求解非线性反问题的大范围收敛梯度正则化算法

基于同伦映射的思想,改进了求解非线性反问题的梯度正则化算法。通过路径跟踪有效地拓宽了梯度正则化算法求解的收敛范围。对于正则化参数的修正,通过引入拟Sigmoid函数,提出了一种下降速率可调的连续化参数修正方法,在保证迭代稳定的条件下,得到较好的计算效率,同时保证该算法具有很好的抵抗观测噪声能力。实际算例表明,该方法收敛范围宽,计算效率高,在存在较强观测噪声的条件下也能得到很好的反演结果。     

An iterative updating method for undamped structural systems

Finite element model updating is a procedure to minimize the differences between analytical and experimental results and can be mathematically reduced to solving the following problem. Problem P: Let M _a ∈SR ^n×n and K _a ∈SR ^n×n be the analytical mass and stiffness matrices and Λ=diag{λ ₁,…,λ _p }∈R ^p×p and X=[x ₁,…,x _p ]∈R ^n×p be the measured eigenvalue and eigenvector matrices, respectively. Find \((\hat{M}, \hat{K}) \in \mathcal{S}_{MK}\) such that \(\| \hat{M}-M_{a} \|^{2}+\| \hat{K}-K_{a}\|^{2}= \min_{(M,K) \in {\mathcal{S}}_{MK}} (\| M-M_{a} \|^{2}+\|K-K_{a}\|^{2})\), where \(\mathcal{S}_{MK}=\{(M,K)| X^{T}MX=I_{p}, MX \varLambda=K X \}\) and ∥?∥ is the Frobenius norm. This paper presents an iterative method to solve Problem P. By the method, the optimal approximation solution \((\hat{M}, \hat{K})\) of Problem P can be obtained within finite iteration steps in the absence of roundoff errors by choosing a special kind of initial matrix pair. A numerical example shows that the introduced iterative algorithm is quite efficient.     

基于Kriging代理模型的迭代更新高效反演方法

为提高混凝土坝等大体积结构参数反演效率和精度,减少由于应用有限元进行大量正分析而产生的计算机时,建立了一种结合Kriging代理模型和粒子群优化(PSO)算法的迭代更新反演方法。通过拉丁超立方抽样(LHS)方法确定初始样本点的空间分布,并使用有限元正分析获取对应的响应值,构建粗糙的初始代理模型,结合具有全局寻优能力的PSO算法,反演大体积结构的分区弹性模量,随之再代入有限元模型中,计算获取新的位移响应,并将其作为新样本加入到样本集中,通过迭代更新获得局部更高精度的代理模型。工程实际算例表明,该方法对混凝土坝等大体积结构参数反演精度较高和适用性好,且能大幅减少传统有限元模型反演方法所需消耗的正分析机时,提高反演效率。     

结构可靠指标求解的一种新的迭代方法

由国际安全度联合委员会推荐的一次二阶矩可靠度方法是国际工程界公认的一种较好的可靠度分析方法（简称ＪＣ法）。这种方法具有迭代格式简单，收敛快的特点。但许多实际计算表明，这种方法只适用于功能函数非线性程度不高的情况，否则不收敛。本文提出一种新的迭代方法，这种方法迭代格式与ＪＣ法同样简单，一般情况下均能保证收敛．     

Research on the iterative method for model updating based on the frequency response function

Model reduction technique is usually employed in model updating process.In this paper,a new model updating method named as cross-model cross-frequency response function(CMCF) method is proposed and a new iterative method associating the model updating method with the model reduction technique is investigated.The new model updating method utilizes the frequency response function to avoid the modal analysis process and it does not need to pair or scale the measured and the analytical frequency response function,which could greatly increase the number of the equations and the updating parameters.Based on the traditional iterative method,a correction term related to the errors resulting from the replacement of the reduction matrix of the experimental model with that of the finite element model is added in the new iterative method.Comparisons between the traditional iterative method and the proposed iterative method are shown by model updating examples of solar panels,and both of these two iterative methods combine the CMCF method and the succession-level approximate reduction technique.Results show the effectiveness of the CMCF method and the proposed iterative method.     

Nonlinear implicit iterative method for solving nonlinear ill-posed problems

In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.     

A reduction scheme for problems of structural dynamics

A method for reducing the size of finite element systems in dynamics is presented. The technique is based upon a variational theorem in which it is admissible to describe the inertial properties of structures by way of independent displacement, velocity and momentum fields. This theorem allows us to construct reduced systems for problems in structural mechanics which retain the full rate of convergence of systems employing “consistent” mass matrices. An error analysis of the scheme and numerical examples are presented.     

Preconditioned iterative methods for solving weighted linear least squares problems

A class of preconditioned iterative methods,i.e.,preconditioned generalized accelerated overrelaxation(GAOR) methods,is proposed to solve linear systems based on a class of weighted linear least squares problems.The convergence and comparison results are obtained.The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods.Furthermore,the effectiveness of the proposed methods is shown in the numerical experiment.     

A gradient smoothing method (GSM) for fluid dynamics problems

A novel gradient smoothing method (GSM) based on irregular cells and strong form of governing equations is presented for fluid dynamics problems with arbitrary geometries. Upon the analyses about the compactness and the positivity of coefficients of influence of their stencils for approximating a derivative, four favorable schemes (II, VI, VII and VIII) with second‐order accuracy are selected among the total eight proposed discretization schemes. These four schemes are successively verified and carefully examined in solving Poisson's equations, subjected to changes in the number of nodes, the shapes of cells and the irregularity of triangular cells, respectively. Numerical results imply us that all the four schemes give very good results: Schemes VI and VIII produce a slightly better accuracy than the other two schemes on irregular cells, but at a higher cost in computation. Schemes VII and VIII that consistently rely on gradient smoothing operations are more accurate than Schemes II and VI in which directional correction is imposed. It is interestingly found that GSM is insensitive to the irregularity of meshes, indicating the robustness of the presented GSM. Among the four schemes of GSM, Scheme VII outperforms the other three schemes, for its outstanding overall performance in terms of numerical accuracy, stability and efficiency. Finally, GSM solutions with Scheme VII to some benchmarked compressible flows including inviscid flow over NACA0012 airfoil, laminar flow over flat plate and turbulent flow over an RAE2822 airfoil are presented, respectively. Copyright © 2008 John Wiley & Sons, Ltd.     

基于Kriging模型和改进MCMC算法的随机有限元模型修正

针对待修正参数维数较高时,标准马尔可夫链蒙特卡罗MCMC (Markov Chain Monte Carlo)算法不易收敛、拒绝率高的问题,提出了基于Kriging模型和在MCMC中融合花朵授粉算法的修正方法.首先,以待修正参数作为输入,以应变模态作为输出,建立Kriging模型,通过蝙蝠算法确定Kriging模型的相关系数;然后,采用最大熵的贝叶斯方法估计参数的后验概率密度函数,将花朵授粉算法融入MH (M etropolis-Hasting)抽样算法,提高局部寻优和全局寻优能力;最后,通过三自由度弹簧-质量系统和三维桁架结构的数值算例验证所提模型修正方法,修正后参数相对误差均低于0.86％.结果 表明,所提方法修正后较高维参数的马尔可夫链能够快速收敛且样本接受率也有所提高,该方法也对随机噪声具有一定的鲁棒性.     

Sensitivity analysis based on Lanczos algorithm in structural dynamics

IntroductionTheproblemforcomputingeigenpairderivativeshasoccupiedmanyresearchersinthepastseveraldecades.SurveypaperbyAdelmanandHaftka[1]isanexcellentintroductiontothetopicandalsoindicatevariousdisciplinesofapplications.Thereasonwhysomanypeopleareinterestedinthisproblemisthatsensitivitiesplayaveryimportantroleinstructuraldynamics,optimalanalysisandcontrolsystemdesign ,andmayalsobeanexpensiveandtime_consumingtask.Researchonsensitivityofmultipleeigenvalueshasbeenanareaofsignificantinterestinrece…     

结构动力问题的高精度组合差分时程积分法

基于Taylor级数展开得到位移和加速度的中心差分格式,并结合速度的后差分格式,构造了一种求解结构动力问题的组合差分格式的时程积分算法,该算法为自起步的两步高精度算法。通过求解递推格式的传递矩阵及其特征值,对该算法的稳定性和精度进行了理论分析,结果表明,本文提出的算法虽属条件稳定,但其精度极高,具有周期延长率小、没有振幅衰减等优点。数值分析结果也证明本文提出的算法具有较高精度。     

A new algorithm for solving differential/algebraic equations of multibody system dynamics

I.Intr0ductionTheequationsofmoti0nofconstrainedmultibodysystemdynamicscanbewrittenasfollows11lwherelistimeparameter*q6R'isgeneralizedcoordinatesvectorofsystem,M(q,t):RnXR-R"xnisgeneralizedmassn1atrixofsystem,k6RmisLagrangemultipliervector,fo(q,t):RnXR-R"(…     

受随机激励作用结构的演化设计算法

提出了研究受随机激励作用的结构动力优化的演化设计方法,演化模型以随机激力作用下结构的位移方差为约束,寻求最优的构件尺寸使结构的重量最轻。演化算法采用多种群遗传与搜索空间收缩策略,并利用高效的虚拟随机激励法进行随机响应重分析和准精确罚函数处理约束,保证了算法稳定而迅速地收敛于最优解,算例显示出本文方法的有效性。     

A time integral formulation and algorithm for structural dynamics with nonlinear stiffness

A newly-developed numerical algorithm, which is called the new Generalized-α (G-α) method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zero-stable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.The English text was polished by Keren Wang.     

基于螺旋修正的卫星位姿更新算法

由于卫星运动的不可交换性,在卫星测量过程中引入螺旋修正算法描述编队卫星中主从星的相对位置和姿态信息,提出了基于螺旋修正的编队卫星相对位姿测量算法。首先基于典型的螺旋环境,设计了螺旋修正算法,论证了其与传统圆锥修正算法和划船修正算法的一致性,采用三子样螺旋修正算法进行仿真并与传统算法的精度进行比较。仿真结果表明该算法的位置和姿态精度分别可以达到10-3 m和10-6数量级,满足测量精度要求。该算法不用像传统算法分别为卫星的位置更新和姿态更新设计两组优化系数,因此降低了算法复杂度。     

A dislocation density based strain gradient model

Strain gradients play a vital role in the prediction of size-effects in the deformation behavior of metals at the micrometer scale. At this scale the behavior of metals strongly depends on the dislocation distribution. In this paper, a dislocation density based strain gradient model is developed aiming at predictions of size-effects for structural components at this scale. For this model, the characteristic length is identified as the average distance of dislocation motion, which is deformation dependant and can be determined experimentally. The response of the model is compared to the strain gradient plasticity model of Huang et al. [Huang, Y., Qu, S., Hwang, K.C., Li, M., Gao, H., 2004. A conventional theory of mechanism-based strain gradient plasticity. Int. J. Plasticity 20, 753–782]. It is shown that the present strain gradient model, which only requires a physically measurable length-scale, can successfully predict size effects for a bar with an applied body force and for void growth.