有限元模型修正的虚拟拉直算法

在拉直算法的基础上,提出了一种新的有限元模型修正方法.拉直算法主要适合于模型修正模型中的约束方程不出现矛盾方程的情况,而对于出现矛盾的约束方程,修正效果可能会很差,其主要原因是修正变量较少,这也导致了拉直算法不适合于含高阶实验模态数据的修正.因此,为了避免矛盾方程的出现和获得可行的修正模型,提出增加带宽的方式(即附加虚拟元素)以增加未知变量的个数,并提出了虚拟拉直修正方法,该方法可有效地修正含高阶模态的实验模态数据.最后以一个平面框架结构为例来说明本文方法的可行性.     

基于贝叶斯法的复杂有限元模型修正研究

从概率思维角度出发,证明基于最大熵原理的贝叶斯反分析准则函数法和解不适定问题的正则化方法是一致的,提出一种基于信息融合和贝叶斯理论的模型修正方法。该方法采用试验设计构造样本,采用二次响应面作为快速运行模型,通过响应面自身的特性和精度要求进行收敛判断,在响应面迭代中确定信息融合系数（设计规范、有限元计算信息、实测信息）和待修正的设计参数值。该方法充分利用先验信息,迭代计算量较小,可推广至大型复杂非线性结构。某抽水蓄能电站地下厂房结构的有限元模型修正结果验证了该方法的有效性     

基于模态柔度的有限元模型修正方法

以各阶模态柔度矩阵中各元素相对变化作为指标,提出了基于模态柔度灵敏度解析表达式的有限元模型修正方法,推导了模态柔度灵敏度解析表达式,结构严谨,编程方便。以一平面简支梁为例,考虑运用不同的模态阶数、测点自由度及测试误差,利用Tikhonov正则化方法进行模型修正,通过多次模拟计算,分析了相关因素对模型修正结果的影响。实例计算表明,当噪声较小时,修正效果很好,但随着测试噪声水平的增加,修正结果稳定性变得相对较差;利用较高阶模态修正结果比利用较低阶模态修正后结果要好;同时测试自由度不完整性也是模型修正结果的不利因素。     

An improved perturbation method for stochastic finite element model updating

In this paper, an improved perturbation method is developed for the statistical identification of structural parameters by using the measured modal parameters with randomness. On the basis of the first‐order perturbation method and sensitivity‐based finite element (FE) model updating, two recursive systems of equations are derived for estimating the first two moments of random structural parameters from the statistics of the measured modal parameters. Regularization technique is introduced to alleviate the ill‐conditioning in solving the equations. The numerical studies of stochastic FE model updating of a truss bridge are presented to verify the improved perturbation method under three different types of uncertainties, namely natural randomness, measurement noise, and the combination of the two. The results obtained using the perturbation method are in good agreement with, although less accurate than, those obtained using the Monte Carlo simulation (MCS) method. It is also revealed that neglecting the correlation of the measured modal parameters may result in an unreliable estimation of the covariance matrix of updating parameters. The statistically updated FE model enables structural design and analysis, damage detection, condition assessment, and evaluation in the framework of probability and statistics. Copyright © 2007 John Wiley & Sons, Ltd.     

An accelerated pseudo-genetic algorithm for dynamic finite element model updating

An effective accelerated pseudo-genetic algorithm (APGA), which combines an adaptive pseudo-genetic algorithm (P-GA) with an accelerated random search (ARS) method, is proposed to update finite element (FE) models in the presence of measured data. The algorithm explores the higher probability of converging to a global solution provided by genetic algorithms and the accelerated hill-climbing ability given by ARS. The objective of the optimization problem is to minimize the difference between measured and numerical FE vibration data. The effectiveness of the approach is first tested on mathematical benchmark functions. The best version of APGA is then applied to a simulated beam structure to test the applicability of the new approach for FE model updating. Finally, the algorithm is applied to update two real structures using measured modal data. The application of this new algorithm obtains results that correlate well with experiments in reduced time.     

Finite element model updating using Hamiltonian Monte Carlo techniques

Bayesian techniques have been widely used in finite element model (FEM) updating. The attraction of these techniques is their ability to quantify and characterize the uncertainties associated with dynamic systems. In order to update an FEM, the Bayesian formulation requires the evaluation of the posterior distribution function. For large systems, this function is difficult to solve analytically. In such cases, the use of sampling techniques often provides a good approximation of this posterior distribution function. The hybrid Monte Carlo (HMC) method is a classic sampling method used to approximate high-dimensional complex problems. However, the acceptance rate of HMC is sensitive to the system size, as well as to the time step used to evaluate the molecular dynamics trajectory. The shadow HMC technique (SHMC), which is a modified version of the HMC method, was developed to improve sampling for large system sizes by drawing from a modified shadow Hamiltonian function. However, the SHMC algorithm performance is limited by the use of a non-separable modified Hamiltonian function. Moreover, two additional parameters are required for the sampling procedure, which could be computationally expensive. To overcome these weaknesses, the separable shadow HMC (S2HMC) method has been introduced. This method uses a transformation to a different parameter space to generate samples. In this paper, we analyse the application and performance of these algorithms, including the parameters used in each algorithm, their limitations and the effects on model updating. The accuracy and the efficiency of the algorithms are demonstrated by updating the finite element models of two real mechanical structures. It is observed that the S2HMC algorithm has a number of advantages over the other algorithms; for example, the S2HMC algorithm is able to efficiently sample at larger time steps while using fewer parameters than the other algorithms.     

基于高斯过程响应面的结构有限元模型修正方法

作为一种基于贝叶斯原理的非参数模型,高斯过程模型近年来得到研究人员的广泛关注。高斯过程具有灵活的协方差函数形式、预测精度高和量化预测不确定性等优点。基于此,本文提出了一种基于高斯过程响应面的有限元模型修正方法,并介绍了高斯过程响应面方法的基本理论。算例结果表明,相对于传统参数型响应面方法,高斯过程响应面方法应用于有限元模型修正更具优势。     

实测模态和结构模型同步修正的结构损伤识别方法

在基于灵敏度分析的有限元模型修正方法基础上,提出一种对实测模态和结构模型同步修正的结构损伤识别方法。即利用有损结构模态与测量噪声在时频域内的差异,以结构有限元模型为基准,对实测模态差进行小波去噪处理,再利用修正后的模态构造目标函数,进行有限元模型修正,经过迭代计算最终可识别结构的损伤。数值算例表明该方法可有效降低噪声的影响,提高损伤识别的精度。     

Damage identification in three-dimensional structures using single-objective evolutionary algorithms and finite element model updating: evaluation and comparison

This study presents a methodology which integrates single-objective evolutionary algorithms (EAs) and finite element (FE) model updating for damage inference in three-dimensional (3D) structures. First, original well-known EAs, namely the genetic algorithm, differential evolution (DE) and particle swarm optimization (PSO), are combined with FE model updating for detecting damage in a 3D four-storey modular structure and their performances are compared. Next, to obtain more accurate results, hybrid Lévy flights–DE and hybrid artificial bee colony–PSO are developed for enhancing damage identification. With each method, the objective function composed of modal strain energy and mode shape residuals, taken from the FE model of the intact structure and the simulated damage responses, is initially created. Then, the performance of each algorithm combined with FE model updating for damage detection is assessed in terms of three characteristics: consistency, computational cost and accuracy, and the best performing algorithm is recommended.     

Finite element model updating using crow search algorithm with Levy flight

The accuracy of the finite element model is essential for fatigue analysis and vibration of a flexible body. This paper presents a finite element model updating (FEMU) algorithm based on crows search algorithm incorporated with Levy flight (LFCSA). The proposed algorithm is tested on the updating of two different cases: a simple structure (beam) and a complex structure (gearbox housing). To verify the performance of LFCSA, two optimization algorithm, which is the standard CSA and the particle swarm optimization algorithm with Levy flight (LFPSO), are applied to FEMU of the simple beam. The result of the comparison shows that the LFCSA has sufficient convergence speed and global search ability in the implementation of FEMU. In the case of gearbox housing, the error of frequencies and mode shapes are analyzed to indicate that the LFCSA gives a satisfactory result in a complex structure.     

去噪正则化模型修正方法在桥梁损伤识别中的应用

以传统基于灵敏度分析的有限元模型修正方法为基础,提出一种结合小波去噪过程的正则化模型修正损伤识别方法.为改进模型修正方法损伤识别效果,一方面利用有损结构模态与模态噪声的波形在时频域内的差异,以结构有限元模型为基准,对实测模态差进行小波去噪处理,并利用修正后的模态构造目标函数;一方面采用正则化方法改善反问题求解的非适定性.由于从输入数据和求解过程两方面同时改善了结构损伤识别反问题的求解,因此可以有效抑制实测模态参数中噪声的影响,正确识别结构损伤.以连续梁桥模型为例的损伤识别数值模拟表明,所提出方法在保持识别算法鲁棒性、抑制噪声的同时,可有效提高桥梁结构损伤的识别精度.     

Frequency domain damage detection of plate and shell structures by finite element model updating

Plate- and shell-like elements are the main constituent of many engineering structures such as ships and airplanes. This paper develops a frequency domain model updating method using power spectral density function and seeks its viability in damage identification of plates and shells. The derivation of the sensitivity equation is exact and measured natural frequencies of few lower modes are used to overcome the drawbacks of incomplete measurement. The method is numerically examined in several damage cases. The robustness of method against measurement and mass modelling error is numerically assessed using Monte-Carlo analysis and numerically simulated error contaminated data. The method proves to be robust against both kind of errors and performs well, both in cases of plate and shell elements.     

基于最敏感设计参数的斜拉索有限元动力模型修正

基于较完善的斜拉索有限元模型,分析讨论了斜拉索张力、抗拉刚度、抗弯刚度以及线密度等不同设计参数对长索和短索计算频率的相对灵敏度,确定了最敏感设计参数.在此基础上,根据优化理论,对洞庭湖大桥拉索进行基于最敏感设计参数的动力模型修正,修正后的模型的动力特性更加趋近于实测值.修正后的斜拉索有限元模型可以作为拉索张力评估的基准.     

基于响应面的大型输电塔结构有限元模型动力修正

针对基于灵敏度分析的有限元模型动力修正方法计算效率较低、迭代收敛慢的不足,将响应面法引入500 kV大跨越输电塔基准模型修正.选择塔脚弹性支承刚度为修正参数,依次进行单因素试验、样本值计算、响应面建立与分析、参数优化.修正后,有限元模型非常准确地复现了单塔横、纵两个方向的-阶弯曲动态特性,修正效果与基于灵敏度分析的模型修正方法接近,证明响应面法在有限元模型动力修正领域的应用价值.还探讨了塔架结构修正参数的选取问题,为相关研究提供参考.     

Re-analysis procedure for laminated plates using FSDT finite element model

 A new method is proposed for effective analysis of laminated plates incorporating accurate through-the-thickness distribution of displacements, strains and stresses in the finite element formulation. It is a two-step analysis procedure. In the first step, displacements are obtained using a post-processing procedure based on the three-dimensional stress equilibrium equations and the thermoelasticity equations, from the results of FSDT finite element analysis. In the second step, the higher-order through-the-thickness distribution of displacements are reflected on the subsequent finite element analysis. The effectiveness of the present approach for the analysis of laminated plates is shown by numerical examples. Received: 13 September 2001 / Accepted: 23 May 2002     

采用等效有限元模型的复合材料机翼结构优化

在机翼设计过程中,将等效有限元模型(EFEM)方法应用于考虑静力学和动力学要求的机翼结构优化。提出了"三步走"的结构优化策略,将一个多变量的复杂优化问题转换为一系列少变量的简单优化问题,对某支线客机的复合材料机翼进行了优化设计。首先以位移、静强度和颤振速度作为约束条件对机翼复合材料铺层比例进行优化;然后以静强度和结构稳定性作为约束,以最小化结构质量和结构效率作为优化目标,对各翼肋之间的加强壁板进行优化设计;最后再以位移和颤振速度为约束,对机翼结构总体刚度进行优化设计。结果表明:EFEM方法具有快速建模和计算量少的优点,采用"三步走"优化策略具有更高的效率,适用于初步机翼结构优化设计。     

Pointwise error estimation and adaptivity for the finite element method using fundamental solutions

In this paper, we present a goal-oriented a posteriori error estimation technique for the pointwise error of finite element approximations using fundamental solutions. The approach is based on an integral representation of the pointwise quantity of interest using the corresponding Green's function, which is decomposed into an unknown regular part and a fundamental solution. Since only the regular part must be approximated with finite elements, very accurate results are obtained. The approach also allows the derivation of error bounds for the pointwise quantity, which are expressed in terms of the primal problem and the regular part problem. The presented technique is applied to linear elastic test problems in two-dimensions, but it can be applied to any linear problem for which fundamental solutions exist.     

大跨度高空钢结构连廊的有限元模型修正

使用基于灵敏度分析和贝叶斯估计的有限元模型修正方法对复杂连体高层建筑群杭州市民中心的高空钢结构连廊进行了有限元模型修正.通过频率误差和模态置信因子计算,比较分析了修正前连廊数值模型的模态参数和基于环境激励下实测得到的连廊模态参数,以确定数值模型动力特性与实际结构动力特性的差异.通过模态参数对连廊构件物理参数的敏感度分析构造灵敏度矩阵,并在此基础上筛选出对结构模态参数影响程度大的参数.基于贝叶斯估计法构造参数加权矩阵和响应加权矩阵,根据待修正参数初始设计值的置信度设置参数允许的上下边界值,按一定的收敛准则进行迭代修正.修正后连廊模型的动力特性与实测动力特性有很好的一致性,修正模型可以用来对连廊进行振动控制、响应预测及性态评估.     

Backscatter coefficient estimation using array transducers

This paper describes an extension of our broadband method for estimating backscatter coefficients from random media to include data from array transducers. Four different transducer designs have now been considered: oneand two-dimensional linear arrays, annular arrays, and single-element focused pistons commonly used in mechanical sector scanners. The analysis shows that if the backscatter echo spectrum is properly normalized, the shape of the piezoelectric elements affects only the magnitude and not the frequency dependence of the backscatter coefficient estimates. Experimental data were acquired using laboratory and clinical imaging instrumentation to verify the analysis. We compared backscatter coefficients measured as a function of frequency from well-defined scattering media that were obtained using a 1-D linear array and focused piston transducers. Instrument-independent results were found that matched theoretical predictions within the measurement error between 2 and 12 MHz. We conclude from this study that accurate backscatter coefficient estimates may be easily obtained using current clinical imaging instrumentation.