基于正则化技术的混凝土梁结构模型修正(附模拟程序)

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基于正则化技术的混凝土梁结构模型修正(附模拟程序)(任务书,开题报告,外文翻译,论文22000字,模拟程序)
摘  要
近十年来,随着我国基建事业的蓬勃发展,各种大型基础设施和大型建筑不断涌现出来,与此同时,人们也越来越关心建筑的安全性,于是有限元建模技术方法在实际工程中得以广泛应用。但由于施工和环境的影响,实际的工程结构与所建立的初始有限元模型会有一定的偏差,有时甚至误差很大。如果不对建立的初始模型加以修正,得出的分析结果与实际出入较大。因此,非常有必要开展有限元模型修正的研究。在进行模型修正时,测量往往不完备,从而导致修正问题求解的不适定性。本文简要地总结了有限元模型静力修正的已有方法,在此基础上,开展了基于正则化的梁结构静力修正的研究,在模型修正中使用Tikhonov正则化技术,即L2范数正则化技术,对欠定矩阵方程的求解进行优化,得到修正系数稳定的近似解,从而实现了对混凝土梁结构模型修正。本文主要做了以下几方面的内容:
1、介绍几种常见的用于求解不适定问题的正则化技术。重点介绍Tikhonov正则化技术和Landweber正则化技术。Landweber迭代正则化法具有求解容易、稳定性高的优点,但其算法应用于大型结构时会出现收敛速度慢的缺点,而Tikhonov正则化技术的收敛速度快,求到的解也比较稳定。因此在本文中采用Tikhonov正则化技术。
2、介绍一种不考虑测量误差的基于静力加载的有限元模型修正方法,该方法利用静力凝聚法和一阶泰勒展开建立修正系数的控制方程,然后利用正则化技术对欠定矩阵方程的求解进行优化,得到修正系数的近似解,从而达到模型修正的目的。
3、选用简支梁作为模拟算例进行分析,结合梁的一般形式,在模拟的实际模型算例中设置刚度退化,得到实际模型的竖向位移响应,再根据文中的方法计算结果得出理想模型的修正系数,比较初始模型修正后的竖向位移响应。说明本文介绍方法的可行性。
4、分别将混凝土简支梁分为8单元、15单元、45单元的三种工况作为模拟算例,研究本文方法的修正效果,并与最小二乘法得到的结果进行对比。结果表明,本文方法得到的解的误差要比最小二乘法得出的结果小,从而说明本文方法的优越性。

关键词:模型修正;静力凝聚;修正系数;正则化

Abstract
In nearly a decade, with the vigorous development of the our country construction enterprise, all kinds of large-scale infrastructure and large buildings emerge unceasingly, at the same time, people also more and more concerned about construction safety, the finite element modeling method is widely used in practical engineering. However, due to the impact of construction and environment, the actual engineering structure and the initial finite element model established will have some deviation, sometimes even a large error. If the initial model is not modified, the analysis results obtained are of no reference value. Therefore, it is very necessary to carry out the research of finite element model modification. When the model is modified, the measurement is often incomplete, which leads to the unsuitability of the solution of the modified problem. This article briefly summarizes the existing method of finite element model static correction, based on this, carried out based on the research of regularization of the beam structure static correction, used in the model modified Tikhonov regularization method, namely the L2-regularization method, optimize the underdetermined matrix equation solving, corrected coefficient and stable approximate solution, so as to realize the structure of concrete beam model is fixed. This paper mainly focuses on the following aspects:
1. Introduce several common regularization methods for solving ill-posed problems. The Tikhonov regularization method and Landweber regularization method are introduced. Landweber iterative regularization method has the advantages of easy solution and high stability, but its algorithm has the disadvantage of slow convergence when applied to large structures, while Tikhonov regularization method has fast convergence and relatively stable solution. Therefore, Tikhonov regularization method is adopted in this paper.
2, this paper introduces a regardless of the measurement error of the finite element model updating method based on static load, the method using the static condensation method and the control equation of first order Taylor expansion to establish correction coefficient, and then use regularization method for solving the underdetermined matrix equation is optimized, the approximate solution of the corrected coefficient, so as to achieve the purpose of the model updating.
3. The simply supported beam was selected as the simulation example for analysis. Combined with the general form of the beam, the stiffness degradation was set in the simulation example of the actual model to obtain the vertical displacement response of the actual model. The feasibility of this method is illustrated.
4. The concrete simply supported beam is divided into 8 units, 15 units and 45 units, respectively, as simulation examples, to study the correction effect of the method in this paper, and to compare with the results obtained by the least square method. The results show that the error of the proposed method is smaller than that of the least square method.
Keywords:model updating;static condensation;correction coefficient;regularization

本文研究的主要内容
本文以混凝土简支梁为研究对象,基于静力荷载位移响应值,研究和探讨了有限元结构模型的修正方法。在无测量误差的情况下,利用静力凝聚法消去混凝土梁模型的转动自由度,根据一阶泰勒展开缩减平衡方程,建立各单元刚度的修正系数的控制方程,然后利用Tikhonov正则化技术对得到的修正系数的求解进行优化,得到修正系数,求出模型修正后的荷载位移响应,进而对修正效果进行评估,并完成以下工作。
1、总结并简要阐述近年来国内外在模型修正方面的所做的研究以及修正的方法,分析它们的优缺点并加以比较。
2、总结并简要阐述如今在国内外比较常用的几种正则化技术,分析它们的优缺点并加以比较。理解为什么正则化技术可以应用于不适定问题优化求解之中,以及为什么正则化技术可以应用于有限元结构模型修正之中。重点阐述Tikhonov正则化(即L2正则化技术)以及对比其和最小二乘法和Landweber正则化的优点。
3、研究基于静力实测数据的混凝土梁结构有限元模型修正方法,得出修正系数的控制方程。
4、研究结合正则化技术优化的修正系数反求,通过模拟算例,得到实际模型和修正模型的荷载位移响应,验证本文方法的可行性

目录
第一章  绪论    1
1.1引言    1
1.2 研究概况    2
1.3 结构模型修正的主要方法    3
1.3.1 矩阵型修正法和参数型修正法    3
1.3.2 静力、动力、静动力结合三种模型修正方法    4
1.3.3 其他方法    5
1.4 本文研究的主要思路    5
第二章  正则化方法    7
2.1 引言    7
2.2 正则化方法的研究现状与发展    7
2.3 一般的正则化理论    8
2.4  Tikhonov正则化    9
2.4  Landweber正则化    10
2.5 本章小结    10
第三章  基于正则化技术的梁结构模型修正    11
3.1 引言    11
3.2 基于静力竖向位移响应的修正系数控制方程    11
3.2.1 静力凝聚法    12
3.2.2 梁结构的整体刚度方程    13
3.2.3结构模型修正系数及控制方程    14
3.3 基于Tikhonov正则化技术的修正系数求解    15
3.4 本章小结    16
第四章  简支梁模型修正模拟算例    17
4.1 引言    17
4.2 数值算例    17
4.2.1  8单元简支梁算例    17
4.2.2  15单元简支梁算例    21
4.2.2  30单元简支梁算例    25
4.3本章小结    30
第五章  结论与展望    31
5.1 结论    31
5.2 展望    31
参考文献    33
致谢    34