of China(62203118)。
文摘Piezo actuators are widely used in ultra-precision fields because of their high response and nano-scale step length.However,their hysteresis characteristics seriously affect the accuracy and stability of piezo actuators.Existing methods for fitting hysteresis loops include operator class,differential equation class,and machine learning class.The modeling cost of operator class and differential equation class methods is high,the model complexity is high,and the process of machine learning,such as neural network calculation,is opaque.The physical model framework cannot be directly extracted.Therefore,the sparse identification of nonlinear dynamics(SINDy)algorithm is proposed to fit hysteresis loops.Furthermore,the SINDy algorithm is improved.While the SINDy algorithm builds an orthogonal candidate database for modeling,the sparse regression model is simplified,and the Relay operator is introduced for piecewise fitting to solve the distortion problem of the SINDy algorithm fitting singularities.The Relay-SINDy algorithm proposed in this paper is applied to fitting hysteresis loops.Good performance is obtained with the experimental results of open and closed loops.Compared with the existing methods,the modeling cost and model complexity are reduced,and the modeling accuracy of the hysteresis loop is improved.
