基于逆有限元的应变模态损伤检测方法
Strain Modal Method for Damage Detection Based on iFEM

基于光纤光栅传感器(fiber Bragg grating,简称FBG)逆有限元方法(inverse finite element method,简称iFEM)，仅利用有限测点的应变数据进行全域应变场重构，得到近似完全测量应变模态，提高了直接采用实测应变数据来构建应变模态损伤指标的实用性。利用基于损伤应变模态差分原理的损伤指标法，只需用损伤后应变模态数据即能定位损伤，并给出了损伤指标数学模型。计算结果表明，基于光纤光栅传感器和逆有限元方法可以快速进行全域应变场重构，为基于应变模态的损伤检测提供数据保障，而应变模态差分曲线只在损伤处发生剧烈变化，损伤程度不同，曲线突变程度略有不同但规律一致。最后以某板的实验结果证明了该方法的有效性。
While the strain modal index method is commonly used in damage detection, current damage indices based on strain often need complete measured modes and modal parameters before and after damage, both of which are difficult to obtain in practical engineering. We combined the fiber Bragg grating (FBG) sensor and inverse finite element method (iFEM) in order to reconstruct the global strain field based on measured strain data of limited points. We acquired an approximate complete measured mode based on the global strain field. Thus, the strain modal damage index has a natural advantage in directly making use of strain. Then, we proposed a direct damage detection index based on strain model shape, which could locate damage with only the strain modal data after injury and did not require data before damage. The calculation results showed that the global strain field could be reconstructed quickly based on FBG and iFEM, thus supporting damage detection based on the strain modal method. In the strain modal difference curve, the positive and negative changes occurred at damage locations besides the constrained point, and the mutation degree was slightly different than damage degree, but the pattern was similar. In addition, the proposed direct damage detection index had nothing to do with the model order after regularization. The results of the actual plate experiment also validated the proposed method.