China
Africa
Explore chapters and articles related to this topic
Parameter Estimation
Published in Alex Martynenko, Andreas Bück, Intelligent Control in Drying, 2018
To ensure meaningful parameter estimates, a sophisticated identifiability analysis is of significant importance. Identifiability measures if and how good parameters can be estimated based on an assumed model structure (determined with either white-, grey-, or black-box modeling approach) and available experimental data. A model is called structurally identifiable if there is a unique solution of the inverse problem, that is, there is one optimal parameter set enabling the optimal fit between measurement and model data.
Modeling: Applications in Biokinetics
Published in José Guillermo Sánchez León, ® Beyond Mathematics, 2017
The transfer rates ki j are usually estimated using experimental data as shown in the next section. The problem that often arises is that there is no unique value of ki j that satisfies the model but a finite number of values. This issue is addressed by a group of mathematical methods named identifiability analysis. The Laplace transforms are very useful in this kind of analysis.
Phenomenological modelling of phase transitions with hysteresis in solid/liquid PCM
Published in Journal of Building Performance Simulation, 2019
Tilman Barz, Johannn Emhofer, Klemens Marx, Gabriel Zsembinszki, Luisa F. Cabeza
The quality of the parameter estimates is assessed by an identifiability analysis. It is a local analysis based on the condition of the sensitivity matrix at the solution of the regression problem, for details see López Cárdenas et al. (2015). For heating, the condition number of the sensitivity matrix is 11,669. This value exceeds the maximum threshold of 1000 and diagnoses an ill-conditioned matrix. However, none of the singular values is very close to zero (values between 5.14 and 59,984) and the collinearity index is 0.195 and below its maximum threshold of 15. Therefore the problem can be considered rank-deficient. For cooling, the condition number is 4035 diagnosing ill-conditioning. However, the singular values are well above zero (between 11.9 and 48,050) and the collinearity index is with 0.084 below the critical threshold. Thus, the problem can also be considered rank-deficient. It can be concluded that for both, heating and cooling, the estimated parameter values are not severely affected by the ill-conditioning of the sensitivity matrix.