参数变化识别问题的稀疏约束正则化方法及应用

发布时间：2018-06-02 10:25

本文选题：反演 + 正则化　；参考：《哈尔滨工业大学》2015年硕士论文

【摘要】：参数识别问题是人们研究的反问题中非常重要的一种。但近几年来,随着各项技术的高速发展,人们已经不再满足于单纯的参数识别反问题,而是更加关注,当参数变化时,怎么才能快速准确地对参数变化情况进行识别。从而将传统的静态反演推广到动态反演,进而对待识别参数的动态变化进行准确刻画,而参数变化识别问题研究的就是这类反问题。这类问题即与传统的参数识别问题相似但又不完全相同,近年来以时间推移地震为代表的这类问题引起了许多学者的极大关注。本文旨在利用稀疏约束正则化理论,针对参数变化识别问题展开算法与应用研究。首先介绍了参数识别反问题和稀疏约束正则化的研究现状,并阐述了课题的背景及研究的目的和意义。接着,介绍了相关的稀疏约束正则化理论,并分析了参数识别问题解的稀疏化表示,通过数值模拟,验证了稀疏优化反演方法求解这类问题的可行性。然后,分析了参数变化识别问题的特点,引入了局域化反演模型,该模型有效的描述了参数变化识别问题。在该模型基础上,基于2l?范数和1l?范数的一个凸组合来构造目标泛函,给出了混合正则化反演算法,该算法用两步来求解目标泛函极值点,分别使用正则Gauss-Newton法及软阈值收缩法来进行求解,从而得到目标泛函有关的极小解。最后,通过对三个简化模型的数值模拟,验证了算法是切实有效的,并通过分析参数不同变化范围的误差曲线,给出了算法的适用性。
[Abstract]:The problem of parameter identification is very important in the inverse problem of people's research. But in recent years, with the rapid development of various technologies, people are no longer satisfied with the simple parameter identification and inverse problem, but pay more attention to how to identify the change of parameters quickly and accurately when the parameters change. State inversion is extended to dynamic inversion, and then the dynamic changes of identification parameters are accurately depicted, and the problem of parameter identification is the inverse problem. This kind of problem is similar to the traditional parameter identification problem, but it is not exactly the same. In recent years, many scholars have been caused by the time lapse earthquake as the representative of this kind of problem. The aim of this paper is to make use of the theory of sparse constraint regularization to expand the algorithm and application of parameter identification problem. First, the research status of the inverse problem of parameter identification and the regularization of sparse constraint is introduced, and the background and purpose and significance of the research are expounded. Then the related sparse constraint regularization theory is introduced. In addition, the sparse representation of the solution of parameter identification is analyzed and the feasibility of the sparse optimization inversion method is verified by numerical simulation. Then, the characteristics of the parameter identification problem are analyzed and the localization inversion model is introduced. The model describes the parameter identification problem effectively. Based on the model, the model is based on the model. The objective functional is constructed by a convex combination of 2l norm and 1L norm. The hybrid regularization inversion algorithm is given. The algorithm uses two steps to solve the extreme point of target functional. The algorithm is solved by the regular Gauss-Newton method and the soft threshold contraction method respectively, and then the minimal solutions related to the target flooding are obtained. Finally, three simplified models are adopted. The numerical simulation shows that the algorithm is effective and the applicability of the algorithm is given by analyzing the error curves of different parameter ranges.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.4;TP391.4

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