非线性问题

In this project, we have tackled the robust fault detection and diagnosis problem for affine nonlinear sampled-data systems based on nonlinear H∞ filtering theory,and focused on the design of robust fault dtetction filter. The main contribution of this project is that we (1)present design methods of robust fault estimator for nonlinear discrete-time systems based on least square estimation and linear matrix inequality;(2)improve the bounded real lemma of systems with finite discrete jumps;(3)develop the robust fault detection filters for affine nonlinear sampled-data systems with parameter uncertainties based on the improved bounded real lemma.

本项目以提高故障的正确检测率为目的，以非线性H∞滤波理论为基础，对不确定仿射非线性采样系统的鲁棒故障检测与诊断问题进行了研究，重点研究了不确定仿射非线性采样系统的鲁棒故障检测滤波器设计问题，取得了一些新的成果，主要成果有：(1)基于最小二乘估计和线性矩阵不等式，给出了非线性离散系统的鲁棒故障估计器设计方法；(2)改进了有限跳跃点系统的有界实引理；（3）基于改进的有界实引理，给出了不确定仿射非线性采样系统的鲁棒故障检测滤波器的设计方法。

The nonlinear Winkler-Kelvin sub-grade model is adopted in this simplified model and the complicated 3-D problems of the soil-single piles dynamic interaction are simplified to the 1-D, that is to say, the lateral nonlinear acting force of the soil to the pile shift is simulated with thehorizontal nonlinear springs which have the continuous uniform distribution, while the nonlinear spring restoring force is described by the deteriorated Bouc-Wen model; the radiation damping and material damping due to the energy dissipation and inner friction in the soil are displayed with the dashpots which are in parallel with the horizontal nonlinear springs.

该模型采用非线性Winkler-Kelvin地基模型，将复杂的地基土-单桩动力相互作用的三维问题，简化为一维问题，即，地基土对桩轴的横向非线性作用力，由随深度均匀分布的水平非线性弹簧模拟，非线性弹簧恢复力由退化的Bouc-Wen模型描述；地基土中由于能量耗散和内部摩擦而产生的幅射阻尼和材料阻尼，由与水平非线性弹簧并联的粘壶表示。

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

The non-linear problem of phase-change was solved by using the equivalent specific heat method, and the variation of contact areas were simulated by coupling different sets of nodes.

采用等效比热法解决相变的非线性问题，同时采用耦合不同节点自由度的方法模拟接触面积的变化。

Slab ; shell ; reinforced concrete ; finite strip analysis/materially nonlinear prob- lem

板； 壳；混凝土；有限条法／材料非线性问题

Artificial neural network can deal with both complex non-linear and linear problems and is often used in vehicle fault diagnosis.

人工神经网络具有适合于解决复杂的非线性问题的特点，因此经常被用于车辆故障诊断。

In past, the processing mode as to the electro-hydraulic servo-system nonlinear problem is that using the Tais lux formula obtains the part linear pattern behind the series expansion at the stable state work-point. This kind of linear model is feasible to this system which work point is in small scope changing.

过去对于非线性问题的处理方式是在稳态工作点处进行泰勒级数展开后得到局部线性化模型，这种线性化模型对于系统在设计工况点附近小范围变化时是可行的。

The force transmission, due to the crane trolley wheel pressure, from rail to bias-rail box girder belongs to the nonlinear contact. There is a coupling relationship between the deformation of contact area and the stress distribution.

小车轮压作用下，轨道与偏轨箱形梁之间力的传递属于接触非线性问题，接触面间的变形和应力分布存在相互耦合的关系。

The following are main contents studied: A finite element method for Navier-Stokes equation with ALE formulation is considered and by combined with theNewmark method of numerical intergration a pressure correction scheme is obtained for the solution of the FE formulation of N-S equation. Because the incompressibility condition can be satisfied approximately in this scheme, the interpolation functions of elements can be equalorder for the velocity field and pressure field. In the ALE formulation the fluid-solid interaction analysis became a three-field coupling problem of the fluid field, the solid field and the fluid dynamic mesh. The properties and charactiristices of this three-field coupling problem are deeply discussed.

研究的主要内容有：主容器中流体大晃动是一种强非线性问题，文中研究了求解ALE描述的粘性流体N-S方程的有限元方法，以有利于大晃动自由液面的跟踪和流体大晃动中非线性现象的描述；并结合Newmark数值积分法推出了求解ALE型N-S方程的压力修正解法，由于这种解法可以近似满足不可压条件，因此可以采用速度场和压力场等阶插值的有限元离散格式，从而较好地解决了普遍采用的不等阶插值解法中，速度场和压力场数值精度不一致、程序编制不便等的不足。

Nonlinear problems that are dominated by large rotations, werecommend that you do not use PRED,ON.

对于非线性问题，那由大转动决定，要求不可以使用pred，on。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。