Uncertainty management in the activated sludge process: Innovative applications of computational learning theory.

Abstract

In this thesis, the foundations of a new area of research regarding mathematical modelling of biological wastewater treatment (WWT) processes are set. The main feature of this area is the introduction of innovative concepts and tools from emerging information modelling technologies into the traditional field of WWT process modelling. The model identification procedure is viewed as a learning problem or, equivalently, an information transfer from a set of real data into the process model. An innovative mathematical framework for the identification and validation of dynamic mechanistically based WWT process models is developed. Within this framework, a relationship between the model identification procedure and the computational machine learning methodology is established at the foundational level. The deviation D between model prediction and the real process behaviour is characterized mathematically in terms of some simple variables that govern model performance---namely: (1) the size of the data set used for model identification; (2) the quality of these data; (3) the model complexity; (4) the empirical measure of D computed on the basis of the foregoing data set. The development of the relationship between D and these variables is based on a principle called " Inductive Principle of Empirical Risk Minimization" ( IPERM ). The conditions of applicability of IPERM are thoroughly examined in the case of the activated sludge process being described by a simple mechanistic model denoted M . The Vapnik-Chervonenkis (VC) dimension of this model is estimated and two uncertainty models are developed for the activated sludge process (ASP). These two uncertainty models are compared and the differences between them accounted for. The following result is established: empirical data cannot compensate for our limited knowledge of process mechanisms, even if an infinite amount of data and computing power are made available during the model identification procedure. Measures of process model maximal and marginal improvements are developed. It is established that 80% of the model ( M ) maximal improvement occurs at a number of data points of about N80% ≈ 15 to 18. To achieve the other 20%, N has to be increased from the relatively small number N 80% to infinity. Procedures for computing the marginal cost of process model improvement and the guaranteed prediction accuracy of the identified model are developed. A new approach to modelling the activated sludge process itself and dealing with the almost-infinite degree of complexity of the ASP behaviour is developed. The basic idea of this approach is to construct an infinite series NS of nested mechanistic models of increasing complexity. This nested series is developed using the multi-substrate hypothesis. Both the Monod and the Tiessier models are considered in developing this nested series. Another principle called "Inductive Principle of Structural Risk Minimization" ( IPSRM ) is introduced and implemented to determine the optimal model structure complexity, for a fixed and small number N of data points. Computer simulations are carried out to confirm the theory and illustrate the use of the IPSRM and that of the nested series NS of ASP models.