Procedures for parameter and state estimation of microbial growth process models

Holmberg, Andrea; Ranta, Jukka

doi:10.1016/0005-1098(82)90107-8

Cited by 150 publications

(67 citation statements)

References 9 publications

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“…Note that such an analysis deals only with the intrinsic properties of the model, i.e., the internal description of the system's behavior {x, ot}, and makes no reference to any particular set of field data, other than that biomass concentration would need to be an observed variable. In fact, given a set of observations from an entirely deterministic simulated system (the noise processes I; and 11 being identically zero in (2)), Holmberg and Ranta [1982] have shown further that a typical least squares parameter estimation algorithm has great difficulty in converging to an optimal and unique pair of estimates for the maximum specific growth rate and saturation concentration constants. The essential problem is that the surface of the (squared-error) objective function has the shape of a long, narrow, steep-sided valley running roughly parallel to the axis of the saturation concentration constant in the two-dimensional parameter space.…”

Section: Identifiability and Experimental Designmentioning

confidence: 99%

Water quality modeling: A review of the analysis of uncertainty

Beck¹

1987

Water Resources Research

863

431

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This paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction. More specifically, four problem areas are examined in detail: uncertainty about model structure, uncertainty in the estimated model parameter values, the propagation of prediction errors, and the design of experiments in order to reduce the critical uncertainties associated with a model. The review is rather lengthy, and it has therefore been prepared in effect as two papers. There is a shorter, largely nontechnical version, which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling. Enclosed by this shorter discussion is the main body of the review dealing in turn with (1) identifiability and experimental design, (2) the generation of preliminary model hypotheses under conditions of sparse, grossly uncertain field data, (3) the selection and evaluation of model structure, (4) parameter estimation (model calibration), (5) checks and balances on the identified model, i.e., model “verification” and model discrimination, and (6) prediction error propagation. Much time is spent in discussing the algorithms of system identification, in particular, the methods of recursive estimation, and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first‐order error analysis. There are two obvious omissions from the review. It is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty, although clearly some reference must be made to these topics. In brief, the review concludes (not surprisingly) that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality, and much remains to be done. A lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior, and there is ample evidence to show that the “larger,” more “comprehensive” models are easily capable of generating highly uncertain predictions of future behavior. For the future of the subject, it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification, a need for new questions to be posed in the problem of prediction, and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence.

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Section: Identifiability and Experimental Designmentioning

confidence: 99%

Water quality modeling: A review of the analysis of uncertainty

Beck¹

1987

Water Resources Research

863

431

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“…However, correct identification of the parameters is not a trivial task since (i) the experimental data points are scarce and (ii) batch experiments are known as not the most optimal setup for estimation of both Monod constants at once (Holmberg and Ranta, 1982). It has been proved that the extension of the batch experiment by a feeding phase with time-varying feed rate leads to a higher accuracy of the parameter estimates.…”

Section: Macroscopic Modelling and Optimal Experiments Designmentioning

confidence: 99%

Identifying New Drug Targets to Combat Pathogenic Infections: An Interdisciplinary Approach

Smets

Cappuyns

Bernaerts

et al. 2005

IFAC Proceedings Volumes

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Todays' medical treatments are faced with alarming resistance development of pathogenic bacteria, due to (amongst other factors) the abundant and often inappropriate use of antibiotics. The development of a novel class of antibiotics has therefore become a major research theme. This paper presents a conceptual overview of how this quest is tackled in a multidisciplinary fashion when the focus lies on detecting and understanding regulatory pathways that lead to virulence. The importance of well designed and controlled bioreactor experiments as well as the integration (into mathematical models) of data, collected at different levels and from different sources, will be stressed.

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“…Regardless of the type of model employed, the model parameters are often as sumed to have biological significance and are treated as characteristic of the process, although the identification of a unique set of physically meaningful parameters may not be feasible for many systems. While any such interpretation is limited by the validity of the model, changes in model parameters may indicate physico chemical changes inside the process (Holmberg & Ranta, 1982). The rational design of advanced control and optimization schemes for bio-processes is therefore intricately linked to the identification of kinetic rate parameters accurately and in real-time (Van Impe & Bastin, 1995;Thatipamala, Hill & Rohani, 1996).…”

Section: Bio-process Model Identificationmentioning

confidence: 99%

“…Aborhey and Williamson (1978) reported the esti mation of Monod parameters and yield coefficient as functions of culture temperature and Golden and Yd stie (1989) used recursive least squares with forgetting factors. The RLS algorithms suggested in the literature are adaptations of schemes developed for time-invari ant systems and they fare poorly when used for moni toring parameters that drift with time, besides being very sensitive to noise (Holmberg & Ranta, 1982). Estimation of time varying parameters in a linearized discrete fermentation model are also reported in the literature (Zhou & Cluett, 1996).…”

Section: Bio-process Model Identificationmentioning

confidence: 99%

Time-varying system identification using modulating functions and spline models with application to bio-processes

Ungarala

2000

Computers & Chemical Engineering

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Procedures for parameter and state estimation of microbial growth process models

Cited by 150 publications

References 9 publications

Water quality modeling: A review of the analysis of uncertainty

Water quality modeling: A review of the analysis of uncertainty

Identifying New Drug Targets to Combat Pathogenic Infections: An Interdisciplinary Approach

Time-varying system identification using modulating functions and spline models with application to bio-processes

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