Engineering Applications of Artificial Intelligence 20 (2007) 912–923 Fault detection in catalytic cracking converter by means of probability density approximation Krzysztof Patan à , Jo´zef Korbicz Institute of Control and Computation Engineering, University of Zielona Go´ra, ul. Podgo´rna 50, 65-246 Zielona Go´ra, Poland Received 10 December 2006; accepted 20 December 2006 Available online 2 March 2007 Abstract The paper deals with a model-based fault diagnosis for a catalytic cracking converter process realized using artificial neural networks. Modelling of the considered process is carried out by using a locally recurrent neural network. Decision making about possible faults is performed using statistical analysis of a residual. A neural network is applied to density shaping of a residual. After that, assuming a significance level, a threshold is calculated. The proposed approach is tested on the example of a catalytic cracking converter at the nominal operating conditions as well as in the case of faults. r 2007 Elsevier Ltd. All rights reserved. Keywords: Identification; Neural network; Fault diagnosis; Density shaping; Decision making 1. Introduction Fault diagnosis becomes an important issue in modern control systems due to their increasing complexity. Mal- functions of plant components, equipments or sensors could reduce production efficiency, damage of equipment, lead to plant shut downs. An early diagnosis of faults that might occur in the supervised process, renders it possible to perform important preventing actions. Moreover, it allows one to avoid heavy economic losses involved in stopped production, replacement of elements and parts, etc. Various approaches to fault diagnosis have been proposed utilizing methods from different areas (Patton et al., 2000; Karpenko et al., 2003; Witczak, 2006; Zhang, 2006). The most frequently used is the model-based approach (Patton et al., 2000; Chen and Patton, 1999; Isermann and Balle´, 1997). The basic idea of model-based fault diagnosis is to generate signals that reflect inconsistencies between nom- inal and faulty system operating conditions. Such signals, called residuals, are usually calculated by using analytical methods such as observers, parameter estimation methods or parity equations (Chen and Patton, 1999; Gertler, 1999; Isermann and Balle´, 1997). Unfortunately, the common drawback of these approaches is that an accurate mathematical model of the diagnosed plant is required. An alternative solution can be obtained through artificial intelligence, e.g. neural networks (Frank and Ko¨ppen- Seliger, 1997; Patton and Korbicz, 1999; Korbicz et al., 2004). Neural network based fault diagnosis systems are very attractive because are easy to develop and can cope with non-linearities. An attractive property of neural networks is the self-learning ability. A neural network can extract the system features from historical training data using the learning algorithm, requiring a little or no a priori knowledge about the process. This provides modelling of non-linear systems a great flexibility (Haykin, 1999; Nelles, 2001). One of the most interesting solutions of the dynamic system identification problem is the application of locally recurrent networks (Tsoi and Back, 1994; Campolucci et al., 1999; Patan and Parisini, 2005). Such networks have the feed-forward multi-layer architecture and their dy- namic properties are obtained using a specific kind of neuron models. Such models consist of inner feedbacks, thus the neuron activation depends on its current inputs as well as past inputs and outputs. In this paper locally ARTICLE IN PRESS www.elsevier.com/locate/engappai 0952-1976/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.engappai.2006.12.009 à Corresponding author. E-mail addresses: k.patan@issi.uz.zgora.pl (K. Patan), j.korbicz@issi.uz.zgora.pl (J. Korbicz).