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
This paper is concerned with the following variable-order fractional Laplacian equations , where N ≥ 1 and N > 2s(x,y) for (x,y) ∈ Ω × Ω, Ω is a bounded domain in R<sup>N</sup>, s(⋅)...This paper is concerned with the following variable-order fractional Laplacian equations , where N ≥ 1 and N > 2s(x,y) for (x,y) ∈ Ω × Ω, Ω is a bounded domain in R<sup>N</sup>, s(⋅) ∈ C (R<sup>N</sup> × R<sup>N</sup>, (0,1)), (-Δ)<sup>s(⋅)</sup> is the variable-order fractional Laplacian operator, λ, μ > 0 are two parameters, V: Ω → [0, ∞) is a continuous function, f ∈ C(Ω × R) and q ∈ C(Ω). Under some suitable conditions on f, we obtain two solutions for this problem by employing the mountain pass theorem and Ekeland’s variational principle. Our result generalizes the related ones in the literature.展开更多
A method utilizing variable depth increments during incremental forming was proposed and then optimized based on numerical simulation and intelligent algorithm.Initially,a finite element method(FEM) model was set up a...A method utilizing variable depth increments during incremental forming was proposed and then optimized based on numerical simulation and intelligent algorithm.Initially,a finite element method(FEM) model was set up and then experimentally verified.And the relation between depth increment and the minimum thickness tmin as well as its location was analyzed through the FEM model.Afterwards,the variation of depth increments was defined.The designed part was divided into three areas according to the main deformation mechanism,with Di(i=1,2) representing the two dividing locations.And three different values of depth increment,Δzi(i=1,2,3) were utilized for the three areas,respectively.Additionally,an orthogonal test was established to research the relation between the five process parameters(D and Δz) and tmin as well as its location.The result shows that Δz2 has the most significant influence on the thickness distribution for the corresponding area is the largest one.Finally,a single evaluating indicator,taking into account of both tmin and its location,was formatted with a linear weighted model.And the process parameters were optimized through a genetic algorithm integrated with an artificial neural network based on the evaluating index.The result shows that the proposed algorithm is satisfactory for the optimization of variable depth increment.展开更多
Dual-point composition control for a high-purity ideal heat integrated distillation column (HIDiC) is addressed in this work. Three measures are suggested and combined for overcoming process inherent nonlinearities:(1...Dual-point composition control for a high-purity ideal heat integrated distillation column (HIDiC) is addressed in this work. Three measures are suggested and combined for overcoming process inherent nonlinearities:(1) variable scaling; (2) multi-model representation of process dynamics and (3) feedforward compensation. These strategies can offer the developed control systems with several distinct advantages: (1) capability of dealing with severe disturbances; (2) tight tuning of controller parameters and (3) high robustness with respect to variation of operating conditions. Simulation results demonstrate the effectiveness of the proposed methodology.展开更多
Aiming at the problem that the draft-position integrated tillage depth control method with fixed comprehensive coefficient of tractor electro-hydraulic hitch system is difficult to adapt to the working environment wit...Aiming at the problem that the draft-position integrated tillage depth control method with fixed comprehensive coefficient of tractor electro-hydraulic hitch system is difficult to adapt to the working environment with large changes in soil conditions,a tractor draft-position integrated tillage depth control method with variable comprehensive coefficient was proposed.A comprehensive coefficient control scheme based on traction resistance was designed and its working principle was clarified.Aiming at the time-varying tillage depth control system,a tillage depth control algorithm based on the sliding mode control with a differential observer was designed.In order to verify the performance of the control scheme,a control system simulation model and a bench test platform were built,and the performance was compared with the draft-position integrated control method with a fixed comprehensive coefficient of 0.5.The results showed that the variable comprehensive coefficient tillage depth control method can automatically adjust the comprehensive coefficient according to the change of soil conditions,and has higher traction efficiency.In the small resistance range,it can better ensure the quality of operation;in the large resistance range,it can ensure the engine performance and protect the tractor from damage.This method is more adaptable to the complex field operation environment,which provides a reference for the research of tillage depth control method.展开更多
We established a photoacoustic imaging(PAI)system that can provide variable gain at different depths.The PAI system consists of a pulsed laser with an optical parametric oscillator working at a 728 nmwavelength and an...We established a photoacoustic imaging(PAI)system that can provide variable gain at different depths.The PAI system consists of a pulsed laser with an optical parametric oscillator working at a 728 nmwavelength and an imaging-acquisition-and-processing unit with an ultrasound transducer.Avoltage-controlled attenuator was used to realize variable gain at different depths when acquiring PAI signals.The proof-of-concept imaging results for variable gain at different depths were achieved using specic phantoms.Both resolution and optical contrast obtained through the results of variable gain for a targeted depth range are better than those of constant gain for all depths.To further testify the function,we imaged the sagittal section of the body of in vivo nude mice.In addition,we imaged an absorption sample embedded in a chicken breast tissue,reaching a maximum imaging depth of4.6 cm.The results obtained using the proposed method showed better resolution and contrast than when using 50 dB gain for all depths.The depth range resolution was1 mm,and the maximum imaging depth of our system reached4.6 cm.Furthermore,blood vessels can be revealed and targeted depth range can be selected in nude mice imaging.展开更多
This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the beh...This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.展开更多
This article proposes an adaptive extended Kalman filter(EKF)for nonlinear cyber-physical systems(CPSs)under unknown inputs and non-Gaussian noises.It is known that the traditional extended Kalman filter is applicable...This article proposes an adaptive extended Kalman filter(EKF)for nonlinear cyber-physical systems(CPSs)under unknown inputs and non-Gaussian noises.It is known that the traditional extended Kalman filter is applicable to nonlinear systems with Gaussian white noise.The system is reformulated with intermediate variables to expand the application of nonlinear systems under unknown inputs and non-Gaussian noises,which help decompose unknown input estimation into residual tracking and state observation subproblems.By introducing the orthogonal principle of innovation and attenuation factor,the intermediate variables-based filter can improve the estimation performance under non-Gaussian noises and unknown inputs.Simulation results validate the effectiveness of the proposed method.展开更多
The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ...The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.展开更多
针对目前雷达干扰抑制决策智能化程度低的问题,提出了一种基于双深度优先经验回放和可变贪婪算法改进的双重竞争深度Q网络(double dueling deep Q network,D3QN)决策的雷达干扰抑制方法。首先对雷达目标回波和干扰混合信号进行特征提取...针对目前雷达干扰抑制决策智能化程度低的问题,提出了一种基于双深度优先经验回放和可变贪婪算法改进的双重竞争深度Q网络(double dueling deep Q network,D3QN)决策的雷达干扰抑制方法。首先对雷达目标回波和干扰混合信号进行特征提取;然后根据信号特征通过可变贪婪算法选择动作作用于干扰,并将动作前后的信号特征存储于双深度优先经验回放池后,经过学习决策出最优的干扰抑制策略;最后使用该策略抑制干扰后输出。实验结果表明,该方法有效改善了信号的脉压结果,显著提升了信号的信干噪比,相较于基于D3QN的传统干扰抑制方法,在策略准确率和收敛速度上分别提升了7.3%和8.7%。展开更多
In this paper, a semiactive variable stiffness （SVS） device is used to decrease cable oscillations caused by parametric excitation, and the equation of motion of the parametric vibration of the cable with this SVS d...In this paper, a semiactive variable stiffness （SVS） device is used to decrease cable oscillations caused by parametric excitation, and the equation of motion of the parametric vibration of the cable with this SVS device is presented. The ON/OFF control algorithm is used to operate the SVS control device. The vibration response of the cable with the SVS device is numerically studied for a variety of additional stiffness combinations in both the frequency and time domains and for both parametric and classical resonance vibration conditions. The numerical studies further consider the cable sag effect. From the numerical results, it is shown that the SVS device effectively suppresses the cable resonance vibration response, and as the stiffness of the device increases, the device achieves greater suppression of vibration. Moreover, it was shown that the SVS device increases the critical axial displacement of the excitation under cable parametric vibration conditions.展开更多
为了实现离子束对高精度光学表面的确定性加工,加强对加工过程中离子束去除函数的精确控制,建立细束径离子束的变去除函数补偿模型。实现对加工过程中细束径变去除函数问题的研究、分析、补偿和优化。根据实际加工中去除函数不稳定的问...为了实现离子束对高精度光学表面的确定性加工,加强对加工过程中离子束去除函数的精确控制,建立细束径离子束的变去除函数补偿模型。实现对加工过程中细束径变去除函数问题的研究、分析、补偿和优化。根据实际加工中去除函数不稳定的问题进行理论分析,结合理论推导探究影响去除函数的直接因素和间接因素,直接因素包括热积累和能量分配问题,间接因素为驻留时间和进给速度。通过动态去除函数实验验证驻留时间对加工过程中去除速率的影响,对两组不同尺寸束径的实验证明了该规律的重复性。最后,提出了基于进给速度对去除速率的影响规律给出补偿方案及加工建议。实验结果表明:通过控制驻留时间/进给速度的方式,可以有效提高细束径在高精度光学表面的加工收敛率。在亚纳米光学加工的实验验证中,在100 mm ULE平面反射镜上达到0.332 nm RMS的加工结果,满足细束径离子束在实际应用中的稳定可靠、精度高、确定性强等要求。展开更多
In this paper,we consider a class of Kirchhoff equation,in the presence of a Kelvin-Voigt type damping and a source term of general nonlinearity forms.Where the studied equation is given as followsutt-K(Nu(t))[Δ_(p(x...In this paper,we consider a class of Kirchhoff equation,in the presence of a Kelvin-Voigt type damping and a source term of general nonlinearity forms.Where the studied equation is given as followsutt-K(Nu(t))[Δ_(p(x))^(u)+Δ_(r(x))^(ut)]=F(x,t,u).Mere,K(Nu(t))is a Kirchhoff function,Δ_(r(x))^(ut)represent a Kelvin-Vbigt strong damp-ing term,and F(x,t,u)is a source term.According to an appropriate assumption,we obtain the local existence of the weak solutions by applying the Galerkin's approximation method.Furthermore,we prove a non-global existence result for certain solutions with negative/positive initial energy.More precisely,our aim is to find a sufficient conditions for p(x)/q(x)/r(x)/F(x/t/u)and the initial data for which the blow-up occurs.展开更多
The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (...The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (VSC),two-level and decentralized variable structure control laws for this kind of systems are presented respectively,which achieve asymptotically stabilization despite the uncertainties and disturbances. At last,sirnulation of the disturbed two-pendulum system is given to illustrate the feasibility of proposed technique.展开更多
With the global climate change,the high-altitude detection is more and more important in the climate prediction,and the input-output characteristic curve of the air pressure sensor is offset due to the interference of...With the global climate change,the high-altitude detection is more and more important in the climate prediction,and the input-output characteristic curve of the air pressure sensor is offset due to the interference of the tested object and the environment under test,and the nonlinear error is generated.Aiming at the difficulty of nonlinear correction of pressure sensor and the low accuracy of correction results,depth neural network model was established based on wavelet function,and Levenberg-Marquardt algorithm is used to update network parameters to realize the nonlinear correction of pressure sensor.The experimental results show that compared with the traditional neural network model,the improved depth neural network not only accelerates the convergence rate,but also improves the correction accuracy,meets the error requirements of upper-air detection,and has a good generalization ability,which can be extended to the nonlinear correction of similar sensors.展开更多
In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonli...In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonlinearity p(·)and g are given functions.Under arbitrary positive initial energy and specific conditions on the relaxation function g,we prove a finite-time blow-up result.We also give some numerical applications to illustrate our theoretical results.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.
文摘This paper is concerned with the following variable-order fractional Laplacian equations , where N ≥ 1 and N > 2s(x,y) for (x,y) ∈ Ω × Ω, Ω is a bounded domain in R<sup>N</sup>, s(⋅) ∈ C (R<sup>N</sup> × R<sup>N</sup>, (0,1)), (-Δ)<sup>s(⋅)</sup> is the variable-order fractional Laplacian operator, λ, μ > 0 are two parameters, V: Ω → [0, ∞) is a continuous function, f ∈ C(Ω × R) and q ∈ C(Ω). Under some suitable conditions on f, we obtain two solutions for this problem by employing the mountain pass theorem and Ekeland’s variational principle. Our result generalizes the related ones in the literature.
文摘A method utilizing variable depth increments during incremental forming was proposed and then optimized based on numerical simulation and intelligent algorithm.Initially,a finite element method(FEM) model was set up and then experimentally verified.And the relation between depth increment and the minimum thickness tmin as well as its location was analyzed through the FEM model.Afterwards,the variation of depth increments was defined.The designed part was divided into three areas according to the main deformation mechanism,with Di(i=1,2) representing the two dividing locations.And three different values of depth increment,Δzi(i=1,2,3) were utilized for the three areas,respectively.Additionally,an orthogonal test was established to research the relation between the five process parameters(D and Δz) and tmin as well as its location.The result shows that Δz2 has the most significant influence on the thickness distribution for the corresponding area is the largest one.Finally,a single evaluating indicator,taking into account of both tmin and its location,was formatted with a linear weighted model.And the process parameters were optimized through a genetic algorithm integrated with an artificial neural network based on the evaluating index.The result shows that the proposed algorithm is satisfactory for the optimization of variable depth increment.
基金Supported by the New-Energy and Industry Technology Development Organization (NEDO) through the Energy Conservation Center of Japan.
文摘Dual-point composition control for a high-purity ideal heat integrated distillation column (HIDiC) is addressed in this work. Three measures are suggested and combined for overcoming process inherent nonlinearities:(1) variable scaling; (2) multi-model representation of process dynamics and (3) feedforward compensation. These strategies can offer the developed control systems with several distinct advantages: (1) capability of dealing with severe disturbances; (2) tight tuning of controller parameters and (3) high robustness with respect to variation of operating conditions. Simulation results demonstrate the effectiveness of the proposed methodology.
基金National Key Research and Development Plan of China(Grant No.2022YFD2001202)The Open Project of the State Key Laboratory of Intelligent Agricultural Power Equipment(SKLIAPE2023019)The Postgraduate Research and Practice Innovation Program of Jiangsu Province,China(Grant No.KYCX22_0716).
文摘Aiming at the problem that the draft-position integrated tillage depth control method with fixed comprehensive coefficient of tractor electro-hydraulic hitch system is difficult to adapt to the working environment with large changes in soil conditions,a tractor draft-position integrated tillage depth control method with variable comprehensive coefficient was proposed.A comprehensive coefficient control scheme based on traction resistance was designed and its working principle was clarified.Aiming at the time-varying tillage depth control system,a tillage depth control algorithm based on the sliding mode control with a differential observer was designed.In order to verify the performance of the control scheme,a control system simulation model and a bench test platform were built,and the performance was compared with the draft-position integrated control method with a fixed comprehensive coefficient of 0.5.The results showed that the variable comprehensive coefficient tillage depth control method can automatically adjust the comprehensive coefficient according to the change of soil conditions,and has higher traction efficiency.In the small resistance range,it can better ensure the quality of operation;in the large resistance range,it can ensure the engine performance and protect the tractor from damage.This method is more adaptable to the complex field operation environment,which provides a reference for the research of tillage depth control method.
基金the financial support fromNational Natural Science Foundation of China(NSFC)(61675113,61527808,81401539,and 31271056)Science and Technology Research Program of Shenzhen City(JSGG20150331151536448,JCYJ20160428182247170,and JCYJ20170412170255060)+1 种基金Shenzhen basic research layout project(JCYJ20160324163759208)the projects in Shenzhen Medical Engineering Laboratory For Human Auditory-equilibrium Function。
文摘We established a photoacoustic imaging(PAI)system that can provide variable gain at different depths.The PAI system consists of a pulsed laser with an optical parametric oscillator working at a 728 nmwavelength and an imaging-acquisition-and-processing unit with an ultrasound transducer.Avoltage-controlled attenuator was used to realize variable gain at different depths when acquiring PAI signals.The proof-of-concept imaging results for variable gain at different depths were achieved using specic phantoms.Both resolution and optical contrast obtained through the results of variable gain for a targeted depth range are better than those of constant gain for all depths.To further testify the function,we imaged the sagittal section of the body of in vivo nude mice.In addition,we imaged an absorption sample embedded in a chicken breast tissue,reaching a maximum imaging depth of4.6 cm.The results obtained using the proposed method showed better resolution and contrast than when using 50 dB gain for all depths.The depth range resolution was1 mm,and the maximum imaging depth of our system reached4.6 cm.Furthermore,blood vessels can be revealed and targeted depth range can be selected in nude mice imaging.
基金Supported by Shandong Provincial Natural Science Foundation(Grant Nos.ZR2021MA003 and ZR2020MA020).
文摘This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.
基金Supported by the Foreign Experts Project of the Belt and Road Innovative Talent Exchange(No.DL2023016005L).
文摘This article proposes an adaptive extended Kalman filter(EKF)for nonlinear cyber-physical systems(CPSs)under unknown inputs and non-Gaussian noises.It is known that the traditional extended Kalman filter is applicable to nonlinear systems with Gaussian white noise.The system is reformulated with intermediate variables to expand the application of nonlinear systems under unknown inputs and non-Gaussian noises,which help decompose unknown input estimation into residual tracking and state observation subproblems.By introducing the orthogonal principle of innovation and attenuation factor,the intermediate variables-based filter can improve the estimation performance under non-Gaussian noises and unknown inputs.Simulation results validate the effectiveness of the proposed method.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)the National Natural Science Foundation of China(Grant No.12261131495)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21).
文摘The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.
文摘针对目前雷达干扰抑制决策智能化程度低的问题,提出了一种基于双深度优先经验回放和可变贪婪算法改进的双重竞争深度Q网络(double dueling deep Q network,D3QN)决策的雷达干扰抑制方法。首先对雷达目标回波和干扰混合信号进行特征提取;然后根据信号特征通过可变贪婪算法选择动作作用于干扰,并将动作前后的信号特征存储于双深度优先经验回放池后,经过学习决策出最优的干扰抑制策略;最后使用该策略抑制干扰后输出。实验结果表明,该方法有效改善了信号的脉压结果,显著提升了信号的信干噪比,相较于基于D3QN的传统干扰抑制方法,在策略准确率和收敛速度上分别提升了7.3%和8.7%。
基金National Natural Science Foundation of China Under Grant No. 50178025
文摘In this paper, a semiactive variable stiffness （SVS） device is used to decrease cable oscillations caused by parametric excitation, and the equation of motion of the parametric vibration of the cable with this SVS device is presented. The ON/OFF control algorithm is used to operate the SVS control device. The vibration response of the cable with the SVS device is numerically studied for a variety of additional stiffness combinations in both the frequency and time domains and for both parametric and classical resonance vibration conditions. The numerical studies further consider the cable sag effect. From the numerical results, it is shown that the SVS device effectively suppresses the cable resonance vibration response, and as the stiffness of the device increases, the device achieves greater suppression of vibration. Moreover, it was shown that the SVS device increases the critical axial displacement of the excitation under cable parametric vibration conditions.
文摘为了实现离子束对高精度光学表面的确定性加工,加强对加工过程中离子束去除函数的精确控制,建立细束径离子束的变去除函数补偿模型。实现对加工过程中细束径变去除函数问题的研究、分析、补偿和优化。根据实际加工中去除函数不稳定的问题进行理论分析,结合理论推导探究影响去除函数的直接因素和间接因素,直接因素包括热积累和能量分配问题,间接因素为驻留时间和进给速度。通过动态去除函数实验验证驻留时间对加工过程中去除速率的影响,对两组不同尺寸束径的实验证明了该规律的重复性。最后,提出了基于进给速度对去除速率的影响规律给出补偿方案及加工建议。实验结果表明:通过控制驻留时间/进给速度的方式,可以有效提高细束径在高精度光学表面的加工收敛率。在亚纳米光学加工的实验验证中,在100 mm ULE平面反射镜上达到0.332 nm RMS的加工结果,满足细束径离子束在实际应用中的稳定可靠、精度高、确定性强等要求。
文摘In this paper,we consider a class of Kirchhoff equation,in the presence of a Kelvin-Voigt type damping and a source term of general nonlinearity forms.Where the studied equation is given as followsutt-K(Nu(t))[Δ_(p(x))^(u)+Δ_(r(x))^(ut)]=F(x,t,u).Mere,K(Nu(t))is a Kirchhoff function,Δ_(r(x))^(ut)represent a Kelvin-Vbigt strong damp-ing term,and F(x,t,u)is a source term.According to an appropriate assumption,we obtain the local existence of the weak solutions by applying the Galerkin's approximation method.Furthermore,we prove a non-global existence result for certain solutions with negative/positive initial energy.More precisely,our aim is to find a sufficient conditions for p(x)/q(x)/r(x)/F(x/t/u)and the initial data for which the blow-up occurs.
文摘The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (VSC),two-level and decentralized variable structure control laws for this kind of systems are presented respectively,which achieve asymptotically stabilization despite the uncertainties and disturbances. At last,sirnulation of the disturbed two-pendulum system is given to illustrate the feasibility of proposed technique.
基金This paper is supported by the following funds:National Key R&D Program of China(2018YFF01010100)National natural science foundation of China(61672064),Beijing natural science foundation project(4172001)Advanced information network Beijing laboratory(PXM2019_014204_500029).
文摘With the global climate change,the high-altitude detection is more and more important in the climate prediction,and the input-output characteristic curve of the air pressure sensor is offset due to the interference of the tested object and the environment under test,and the nonlinear error is generated.Aiming at the difficulty of nonlinear correction of pressure sensor and the low accuracy of correction results,depth neural network model was established based on wavelet function,and Levenberg-Marquardt algorithm is used to update network parameters to realize the nonlinear correction of pressure sensor.The experimental results show that compared with the traditional neural network model,the improved depth neural network not only accelerates the convergence rate,but also improves the correction accuracy,meets the error requirements of upper-air detection,and has a good generalization ability,which can be extended to the nonlinear correction of similar sensors.
基金Birzeit UniversitySharjah University for their supportsponsored by MASEP Research Group in the Research Institute of Sciences and Engineering at University of Sharjah.Grant No.2002144089,2019-2020。
文摘In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:utt-△u+∫_(0)^(t)g(t-τ)△u(x,τ)dτ+μut=|u|^(p(x)-2)-u,whereμis a nonnegative constant and the exponent of nonlinearity p(·)and g are given functions.Under arbitrary positive initial energy and specific conditions on the relaxation function g,we prove a finite-time blow-up result.We also give some numerical applications to illustrate our theoretical results.
