Best L1 Piecewise Monotonic Data Modelling

Let us consider n data measurements of a univariate process that have been altered by random errors. We assume that an underlying model function has a substantially smaller number of turning points than the observed ones. We propose algorithms that make least the sum of the moduli of the errors by requiring k monotonic sections, alternately increasing and decreasing, in the sequence of the smoothed values. The main difficulty in this calculation is that the optimal positions of the joins of the monotonic sections have to be found automatically among so many combinations that it is impossible to test each one separately. Moreover, the calculation seems to be very intractable to general optimization techniques because O(n^k) local minima can occur. It is shown that dynamic programming can be used for separating the data into optimal disjoint sections of adjacent data, where each section requires a single L₁ monotonic calculation. This procedure is highly efficient, requiring at most O(kn²) computer operations and O(n) best L₁ monotonic calculations to subranges of data for a global minimum.     

Isometric Piecewise Polynomial Curves

The main preoccupations of research in computer-aided geometric design have been on shape-specification techniques for polynomial curves and surfaces, and on the continuity between segments or patches. When modelling with such techniques, curves and surfaces can be compressed or expanded arbitrarily. There has been relatively little work on interacting with direct spatial properties of curves and surfaces, such as their arc length or surface area. As a first step, we derive families of parametric piecewise polynomial curves that satisfy various positional and tangential constraints together with arc-length constraints. We call these curves isometric curves. A space curve is defined as a sequence of polynomial curve segments, each of which is defined by the familiar Hermite or Bézier constraints for cubic polynomials; as well, each segment is constrained to have a specified arc length. We demonstrate that this class of curves is attractive and stable. We also describe the numerical techniques used that are sufficient for achieving real time interaction with these curves on low-end workstations.     

Uniform modeling of parameter dependent nonlinear systems

This paper addresses the problem of approximating parameter dependent nonlinear systems in a unified framework. This modeling has been presented for the first time in the form of parameter dependent piecewise affine systems. In this model, the matrices and vectors defining piecewise affine systems are affine functions of parameters. Modeling of the system is done based on distinct spaces of state and parameter, and the operating regions are partitioned into the sections that we call ’multiplied simplices’. It is proven that this method of partitioning leads to less complexity of the approximated model compared with the few existing methods for modeling of parameter dependent nonlinear systems. It is also proven that the approximation is continuous for continuous functions and can be arbitrarily close to the original one. Next, the approximation error is calculated for a special class of parameter dependent nonlinear systems. For this class of systems, by solving an optimization problem, the operating regions can be partitioned into the minimum number of hyper-rectangles such that the modeling error does not exceed a specified value. This modeling method can be the first step towards analyzing the parameter dependent nonlinear systems with a uniform method.     

New results on PWARX model identification based on clustering approach

This paper deals with the problem of piecewise auto regressive systems with exogenous input(PWARX) model identification based on clustering solution. This problem involves both the estimation of the parameters of the affine sub-models and the hyper planes defining the partitions of the state-input regression. The existing identification methods present three main drawbacks which limit its effectiveness. First, most of them may converge to local minima in the case of poor initializations because they are based on the optimization using nonlinear criteria. Second, they use simple and ineffective techniques to remove outliers. Third, most of them assume that the number of sub-models is known a priori. To overcome these drawbacks, we suggest the use of the density-based spatial clustering of applications with noise(DBSCAN) algorithm. The results presented in this paper illustrate the performance of our methods in comparison with the existing approach. An application of the developed approach to an olive oil esterification reactor is also proposed in order to validate the simulation results.     

多交叉混沌选择反向小生境遗传算法

为提高小生境遗传算法的全局以及局部搜索能力,提出一种多交叉混沌选择反向小生境遗传算法。利用分段线性混沌映射函数生成一组混沌数序列,在每次进行交叉操作前,依据序列中对应元素的数值大小选择不同的交叉算子进行操作,通过小生境遗传算法产生较优的子代种群。针对子代种群,应用反向搜索策略获得反向种群,在子代种群和反向种群中进行精英选择得到最终新种群,以进一步加强算法的局部寻优能力。仿真实验结果表明,该算法在最优解及均值方面好于小生境遗传算法,从而证明其可行性和优越性。     

Characteristics of oxygen consumption of coal at programmed temperatures

Oxygen consumption is an important index of coal oxidation.In order to explore the coal-oxygen reaction,we developed an experimental system of coal spontaneous combustion and tested oxygen consumption of differently ranked coals at programmed temperatures.The size of coal samples ranged from 0.18~0.42 mm and the system heat-rate was 0.8℃/min.The results show that,for high ranked coals,oxygen consumption rises with coal temperature as a piecewise non-linear process.The critical coal temperature is about 50%.Below this temperature,oxygen consumption decreases with rising coal temperatures and reached a minimum at 50℃,approximately.Subsequently,it begins to increase and the rate of growth clearly increased with temperature.For low ranked coals,this characteristic is inconspicuous or even non-existent.The difference in oxygen consumption at the same temperatures varies for differently ranked coals.The results show the difference in oxygen consumption of the coals tested in our study reached 78.6% at 100 ℃.Based on the theory of coal-oxygen reaction,these phenomena were analyzed from the point of view of physical and chemical characteristics,as well as the appearance of the coal-oxygen complex.From theoretical analyses and our experiments,we conclude that the oxygen consumption at programmed temperatures reflects the oxidation ability of coals perfectly.     

一类差分方程的渐近概周期序列解的存在性

利用渐近概周期函数以及序列的定义和基本性质,得出下面离散系统存在正渐近概周期序列解唯一性的充分条件.     

大学生体质健康评价模型及不同评分标准的相通性

为更准确、客观的测定每个大学生体质健康等级,利用分段拟合方法分别构建大学男、女生体质健康评价模型,并得到体质测试分及各项测试项目基本得分间的具体表达式．后又具体论析了模型求解过程中,所涉及四个测试项目均占0．25的权重值与《国家体质健康标准》中公布的权重值之间是相通的．     

低照度图像的分段非线性化处理算法

为增强低照度图像,在考虑人视觉分辨力的基础上,对图像固有的信息使用图像前景像素值与背景像素值的灰度值之差的绝对值作为图像的对比度,通过均衡化因子,用非线性均衡化方法把隐藏在低照度图像中的信息提取出来.该方法在对图像灰度谱分段非线性化时,通过优化补偿因子,提高其补偿迭代速度,快速获得所需要的图像.     

近似非齐次无偏GM(1,1) 模型的递推解法及应用

针对传统近似非齐次灰建模可能出现参数复数解的问题, 提出无偏灰色GM(1,1) 模型的递推解法, 从而减少由差分方程向微分方程跳跃而导致误差的问题. 给出不同初始条件下非齐次无偏GM(1,1) 模型的递推预测公式,并在此基础上, 将递推公式运用于时间序列分段, 提出基于近似非齐次无偏GM(1,1) 模型的时间序列分段表示方法. 实例结果表明, 所提出的递推模型能够获得较高的拟合精度, 分析结果验证了基于灰色预测模型在时间序列分段表示中的有效性和实用性.