A Dimension-Reduction Interval Analysis Method for Uncertain Problems

In this paper,an efficient interval analysis method called dimension-reduction interval analysis(DRIA)method is proposed to calculate the bounds of response functions with interval variables,which provides a kind of solution method for uncertainty analysis problems of complex structures and systems.First,multi-dimensional function is transformed into multiple one-dimensional functions by extending dimension reduction method to the interval analysis problem.Second,all the one-dimensional functions are transformed to standard quadratic form by second order Taylor expansion method.As a result,the multi-dimensional function is approximately represented by the functions that each interval variable occurs once,and interval power arithmetic can be used to efficiently calculate the bounds of response functions in restricted overestimation.Finally,three numerical examples and an engineering application are investigated to demonstrate the validity of the proposed method.

Using Pearson’s System of Curves to Approximate the Distributions of the Difference between Two Correlated Estimates of Signal-to-Noise Ratios: The Cases of Bivariate Normal and Bivariate Lognormal Distributions

Background: The signal-to-noise ratio (SNR) is recognized as an index of measurements reproducibility. We derive the maximum likelihood estimators of SNR and discuss confidence interval construction on the difference between two correlated SNRs when the readings are from bivariate normal and bivariate lognormal distribution. We use the Pearsons system of curves to approximate the difference between the two estimates and use the bootstrap methods to validate the approximate distributions of the statistic of interest. Methods: The paper uses the delta method to find the first four central moments, and hence the skewness and kurtosis which are important in the determination of the parameters of the Pearsons distribution. Results: The approach is illustrated in two examples;one from veterinary microbiology and food safety data and the other on data from clinical medicine. We derived the four central moments of the target statistics, together with the bootstrap method to evaluate the parameters of Pearsons distribution. The fitted Pearsons curves of Types I and II were recommended based on the available data. The R-codes are also provided to be readily used by the readers.

Rotational nanofluids for oxytactic microorganisms with convective boundary conditions using bivariate spectral quasi-linearization method

In this study,we considered the three-dimensional flow of a rotating viscous,incompressible electrically conducting nanofluid with oxytactic microorganisms and an insulated plate floating in the fluid.Three scenarios were considered in this study.The first case is when the fluid drags the plate,the second is when the plate drags the fluid and the third is when the plate floats on the fluid at the same velocity.The denser microorganisms create the bioconvection as they swim to the top following an oxygen gradient within the fluid.The velocity ratio parameter plays a key role in the dynamics for this flow.Varying the parameter below and above a critical value alters the dynamics of the flow.The Hartmann number,buoyancy ratio and radiation parameter have a reverse effect on the secondary velocity for values of the velocity ratio above and below the critical value.The Hall parameter on the other hand has a reverse effect on the primary velocity for values of velocity ratio above and below the critical value.The bioconvection Rayleigh number decreases the primary velocity.The secondary velocity increases with increasing values of the bioconvection Rayleigh number and is positive for velocity ratio values below 0.5.For values of the velocity ratio parameter above 0.5,the secondary velocity is negative for small values of bioconvection Rayleigh number and as the values increase,the flow is reversed and becomes positive.

用Bivariate－Test方法分析温度资料的不均一性

Ｂｉｖａｒｉａｔｅ－Ｔｅｓｔ方法（以下简称Ｂ－Ｔ方法）是一种基于二维正态分布随机矢量的假设检验方法，可以在一个分量的均值不改变的前提下，检验另一分量的均值有无改变。一些气象研究工作者最早用这种方法来分析年降水量的均一性。从温度资料不均一性产生的原因看，一般可分为两类：突变型不均一及渐变型不均一。对两种类型的不均一性，我们分别推导了理想情形下Ｂ－Ｔ方法的检验结果．并用随机试验的方法分析了检验结果对资料的敏感性。以上两方面的结果表明。渐变型及突变型不均一分别对应明显不同的Ｂ－Ｔ检验结果，在实际分析中这种差异可以用来定性判断不均一性的类型。东北区２０站３０年年平均温度资料的试算结果表明，有７站资料不能通过信度９５％的Ｂ－Ｔ检验，有３站资料不能通过信度９０％的Ｂ－Ｔ检验。其中有４个站的检验结果与理想情形下渐变型不均一的检验结果相似，有４个站的检验结果与理想情形下突变型不均一的检验结果相似。有一个站存在个别点的资料错误，有一个站可能有一次以上的不均一性发生。计算结果也表明，尽管Ｂ－Ｔ方法按照理论推导只是用来检测资料的不均一性，但对个别点上的资料质量问题也有一定的检测效果。

Residual life estimation based on bivariate Wiener degradation process with measurement errors

An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degradation data. Once new degradation information was available, the residual life of the product being monitored could be estimated in an adaptive manner. Here, it was assumed that the degradation of each PC over time was governed by a Wiener degradation process and the dependency between them was characterized by the Frank copula function. A bivariate Wiener process model with measurement errors was used to model the degradation measurements. A two-stage method and the Markov chain Monte Carlo (MCMC) method were combined to estimate the unknown parameters in sequence. Results from a numerical example about fatigue cracks show that the proposed method is valid as the relative error is small.

Generating function of product of bivariate Hermite polynomials and their applications in studying quantum optical states

By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.

Block Based Bivariate Blending Rational Interpolation via Symmetric Branched Continued Fractions

This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.

Construction of n-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.

Two 8-node quadrilateral spline elements by B-net method

Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.

A method for extracting anomaly map of Au and As using combination of U-statistic and Euclidean distance methods in Susanvar district,Iran

Quantitative descriptions of geochemical patterns and providing geochemical anomaly map are important in applied geochemistry. Several statistical methodologies are presented in order to identify and separate geochemical anomalies. The U-statistic method is one of the most important structural methods and is a kind of weighted mean that surrounding points of samples are considered in U value determination. However, it is able to separate the different anomalies based on only one variable. The main aim of the presented study is development of this method in a multivariate mode. For this purpose, U-statistic method should be combined with a multivariate method which devotes a new value to each sample based on several variables. Therefore, at the first step, the optimum p is calculated in p-norm distance and then U-statistic method is applied on p-norm distance values of the samples because p-norm distance is calculated based on several variables. This method is a combination of efficient U-statistic method and p-norm distance and is used for the first time in this research. Results show that p-norm distance of p=2(Euclidean distance) in the case of a fact that Au and As can be considered optimized p-norm distance with the lowest error. The samples indicated by the combination of these methods as anomalous are more regular, less dispersed and more accurate than using just the U-statistic or other nonstructural methods such as Mahalanobis distance. Also it was observed that the combination results are closely associated with the defined Au ore indication within the studied area. Finally, univariate and bivariate geochemical anomaly maps are provided for Au and As, which have been respectively prepared using U-statistic and its combination with Euclidean distance method.

基于双元变换的一类反常积分问题的计算

针对一类被积函数分母含ax^(4)+bx^(2)+c的有理分式的反常积分问题,利用引入双元变换的方法,结合组合计算方法和高次有理分式化成部分有理真分式的理论,给出了积分问题的计算方法.利用所给结论,计算并证明了二类积分问题.

结构可靠性分析的变量分解法

针对隐式非线性极限状态的复杂结构可靠性预测,提出了一种变量分解方法.该方法利用双变量分解法将求解功能函数统计矩的多维积分转化为多个低维积分,并利用高斯-埃尔米特数值积分对低维积分进行求积.在获得功能函数的统计矩后,应用最大熵原理确定用于可靠性分析的功能函数的最佳概率密度函数.该方法只需进行一次结构功能函数的概率密度函数求解,就能获得不同极限状态值的可靠度.算例分析结果表明,该方法的结果与Monte Carlo法100万次模拟结果相比,其相对误差不超过0.5%,具有很好的计算精度.

计及风速-负荷相关性的配电网可靠性评估Monte Carlo模拟法

为了准确分析风速与系统负荷之间的相关性,提出一种计及风速-负荷相关性含风电机组(Wind Turbine Generator,WTG)的配电网可靠性评估方法。利用多元统计方法建立风速与负荷的正态分布模型,计算二者的相关系数,得到风速-负荷联合二元正态分布函数。采用该方法对改进RBTS系统进行计算,根据联合分布函数用Monte Carlo法对风速-负荷序列进行抽样,结合WTG出力模型,得到其对孤岛的供电能力范围,分别计算每种抽样结果的可靠性指标,最后得到系统可靠性指标,并分析多种因素对可靠性指标的影响。该方法能准确反映时序风速和负荷的相关性,从而提高可靠性计算的精确性。

改进型GMSM建模方法及其应用

本文提出了一种改进的GMSM建模方法。该方法以二元插值多项式作为各层的部分描述式,利用ISM方法进行输入变量预处理,简化了原方法的整体结构。建模结果表明:改进方法对建立一般复杂过程的数学模型是有效的。

基于时变区间和穿阈模型的机械时变可靠性分析方法

现有机械时变可靠性模型主要以概率论为基础,依赖于基本随机变量的大样本空间,当没有足够的数据来验证这些随机变量的概率密度正确性时,分析结果的准确性和置信度值得怀疑,概率可靠性方法存在局限性。在航天机构中,由于成本高,在复杂服役环境中可观测性差、检测难,积累信息难、统计类信息往往难以获得,主要存在区间类信息,为保证分析结果更加精确,考虑时变区间变量,研究并提出非概率时变可靠性分析方法:将时变区间转化为服从截断正态分布的随机过程,求出在时变区间内的上穿率,针对正态截断分布变量,利用改进的非概率PHI方法,求得累积失效概率。解决区间变量随时间变化下的非概率时变可靠性问题。利用算例和工程实例验证本方法的准确性和可行性。

基于等几何分析的边界元法求解Helmholtz问题

将基于一类局部双变量B样条函数的等几何分析方法和Burton-Miller方法相结合,分析三维Helmholtz问题.对于某些从二维参数域映射到三维空间具有奇异点的参数曲面,该方法可以有效地避免奇异点处大量奇异与近奇异积分的计算.数值算例表明该方法具有较好的计算精度和计算效率.复杂问题的分析表明,该方法具有良好的工程应用前景.

基于二元多项式拟合法的压力传感器输入信号重构

为了同时解决压力传感器输出特性的非线性和温度漂移问题,提出利用二元多项式根据传感器输出信号及其内部温度来重构被测压力。给出了被测压力重构模型的具体形式,以传感器静态特性标定试验数据为依据,利用最小二乘法求解模型系数矩阵,利用单点最大拟合误差、误差平方和模型阶次三项指标进行模型择优。基于重构模型给出了测量电路检测精度估算方法。本方法在传感器静态特性标定数据范围内得到了便于工程计算的一致表达式,同时解决了传感器的非线性和温度漂移两个主要问题,计算所用数据量大大小于插值法。某型硅谐振压力传感器的应用验证了本方法的合理性和有效性。

改进的LPG-PCA的图像去噪方法

主成分分析(PCA)变换能够去除信号之间的相关性,并且在PCA域中,很容易把信号和噪声区分出来。在对目标像素块进行处理前,首先要在一定的搜索域中寻找与其结构相似的局部像素块作为训练样本,对图像进行复制,使用双参数收缩算法对复制图像进行处理,然后使用在复制图像中对应的像素块之间的欧氏距离,来代替目标像素块与局部像素块之间的相似性,减小了噪声所带来的影响,对后续的PCA变换起到了重要作用。仿真实验表明,改进的LPG-PCA方法相对于改进之前,使图像的质量有了一定提高。

中国人口老龄化问题的分析与预测

利用最小二乘法构造了我国人口老龄化的二元回归预测模型，得到2005～2050年我国人口老龄化（65岁以上）系数，并依此预测出我国老年人口数量多、老龄化速度快、高龄趋势明显等特点．

床面粗糙形态的二元分形插值模拟

针对床面粗糙形态具有自相似性的特点,应用二元分形插值迭代函数系统,对床面粗糙形态进行了分形插值模拟,模拟中分形插值邻域Ak根据Kriging空间插值方法的变异函数球状模型确定,垂直比例因子sm,n通过基于插值点数据的多元统计分析确定。结果表明:分形插值重构的床面粗糙形态与原床面形态的相似程度将随着插值点信息量ic的增加而提高,且ic仅需达到某一较小值(如ic≥0.0625),得到的床面粗糙形态即可具有较高的逼真度,其分维数也与理论值接近。因此,在测量数据不足的情况下,采用二元分形插值模拟方法可获得逼真度较高的精细床面粗糙形态。