J. Basic. Appl. Sci. Res. , 2(1)105-113, 2012 © 2012, TextRoad Publication ISSN 2090-4304 Journal of Basic and Applied Scientific Research www.textroad.com *Corresponding Author: Fereshteh Khalaj, Department of Statistics, Tehran North Branch, Islamic Azad University, Tehran, Iran Tel/Fax/Mob: +982144005339/+982144140491/+989124960689, Email: Khalaj82@gmail.com Engine Fault Diagnosis Decision-Making with Incomplete Information Using Dempster-Shafer Theory H.R Mostafaei 1 , M. Khalaj 2 , F. Khalaj 1,* , A.H. Khalaj 3, A. Makui 4 1 Department of Statistics, Tehran North Branch, Islamic Azad University, Tehran, Iran 2 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran 3 Department of management and accounting, EslamShahr Branch, Islamic Azad University, Tehran, Iran 4 Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran ______________________________________________________________________________________ ABSTRACT In this paper, a Demster-Shafer method is proposed for engine diagnosis with incomplete information that obtains from multi-sensor. We apply the Dempster-Shafer method to solve fault diagnosis problems based on incomplete matrix of engine condition that describes an aspect of N types of engine states (or faults) that provided by M sensor. Thus we make rational decision with respect to this matrix. On the base of DS theory, first we identify all possible focal elements from the incomplete matrix, and then the basic probability assignment of each focal element and the belief interval of each decision alternative are calculated to identify the fault states of engine. Preference relations among all decision alternatives about fault states are determined by comparing their belief intervals. Within this framework we proposed a new way for identify the basic probability assignment based on ambiguity measures associated with information obtained from each sensor. This measure is defined by Shannon’s entropy. A numerical example is studied to illustrate the detailed implementation process of the DS approach and demonstrate its potential applications in dealing with decision alternative about engine fault diagnosis problems with incomplete information. Keywords: Dempster-Shafer (DS) method; fault diagnosis; multi-diagnosis decision matrix; decision- alternative 1-INTROUDUCTION The performance of structures and principle of engines and mechanical systems deteriorates during their service life. Therefore, the ability to fault diagnosis of these systems is becoming increasingly important from both economic and life-safety viewpoints. Single sensor cannot reliably obtain all the information required for fault diagnosis, thus engine diagnostics is a typically multi-sensor fusion problem. A main question in fault diagnosis technique is, precise and reliable information that cues about potential faults by incorporating complementary, and possibly redundant, multiple sensors [1]: There has been a substantial amount of research work that conducted in the area of decision fusion with regard to making more reasonable inferences based on multi-sensor information. Most of these methods to fault diagnosis are built around Artificial neural network (ANN), Bayes theory, fuzzy logic inference and Dempster–Shafer evidence theory (DS theory) [2]. ANN based technique for fault diagnosis have been evolving in fields such as: combine the pressure, sound and vibration features to detect the faults of a diesel engine that is reported by Sharkey et al. [3], fault diagnosis method by the use of extract features from data acquired from multiple sensors attached on a helicopter gearbox based on fuzzy neural network that is reported by Eassawy [4], a data fusion method of ANN combined with wavelet analysis for structural damage detection is proposed by Xiao et al. [5]. For Bayesian inference techniques for fault diagnosis, we can refer to Dromigny and Zhu [6] who improve the dynamic range of a real-time X-ray imaging system by integration information acquired under two different acquisition conditions. Lucas [7] is used Bayesian network and logical reasoning to minimize decision uncertainty of fault diagnosis. M.A. Rodrigues and et al. [8–12] used the Bayesian network to combine probabilistic reasoning with time dependent. Beck and his partners have series of research on Bayesian probabilistic framework for structural modal updating and damage identification For fuzzy logic inference, on-line health monitoring system for hydraulic pumps was propose by Amin et al. [13] that utilizes feature extraction, based on fuzzy inference systems and knowledge fusion. 105