本文選題：反演 + 正則化��； 參考：《哈爾濱工業(yè)大學(xué)》2015年碩士論文

【摘要】：參數(shù)識別問題是人們研究的反問題中非常重要的一種。但近幾年來,隨著各項(xiàng)技術(shù)的高速發(fā)展,人們已經(jīng)不再滿足于單純的參數(shù)識別反問題,而是更加關(guān)注,當(dāng)參數(shù)變化時(shí),怎么才能快速準(zhǔn)確地對參數(shù)變化情況進(jìn)行識別。從而將傳統(tǒng)的靜態(tài)反演推廣到動態(tài)反演,進(jìn)而對待識別參數(shù)的動態(tài)變化進(jìn)行準(zhǔn)確刻畫,而參數(shù)變化識別問題研究的就是這類反問題。這類問題即與傳統(tǒng)的參數(shù)識別問題相似但又不完全相同,近年來以時(shí)間推移地震為代表的這類問題引起了許多學(xué)者的極大關(guān)注。本文旨在利用稀疏約束正則化理論,針對參數(shù)變化識別問題展開算法與應(yīng)用研究。首先介紹了參數(shù)識別反問題和稀疏約束正則化的研究現(xiàn)狀,并闡述了課題的背景及研究的目的和意義。接著,介紹了相關(guān)的稀疏約束正則化理論,并分析了參數(shù)識別問題解的稀疏化表示,通過數(shù)值模擬,驗(yàn)證了稀疏優(yōu)化反演方法求解這類問題的可行性。然后,分析了參數(shù)變化識別問題的特點(diǎn),引入了局域化反演模型,該模型有效的描述了參數(shù)變化識別問題。在該模型基礎(chǔ)上,基于2l?范數(shù)和1l?范數(shù)的一個(gè)凸組合來構(gòu)造目標(biāo)泛函,給出了混合正則化反演算法,該算法用兩步來求解目標(biāo)泛函極值點(diǎn),分別使用正則Gauss-Newton法及軟閾值收縮法來進(jìn)行求解,從而得到目標(biāo)泛函有關(guān)的極小解。最后,通過對三個(gè)簡化模型的數(shù)值模擬,驗(yàn)證了算法是切實(shí)有效的,并通過分析參數(shù)不同變化范圍的誤差曲線,給出了算法的適用性。
[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.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：P631.4;TP391.4

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本文編號：1968419