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Description
The main objective of this work is to analyze damage detection in certain steel lattice structures using the Discrete Wavelet Transform (DWT) [1]. A structural response signal of a considered structure may be considered as a discrete set of static or dynamic displacements, which can be processed further using this DWT. It allows for high accuracy and high-resolution estimation of possible structural weaknesses such as cracks, micro-failures, or aging (corrosion) stiffness reductions. The one-dimensional wavelet transform will be used, and dynamic excitation will follow the spectrum of the Bucharest earthquake in 1986 [2]. The Finite Element Method (FEM) approach would allow for the structural response numerical recovery. The location of the weakened parts of the structure may have a random character and can be identified by the wavelet function parameters. A finite set of deterministic FEM solutions would enable for the Least Squares Method (LSM) approximation of the structural responses and its polynomial form with respect to the given uncertainty sources. Then, assuming a continuous probability distribution of the occurrence of a given random feature as Gaussian, probabilistic moments [3,4] and relative entropies [5] of the structural deformations are determined using three alternative probabilistic methods: semi-analytical direct integration method, Monte-Carlo simulation, and Stochastic Perturbation Technique (SPT).
References
[1] A. Knitter-Piątkowska, M. Guminiak, M. Przychodzki. Application of Discrete Wavelet Transformation to defect detection in truss structures with rigidly connected bars. Engineering Transactions. 2016; 64(2): 157–170.
[2] Axis VM, https://gammacad.pl/axisvm.
[3] Kamiński M., Lenartowicz A., Guminiak M., Przychodzki M. Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers. Materials. 2022, 15(19): 6811
[4] Kamiński M. On iterative scheme in determination of the probabilistic moments of the structural response in the Stochastic perturbation-based Finite Element Method. International Journal for Numerical Methods in Engineering. 2015; 104(11):1038–1060.
[5] Bhattacharyya A. On a measure of divergence between two multinomial populations. Indian J. Stat. 7:401–406, 1946, https://doi.org/10.1038/157869b0.
