智能材料损伤检测的多重分形应用

The Application of Multi-fractal on Diagnosis of Smart Material Structures

多重分形谱所蕴含的信息比单一的分数维要深刻而全面,在解决实际问题中多重分形主要用来描述物理量不均匀的随机概率分布。在智能复合材料有损伤前后其内部受力的空间分布发生变化,利用多重分形方法将其量化,多重分形谱从平缓到陡峭的变化反映了分形结构复杂性的增加和材料内部应力分布不均匀性的增加。数据仿真计算结果和对在一块埋置有5×5传感光纤的复合材料试件实测数据的计算结果表明该方法的有效性与实用性。

The implication of multi-fractal spectrum is more profound and with profusion of information than the simply fractal dimension. The multi-fractal spectrum of space distribution of interior strain changes from central- ized to loose indicates that complexity of damage fractal structure and the inhomogeneity of space distribution are both increasing. The physical essence of multi-fractal spectrums before and after the damage of smart materials and structures occurrence is a ever-changing process from homogeneous to inhomogeneous, from simple to com- plex. The calculated result upon the data of a specimen, into which fiber sensors network is embedded and its size is 5×5, indicates that the diagnosis method is reliable and practical.