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Methods for the careful design of optimal experiments for the identification of the structure and parameters of transport models often strongly depend on a-priori knowledge about the unknown model. However, this kind of knowledge is usually poor for complex systems. We propose a novel procedure that is less sensitive with respect to poor a-priori knowledge; it relies on an optimization problem to maximize the information content of the measurement data for the purpose of model identification. Specifically, based on existing model-based methods, optimal design of experiments is addressed in the context of three-dimensional, time-dependent transport problems by introducing experiment design variables and the transport coefficient as degrees of freedom of the optimization. The problem is solved by means of an iterative strategy that – by sequentially designing a series of experiments – strives to adjust the settings of the experimental conditions by exploiting the results from previous experiments. The key methodical ingredient of the novel procedure is the use of incremental model identification introduced previously. The suggested procedure is illustrated by means of an extensive numerical case study for a convection–diffusion equation originating from the modeling and simulation of energy transport in laminar wavy film flow. [ABSTRACT FROM AUTHOR]

A rigorous method is presented for the systematic identification of the structure and the parameters of transport coefficient models in three-dimensional, transient convection-diffusion systems using high-resolution measurement data. The transport is represented by a convection term with known convective velocity and a diffusion term with an unknown, generally state-dependent, transport coefficient. The identification of a transport coefficient model constitutes an ill-posed, highly nonlinear inverse problem. In our previous work [Kaxalashvili et al., SIAM J. Sci. Comput., 30 (2008), pp. 3249-3269], we presented a novel incremental identification method, which decomposes this inverse problem into easier-to-handle inverse subproblems. This way, the incremental identification method not only allows for the identification of the structure and the parameters of the model, but also supports the rigorous decision making on the best-suited transport model structure. Due to the decomposition approach, the identified transport model structure and parameters are subject to errors. To cope with the error propagation inherent in the incremental method, the present work suggests a model correction procedure as a supplement to the incremental identification method of our previous work, which results in a transport model of higher precision. The correction refers to both the model structure and parameters. No a priori knowledge on the unknown transport model structure is necessary. The identification approach is numerically illustrated for a three-dimensional, transient convection-diffusion equation which has its origin in the modeling and simulation of energy transport in a laminar wavy film flow. [ABSTRACT FROM AUTHOR]

The article presents a methodology for developing process models for multi-phase reaction systems. The methodology, which enables the systematic decomposition of mass transfer and chemical reaction and allows the identification of multi-phase reaction systems, is based upon the Incremental Identification Method (IIM). The IIM is described, noting that it allows researchers to test the identifiability of a system using measurement data they have available. A simulated two-phase enzyme reaction system is presented to demonstrate the identification of the intrinsic reaction kinetics in a sound and numerically robust way.

In this paper, an incremental approach for the identification of a model for transport coefficients in convection-diffusion systems on the basis of high-resolution measurement data is presented. The transport is represented by a convection term with known convective velocity and by a diffusion term with an unknown, generally state-dependent transport coefficient. The identification of the transport model for this transport coefficient constitutes an ill-posed nonlinear inverse problem. We present a novel decomposition approach in which this inverse problem is split into a sequence of inverse subproblems. In the first identification step of this incremental approach a source is estimated by solving an affine-linear inverse problem by means of the conjugate gradient method. In the second identification step a nonlinear inverse problem has to be solved to reconstruct a transport coefficient. A Newton-type method using the conjugate gradient method in its inner iteration is used to solve this nonlinear inverse problem of coefficient estimation. Finally, in the third identification step a transport model structure is proposed and identified on the basis of the model-free transport coefficient reconstructed in the two previous steps. The ill-posedness of each inverse problem is examined by using artificially perturbed transient simulation data and appropriate regularization techniques. The identification methodology is illustrated for a three-dimensional convection-diffusion equation which has its origin in the modeling and simulation of energy transport in a laminar wavy film flow. [ABSTRACT FROM AUTHOR]

We propose a novel approach for the parametrically robust design of dynamic systems. The approach can be applied to system models with parameters that are uncertain in the sense that values for these parameters are not known precisely, but only within certain bounds. The novel approach is guaranteed to find an optimal steady state that is stable for each parameter combination within these bounds. Our approach combines the use of a standard solver for constrained optimization problems with the rigorous solution of nonlinear systems. The constraints for the optimization problems are based on the concept of parameter space normal vectors that measure the distance of a tentative optimum to the nearest known critical point, i.e., a point where stability may be lost. Such normal vectors are derived using methods from nonlinear dynamics. After the optimization, the rigorous solver is used to provide a guarantee that no critical points exist in the vicinity of the optimum, or to detect such points. In the latter case, the optimization is resumed, taking the newly found critical points into account. This optimize-and-verify procedure is repeated until the rigorous nonlinear solver can guarantee that the vicinity of the optimum is free from critical points and therefore the optimum is parametrically robust. In contrast to existing design methodologies, our approach can be automated and does not rely on the experience of the designing engineer. A simple model of a fermenter is used to illustrate the concepts and the order of activities arising in a typical design process. [ABSTRACT FROM AUTHOR]

Even though multicomponent mixtures are ubiquitous in mass transfer processes, mutual diffusion data in these systems are scarce. This is due to the fact that established diffusion measurements are laborious. In particular, several experiments are required to determine multicomponent diffusion coefficients at a single composition. In order to overcome these deficiencies, a diffusion experiment employing one-dimensional Raman spectroscopy is presented. Concentrations of the individual species are resolved with high spatial and temporal resolution during the diffusion process. In this work, it is shown that these data allow determining the ternary Fick diffusion matrix from a single isothermal diffusion experiment. The experimental procedure is further optimized using model-based experimental design techniques, where general design guidelines for diffusion experiments are derived. Thereby, precision of the diffusion measurements can be improved by an order of magnitude. The theoretical calculations are validated by experimental results for the system n-propanol + 1-chlorobutane + n-heptane. [ABSTRACT FROM AUTHOR]

Short cut procedures such as the differential method are still popular for the identification of reaction kinetics. Despite their lack of statistical rigor their computational efficiency makes them a valuable tool for initial analysis. A new incremental approach is introduced here to extend the differential method. This identification procedure is split in a sequence of inverse problems, thereby reducing uncertainty and computational complexity. Since error propagation remains critical for the success of such a stepwise approach the influence of error propagation has to be analyzed. Consequently, the performance of the incremental strategy is compared to that of the simultaneous approach which exhibits optimal statistical properties. A pedagogical example is considered in detail to extract general conclusions. [Copyright &y& Elsevier]

Predictive models for diffusion in liquids contain still large uncertainties due to a lack of experimental data. Modern measurement techniques offer high-resolution concentration data but data analysis tools are usually designed for scarce data. A new incremental approach to model identification is therefore introduced and applied to the estimation of diffusion coefficients. The identification problem is split here in a sequence of inverse problems following the steps of model development. Thereby, model uncertainty and computational cost are minimized. The concentration dependence of binary diffusion coefficients can now be efficiently established from a single experiment. Furthermore, the robust estimation of the ternary diffusion matrix from a single data set is demonstrated. [Copyright &y& Elsevier]

Abstract: In this work the normal vector method is extended to the simultaneous treatment of parametric uncertainty and disturbances. This method ensures that desired dynamic properties hold despite parametric uncertainty by maintaining a minimal distance between the operating point and so-called critical manifolds where the process behavior changes qualitatively. Here, unknown exogeneous disturbances and uncertain model and process parameters are considered simultaneously. To address this simultaneous problem formulation, the augmented systems developed for only parameterized disturbances in previous works have to be modified and extended. A generalized formulation of the robust optimization problem results, which includes normal vector constraints on critical manifolds of steady states and of bounds on the state transient. The numerical methods are further developed to prepare for the treatment of high-dimensional problems. Illustrative case studies considering the design of a continuous mixed-suspension mixed-product removal crystallization process and the Tennessee Eastman process are presented. [Copyright &y& Elsevier]

Abstract: Estimating the parameters of a dynamical system based on measurement data is an important but complex task in industrial and scientific practice [Schittkowski, K. (2002). Numerical data fitting in dynamical systems: A practical introduction with applications and software. Kluwer Academic Publishers]. Due to its importance, different approaches to solve this kind of problem have been developed. The most established ones are single shooting [Bard, Y. (1974). Nonlinear parameter estimation. New York: Academic Press], multiple shooting [Bock, H. G. (1983). Recent advances in parameter identification techniques for ODE. In P. Deuflhard, & E. Hairer (Eds.), Numerical treatment of inverse problems in differential and integral equations (pp. 95–121). Boston: Birkhäuser] and full discretization techniques [Biegler, L. T. (1984). Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation. Computers & Chemical Engineering, 8, 243–248]. Single shooting is the most natural and simple approach to the problem, directly combining numerical integration and optimization techniques. However, for unstable or singular systems the numerical integration of the dynamic model may fail. This problem is especially severe in the framework of parameter estimation, since the dynamic model has to be integrated many times with different parameter estimates. Multiple shooting and full discretization aim at overcoming these deficiencies but suffer from other drawbacks. Therefore single shooting is still widely applied in industry and academia. In this work we present a novel method called Incremental Single Shooting or ISS for short, which aims at overcoming the deficiencies of the classical single shooting approach while keeping its advantages. [Copyright &y& Elsevier]

Estimating the parameters of a dynamical system based on measurements is an important task in industrial and scientific practice. Since a model’s quality is directly linked to its parameter values, obtaining globally rather than locally optimal values is especially important in this context. In practice, however, local methods are used almost exclusively. This is mainly due to the high computational cost of global dynamic parameter estimation, which limits its application to relatively small problems comprising no more than a few equations and parameters. In addition, there is still a lack of software packages that allow global parameter estimation in dynamical systems without expert knowledge. Therefore, we propose an efficient computational method for obtaining globally optimal parameter estimates of dynamical systems using well-established, user-friendly software packages. The method is based on the so-called incremental identification procedure, in combination with deterministic global optimization tools for nonlinear programs. [ABSTRACT FROM AUTHOR]

Abstract: A novel model reduction methodology is proposed to approximate large-scale nonlinear dynamical systems. The methodology amounts to finding computationally efficient substitute models for the nonlinear subsystems. Model reduction is pursued by viewing the system as a grey-box (or hybrid) model with a mechanistic (white-box) component and an empirical (black-box) component. Before identifying the substitute model, the mechanistic subsystem is reduced by projection using proper orthogonal decomposition. Subsequently, the empirical component is identified by parameter estimation to substitute the nonlinear subsystem. As a consequence, a reduced model with less nonlinear complexity is obtained. An example involving a distributed parameter system is provided. [Copyright &y& Elsevier]

Abstract: In this paper we apply the incremental method for the identification of reaction kinetics [Brendel, M., Bonvin, D., Marquardt, W., 2006. Incremental identification of complex reaction kinetics in homogeneous systems. Chemical Engineering Science 61, 5404–5420] to the oxidation of formate by dehydrogenase. For the identification task little a priori knowledge is assumed and thus a high number of model candidates have to be considered. In order to identify the best model from a set of candidates the number of candidates is efficiently reduced in a first step using the incremental method. In a second step the best model and its parameters are determined based on the reduced candidate set in a statistically sound manner using the classical simultaneous method. [Copyright &y& Elsevier]