Generalized multivariate ridge regression estimate and criteria q(c) for choosing matrixK

When multicollinearity is present in a set of the regression variables, the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference. In this paper, generalized ridge estimate β(K) of the regression coefficient β =vec(B) is considered in multivaiate linear regression model. The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter matrix K. Moreover, it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several weaknesses. In order to overcome these weaknesses, a new family of criteria Q(c) is adpoted which includes the criterion MSE and criterion LS as its special case. The good properties of the criteria Q(c) are proved and discussed from theoretical point of view. The statistical meaning of the scale c is explained and the methods of determining c are also given. The projects Supported by Natural Science Foundation of Fujian Province     

GENERALIZED MULTIVARIATE RIDGE REGRESSION ESTIMATE AND CRITERIA Q(e)FOR CHOOSING MATRIX K

When multicollinearity is present in a set of the regression variables,the leastsquare estimate of the regression coefficient tends to be unstable and it may lead toerroneous inference.In this paper,generalized ridge estimateβ(K)of the regression coefficientβ=vec(B)is considered in multivaiate linear regression model.The MSE of the aboveestimate is less than the MSE of the least square estimate by choosing the ridgeparameter matrix K.Moreover,it is pointed out that the Criterion MSE for choosingmatrix K of generalized ridge estimate has several weaknesses.In order to overcomethese weaknesses,a new family of criteria Q(c)is adpoted which includes the criterionMSE and criterion LS as its special case.The good properties of the criteria Q(c)areproved and discussed from theoretical point of view.The statistical meaning of thescale c is explained and the methods of determining c are also given.     

微机械陀螺温度混合线性回归补偿方法

环形振动微机电陀螺受温度影响较大,并且还具有很强的自回归特性。针对传统的分段拟合等温度模型均难以精确补偿陀螺受温度影响的问题,提出了一种基于混合线性回归的温度补偿模型。该方法根据混合线性回归模型的特点将陀螺自身的影响以及温度变化等因素考虑到温度补偿模型中,采用多元线性回归方法确定各项的系数,通过对残差的正态检验确定模型是否能够较好的符合陀螺数据的变化规律。验证试验结果表明:补偿后的均值可以减小1～2个数量级,并且该温度误差补偿方法重复性好,具有重大的工程应用参考价值。     

基于变形场测量数据主元压缩的模型参量反求方法

利用主元分析法对数字图像相关技术所测结构变形信息进行数据压缩,并进一步用于力学模型未知参量的反求计算。首先,为降低数字图像相关技术所测庞大数据的应用成本,提出利用主元分析法对结构表面变形场数据进行压缩,实现在保留结构表面变形信息主要特征的前提下显著降低数据量的目的;其次,针对压缩后的数据建立了基于最小二乘法的力学模型参量反求模型,并利用高斯牛顿法进行求解;最后,以具体算例从计算精度、收敛速度和抗噪性等方面验证了数据压缩对模型参量反求的效果。研究结果表明,所提方法在显著降低使用数据量的前提下,能够有效提高力学模型参量反求计算的收敛速度,特别是对于包含多个模型参数的反求问题,具有较高的精度和较好的稳定性。     

A least square extrapolation method for the a posteriori error estimate of the incompressible Navier Stokes problem

A posteriori error estimators are fundamental tools for providing confidence in the numerical computation of PDEs. To date, the main theories of a posteriori estimators have been developed largely in the finite element framework, for either linear elliptic operators or non‐linear PDEs in the absence of disparate length scales. On the other hand, there is a strong interest in using grid refinement combined with Richardson extrapolation to produce CFD solutions with improved accuracy and, therefore, a posteriori error estimates. But in practice, the effective order of a numerical method often depends on space location and is not uniform, rendering the Richardson extrapolation method unreliable. We have recently introduced (Garbey, 13th International Conference on Domain Decomposition, Barcelona, 2002; 379–386; Garbey and Shyy, J. Comput. Phys. 2003; 186 :1–23) a new method which estimates the order of convergence of a computation as the solution of a least square minimization problem on the residual. This method, called least square extrapolation, introduces a framework facilitating multi‐level extrapolation, improves accuracy and provides a posteriori error estimate. This method can accommodate different grid arrangements. The goal of this paper is to investigate the power and limits of this method via incompressible Navier Stokes flow computations. Copyright © 2005 John Wiley & Sons, Ltd.     

陀螺零偏二次模型参数的系统级辨识算法

以单轴旋转光学捷联惯性导航系统为原型,假设水平陀螺常值漂移的影响得以完全调制,方位陀螺漂移为随时间变化的二次模型,在水平阻尼工作模式下推导了系统位置误差与方位陀螺漂移之间严格的数学关系。分别设置了方位陀螺漂移仅有常值项、一次项、二次项和全系数误差的误差模型,利用递推最小二乘算法成功辨识出设定的二次模型中各个参数值。仿真结果表明,常值项首先被辨识出来,估计时间约为14 h,估计误差为6.54e-6(°)/h;一次项系数估计时间约为30 h,估计误差为2.73e-8(°)/h;二次项系数估计时间约为42 h,估计误差为1.51e-9(°)/h;全系数估计需要45 h,估计误差为7.28e-6(°)/h。辨识结果验证了该算法的正确性。实际系统中,可适当增加总的辨识估计时间,以达到更高精度的辨识结果。     

The site model theory and the standard linear solid

Summary The site model theory (SMT) is shown to lead to the same deformation behaviour as that displayed by the standard linear solid (SLS), group I, for all loading conditions. If a second deformation mechanism (inter-molecular slip) is introduced the result is the same as that obtained with the standard linear solid, group II, and models the behaviour of a polymer melt near to the solidification temperature.

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Zusammenfassung Es wird gezeigt, daß ein einfaches Platzwechsel-Modell (site model theory) bei allen Belastungsbedingungen das gleiche Deformationsverhalten voraussagt wie der lineare Drei-Parameter-Festkörper (standard linear solid, group I). Wenn ein weiterer Deformationsmechanismus (zwischenmolekulare Gleitung) eingeführt wird, entspricht das Verhalten dagegen demjenigen einer linearen Drei-Parameter-Flüssigkeit (standard linear solid, group II), welche das Verhalten einer Polymerschmelze in der Nähe der Schmelztemperatur beschreibt.

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a = ₁₂ ⁰ + ₂₁ ⁰ , see eq. [1] - b =N ₁ ⁰ ₁₂ ⁰ (V ₁₂ +V ₂₁), see eq. [1] - c = 2N _s ⁰ V _s see eq. [6] - k Boltzmann constant - t time - E,E ₁,E ₂ spring constants, see figures 1 and 3 - E _u unrelaxed modulus - N ₁ ⁰ site 1 equilibrium population in the unstressed state - N _s number of units available for slip - N(t) decrease in site 1 population - N _s (t) net number of slip jumps in the stressaided direction - T temperature (K) - V _i,j activation volume for jumps in directioni j - V _s activation volume for the slip process - strain - strain rate - incremental change in strain per unit change in site population - µ,µ ₁,µ ₂ dashpot constants, see figures 1 and 3 - applied stress - ₀ initial applied stress, (stress relaxation) =(t) (creep) - incremental change in stress per unit change in site population - ⁰ jump rate for slip in the unstressed state - _i,j ⁰ jump rate in the directioni j in the unstressed state With 3 figures and 3 tables     

超磁致伸缩车削加工刀架特性实验分析

利用光栅测微传感器(DG-10)和自行开发研制的优化后的超磁致伸缩车削加工刀架,对不同预压力、电流强度下刀架性能进行实验研究。实验中分别由压力传感器和改进后的控制电路调整所加预压力、电流的大小,通过数据采集系统记录光栅测微传感器所测得的磁致伸缩量。实验结果表明:在不同预压力下,刀架输出位移随着激励电流的增大而增大,直到达到饱和;同时在最大工作电流作用下,刀架的输出位移随着预压力的增大而增大,但当预压力增大到一定数值后,刀架的输出位移随着预压力的增大而减小。利用最小二乘曲线拟合、线性回归等数学方法得出了刀架在最大工作电流下,预压力与磁致伸缩量之间的拟合曲线及函数多项式,并确立了最佳工作预压力。建立了最佳工作预压力下电流与磁致伸缩量之间的函数关系式。通过误差分析看出理论分析和实验结果吻合的很好。     

一种基于半参数回归的加速度计误差模型辨识方法

为了解决加速度计离心机试验中系统误差和未建模误差对加速度计模型辨识的影响,将统计学中的半参数回归方法引入到加速度计的模型辨识中,建立了加速度计的半参数回归模型,提出了一种基于最小二乘-半参数回归模型(LS-SPRM)的估计方法,该估计方法利用最小二乘法估计加速度计的误差模型系数,利用半参数回归方法估计加速度计测试中的系统误差,并通过检验残差是否为白噪声作为判断是否有系统误差的条件。在半参数模型的估计中,采用二阶段估计方法,利用三次样条函数进行非参数部分的估计,并讨论了光滑参数的选取方法。仿真试验结果表明,采用该方法能够较好地补偿由于系统误差和未建模误差带来的影响,使加速度计模型辨识的标准差较普通最小二乘法减小45%左右,估计的残差也减小了近一倍。     

考虑侧面摩擦的侧限压缩模型的数值解法

海上箱筒型基础结构下沉到位后,舱内土体的受力变形可以看作是侧限压缩模型问题,上部荷载引起的侧壁摩擦力与土体应力之间的关系较为复杂。本文通过简化模型,列出了侧限压缩模型的平衡微分方程,分析了方程解析计算时存在的难点,结合摩擦应力边界条件的特点,构造函数迭代法对该方程进行数值求解,展示了计算的收敛过程,得到接触侧面上水平应力和土体表面位移的非线性分布规律,并将其结果与ABAQUS数值模拟结果进行了对比。结果表明,函数迭代法收敛速度较快,计算过程稳定,对其他存在变量耦合边界条件的微分方程数值求解有一定的参考价值。     

内聚滑移爆轰加载下金属圆管压缩过程的工程分析

对内聚滑移爆轰加载下圆管压缩运动过程进行工程分析,分析解与数值模拟结果吻合。利用工程模型得到了不同管道参数（包括内径、厚度）下管道封闭所需要的炸药量和封闭时间表达式,可为相关研究工作提供参考。

     

Data assimilation of forecasted errors in hydrodynamic models using inter‐model correlations

Data‐assimilation techniques of the Kalman filter type are considered to be the state‐of‐the‐art approach for combining data information and deterministic numerical models with the objective of operational forecasting. This paper introduces, as an alternative, a faster and simpler data‐assimilation technique that exploits inter‐model correlations to distribute predicted errors. This scheme is performed in two steps: (i) prediction of the deterministic model errors at observation points using so‐called local linear models and (ii) distribution of the forecasted errors over the computational domain employing a scheme based on deterministic inter‐model correlations which describe the spatial nature of error structure. The method's advantage is that systematic error can be predicted by the error correction scheme, while the dynamics remain described by the deterministic model, which also establishes a basis for the spatial error distribution scheme. This relatively simple approach is inspired by original Kalman filter techniques but distinguishes error prediction and distribution in two different stages, hence allowing for data‐driven error forecasting and off‐line correction. In order to test the scheme's performance, a deterministic model of an artificial bay was constructed and run. The system was driven by specific forcing conditions and characterized by physical parameters that, in subsequent simulations, were deliberately manipulated to introduce errors into the model and test the scheme's capability. Copyright © 2007 John Wiley & Sons, Ltd.     

The asymptotic stability analysis in stochastic logistic model with Poisson growth coefficient

The asymptotic stability of a discrete logistic model with random growth coefficient is studied in this paper. Firstly, the discrete logistic model with random growth coefficient is built and reduced into its deterministic equivalent system by orthogonal polynomial approximation. Then, the linear stability theory and the Jury criterion of nonlinear deterministic discrete systems are applied to the equivalent one. At last, by mathematical analysis, we find that the parameter interval for asymptotic stability of nontrivial equilibrium in stochastic logistic system gets smaller as the random intensity or statistical parameters of random variable is increased and the random parameter's influence on asymptotic stability in stochastic logistic system becomes prominent.     

Study of linear response identification techniques and reduced‐order model generation for a 2D CFD scheme

Reduced‐Order Models (ROMs) have been the focus of research in various engineering situations, but it is only relatively recently that such techniques have begun to be introduced into the CFD field. The purpose of generating such models is to capture the dominant dynamics of the full set of CFD equations, but at much lower cost. One method that has been successfully implemented in the field of fluid flows is based on the calculation of the linear pulse responses of the CFD scheme coupled with an Eigensystem Realization algorithm (ERA), resulting in a compact aerodynamic model. The key to the models is the identification of the linear responses of the non‐linear CFD code. Two different methods have been developed and reported in literature for linear response identification; the first method linearizes the CFD code and the second method uses Volterra theory and the non‐linear code. As these methods were developed independently they have not previously been brought together and compared. This paper first explains the subtle, but fundamental differences between the two methods. In addition, a series of test cases are shown to demonstrate the performance and drawbacks of the ROMs derived from the different linear responses. The conclusions of this study provide useful guidance for the implementation of either of the two approaches to obtain the linear responses of an existing CFD code. Copyright © 2006 John Wiley & Sons, Ltd.     

The existence of the solution for linear complementary problem

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The effect of dispersion model on the linear stability of miscible displacement in porous media

Chang and Slattery (1986, 1988b) introduced a simplified model of dispersion that contains only two empirical parameters. The traditional model of dispersion (Nikolaevskii, 1959; Bear, 1961; Scheidegger, 1961; de Josselin de Jong and Bossen, 1961; Peaceman, 1966; Bear, 1972) has three empirical parameters, two of which can be measured in one-dimensional experiments while the third, the transverse dispersivity, must be measured in experiments in which a two-dimensional concentration profile develops. It is found that nearly the same linear stability behavior results from using either model.     

Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

THE POSITIVE SOLUTION OF CLASSICAL GELFAND MODEL WITH COEFFICIENT THAT CHANGE SIGN

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The inefficiency of the least squares estimator and its bound

It was suggested by Pantanen that the mean squared error may be used to measurethe inefficiency of the least squares estimator.Styan and Rao et al.discussed thisinefficiency and its bound later.In this paper we propose a new inefficiency of the leastsquares estimator with the measure of generalized variance and obtain its bound.     

Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

The weakly forced vibration of an axially moving viscoelastic beam is investigated.The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved.The nonlinear equations governing the transverse vibration are derived from the dynamical,constitutive,and geometrical relations.The method of multiple scales is used to determine the steady-state response.The modulation equation is derived from the solvability condition of eliminating secular terms.Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation.The stability of nontrivial steady-state response is examined via the Routh-Hurwitz criterion.