(374h) A Computer-Aided Modeling Tool for Efficient Model Identification and Analysis

Computer-aided simulation of chemical and biochemical systems has a wide range of applications due to its potential of partly replacing cost-intensive and time-consuming experiments but also delivering truly innovative solutions that are not necessarily obtained by conventional approaches. A further benefit is a better understanding and analysis of complex systems. However, the prerequisite of all this is the development and identification of validated and predictive models that are able to represent the system under investigation. This can be a very challenging task involving numerous steps, expert skills (process knowledge, numerical analysis, statistical methods, etc.) and different tools.

Model identification problems can be of different types. In some cases a large amount of data on the system is available, while the theoretical knowledge underlying the system behavior and the observed phenomena is rather limited. The opposite situation, where significant knowledge on the theoretical background of the system is available, whereas only few experimental data, is also the conceivable. In any case at least some data needs to be available to identify the model parameters. The available experimental data may also have uncertainties in their measured values due to measurement inaccuracies. In many cases these uncertainties cannot be neglected and need to be taken into account by the solution method. Another point to be emphasized here is the importance of model analysis as a basic step in the problem solution procedure. Model analysis with respect to stability of the solution (depends on the type of model), reduction of the equation set, sensitivity of the model parameters, ordering of equations for efficient numerical solution, etc., helps defining and solving model identification problems in an efficient, reliable and robust manner.

In this study, a computer-aided framework that combines all the above mentioned features for model identification is presented. The purpose of this framework is to generate a systematic work-flow of the process and increase its efficiency. This is achieved by guiding the user through the work-flow to solve the model identification problem and combining all required tools in one platform, providing database connections, allowing storage and re-use of models and offering expertise the user might not have. Model analysis is incorporated as a separate step due to its importance for the understanding and the success of the solution procedure. In this step the degree of freedom and the incidence matrix are determined. The tool orders the equations to a lower triangular form to the extent possible. Moreover, the modeling tool performs checks on the model equations, for example for singularities. The presented computer-aided modeling framework also contains methods for sensitivity analysis, advanced parameter regression solvers and the generation of a statistical report which helps the user to evaluate the determined solution.

An exemplary case study that highlights the features and step-wise model identification applying the computer-aided framework is presented. The case study is related to combustion and consequently the investigated system contains a large number of equations, chemical compounds and parameters what makes it an excellent example for the application of sensitivity analysis in model identification. In total the model contains 345 equations. These are subdivided into 330 explicit algebraic equations and 15 ordinary differential equations. The system contains 18 compounds and 263 parameters. First, an initial set of local parameter values were obtained. Then a sensitivity analysis was performed to ?fine-tune? the most sensitive parameters to obtain an improved fit of the experimental data. Furthermore, correlations between the parameters were analyzed.