**6. References**

172 Recurrent Neural Networks and Soft Computing

Fig. 18. ROC graph for the RSOM model in 9x9 grid with variation

classification performance, as long as, using intermediate values.

**5. Conclusion** 

in terms of the lightning occurrences.

in the following main conclusions:

core values within the range of 0 to 1;

In summary, we can say that the RSOM network was the one which offered the best clusters

This work aimed to evaluate the applicability of the self-organizing map local temporal extensions (Temporal Kohonen Map and Recurrent Self-Organizing Map) in the severe weather patterns recognition. The study area was the eastern Amazon region, one of the areas of the Earth with higher frequency and intensity of extreme weather events, especially

Its purpose was to contribute in the identification of a useful tool for the weather studies, to reduce the damages associated with this natural phenomenon. The performance analysis of the recurrent neural networks (TKM and RSOM) with relation to the original SOM resulted

There is significant change in the global accuracy of the TKM and RSOM classifiers

 The recurrent neural networks (TKM and RSOM), used as classifiers, presented improved performance over the original SOM when adjusted its time coefficients with

depending on the choice of the time coefficients (*d* and ), respectively;


**9** 

*Mexico* 

**Centralized Distributed Parameter Bioprocess** 

Ieroham Baruch1, Eloy Echeverria-Saldierna1 and Rosalba Galvan-Guerra2

In the last two decades new identification and control tools, like Neural Networks (NN), have been used for biotechnological plants (Boskovic & Narendra, 1995). Among several possible network architectures the ones most widely used are the Feedforward NN (FFNN) and the Recurrent NN (RNN), (Haykin, 1999). The main NN property namely the ability to approximate complex non-linear relationships without prior knowledge of the model structure makes them a very attractive alternative to the classical modeling and control techniques. This property has been proved for both types of NNs by the universal approximation theorem (Haykin, 1999). The preference given to NN identification with respect to the classical methods of process identification is clearly demonstrated in the solution of the "bias-variance dilemma" (Haykin, 1999). The FFNN and the RNN have been applied for Distributed Parameter Systems (DPS) identification and control too. In (Deng & Li, 2003; Deng et al. 2005; Gonzalez et al, 1998), an intelligent modeling approach is proposed for Distributed Parameter Systems (DPS). In ( Gonzalez et al, 1998), it is presented a new methodology for the identification of DPS, based on NN architectures, motivated by standard numerical discretization techniques used for the solution of Partial Differential Equations (PDE). In (Padhi et al, 2001), an attempt is made to use the philosophy of the NN adaptive-critic design to the optimal control of distributed parameter systems. In (Padhi & Balakrishnan, 2003) the concept of proper orthogonal decomposition is used for the model reduction of DPS to form a reduced order lumped parameter problem. In (Pietil & Koivo, 1996), measurement data of an industrial process are generated by solving the PDE numerically using the finite differences method. Both centralized and decentralized NN models are introduced and constructed based on this data. The multilayer feedforward NN realizing a NARMA model for systems identification has the inconvenience that it is sequential in nature and require input and feedback tap-delays for its realization. In (Baruch et al, 2002; Baruch et al, 2004; Baruch et al, 2005a; Baruch et al, 2005b; Baruch et al, 2007a; Baruch et al, 2007b; Baruch et al, 2008; Baruch & Mariaca-Gaspar, 2009; Baruch & Mariaca-Gaspar, 2010), a new completelly parallel canonical Recurrent Trainable NN (RTNN) architecture, and a dynamic BP learning algorithm has been applied for systems identification and control of nonlinear

**1. Introduction** 

*2ESIMEZ-IPN, Mexico City, Department of Control and Automation Engineering,* 

**Identification and I-Term Control Using** 

*1CINVESTAV-IPN, Mexico City, Department of Automatic Control,* 

**Recurrent Neural Network Model** 

