SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES

The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.

Dual-mode Nonlinear MPC via Terminal Control Laws With Free-parameters

The paper presents a new dual-mode nonlinear model predictive control(NMPC) scheme for continuous-time nonlinear systems subject to constraints on the state and control.The idea of control Lyapunov functions for nonlinear systems is used to compute the terminal regions and terminal control laws with some free-parameters in the dual-mode NMPC framework.The parameters of the terminal controller are selected offline to estimate the terminal region as large as possible;and the parameters are optimized online to gain optimality of the terminal controller with respect to given cost functions.Then a dual-mode NMPC algorithm with varying time-horizon is formulated for the constrained system.Recursive feasibility and closed-loop stability of this NMPC are established.The example of a spring-cart is used to demonstrate the advantages of the presented scheme by comparing to the dual-mode NMPC via the linear quadratic regulator(LQR) method.

EXACT SOLUTION AND ITS BEHAVIOR CHARACTERISTIC OF NONLINEAR DUAL-POROSITY MODEL

A nonlinear dual-porosity model considering a quadratic gradient term is presented. Assuming the pressure difference between matrix and fractures as a primary unknown, to avoid solving the simultaneous system of equations, decoupling of fluid pressures in the blocks from the fractures was furnished with a quasi-steady-state flow in the blocks. Analytical solutions were obtained in a radial flow domain using generalized Hankel transform. The real value cannot be gotten because the analytical solutions were infinite series. The real pressure value was obtained by numerical solving the eigenvalue problem. The change law of pressure was studied while the nonlinear parameters and dual-porosity parameters changed, and the plots of typical curves are given. All these result can be applied in well test analysis.

A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM

The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.

NONLINEAR EFFECT OF THE DUALFREQUENCY IP SPECTRUM

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Parameter estimation for dual-rate sampled Hammerstein systems with dead-zone nonlinearity

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.

Numerical Analyses Optical Solitons in Dual Core Couplers with Kerr Law Nonlinearity

In this paper, we present the results of numerical analysis of optical solitons in dual core couplers. We studied the optical couplers as an application for the non-linear Schrödinger equation in the case of Kerr law for non-linear and clarify the exact solution in this case. Then we have provided a numerical study of the effect of changing the constants in the form of the three types of solitons: bright soliton and dark solitons and singular soliton.

APPLICATION OF THE DUAL RECIPROCITY BOUNDARY ELEMENT METHOD TO SOLUTION OF NONLINEAR DIFFERENTIAL EQUATION

In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation del(2) u + u + epsilon u(3) = b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method (DRM) in solving nonlinear differential equations.

Dual-stage Optimal Iterative Learning Control for Nonlinear Non-affine Discrete-time Systems

根据沿着重复轴的一种新动态 linearization 技术，双阶段的最佳的反复的学习控制为非线性、非仿射的分离时间的系统被介绍。双阶段显示二个最佳的学习阶段分别地被设计反复地改进控制输入顺序和学习获得。主要特征是控制器设计和集中分析仅仅取决于动态系统的 I/O 数据。换句话说，没有知道系统的任何另外的知识，我们能容易选择控制参数。模拟学习沿着重复轴说明介绍方法的几何集中，在哪个马路的一个例子控制为它的内在的工程重要性是引人注目的交通反复的学习。

Surrogate dual method for multi-dimensional nonlinear knapsack problems

Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of problems. Multiply constrained problem was relaxed to a singly constrained problem by using the surrogate technique. To compute tighter bounds of the primal problem, the cutting plane method was used to solve the surrogate dual problem, where the surrogate relaxation problem was solved by the 0-1 linearization method. The domain cut technique was employed to eliminate the duality gap and thus to guarantee the convergence of tile algorithm. Numerical results were reported for large-scale multi-dimensional nonlinear knapsack problems.

NONLINEAR CHARACTERIZATION OF CONCURRENT DUAL-BAND RF POWER AMPLIFIERS

In this paper, the synchronous concurrent dual-band RF signal is used to drive the RF Power Amplifier (PA). The nonlinear characterization of a concurrent dual-band RF PA is discussed while two band signals in the dual-band are modulated by CDMA2000 and WCDMA signals. When the two band signals in the dual-band of the PA are modulated with the same signals, it is found that the nonlinearity of the PA can be expressed by any of the two corresponding baseband data. On the other hand, when the two band signals in the dual-band of the PA are modulated with two different signals, the PA nonlinearity cannot be characterized by any of the two corresponding baseband data. In this case, its nonlinearity has to be denoted by a composite signals consisting of the two baseband signals. Consequently, the requirements for the speed of the A/D converter can be largely reduced. The experimental results with CDMA2000 and WCDMA signals demonstrate the speed of the A/D converter required is only 30 M Sample Per Second (SaPS), but it will be at least 70 M SaPS for the conventional method.

Analysis on Nonlinear Dynamic Properties of Dual-Rotor System

In order to clarify the effects of support structure on a dual-rotor machine,a dynamic model is established which takes into consideration the contact force of ball bearing and the cubic stiffness of elastic support. Bearing clearance,Hertz contact between the ball and race and the varying compliance effect are included in the model of ball bearing. The system response is obtained through numerical integration method,and the vibration due to the periodic change of bearing stiffness is investigated. The motions of periodic,quasiperiodic and even chaotic are found when bearing clearance is used as control parameter to simulate the response of rotor system. The results reveal two typical routes to chaos: quasi-periodic bifurcation and intermittent bifurcation. Large cubic stiffness of elastic support may cause jump and hysteresis phenomena in resonance curve when rotors run at the critical-speed region. The modeling results acquired by numerical simulation will contribute to understanding and controlling of the nonlinear behaviors of the dual-rotor system.

A Primal-dual Interior Point Method for Nonlinear Programming

In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.

Optimization of Nonlinear Energy Sink for Vibration Suppression of Systems Under Dual-Frequency Excitation

Aiming to decrease the vibration of wing induced by dual-rotor civil turbofan engines,the dynamic models of a single-degree of freedom (DOF) linear main oscillator coupled with single-DOF and two-DOF nonlinear energy sink (NES) are established.According to the related energy criteria for the optimization of the dynamic vibration absorber,focusing on the effects of external excitation on the kinetic energy of the primary mass and total system energy,the vibration suppression effects of single-DOF,two-DOF serial and parallel NES on the main oscillator system are studied.Under the condition that the characteristic parameters of the main oscillator system and additional total mass of the vibration absorber remain unchanged,results show that the two-DOF parallel NES has the best vibration energy suppression effects,which can provide data reference for the optimal design of NES vibration suppression under dual-frequency excitation.

Remaining useful lifetime prediction for equipment based on nonlinear implicit degradation modeling

Nonlinearity and implicitness are common degradation features of the stochastic degradation equipment for prognostics.These features have an uncertain effect on the remaining useful life(RUL)prediction of the equipment.The current data-driven RUL prediction method has not systematically studied the nonlinear hidden degradation modeling and the RUL distribution function.This paper uses the nonlinear Wiener process to build a dual nonlinear implicit degradation model.Based on the historical measured data of similar equipment,the maximum likelihood estimation algorithm is used to estimate the fixed coefficients and the prior distribution of a random coefficient.Using the on-site measured data of the target equipment,the posterior distribution of a random coefficient and actual degradation state are step-by-step updated based on Bayesian inference and the extended Kalman filtering algorithm.The analytical form of the RUL distribution function is derived based on the first hitting time distribution.Combined with the two case studies,the proposed method is verified to have certain advantages over the existing methods in the accuracy of prediction.

工质非线性变比热比不可逆Dual-Miller循环生态学目标函数优化

考虑工质非线性变比热比特性,存在气缸传热损失、活塞摩擦损失和其他内不可逆性损失,应用有限时间热力学理论分析和优化空气标准Dual-Miller循环性能,推导出了功率、效率和生态学目标函数等性能参数表达式,并由数值计算得到功率和效率与压缩比、功率与效率、生态学目标函数与功率和效率的特性关系,分析升压比和活塞冲程对各性能指标的影响,并分析比较各种不同优化目标下的性能特点。

Exact periodic solution in coupled nonlinear Schodinger equations

The coupled nonlinear Schodinger equations （CNLSEs） of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions.

工质非线性变比热比内可逆Dual-Miller循环功率、效率和生态学函数优化

考虑工质非线性变比热比和传热损失,应用有限时间热力学理论分析和优化空气标准内可逆DualMiller循环性能。推导功率、效率和生态学函数等性能参数表达式,并通过数值计算得到了功率、效率、生态学函数与压缩比的特性关系;当设计参数取某些特定值时,比较了Dual-Miller循环与Otto、Dual和Miller循环的功率、效率和生态学函数等性能差异;分析了预胀比和Miller循环比对功率、效率、生态学函数等性能的影响。

Symplectic multi-level method for solving nonlinear optimal control problem

By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state variables at two ends of the time interval are taken as independent variables.Based on the dual variable principle,nonlinear optimal control problems are replaced with nonlinear equations.Furthermore,in the implementation of the symplectic algorithm,based on the 2N algorithm,a multilevel method is proposed.When the time grid is refined from low level to high level,the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve efficiency.Numerical simulations show the precision and the efficiency of the proposed algorithm in this paper.

双能量CT非线性融合和噪声优化的虚拟单能量图像技术在喉鳞状细胞癌中的应用

目的:探讨双能量CT线性融合图像(linear blending imaging,LBI)、非线性融合图像(nonlinear blending image,NBI)和噪声优化的虚拟单能量图像(noise-optimized virtual monoenergetic image,VMI+)技术在喉鳞状细胞癌中的应用价值。方法:回顾性分析2019年6月至2022年3月61例经病理证实为喉鳞状细胞癌患者的双能量CT资料。双能量图像采用LBI[融合系数为1(80 kV)和0.6(M0.6)]、NBI和VMI+(40 keV、55 keV)技术重建。比较5组图像的客观图像质量[对比噪声比(contrast-tonoise ratio,CNR)、肿瘤CT值、噪声]和主观图像质量(肿瘤边界评分和整体图像质量评分)。结果:40 keV的CNR、肿瘤CT值和肿瘤边界评分均明显高于80 kV、M0.6、NBI和55 keV,差异均有统计学意义(均P<0.05)。NBI的整体图像质量评分明显高于80 kV、M0.6、40 keV和55 keV,差异均有统计学意义(均P<0.05)。NBI的噪声明显低于80 kV、40 keV和55 keV,差异均有统计学意义(均P<0.05)。结论:在喉鳞状细胞癌的双能量CT中,采用VMI+技术(40 keV)能提供更好的CNR、肿瘤CT值和肿瘤边界,采用NBI技术能提供更低的噪声和更好的整体图像质量。