**1. Introduction**

There are several representations of industrial processes: linear, nonlinear or other technique using fuzzy logic and/or neural networks. Nonlinear models are found in a large part and are used to properly represent the dynamics of real processes. However, their comlexcity proves a real obstacle for control or when designing an observer or in a diagnostic strategy. So, the multimodel approach is a powerful approach developed in the aim to overcome problems related to modeling and control of industrial processes which are often complex, nonlinear and/or nonstationary.

The multimodel approach supposes the representation of the nonlinear model by a set of linear models (as designed in future by submodels or model's base) thus

forming what is called a model library or model's base. The interaction of each models of this model's base through a certain normalized validity calculation forming the global nonlinear system in its all area of operating.

The different models of the base could be of different structures and orders and no model can represent the system in its whole operating domain. Therefore, the multimodel approach aims at lowering the system complexity by studying its behavior under specific condition. **Figure 1** illustrates the concept of a process formed by a multimodel approach. This mechanism evaluates the contribution of each model in the description system's behavior.

The decision unit estimates by means of the numerical validity of each model the selection of the most relevant models at each time. The contribution of the different model's is made by a decision output unit that compute the multimodel output.

Several researchers have been interested in multimodel analysis and control and many applications have been proposed in different contexts. The multimodel approach has knowledgeable a sure interest since the publication of the work of [1]. The idea of the multimodel approach is to describe the complex nonlinear systems by a set of local models (linear or affine) characterizing the operation of the system in different areas of operation. In spite of its success in many fields, the multi-model approach remains confronted with several difficulties and some design problems such as the determination of the models' base and the adequate validity computation. Several works have treated these two points in the literature. We can refer to the works presented in [2–8]. Indeed once the model library is built it will remain intact. The number of model found is, first responsible to adequately represent the nonlinear model of the system and second, it will remain static when it is used in control or diagnosis. In this context there are very few works that have tried to reduce the models' base once it is built and this opens up a new axis of research added to the design of the multimodel approach in the representation of nonlinear systems. We can cite in this context the works of Gasso in [9–11], where the reduction of the models' base is based on an iterative procedure which include tree operation that is: elimination of less important local submodel, merging of the neighbouringsubmodel that describe the same behavior of the nonlinear system and finally a parameters optimization of the resultant structure is made on. In [12–15], The nonlinear system is modeled by a set of linear models and with the of a Gap metric in the model based control technique we can decide how many models are sufficient for control. In other context, when the process can be represented by a fuzzy model, the complexity of rule base can be minimized through two procedure: illumination of the less important rule and merging of neighboring rules that can

**Figure 1.** *Multimodel representation.*

#### *An Optimization Procedure of Model's Base Construction in Multimodel Representation… DOI: http://dx.doi.org/10.5772/intechopen.96458*

describe the same behavior of the nonlinear system [16]. The Chiu's classification method [17] is used in order to obtain the optimal systematic determination of model's base [18]. The latest work is a new approach permit to optimize the number of submodels with respect to the submodel complexity is presented. In [19] the optimal number of submodels is done based on both a reinforced combinatorial particle swarm optimization and a hybrid K-means.

In this chapter book we study a very relevant modeling approach especially where do not have an adequate model of the process. We will use the data set relative to the identification of the process in its area of operating. On the other hand the input and output measurement. The multimodel approach in this case becomes a very efficient method to overcome the problem of modeling.

The outline of this work is as follows: in Section 2, we will present the procedure used in the multimodel representation of complex nonlinear systems. Indeed, the number of models is determined using frequency-sensitive competitive learning algorithm and the operating clusters are identified using Fuzzy K- means algorithm. The structure of each local model and the validity computation are also presented to each submodel of the model's base (number of model built). Section 3 presents the recommended approach to reduce the number of submodels. Then, focusing on the use of both two type of validity calculation for each submodel and an SVD technique is used to evaluate the adequate number that can be retained in the model's base.
