本文選題：小波分析 + 遺傳算法�。� 參考：《長沙理工大學》2014年碩士論文

【摘要】：工程結構在長期使用過程中受到外界環(huán)境腐蝕、材料自身老化以及疲勞荷載等因素的作用會發(fā)生損傷,當損傷積累到一定程度時會影響結構的正常使用,甚至可能導致結構的倒塌。盡早的發(fā)現(xiàn)并及時的修復這些損傷,不僅能夠大大減少結構的維護、維修費用,還可以預防不必要的生命財產損失。因此,研究結構損傷識別方法具有重要的理論意義和工程應用價值。本文以小波分析和遺傳算法理論為基礎,小波分析在時頻兩域上有著優(yōu)越的局部分析特性和變焦特點,遺傳算法具有很好自組織、自適應、并行性和全局搜索能力強等特點,本文將這兩者的優(yōu)點進行有機的結合,提出了小波-遺傳算法的概念,建立了一種既能識別結構損傷位置又能確定損傷程度的小波遺傳算法。首先以有限元分析求解結構振型模態(tài)為基礎,用db小波做連續(xù)小波變換,由小波系數(shù)模極大值識別損傷的位置。然后以單元剛度折減系數(shù)為遺傳算法的優(yōu)化變量,用振型和頻率的誤差函數(shù)加權來構造目標函數(shù),并通過損傷位置的確定來簡化目標函數(shù)的變量,再用遺傳算法對目標函數(shù)進行極小化,從而確定結構的損傷程度。本文以簡支梁為例,分別用小損傷、大損傷和不同位置不同損傷程度的損傷來檢驗該方法的有效性。建立含損傷簡支梁的有限元模型,對有限元模型進行模態(tài)分析以得到頻率和振型等模態(tài)參數(shù),將位移模態(tài)進行連續(xù)小波變換得小波系數(shù)圖,根據小波系數(shù)圖的模極大值點確定了簡支梁的損傷位置。基于損傷位置的確定對目標函數(shù)進行簡化,然后用遺傳算法極小化目標函數(shù),得到對應損傷位置的損傷程度。本文以連續(xù)梁為研究對象,分別建立了三種不同損傷工況下連續(xù)梁的有限元模型,用Lanczos法分析連續(xù)梁有限元模型,提取頻率和振型等模態(tài)參數(shù),對位移模態(tài)進行連續(xù)小波變換,得到小波系數(shù)圖,然后由系數(shù)圖的模極大值點確定了損傷的位置。用振型和頻率的誤差函數(shù)加權來定義目標函數(shù),在損傷位置確定的基礎上對目標函數(shù)的未知量進行簡化,最后用遺傳算法極小化目標函數(shù),以得到連續(xù)梁的損傷程度。結果驗證了本文的方法不僅能有效識別損傷的位置而且能夠準確識別損傷的程度,該方法對梁的損傷識別具有重要的指導意義。
[Abstract]:Engineering structure will be corroded by the external environment in the long-term use process, the material itself aging and fatigue load and other factors will damage, when the damage accumulates to a certain extent, it will affect the normal use of the structure. It may even cause the structure to collapse. Early detection and timely repair of these injuries can not only greatly reduce the maintenance and repair costs of the structure, but also prevent unnecessary loss of life and property. Therefore, the study of structural damage identification method has important theoretical significance and engineering application value. Based on the theory of wavelet analysis and genetic algorithm, wavelet analysis has the advantages of local analysis and zoom in time-frequency domain. Genetic algorithm has the characteristics of good self-organization, self-adaptation, parallelism and strong global search ability. In this paper, the advantages of these two methods are combined organically, the concept of wavelet genetic algorithm is put forward, and a wavelet genetic algorithm which can identify the damage location and the damage degree of the structure is established. Firstly, based on the finite element analysis to solve the modal of the structure, the continuous wavelet transform is made with db wavelet, and the damage position is identified by the modulus maximum of the wavelet coefficient. Then the element stiffness reduction coefficient is taken as the optimization variable of genetic algorithm, the objective function is constructed by weighted error function of mode and frequency, and the variable of objective function is simplified by determining the damage position. Then the objective function is minimized by genetic algorithm to determine the damage degree of the structure. In this paper, a simple supported beam is taken as an example to test the effectiveness of the method with small damage, large damage and different damage degree in different positions. The finite element model of simply supported beam with damage is established. Modal analysis of the finite element model is carried out to obtain modal parameters such as frequency and mode shape, and wavelet coefficients are obtained by continuous wavelet transform of displacement mode. According to the modulus maximum of wavelet coefficient graph, the damage position of simply supported beam is determined. The objective function is simplified based on the determination of the damage location, and the damage degree of the corresponding damage position is obtained by minimizing the objective function with genetic algorithm. In this paper, three finite element models of continuous beam under different damage conditions are established. The finite element model of continuous beam is analyzed by Lanczos method. The modal parameters such as frequency and mode are extracted, and the displacement mode is transformed by continuous wavelet transform. The wavelet coefficient graph is obtained, and then the damage position is determined by the modulus maximum of the coefficient graph. The objective function is defined by weighted error function of mode and frequency. The unknown quantity of the objective function is simplified on the basis of determining the damage position. Finally, the objective function is minimized by genetic algorithm to obtain the damage degree of continuous beam. The results show that the proposed method can not only effectively identify the location of the damage but also accurately identify the degree of damage. This method has important guiding significance for the damage identification of the beam.
【學位授予單位】：長沙理工大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TU317
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本文編號：1890240