Abstract
We study the application of artificial neural networks (ANNs) to the classification of spectra from impact-echo signals. In this paper we focus on analyses from experiments. Simulation results are covered in paper I. Impact-echo is a procedure from Non-Destructive Evaluation where a material is excited by a hammer impact which produces a response from the material microstructure. This response is sensed by a set of transducers located on material surface. Measured signals contain backscattering from grain microstructure and information of flaws in the material inspected (Sansalone & Street, 1997). The physical phenomenon of impact-echo corresponds to wave propagation in solids. When a disturbance (stress or displacement) is applied suddenly at a point on the surface of a solid, such as by impact, the disturbance propagates through the solid as three different types of stress waves: a P-wave, an S-wave, and an R-wave. The P-wave is associated with the propagation of normal stress and the S-wave is associated with shear stress, both of them propagate into the solid along spherical wave fronts. In addition, a surface wave, or Rayleigh wave (R-wave) travels throughout a circular wave front along the material surface (Carino, 2001). After a transient period where the first waves arrive, wave propagation becomes stationary in resonant modes of the material that vary depending on the defects inside the material. In defective materials propagated waves have to surround the defects and their energy decreases, and multiple reflections and diffraction with the defect borders become reflected waves (Sansalone, Carino, & Hsu, 1998). Depending on the observation time and the sampling frequency used in the experiments we may be interested in analyzing the transient or the stationary stage of the wave propagation in impact- echo tests. Usually with high resolution in time, analyzes of wave propagation velocity can give useful information, for instance, to build a tomography of a material inspected from different locations. Considering the sampling frequency that we used in the experiments (100 kHz), a feature extracted from the signal as the wave propagation velocity is not accurate enough to discern between homogeneous and different kind of defective materials. The data set for this research consists of sonic and ultrasonic impact-echo signal (1-27 kHz) spectra obtained from 84 parallelepiped-shape (7x5x22cm. width, height and length) lab specimens of aluminium alloy series 2000. These spectra, along with a categorization of the quality of materials among homogeneous, one-defect and multiple-defect classes were used to develop supervised neural network classifiers. We show that neural networks yield good classifications (
TopIntroduction
We study the application of artificial neural networks (ANNs) to the classification of spectra from impact-echo signals. In this paper we focus on analyses from experiments. Simulation results are covered in paper I.
Impact-echo is a procedure from Non-Destructive Evaluation where a material is excited by a hammer impact which produces a response from the material microstructure. This response is sensed by a set of transducers located on material surface. Measured signals contain backscattering from grain microstructure and information of flaws in the material inspected (Sansalone & Street, 1997). The physical phenomenon of impact-echo corresponds to wave propagation in solids. When a disturbance (stress or displacement) is applied suddenly at a point on the surface of a solid, such as by impact, the disturbance propagates through the solid as three different types of stress waves: a P-wave, an S-wave, and an R-wave. The P-wave is associated with the propagation of normal stress and the S-wave is associated with shear stress, both of them propagate into the solid along spherical wave fronts. In addition, a surface wave, or Rayleigh wave (R-wave) travels throughout a circular wave front along the material surface (Carino, 2001).
After a transient period where the first waves arrive, wave propagation becomes stationary in resonant modes of the material that vary depending on the defects inside the material. In defective materials propagated waves have to surround the defects and their energy decreases, and multiple reflections and diffraction with the defect borders become reflected waves (Sansalone, Carino, & Hsu, 1998). Depending on the observation time and the sampling frequency used in the experiments we may be interested in analyzing the transient or the stationary stage of the wave propagation in impact-echo tests. Usually with high resolution in time, analyzes of wave propagation velocity can give useful information, for instance, to build a tomography of a material inspected from different locations. Considering the sampling frequency that we used in the experiments (100 kHz), a feature extracted from the signal as the wave propagation velocity is not accurate enough to discern between homogeneous and different kind of defective materials.
The data set for this research consists of sonic and ultrasonic impact-echo signal (1-27 kHz) spectra obtained from 84 parallelepiped-shape (7x5x22cm. width, height and length) lab specimens of aluminium alloy series 2000. These spectra, along with a categorization of the quality of materials among homogeneous, one-defect and multiple-defect classes were used to develop supervised neural network classifiers. We show that neural networks yield good classifications (<15% error) of the materials in four levels of classification detail as material condition, kind of defect, defect orientation and defect dimension. Results for Multilayer Perceptron (MLP) and Radial Basis Function (RBF) neural networks, Linear Discriminant Analysis (LDA), and k-Nearest Neighbours (kNN) algorithms (Duda, Hart, & Stork, 2000), (Bishop C.M., 2004) are presented. Figure 1 shows the scheme of categories proposed as a hierarchical layout with different levels of knowledge on the material defects (the percentage of success in classification is explained in Experimental Result section).
Figure 1. Classification tree with percentages of success in classification by RBF network. Numbers in brackets are results for simulations (paper I). General results are weighted by class probability since classes are not equally-probable.
TopBackground
The phenomenon of volumetric wave propagation in impact-eco can be modelled by means of the following two equations (Cheeke J.D., 2002),
(1) (2) where
Key Terms in this Chapter
Dimensionality Reduction: A process to reduce the number of variables of a problem. Dimension of a problem is given by the number of variables (features or parameters) that represent the data. After signal feature extraction (that reduce the original signal sample space), the dimensionality may be reduced more by feature selection methods.
Signal Conditioner (SC): A device that converts one type of electronic signal into another type of signal. Its primary use is to convert a signal that may be difficult to read by conventional instrumentation into a more easily read format. Typical SC functions are amplification, electrical isolation, and linearization.
Leave-One-Out: A method used in classification with the following steps: i.) Label the database cases with the known classes. ii.) Select a case of the database. iii.) Estimate the class for selected case by a classifier using the remaining cases as training data. iv.) Repeat steps ii and iii until the end of the cases. v.) Calculate the mean percentage of success for classification results.
Accelerometer: A device that measures acceleration which is converted into an electrical signal that is transmitted to signal acquisition equipment. In impact-echo testing, the measured acceleration refers to vibration displacements caused by the excitation of the short impact.
Feature Extraction (FE): A process to map a multidimensional space into a space of fewer dimensions. In signal processing, instead of processing raw signals with thousands of samples is more efficient to process features extracted from the signals, such as, signal power, principal frequency, and attenuation coefficient.
Feature Selection (FS): A technique that selects a subset of features from a given set of features that represent the relevant properties of the data. FS also may be define as the task of choosing a small subset of features which is sufficient to predict the target labels well, is crucial for efficient learning. There are several FS methods based on margins (e.g., relief, simba) or information theory (e.g., infogain). Supervised FS methods use a priori knowledge on a classification variable, to select variables high correlated with the known variable.
Fast Fourier Transform (FFT): A class of algorithms used in digital signal processing to compute the Discrete Fourier Transform (DFT) and its inverse. It has the capability of taking functions from the time domain to the frequency domain. The frequency components obtained are the spectra of the signal.