Reliability-based Robust Optimization Design of Automobile Components with Non-normal Distribution Parameters

In the reliability designing procedure of the vehicle components, when the distribution styles of the random variables are unknown or non-normal distribution, the result evaluated contains great error or even is wrong if the reliability value R is larger than 1 by using the existent method, in which case the formula is necessary to be revised. This is obviously inconvenient for programming. Combining reliability-based optimization theory, robust designing method and reliability based sensitivity analysis, a new method for reliability robust designing is proposed. Therefore the influence level of the designing parameters’ changing to the reliability of vehicle components can be obtained. The reliability sensitivity with respect to design parameters is viewed as a sub-objective function in the multi-objective optimization problem satisfying reliability constraints. Given the first four moments of basic random variables, a fourth-moment technique and the proposed optimization procedure can obtain reliability-based robust design of automobile components with non-normal distribution parameters accurately and quickly. By using the proposed method, the distribution style of the random parameters is relaxed. Therefore it is much closer to the actual reliability problems. The numerical examples indicate the following: (1) The reliability value obtained by the robust method proposed increases (】0.04%) comparing to the value obtained by the ordinary optimization algorithm; (2) The absolute value of reliability-based sensitivity decreases (】0.01%), and the robustness of the products’ quality is improved accordingly. Utilizing the reliability-based optimization and robust design method in the reliability designing procedure reduces the manufacture cost and provides the theoretical basis for the reliability and robust design of the vehicle components.

Estimating distribution of water uptake with depth of winter wheat by hydrogen and oxygen stable isotopes under different irrigation depths

Crop root system plays an important role in the water cycle of the soil-plant-atmosphere continuum. In this study, com- bined isotope techniques, root length density and root cell activity analysis were used to investigate the root water uptake mechanisms of winter wheat （Triticum aesfivum L.） under different irrigation depths in the North China Plain. Both direct inference approach and multisource linear mixing model were applied to estimate the distribution of water uptake with depth in six growing stages. Results showed that winter wheat under land surface irrigation treatment （Ts） mainly absorbed water from 10-20 cm soil layers in the wintering and green stages （66.9 and 72.0%, respectively）; 0-20 cm （57.0%） in the jointing stage; 0-40 （15.3%） and 80-180 cm （58.1%） in the heading stage; 60-80 （13.2%） and 180-220 cm （35.5%） in the filling stage; and 0-40 （46.8%） and 80-100 cm （31.0%） in the ripening stage. Winter wheat under whole soil layers irrigation treatment （Tw） absorbed more water from deep soil layer than Ts in heading, filling and ripening stages. Moreover, root cell activity and root length density of winter wheat under TW were significantly greater than that of Ts in the three stages. We concluded that distribution of water uptake with depth was affected by the availability of water sources, the root length density and root cell activity. Implementation of the whole soil layers irrigation method can affect root system distribution and thereby increase water use from deeper soil and enhance water use efficiency.

A new early warning method for dam displacement behavior based on non-normal distribution function

Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution.This assumption deviates from the reality,thereby affecting the reliability of early warning results and leading to misjudgments of dam displacement behavior.To solve this problem,this study proposed an early warning method using a non-normal distribution function.A new early warning index was developed using cumulative distribution function(CDF)values.The method of kernel density estimation was used to calculate the CDF values of residual displacements at a single point.The copula function was used to compute the CDF values of residual displacements at multiple points.Numerical results showed that,with residual displacements in a non-normal distribution,the early warning method proposed in this study accurately reflected the dam displacement behavior and effectively reduced the frequency of false alarms.This method is expected to aid in the safe operation of dams.

Effects of Long-Term Fertilization on the Distribution of Carbon, Nitrogen and Phosphorus in Water-Stable Aggregates in Paddy Soil

We investigated the size distribution of water-stable aggregates and the soil carbon, nitrogen and phosphorus concentration over aggregate size fractions based on a long-term （1990-2006） fertilization experiment in a reddish paddy soil. The results showed that the largest water-stable aggregate （WSA） （〉5 mm） and the smallest WSA （〈0.25 mm） took up the first largest proportion （38.3%） and the second largest proportion （23.3%）, respectively. Application of organic materials increased the proportion of the large WSA （〉2 mm） and decreased the proportion of the small WSA （〈1 ram）, resulting in an increase in the mean weight diameter of WSA, whereas application of chemical fertilizer had little effect. Application of organic materials, especially combined with chemical fertilizers, increased total carbon, nitrogen and phosphorus concentrations in all sizes of WSA, and total carbon, nitrogen and phosphorus were prone to concentrate in the large WSA. Further more, application of organic materials improved the supply effectiveness of available phosphorus, whereas had little influence on the labile carbon in WSA. Application of chemical fertilizers improved concentrations of total and available phosphorus in all sizes of WSA, whereas had little influence on total carbon and nitrogen contents. Economical fertilization model maintained the soil fertility when compared with full dose of chemical fertilizers, indicating that using organic materials could reduce chemical fertilizers by about one third.

A NEW CORRENTROPY BASED TDE METHOD UNDER α-STABLE DISTRIBUTION NOISE ENVIRONMENT

This paper presents a robust time delay estimation algorithm for the α-Stable noise based on correntropy. Many time delay estimation algorithms derived for impulsive stable noise are based on the theory of Fractional Lower Order Statistics (FLOS). Unlike previously introduced FLOS-type algorithms, the new algorithm is proposed to estimate the time delay by maximizing the generalized correlation function of two observed signals needing neither prior information nor estimation of the numerical value of the stable noise's characteristic exponent. An interval for kernel selection is found for a wide range of characteristic exponent values of α-Stable distribution. Simulations show the proposed algorithm offers superior performance over the existing covariation time delay estimation, least mean p-norm time delay estimation and achieves slightly improved performance than fractional lower order covariance time delay estimation at lower signal to noise ratio when the noise is highly impulsive.

UHAS-MIDA Software Package: Mass Isotopomer Distribution Analysis-Applying the Inverse Matrix for the Determination of Stable Isotopes of Chromium Distribution during Red Blood Cell Labelling

Clinical assessment of fluid volume status in children during malaria can be taxing and often inaccurate. During malaria, changes in fluid volume are rather multifarious and estimating this parameter, especially in sick children is very challenging for clinicians who frequently rely on indices such as long capillary refill times, tachycardia, central venous pressure and decreased urine volume as guides. Here, we present the UHAS-MIDA, an open-source software tool that calculates the red blood cell (RBC) concentration and blood volume during malaria in children determined using a stable isotope of chromium (53Cr as the label) by gas chromatography-mass spectrometry in selective ion monitoring (GC/MS-SIM) analysis. A key component involves the determination of the compositions of the most abundant naturally occurring isotopes of Cr (50Cr, 52Cr, 53Cr), and converting the proportions into a 3 × 3 matrix. To estimate unknown proportions of chromium isotopic mixtures from the measured abundances of three ions, an inverse matrix was calculated. The inverse together with several inputs is then used to calculate the corrected MS ion abundances. Thus, we constructed the software tool UHAS- MIDA using HTML, CSS/Bootstrap, JavaScript, and PHP scripting languages. The tool enables the user to efficiently determine RBC concentration and fluid volume. The source code, binary packages and associated materials for UHAS-MIDA are freely available at https://github.com/bentil078/Abaye-et-al_UHASmida

Robust Linear Regression Models:Use of a Stable Distribution for the Response Data

In this paper, we study some robustness aspects of linear regression models of the presence of outliers or discordant observations considering the use of stable distributions for the response in place of the usual normality assumption. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, under a Bayesian approach, the use of a latent or auxiliary random variable gives some simplification to obtain any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to a standard linear regression model with an explanatory variable and the other is related to a simulated data set assuming a 23 factorial experiment. Posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) methods and the OpenBugs software.

基于极大值截尾和偏斜分类的Alpha-stable分布参数估计新方法

在分析Alpha-stable分布概率密度函数特性的基础上,充分利用Alpha-stable分布拖尾的渐进Pareto特性和不对称性,本文提出了一种新的Alpha-stable分布极大值估计方法。仿真和分析表明该方法提高了参数估计的准确性和稳定性。

基于α-stable分布的多目标粒子群算法研究及应用

多目标的粒子群算法(MOPSO)在各个领域的优化设计中得到了广泛应用及改进,但是目前仍然存在着在进化后期容易陷入局部最优导致收敛精度低、解的多样性差等问题。引入α-stable分布理论,发展建立了一种新的基于α-stable动态变异的多目标粒子群优化算法(ASMOPSO)。通过α-stable分布生成随机数对PSO算法的种群进行变异操作,增加种群的多样性,在算法中动态调整稳定性系数α实现变异范围和幅度的变化,从而使得改进的ASMOPSO算法具有兼顾计算精度和全局寻优的能力。使用ZDT系列无约束函数和带约束的Tanaka及Srinivas函数对改进前后的算法进行了测试,结果显示出了ASMOPSO算法的快速全局寻优性能。将改进后的算法应用到RAE2822跨音速翼型的减阻和力矩绝对值不增大的综合优化中,得到了较好的多目标气动优化结果。

PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS

We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator （LSE） when a small dispersion parameter ε→0 and n →∞ simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.

基于Alpha-stable的粒子群算法变异策略研究及气动优化应用

提出了一种基于Alpha stable分布的新型变异方法。针对粒子群算法容易陷入局部最优的缺点,通过对比分析确定了一种调整Alpha stable分布的稳态系数动态变异策略,使粒子群算法能够在搜索初始阶段具有更强的种群多样性以及算法探索能力,减少陷入局部最优的可能;在算法末期增强粒子群优化算法的局部搜索能力,提高解的精度。将基于Alpha stable变异的粒子群优化算法(Alpha stable particle swarm optimization, ASPSO)与多种改进型粒子群优化算法以及差分进化算法(differential evolution algorithm, DE)进行了比较,基准测试函数结果表明新建立的ASPSO算法极大地提高了算法的收敛速度和精度。将其应用到RAE2822翼型的单点跨声速减阻优化中,在保持种群规模等参数相同的情形下,ASPSO算法的优化效果和效率都远高于传统PSO算法,最终得到的翼型也比PSO优化的翼型具有更高的升阻比,翼面波阻有明显降低。

基于Max-Stable模型的海河流域气候极值变化特征

为了解在全球变暖的背景下海河流域对气候极端事件的响应,基于海河流域1961-2016年气温与降水数据,使用RClimDex模型、MK趋势检验、Max-Stable模型对海河流域气候极值进行建模分析,研究海河流域气温极值、降水极值不同重现期的时空分布、变化特征。结果表明:海河流域温度极值TXx在空间上表现出从北向南递减趋势,值域为30~40℃,其中36~40℃占大部分地区。TXx在南方呈降低趋势,北方呈上升趋势。降水极值RX1day空间上表现出从东南向西北方向递减的趋势,值域为50~100mm,其中60~90mm占据绝大部分区域。RX1day整体呈下降趋势,其中渤海地区RX1day下降趋势最大。海河流域GEV模型拟合结果表明,海河流域气温极值主要受纬度、海拔影响,随纬度、海拔增加而降低,其变化波动为北方强于南方。降水极值RX1day受海拔和经度影响较大,主要表现为随海拔增大而下降的空间分布,其次表现为随经度变化由西向东递增的空间分布,其变化波动随海拔升高而降低。通过Q-Q百分位图、非参数极值系数θ、GEV与Max-Stable参数和重现期强度散点图判定系数R2,确定Max-Stable模型可以很好地模拟海河流域气候极值,达到GEV模型同等效果。气候极值TXx与RX1day主要受到纬度、经度和海拔的影响,但距海岸距离的加入仅可以优化TXx模型的建立。2年、10年、50年、100年一遇气温极值TXx的空间分布均表现为自东北向西南递增的分布模式,高值区均分布于西南大部一带,最高温度达40~44℃。2年、10年、50年、100年一遇降水极值TX1day的空间分布主要受纬度影响,其次受经度和海拔的影响,均表现为从西南偏中向北方递减,高值区分布在西南偏中一带,最大降水量达80~200mm。

Alpha-stable分布粗糙土壤表面电磁散射研究

采用空间域合成法生成高度起伏遵守Alpha-stable分布的粗糙土壤表面,运用矩量法研究了锥形入射波入射时粗糙土壤表面的电磁散射特性。数值计算了散射系数随散射角的变化关系,分析了稳定性系数、归一化尺度参数、互相关长度、入射波频率、土壤湿度对散射系数的影响。结果表明,稳定性系数、归一化尺度参数、互相关长度、入射波频率、土壤湿度对散射系数均有较大的影响,遵守不同的规律。

ON THE SINGULARITY OF LEAST SQUARES ESTIMATOR FOR MEAN-REVERTING α-STABLE MOTIONS

We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case （a0, θ0） = （0, 0）. If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case （θ0 = 0） and for ergodic case （θ0 〉 0） are completely different.

Stable isotope in precipitation in China:A review

The isotope ratios in precipitation are associated with various meteorological processes and display obvious spatial and temporal distributions, and thus can be used as impo~_nt techniques in inversing atmospheric processes, tracing vapor sources, and reflect- ing the local weather and climate conditions. The composition and distribution of stable isotopes in precipitation in China are summarized and the factors that influence isotope ratios are elucidated. An overview of related research progress in China during the past several decades is presented and the prospects for future work in this subject area are described.

Alpha-stable粗糙面与下方目标的复合电磁散射研究

基于Alpha-stable分布在通信、电子、雷达等领域的应用,采用空间域合成法生成高度起伏遵守Alphastable分布的粗糙土壤表面,根据四成分模型模拟粉沙壤土的介电常数,运用矩量法研究了锥形入射波入射下粗糙土壤表面与下方三角形截面柱体的复合电磁散射问题.数值计算了散射系数随散射角的变化关系,分析了稳定性系数、归一化尺度参数、互相关长度、入射波频率、土壤湿度、三角形截面柱边长、目标方位角、三角形截面柱埋藏深度对散射系数的影响.该研究结果在军事、民用、通信、工业等多领域具有一定的理论价值.

On the Mechanism of CDOs behind the Current Financial Crisis and Mathematical Modeling with Levy Distributions

This paper aims to reveal the mechanism of Collateralized Debt Obligations (CDOs) and how CDOs extend the current global financial crisis. We first introduce the concept of CDOs and give a brief account of the de-velopment of CDOs. We then explicate the mechanism of CDOs within a concrete example with mortgage deals and we outline the evolution of the current financial crisis. Based on our overview of pricing CDOs in various existing random models, we propose an idea of modeling the random phenomenon with the feature of heavy tail dependence for possible implements towards a new random modeling for CDOs.

Process Capability Indices for Shape Parameter of Weibull Distribution

Process capability analysis is used to determine the process performance as capable or incapable within a specified tolerance. Basic indices Cp, Cpk, Cpm, Cpmk initially developed for normally distributed processes showed inappropriate for processes with non-normal distributions. A number of authors worked on non-normal distributions which were most notably those of Clements, Pearn and Chen, Montgomery and Johnson-Kotz-Pearn (JKP). Obtaining PCIs based on the parameters of non-normal distributions are completely disregarded and ignored. However parameters of some non-normal distributions have significance for knowing the status of process as capable or incapable. In this article we intend to work on the shape parameter of Weibull distribution to calculate PCIs. We work on two data sets for verification and validation purpose. Efficacy of the technique is assessed by bootstrapping the results of estimate and standard error of shape parameter.

Positive Stable Frailty Approach in the Construction of Dependence Life-Tables

Dependence may arise in insurance when the insureds are clustered into groups e.g. joint-life annuities. This dependence may be produced by sharing a common risk acting on mortality of members of the group. Various dependence models have been considered in literature; however, the focus has been on either the lower-tail dependence alone or upper-tail dependence alone. This article implements the frailty dependence approach to life insurance problems where most applications have been within medical setting. Our strategy is to use the conditional independence assumption given an observed association measure in a positive stable frailty approach to account for both lower and upper-tail dependence. The model is calibrated on the association of Kenyan insurers 2010 male and female published rates. The positive stable model is then proposed to construct dependence life-tables and generate life annuity payment streams in the competitive Kenyan market.