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Index of homogeneity for a criterion judging existence of cracks

This paper presents a crack characterization method by spatio-temporal gradient analysis over the Lamb wave field. The guided ultrasound waves that propagate in the direction of the layer are a potential candidate of non-destructive testing (NDT) methodology. The proposed method has an ability to classify the surface acoustic wave field through the rank of the covariance matrix defined over the 4-dimensional vector space which is spanned by following components: a vertical displacement, its vertical velocity, and a pair of shear strains of the surface. The covariance matrix provides the information about cracks. This study, therefore, proposes an index of homogeneity of the object surface based on the determinant of the covariance matrix.