Time domain parameters identification of foundation-structure interaction system

The time domain parameter laenuncauon memoa oi me iounuauon-structure interaction system is presented. On the basis of building the computation mode and the motion equation of the foundation-structure interaction system, the system parameter identification method was established by using the extended Kalman filter （EKF） technique and taking the unknown parameters in the system as the augment state variables. And the time parameter identification process of the foundation-structure interaction system was implemented by using the data of the layer foundation-storehouse interaction system model test on the large vibration platform. The computation result shows that the established parameter identification method can induce good parameter estimation.     

Application of Kalman Filter Finite Element Method and AIC

This paper presents a numerical simulation for application of the Kalman filter finite element method. The Kalman filter is employed frequently for the solution of time series analysis including observation and system noises. Applying the Kalman filter to the finite element method, the present method is capable of the estimation in time and space directions. In this method, the matrix generated by the finite element method is applied to the state transition matrix. Using the Kalman filter finite element method, the characteristics of both the Kalman filter and the finite element method can be strengthened. In this paper, the state transition matrix is based on the shallow water equations which are approximated by the finite element method. This method can estimate the tidal current not only in time but also in space directions.     

On the numerical stability of mixed finite-element methods for viscoelastic flows governed by differential constitutive equations

Mixed finite-element methods for computation of viscoelastic flows governed by differential constitutive equations vary by the polynomial approximations used for the velocity, pressure, and stress fields, and by the weighted residual methods used to discretize the momentum, continuity, and constitutive equations. This paper focuses on computation of the linear stability of the planar Couette flow as a test of the numerical stability for solution of the upper-convected Maxwell model. Previous theoretical results prove this inertialess flow to be always stable, but that accurate calculation is difficult at high De because eigenvalues with fine spatial structure and high temporal frequency approach neutral stability. Computations with the much used biquadratic finite-element approximations for velocity and deviatoric stress and bilinear interpolation for pressure demonstrate numerical instability beyond a critical value of De for either the explicitly elliptic momentum equation (EEME) or elastic-viscous split-stress (EVSS) formulations, applying Galerkin's method for solution of the momentum and continuity equations, and using streamline upwind Petrov-Galerkin (SUPG) method for solution of the hyperbolic constitutive equation. The disturbance that causes the instability is concentrated near the stationary streamline of the base flow. The removal of this instability in a slightly modified form of the EEME formulation suggests that the instability results from coupling the approximations to the variables. A new mixed finite-element method, EVSS-G, is presented that includes smooth interpolation of the velocity gradients in the constitutive equation that is compatible with bilinear interpolation of the stress field. This formulation is tested with SUPG, streamline upwinding (SU), and Galerkin least squares (GLS) discretization of the constitutive equation. The EVSS-G/SUPG and EVSS-G/SU do not have the numerical instability described above; linear stability calculations for planar Couette flow are stable to values of De in excess of 50 and converge with mesh and time step. Calculations for the steady-state flow and its linear stability for a sphere falling in a tube demonstrate the appearance of linear instability to a time-periodic instability simultaneously with the apparent loss of existence of the steady-state solution. The instability appears as finely structured secondary cells that move from the front to the back of the sphere.Financial support for this research was given by the National Science Foundation, the Office of Naval Research, and the Defense Research Projects Agency. Computational resources were supplied by a grant from the Pittsburgh National Supercomputer Center and by the MIT Supercomputer Facility.     

Data assimilation for non-linear tidal models

A data assimilation procedure to incorporate measurements into a non-linear tidal model by using Kalman-filtering techniques is developed. The Kalman filter is based on the two-dimensional shallow water equations. To account for the inaccuracies, these equations are embedded into a stochastic environment by introducing a coloured system noise process into the momentum equations. The continuity equation is assumed to be perfect. The deterministic part of the equations is discretized using an ADI method, the stochastic part using the Euler scheme. Assuming that the system noise is less spatially variable than the underlying water wave process, this stochastic part can be approximated on a coarser grid than the grid used to approximate the deterministic part. A Chandrasekhar-type filter algorithm is employed to obtain the constant-gain extended Kalman filter for weakly non-linear systems. The capabilities of the filter are illustrated by applying it to the assimilation of water level measurements into a tidal model of the North Sea.     

Comparison of sequential data assimilation methods for the Kuramoto–Sivashinsky equation

The Kuramoto–Sivashinsky equation plays an important role as a low‐dimensional prototype for complicated fluid dynamics systems having been studied due to its chaotic pattern forming behavior. Up to now, efforts to carry out data assimilation with this 1‐D model were restricted to variational adjoint methods domain and only Chorin and Krause (Proc. Natl. Acad. Sci. 2004; 101 (42):15013–15017) tested it using a sequential Bayesian filter approach. In this work we compare three sequential data assimilation methods namely the Kalman filter approach, the sequential Monte Carlo particle filter approach and the maximum likelihood ensemble filter methods. This comparison is to the best of our knowledge novel. We compare in detail their relative performance for both linear and nonlinear observation operators. The results of these sequential data assimilation tests are discussed and conclusions are drawn as to the suitability of these data assimilation methods in the presence of linear and nonlinear observation operators. Copyright © 2009 John Wiley & Sons, Ltd.     

Parameter identification of river current and diffusion by reduced Kalman filter finite element method

The objective of this study is to propose a parameter identification of a river current and diffusion coefficients by using the reduced Kalman filter finite element method, which has been previously presented and now extended by the authors. For comparison, the estimation computations of velocity, water elevation, and chemical oxygen demand (COD) concentration are carried out on the basis of nonlinear shallow water flow and compared with the observations carried out at the Teganuma river in Japan. A marked discrepancy in COD concentration is found between the computed and observed results. The correlation factor between the computed and observed results is 0.51. To reduce the discrepancy, the authors believe that the diffusion coefficients should be identified. Assuming that the diffusion coefficient is constant in the entire domain and over the entire total duration, satisfactory results were not obtained. Thus, the computational domain is divided into four subdomains according to the water depth. Assuming that the diffusion coefficients are constant in each subdomain, the identification is carried out. Relatively good, albeit unsatisfactory, results are obtained. The discrepancy between the computed and observed COD concentration has special features. In some time zones, the computed results are larger whereas in other time zones, they are smaller than the observed results. To compensate this discrepancy, we assumed that the diffusion coefficient is a function of COD concentration. The correlation factor is improved to be 0.73. The identified diffusion coefficients are time functions that change cyclically with a period of 24 h. This fact suggests that biological phenomenas occurred in the river. Copyright © 2011 John Wiley & Sons, Ltd.     

Time‐accurate stabilized finite‐element model for weakly nonlinear and weakly dispersive water waves

Introduction of a time‐accurate stabilized finite‐element approximation for the numerical investigation of weakly nonlinear and weakly dispersive water waves is presented in this paper. To make the time approximation match the order of accuracy of the spatial representation of the linear triangular elements by the Galerkin finite‐element method, the fourth‐order time integration of implicit multistage Padé method is used for the development of the numerical scheme. The streamline‐upwind Petrov–Galerkin (SUPG) method with crosswind diffusion is employed to stabilize the scheme and suppress the spurious oscillations, usually common in the numerical computation of convection‐dominated flow problems. The performance of numerical stabilization and accuracy is addressed. Treatments of various boundary conditions, including the open boundary conditions, the perfect reflecting boundary conditions along boundaries with irregular geometry, are also described. Numerical results showing the comparisons with analytical solutions, experimental measurements, and other published numerical results are presented and discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Fuzzy logic adaptive Kalman filtering in the control of irrigation canals

A fuzzy logic adaptive Kalman filtering methodology was developed for the automatic control of an irrigation canal system under unknown disturbances (water withdrawals) acting in the canal. Using a linearized finite difference model of open channel flow, the canal operation problem was formulated as an optimal control problem and an algorithm for gate opening in the presence of arbitrary external disturbances (changes in flow rates) was derived. Based on the linear optimal control theory, the linear quadratic regulator (LQR), assuming all the state variables (flow depths and flow rates) were available, was designed to generate control input (optimal gate opening). As it was expensive to measure all the state variables (flow rates and flow depths) in a canal system, a fuzzy logic adaptive Kalman filter and traditional Kalman filter were designed to estimate the values for the state variables that were not measured but were needed in the feedback loop. The performances of the state estimators designed using the fuzzy logic adaptive Kalman filter methodology and the traditional Kalman filtering technique were compared with the results obtained using the LQR (target loop function). The results of the present study indicated that the performance of the fuzzy logic adaptive Kalman filter was far superior to the performance of the observer design based upon the traditional Kalman filter approach. The obvious advantages of the fuzzy logic adaptive Kalman filter were the prevention of filter divergence and ease of implementation. As the fuzzy logic adaptive Kalman filter requires smaller number of state variables for the acceptable accuracy therefore, it would need less computational effort in the control of irrigation canals. Copyright © 2009 John Wiley & Sons, Ltd.     

基于广义卡尔曼滤波的桥梁结构物理参数识别

基于广义卡尔曼滤波提出了随机荷载作用下桥梁结构物理参数的识别方法。首先,以荷载为观测对象,推导出基于有限元模型的桥梁结构系统的观测方程,以结构待识别的物理参数为状态向量,建立系统状态方程;然后,对该状态方程和观测方程构成的非线性参数系统应用广义卡尔曼滤波,从而识别出结构的物理参数。对一座简支梁桥和一座三跨连续梁桥在不同工况下的物理参数识别进行了数值仿真,结果表明本文方法能够准确地识别桥梁结构全部刚度参数、质量参数和阻尼参数,且具有很强的抗噪性能,从而验证了本文方法的有效性和鲁棒性,可应用于识别大型桥梁结构的物理参数。     

The two-dimensional transmission and reflection of a solitary wave

In the present paper, limited to the discussion of weak non-linear shallow water waves, the transmission and reflection of a planar soliton on a two-dimensional structure are considered. The whole flow field is divided mainly into two subfields. One is in the vicinity of the structure, called the inner field; the other is far from the structure, called the outer field. In the outer field, according to its definition, the influence of the structure on the flow is negligible; to the order O(α, β) the governing equation for the flow is replaced by the Boussinesq equation. In the inner field the effect of the structure on the flow is significant, so the full Laplace equation is adopted as the governing equation for the flow field. Then the matched asymptotic expansion method is employed to connect smoothly the inner and outer solutions. Owing to the irregularity of the bottom of the structure, the boundary element method is incorporated. As an example, the case in which the incoming wave is a solitary wave is calculated and the time histories of transmitted and reflected waves are plotted.     

Nonlinear filters for chaotic oscillatory systems

This paper examines and contrasts the feasibility of joint state and parameter estimation of noise-driven chaotic systems using the extended Kalman filter (EKF), ensemble Kalman filter (EnKF), and particle filter (PF). In particular, we consider the chaotic vibration of a noisy Duffing oscillator perturbed by combined harmonic and random inputs ensuing a transition probability density function (pdf) of motion which displays strongly non-Gaussian features. This system offers computational simplicity while exhibiting a kaleidoscope of dynamical behavior with a slight change of input and system parameters. An extensive numerical study is undertaken to contrast the performance of various nonlinear filtering algorithms with respect to sparsity of observational data and strength of model and measurement noise. In general, the performance of EnKF is better than PF for smaller ensemble size, while for larger ensembles PF outperforms EnKF. For moderate measurement noise and frequent measurement data, EKF is able to correctly track the dynamics of the system. However, EKF performance is unsatisfactory in the presence of sparse observational data or strong measurement noise.     

A study of shallow water waves with Gardner’s equation

In this paper the dynamics of solitary waves governed by Gardner’s equation for shallow water waves is studied. The mapping method is employed to carry out the integration of the equation. Subsequently, the perturbed Gardner equation is studied, and the fixed point of the soliton width is obtained. This fixed point is then classified. The integration of the perturbed Gardner equation is also carried out with the aid of He’s semi-inverse variational principle. Finally, Gardner’s equation with full nonlinearity is solved with the aid of the solitary wave ansatz method.     

饱和非饱和土壤中溶质运移的数值模拟

本文结合拉格朗日观点的运动坐标与欧拉观点的固定坐标,分别求解对流—弥敌方程的对流效应和弥散效应,并在从固定坐标向运动坐标投影时利用了三次样条插值方法,使模型更为精确而简单。通过与特定情况下的理论解比较,说明模型是准确可靠的。通过与实验室室内试验结果的比较,模型的可靠性得到了进一步的验证。利用模型对淡水洗盐结合浅群井抽排咸水治理盐碱地过程的模拟分析,认为结合浅群井抽排可较大地提高淡水洗盐的效果。     

Research on data assimilation strategy of turbulent separated flow over airfoil

In order to increase the accuracy of turbulence field reconstruction, this paper combines experimental observation and numerical simulation to develop and establish a data assimilation framework, and apply it to the study of S809 low-speed and high-angle airfoil flow. The method is based on the ensemble transform Kalman filter(ETKF) algorithm, which improves the disturbance strategy of the ensemble members and enhances the richness of the initial members by screening high flow field sensitivity ...     

Numerical modelling of shear-dependent mass transfer in large arteries

A numerical scheme for the simulation of blood flow and transport processes in large arteries is presented. Blood flow is described by the unsteady 3D incompressible Navier–Stokes equations for Newtonian fluids; solute transport is modelled by the advection–diffusion equation. The resistance of the arterial wall to transmural transport is described by a shear-dependent wall permeability model. The finite element formulation of the Navier–Stokes equations is based on an operator-splitting method and implicit time discretization. The streamline upwind/Petrov–Galerkin (SUPG) method is applied for stabilization of the advective terms in the transport equation and in the flow equations. A numerical simulation is carried out for pulsatile mass transport in a 3D arterial bend to demonstrate the influence of arterial flow patterns on wall permeability characteristics and transmural mass transfer. The main result is a substantial wall flux reduction at the inner side of the curved region. © 1997 John Wiley & Sons, Ltd.     

Multiscale evaluation method of the drag effect on shallow water flow through coastal forests based on 3D numerical simulations

This study presents a method for determining the drag parameter in the 2D shallow water (SW) equation for flows through a coastal forest by conducting a series of 3D numerical simulations (3D NSs). Following the theory of multiscale modeling, an evaluation method procedure is proposed. We first prepare a local test domain that contains a sufficient number of trees to constitute part of a coastal forest. Then, 3D NSs are conducted in this test domain with various inflow conditions. Based on the corresponding results, the momentum losses over the test domain are converted into the drag parameter of the global SW equation. A response surface of the drag parameter is constructed as a function of the flow conditions. The stabilized finite element method is employed for both the local and the global NSs, and the phase-field method is utilized to represent 3D free surfaces. Comparisons between the 2D SW calculation results and the 3D NS results are also performed to verify the validity of the proposed method.     

On the aeroelastic stability and bifurcation structure of subsonic nonlinear thin panels subjected to external excitation

Dynamic behavior of panels exposed to subsonic flow subjected to external excitation is investigated in this paper. The von Karman’s large deflection equations of motion for a flexible panel and Kelvin’s model of structural damping is considered to derive the governing equation. The panel under study is two-dimensional and simply supported. A Galerkin-type solution is introduced to derive the unsteady aerodynamic pressure from the linearized potential equation of uniform incompressible flow. The governing partial differential equation is transformed to a series of ordinary differential equations by using Galerkin method. The aeroelastic stability of the linear panel system is presented in a qualitative analysis and numerical study. The fourth-order Runge-Kutta numerical algorithm is used to conduct the numerical simulations to investigate the bifurcation structure of the nonlinear panel system and the distributions of chaotic regions are shown in the different parameter spaces. The results shows that the panel loses its stability by divergence not flutter in subsonic flow; the number of the fixed points and their stabilities change after the dynamic pressure exceeds the critical value; the chaotic regions and periodic regions appear alternately in parameter spaces; the single period motion trajectories change rhythmically in different periodic regions; the route from periodic motion to chaos is via doubling-period bifurcation.     

Bathymetry reconstruction based on the zero-inertia shallow water approximation

The knowledge of the channel bed topography is paramount in modeling the hydrodynamics of open channel flows. Indeed, flow models based on the Shallow Water Approximation require prior information on the channel bed topography to accurately capture the flow features in natural rivers, estuaries, and flood plains. We present here a numerical technique for reconstructing the channel bed topography from given free surface elevation data for steep open channel flows for which the zero-inertia shallow water approximation holds. In this context, the shallow water equations are modified by neglecting inertia terms while retaining the effects of the bed slope and friction terms. We show in this work that by algebraic manipulation, we can recast the governing equations into a single first-order partial differential equation which describes the inverse problem which consists in finding the bed topography from known free surface elevation data. Interestingly, the analysis shows that the inverse problem does not require the knowledge of the bed roughness. The forward problem is solved using MacCormack’s explicit numerical scheme by considering unsteady modified shallow water equations. However, the inverse problem is solved using the method of characteristics. The results of the inverse and the forward problem are successfully tested against each other on two different test cases.     

The equations of complete depth-averaged turbulence model in general orthogonal coordinates

ＤｉｎｇＹａｎ（丁剡）;ＺｈｏｕＸｕｅｙｉ（周雪漪）;ＹｕＣｈａｎｇｚｈａｏ（余常昭）;ＬｉａｎｇＤｏｎｇ（梁栋）（ＲｅｃｅｉｖｅｄＪｕｎｅ１４,１９９４;ＣｏｍｍｕｎｉｃａｔｅｄｂｙＢｉａｎＹｉｎｇｕｉ）ＴＨＥＥＱＵＡＴＩＯＮＳＯＦＣＯＭＰＬＥＴＥ...     

基于平方根中心差分卡尔曼滤波的大方位失准角初始对准

基于大方位失准角条件下捷联惯导系统误差模型的非线性特点,采用非线性滤波方法进行初始对准.扩展卡尔曼滤波存在精度低,且需要计算雅可比矩阵等不足,而中心差分卡尔曼滤波在递推过程中具有计算量大,数值不稳定等缺点.针对上述问题采用了一种改进的中心差分滤波算法一一平方根中心差分卡尔曼滤波.仿真结果表明,与扩展卡尔曼滤波相比,平方...