Cam shape optimisation by genetic algorithm

This article overviews a genetic algorithm based computer-aided approach for preliminary design and shape optimisation of cam profiles for cam operated mechanisms. The primary objective of the work was to create a complete systematic approach for preliminary cam shape design including cam shape design automation and true cam shape optimisation with respect to the simulated computer models of cam mechanisms. Typically, shape optimisation of a cam cross-section is a multiobjective optimisation problem of two-dimensional geometric shape in a heavily constrained environment. In order to illustrate the genetic algorithm based cam shape optimisation approach, a cam shape design example is described, in which a cam shape designed by genetic algorithm is compared with its more conventionally designed counterpart.     

分段阻尼隔振系统的动力学特性分析

针对传统线性隔振器在降低共振峰值的同时会牺牲隔振性能的矛盾,设计了一种含分段阻尼的隔振器.首先,采用移动凸轮变阻尼装置,通过凸轮廓线的设计使系统的垂向阻尼系数的受振动位移大小控制并呈现分段线性特征,分析了该装置的阻尼特性.然后将分段阻尼装置应用于隔振器中,建立了含分段阻尼的积极隔振系统模型及其动力学方程,通过能量等效原理求出了分段阻尼系统的等效线性阻尼系数,求解了简谐力激励下系统响应的理论解,并用四阶龙格—库塔法数值仿真验证了理论解的正确性.最后研究了分段阻尼隔振系统的动态特性,分析了主要参数对幅频响应特性与力传递率特性的影响.结果表明,通过合理的参数选择,分段阻尼隔振器可兼顾无阻尼隔振器与线性阻尼隔振器的优点,既能有效降低系统的共振峰值,又能保证高频区域的优秀隔振性能,为新型非线性隔振器的设计提供了理论依据.     

Numerical approach for solving linear Fredholm integro-differential equation with piecewise intervals by Bernoulli polynomials

In this paper a numerical method is given for the solution of linear Fredholm integro-differential equation (FIDE) with piecewise intervals under the mixed conditions using the Bernoulli polynomials. The aim of this article is to present an efficient numerical procedure for solving linear FIDE with piecewise intervals. This method transforms linear FIDE with piecewise intervals and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. Finally, some experiments and their numerical solutions are given. The results reveal that this method is reliable and efficient.     

一类正交函数系的离散表示及快速变换

V系统是L2[0,1]上一类新的完备正交函数系,它由分段多项式组成,具有多分辨分析特性和全局/局部性,在几何模型的正交表达方面具有明显的优势,但其快速算法难以得到。利用Haar函数和Legendre多项式构造了一类由分段次多项式组成的函数系(文中称为W系),在该函数系上作函数逼近的效果等同于在V系统上的效果,并进一步讨论了一次离散W变换的快速算法,从而部分克服了直接对V系统设计快速算法的困难。     

The piecewise optimisation method for approximating uncertain optimal control problems under optimistic value criterion

In this paper, we introduce an approximate model and propose a piecewise optimisation method to simplify the expression of optimal control for an uncertain linear quadratic optimal control problem. First, we consider an optimal control problem of uncertain linear quadratic model under optimistic value criterion. Based on the equation of optimality, we deduce an analytic expression of optimal control. Then, we study an approximate model with control parameter and propose a piecewise optimisation method for solving the optimal parameter of such an approximate model. As an application, a four-wheel steering vehicle optimal control problem is given to show the utility of the proposed approximate model and the efficiency of the proposed piecewise optimisation method.     

Integral and non-negativity preserving Bernstein-type polynomial approximations

In this paper, we consider the problem of approximating a function by Bernstein-type polynomials that preserve the integral and non-negativity of the original function on the interval [0, 1], obtaining the Kantorovich–Bernstein polynomials, but providing a novel approach with advantages in numerical analysis. We then develop a Markov finite approximation method based on piecewise Bernstein-type polynomials for the computation of stationary densities of Markov operators, providing numerical results for piecewise constant and piecewise linear algorithms.     

The piecewise parametric optimal control of uncertain linear quadratic models

The optimal control of linear quadratic model is given in a feedback form and determined by the solution of a Riccati equation. However, the control-related Riccati equation usually cannot be solved analytically such that the form of optimal control will become more complex. In this paper, we consider a piecewise parametric optimal control problem of uncertain linear quadratic model for simplifying the form of optimal control. By introducing a piecewise control parameter, a piecewise parametric optimal control model is established. Then we present a parametric optimisation method for solving the optimal piecewise control parameter. Finally, an uncertain inventory-promotion optimal control problem is discussed and a comparison is made to show the effectiveness of proposed piecewise parametric optimal control model.     

正交U变换及其快速算法

采用递推方法构造一种正交变换,称之为U变换,该变换含有分段常数基向量、分段一次多项式基向量以及分段二次多项式基向量,是对Walsh变换、斜变换的推广。根据递推方式,可以得到相应的快速算法。利用平移复制算子和Kronecher积的性质,推导基于Kronecher积的快速算法和正交U变换的直接分解算法。将该变换应用于图像压缩中,构造基于人类视觉系统的量化表,实验结果表明,正交U变换的图像压缩性能明显优于斜变换的图像压缩性能,与DCT变换的图像压缩性能相当,为图像压缩提供了一种新的选择。     

A patchy approximation of explicit model predictive control

The explicit solution of multi-parametric optimisation problems (MPOP) has been used to construct an off-line solution to relatively small- and medium-sized constrained control problems. The control design principles are based on receding horizon optimisation and generally use linear prediction models for the system dynamics. In this context, it can be shown that the optimal control law is a piecewise linear (PWL) state feedback defined over polytopic cells of the state space. However, as the complexity of the related optimisation problems increases, the memory footprint and implementation of such explicit optimal solution may be burdensome for the available hardware, principally due to the high number of polytopic cells in the state-space partition. In this article we provide a solution to this problem by proposing a patchy PWL feedback control law, which intend to approximate the optimal control law. The construction is based on the linear interpolation of the exact solution at the vertices of a feasible set and the solution of an unconstrained linear quadratic regulator (LQR) problem. With a hybrid patchy control implementation, we show that closed-loop stability is preserved in the presence of additive measurement noise despite the existence of discontinuities at the switch between the overlapping regions in the state-space partition.     

基于正交完备U-系统的图形分类与识别方法

为了探索有效的图形分类与识别的新方法,引进一类正交完备的分段k次多项式系统(简称U-系统).U-系统是一类属于L²[0,1]的正交完备分段k次多项式系统.该系统下的U级数展开式具有良好的平方逼近及一致逼近性质.基于U-系统理论,提出了U描述子的概念,给出了U描述子的性质并在理论上予以证明.为了更好地对图形分类与识别,对U描述子进行了归一化,同时在理论上证明了归一化U描述子具有旋转、平移、尺度大小等不变的性质.实验表明,归一化的U描述子能够高效、准确地对图形进行分类与识别,与Fourier描述子相比,具有更好的识 别率.