基于区间理论的隧道结构不确定性正反演分析

发布时间：2018-06-25 07:29

本文选题：区间模型 + 不确定性　；参考：《大连交通大学》2014年硕士论文

【摘要】：以往针对隧道结构进行的分析多是基于确定性假设进行的,即将结构参数、初始条件及边界条件等均视为确定量来进行分析。但是,工程实际中存在着大量的不确定性,基于确定性假设进行的分析并不能反映结构的不确定性问题,而且有可能会得到不合理或与实际相矛盾的分析结论。随机方法、模糊方法以及区间分析方法是目前用于分析不确定性问题的主要方法。在统计数据不足以描述概率分布或隶属函数的情况下,区间分析方法能仅通过相关不确定量的区间范围对不确定性问题进行求解。本文针对隧道结构不确定性问题,进行了基于区间分析方法的分析。主要工作内容如下： (1)基于区间理论的静力响应分析在基本有限元方法的基础上,引入区间摄动理论,推导了基于单元的区间摄动有限元控制方程。针对二维隧道结构,建立了基于所推导控制方程的数值算例,并对之进行了求解。 (2)基于区间理论的动力响应分析基于区间摄动理论、有限元法和四阶龙格库塔法,给出了结构动力不确定性问题的区间求解方法。将隧道结构的不确定性参量用区间数表示,考虑结构组成材料的均匀性情况,给出并求解了所给出方法的数值算例。 (3)基于区间理论的反问题分析在所给出结构不确定性正演分析的静力方法和动力方法的基础上,基于蚁群算法,建立了不确定性反问题的区间求解模型。以正演分析结果为量测信息,给出了相应数值算例,并对数值算例进行了求解。数值算例的分析结果表明,针对隧道结构不确定性问题,采用本文方法能有效、可行的进行分析,并且计算精度满足工程实际的要求。本文研究方法有望应用到工程实际中去。
[Abstract]:In the past, the analysis of tunnel structure is based on the deterministic hypothesis, that is, the structural parameters, initial conditions and boundary conditions are all regarded as determinants to analyze. However, there are a lot of uncertainties in engineering practice. The analysis based on deterministic assumption can not reflect the uncertainty of structure, and it may lead to unreasonable or contradictory conclusions. Stochastic methods, fuzzy methods and interval analysis methods are the main methods used to analyze uncertain problems. When the statistical data are not sufficient to describe the probability distribution or membership function, the interval analysis method can solve the uncertain problem only through the interval range of the correlation uncertainty. In this paper, the interval analysis method is used to analyze the uncertainty of tunnel structure. The main work is as follows: (1) the static response analysis based on interval theory and the interval perturbation theory are introduced on the basis of the basic finite element method, and the governing equations of the interval perturbation finite element based on the element are derived. For two-dimensional tunnel structure, a numerical example based on the derived control equation is established and solved. (2) the dynamic response analysis based on interval theory is based on interval perturbation theory. The finite element method and the fourth order Runge-Kutta method are used to solve the dynamic uncertainty problems of structures. The uncertain parameters of tunnel structure are expressed by interval number, and the homogeneity of structural materials is considered. Numerical examples of the given method are given and solved. (3) the inverse problem analysis based on interval theory is based on ant colony algorithm. The interval solution model of the inverse problem with uncertainty is established. Taking the forward analysis result as the measurement information, the corresponding numerical example is given and the numerical example is solved. The analysis results of numerical examples show that the proposed method can be used to analyze the tunnel structure uncertainty effectively and feasible, and the calculation accuracy can meet the requirements of engineering practice. The research method in this paper is expected to be applied to engineering practice.
【学位授予单位】：大连交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U451

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