Generation of discrete first‐ and second‐order sensitivities for single shooting

Barz, Tilman; Kraus, R.H.; Zhu, Liming; Wozny, Günter; Arellano‐García, Harvey

doi:10.1002/aic.13720

Cited by 11 publications

(10 citation statements)

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“…The linear implicit DAE system of the type shown in Eq. 1 is numerically solved using the initial value solver sDACl, a sparse DAE solver based on the orthogonal collocation on finite elements method . The integration is performed using an orthogonal collocation discretization along with the element‐wise solution of the discretized nonlinear equation systems.…”

Section: Case Studymentioning

confidence: 88%

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Experimental evaluation of an approach to online redesign of experiments for parameter determination

et al. 2012

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The online redesign of experiments for parameter determination of nonlinear dynamic systems has been studied recently by different research groups. In this article, this technique is assessed in a real case study for the first time. The presented algorithm adopts well-known concepts from model-based control. Compared to previous studies, special attention is given to the efficient treatment of the underlying nonlinear and possibly ill-conditioned parameter estimation and experiment design problems. These problems are solved with single shooting and gradient-based nonlinear programming (NLP) solvers. We use an initial value solver, which generates first- and second-order sensitivities to compute exact derivatives of the problem functions. As a special feature, we propose the integration of a local parameter identifiability analysis and a corresponding algorithm that generates well-conditioned problems. The practical applicability is demonstrated by experimental application to a chromatography column system where A, D, and E optimal experiments are performed

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Section: Case Studymentioning

confidence: 88%

“…Parallel programming was not used. The C++ implementation of the integrator sDACl was interfaced with Matlab using mex functions. The PE and ED problems were solved using Matlab's Optimization Toolbox solvers lsqnonlin/ trust‐region‐reflective and fmincon/sqp , respectively.…”

Section: Case Studymentioning

confidence: 99%

Experimental evaluation of an approach to online redesign of experiments for parameter determination

et al. 2012

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“…with a diagonal covariance matrix of measurements C yy based on Equation (2). The output sensitivities dy dθ can be obtained by integrating the sensitivity differential equations [45] or, as it is done here, by using orthogonal collocation as differential equation solver, which allows us to explicitly determine the sensitivities S in parallel to the integration of the system differential equation [46]. The output sensitivities needed in Equation ( 4) are then readily derived.…”

Section: Parameter Uncertaintymentioning

confidence: 99%

Model-Based Process Optimization for the Production of Macrolactin D by Paenibacillus polymyxa

2020

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In this study, we show the successful application of different model-based approaches for the maximizing of macrolactin D production by Paenibacillus polymyxa. After four initial cultivations, a family of nonlinear dynamic biological models was determined automatically and ranked by their respective Akaike Information Criterion (AIC). The best models were then used in a multi-model setup for robust product maximization. The experimental validation shows the highest product yield attained compared with the identification runs so far. In subsequent fermentations, the online measurements of CO 2 concentration, base consumption, and near-infrared spectroscopy (NIR) were used for model improvement. After model extension using expert knowledge, a single superior model could be identified. Model-based state estimation with a sigma-point Kalman filter (SPKF) was based on online measurement data, and this improved model enabled nonlinear real-time product maximization. The optimization increased the macrolactin D production even further by 28% compared with the initial robust multi-model offline optimization.

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“…Diese sind für jede Integration des DAE-Systems zu berechnen. In dieser Arbeit wurde der Integrator sDACl eingesetzt, der exakte Sensitivitäten erster und zweiter Ordnung zusammen mit der Lösung von DAE-Systemen erzeugt [44].…”

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Calibration of Dynamic Models through Adaptive Optimal Input Designs

Barz

Wozny

2014

Chemie Ingenieur Technik

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Calibration of Dynamic Models through Adaptive Optimal Input DesignsThe optimum experimental design is a methodical approach to calibrate and validate models with experimental data. It shows great potential towards reduction of experimental efforts and maximizing model accuracy. This article discusses the recent developments in the optimization of the method adaptivity leading to a broader application. Besides concrete examples, the experimental use of the automatic real-time calibration method is presented for a chromatography model.

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Generation of discrete first‐ and second‐order sensitivities for single shooting

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Cited by 11 publications

References 37 publications

Experimental evaluation of an approach to online redesign of experiments for parameter determination

Experimental evaluation of an approach to online redesign of experiments for parameter determination

Model-Based Process Optimization for the Production of Macrolactin D by Paenibacillus polymyxa

Calibration of Dynamic Models through Adaptive Optimal Input Designs

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