含区间参数不确定结构的损伤识别方法

针对损伤识别中遇到的含统计信息不足的不确定参数的结构，以区间向量来描述其中的不确定参数。基于有限元理论给出了应变模态的测试方法，进一步将应变模态表示为区间参数的函数，结合一阶Taylor展开与区间分析，计算了参数不确定条件下应变模态的界限，给出了一种考虑参数不确定的结构损伤识别方法，并在理论上对比分析了与基于概率方法的区别与联系。为验证方法的合理性，对简支梁在不同位置损伤的情况进行了数值模拟，分析了不同损伤程度以及参数不同不确定程度下简支梁应变模态的变化规律，简要讨论了噪声对识别准确性的影响。为含不确定参数的结构的损伤识别提供了一种新的方法和思路。 

Damage detection of structures with interval uncertain parameters

To deal with structures with uncertain parameter which often lacks sufficient statistical information in damage detection, the uncertain parameters were modeled as interval numbers. The structural strain modal testing method was introduced using finite element method, and the strain modal was further expressed as the function of the interval parameter. Combined with the first order Taylor expansion and interval analysis, the range of each strain modal under parameter uncertainty is estimated, and thus we obtained an approach for structural damage detection considering uncertainty. Comparison between the proposed method and the traditional probabilistic method was conducted. Numerical simulations of a simply supported beam under different damage were performed by investigating the change of strain modes due to different damage levels and uncertainty levels. The influence rules of damage and uncertainty on strain modal were obtained, and a brief discussion of the impact of noise on damage detection was performed. The work of this paper provides a new technique and thought for damage detection of uncertain structures.