Mining the fuzzy control rules of aeration in a Submerged Biofilm Wastewater Treatment Process

Abstract

This paper presents a special rule base extraction analysis for optimal design of an integrated neural-fuzzy process controller using an “impact assessment approach.” It sheds light on how to avoid some unreasonable fuzzy control rules by screening inappropriate fuzzy operators and reducing over fitting issues simultaneously when tuning parameter values for these prescribed fuzzy control rules. To mitigate the design efforts, the self-learning ability embedded in the neural networks model was emphasized for improving the rule extraction performance. An aeration unit in an Aerated Submerged Biofilm Wastewater Treatment Process (ASBWTP) was picked up to support the derivation of a solid fuzzy control rule base. Four different fuzzy operators were compared against one other in terms of their actual performance of automated knowledge acquisition in the system based on a partial or full rule base prescribed. Research findings suggest that using bounded difference fuzzy operator (O_b) in connection with back propagation neural networks (BPN) algorithm would be the best choice to build up this feedforward fuzzy controller design.

Introduction

Fuzzy control algorithms have been widely applied to pursue better effluent quality and higher economic efficiency on both aerobic biological treatment processes (Tsai et al., 1994; Rodrigo et al., 1997; Fu and Poch, 1998; Ferrer et al., 1998; Kalker et al., 1999) and anaerobic biological treatment processes (Estaben et al., 1997; Tay and Zhang, 1999, Tay and Zhang, 2000; Murnleitner et al., 2002). To increase the settling process efficiency, Traore et al. (2006) successfully used fuzzy algorithm to control sludge height in a secondary settler. In regulating aeration, Fiter et al. (2005) tried to save energy by fuzzy logical control. They used 42 different rules defined in accordance with expert knowledge to shape a fuzzy control rule base. Yet the construction of a fuzzy control rule base has to involve sort of complexity. In spite of some successful practical applications, there is still no all-inclusive procedure or method to design such intelligent controllers by far because of its semi-empirical nature.

In fact, the construction of a good fuzzy control rule base for wastewater treatment is a time consuming task because of the inherent nonlinear nature embedded in those complex systems. This turns out to be even an obstacle sometimes when coping with systems without having enough prior information in biological wastewater treatment units. To ease the efforts in describing these highly nonlinear systems, a workable skill, in which the control domain can be expressed by a set of linear combinations of several input variables, was presented by Takagi and Sugeno (1985). Searching for such Takagi–Sugeno (T–S) fuzzy control rules basically involves performing knowledge acquisition, defining fuzzy membership functions, and tuning the parameter values for these prescribed fuzzy control rules. On the top of the theoretical progress of T–S fuzzy control algorithm, a new paradigm in intelligent control regime focuses on the integration of various merits embedded in different soft computing techniques in order to meet differing control needs and minimize both the environmental and economic impacts (Spall and Cristion, 1997; Lee and Park, 1999; Chang et al., 2001; Chen et al., 2003a, Chen et al., 2003b). Some of previous works pinpointed an advanced need of using proper tool for screening out the essential control rules based on experimental input–output data pairs that lack linguistic or knowledge information; moreover, the learning ability of neural networks (NNs) for searching the optimal parameter values was particularly stressed in the literature (Enbutsu et al., 1993; Tay and Zhang, 2000). Applications of back propagation NNs models can be found in the literature worldwide (Boger, 1992; Syu and Chen, 1998; Zhang and Stanley, 1999; De Veaux et al., 1999; Melas et al., 2000).

If the total number of observations is not enough to support a smooth fuzzy control rule extraction, the complexity in the construction of a fuzzy control rule base might become insurmountable. In response to such a challenge, hybrid fuzzy control via fusion technology was therefore emphasized in this study. This paper aims at developing a special rule base extraction analysis for optimal design of an integrated neural-fuzzy process controller using an “impact assessment approach.” It sheds light on how to avoid some unreasonable fuzzy control rules by scrutinizing inadequate membership functions, screening inappropriate fuzzy operators, and reducing over fitting issues simultaneously when tuning parameter values for these prescribed fuzzy control rules. To mitigate the design efforts, the self-learning ability embedded in the NNs model was emphasized for improving the rule extraction performance. Four different fuzzy operators used for the integration of T–S fuzzy control algorithm and NNs model were compared against each other with respect to the actual performance of automated knowledge acquisition when dealing with the fuzzy control rule base. It leads to provide a standard procedure for eliminating inadequate structure in membership functions, screening inappropriate fuzzy operator, and reducing over fitting potentials in NN model in the way to build up the representative fuzzy control rules. An aeration unit in an Aerated Submerged Biofilm Wastewater Treatment Process (ASBWTP) was picked up to support the derivation of a solid fuzzy control rule base. With such a revised T–S fuzzy control algorithm, the proposed controller may lead to determine the optimal airflow rate over operational time period that could end up saving energy and eliminating the use of the equalization tank in the ASBWTP.