Wu Zhifeng, Huang Bin, Tee Kong Fah, Zhang Weidong
School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China.
School of Engineering, University of Greenwich, Kent ME4 4TB, UK.
Sensors (Basel). 2021 Mar 29;21(7):2366. doi: 10.3390/s21072366.
This paper proposes a new damage identification approach for beam structures with stochastic parameters based on uncertain static measurement data. This new approach considers not only the static measurement errors, but also the modelling error of the initial beam structures as random quantities, and can also address static damage identification problems with relatively large uncertainties. First, the stochastic damage identification equations with respect to the damage indexes were established. On this basis, a new homotopy analysis algorithm was used to solve the stochastic damage identification equations. During the process of solution, a static condensation technique and a L1 regularization method were employed to address the limited measurement data and ill-posed problems, respectively. Furthermore, the definition of damage probability index is presented to evaluate the possibility of existing damages. The results of two numerical examples show that the accuracy and efficiency of the proposed damage identification approach are good. In comparison to the first-order perturbation method, the proposed method can ensure better accuracy in damage identification with relatively large measurement errors and modelling error. Finally, according to the static tests of a simply supported concrete beam, the proposed method successfully identified the damage of the beam.
本文基于不确定的静态测量数据，提出了一种针对具有随机参数的梁结构的新型损伤识别方法。这种新方法不仅考虑了静态测量误差，还将初始梁结构的建模误差视为随机量，并且能够解决具有较大不确定性的静态损伤识别问题。首先，建立了关于损伤指标的随机损伤识别方程。在此基础上，采用一种新的同伦分析算法来求解随机损伤识别方程。在求解过程中，分别采用静态凝聚技术和L1正则化方法来处理有限的测量数据和不适定问题。此外，还提出了损伤概率指标的定义，以评估现有损伤的可能性。两个数值算例的结果表明，所提出的损伤识别方法的精度和效率良好。与一阶摄动法相比，该方法在具有较大测量误差和建模误差的损伤识别中能够确保更好的精度。最后，根据简支混凝土梁的静态试验，该方法成功识别了梁的损伤。
