结构损伤识别的小波—遗传算法研究

发布时间：2018-05-15 00:45

  本文选题：小波分析 + 遗传算法　； 参考：《长沙理工大学》2014年硕士论文

【摘要】：工程结构在长期使用过程中受到外界环境腐蚀、材料自身老化以及疲劳荷载等因素的作用会发生损伤,当损伤积累到一定程度时会影响结构的正常使用,甚至可能导致结构的倒塌。尽早的发现并及时的修复这些损伤,不仅能够大大减少结构的维护、维修费用,还可以预防不必要的生命财产损失。因此,研究结构损伤识别方法具有重要的理论意义和工程应用价值。本文以小波分析和遗传算法理论为基础,小波分析在时频两域上有着优越的局部分析特性和变焦特点,遗传算法具有很好自组织、自适应、并行性和全局搜索能力强等特点,本文将这两者的优点进行有机的结合,提出了小波-遗传算法的概念,建立了一种既能识别结构损伤位置又能确定损伤程度的小波遗传算法。首先以有限元分析求解结构振型模态为基础,用db小波做连续小波变换,由小波系数模极大值识别损伤的位置。然后以单元刚度折减系数为遗传算法的优化变量,用振型和频率的误差函数加权来构造目标函数,并通过损伤位置的确定来简化目标函数的变量,再用遗传算法对目标函数进行极小化,从而确定结构的损伤程度。本文以简支梁为例,分别用小损伤、大损伤和不同位置不同损伤程度的损伤来检验该方法的有效性。建立含损伤简支梁的有限元模型,对有限元模型进行模态分析以得到频率和振型等模态参数,将位移模态进行连续小波变换得小波系数图,根据小波系数图的模极大值点确定了简支梁的损伤位置。基于损伤位置的确定对目标函数进行简化,然后用遗传算法极小化目标函数,得到对应损伤位置的损伤程度。本文以连续梁为研究对象,分别建立了三种不同损伤工况下连续梁的有限元模型,用Lanczos法分析连续梁有限元模型,提取频率和振型等模态参数,对位移模态进行连续小波变换,得到小波系数图,然后由系数图的模极大值点确定了损伤的位置。用振型和频率的误差函数加权来定义目标函数,在损伤位置确定的基础上对目标函数的未知量进行简化,最后用遗传算法极小化目标函数,以得到连续梁的损伤程度。结果验证了本文的方法不仅能有效识别损伤的位置而且能够准确识别损伤的程度,该方法对梁的损伤识别具有重要的指导意义。
[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.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU317
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本文编号：1890240