Use of neurofuzzy networks to improve wastewater flow-rate forecasting

Abstract

A neurofuzzy wastewater flow-rate forecasting model (NFWFFM) has been developed and tested with actual data measured at the input of two wastewater treatment facilities which treat the wastewater corresponding to 150,000 and 1,250,000 p.e., respectively. Good agreements between forecasted and actual flow-rates were obtained. The artificial intelligence algorithm uses only two input variables (day of the week and average daily flow-rate of day before) and one output variable (predicted average daily flow-rate). Using three months data for training the network, a long-term forecast (one month) is made with average errors below 10%. Results were compared with those obtained by applying the Census Method II (a commonly used decomposition/recomposition time series method) observing that forecast made by the NFWFFM is more accurate than the one made by this commonly used statistical method.

Introduction

During the recent years, a large number of control algorithms have been developed for controlling the biological processes of wastewater treatment facilities (WWTFs). Probably, the more significant one is the predictive model-based controller (PMBC). This algorithm uses computer simulation to predict the behaviour of a facility and later, with this information, modifies the inputs of the process to optimise the operational results and/or costs. In order to use properly a predictive model-based controller in a WWTF, a forecasting tool that let the computer to know future flow-rates and pollutant loads, is needed. The most frequently used forecasting methods are decomposition/recomposition of time series models (BLS, Census Methods, etc), auto regressive moving average (ARMA) models and auto regressive integrated moving average (ARIMA) models (Koutroumanidis et al., 2006). In addition, new models based on artificial intelligence are used as predictive models, especially neural networks (NNs). These techniques have been compared with the traditional ones showing significant improvements (White, 1988, Wong et al., 1992, Weigend et al., 1992, Tamada et al., 1993, Onkal-Engin et al., 2005, Raduly et al., 2007, Al-Alawi et al., 2008), which makes their application in the PMBC very interesting. In the same way that NN, fuzzy logic (another branch of the artificial intelligence) has important characteristics that make it suitable for different uses (Yong et al., 2006, Barreto-Neto and de Souza Filho, 2008). Moreover, neural networks and fuzzy logic share the common ability to deal with difficulties arising from uncertainty, imprecision, and noise in a natural environment. In this context, learning capabilities of NN, and as a consequence their potential use as universal approximators (Hornik et al., 1989, Poggio and Girosi, 1990), is the main factor in their selection as forecasting methods. About fuzzy systems, they are also used as approximators, since they can easily approximate any continuous function on a compact set (Kosko, 1992).

In order to get both, the benefits of neural networks and fuzzy logic systems, avoiding at the same time their respective problems, many authors proposed to combine them into an integrated system, such that the low level-learning and computation power of neural networks can be implemented into the fuzzy logic systems, and also, provide the high-level human-like thinking and reasoning of fuzzy logic systems into the neural networks. These systems are called fuzzy neural network (FNN) and they have been widely used in many different applications during the last decades (Enbutsu et al., 1993, Tanaka et al., 1995, Hiraga et al., 1995, Gobi and Pedrycz, 2006, Luo et al., 2007, Modi et al., 2008).

The main objective of this work has been to use FNN to model the influent flow-rates in different WWTFs. The input data used consisted of the influent flow-rate to the WWTFs during the previous day and the day of the week. The single output consists of the influent flow-rate forecast. Daily data during 3 months were used for training the network (parameter estimation) whereas a different set of flow-rate data (which contains the flow-rates of one month) was used to test the generalisation ability of the FNN at various stages of learning (model validation). The Performance Index (P.I.) as defined by Lin and Cunningham (1995) was used to evaluate the generalisation ability of the FNN, being the cross-validation criterion (Amari et al., 1997) used to determine the best moment to stop the learning process.

In order to increase the credibility and impact of the model presented here, the 10 iterative steps for good, disciplined development of models (Jakeman et al., 2006) were taken into account. Thus, the objective proposed for the model was not only to reproduce the observed flow-rates but also to be a first stage in the development of a procedure to obtain rules with a physical meaning from raw flow-rate data. These rules would be subsequently used in a PMBC in order to enhance the WWTF control. Because of their final users, personnel of WWTFs, one of the constrains of the model is that it should not be too complex. Taking this in mind, the topology of the network used corresponded to the three stages in the development of a fuzzy system: fuzzification, rules and defuzzification. This topology was selected because it allowed to consider the neural network not as a black box model but as a model that can obtain rules with a physical meaning from raw flow-rate data. The parameter estimation was obtained by applying two learning algorithms, a self-organised and a back-propagation one and the train a validation of the model was carried out using experimental observations in the WWTFs. In addition, it is important to bear in mind that the model proposed is not the final step of our research line but just a stage in a more ambitious program that aims to:

• Develop a procedure that allows to obtain meaningful rules (expert system) from flow-rate data without the direct cooperation of human thinking (primary fundamental objective). In a next step (future work) this will allow to simplify the design of expert systems to control of WWTP.

• Develop a procedure that can be implemented in a supervisory control scheme particularly inside a model predictive controller for optimizing the performance of WWTF (primary practical objective).

For this reason, and in order to avoid any problem due to software connectivity a home-made code was developed and used instead of using a commercial software package.