针对连续小波变换与Lipschitz指数在识别信号奇异性上的优越性，以裂缝模拟桥梁损伤，提出基于小波变换与Lipschitz指数的损伤识别方法。对损伤结构位移模态进行小波变换，用小波系数灰度图及模极大值轨迹图进行损伤定位，并用Lipschitz指数评价损伤程度。理论推导裂缝梁的Lipschitz指数范围，并数值计算验证该方法识别结构裂缝损伤的有效性。考察Euler梁及Timoshenko梁、不同程度损伤、多位置损伤、稀疏测点布置及噪声测试等多种因素对损伤识别效果影响。
Abstract
The Continuous Wavelet Transform and Lipschitz exponent perform well in detecting signal singularity. With the bridge damage modeled as cracks, the damage identification method based on wavelet transform and Lipschitz exponent is proposed. With the Wavelet Transform is applied to structural displacement mode, the damage can be located by the contour plot and the locus of modulus maximum of wavelet coefficients. The range of Lipschitz exponent of cracked beam is derived theoretically. Numerical examples show that this method can identify the damage effectively. Furthermore, some influence factors such as Euler and Timoshenko beam, different damage extents, multiple damage, sparse measure points and test noise are studied.
关键词
小波变换 /
Lipschitz指数 /
奇异性 /
损伤识别 /
位移模态
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Key words
wavelet transform /
lipschitz exponent /
singularity /
damage identification /
displacement mode
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