基于DWT与零空间法的结构非线性检测  

Structural Non-Linearity Detection Based on the DWT and Null Space Method

作　　者：姜绍飞[1] 陈志刚[1] 麻胜兰 

机构地区：[1]福州大学土木工程学院,福建福州350108

出　　处：《沈阳建筑大学学报（自然科学版）》2016年第1期1-9,共9页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家自然科学基金项目(51278127);国家十二五科技支撑计划项目(2015BAK14B02);闽江学者特聘教授奖励计划项目

摘　　要：目的研究一种新的非线性状态检测策略,为判断结构状态类型提供新的理论依据.方法首先,对结构响应数据进行离散小波变换(DWT),获得低频响应信号;其次,用低频响应信号构建Hankel矩阵,并进行奇异值分解(SVD),以此划分零空间与非零空间;最后,研究提出了两个指标(theta和DON)进行非线性检测,并构造了相应的线性基准值(LL).通过非线性数值仿真和一个3层非线性框架试验进行了方法验证.结果结构处于线性状态时,theta明显小于其线性基准值(LL),DON基本为1;而当结构进入非线性状态时,theta明显大于LL,DON也明显大于1,且两个指标都随非线性程度增加而增大.结论所提方法能较好地用于结构非线性检测,具有较强鲁棒性和工程实用性.In order to provide theoretical references for detection of structural status in civil engineering,this paper proposed a novel structural non-linearity detection strategy based on the discrete wavelet transform（ DWT） and null space method. Firstly,the structural response was separated by DWT to obtain the approximate signal in low frequency band. Then,the obtained approximate signals were used to construct a Hankel matrix,which was decomposed by singular value decomposition（ SVD） to divide the null and non-null spaces. Finally,two new index,theta and DON,were proposed to detect the non-linearity; furthermore,a limit of linearity（ LL） was constructed. A numerical example and a laboratory test were conducted to verify effectiveness of the proposed method. Results show that theta is significantly less than its LL and DON is almost equal to 1 when thestructure is linear; in contrast,when the structure is nonlinear,both theta and DON are significantly larger than their LL and increase with the degree of non-linearity. Conclusion is that the proposed method is able to effectively detect the structural non-linearity,furthermore,the proposed method has excellent robustness and engineering practicability.

关 键 词：结构非线性检测 离散小波变换(DWT) 零空间法 非线性指标 

分 类 号：TU317[建筑科学—结构工程]