A method for the transfer function matrix of combined primary–secondary systems using classical modal decomposition

An iterative method is presented to compute the transfer function matrix of combined primary–secondary systems for seismic response analysis. It accounts for non‐proportional damping and dynamic interaction of the combined system. A closed form sequence is developed for the iterative computation of the transfer function matrix. Such sequence is assembled using independently the real classical mode frequencies, shapes and damping ratios of the primary system, and the natural frequency and critical damping ratio of the SDOF secondary system. The necessary and sufficient condition for convergence of the sequence is given in the paper. The method is illustrated through a couple of examples, including one of an appendix connected to a multi‐storey shear building. Convergence of the method is thoroughly analysed and peak responses are obtained using a spectral density function approach. Copyright © 2005 John Wiley & Sons, Ltd.     

A pseudo‐force iterative method with separate scale factors for dynamic analysis of structures with non‐proportional damping

Dynamic equilibrium equations of structural systems with non‐proportional damping are coupled through the damping terms. Such coupling invalidates application of the classical modal superposition method. In this paper, a mode‐superposition pseudo‐force method is proposed. The coupled equilibrium equations are solved by an iterative process in which the coupling terms are treated as pseudo‐forces. A scale factor for each mode of the system is obtained by optimizing the iteration convergence. Through these uniquely solved scale factors, the modified modal equations not only converge much faster but also yield results with higher accuracy. A proof of the convergence of the iterative process is also presented. Copyright © 2002 John Wiley & Sons, Ltd.     

A modal superposition pseudo-force method for dynamic analysis of structural systems with non-proportional damping

A modal superposition pseudo-force method for the dynamic analysis of structural systems with non-proportional damping is presented. The method combines the advantages of the classical modal superposition method and the pseudo-force method. When the system damping is non-proportional, the dynamic equilibrium equations in generalized coordinates are coupled through the damping terms. In the present method, these coupled equations are solved by an iterative process in which the coupling terms are treated as pseudo-forces. A proof of the convergence of the iterative process is given. Numerical examples show the good convergence characteristics of the process and the good accuracy of the obtained results.     

频率域波动方程正演基于多重网格预条件的迭代算法研究

频率域全波形反演是重要的地震成像方法,而频率域波动方程数值模拟是频率域全波形反演的基础.对于大规模的问题,由于受存储和计算量的限制,基于LU分解的直接方法一般不再适用,而是采用迭代方法.基于多重网格预条件的双共轭梯度稳定化方法是一种重要的迭代方法.本文重点讨论了多重网格预条件求解过程中的松弛因子选择方法,研究结果表明,(1)对于一般选取的松弛因子,随模型复杂性的增加,所能计算的重数逐渐下降,方法的实用性也随之下降;(2)对于复杂模型,采用局部模式分析方法选取松弛因子,提高了所能计算的重数,保证了多重网格方法的收敛性和实用性.这些研究成果对基于多重网格预条件的迭代算法的实际应用具有重要意义.     

基于谱元法的频率域三维海洋可控源电磁正演模拟

高精度、快速有效的正演模拟算法是三维电磁正反演的前提.为了提高海洋电磁三维数值模拟的精度和效率,本文提出利用基于Gauss-Lobatto-Chebyshev（GLC）基函数的谱元法进行海洋可控源三维电磁正演模拟.谱元法结合有限元法和谱方法的优点.我们通过应用伽辽金加权残差法离散二次电场矢量亥姆赫兹方程,在单元内选择混合阶GLC多项式的张量积作为高阶矢量插值基函数,在求解大型稀疏线性方程组时利用直接求解器进行快速求解,从而实现了三维海洋可控源电磁快速高精度正演模拟.一维和三维模型正演结果验证了本文算法的有效性和准确性.典型模型的数值结果表明谱元法是一种有效的三维海洋可控源电磁正演数值方法,能在稀疏网格剖分情况下获得精确的海洋电磁正演模拟响应.     

Lanczos method for the solution of groundwater flow in discretely fractured porous media

One of the more advanced approaches for simulating groundwater flow in fractured porous media is the discrete-fracture approach. This approach is limited by the large computational overheads associated with traditional modeling methods. In this work, we apply the Lanczos reduction method to the modeling of groundwater flow in fractured porous media using the discrete-fracture approach. The Lanczos reduction method reduces a finite element equation system to a much smaller tridiagonal system of first-order differential equations. The reduced system can be solved by a standard tridiagonal algorithm with little computational effort. Because solving the reduced system is more efficient compared to solving the original system, the simulation of groundwater flow in discretely fractured media using the reduction method is very efficient. The proposed method is especially suitable for the problem of large-scale and long-term simulation. In this paper, we develop an iterative version of Lanczos algorithm, in which the preconditioned conjugate gradient solver based on ORTHOMIN acceleration is employed within the Lanczos reduction process. Additional efficiency for the Lanczos method is achieved by applying an eigenvalue shift technique. The “shift” method can improve the Lanczos system convergence, by requiring fewer modes to achieve the same level of accuracy over the unshifted case. The developed model is verified by comparison with dual-porosity approach. The efficiency and accuracy of the method are demonstrated on a field-scale problem and compared to the performance of classic time marching method using an iterative solver on the original system. In spite of the advances, more theoretical work needs to be carried out to determine the optimal value of the shift before computations are actually carried out.     

基于条分模式的边坡可靠度近似计算方法

通过对边坡稳定分析方法中的条分理论和响应面法的研究,针对边坡可靠性计算往往没有明确的解析表达式,以及稳定性系数计算方法和响应面法（RSM）的特点,将响应面法中的有限元数值模拟以条分模式中的稳定性系数隐式方程的迭代计算方法代替,建立了条分模式下的边坡可靠性计算的极限状态方程,从而形成了一种新的边坡稳定可靠性响应面分析方法。本文提出的改进的响应面法原理简单,计算效率较高并具有一定的精度,适用于对边坡可靠度的近似计算。     

A new look at the response surface method for reliability analysis using chaos theory

To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results.     

正则化预处理迭代算法在频率域声波模拟中的应用

高精度及高效频率域声波数值模拟的关键在于高效求解声波方程经离散化后得到的大型稀疏线性方程组.该方程组系数矩阵具有很强的稀疏性,非对称性和非正定性等特征,常用的迭代算法难以准确、高效地求解.为了改善数值模拟迭代算法的收敛性与稳定性,在算法基础上添加预条件算子是求解该类方程的常用方案.本文基于以上思路,引入正则化技术来构造合适的预条件算子,提出正则化预条件迭代算法,以加速求解方程组.通过包含有均匀介质和高非均匀度介质(Marmousi)模型的数值模拟实验结果表明:与单独使用迭代算法相比,本文提出的正则化预条件迭代算法在计算量方面仅多了一次矩阵-矢量相乘,内存消耗未增加;同时,基于该算法的数值模拟结果能够满足精度要求,较单独使用迭代法能够有效改善收敛性质,加快收敛速度;而且,在二维模型算例下,与LU分解算法相比,基于该算法的内存消耗大幅下降.     

Non‐iterative time integration scheme for non‐linear dynamic FEM analysis

This paper proposes a non‐iterative time integration (NITI) scheme for non‐linear dynamic FEM analysis. The NITI scheme is constructed by combining explicit and implicit schemes, taking advantage of their merits, and enables stable computation without an iteration process for convergence even when used for non‐linear dynamic problems. Formulation of the NITI scheme is presented and its stability is studied. Although the NITI scheme is not unconditionally stable when applied to non‐linear problems, it is stable in most cases unless stiffness hardening occurs or the problem has a large velocity‐dependent term. The NITI scheme is applied to dynamic analysis of the non‐linear soil–structure system and computation results are compared with those by the central difference method (CDM). Comparison shows that the stability of the NITI scheme is superior to that of the CDM. Accuracy of the NITI scheme is verified because its results are identical with those by the CDM in which the time step is set as 1/10 of that for the NITI scheme. The application of the NITI scheme to the mesh‐partitioned FEM is also proposed. It is applied to dynamic analysis of the linear soil–structure system. It yields the same results as a conventional single‐domain FEM analysis using the Newmark β method. This result verifies the usability of mesh‐partitioned FEM analysis using the NITI scheme. Copyright © 2003 John Wiley& Sons, Ltd.     

基于CV模型的CT图像分割研究

由于医学图像边缘模糊、不均匀性等特点,使用传统的Chan—gese（CV）模型方法难以达到分割要求,同时该方法存在计算量大、分割速度慢的问题。本文提出了一种基于CV模型改进的分割算法,在水平集演化迭代过程中,根据当前主动轮廓线的位置,引入图像局部灰度信息,提高了水平集能量项的有效性和该模型的收敛速度,并提出了一种关于图像序列的分割方法。实验结果表明,运用本文提出的方法能够快速、准确地提取图像中感兴趣目标,是一种较为理想的医学图像分割方法。     

AN ITERATIVE SOLUTION METHOD FOR DYNAMIC RESPONSE OF BRIDGE–VEHICLES SYSTEMS

An iterative solution method is presented and illustrated to analyse the dynamic response of bridge–vehicle systems. The method consists in dividing the whole system into 2 subsystems at the interface of the bridge and vehicles; these 2 subsystems are solved separately; their compatibility at the interface is achieved by an iterative procedure with under-relaxation or with Aitken acceleration. The characteristics of this method are explained on a simplified system with 2 degrees of freedom (DOF). The numerical results for a simple example demonstrate the high performances of the proposed method: good convergence rate and high accuracy. Finally, the method is applied to a practical example: the linear dynamic response of the Yangtze-River Bridge at Wuhan under a moving train with 2 locomotives and 4 freight cars. The efficiency is attained because neither formation nor factorisation of the coefficient matrices for the equations of the system are needed at every time step in linear analysis. The Aitken acceleration technique is more efficient in systems with multi-degrees of freedom than the relaxation technique. The proposed method will be even more efficient in non-linear dynamic response because, in this case, the iterations are necessary whether the system is solved as a whole or not.     

EFFICIENT ITERATIVE ARMA APPROXIMATION OF MULTIVARIATE RANDOM PROCESSES FOR STRUCTURAL DYNAMICS APPLICATIONS

An efficient Auto-Regressive Moving–Average (ARMA) approximation method is presented for simulating stationary random processes with specified (target) power spectra in conjunction with structural dynamics applications. It involves an iterative algorithm developed for minimizing a physically motivated ‘energy’ measure, in the frequency domain, of the ARMA approximation of an AR representation of the target spectrum. The iterative algorithm can be used to adjust, for better spectral matching, the parameters of an arbitrary ARMA approximation of the random process determined by any other method; this is accomplished without increasing the requisite order of the ARMA approximation. The efficiency of the proposed method is demonstrated by considering spectra which are commonly used in earthquake engineering and ocean engineering.     

Double parameterized regularization inversion method for migration velocity analysis in transversely isotropic media with a vertical symmetry axis

Simultaneous estimation of velocity gradients and anisotropic parameters from seismic reflection data is one of the main challenges in transversely isotropic media with a vertical symmetry axis migration velocity analysis. In migration velocity analysis, we usually construct the objective function using the l₂ norm along with a linear conjugate gradient scheme to solve the inversion problem. Nevertheless, for seismic data this inversion scheme is not stable and may not converge in finite time. In order to ensure the uniform convergence of parameter inversion and improve the efficiency of migration velocity analysis, this paper develops a double parameterized regularization model and gives the corresponding algorithms. The model is based on the combination of the l₂ norm and the non‐smooth l₁ norm. For solving such an inversion problem, the quasi‐Newton method is utilized to make the iterative process stable, which can ensure the positive definiteness of the Hessian matrix. Numerical simulation indicates that this method allows fast convergence to the true model and simultaneously generates inversion results with a higher accuracy. Therefore, our proposed method is very promising for practical migration velocity analysis in anisotropic media.     

RESIDUAL STATIC CORRECTIONS—ITERATIVE SOLUTION ANALYSIS*

The iterative estimation process of residual static corrections published earlier is further analyzed. The convergence and convergence rate of the iterative solution are analysed for components of different relative wave length with results of both theoretical and practical value. Relative wave length components practically determinable and indeterminable are defined. One model example is presented for illustrative purposes.     

Hydraulic diffusivity in a coastal aquifer: spectral analysis of groundwater level in responses to marine system

The hydraulic diffusivity gives a measure of diffusion speed of pressure disturbances in groundwater system; large values of hydraulic diffusivity lead to fast propagation of signals in aquifer. This research provides a novel design and derives spectral representation to determine hydraulic diffusivity using spectral analysis of groundwater levels coupled with time-dependent boundary adjacent to marine system and no flow boundary in aquifer system. To validate the proposed method, water levels of fluctuated boundary and groundwater well in a sandy confined aquifer were collected. The hydraulic diffusivity is then obtained by an inverse process in the non-linear complex form of spectral relationship. The method essentially is constructed on the conceptual design of natural forcing transmitted in large aquifer. It is unlike the conventional field pumping test which is only used to determine hydraulic properties of groundwater in small range around the well. Hydraulic diffusivity of the confined aquifer is determined using real observation and then checked by comparing to the published range. It suggests that without local aquifer test to estimate hydraulic diffusivity in a coastal aquifer using spectral representation with its relevant flow system and boundary has become feasible.     

Ground penetrating radar inversion in 1-D: an approach for the estimation of electrical conductivity, dielectric permittivity and magnetic permeability

This paper presents a method for inverting ground penetrating radargrams in terms of one-dimensional profiles. We resort to a special type of linearization of the damped E-field wave equation to solve the inverse problem. The numerical algorithm for the inversion is iterative and requires the solution of several forward problems, which we evaluate using the matrix propagation approach. Analytical expressions for the derivatives with respect to physical properties are obtained using the self-adjoint Green's function method. We consider three physical properties of materials; namely dielectrical permittivity, magnetic permeability and electrical conductivity. The inverse problem is solved minimizing the quadratic norm of the residuals using quadratic programming optimization. In the iterative process to speed up convergence we use the Levenberg–Mardquardt method. The special type of linearization is based on an integral equation that involves derivatives of the electric field with respect to magnetic permeability, electrical conductivity and dielectric permittivity; this equation is the result of analyzing the implication of the scaling properties of the electromagnetic field. The ground is modeled using thin horizontal layers to approximate general variations of the physical properties. We show that standard synthetic radargrams due to dielectric permittivity contrasts can be matched using electrical conductivity or magnetic permeability variations. The results indicate that it is impossible to differentiate one property from the other using GPR data.     

On the use of the fitting method in solving inverse problems of gravimetry and magnetometry

An analytical approach to the gravity and magnetic data inversion by the fitting method is described. The problems of the uniqueness of the solution and the convergence and stability of the iterative process are considered.     

Stochastic characterization of earthquakes through their response spectrum

If earthquakes are modelled by a stochastic process, it is possible to interpret the associated response spectrum in terms of the statistics of extreme values of oscillator response to the process. For a stationary earthquake model this interpretation leads to a relationship between the power spectral density function of the process and the response spectrum. This relationship is examined in this paper and forms the basis for two methods presented to obtain the power spectrum of the earthquake process from its response spectrum. One of these methods is approximate but leads to an explicit representation of the power spectral density function in terms of the response spectrum. The other method is exact wherein an iterative scheme for the solution of the problem is established. An example problem is solved to illustrate the use of the two methods and it is shown that for small values of damping, the approximate derivation yields a fairly accurate solution.     

关于能力谱方法收敛性的讨论

给出了ATC-40迭代求解方法A收敛性的一个数学解释。分析了ATC-40迭代求解方法A和改进的能力谱方法在迭代上的差异,并从数学上证明了改进的能力谱方法有收敛的结果。