Date of Award

Fall 1990

Document Type

Dissertation - Restricted

Degree Name

Doctor of Philosophy (PhD)


Civil, Construction, and Environmental Engineering


In order to control and operate a wastewater treatment plant, a good representing model becomes necessary. By observing the temporal series of the output values from such a plant, it can be determined that the system behaviour is in part conditioned by its immediate past history: such a system is called a dynamic system. An ideal model of a dynamic system should be predictive and adaptive, other than representative. Predictive means that the model should allow prediction of the status of the system at some point into the future, based on observations currently available, and with a given degree of confidence. Adaptive means that the model should be suitable to be easily adapted to variations that may occur in the behaviour of the system, due to changes in the system itself, or to changes in the population of its variables. The question that this dissertation attempts to answer is whether or not it is possible to develop a modeling of wastewater treatment operation based on stochastic relationships. This line of research is based on the application of stochastic modeling and time-series analysis to wastewater treatment processes. Two basic methodologies have been applied to the system identification analysis: the linear filter model and the transfer function model. The first has been earlier described by Box and Jenkins. A new approach to the subject was however proposed in 1983 by Pandit and Wu, and will be applied in this research effort. Linear filter models describe the behavior of single time series in terms of a random input (white noise), transfer function models can describe more complex systems in which the output is stochastically dependent on a measured input, or more measured inputs. During this research a generalized procedure has been identified to analyze available data according to the principles of system identification theory. Model-building techniques which lead to the practical implementation of transform functions for the description and prediction of the behavior of any chosen system have been applied. The following tasks have been completed: - literature review for both "conventional" treatment process modeling and theoretical and practical aspects of stochastic modeling applied to wastewater treatment and comparable industrial processes; -identification of a class of (stochastic) models within which to operate a search for an "ideal" model. Physical insight in the processes to be described has been considered in this selection; - definition of a model (that is, determination of its order and estimation of its parameters) that represents the physical system satisfactorily; and, finally, - verification of the performance accuracy of the model. It is important to stress that the proposed modeling technique is not intended as a substitute to the established process theories. It can be described as a flexible, self-correcting technique that may be used for process control purposes and can, in effect, include the theoretical structure and physical knowledge of the processes investigated, while retaining as a major advantage the continuous use of data from the immediate past for a recursive adaptation to the evolving dynamics of the real-world processes. The resulting models are site-specific, that is, they are a functional consequence of the performance records of each treatment plant. This accounts for those unique conditions which are necessarily not considered in the general theory. This type of technique can be further implemented in control procedures that can be interactively used at a "friendly" level by skilled staff of treatment facilities, or even be completely automated, as already proven by applications in several areas of industry. These control procedures have a definite advantage over classical "rules-of-thumb", in that they not only provide an indication of the line of action to be followed, but also the prediction of the expected error (or success probability) when the operator is faced with different options.



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