随机激励下用分形维数曲率差概率法定位损伤

Damage Localization Based on the Curvature Difference Probability Method of Waveform Fractal Dimension with Stochastic Excitation

针对简支梁提出了脉冲或阶跃激励下基于分形维数波形曲率差概率的损伤定位方法,然而在工程中这类激励有较大的局限性,为此,研究了方法在基底承受随机激励的结构上的适用性。从分形理论入手提取结构加速度的特征量,结合曲率差法对各测点特征量进行处理,最后引入多次识别结果的统计分析值(损伤概率)作为损伤判断和定位依据。基于最基本的质量-弹簧-阻尼系统模拟研究了某20自由度系统在基底白噪声激励下的单、多损伤工况,设计、建造一个6层集中质量框架模型,并基于它的振动台试验进行验证。结果表明,基底随机激励下该法能准确地对结构损伤进行定位,具有非常好的抗噪性,并且该法不需要结构有限元模型。

The author′s previous work proposed the curvature difference probability method of the waveform fractal dimension for a simply supported beam with pulse or step excitation.However,such excitation methods suffer from limitations in engineering.The main purpose of this paper is to study the method′s applicability to the structures excited by stochastic excitation at their bases.Firstly,the characteristic value of the acceleration signal is extracted based on the fractal dimension.Then,the curvature difference method is used to deal with these characteristic values.Finally,the statistic value from multiple identifications(i.e.damage probability)is determined as the index to identify and locate the damage.Based on the most basic system,i.e.the mass-spring-damper(MSD)system,many single and multiple damage cases of a 20 DOF MSD system with white noise excitation at the base are studied.Furthermore,a 6-story lumpedmass shear frame model is built in the laboratory,and experimental cases based on the shaking table are also implemented.Results show that the proposed technique can locate the damage very well with the stochastic excitation at the base of the structure,and has very strong robustness against the noise(it still works at a 15% noise level).Morever,the technique has low dependence on the accuracy of the structural finite element model.All of these lay agood foundation for its applications in engineering.