基于小波变换与 Lipschitz 指数的桥梁损伤识别研究

摘要

The continuous wavelet transform and Lipschitz exponent perform well in detecting signal singularity. With the bridge damage modeled as a crack failure a damage identification method based on wavelet transform and Lipschitz exponent was proposed.With the wavelet transform applied to structural modal displacement,the damage can be located in the light of the contour plot and the locus of maximum modulus of wavelet coefficients.The range of Lipschitz exponent of cracked beams was derived theoretically.Some numerical examples show that the method can identify the damage effectively.Furthermore,some influential factors such as the effect of Euler or Timoshenko beam,different damage extent,multiple damage,sparse measuring points arrangement and test noise were studied.%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。