Validities computation

The multimodel approach offers a very satisfactory results in modelling, diagnose and control of complex systems. In the modelling case, this approach passes by three steps: the determination of the model's library, the validities computation and the establishment of the final model. In this context, this paper focuses on the elaboration of a comparative study between three recent methods of validities computation. Thus, it highlight the method that offers the best performances in term of precision. To achieve this goal, we apply, these three methods on two simulation examples in order to compare their performances. 1. INTRODUCTION The establishment of a mathematical model is the first concerns of researchers for application of the advanced techniques of analyses, monitoring, prediction, control and diagnose of complex systems [1, 2]. The multimodel approach has proved a very satisfactory results and a potential benefit in both modelling and identification of complex, nonlinear and/or ill-defined systems, compared to a ˝single model approach˝. Indeed, the ˝single model approach˝ consists in determining one model that describes the comportment of the system in all its operating regions. This mission is very difficult and can sometimes be impossible when the system includes set-point changes or/and the coexistence of multiple operating modes [3, 4]. Although, the multimodel approach consists on partitioning the global system's full range operation into multiple smaller ranges. To each range is associated a local model that describes the system behavior in this specific range. The set of the local models forms the called models-library or models-base. A coefficient called validity is associated to each local model of the models-library. Validity estimates each library-model contribution in the reproduction of the real process behavior. Several validities' computation methods have been proposed in the literature [5-13]. These methods depend firstly on the way the library-models were determined and secondly, on the information available on the system. We distinguish two major classes of validities. Firstly the a priori validities which can be determined offline by exploiting the a priori knowledge available on the system. Secondly, the a posteriori validities which must be calculated online by considering the measures carried out at each instant. The present paper is interested by a postoriori validity. The majority of methods belonging to the last class are based on the residues computation and are established by measuring omline, at each instant, the distance between the process output and those of the variaous models of the base. These methods are suitable when there is overlapping between data of the different models of