多维相关参数模型近似和随机分析方法研究及应用

发布时间：2018-10-24 12:19

【摘要】：对于半刚性连接的研究,主要集中于连接的本构关系弯矩-转角曲线的确定,然而这一曲线关系,无论是试验研究还是理论研究,都是基于结构设计变量完全确定的假定,单独考虑设计变量变化对结构整体响应的影响程度,忽略了各设计变量间的相关关系。经研究发现,由单因素变化拟合得到的曲线关系函数表达式往往在实际应用中会有悖常理。同样,参数相关性问题普遍存在于工程分析和决策评估领域,不能充分考虑参数之间的相关关系将直接导致偏差较大甚至错误的分析结果,因此基于参数相关性研究的重要意义并不仅仅局限于对半刚性节点分析。在对基于参数相关特性的半刚性节点研究过程中发现了诸多问题,包括有限元计算软件的局限性和算法上有待改进。在有限元计算过程中,软件对参数变化范围的限定成为了将确定尺寸节点的弯矩-转角关系推广到同类型节点形式的瓶颈。在有限元分析软件中抽样过程是基于蒙特卡罗法,因此在进行概率性设计时,有限元分析过程就会随着抽样次数的增加而增加,这就造成在分析确定参数的结构时要进行大量的有限元仿真分析,需要耗费大量的机时,这种方法对于处理同一类型的半刚性节点弯矩-转角曲线是难以实现的。基于此,有必要在数学方法上研究这类问题的改进计算。针对节点研究过程中衍生出的蒙特卡罗相关概率设计问题和随机性分析问题,论文的主要研究内容分为以下几个部分:首先解决在蒙特卡罗抽样中考虑参数相关性的分离变量研究方法,通过该方法可以方便的控制抽样过程,核心是将原有的相关因素变为不相关因素,这种参数转换思路在其他考虑相关因素的综合评价和规划评估问题中也起到重要作用。然后利用混合神经网络良好的小样本学习和泛化能力构建结构响应复杂的函数关系,采用改进的混沌粒子群算法优化网络寻址结构,建立与元模型匹配程度高的近似模型。同时对近似模型的构建方法进入深入的研究,探索不同方法之间的利弊。结合蒙特卡罗法对结构进行随机性分析,并提出新的灵敏度度量参数计算方法以分析随机变量的全局灵敏度系数,并在灵敏度分析过程中考虑参变量之间的相关关系,以使得最终灵敏度分析结果更符合实际情况。最后将随机分析方法与灵敏度计算方法应用于半刚性节点的弯矩-转角模型研究中,期望通过简便高效的计算方法拟合出便于工程应用的半刚性节点初始转动刚度关系式。
[Abstract]:The research of semi-rigid connections is mainly focused on the determination of the moment-angle curve of the constitutive relation of the connection. However, this curve relationship, whether it is an experimental study or a theoretical study, is based on the assumption that the structural design variables are completely determined. The influence of the design variables on the overall response of the structure is considered separately, and the correlation among the design variables is neglected. It is found that the expression of curve relation function derived from single factor variation fitting is often contrary to common sense in practical application. Similarly, the problem of parameter correlation generally exists in the field of engineering analysis and decision evaluation, and it will lead to large deviation or even wrong analysis results if the correlation between parameters is not fully considered. Therefore, the significance of parameter-based correlation study is not limited to the analysis of semi-rigid nodes. Many problems have been found in the research of semi-rigid nodes based on parameter-dependent characteristics, including the limitation of finite element software and the need for improvement in the algorithm. In the process of finite element calculation, the limitation of the parameter variation range of the software becomes the bottleneck of extending the moment-rotation relation of the defined size node to the same type of node form. In the finite element analysis software, the sampling process is based on Monte Carlo method, so in the probability design, the finite element analysis process will increase with the increase of sampling times. As a result, a lot of finite element simulation analysis is needed when analyzing and determining the structure of parameters, and it needs a lot of machines. This method is difficult to realize for the same type of semi-rigid joint bending moment-rotation curve. Based on this, it is necessary to study the improved calculation of this kind of problem in mathematical method. In view of the Monte Carlo correlation probability design problem and the stochastic analysis problem derived from the nodal research process, The main research contents of this paper are as follows: firstly, the research method of separating variables considering the correlation of parameters in Monte Carlo sampling is solved, through which the sampling process can be controlled conveniently. The core is to change the original related factors into independent factors, and this idea of parameter conversion also plays an important role in the comprehensive evaluation and planning evaluation of other relevant factors. Then using the good small sample learning and generalization ability of the hybrid neural network to construct the complex function relation of the structure response, the improved chaotic particle swarm optimization algorithm is used to optimize the network addressing structure, and the approximate model with high matching degree with the metamodel is established. At the same time, the construction method of approximate model is studied deeply, and the advantages and disadvantages between different methods are explored. Based on the Monte Carlo method, the randomness of the structure is analyzed, and a new sensitivity measurement parameter calculation method is proposed to analyze the global sensitivity coefficient of random variables, and the correlation between parameters is considered in the process of sensitivity analysis. In order to make the final sensitivity analysis results more in line with the actual situation. Finally, the stochastic analysis method and the sensitivity calculation method are applied to the study of the moment and rotation angle model of semi-rigid joints. It is expected that the relationship between the initial rotational stiffness of semi-rigid joints and the engineering application can be fitted by a simple and efficient calculation method.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TU391

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