Abstract
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.
TopIntroduction
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.
Figure 1. Finite element models with different defects and 7-sensor configuration
TopBackground
Neural networks applications in impact-echo testing include: detect flaws on concrete slabs, combining spectra of numerical simulations and real signals for network training (Pratt & Sansalone, 1992), identification of unilaterally working sublayer cracks using numerically generated waveforms as network inputs (Stavroulakis, 1999), classification of concrete slabs in solid and defective (containing void or delamination), use of training features extracted from many repetitions of impact-echo experiments on three specimens to be classified in three classes (Xiang & Tso, 2002), and to predict shallow crack depths in asphalt pavements using features from an extensive real signal dataset (Mei, 2004). All these studies used multilayer perceptron neural network and monosensor impact-echo systems.
Key Terms in this Chapter
Artificial Neural Network (ANN): A mathematical model inspired in biological neural networks. The units are called neurons connected in various input, hidden and output layers. For a specific stimulus (numerical data at the input layer) some neurons are activated following an activation function and producing numerical output. Thus ANN is trained, storing the learned model in weight matrices of the neurons. This kind of processing has demonstrated to be suitable to find nonlinear relationships in data, being more flexible in some applications than models extracted by linear decomposition techniques.
Principal Component Analysis (PCA): A method for achieving a dimensionality reduction. It represents a set of N-dimensional data by means of their projections onto a set of r optimally defined axes (principal components). As these axes form an orthogonal set, PCA yields a data linear transformation. Principal components represent sources of variance in the data. Thus the most significant principal components show those data features which vary the most.
Pattern Recognition: An important area of research concerned to discover or identify automatically figures, characters, shapes, forms, and patterns without active human participation in the decision process. It is also related with classify data in categories. Classification consists in learning a model for separating the data categories, that kind of machine learning can be approached using statistical (parametric or no-parametric models) or heuristic techniques. If some prior information is given in learning process, it is called supervised or semi-supervised, else it is called unsupervised.
Non-Destructive Evaluation (NDE): NDE, ND Testing or ND Inspection techniques are used in quality control of materials. Those techniques do not destroy the test object and extract information on the internal structure of the object. To detect different defects such as cracking and corrosion, there are different methods of testing available, such as X-ray (where cracks show up on the film), ultrasound (where cracks show up as an echo blip on the screen) and impact-echo (cracks are detected by changes in the resonance modes of the object).
Finite Element Method (FEM): It is a numerical analysis technique to obtain solutions to the differential equations that describe, or approximately describe a wide variety of problems. The underlying premise of FEM states that a complicated domain can be sub-divided into a series of smaller regions (the finite elements) in which the differential equations are approximately solved. By assembling the set of equations for each region, the behavior over the entire problem domain is determined.
Signal Spectra: Set of frequency components decomposed from an original signal in time domain. There exist several techniques to map a function in time domain to frequency domain as Fourier and Wavelet transforms, and its inverse transforms that allow reconstructing the original signal.
Impact-Echo Testing: A non-destructive evaluation procedure based on monitoring the surface motion resulting from a short-duration mechanical impact. From analyses of the vibrations measured by sensors, a diagnosis of the material condition can be obtained.