Wastewater treatment plants (WWTPs) face increasingly stringent effluent quality constraints as a result of rising environmental concerns. Efficient operation of the secondary clarification process is essential to be able to meet these strict regulations. Treatment plants can benefit greatly from making better use of available resources through improved automation and implementing more process systems engineering techniques to enhance plant performance. As such, the primary objective of this research is to utilize data-driven modeling techniques to obtain a representative model of a simplified secondary clarification unit in a WWTP. First, a deterministic subspace-based identification approach is used to estimate a linear state-space model of the secondary clarification process that can accurately predict process dynamics, with the ultimate objective of motivating the use of the subspace model in a model predictive control (MPC) framework for closed-loop control of the clarification process. To this end, a low-order subspace model which relates a set of typical measured outputs from a secondary clarifier to a set of typical inputs is identified and subsequently validated on simulated data obtained via Hydromantis's WWTP simulation software, GPS-X. Results illustrate that the subspace model is able to approximate the nonlinear process behaviour well and can effectively predict the dynamic output trajectory for various candidate input profiles, thus establishing its candidacy for use in MPC. Subsequently, a framework for forecasting the occurrence of sludge bulking--and consequently clarification failure--based on an engineered interaction variable that aims to capture the relationship between key input variables is proposed. Partial least squares discriminant analysis (PLS-DA) is used to discriminate between process conditions associated with clarification failure versus effective clarification. Preliminary results show that PLS-DA models augmented with the interaction variable demonstrate improved predictions and higher classification accuracy. / Thesis / Master of Applied Science (MASc)

In this thesis, we propose a novel hyper-rectangle cover theory which provides a new approach to analyzing mathematical problems with nonnegativity constraints on variables. In this theory, two fundamental concepts, cover order and cover length, are introduced and studied in details. In the same manner as determining the rank of a matrix, we construct a specific e ́chelon form of the matrix to obtain the cover order of a given matrix efficiently and effectively. We discuss various structures of the e ́chelon form for some special cases in detail. Based on the structure and properties of the constructed e ́chelon form, the concepts of non-negatively linear independence and non-negatively linear dependence are developed. Using the properties of the cover order, we obtain the necessary and sufficient conditions for the existence and uniqueness of the solutions for linear equations system with nonnegativity constraints on variables for both homogeneous and non-homogeneous cases. In addition, we apply the cover theory to analyze some typical problems in linear algebra and optimization with nonnegativity constraints on variables, including linear programming problems and non-negative least squares (NNLS) problems. For linear programming problem, we study the three possible behaviors of the solutions for it through hyper-rectangle cover theory, and show that a series of feasible solutions for the problem with the zero-cover e ́chelon form structure. On the other hand, we develop a method to obtain the cover length of the covered variable. In the process, we discover the relationship between the cover length determination problem and the NNLS problem. This enables us to obtain an analytical optimal value for the NNLS problem. / Thesis / Doctor of Philosophy (PhD)

To further support and optimise the production of diving tables for the Armed Forces of Sweden, a research team has developed a new machine called IGUM (Inert Gas UndersökningsMaskin) which aims to measure how inert gas is taken up and exhaled. Due to the new design of machine, the goal of this thesis was to statistically validate its accuracy and verify its reliability.  In the first stage, a quality assurance of the linear position conversion key of IGUM in a steady and known gas flow was conducted. This was done by collecting and analysing data in 29 experiments followed by examination with ordinary least squares, hypothesis testing, analysis of variance, bootstrapping and Bayesian hierarchical modelling. Autocorrelation among the residuals were detected but concluded to not have an impact on the results due to the bootstrap analysis. The results showed an estimated conversion key equal to 1.276 ml/linear position which was statistically significant for all 29 experiments.  In the second stage, it was examined if and how well IGUM could detect small additions of gas in a dynamic flow. The breathing machine ANSTI was used to simulate the sinus pattern of a breathing human in 24 experiments where 3 additions of 30 ml of gas manually was added into the system. The results were analysed through sinusoidal regression where three dummy variables represented the three additions of gas in each experiment. To examine if IGUM detects 30 ml for each input, the previously statistically proven conversion key at 1.276ml/linear position was used. An attempt was made to remove the seasonal trend in the data, something that was not completely successful which could influence the estimations. The results showed that IGUM indeed can detect these small gas additions, where the amount detected showed some differences between dummies and experiments. This is most likely since not enough trend has been removed, rather than IGUM not working properly.

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