Hybrid Model Identification for Fault Diagnosis of Non–linear Dynamic Processes Silvio Simani Abstract— This work addresses an approach for fault diag- nosis of industrial processes using hybrid models. A non–linear dynamic process can, in fact, be described as a composition of different affine submodels selected according to the process operating conditions. This paper concerns the identification of the hybrid model parameters through the input–output data acquired from the non–linear process. Therefore, the fault detection scheme adopted to generate residual signals exploits this estimated hybrid model. In order to show the effectiveness of the developed technique, the results obtained in the fault diagnosis of a real industrial plant are finally reported. I. INTRODUCTION There is an increasing interest in the development of model-based fault detection and fault diagnosis methods, as can be seen in the many papers submitted to the IFAC (International Federation of Automatic Control) Congress and IFAC Symposium SAFEPROCESS [1], [2], [3]. The majority of real industrial processes are non–linear [4], [5] and cannot be modelled by using a single model for all operating conditions. Since a mathematical model is a description of system behaviour, accurate modelling for a complex non–linear system is very difficult to achieve in practice. Sometime for some non–linear systems, it can be impossible to describe them by analytical equations. Instead of exploiting complicated non–linear models obtained by modelling techniques, it is also possible to approximate the plant by a collection of local affine models obtained by identification procedures [6]. Residual are signals representing inconsistencies between the model and the actual system being monitored. Any inconsistency will indicate a fault in the system. Residual must, therefore, be different from zero when a fault occurs and zero otherwise. However, the deviation between the model and the plant is influenced not only by the presence of the fault but also the modelling error. Several techniques had been proposed for Fault Detection and Isolation (FDI) in dynamic systems using either unknown input observers, parity relations, sliding mode observers, gain–parametrised observers [3], [9]. In particular, in this work, hybrid model [8], [6] iden- tification is combined with the model–based method to formulate a diagnosis technique using the estimated model itself for residual generation. Hybrid models can, in fact, be exploited to describe the behaviour of non–linear dynamic systems since these prototypes are described by a compo- sition of affine models. Each submodel approximates the S. Simani is with the Dipartimento di Ingegneria of the Univer- sit` a di Ferrara. Via Saragat, 1. 44100 Ferrara (FE) - ITALY. ssi- mani@ing.unife.it system locally around an operating point and a selection procedure determines which particular submodel has to be used. Such a multiple–model structure is called multiple– model approach. Under such an identification and diagnosis scheme, a number of local affine models are designed and the estimate of outputs is given by a composition of local outputs. The diagnostic signal (residual) is the difference between the estimated and actual system output [3], [9]. In this paper, the different operating points can be selected by means of clustering method [9]. On the basis of knowledge of the operating point regions, the identification of the structure and the parameters of each local model composing the hybrid system can be performed [10], [11], [9]. The remainder of this paper is organised as follows. Section II presents the structure of the hybrid model, while Section III illustrates how to integrate the Frisch scheme [12] method for the identification of linear systems within a general procedure for hybrid model identification. Section IV shows the design of the diagnostic scheme for FDI of dynamic systems. The application of such a fault detection and identification approach to a real industrial plant is described in Section V. The example demonstrates the effectiveness of the technique proposed. Finally, some concluding remarks are included in Section VI. II. HYBRID PROTOTYPE MODELLING The main idea underlying the mathematical description of non–linear dynamic systems is based on the interpretation of single input–single output, non–linear, time–invariant regression models in the form: [9], [6] such as: y(t +n)= F ( y(t +n −1), ··· ,y(t),u(t +n −1), ··· ,u(t) ) (1) where u(·) and y(·) belong respectively to the bounded input U and output Y sets, n is the finite system memory (i.e. the model order) and F (·) is a continuous non–linear function defining a hypersurface from a A n to Y , being A n the Cartesian product U n ×Y n . The identification of the non–linear system can be translated to the approximation of its mathematical model in the form of Eq. (1) using a parametric structure that exhibits arbitrary accuracy inter- polation properties. A hybrid prototype defined through the composition of simple models having local validity is the natural candidate to perform this task, as it combines function interpolation properties with mathematical tractability. In the following the proposed hybrid structure is defined and its properties in terms of interpolation characteristics of arbitrary non–linear