Linear-regression models and algorithms based on the Total-Least-Squares principle

In classical regression analysis, the error of independent variable is usually not taken into account in regression analysis. This paper presents two solution methods for the case that both the independent and the dependent variables have errors. These methods are derived from the condition-adjustment and indirect-adjustment models based on the Total-Least-Squares principle. The equivalence of these two methods is also proven in theory.

The Principle of Square Hole Machining and It＇s Tooling Structure Design

In order to meet the rapid needs of processing square hole in mechanical equipment, the paper expounds the square hole processing method： planetary wheel method, and analyze the principle of tooling structure and process with computer graphics parameters design. The results that, as long as the appropriate parameters, using the above method not only can punch the square hole, can also be processed triangle, the five angle and hexagonal regular polygon holes. The square hole processing method can provide theoretical basis and engineering reliable reference for related engineering and technical personnel.

Parameter identification of hysteretic model of rubber-bearing based on sequential nonlinear least-square estimation

In order to evaluate the nonlinear performance and the possible damage to rubber-bearings （RBs） during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB （GZN 110） under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least- square estimation （SNLSE）, is introduced to identify the model parameters. It is shown that the proposed simplified Bouc- Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.

Squaring the Circle Is Possible When Taking into Consideration the Heisenberg Uncertainty Principle

Squaring the circle is one of the oldest challenges in mathematical geometry. In 1882, it was proven that π was transcendental, and the task of squaring the circle was considered impossible. Demonstrating that squaring the circle was not possible took place before discovering quantum mechanics. The purpose of this paper is to show that it is actually possible to square the circle when taking into account the Heisenberg uncertainty principle. The conclusion is clear: it is possible to square the circle when taking into account the Heisenberg uncertainty principle.

方孔夫琅禾费衍射的数值模拟fsquarehole,HouZhi-qing,

根据惠更斯-菲涅耳原理,利用数值计算的方法对方孔夫琅禾费衍射实验进行了模拟,在验证衍射理论的同时,还得到了非傍轴区域和微方孔的衍射图,拓展了衍射的概念,为深入理解光的衍射提供了参考.

A CLASS OF EXPLICIT FORWARD TIME-DIFFERENCE SQUARE CONSERVATIVE SCHEMES

In the present paper, a class of explicit forward time-difference schemes are established from a geometric view with strict analytical deductions. This class includes the schemes with a constant time interval and with adjustable time intervals, which is proved to be effective and remarkably time-saving in numerical tests and applications.

Calculation of Significant Wave Height Using the Linear Mean Square Estimation Method

Significant wave height is an important criterion in designing coastal and offshore structures.Based on the orthogonality principle, the linear mean square estimation method is applied to calculate significant wave height in this paper.Twenty-eight-year time series of wave data collected from three ocean buoys near San Francisco along the California coast are analyzed.It is proved theoretically that the computation error will be reduced by using as many measured data as possible for the calculation of significant wave height.Measured significant wave height at one buoy location is compared with the calculated value based on the data from two other adjacent buoys.The results indicate that the linear mean square estimation method can be well applied to the calculation and prediction of significant wave height in coastal regions.

WRINKLE LIMIT BLANK HOLDER FORCE MODELS IN SQUARE-BOX DEEP DRAWING WITH VARIABLE SEGMENT BLANK-HOLDERS

Constituting the reasonable control models of the wrinkle limit blank holder forces is the sticking point of the processes of the deep drawing with variable blank-holder forces, especially in the square-box forming. To begin with, a mode of segmenting flange of the square-box into eight zones is put forward according to the fact that the uniformity of flange deforming can be improved by control-ling segment blank-holders. Considering the integral influence of shear stress, a new concept, strain relaxation factor is defined. Hereby, the law of distribution of stress and stain in the deforming flange of square-box is achieved. Then based on these mechanical analysis models and the energy principle, the wrinkling flexivity functions of the straight flange and the circle flange are given, and the corresponding formulae of wrinkling limit blank-holder force in these two situations are also educed. In these processes, ply-anisotropy, strain hardening, thickness and friction are considered. In the end, a calculating example is designed to validate the rationality of the formulae of wrinkling limit blank-holder force, at the same time, the influences of the ply-anisotropy exponent and the strain hardening exponent on the wrinkle limit blank holder forces are also analyzed.

Stochastic Maximum Principle for Square-Integrable Optimal Control of Linear Stochastic Systems

The authors give a stochastic maximum principle for square-integrable optimal control of linear stochastic systems.The control domain is not necessarily convex and the cost functional can have a quadratic growth.In particular,they give a stochastic maximum principle for the linear quadratic optimal control problem.

Squaring the Dialectic of Inference and Chance

Instead of merely inferring that our beliefs are in a correlation to the facts, I will contend that what matters is the logic of their inferential structure. This will reveal what is actually true for their relation and not just real for experience. Given one and two-sided inferences, the conditions of their functional relation will be consistent within a square of opposition; for contraries, contradictions and sub-contraries in a way that probability theory is not. Within this model of inferences, the two-sided concept of inferences will also have a modal value for its relation to the one-sided concept of inferences. Proposing that empirical, formal, speculative, and an Intuitionist Speculative understanding of logic will have a modal identity within a dialectical principle.

A Procedure for the Squaring of a Circle (of Any Radius)

This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using only an unmarked ruler and a compass), produced a square equal in area to the given circle, which is 50 cm2. This result was a clear demonstration that not only is the construction valid for the squaring of a circle of any radius, but it is also capable of achieving absolute results (independent of the number pi (π), in a finite number of steps), when carried out with precision.

A Method for the Squaring of a Circle

This paper presents a Method for the squaring of a circle (i.e., constructing a square having an area equal to that of a given circle). The construction, when applied to a given circle having an area of 12.7 cm2, it produced a square having an area of 12.7 cm2, using only an unmarked ruler and a compass. This result was a clear demonstration that not only is the construction valid for the squaring of a circle but also for achieving absolute results (independent of the number pi (π) and in a finite number of steps) when carried out with precision.

相依风险模型下保险公司和再保险公司的鲁棒最优再保险和投资策略

在具有共同冲击相依风险模型下,研究了保险公司和再保险公司共同利益的最优再保险和投资问题。假设保险公司和再保险公司的盈余过程由扩散逼近模型来刻画,并且保险公司可以购买比例再保险来分散风险,再保险保费由均值方差保费原则计算。同时,保险公司和再保险公司都可投资于无风险资产和风险资产,其中风险资产的价格过程遵循平方根因子过程,在使保险公司和再保险公司终端财富加权和的期望指数效用最大化的条件下,应用随机控制理论,建立了鲁棒Hamilton-Jacobi-Bellman (HJB)方程并且得到了最优再保险和投资策略以及相应的值函数。此外,通过一些数值例子来说明某些模型参数对最优再保险和投资策略的影响。

小子样条件下镁合金焊接接头疲劳评估方法研究

以小子样条件下镁合金焊接接头的疲劳试验数据为基础,基于样本信息聚集原理提出分阶段信息聚集方法,与最小二乘法相结合,提出一种小子样条件下镁合金焊接接头疲劳寿命评估模型。首先,利用样本信息聚集原理将数据样本的容量扩大,并统计分布特征;其次,对镁合金焊接接头进行高周疲劳试验,得到小子样条件下的疲劳寿命试验数据;最后,通过改进前和改进后的样本信息聚集方法与最小二乘法结合对试验数据进行拟合并对比。结果表明:分阶段样本信息聚集方法结合最小二乘法得到的p-S-N曲线疲劳寿命评估模型的样本数据具有分散性更小的特征,拟合优度更好,可以确保小子样数据的拟合精度。

发动机转静子同轴度偏心工艺优化研究

中涵道比涡扇发动机高压涡轮单元体安装时,由于存在套齿配合间隙、轴承径向游隙和弹性支座变形的同轴度影响因素,使得高压涡轮转子封严篦齿发生偏心向下,造成与静子空气挡油圈的碰磨故障。利用有限元静力学方法,分析得到弹性支座具体形位变化,利用最小二乘法原理,计算得到转子封严篦齿的偏心量。提出一种新型高压涡轮转静子偏心装配工艺,设计高压涡轮模拟工艺轴,基于工艺轴安装时套齿配合间隙与轴承径向游隙的装配偏差,结合发动机真轴装配偏差影响因素,综合得到静子空气挡油圈的最终偏心调整量,可实现高压涡轮转静子的封严间隙优化同心,避免发动机转静子发生碰磨,解决了发动机振动过大、轴承腔漏油等问题。该工艺方法经过装配试验验证有效,研究结果可为其他型号发动机转静子同轴度装配工艺设计提供参考。

最大模原理在无穷域中的运用及其推广

本文运用最大模原理,研究了一类在复平面中以原点为对称中心的正n边形内连续且全纯的函数f。如果|f|在该正n边形内的上确界为M,且在该正n边形的某条边上的上确界为m,则可得出|f|在以原点为顶点和该条边为底边所形成的闭三角形内的上界。进而研究了一类在复平面中无穷条形区域以及无穷扇形区域内连续且全纯的函数f,并将它们推广到两种月牙形区域和两相切抛物线所形成的无穷区域,从而得到了一些重要的结论。

最大相关最小冗余两阶段文本特征选择方法

目的为解决传统卡方统计法(CHI)仅考虑文本特征与文本类别的相关性进行特征选择,未考虑特征之间的冗余性,导致文本分类的性能不佳的问题。方法使用最大相关最小冗余原则,对CHI法初次选择的特征子集,利用强相关低冗余思想有目的地筛选低冗余特征,提升文本特征选择效果,提出一种基于最大相关最小冗余的两阶段文本特征选择方法(CHI_impMI)。结果对复旦大学新闻文本语料进行分类,相比于CHI和CHI_MI特征选择方法,CHI_impMI方法的性能指标均为最优,文本分类效果最好。结论CHI_impMI方法在相关度与冗余度之间达到了很好的平衡,从而有效提升文本分类性能。

基于BUCK变换器非爆炸本安评价系统研究

应用在煤矿等危险环境下开关变换器必须满足防爆要求,本安型变换器必须在GB 3836标准的爆炸试验平台测试其是否满足输出本安的要求,这种方法耗时过长、不能直接指导本安电路的设计与制造。为了方便评价BUCK变换器的输出本安性能,以电容电路最小点燃电压曲线的数值拟合为依据,建立了输出本安性能评价系统。利用能量等效原理将BUCK电路等效变换为电容电路,并采用最小二乘法对电容电路的最小点燃曲线进行拟合,实现了最小点燃曲线的数值化;其次,利用仿真软件搭建了可以通过界面显示的本安判据结果的评价系统。最终采用2组实验结果对本安评价系统进行测试,验证了所搭建本安评价系统的可行性。

车辆荷载引起地面振动的实测研究

对行驶重载卡车引起的地面振动进行现场实测,从加速度峰值、频谱和振级上分析了振动的衰减情况,并用两种方法讨论了扣除背景振动的振级,然后用基于最小二乘原理的模式搜索法拟合出了振动的衰减公式。研究表明:卡车引起的振动主要以垂向为主,随着振源距离的增大,振动逐渐衰减,而且振动在较近的距离内衰减很快,高频部分几乎可以完全衰减,而低频部分的振动随着距离振源的增大,衰减相对较缓,甚至在100 m处还有其残余振动。

推算室内固结系数的剩余沉降对数法

试样剩余沉降(最终沉降与沉降的差值)的对数与时间呈线性关系,由线性方程的系数可推算出试样的固结系数。采用最小二乘原理估计线性方程的系数时需事先确定最终沉降,由于线性方程的线性相关系数是最终沉降的函数,为使线性拟合达到最佳,最终沉降应使线性相关系数取到极值,根据这一条件可解析出最终沉降。与推算固结系数的时间平方根法和时间对数法等方法相比,本文方法无需固结试验初始阶段和最后阶段的数据,从而避免了初始沉降和后期次固结沉降的影响,并加快了固结试验的进程。