An efficient method to reduce ill-posedness for structural dynamic load identification

• Published in: Mechanical systems and signal processing Vol. 95; pp. 273 - 285
• Main Authors: Liu, Jie, Meng, Xianghua, Zhang, Dequan, Jiang, Chao, Han, Xu
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 01-10-2017; Elsevier BV
• Subjects: Decomposition; Finite element analysis; Finite element method; Ill posed problems; Ill-posedness; Interpolation; Interpolation function; Inverse problems; Kernel functions; Load; Load history; Load identification; Mathematical analysis; Matrix; Regularization; Singular value decomposition; Stability; Time element; Well posed problems; Load identification; Time element; Ill-posedness; Interpolation function; Singular value decomposition
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2017.03.039

•A new method for dynamic load identification is proposed.•Dynamic load in each time element is approximated by shape function.•Accuracy is improved and the ill-podedness is decreased effectively.•Direct inverse operation can be adopted with better identified results.
For the inverse problem of structural dynamic load identification, high system ill-posedness is a main cause leading to instability and low accuracy. In this study, an efficient interpolation-based method is proposed to reduce ill-posedness availably and identify dynamic load stably. The load history is discretized into a series of time elements, and the load profile in each time element is approximated through interpolation functions. Then, in the whole time domain, the dynamic responses under interpolation function loads are calculated through a few finite element analysis and then assembled together to form a global kernel function matrix for load identification. Using singular value decomposition (SVD), the ill-posed degree of the global kernel function matrix can be analyzed. Compared with the conventional Green kernel function method (GKFM), the ill-posedness of global kernel function matrix in the proposed method is significantly reduced. Especially, when the length of time element is selected appropriately, the global kernel function matrix is entirely well-posed and the corresponding dynamic load can be stably identified without any regularization operation. Numerical examples demonstrate the effectiveness of the proposed method and the correctness of identified load.