A procedure for selecting best identifiable parameters in calibrating activated sludge model no. 1 to full-scale plant data

Abstract

A systematic procedure for selecting identifiable parameter subsets for a given set of measured outputs is proposed. The aim is to only select those parameters which can be estimated uniquely from the dataset used. The proposed procedure consists of first selecting a reduced set of most sensitive parameters by sensitivity analysis and subsequently selecting identifiable parameter subsets using the Fisher information matrix. For a particular set of outputs obtained from a typical calibration exercise at a carrousel-type nitrogen removal plant, parameter subsets ranging from two to eight parameters were selected by this procedure. The procedure proved successful as the parameter subsets thus selected could be estimated accurately from simulated data without and with noise as well as from real data. However, the procedure is based on a property which is local in parameter space. Consequently, as an a priori assumption on the parameter vales has to be made at the start of the procedure, the selection results might be different from the results which would have been obtained by using the a posteriori parameter values. Hence, the sensitivity towards this a priori assumption was tested explicitly. For this purpose, the parameter space was sampled according to a Latin hypercube sampling scheme and the selection procedure was applied in all sampling points as if these were a priori estimates. From this extensive study it could be concluded that the results of the procedure were not too severely influenced by the a priori assumption on the parameter values. Therefore, the proposed procedure appears to be a powerful and practical tool for efficient and reliable model calibration.

Water quality modelling for small river basins

“…The selection of identifiable parameter subsets is a particularly relevant subject in environmental system identification (Weijers and Vanrolleghem, 1997;Petersen, 2000;Dochain and Vanrolleghem, 2001;Omlin et al, 2001;Brun et al, 2002;Gernaey et al, 2004;De Pauw, 2005). Almost all these studies are based on trajectory sensitivity functions, defined as the incremental ratio between the variation of each output ( j ) and that of the perturbed parameter (i), i.e.…”

Selection of Model Parameters for Off-Line Parameter Estimation

“…The absolute value of the principal components element reflects the contribution of the th parameter to the variance of the th output. The weighted sum of the nonzero eigenvalues and their corresponding principal component elements is used as a measure of the overall effect of the th parameter (12) where . The measure reflects the difficulty in determining the th parameter when only a single parameter is estimated.…”

“…As originally proposed, the FIM-based method [12] discussed in Section I requires a subjective choice of the parameters that yield the best tradeoff between minimization of the FIM-condition number and minimization of the FIM determinant . To eliminate this subjectivity, we have modified the FIM-based approach such that the estimated parameters are chosen to minimize the product of these two measures.…”

“…Several investigators have proposed the use of multiple objectives to achieve better results. For example, a parameter selection procedure which utilizes both the FIM determinant and the FIM condition number has been applied to a standard model of the activated sludge process [12]. First the parameter-sensitivity matrix is computed to identify insensitive parameters that are eliminated from the subsequent analysis.…”

Real time optimization in chemical process: evaluation of strategies, improvements and industrial application.

“…Initially, Weijers and Vanrolleghem (1997) The present Chapter is ordered as follows: the selected estimation methods are described in Section 3.1, Section 3.2 discusses the local parametric sensitivity method, Section 3.3 and 3.4 are devoted to explain the case studies. The main findings are presented and discussed in Sections 3.5 and 3.6, respectively.…”