Paper: A theoretical analysis of recursive identification methods

Wastewater treatment processes are inherently dynamic because of the large variations in the influent wastewater flow rate, concentration and composition. Moreover, these variations are to a large extent not possible to control. The adaptive behaviour of the involved microorganisms imposes further difficulties in terms of time-varying process parameters. Mathematical models and computer simulations are essential to describe, predict and control the complicated interactions of the processes. The number of reactions and organism species that are involved in the system may be very large. An accurate description of such systems can therefore result in highly complex models, which may not be very useful from a practical, operational point of view. A reduced order dynamic model, describing an activated sludge process performing carbonaceous removal, nitrification and denitrification with reasonable accuracy, is presented. The main objective is to combine knowledge of the process dynamics with mathematical methods for estimation and identification. The identifiability of the model is investigated using both off-line and on-line methods, and its dynamic behaviour is validated by simulations of a recognized model. The information required by the identification algorithms is based on directly measurable real-time data. The simplified model may serve as a tool for predicting the dynamic behaviour of an activated sludge process, since the parameters can be tracked on-line during varying operating conditions. The model is aimed for operation and control purposes as an integral part of a hierarchical control structure. The main objective of the work on settler modelling is to enlighten recent theoretical results. A new one-dimensional settler model is compared to a traditional layer model by means of numerical simulations. Emphasis is put on the numerical solution¹s ability to approximate the analytical solution of the conservation law written as a non-linear partial differential equation. The new settler model is consistent in this respect. Several problems that occur when integrating a model of the biological reactor with a model of the settler are also discussed. In particular, the concentrations of the biological components of the particulate material are of importance for an accurate description of the sludge that is recycled to the biological reactor. Two one-dimensional algorithms have been evaluated. The first algorithm is commonly used and some of its inherent problems are discussed. The second algorithm is a new analytically derived method. Few attempts have been made to take into account the influence of higher order organisms in biofilm systems when developing or applying mathematical models. This work describes a simplified modelling approach to include some possible effects of higher order organisms on nitrification, based on a proposed hypothesis of their oxygen consumption in the biofilm. Three different models are developed and investigated. Model simulations are validated using data from a laboratory experiment using continuous-flow suspended-carrier biofilm reactors, where the predators were selectively inhibited. The proposed models are capable of reproducing several of the observed effects. They are primarily aimed at capturing the steady-state behaviour of the biofilm but may also prove to be a useful basis for describing the dynamics. (Less)

/pdf/modelling-aspects-of-wastewater-treatment-processes-36vj6gx2tk.pdf

Modelling Aspects of Wastewater Treatment Processes

The Total Least Squares (TLS) method has been devised as a more global fitting technique than the ordinary least squares technique for solving overdetermined sets of linear equations $AX \approx B$ when errors occur in all data. This method, introduced into numerical analysis by Golub and Van Loan, is strongly based on the Singular Value Decomposition (SVD). If the errors in the measurements A and B are uncorrelated with zero mean and equal variance, TLS is able to compute a strongly consistent estimate of the true solution of the corresponding unperturbed set $A_0 X = B_0 $. In the statistical literature, these coefficients are called the parameters of a classical errors-in-variables model.In this paper, the TLS problem, as well as the TLS computations, are generalized in order to maintain consistency of the parameter estimates in a general errors-in-variables model; i.e., some of the columns of A may be known exactly and the covariance matrix of the errors in the rows of the remaining data matrix may be...

Analysis and properties of the generalized total least squares problem AX≈B when some or all columns in A are subject to error

The experimental determination of the vibration characteristics of rotating engine blades is very important for fatigue failure considerations. One of the most promising techniques for measuring the frequency of blade vibrations is blade tip timing. In this paper, three vibration analysis methods were specifically formulated and applied to the tip timing problem for the first time, using data obtained from a simple mathematical blade tip timing simulation. The results from the methods were compared statistically in order to determine which of the techniques is more suitable. One of the methods, the global autoregressive instrumental variables approach, produced satisfactory results at realistic noise levels. However, all of the techniques produced biased results under certain circumstances.

/pdf/a-comparison-of-blade-tip-timing-data-analysis-methods-1ksre9g6su.pdf

A Comparison of Blade Tip-Timing Data Analysis Methods

The least-squares method in system identification leads generally to biased parameter estimates. A conceptually simple modification is to estimate the bias and to compute compensated parameter estimates. When white output noise is the only disturbance this principle (compensated least squares, CLS) can readily be used to obtain consistent estimates. The main purpose of the paper is to investigate the accuracy of the parameter estimates obtained when the CLS method is used. It is proved that the estimates are asymptotically gaussian distributed. An explicit expression for the covariance matrix is given. It is also shown that a commonly used instrumental variable method gives (asymptotically) better accuracy than the compensated least-squares method.

Bias correction in least-squares identification

Using an unbiased objective function and a fast algorithm which employs an iterative least-squares technique, consistent estimates are obtained for the parameters of a linear difference equation which describes a system having an output corrupted by correlated noise. The method is applied to a simulated process and compared with the generalised least-squares method.

Suboptimal estimation of the parameters of discrete systems in the presence of correlated noise

A study of inertial effects in sedimentation

A comparison of parameter estimation algorithms for discrete systems

On the use of residence time distributions for the design of clarifiers

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Papers

Suboptimal estimation of the parameters of discrete systems in the presence of correlated noise

A study of inertial effects in sedimentation

A comparison of parameter estimation algorithms for discrete systems

On the use of residence time distributions for the design of clarifiers