Dynamic system multivariate calibration for optimal primary output estimation
Doctoral thesis, Peer reviewed
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In industrial plants and other types of dynamic systems, it is a common situation that measurements of primary system outputs are not available on-line. The primary outputs may for example be quality properties, that can be determined only through costly laboratory analyses, i.e. they can be measured only at a low sampling rate and with a considerable time delay. Since the primary outputs give vital information on the system performance, and in fact may be the sole purpose of the system, it is of interest to estimate them continuously or at a high samplingrate. This can be done by use of a system model utilizing all available informationin both the known system inputs and the secondary system outputs that often are available at a high sampling rate.The thesis considers the identification of optimal primary output estimators for this purpose from experimental data, using known system inputs and secondary measurements as estimator inputs. The estimators are based on underlying Kalman filters, and the identification can be done by use of an ordinary predictionerror method. However, an optimal utilization of the secondary output informa-tion may require that an output error (OE) model structure is specified. This is one of the major new insights provided by the thesis. With low noise secondary measurements, it is in some cases possible to use estimators of reduced complexity. This is found from an analysis of perfect measurement cases, and further developed into a systematic method for finding aparsimonious estimator with a minimized mean-squared validation error.The experimental data must include primary output measurements. It is, however, shown in the thesis that also low and even irregular primary output sampling rate data may be used for the purpose, provided that the prediction error method is appropriately modified. This is a direct consequence of the OE structure used, including the use of secondary measurements as estimator inputs,and it is considered to be of significant practical and economical importance. It is also shown in the thesis that the ordinary least squares (LS) estimator for static systems is a special case of the general current (a posteriori) OE estimator for dynamic systems. This also forms a link from Kalman filtering to principalcomponent analysis (P CA), and to the chemometrical principal component regres-sion (PCR) and partial least squares regression (PLSR) methods based on data compression into latent variables. These methods make use of data weighting matrices, and assuming a latent variable data structure, the optimal weighting matrixis shown to be a transposed Kalman gain. It is further shown that in cases witha few independent and many dependent and collinear regressor variables, the best solution may be obtained by use of a two-step PCA/PLSR+LS solution, where the independent variables are used only in the second step.The static latent variables methods are finally combined with the developed methods for identification of dynamic primary output estimators, leading to two-step PCA+OE and PLSR+OE methods, where the known inputs are used only inthe second step. The theory and methods developed are tested on simulated data. They are also tested on data from industrial plants and experimental test rigs, primarily with operator support applications in mind. Further applications in e.g. failure detection and feedback control are given a preliminary discussion.
Avhandling (dr.ing.) - Høgskolen i Telemark / Norges teknisk-naturvitenskapelige universitet