Extraction of Opening and Closing States of Cracked Structure using Adaptive Volterra Filter Model

What is it about?

Fatigue cracks often exist in structures during the service life of the structure and need to detect at its earliest stage before it leads to catastrophic failure. The fatigue breathing crack problem exhibits an instantaneous change in the stiffness of the structure due to change in the state of the cracked domain from open to close and vice versa. Therefore these fatigue cracks exhibit breathing like phenomena, hence widely referred as breathing cracks. The present work attempts to separate the opening and closing of the cracked structure from the global response using adaptive Volterra Filter Model. Adaptive Volterra Filter model is a generalization of the linear convolution and the impulse response function to nonlinear structures in discrete form. The dynamical properties of the nonlinear system in the Volterra series representation or adaptive Volterra Filter Model are completely characterized by a sequence of multi-dimensional weighting function called Volterra kernels. These Volterra kernels are the backbone of adaptive Volterra filter approach in nonlinear analysis and system identification and diverse range of techniques are reported in the literature for Volterra kernel estimation. Adaptive Volterra series based Least square is used in the present work to estimate Volterra kernels. The various states of the cracked structure are then estimated using these Volterra kernels. Numerical simulation studies are carried out on a simple beam example to demonstrate the capability of the proposed adaptive Volterra filter in extracting the opening and closing state response from the global response of the cracked structure.

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