本文關(guān)鍵詞： 模態(tài)應(yīng)變能 靈敏度 結(jié)構(gòu)損傷識別 貝葉斯統(tǒng)計 有限元　出處：《重慶大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：近幾十年來，由于結(jié)構(gòu)損傷沒有及時被發(fā)現(xiàn)及處理而帶來人員傷亡、經(jīng)濟損失的事件屢見不鮮。為了確保工程結(jié)構(gòu)和生命的安全，減少經(jīng)濟損失、避免更大的災(zāi)難，對現(xiàn)有結(jié)構(gòu)進(jìn)行損傷檢測已經(jīng)刻不容緩，良好的結(jié)構(gòu)損傷識別方法能夠提供有效的結(jié)構(gòu)損傷信息，使人們可以對結(jié)構(gòu)進(jìn)行及時的修復(fù)，以便降低結(jié)構(gòu)損傷積累的程度，保證工程結(jié)構(gòu)的正常運行。因此，基于結(jié)構(gòu)損傷檢測的重要性，本文首先對當(dāng)前結(jié)構(gòu)損傷識別方法的基本現(xiàn)狀進(jìn)行了綜述，其中重點闡述了基于單元模態(tài)應(yīng)變能的損傷識別方法及基于貝葉斯統(tǒng)計的概率損傷識別方法的研究發(fā)展現(xiàn)狀，然后提出了本文研究的主要內(nèi)容和具體思路。 本文在結(jié)構(gòu)動力分析有限元方法、模態(tài)應(yīng)變能和一階泰勒展開等理論基礎(chǔ)上，假定結(jié)構(gòu)損傷表現(xiàn)為單元剛度的降低，，推導(dǎo)出結(jié)構(gòu)單元模態(tài)應(yīng)變能對單元剛度損傷指標(biāo)的靈敏度的表達(dá)式，再運用結(jié)構(gòu)動力特征方程，提出了基于單元模態(tài)應(yīng)變能靈敏度的結(jié)構(gòu)損傷識別方法，并推導(dǎo)出了結(jié)構(gòu)單元損傷方程組，然后又采用解單元損傷病態(tài)方程組的四種不同的解法求解單元損傷方程組，使得該損傷識別方法可以同時對結(jié)構(gòu)的損傷位置與損傷程度進(jìn)行識別。接著本文考慮模態(tài)測量的不確定性，闡述了基于貝葉斯統(tǒng)計的損傷定位原理和損傷定量原理，從概率統(tǒng)計層面上推導(dǎo)出了單元損傷概率表達(dá)式，提出兩種基于單元模態(tài)應(yīng)變能靈敏度的貝葉斯統(tǒng)計損傷識別方法：基于貝葉斯統(tǒng)計定量原理的同時定位與定量的損傷識別方法及改進(jìn)后的基于貝葉斯統(tǒng)計的先定位后定量的兩階段損傷識別方法。通過以貝葉斯理論為基礎(chǔ)的兩種方法不僅可以對結(jié)構(gòu)進(jìn)行定位與定量的損傷識別，而且能計算有限單元損傷存在的概率，這樣便可以達(dá)到更確切描述結(jié)構(gòu)損傷的目的。 最后用本文所涉及的理論和方法自主編寫了基于單元模態(tài)應(yīng)變能靈敏度損傷識別方法及其貝葉斯統(tǒng)計改進(jìn)前后的損傷識別法的Matlab程序，并對一個簡支梁數(shù)值算例和一個連續(xù)梁數(shù)值算例進(jìn)行各損傷工況下的損傷識別模擬，探討了單元損傷程度、測量噪聲水平等對以上各種損傷識別方法識別結(jié)果的影響。識別結(jié)果表明，基于單元模態(tài)應(yīng)變能靈敏度損傷識別方法對單元損傷可以準(zhǔn)確定位，也可以得到較精確的損傷定量，且具有一定的抗噪能力；而基于單元模態(tài)應(yīng)變能靈敏度的貝葉斯統(tǒng)計的兩種損傷識別方法利用一階模態(tài)信息及較少的模態(tài)測量次數(shù)均可得出良好的單元剛度損傷指標(biāo)統(tǒng)計識別結(jié)果及單元損傷存在概率。 文章最后針對本文研究內(nèi)容的不足，提出了有待后人進(jìn)一步研究的相關(guān)問題。
[Abstract]:In recent decades, economic losses are common because structural damage has not been detected and dealt with in time. In order to ensure the safety of engineering structures and lives, to reduce economic losses, and to avoid even greater disasters, It is urgent to detect the damage of existing structures. A good method of structural damage identification can provide effective structural damage information and people can repair the structures in time in order to reduce the degree of structural damage accumulation. Therefore, based on the importance of structural damage detection, this paper first summarizes the current basic status of structural damage identification methods. The research and development of damage identification method based on element modal strain energy and probabilistic damage identification method based on Bayesian statistics are described in detail, and the main contents and specific ideas of this paper are put forward. Based on the theory of finite element method, modal strain energy and first order Taylor expansion, the structural damage is assumed to be the reduction of element stiffness. The expression of the sensitivity of structural element modal strain energy to element stiffness damage index is derived, and the structural damage identification method based on element modal strain energy sensitivity is proposed by using the structural dynamic characteristic equation. The damage equations of structural elements are derived, and the damage equations are solved by four different solutions. The damage identification method can identify the damage location and damage degree simultaneously. Secondly, considering the uncertainty of modal measurement, the damage location principle and damage quantitative principle based on Bayesian statistics are described. From the level of probability and statistics, the probabilistic expression of cell damage is derived. Two methods of Bayesian statistical damage identification based on strain energy sensitivity of element mode are proposed: the damage identification method based on Bayesian statistical quantitative principle and the improved method based on Bayesian statistics. The two methods based on Bayesian theory can not only locate and quantitatively identify the damage of structures. Furthermore, the probability of finite element damage can be calculated, so that the structure damage can be described more accurately. Finally, the Matlab program of damage identification method based on the strain energy sensitivity of element mode and the damage identification method before and after Bayesian statistical improvement is programmed by using the theory and method mentioned in this paper. At the same time, a simple supported beam numerical example and a continuous beam numerical example are simulated under various damage conditions, and the damage degree of the element is discussed. The results show that the damage identification method based on the strain energy sensitivity of element mode can locate the damage accurately and obtain more accurate damage quantification. And has certain anti-noise ability; Two damage identification methods based on Bayesian statistics of element modal strain energy sensitivity can obtain good statistical identification results of element stiffness damage index and damage probability using first-order modal information and less number of modal measurements. Finally, aiming at the deficiency of the research content, the paper puts forward the related problems to be further studied by future generations.
【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TU317

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