基于模态参数灵敏度的损伤方程组求解正则化方法研究

基于模态参数的结构损伤识别方法是振动损伤识别领域中应用最为广泛的方法。利用模态参数灵敏度构建结构损伤方程组,对其进行求解可以识别结构损伤位置和程度。由于实际工程中模态参数不完备性和噪声的影响,结构损伤方程易出现病态问题,直接求解可能产生错误的结果。为了解决这一问题,可以引入正则化方法进行求解。然而,各类正则化方法的基本原理、区别和联系及其在结构损伤识别中的应用没有系统的研究和对比。本文梳理了几类常用的正则化方法,对比分析其在基于模态参数灵敏度的损伤方程组求解中的适用性,讨论损伤程度、噪声水平和测点数目对几类方法识别结果的影响,为结构损伤识别中的正则化方法选择提供依据。通过连续梁和框架结构数值算例分析表明,在求解损伤方程的应用中,L1范数正则化方法鲁棒性较强,贝叶斯正则化方法次之,奇异值截断算法和L2范数正则化方法的鲁棒性较差;L1范数正则化方法能够产生更少的假阳性损伤单元,受噪声和测点数目影响较小,更适合损伤识别的应用。     

基于1范数正则化的模型修正方法在结构损伤识别中的应用

以基于灵敏度分析的有限元模型修正方法为基础，提出了一种基于1范数正则化过程的结构损伤识别方法。通过与以Tikhonov正则化为代表的二次型正则化过程相比较，本文的理论分析表明1范数正则化方法在迭代计算过程中能根据上一迭代步损伤识别结果自适应地调整正则化项中的损伤参数权系数，从而显著改善了Tikhonov正则化识别结果过度光滑的缺陷，更利于识别结构的局部损伤。为解决引入1范数造成的数值计算困难，文中还对基于1范数正则化的模型修正算法进行了改进。以二维框架模型为例的损伤识别数值模拟表明：1范数正则化方法与模型修正方法相结合可以有效抑制实测模态参数中噪声的影响，体现出较好的鲁棒性；在模态噪声水平达到10%的情况下，仍能有效抑制噪声干扰，凸显结构局部损伤位置，准确识别损伤程度。     

面载荷识别的TSVD正则化方法

线性系统的响应可以表示为单位脉冲响应函数与动态载荷的卷积分,经离散后得到载荷识别反问题。引入TSVD正则化方法处理反问题的不适定性,对不同噪声的实测响应进行了面载荷的反演求解,并对识别精度做出了分析。算例表明,TSVD正则化方法对响应误差的适应性强,识别精度高。     

网络RTK参考站间模糊度动态解算中病态方程的一种解算方法

在网络RTK参考站间的模糊度估计中，若误差方程严重病态，将导致模糊度解与其准确值偏差较大或整周模糊度无法固定，因此提出了一种适于网络RTK模糊度动态解算的新方案：1）法方程病态性的判断；2）Tikhonov正则化解算病态方程；3）LAMBDA方法搜索固定整周模糊度。同时，深入研究了Tikhonov正则化矩阵的构造方法和正则化参数的选取准则。最后以实例验证了采用此方案解算病态方程是可行的，通过选取合适的正则化参数可以解得准确的整周模糊度；详细讨论了选择不同的正则化参数对模糊度解算结果的影响。     

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。     

基于L1正则化的随机梁式结构静力损伤识别方法

提出了一种结合摄动法和L1正则化方法的随机梁式结构静力损伤识别方法。考虑初始模型误差和测量误差的影响,建立了关于随机损伤指数的控制方程,并将摄动法和L1正则化方法相结合,对随机损伤指数的控制方程进行求解,进而从概率的角度对结构的损伤进行识别。损伤试验结果表明,和传统的最小二乘求解法相比,本文方法能够更为准确地识别多处局部损伤的位置及大小,对实际结构损伤检测具有较好的参考价值。     

一种用于重力梯度动态测量的载体环境引力梯度补偿方法

重力梯度仪动态测量时,重力梯度敏感器一直稳定在地理坐标系下,载体姿态变化使载体质量分布相对敏感器的位置发生变化,形成载体环境引力梯度变化。为提高重力梯度仪动态测量精度,提出一种基于Tikhonov正则化的载体环境引力梯度补偿方法。首先,推导了载体环境引力梯度的解析模型,建立了引力梯度变化的回归方程。然后,针对回归算子病态性问题,提出了Tikhonov正则化方法,通过半物理仿真确定最优正则化参数,使补偿量的误差控制在2%以内。最后,利用该参数处理船载试验实测数据,结果表明:所提出的方法对载体环境梯度变化补偿具有明显的效果,可将两路重力梯度测量信号内符合中误差分别降低19 E和21 E,补偿后重力梯度测量精度达到10 E的精度水平。     

接触力优化设计的熵正则化方法

包含单侧接触的机械和结构系统中,接触面间的局部接触力很大时,容易导致结构局部磨损和破坏。利用结构优化的手段极小化接触面上的最大接触力是调整接触面上接触力分布的一个有效途径。然而在数学上,目标函数的不可微和约束中的接触条件导致该结构优化问题属于非光滑和非凸优化问题,因而常用优化算法的优化结果是不可靠的。为此,本文提出接触力优化的一个熵正则化模型,并利用基于正则化过程的序列二次结构优化算法求解。所提的方法在数值上避免了处理不可微问题,而且正则化参数的调整还有助于获得更小的局部最优解。以离散结构为例的数值算例验证了本文的模型和算法。     

材料物性参数识别的梯度正则化方法

本文对梯度正则化方法（Ｇｒａｄｉｅｎｔ－Ｒｅｇｕｌａｒｉｚａｔｉｏｎ Ｍｅｔｈｏｄ）作了进一步的研究,给出一种建立了梯度正则化迭代算法和选择正参数的简明实用方法。文中椭圆算子方程参数识别算例不仅说明了ＧＲ法具有广泛的适应性和一定的抗噪声能力,而且收敛速度较快,具有较大的收敛范围。     

微分方程反问题的梯度正则化法

本文在微分方程反问题研究当前发展状况的基础上,提出了一种求解微分方程反问题的比较统一的方法——梯度正则化法。该方法将反问题的求解分为两个主要部分,一是展开以求补充条件对未知参数的梯度矩阵,二是正则化以解不适定的线性方程组。梯度正则化法从反问题的共性入手,未附加任何特殊的约束,所以可以适用各种类型的反问题,且在求解时不受空间维数的限制。     

Preface: Current research progress on mechanics of high speed rail

The construction and operation of high-speed rail（HSR）grid within the past two decades in China,in terms of the scale,may be possibly comparable to any national-wide construction in the history of China,even the Great Wall.By counting railways with commercial train service at the speed of200 km/h,China has the world’s longest HSR network with over 19 369.8 km of track in service today and this number     

ACTA MECHANICA SINICA 2014 ANNUAL SUBJECT INDEX

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人造地震动合成中的位移误差分析

三角函数级数法是合成人工地震动常用算法之一,但是通过对加速度积分求取位移时,却存在与零线漂移相类似的位移漂移现象。     

Rainwater rivulets on a cable subject to windFilets d'eau de pluie sur un câble soumis au vent

Rainwater rivulets appear on inclined cables of cable-stayed bridges when wind and rain occur simultaneously. In a restricted range of parameters this is known to cause vibrations of high amplitudes on the cable. The mechanism underlying this effect is still under debate but the role of rainwater rivulets is certain. We use a standard lubrication model to analyse the dynamics of a water film on a cylinder under the effect of gravity and wind load. A simple criterion is then proposed for the appearance and position of rivulets, where the Froude number is the control parameter. Experiments with several geometries of cylinder covered with water in a wind tunnel show the evolution of the rivulets with the Froude number. Comparison of the prediction by the model with these experimental data shows that the main mechanism of rivulet formation and positioning is captured. To cite this article: C. Lemaitre et al., C. R. Mecanique 334 (2006).     

Hermitian space-time finite elements for estuarine mass transport

Space-time finite element solutions of the convection–dispersion equation using higher-order nodal continuity and Hermitian polynomial shape functions are described. Five separate elements ranging from a complete linear element with C^0,0 nodal continuity to a complete first-order Hermitian element with C^1,1 nodal continuity are subjected to detailed analysis. Wave deformation analyses identify the source of leading or trailing edge oscillations, trailing edge oscillations being the major source of difficulty. These observations are confirmed by numerical experiments which further demonstrate the potential of higher-order nodal continuity. The performance of the complete first-order Hermitian element is quite satisfactory and measurably superior to the linear element.     

Cristallisation par onde acoustique : le cas de l'héliumCrystallization by acoustic waves: the case of helium

We establish a theoretical model to explain the nucleation of a crystal of helium by an acoustic over-pressure. We explain the interfacial laws for this ultra-fast cristallization, close to the sound speed. Assuming spherical symmetry and taking into account the experimental data, we recover the dynamics of the growth and melting during an over-pressure impulse. To cite this article: M. Ben Amar et al., C. R. Mecanique 331 (2003).     

Structure initiale et propriétés de liquéfaction statique d'un sableInitial structure and static liquefaction properties of sand.

Based on the use of two different preparation procedures for reconstituting triaxial samples of sand, i.e. wet tamping and dry pluviation, significant differences in associated mechanical behaviour are observed on a reference sand with respect to the phenomenon of ‘static’ liquefaction. Wet tamping favours the initiation of liquefaction instability, whereas dry pluviation favours a more stable behaviour, less susceptible to liquefaction. Microscopic observation of corresponding sand specimens allows us to identify two well differentiated structures, i.e., for wet tamping, an irregular structure with predominance of aggregates (aggregated grains) and macropores, very contractant and unstable and, for dry pluviation, a more regular structure, without macropores, more dilatant and more stable. These observations show the importance of further characterization, based on the introduction of appropriate parameters, of the initial structure of sandy materials, strongly dependant upon their mode of formation (natural or artificial). To cite this article: N. Benahmed et al., C. R. Mecanique 332 (2004).     

Sources of Complexity in Human Systems

Complex is a special attribute we can give to many kinds of systems. Although it is used often as a synonym of difficult, it has a specific epistemological meaning, which is going to be shared by the incoming science of complexity. Difficult is an object which, by means of an adequate computational power, can be deterministically or stochastically predictable. On the contrary complex is an object which can not be predictable because of logical impossibility or because its predictability would require a computational power far beyond any physical feasibility, now and forever. For complexity refers to some observing system, it is always subjective, and thus it is defined as observed irreducible complexity. Human systems are affected by several sources of complexity, belonging to three classes, in order of descending restrictivity. Systems belonging to the first class are not predictable at all, those belonging to the second class are predictable only through an infinite computational capacity, and those belonging to the third class are predictable only through a trans-computational capacity. The first class has two sources of complexity: logical complexity, directly deriving from self-reference and Gödel's incompleteness theorems, and relational complexity, resulting in a sort of indeterminacy principle occurring in social systems. The second class has three sources of complexity: gnosiological complexity, which consists of the variety of possible perceptions; semiotic complexity, which represents the infinite possible interpretations of signs and facts; and chaotic complexity, which characterizes phenomena of nonlinear dynamic systems. The third class coincides with computational complexity, which basically coincides with the mathematical concept of intractability. Artificial, natural, biological and human systems are characterized by the influence of different sources of complexity, and the latter appear to be the most complex.