Morphological processing of proper orthogonal modes for crack detection in beam structures

A two-step approach for crack detection in beam structures is presented. As a first step, a number of proper orthogonal modes (POMs) of a beam are extracted, using proper orthogonal decomposition, a powerful and elegant method (closely related to principal component analysis) aimed at obtaining low-dimensional approximations of high-dimensional processes, taking into account nonlinearities and minimizing noise effects. Then, alternatively to other approaches, morphological processing is proposed for the further processing of the POMs. The basic concept of morphological processing is to modify the shape of an object by transforming it through its interaction with another object, called the structuring element. Using an appropriate morphological processing procedure, the position and the depth of the cracks can be estimated by isolating the sudden local change effect of the cracks on the spatial variation of the shape of each POM. For this purpose, the four basic morphological operators (dilation, erosion, opening, closing) are compared, using two different types of structuring elements. The erosion operator with a spline structuring element is shown to present the best results. Finally, the performance of the method is assessed on different beam structures affected by breathing cracks, with respect to the influence of several factors, such as boundary conditions, crack location, crack depth, crack distance, measurement noise level and space resolution of measurement points. In all cases, the method presents a robust behavior.