F-rough law and the discovery of rough law

By using function one direction S-rough sets （function one direction singular rough sets）, this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of F-law relation metric, two orders theorem of F-rough law relation metric, the attribute theorem of F-rough law band, the extremum theorem of F-rough law relation metric, the discovery principle of F-rough law and the application of F-rough law.

Function S-rough sets and mining-discovery of rough law in systems

Function S-rough sets （function singular rough sets） is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of a-function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.

Rough law generation and its separation-recognition

By using function S-rough sets（function singular rough sets）, this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the theorem of rough law separation, the compound generation theorem of rough law bands, and the principle of rough law bands.In the end, an application of rough law separation in recognizing the risk law of profit is presented.

Rough law energy and measurement of ■-decomposition rough law

By employing function one-direction S-rough sets and rough law generation method based on function S-rough sets, ^-f-decomposition law and ^-F-decomposition rough law are proposed, and the measurement of rough law variation in the process of rough law ^-F-decomposition is researched. The concepts of law energy and attdbute ^-f-interference degree are presented, which make the variation of rough law become measurable. ^-f-decomposition law energy characteristic theorem, ^-f- decomposition law energy inequality theorem, ^-F-decomposition rough law energy characteristic theorem, and ^-f-decomposition law energy mean value theorem are presented.

One Direction Rough Law Generation and Its Security Transmission

By using function one direction S-rough sets （function one direction singular rough sets）, the concept of one direction rough law is proposed, where one direction rough law is the law pair { w（x）-, w（x） - } composed by w（x）- and w（x）-, ffthe attribute set {a_ , a-} of function one direction S-rough sets changes, then one direction rough law { w（x）_, w（x）- } will change, too. By employing ellipse curves, the concept of one direction rough law security is presented, the security theorem of one direction rough law is proposed and the applications are given. One direction rough law security, which is generated by the intersection and penetration between function one direction S-rough sets and ellipse curves, is a new applied research direction of function S-rough sets.

S-rough Laws and Its Dependent Separation by F-Interference

By employing function S-rough sets,the concepts of f-interference generation and separation of law,and the F-interference generation and separation of S-rough laws were proposed. Base on the concepts above,the F-interference relation theorems,the F-interference discernibility theorem,the dependent separation theorem by interfereence,and the dependent separation principle by interference were presented; finally the application was given. By employing F-interference dependence and separation of S-rough laws,the changes of characteristic of dynamic systemic regularities could be recognized.

Function S-rough sets and two law forecast

Function S-rough sets has the properties of dynamics, heredity, and memory. Function S-rough sets is penetrated and crossed with the issue of economic law forecast, then a new forecast model based on function S-rough sets namely the two law forecast model is proposed, which includes upper law forecast model and lower law forecast model; and its＇ implement algorithm is given. Finally, the validity of the model is demonstrated by the forecast for region economic development of Hainan Province.

沥青道路粗糙度对径流颗粒物冲刷输出特性的影响

采用粗糙度量化沥青道路的表面特征,通过模型模拟、相关性分析等方法分析了道路表面粗糙度对降雨径流颗粒物冲刷输出特性的影响。结果表明:道路粗糙度、降雨强度是影响道路表面径流颗粒物冲刷输出过程的关键因素,道路粗糙度越低、降雨强度越大,道路表面径流颗粒物冲刷效应越强烈、场次降雨径流颗粒物累积冲刷量越大、径流颗粒物冲刷输出总体水平越高;道路粗糙度与降雨强度、径流历时共同影响径流颗粒物粒径分布,道路粗糙度为影响径流颗粒物粒径分布的主导因素,道路粗糙度越低、径流历时越长、降雨强度越大,径流中粒径不小于150μm的颗粒物体积占比越高,粒径小于75μm的颗粒物体积占比越低。

Function S-Rough sets and its applications

Based on S-rough sets（singular rough sets）, this paper presents function S-rough sets （function singular rough sets）and its mathematical structures and features. Function S-rough sets has two forms： function one direction S-rough sets （function one direction singular rough sets） and function two direction S-rough sets （function two direction singular rough sets）. This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function S-rough sets is the general form of S-rough sets, and S-rough sets is the special ease of function S-rough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system.

Hiding dependence-discovery of F-hiding laws and system laws

Function one direction S-rough sets have dynamic characteristics and law characteristics. By using the function one direction S-rough sets, this article presents the concepts of the f-hiding law, F-hiding law, f-hiding law dependence and F-hiding law dependence. Based on the concepts above, this article proposes the hidingdependence theorem of f-hiding laws, the hiding-dependence theorem of F-hiding laws, the hiding-dependence separation theorem, the hiding dependence-discovery principle of unknown laws. Finally, the application of the hiding dependence of hiding laws in the discovery of system laws is given.

Influence of Fracture Roughness on Aperture Fracture Surface and in Fluid Flow on Coarse-Grained Marble, Experimental Results

Wetting fluid flow through rock discontinuities influence a great number of project among others: dam construction, underground projects, CO2 storage in underground schemes, geological disposal of radioactive wastes;Hydrocarbon storage caverns. Flow through fractures is considered to be laminar due to small aperture of the fracture walls and slow velocity. The fluid model called “Cubic law” describes the flow assuming parallel infinite plates. However, natural discontinuities on rock have roughness. In this experimental study an induced fracture on a sample of medium-grained marble was used, to determine the influence of roughness in water flow. This study is a preliminary part of research funding program for flow of CO2 through rocks (AUTH-GEOMechanics and Environment of CO2 geological Storage, Project No. 456,400).

F-generation law and recognition of system law

If a system is not disturbed （or invaded） by some law, there is no doubt that each system will move according to the expected law and keep stable. Although such a fact often appears, some unknown law breaks into the system and leads it into turbulence. Using function one direction S-rough sets, this article gives the concept of the F-generation law in the system, the generation model of the F-generation law and the recognition method of the system law. Function one direction singular rough sets is a new theory and method in recognizing the disturbance law existing in the system and recognizing the system law.

F-interference law generation and its feature recognition

By using two-directional S-rough sets, the concepts of （f, f）-interference generation and （f, f）- interference law generation of knowledge, F-interference generation and F-interference law generation of two-directional S-rough sets are proposed. Based on the concepts above, the relation theoreras between F-interference loss and F-interference degree, the relation theorems between F-interference loss law and F-interference degree law, the dis- cernibility theorems between F-interference and F-interference law are presented. At last, the recognition criterion of F-interference law and its application are given.

F-Law collision and system state recognition

Using function one direction S-rough sets （function one direction singular rough sets）, f-law and F- law and the concept of law distance and the concept of system law collided by F-law are given. Using these concepts, state characteristic presented by system law collided by F-law and recognition of these states characteristic and recognition criterion and applications are given. Function one direction S-rough sets is one of basic forms of function S-rough sets （function singular rough sets）. Function one direction S-rough sets is importance theory and is a method in studying system law collision.

■-law collision and system state recognition

Using dual function one direction S-rough sets, this article gives the f-law, the F-law, law distance and the concept of system law collided by the F-law. The characteristics presented by the system law collided by the F-law, the recognition of these characteristics and recognition criterion are also proposed. The dual function one direction S-rough sets is one of the basic forms of function S-rough sets. Its basic theory and application in the study of system law collision are reviewed.

上游调压室理想阻抗孔面积选择的影响因素分析

针对设置上游阻抗式调压室的引水发电系统,利用特征线法进行大波动过渡过程计算,模拟并分析了引水隧洞长度、两种导叶关闭规律、输水管道糙率以及机组转动惯量对水力过渡过程中调压室理想阻抗孔面积取值的影响。结果表明:在保证其他条件不变的情况下,引水隧洞长度、机组转动惯量以及管道糙率的取值越大,理想阻抗孔的面积越小;先慢后快的导叶关闭规律对阻抗孔面积取值的影响较先快后慢的关闭规律更大。结论对实际工程设计具有参考价值。

基于最优控制策略的起落架振动半主动抑制研究

为提高起落架在着陆及地面滑跑过程中的缓冲减震能力,以支柱式前起落架为研究对象展开研究。首先,在动力学平台中构建起落架多体动力学模型,依据缓冲器工作原理,搭建单腔式缓冲器液压模型;其次,建立半主动起落架着陆线性方程。基于状态空间理论,推导并求解黎卡提矩阵方程,得到最优状态反馈控制律;然后,基于滤波白噪声法推出路面高程的时域模型,并生成机场跑道随机路面仿真模型;最后,提出一种机械-液压-控制联合仿真的起落架半主动控制研究方法,实现了起落架落震及考虑路面不平度的滑跑联合仿真。仿真结果验证了半主动控制方法对于冲击载荷及振动响应抑制的优越性。

基于响应曲面法的超声挤压工艺参数优化

以提高轴类零件超声挤压表面质量为目标,采用单因素试验和响应曲面法对工艺参数进行优化设计。分析了工艺参数对45钢轴零件表面粗糙度的作用规律和影响程度,结果表明,表面粗糙度随着主轴转速、进给速度、静挤压量、振幅的增加呈现先降低后增加的趋势。同时对所建立的响应曲面模型进行了显著性检验和工艺参数优化,分析可知,振幅对表面粗糙度的影响最大,优化后得到最优工艺参数组合如下:主轴转速n为217.48 r/min,进给速度f为0.031 mm/r,静挤压量P为101.013μm,振幅A为8.192μm。试验验证预测值误差小于5%,因此建立的响应面优化模型精度较高,可实现工艺参数优化,并为实际加工及超声设备研制改进提供理论依据。

基于格子Boltzmann法岩体裂隙粗糙特征对渗流的影响

裂隙在岩体中的形貌结构复杂,岩体裂隙的粗糙特征对裂隙的渗透性存在较大影响。目前传统的数值模拟软件主要是以等效连续介质为基础的宏观评价,无法模拟裂隙微小结构内的介观渗流特征;虽然存在考虑裂隙粗糙特征的粗糙裂隙渗透评估模型,但是将粗糙裂隙的剖面高度标准偏差值作为粗糙特征的定量表征缺乏物理意义并且存在局限性。首先运用W-M(Weierstrass-Mandelbrot)函数构建具有不同分形维数的二维粗糙单裂隙数字模型。其次基于格子Boltzmann法理论通过编程实现介观尺度的渗流模拟,并结合以裂隙剖面高度标准偏差值作为粗糙特征定量表征的立方定律公式进行分析。结果表明:以裂隙剖面高度标准偏差值作为粗糙特征定量表征的立方定律公式存在不足;以分形维数作为粗糙特征定量表征的局部修正立方定律公式相对可行。研究对于地下水污染防治以及地下水资源评估有着重要的工程实际意义。

函数S-粗集与粗规律挖掘-分离

研究了函数S-粗集的本质和特性,及其用于挖掘系统的潜在规律。利用函数S-粗集(单向函数S-粗集,双向函数S-粗集)的数学结构和特性,给出系统中粗规律模型的生成方法。给出了利用函数S-粗集进行系统中的粗规律挖掘与分离的讨论,和系统中粗规律分离的应用。例子证明,函数S-粗集是系统规律挖掘的一个有力工具。