Fast computation of satellite gravitational gradient

The computation of the Earth's potential function at high order and degree with the method of reference [1], causes overflow most of the time. The normalized method [2–6] can eliminate the overflows, but leads to formulae much more involved than those in reference [1]; besides, the programming is more complex and the computer time required larger. The method presented in this paper has the following features: each component of the satellite gravitational gradient can be computed; the formulae are short and easy to be programme; the method is much quicker than the normalization method and can be carried out with a micro‐computer, without overflow even in the case of Earth's spherical harmonics of order and degree as high as 1025 or higher. This method satisfies the present demand to compute satellite gravitational gradient with high accuracy. Furthermore, we present formulae for the fast computation, without overflow, of the gravitational gradient corresponding to Earth's spherical harmonics up to order and degree of 3170 × 3170 or higher. This revised version was published online in July 2006 with corrections to the Cover Date.     

Approximate General Solution Of The Two-Dimensional Duffing Dynamical System

This paper presents the approximate general solution of the triple well, double oscillator non-linear dynamical system. This system is non-integrable and the approximate general solution is calculated by application of the Last Geometric Theorem of Poincaré (Birkhoff, 1913, 1925). The original problem, known as the Duffing one, is a 1 degree of freedom system that, besides the conservative force component, includes dumping and external forcing terms (see details in the web site: http://www.uncwil.edu/people/hermanr/chaos/ted/chaos.html). The problem considered here is a 2 degree of freedom, autonomous and conservative one, without dumping, and of axisymmetric potential. The space of permissible motions is scanned for identification of all solutions re-entering after from one to nine oscillations and the precise families of periodic solutions are computed, including their stability parameter, covering all cases with periods T corresponding to 4osc/T. Seven sub-domains of the space of solutions were investigated in detail by zooming, an operation that proved the possibility to advance the accuracy of the approximate general solution to the level permitted by the integration routine. The approximation of the general solution, although impressive, provides clear evidence of the complexity of the problem and the need to proceed to larger period families. Nevertheless, it allows prediction of the areas where chaos and order regions in the Poincaré surfaces of section are to be expected. Examples of such surfaces of sections, as well as of types of closed solutions, are given. Two peculiar points of the space of solutions were identified as crossing, or source points from which infinite families of periodic solutions emanate. The morphology and stability of solutions of the problem are studied and discussed.     

A simplified fragility analysis of fan type cable stayed bridges

A simplified fragility analysis of fan type cable stayed bridges using Probabilistic Risk Analysis (PRA) procedure is presented for determining their failure probability under random ground motion. Seismic input to the bridge support is considered to be a risk consistent response spectrum which is obtained from a separate analysis. For the response analysis, the bridge deck is modeled as a beam supported on springs at different points. The stiffnesses of the springs are determined by a separate 2D static analysis of cable-tower-deck system. The analysis provides a coupled stiffness matrix for the spring system. A continuum method of analysis using dynamic stiffness is used to determine the dynamic properties of the bridges .The response of the bridge deck is obtained by the response spectrum method of analysis as applied to multidegree of freedom system which duly takes into account the quasi - static component of bridge deck vibration. The fragility analysis includes uncertainties arising due to the variation in ground motion, material property, modeling, method of analysis, ductility factor and damage concentration effect. Probability of failure of the bridge deck is determined by the First Order Second Moment (FOSM) method of reliability. A three span double plane symmetrical fan type cable stayed bridge of total span 689 m, is used as an illustrative example. The fragility curves for the bridge deck failure are obtained under a number of parametric variations. Some of the important conclusions of the study indicate that (i) not only vertical component but also the horizontal component of ground motion has considerable effect on the probability of failure; (ii) ground motion with no time lag between support excitations provides a smaller probability of failure as compared to ground motion with very large time lag between support excitation; and (iii) probability of failure may considerably increase for soft soil condition.     

Third-Order Moments for Shear Driven Boundary Layer

A new third-order model for shear driven boundary layer is presented and tested against large-eddy simulation (LES) data. Numerical solutions are obtained using mean flow components and second-order moments as input. The calculated vertical profiles of the variances and turbulent kinetic energy fluxes and those provided by a LES experiment are compared and discussed     

Generalized Sequential Gaussian Simulation on Group Size ν and Screen-Effect Approximations for Large Field Simulations

The modelling of spatial uncertainty in attributes of geological phenomena is frequently based on the stochastic simulation of Gaussian random fields. This paper presents a generalization of the sequential Gaussian simulation method founded upon the group decomposition of the posterior probability density function of a stationary and ergodic Gaussian random field into posterior probability densities of a set of groups of nodes of size . The method, which is termed generalized sequential Gaussian simulation on group size , relies computationally on sharing the neighborhood of adjacent nodes and simulates groups of nodes at a time, instead of the traditional node-by-node simulation. The new method is computationally efficient and suitable for simulation on large grids of nodes. Results suggest that, in terms of computing cost (time), an optimal size of a group is about 80% of the optimal neighborhood used for sequential Gaussian simulation and that computation can be up to 50 times faster than the regular sequential Gaussian method, with little loss in accuracy. The effectiveness of the method is assessed by using a general measure of accuracy, screen-effect approximation loss (SEA loss), defined herein as the mean-square difference between the simulated value posterior to the information in the neighborhood and the simulated value posterior to all information, and shown to be determined by the corresponding posterior variances. The results presented show that both the exponential and the spherical models perform well and can meet the less-than 5% relative SEA loss requirement for any grid setup using a relatively small neighborhood. The Gaussian covariance model was found to have a relatively high relative SEA loss in most cases.     

Comparing Loss Estimation with Observed Damage in a Zone of Ground Failure: A Study of the 1999 Kocaeli Earthquake in Turkey

The building losses in Adapazari following the 17 August 1999 Kocaeli earthquake are estimated for both ground-shaking and ground-failure induced damage and the predictions compared with field observations. The ground-shaking damage is estimated using the capacity spectrum approach and accommodating the results of a previously published calibration of this model. These results, which do not incorporate ground-failure damage, are compared to the observed damage patterns in Adapazari to illustrate the significance of not including the more complex ground failure component in a loss model for a region of high liquefaction susceptibility. A preliminary estimation of ground-failure-induced damage is then presented based upon the HAZUS (FEMA, 2003) default methodology. The benefits of these additional calculations to the overall loss model are assessed to provide some quantitative decision-making guidance for those producing loss estimation models. The findings suggest that the benefits of specifically incorporating ground failure into a loss model only start to be obtained if a detailed approach using in situ geotechnical data as well as adequate representation of building foundations is adopted. Otherwise, the additional input data required is not commensurate with the small potential refinement in the estimated losses, particularly considering the compounded uncertainties associated with the simplified approach.     

CAR模型的阶与时滞的强一致估计

研究随机线性反馈控制系统的结构辨识问题。在已知时滞的下界和模型阶的上界的假定下，通过使修改的Ｂａｙｅｓｉａｎ信息准则最小化，推导出由多输入多输出ＣＡＮ模型描述的系统的未知阶与时滞的估计算法，证明了算法是强一致收敛的，且能在有限步内达到其模型结构参数的真值。讨论了当模型的参数矩阵不满秩时减弱条件Ｈ’ｓ的强一致估计算法。     

不确定度在计量法规中的运用

随着国家质量技术监督局推行国际不确定度建议,不确定度将在我国涉及量值的领域被人们接受然而传统的“准确度”、“精度”等术语和“不确定度”应如何区别,正确使用,技术法规中该如何规定此类技术指标,是目前普遍感困惑的问题。本文就这些问题参与讨论。     

有限水深二维绕射问题的二阶速度势和水动力

本文给出有限水深二维物体二阶绕射势在外域中的解析表达式，从而准确满足二阶绕射势的辐射条件。二阶绕射势在内域自由表面上的边界条件则由一阶势的数值微分求得。然后对内域用简单Ｇｒｅｅｎ函数法求得二阶绕射势。本文对二维浮体和潜体在不同水深和潜深情况下的绕射问题进行了计算，求得了二阶绕射势和二阶定常及倍频波浪力。讨论了水深和潜深对波浪力的影响以及二阶绕射势对非线性波浪力的贡献