Inference model derivation with a pattern analysis for predicting the risk of microbial pollution in a sewer system

Abstract

Developing a mathematical model for predicting fecal coliform bacteria concentration is very important because it can provide a basis for water quality management decisions that can minimize microbial pollution risk to the public. This paper introduces a hybrid modeling methodology which is a combined use of a neural networkbased pattern analysis and an evolutionary process model induction system. The neural network-based pattern analysis technique is applied to extract knowledge on interrelationships between fecal coliform concentrations and other measurable variables in a sewer system. Based on the result of neural network-based pattern analysis, an evolutionary process model induction system is used to derive mathematical inference models that can predict fecal coliform bacteria concentration from easily measurable variables instead of directly measuring fecal coliform bacteria concentration in a sewer system. The neural network-based pattern analysis extracts that temperature and ammonia concentration are the most important driving forces leading to an increase in fecal coliform bacteria concentration in the sewer system at Paraparaumu City, New Zealand. Fecal coliform bacteria concentration is also positively correlated with dissolved phosphorus and inversely with flow rate. The multivariate inference models that are able to predict fecal coliform bacteria concentration are successfully derived as functions of flow rate, temperature, ammonia, and dissolved phosphorus in the form of understandable mathematical formulae using the evolutionary process model induction system, even if a priori mathematical knowledge of the dynamic nature of fecal coliform bacteria is poor. The multivariate inference models evolved by the evolutionary process model induction system produce a slightly better performance than the multi-layer perceptron neural network model.Keywords Fecal coliform bacteria Á Water quality modeling Á Multivariate inference model derivation Á Neural network-based pattern analysis Á Self-Organising Feature Maps Á Evolutionary process model induction system Á Grammar-based genetic programming

Transparent water quality model induction in a reservoir affected by the rainfall-runoff process using a grammar-based genetic programming

“…The non-terminal Variable∈N is to denote any variables (e.g., X, Y, Z) from the input domain. The grammar determines how model expressions can be formed (e.g., what functions and variables can be part of an expression) (Hong and Paik, 2012).…”

“…However, the root will always be a non-terminal and the leaves will always be terminals in Figure 2 (Hong and Paik, 2012). This results in a population of possible models from which models are selected and modified using evolutionary search processes to produce better fitting models.…”

“…Grammar-based genetic programming (GBGP) (Whigham 1995;O'Neill and Ryan 2001;McKay et al 2010) is a variant of GP technique and uses a grammar system to derive possible models that best fit observed data. The grammar system in the GBGP is designed to represent syntactical constraints and to incorporate background knowledge in order to guide the model evolution process (Hong & Paik, 2012). In our proposed GBGP system, a context-free grammar (CFG) (Hopcroft and Ullman, 1979;Chomsky, 1986) is implemented to derive possible models by incorporating arithmetic operators, use-defined function, and variables proposed by proposed by Whigham (1995).…”

“…Genetic programming is an evolutionary computation algorithm that uses a population-based search method that works on a population of individuals whose output is a potential model in the space of search to a given problem (Koza 1992). There are several successful applications of this GP technique to hydrological modeling (Whigham and Crapper, 2001;Hong and Rosen, 2002;Hong et al, 2005, Parasuraman andElshorbagy, 2008;Selle and Muttil, 2011;Fallah-Mehdipour et al, 2013;Chadalawada et al, 2017;Heřmanovský et al, 2017;Liu and Shi,2019;Sepahvand et al, 2019) and water quality modeling (Whigham and Recknagel 2001;Muttil and Lee, 2005;Hong & Paik, 2012). South Korea's typhoon-related rainy season during the months of June to August leads rivers to easily peak and overflow.…”

Reconstructing disease transmission dynamics from animal movements and test data

“…In veterinary epidemiology, this may be the records of tests carried out at a particular location (e.g. a farm) and time or simply the movement of animals, the recording of which is often mandated by governments and provides researchers with a wealth of data with which to analyse the outbreak and transmission of diseases (Moustakas and Evans 2016;Hong and Paik 2012). In many cases the volume of collected data poses a significant statistical and computational challenge to the understanding of both outbreak patterns, transmission dynamics and thus control of the epidemic.…”