复杂分布动载荷识别技术研究

复杂结构的分布动载荷识别技术是动载荷识别技术的难点之一。本文推导了基于广义正交多项式特征技术动载荷识别模型，解决了在一定精度范围内通过有限测量点的振动信息识别具有无限未知量的分布动载荷关键技术，通过动态标定技术的研究和复杂结构有限元模型数值仿真计算，验证了方法的正确性、有效性和工程可用性，适用于具有确定性分布的稳态振动载荷识别．为分布动载荷识别技术的发展打下一定的基础。     

二维分布动载荷识别的频域方法

运用频域法在广义正交域中识别二维分布动载荷。基于数学拟合理论，二维动态载荷在广义正交域中可分解为二维正交函数的级数形式，未知的二维分布动载荷就可以表示为各阶正交基函数线性叠加，这时未知的复杂分布动载荷的识别就可以转化为简单的正交拟合系数的识别。根据线性系统的叠加原理，将待识别载荷的分解基函数看成已知分布动载荷作用于结构时，结构的响应与待识别载荷作用下结构的响应成线性关系。只要结构实测的响应点数大于待识别的系数，就能求出各系数，因而就可以识别分布动载荷。通过计算机仿真验证该方法能有效识别二维分布动载荷，且能与有限元方法结合，识别复杂结构上的分布动载荷。该方法具有很好的通用性，能简单方便运用于工程结构，能很好地抑制噪声的干扰。仿真试验说明该方法具有很好的识别精度。进一步的试验验证了该方法工程适用性。     

分布动载荷频域识别的试验动标定方法研究

分布动载荷识别是工程中最为复杂也亟需解决的结构动力学逆问题，通常可以转化为正交多项式系数的识别，从而衍生出了动标定技术。传统的仿真动标定方法是基于有限元仿真模型来实现的，然而仿真动标定方法存在模型误差，导致载荷识别精度不高。因此本文基于 Legendre 正交多项式和 Gauss?Legendre 积分提出了分布动载荷频域识别的试验动标定方法。该方法的关键是通过测量有限的高斯点和响应点间的频响函数来完成分布载荷识别过程中的动标定，克服了传统标定在试验时无法加载正交多项式载荷计算标定矩阵的局限性，同时避免了模型误差对标定矩阵精度的影响，大大提高了载荷识别的精度。为了验证该方法的有效性和精度，将本文所提出的试验动标定方法与现阶段已有的仿真动标定进行了对比分析，并讨论了不同高斯点数对识别精度的影响及抗噪性能；此外，还通过相应的试验进一步验证了该方法的可行性与工程适用性。     

结构连续分布的动态随机载荷识别方法研究

复杂结构连续分布的动态随机载荷识别技术是结构动载荷识别技术的难点之一。推导了基于广义正交多项式特征技术动态随机载荷识别模型，馋决了在一定精度范围内通过有限测量部位随机振动响应信息识别无限未知量的结构分布动态随机载荷的关键技术，通过动态标定技术的研究和复杂结构有限元模型数值仿真计算验证了方法的正确性、有效性和工程可用性，适用于具有沿结构分布的振动随机载荷识别，为分布动态随机载荷识别技术的发展打下一定的基础。     

基于神经网络模型的动载荷识别

依据结构动力学理论推导了在时域中用于神经网络算法的自回归函数，相应建立了具有时延反馈的神经网络动载荷识别模型。阐明了这种网络的基本学习算法和回忆算法。数值仿真和试验件的验证试验表明该神经网络模型用于动载荷识别时具有精度高、无累积误差、抗干扰能力强等优点，并且适用于各种类型的动载荷，尤其对冲击载荷的识别更具有独特的优势。该模型在动标学习过程中要求信息量小，试验成本低，是一种非常值得在工程中推广应用的新型动载荷识别方法。     

具有连续分布梁模型动载荷的识别技术研究

用正交多项式拟合的方法对连续系统的分布动态载荷进行识别的技术,为用有限的测量信息进行连续系统分布载荷的识别提供了可行的方法。该方法只须获取足够的测量点的响应来识别分布载荷正交多项式的系数,满足识别的精度要求,同时对测量点的位置无特殊限制。实际工程中进行载荷识别时,很多结构只能测量到部分位置的响应,这时该方法能很好地解决这类问题。该方法对测量数据噪声的灵敏度较小,具有很好的抗干扰能力。通过计算机仿真,证明了该方法理论的正确性和工程应用的可行性。     

非线性系统载荷识别的最小二乘支持向量机法

为解除载荷识别问题对原系统先验知识的依赖，本文提出采用最小二乘支持向量机（Least squares support vector machine，LS-SVM）对非线性系统进行逆模型辨识，随后在该逆模型基础上利用工作状态的响应数据识别时域载荷。通过对某一非线性系统的稳态和非稳态激励的仿真计算，验证了该方法的有效性。仿真结果表明LS-SVM能够辨识出可靠的非线性系统的逆模型，进而反演出较精确的时域载荷。该方法不需要了解系统的数学模型及参数，只需少量训练样本即可，因此该方法能够应用于工程实践中。     

轴承动载荷识别方法改进及试验验证

轴承动载荷是影响旋转机械安全稳定运行的重要因素。在基于频响函数求逆法的动载荷识别模型基础上，针对频响函数矩阵病态性问题，提出基于响应点优化和截断奇异值分解（Truncated Singular Value Decomposition，TSVD）法的矩阵病态消除方法。首先，选择条件数最小的测点组合进行响应点优化，再利用TSVD法识别轴承动载荷。在所搭建的双转子实验台上设计识别方案，通过改变轮盘不平衡量，验证了根据该方法识别轴承动载荷的可靠性。     

面向船体结构动冰载荷监测的线性形函数识别方法研究EI北大核心CSCD

船体结构冰载荷监测系统中的载荷识别算法是对船舶在冰区安全运行进行实时评估的关键环节,而常用的影响系数矩阵法尚未考虑冰载荷的动力效应。在时域内将动冰载荷离散为诸多时间元,在每个时间元内利用线性形函数的组合形式逼近构造动冰载荷;通过结构的动力响应分析得到形函数的响应矩阵,并以此建立船体结构冰载荷识别的正问题。利用共轭梯度最小二乘迭代型正则化算法和终止迭代准则对冰载荷识别问题中的不适定性进行控制。该数值算例和试验验证均表明,该冰载荷识别模型具有良好的识别精度、求解速度及稳定性。     

基于Wilson-θ显式算法的动载荷快速定位及重建方法EI北大核心CSCD

通过将Wilson-θ数值算法转变为一种等效的显式表达式,由此建立了一种基于Wilson-θ显式算法的动载荷识别方法。在选取合适的参数θ值以后,该算法是无条件稳定的,并且避免了以往隐式识别算法中由于递推计算产生误差累积导致识别结果严重发散的问题。通过引入响应系数矩阵,该显式算法可以灵活地选取响应类型用于载荷识别计算。同时结合分离变量方法,将载荷位置信息从建立的模型矩阵中提取出来,由此减少矩阵求逆的次数,提高载荷定位计算的效率。结合简支梁的仿真算例与试验测试对该载荷识别方法进行验证。研究结果表明,基于Wilson-θ显式算法的动载荷快速定位及重建方法能够有效地识别得到载荷位置及相应的时间历程。相对于传统载荷识别方法,该方法计算结果的准确性更好,且运算效率更高。     

A novel shape function approach of dynamic load identification for the structures with interval uncertainty

Aiming at uncertain structures, a computational inverse approach is proposed to identify the dynamic load on the basis of the shape function method and interval analysis. The forward model for an uncertain structure is established through the relationship between the uncertain load vector and the assembly matrix of the uncertain responses of the shape function loads in each discrete element in time domain. The uncertainty is characterized by the interval with a closed bounded set of uncertain parameters. On the basis of interval analysis method, the load identification for uncertain structures can be transformed into two kinds of deterministic inverse problems, namely the deterministic dynamic load identification and the first order derivatives of the unknown load to each parameter both at the midpoints of the uncertain parameters. In order to eliminate the ill-posedness of inversion, the regularization method is adopted to solve the deterministic equations. Two numerical examples demonstrates the effectiveness of the proposed method, and example one also gives the identified result using Monte Carlo method to compare with that using the proposed method.     

动态载荷时域识别的联合去噪修正和正则化预优迭代方法

系统响应可表示为单位脉冲响应函数与激励载荷的卷积,将其离散化一组线性方程组,则载荷识别问题即转化为求解线性方程组的反问题。针对响应中带有噪音时载荷识别的困难,提出了联合奇异熵去噪修正和正则化预优的共轭梯度迭代识别方法。一方面对含噪信号进行基于奇异熵的去噪处理,提高反问题求解中输入数据的精度。另一方面利用正则化方法对共轭梯度迭代算法进行预优,改善反问题的非适定性。由于从输入的响应数据去噪和正则化算法两方面同时改善动态载荷识别反问题的求解,因此可以有效地抑制噪声,提高识别精度。通过数值算例分析,表明在不同的噪声水平干扰下,其识别精度均优于常规的正则化方法,能够实现有效稳定地识别动态载荷。最后通过实验研究进一步验证了该方法的正确性和有效性。     

A dynamic XFEM formulation for crack identification

Nelder–Mead (NM) and Quasi-Newton (QN) optimization methods are used for the numerical solution of crack identification problems in elastodynamics. Fracture is modeled by the eXtended Finite Element Method. The Newmark-β method with Rayleigh damping is employed for the time integration. The effects of various dynamical test loads on the crack identification are investigated. For a time-harmonic excitation with a single frequency and a short-duration signal measured along part of the external boundary, the crack is detected through the solution of an inverse time-dependent problem. Compared to the static load, we show that the dynamic loads are more effective for crack detection problems. Moreover, we tested different dynamic loads and find that NM method works more efficient under the harmonic load than the pounding load while the QN method achieves almost the same results for both load types.     

混合遗传算法在结构动力反演中的应用研究

研究了输入荷载未知条件下的结构参数识别及荷载反演问题,该问题最终归结为一个非线性的优化问题求解,根据目标函数、约束条件的具体特性,采用BFGS算法作为局部搜索算子,构造了基于浮点编码的混合遗传算法。针对系统输入未知的激励特性,采用分解反演的计算策略,从而提高了动力反演中混合遗传算法的稳健性和收敛速度。数值算例表明,这种方法具有很好的参数识别精度及荷载反演效果,对测试噪声有较强的适应能力。     

Distributed dynamic load identification based on shape function method and polynomial selection technique

A new approach based on shape function method of moving least square fitting (SFM_MLSF) and polynomial selection technique is proposed in this paper for distributed dynamic load identification. The distributed dynamic load is represented as a product of spatial distribution function and time history, and the two parts are assumed to be independent. The modal transformation of structural dynamic equation throws light on the fact that all modal loads share the same form with the distributed dynamic load in time domain. As the structural modal parameters are known, the time history of dynamic load can be precisely identified through SFM_MLSF method which approximates the local dynamic load with shape functions in the moving supporting time domain. Then, the spatial distribution function of the load is substituted as a series of basic functions, and the identification of distribution function is transformed into a linear fitting problem. Through polynomial selection technique based on error reduction ratio, the significant components are picked out from the basis function responses, which greatly improves stability and precision of the load distribution function. During the inverse analyses of both the time history and distribution function, appropriate regularization methods are still applied to overcome the unavoidable ill-conditioned problem. Numerical examples demonstrate the validity and accuracy of the proposed method.     

Impact force identification using the general inverse technique

The general inverse technique has been applied to the problem of impact force identification. The force identification problem can be stated as follows: ‘Given the response of a structure, what impact force is required to produce this response?’ Experimental measurement data was used to describe the velocity response of an impacted cantilever beam. The inverse technique used these measurements to predict the impact force which resulted in the beam response.

A spectrum analyzer was used to measure the beam accelerations within 40 μs time intervals. The accelerations were integrated so that the response was in suitable velocity form for use in the inverse algorithm. The analyzer and impact hammer also allowed the measurement of the actual dynamic load, and thus provided a means of comparison against the predicted impact force given by the inverse technique.     

An inverse approach for pressure load identification

An inverse approach for the identification of pressure loading on a structure has been proposed and developed. In this approach, surface measurements of structural response (e.g. strain, displacement and velocity field measurements, such as can be measured with 3D digital image correlation) are utilized as input data and are combined with numerical simulations to identify the pressure load on a structure. The inverse approach has been verified by numerical benchmarks involving pressure identification under quasi-static as well as dynamic impulse loading conditions, and also been validated by an experiment involving a quasi-static pressure load. The results indicate that the proposed inverse method can identify not only the magnitude of the quasi-static pressure but also the impulsive pressure loading history. The developed inverse approach offers an opportunity to apply inverse analysis techniques to identify interactive pressure loads (such as those resulting from a blast wave) on structures in explosive events.     

一种基于最优输出跟踪的多源动态载荷识别方法

基于最优输出跟踪的基本思想,提出了一种时域内多源动态载荷识别的方法。该方法从结构动力响应出发,设计一个最优输出跟踪器并构造性能指标,将载荷识别问题转变为最优输出跟踪问题。通过Adams法求解微分方程,实现了多源动态载荷的识别,并采用L曲线法确定了性能指标中的关键参数。数值算例表明,所述的载荷识别方法能够在响应数据含有噪声的情况下,有效稳定地实现多源动态载荷的重构,具有较强的抗噪能力。     

基于接触模型和峭度最优Laplac小波的滚动轴承量化诊断

研究了滚动轴承损伤量化诊断中的正反问题。通过轴承界面相互作用的动态接触理论及摩擦学系统行为的研究,运用振动传递路径表征物理模型。该模型计及负荷分布、游隙的影响,考虑接触滑移、分离作用,由表面轮廓变化描述局部损伤扩展,由测量信号修正模型参数,实现真实工况下轴承运行与模拟研究的有机结合。通过正问题求解构造峭度最优Laplace小波来提取无量纲指标,进而形成损伤矩阵数据库。将反问题计算转化为多维优化问题,利用灰色关联度寻优求解出与输入值几何最相似的样本点,进而测出轴承损伤的位置和具体尺寸。最后的实例分析表明,本文方法具有较好的精度和鲁棒性,且易于在工程实践中推广。