Recurrent Higher Order Neural Observers for Anaerobic Processes

Introduction

Anaerobic digestion is a bioprocess developed in oxygen absence by different populations of bacteria; these micro-organisms degrade progressively complex organic molecules. One of the most important applications of this process is the wastewater treatment, and it is very efficient to treat substrates with high organic load; besides the treated water, this process produces biogas, which is mainly composed of methane and carbon dioxide and it is considered as an alternative energy. However, anaerobic digestion process is very sensitive to changes on operating conditions and parameters, such as hydraulic and organic overloads, pH, temperature, etc. Then, control strategies are required in order to guarantee an adequate operation of the process. Moreover, methane production, biomass growth and substrate degradation are good indicators of biological activity inside the reactor. These variables can be used for monitoring the process and to design control strategies. Some biogas sensors have been developed in order to measure methane production in bioprocesses. However, substrate and biomass measures are more restrictive. The existing biomass sensors are quite expensive, are designed from biological viewpoint and then, they are not reliable for control purposes. Besides, substrate measure is done off-line by chemical analysis and it requires at least two hours. Then, state observers are an interesting alternative in order to deal with this problematic. This chapter deals with the neural estimation of variables hard to measure in anaerobic process.

Nowadays, artificial neural networks are a useful tool for modelling, identification, state estimation and control of a wide variety of processes. Feedforward neural networks are a good option for simple dynamics; however, for complex nonlinear systems, higher order recurrent neural networks (RHONN) are a better alternative due to their excellent approximation capabilities, requiring fewer units (Rovithakis & Christodoulou, 2000). These kind of neural networks, compared to the first order ones, are more flexible and robust when faced with new and or noisy data patterns (Ghosh & Shin, 1992). Besides RHONN performed better than the multilayer first order ones using a small number of free parameters (Ghazali, Hussain & Merabti, 2006; Rovithakis & Christodoulou, 2000). Furthermore, different authors have demonstrated the feasibility and the advantages of using these architectures in applications for system identification and control (Ge, Zhang & Lee, 2004; Narendra & Parthasarathy, 1990; Rovithakis & Christodoulou, 2000; Sanchez & Ricalde, 2003; Yu & Li, 2004).

The best known training approach for recurrent neural networks (RNN) is the back propagation through time learning (Williams & Zipser, 1989). However, it is a first order gradient descent method and hence its learning speed could be very slow (Leunga & Chan, 2003). Recently, the extended Kalman filter (EKF) based algorithms has been introduced to train neural networks (Feldkamp, Prokhorov & Feldkamp, 2003), in order to improve the learning convergence (Leunga & Chan, 2003). The EKF training for neural networks, both feedforward and recurrent ones, has proven to be reliable and practical in many applications over the past fifteen years (Feldkamp, Prokhorov & Feldkamp, 2003; Haykin, 2001; Leunga & Chan, 2003; Williams & Zipser, 1989; Yu & Li, 2004).