非线性半定规划的逐次线性化柔性惩罚法

针对非线性不等式约束半定规划问题提出一种新的逐次线性化方法, 新算法既不要求罚函数单调下降, 也不使用过滤技巧, 尝试步的接受准则仅仅依赖于目标函数和约束违反度, 罚函数中对应于成功迭代点的罚因子不需要单调增加. 新算法或者要求违反约束度量有足够改善, 或者在约束违反度的一个合理范围内要求目标函数值充分下降, 在通常假设条件下, 分析了新算法的适定性及全局收敛性. 最后, 给出了非线性半定规划问题的数值试验结果, 结果表明了新算法的有效性.     

天然气稳态运行优化的混合整数模型及其算法

天然气稳态运行优化问题的难点在于网络结构复杂、规模大、目标函数及约束高度非线性.针对其混合整数非线性规划模型,基于网络约简和线性化技术,建立了线性近似模型,并提出一种新的求解算法.将新算法用于优化我国西部天然气管网系统,结果表明所提算法是有效的.     

On the types and number of plane waves in hypoelastic materials

General principles are formulated for modeling the elastic deformation of materials and analyzing plane waves in nonlinearly elastic materials such as hyperelastic, hypoelastic, and those governed by the general law of elasticity. The results of studying the propagation of plane waves in hypoelastic materials are further outlined. The influence of initial stresses and initial velocities on the types and number of plane waves is studied. Wave effects characteristic of hypoelastic materials are predicted theoretically. One of such effects is blocking of certain types of plane waves by initial stresses __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 96–107, November 2005.     

随机振动的一种加权等价线性化方法

加权等价线性化方法是研究非线性随机振动的一种有效近似方法。关健在于找到一个合适的权函数使之对多数非线性问题都有比较满意的结果。本文提出一种类似峰值概率密度函数的权函数,由此构成一种加权等价线性化方法,借几个各具特点的非线性振动系统进行了可行性验证,表明与一般的等价线性化方法相比,本法所得的均方响应精度有相当程度的改善。     

Comparison of stability and control characteristics of two twin-lift helicopter configurations

The stability and control characteristics of two twin-lift helicopter configurations are analyzed in this paper. In order to address the issue of configuration selection from a handling qualities viewpoint, their open-and closed-loop characteristics are compared. The two twin-lift configurations considered are the twin-lift with spreader bar and twin-lift without spreader bar. The nonlinear models describing the dynamics of these two configurations in the lateral/vertical plane are derived. The open-loop characteristics of the two systems are compared by linearizing the nonlinear models about a symmetric hovering equilibrium condition. The closed-loop characteristics of the two systems are compared using nonlinear controllers based on feedback linearization schemes. The performance of the resulting closed-loop systems in carrying out a typical twin-lift mission is evaluated through nonlinear simulation. Also, the effects of helicopter performance degradation and measurement errors on the overall system performance are discussed.[B] Matrix multiplying the control vector in the nonlinear model[B₁] Matrix multiplying the control vector in the linear model[C] Matrix defining vector of variables to be controlled[C₁] Damping matrixC_ijElement of the damping matrix e Parameter used in the linear model = M ₁ h ₁/I ₁=M ₂ h ₂/I ₂,/ft{f} Vector independent of controls in the nonlinear model g Acceleration due to gravity, ft/sec² h₁, h₂Distance of tether attachment point to the center of gravity for helicopters 1 and 2, ft h Parameter used in the linear model, =h ₁=h ₂, ft h Distance between rotor hub and the helicopter center of gravity, ft h h/l H Distance of the load from the spreader bar c.g., ftH₁, H₂Length of tethers 1 and 2, ftI_RMass moment of inertia of spreader bar, slug-ft² I₁, I₂Roll moments of inertia of helicopters 1 and 2, slug-ft² k Non-dimensional hub control moment coefficientK_DDerivative gainsK_IIntegral gainsK_PProportional gains[K_i] Stiffness matrixK_ijElement of the stiffness matrix l Parameter used in the linear model, =H ₁=H ₂, ft L Spreader bar length, ftNomenclature     

螺旋槽干气密封微尺度流动场的近似计算及其参数优化

应用PH线性化方法、迭代法,近似求解了螺旋槽内稳态微尺度流动场的非线性雷诺方程,求得了气体动压和速度分布的解析解。继而利用多目标优化方法构建了气膜刚度与泄漏量之比的协调函数,并对该目标函数进行了近似求解,获得了最佳的螺旋槽几何参数值。     

Mathematical Modeling and Parameter Identification of a Planar Servo-Pneumatic Test Facility. Part I: Mathematical Modeling and Computer Simulation

High quality multi-axis test facilities used for testing heavy loads and large structures of industrial equipment are usually simulated, designed and controlled based on reduced model equations neglecting the inertia properties of the actuators. The design and control of servo-pneumatic test facilities used for testing small and light structures must take into account extended test facility models including the various inertia properties of the actuators. In this paper (Part I) an extended test facility model is presented including the various inertia properties and joints of the actuators. These extended model equations are represented in a form well suited to be directly implemented in control algorithms based on exact linearization techniques for real time control. This is done by stepwise projecting the inertia properties of the various actuator housings and actuator pistons down to the common mass of the test table and payload. The resulting extended model equations have the same form as the reduced model equations. They only include more complex system matrices and vector functions. These compact model equations turn out to be suitable for an efficient nonlinear controller design of these test facilities. Computer simulations and associated laboratory experiments show the necessity to use extended model equations in case of testing small and light structures. In Part II of this paper [1] the inertia parameters of the planar test facility will be identified in laboratory experiments.     

EXACT LINEARIZATION BASED MULTIPLE-SUBSPACE ITERATIVE RESOLUTION TO AFFINE NONLINEAR CONTROL SYSTEM

To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control, multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.     

On using non-Gaussian distributions to perform statistical linearization

In statistical linearization non-linear elements are approximated by equivalent linear elements according to recipes proposed by the pioneers of the procedure. The recipes require the evaluation of certain statistics which, ideally, should be evaluated using the exact probability distribution of the non-linear response. Because the exact non-linear response distribution is unknown it has become traditional to use a Gaussian distribution as an approximation to the exact distribution. With the modern computing tools now available it is easy to use non-Gaussian distributions which can provide better approximations in cases where Gaussian distributions are not appropriate. Examples are displayed for power-law oscillators with stiffening and softening springs, and for the Duffing oscillator, and for a double-well oscillator. Two families of probability distributions with varying shape are studied.     

Accurate Higher-Order Analytical Approximate Solutions to Large-Amplitude Oscillating Systems with a General Non-Rational Restoring Force

A new approximate analytical approach for accurate higher-order nonlinear solutions of oscillations with large amplitude is presented in this paper. The oscillatory system is subjected to a non-rational restoring force. This approach is built upon linearization of the governing dynamic equation associated with the method of harmonic balance. Unlike the classical harmonic balance method, simple linear algebraic equations instead of nonlinear algebraic equations are obtained upon linearization prior to harmonic balancing. This approach also explores large parameter regions beyond the classical perturbation methods which in principle are confined to problems with small parameters. It has significant contribution as there exist many nonlinear problems without small parameters. Through some examples in this paper, we establish the general approximate analytical formulas for the exact period and periodic solution which are valid for small as well as large amplitudes of oscillation.