Integrated Computer-Aided Engineering 12 (2005) 147–158 147 IOS Press Local discriminant bases in machine fault diagnosis using vibration signals R. Tafreshi a , F. Sassani a,∗ , H. Ahmadi b,c and G. Dumont b a Department of Mechanical Engineering, The University of British Columbia, Vancouver,BC, V6T 1Z4, Canada E-mail: {tafreshi, sassani}@mech.ubc.ca b Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, BC, V6T 1Z4, Canada E-mail: {ahmadi, guyd}@ece.ubc.ca c Department of Electrical Engineering, University of Tehran, Iran Abstract. Wavelets and local discriminant bases (LDB) selection algorithm is applied to vibration signals in a single-cylinder spark ignition engine for feature extraction and fault classification. LDB selects a complete orthogonal basis from a wavelet packet library of bases, which best discriminates the given classes, based on their time-frequency energy maps. An appropriate normalization method in both data and wavelet coefficient domains, and a neural network classifier during the identification phase are used to enhance the classification. By applying LDB to a real-world machine data the accuracy of the algorithm in machine fault diagnosis and classification is shown. 1. Introduction Fault detection and quantification problems may be analyzed within the scope of pattern recognition prob- lems whose goal is to classify objects or patterns into a number of categories or types. Often, signals acquired for use in a fault detection process cannot be used di- rectly in a given classification problem, they need to be preprocessed for order reduction and for feature ex- traction. Preprocessing attempts to associate each class of signals with a certain pattern (signature) that can be used as a feature for classification. In addition, in clas- sification problems, not only we look for features that contain non-superfluous information but also we seek information that can separate classes from each other as distinctly as possible. This type of information is re- ferred to as “discriminant” features of the given signal. Usually, it is the superfluous information that makes the classification a difficult task. The main objective in feature extraction and classification problems is to find ∗ Corresponding auhtor. a coordinate system for projecting the signal along its axes that yields high discriminatory information resid- ing on a few axes with insignificant information along most axes. Figure 1 shows main stages of classifica- tion in which X is input signal, Y , corresponding class label (e.g. faulty or healthy conditions), and F , feature space, which is the discriminant subspace of reduced dimension (m<n). It is computationally more effi- cient to analyze the data in a discriminant subspace of lower dimension. Classification goal is to determine which class a given data X belongs to by constructing a feature space F that provides the highest discriminant information among all classes. This paper deals with the analysis of cylinder-head acceleration data for engine diagnosis and fault de- tection. Vibration signals of a machine always carry information about its dynamic behavior; they can be used to identify faults in machine operation. Vibra- tion signals in internal combustion engines are charac- terized as being transient, time variant and extremely noisy. Wavelets are considered to be highly suitable for the analysis of transient signals for feature extraction used in fault detection problems. An algorithm using ISSN 1069-2509/05/$17.00  2005 – IOS Press and the author(s). All rights reserved