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.     

The compression LS estimate of regression coefficient in multivariate linear model

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广义双剪应力准则角隅模型

本文将广义双剪应力准则变换为π平面和静水应力轴的柱坐标方程,然后将其角隅光滑化,得到了新的光滑、外凸的广义双剪应力准则角隅模型,研究结果表明,近年来作为光滑化Mohr-Coulomb理论提出的各种角隅模型,实际上并不是光滑化的Mohr-Coulomb理论,而是光滑化的广义双剪应力理论。     

基于机器学习对三角堰流量系数的预测研究

为了准确高效得出三角堰泄流系数的大小，本研究基于广义神经网络、最小二乘支持向量机和遗传规划对三角堰流量系数进行智能建模．将无量纲参数堰顶角、弗劳德数、堰顶长与堰高之比、堰顶长与堰顶水深之比作为模型输入参数，流量系数作为模型输出参数．研究表明，最小二乘支持向量机性能优于广义神经网络和遗传规划．在测试阶段，均方根误差为0.000 73，散射指数为0.001 02，决定系数为0.999 59，最大误差为1.7 %．该模型精度较高，预测值较准确，具有较强的工程适用性．本研究通过对三角堰流量系数进行智能建模，采用机器学习对非线性物理关系进行高精度拟合，准确高效得出三角堰流量系数的大小，可为水利水电工程设计人员和我国灌区精确量水用水提供一种新的方法和思路．     

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.     

圆管截面齐次广义屈服函数与结构极限承载力

为克服圆管截面广义屈服准则不满足比例加载条件,导致采用弹性模量调整法求解该类结构极限承载力时存在计算结果受荷载初值影响、计算精度受损等问题,利用回归分析和最小二乘法研究建立了圆管截面广义屈服函数的齐次多项式,通过误差分析确定了齐次化多项式的阶次;据此定义了圆管截面薄壁构件的单元承载比、承载比均匀度和基准承载比,为高承载比薄壁单元的判别及其弹性模量调整提供了动态判据,进而依据能量守恒准则建立了以单元承载比为基本参数的模量调整公式,结合下限原理提出了圆管截面薄壁结构极限承载力分析的弹性模量缩减法。研究表明,选取齐次化多项式的广义屈服函数能更加准确地考虑各项内力对结构极限承载力的综合影响,具有良好的计算精度和效率,可应用于复杂圆管截面薄壁结构的极限承载力分析中。     

Design of Modified Tabs for Testing of Symmetric Composite Thin Walled Tubes Under Pure Torsional and Tensile Loadings

This paper is mainly concerned with designing modified tabbing systems for testing of composite thin-walled tubes with symmetric layup. The modified tabs are presented based on the concept of iso-displacement points—the points of the specimen that move together and behave similarly during a test. Numerical solutions are carried out for tubular specimens in order to find the displacement field and hence the iso-displacement points. The analyses are carried out for two loading cases: pure torsion and pure tension. Finite element analyses are conducted for both cases, to estimate the displacement fields of thin-walled tubular specimens and then predictive equation were determined using multiple nonlinear regression models. The accuracy of these models is evaluated using a multiple coefficient of determination, R ², where 0 ≤ R ² ≤ 1, coupled with predicted squared error (PSE) and mean squared error (MSE). R ² is found to be greater than or equal to 0.98 for all cases considered in this study while PSE and MSE values are minimized, demonstrating the reliability of the model. Comparison between the modified tabs, based on the iso-displacement points determined by predictive equations, with conventional tabs indicates an improvement in the uniformity of stress and strain distribution (which is an important factor in order to have a successful test) within the specimen for both load cases. It is also demonstrated that due to the elimination of the stress and strain non-uniformities, the measured permissible maximum load of the specimens is significantly increased during the test.     

New true-triaxial rock strength criteria considering intrinsic material characteristics

A reasonable strength criterion should reflect the hydrostatic pressure effect, minimum principal stress effect,and intermediate principal stress effect. The former two effects can be described by the meridian curves, and the last one mainly depends on the Lode angle dependence function. Among three conventional strength criteria, i.e.Mohr–Coulomb(MC), Hoek–Brown(HB), and Exponent(EP) criteria, the difference between generalized compression and extension strength of EP criterion experience a firstly increase then decrease process, and tends to be zero when hydrostatic pressure is big enough. This is in accordance with intrinsic rock strength characterization. Moreover, the critical hydrostatic pressure I_c corresponding to the maximum difference of between generalized compression and extension strength can be easily adjusted by minimum principal stress influence parameter K. So, the exponent function is a more reasonable meridian curves, which well reflects the hydrostatic pressure effect and is employed to describe the generalized compression and extension strength.Meanwhile, three Lode angle dependence functions of L_(MN),L_(WW), and L_(YMH), which unconditionally satisfy the convexity and differential requirements, are employed to represent the intermediate principal stress effect. Realizing the actual strength surface should be located between the generalized compression and extension surface, new true-triaxial criteria are proposed by combining the two states of EP criterion by Lode angle dependence function with a same lode angle. The proposed new true-triaxial criteria have the same strength parameters as EP criterion. Finally, 14 groups of triaxial test data are employed to validate the proposed criteria. The results show that the three new true-triaxial exponent criteria,especially the Exponent Willam-Warnke criterion(EPWW)criterion, give much lower misfits, which illustrates that the EP criterion and L_(WW) have more reasonable meridian and deviatoric function form, respectively. The proposed new true-triaxial strength criteria can provide theoretical foundation for stability analysis and optimization of support design of rock engineering.     

Convergence and stability of recursive damped least square algorithm

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Theoretical analysis on the local critical stress and size effect for interfacial debonding in particle reinforced rheological materials

The mechanisms of interfacial debonding of particle reinforced rheological materials are studied. Based on an energy criterion, a simple formula of local critical stress for interfacial debonding is derived and expressed in terms of the interfacial energy. The particle size effect on interface debonding can then be analyzed easily owing to the fact that critical stress is inversely proportional to the square root of particle radius. By taking PP/CaCO₃ system as an example, the present energy criterion is compared with the mechanical debonding criterion, and it is found that under the condition that bond strength is equal to matrix strength and particle radius not over 0.2μm, the mechanical debonding criterion can be automatically satisfied if the energy criterion is satisfied. A relation between critical time and interface energy is calculated by using the energy criterion. The influences of the particle volume fraction and the parlicle size, the loading rate and the relaxation time of the matrix on the critical time of interfacial debonding are also discussed. Supported by the National Natural Science Foundation of China (19632030 and 19872007) and Natural Science Foundation of Jiangsu Province.     

Coupled processes of deformation and long-term damage of fibrous materials with the microdurability of the matrix described by an exponential power function

The theory of long-term damage is generalized to fibrous composites. The damage of the matrix is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–von Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of stress-rupture microstrength described by an exponential power function     

Deformation and long-term damage of fibrous materials with the stress-rupture microstrength of the matrix described by a fractional-power function

The theory of long-term damage is generalized to unidirectional fibrous composites. The damage of the matrix is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of stress-rupture microstrength described by a fractional power function     

Passivity of uncertain neural networks with both leakage delay and time-varying delay

In this paper, the passivity problem is investigated for a class of uncertain neural networks with leakage delay and time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov–Krasovskii functionals, and employing Newton–Leibniz formulation and the free-weighting matrix method, several delay-dependent criteria for checking the passivity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.     

Natural Convection in a Cavity Filled with Porous Layers on the Top and Bottom Walls

Natural convection in a partially filled porous square cavity is numerically investigated using SIMPLEC method. The Brinkman-Forchheimer extended model was used to govern the flow in the porous medium region. At the porous-fluid interface, the flow boundary condition imposed is a shear stress jump, which includes both the viscous and inertial effects, together with a continuity of normal stress. The thermal boundary condition is continuity of temperature and heat flux. The results are presented with flow configurations and isotherms, local and average Nusselt number along the cold wall for different Darcy numbers from 10⁻¹ to 10⁻⁶, porosity values from 0.2 to 0.8, Rayleigh numbers from 10³ to 10⁷, and the ratio of porous layer thickness to cavity height from 0 to 0.50. The flow pattern inside the cavity is affected with these parameters and hence the local and global heat transfer. A modified Darcy–Rayleigh number is proposed for the heat convection intensity in porous/fluid filled domains. When its value is less than unit, global heat transfer keeps unchanged. The interfacial stress jump coefficients β ₁ and β ₂ were varied from  −1 to +1, and their effects on the local and average Nusselt numbers, velocity and temperature profiles in the mid-width of the cavity are investigated.     

Singularly perturbed feedback linearization with linear attitude deviation dynamics realization

A new approach for feedback linearization of attitude dynamics for rigid gas jet-actuated spacecraft control is introduced. The approach is aimed at providing global feedback linearization of the spacecraft dynamics while realizing a prescribed linear attitude deviation dynamics. The methodology is based on nonuniqueness representation of underdetermined linear algebraic equations solution via nullspace parametrization using generalized inversion. The procedure is to prespecify a stable second-order linear time-invariant differential equation in a norm measure of the spacecraft attitude variables deviations from their desired values. The evaluation of this equation along the trajectories defined by the spacecraft equations of motion yields a linear relation in the control variables. These control variables can be solved by utilizing the Moore–Penrose generalized inverse of the involved controls coefficient row vector. The resulting control law consists of auxiliary and particular parts, residing in the nullspace of the controls coefficient and the range space of its generalized inverse, respectively. The free null-control vector in the auxiliary part is projected onto the controls coefficient nullspace by a nullprojection matrix, and is designed to yield exponentially stable spacecraft internal dynamics, and singularly perturbed feedback linearization of the spacecraft attitude dynamics. The feedback control design utilizes the concept of damped generalized inverse to limit the growth of the Moore–Penrose generalized inverse, in addition to the concepts of singularly perturbed controls coefficient nullprojection and damped controls coefficient nullprojection to disencumber the nullprojection matrix from its rank deficiency, and to enhance the closed loop control system performance. The methodology yields desired linear attitude deviation dynamics realization with globally uniformly ultimately bounded trajectory tracking errors, and reveals a tradeoff between trajectory tracking accuracy and damped generalized inverse stability. The paper bridges a gap between the nonlinear control problem applied to spacecraft dynamics and some of the basic generalized inversion-related analytical dynamics principles.     

State estimation for Markovian jumping recurrent neural networks with interval time-varying delays

The paper is concerned with the state estimation problem for a class of neural networks with Markovian jumping parameters. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error are globally stable in the mean square. A new type of Markovian jumping matrix P _i is introduced in this paper. The discrete delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

基于多元线性回归分析的土坡有限元失稳判据定量研究

塑性区连通程度是有限单元法判别土坡是否达到极限状态的重要依据,鉴于此判据目前尚未取得统一,本文着重对均质土坡失稳判据进行了定量研究。在主要考虑对土坡稳定性影响较大的三大参数(黏聚力c、内摩擦角φ、坡比λ)的前提下,通过经典条分法选取了多组处于极限平衡状态的土坡参数组合,对这些参数组合进行有限元程序计算,求得极限平衡状态下土坡剪切带等效塑性应变中值连通率,再采用多元线性统计回归方法,得出塑性区中值连通率与土坡参数的关系公式y=0.020702c+0.024417φ-0.67898λ+0.46799,从而为土坡有限元稳定性分析提供了定量失稳判据,并且使得有限单元法与经典条分法计算成果具有一定的可比性。算例分析表明,利用本文判据公式得到的安全系数与Bishop法计算成果相吻合,从而验证了失稳判据公式的正确性。     

Deformation and long-term damage of physically nonlinear particulate composites

The theory of long-term damage is generalized to particulate composite materials with physically nonlinear components. The damage of the components is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the components at an arbitrary time is formulated. Algorithms of calculating the time dependence of are developed. The effect on the nonlinearity of the matrix on the damage and macrodeformation curves is examined