What is Signal Spectra

We investigate the application of artificial neural networks (ANNs) to the classification of spectra from impact-echo signals. In this paper we provide analyses from simulated signals and the second part paper details results of lab experiments. The data set for this research consists of sonic and ultrasonic impact-echo signal spectra obtained from 100 3D-finite element models. These spectra, along with a categorization of the materials among homogeneous and defective classes depending on the kind of material defects, were used to develop supervised neural network classifiers. Four levels of complexity were proposed for classification of materials as: material condition, kind of defect, defect orientation and defect dimension. Results from Multilayer Perceptron (MLP) and Radial Basis Function (RBF) neural networks with Linear Discriminant Analysis (LDA), and k-Nearest Neighbours (kNN) algorithms (Duda, Hart, & Stork, 2000), (Bishop C.M., 2004) are compared. Suitable results for LDA and RBF were obtained. The impact-echo is a technique for non-destructive evaluation based on monitoring the surface motion resulting from a short-duration mechanical impact. It has been widely used in applications of concrete structures in civil engineering. Cross-sectional resonant modes in impact-echo signals have been analyzed in elements of different shapes, such as, circular and square beams, beams with empty ducts or cement fillings, etc. In addition, frequency analyses of the displacement of the fundamental frequency to lower values for detection of cracks have been studied (Sansalone & Street, 1997), (Carino, 2001). The impact-echo wave propagation can be analyzed from transient and stationary behaviour. The excitation signal (the impact) produces a short transient stage where the first P (normal stress), S (shear stress) and Rayleigh (superficial) waves arrive to the sensors; afterward the wave propagation phenomenon becomes stationary and a manifold of different mixtures of waves including various changes of S-wave to P-wave propagation mode and viceversa arrive to the sensors. Patterns of waveform displacements in this latter stage are known as the resonant modes of the material. The spectra of impact-echo signals provide of information for classification based on resonant modes the inspected materials. The classification tree approached in this paper has four levels from global to detailed classes with up to 12 classes in the lowest level. The levels are: (i) Material condition: homogeneous, one defect, multiple defects, (ii) Kind of defect: homogeneous, hole, crack, multiple defects, (iii) Defect orientation: homogeneous, hole in axis X or axis Y, crack in planes XY, ZY, or XZ, multiple defects, and (iv) Defect dimension: homogeneous, passing through and half passing through types of holes and cracks of level iii, multiple defects. Some examples of defective models are in Figure 1.