Model validation, optimal design

Strube (1996) has shown that an increasing interaction of components or a decreasing number of columns per section results in significant deviations of both the calculated concentration profiles and purities. Model based optimal design requires a correct description of the dynamic behavior of the SMB process. Therefore, Diinnebier et al. (2000a) recommend the use of the detailed SMB model. These considerations are also valid for SMBR processes. Additionally, Lode et al. (2003a) have shown that the residence time calculated with the TMBR model differs from that in the SMBR model and, in consequence, different conversion rates are calculated. 

Furthermore, optimal design theory assumes that the model is true within the region defined by the candidate design points, since the designs are optimal in terms of minimizing variance as opposed to bias due to lack-of-fit of the model. In reality, the response surface model is only assumed to be a locally adequate polynomial approximation to the truth it is not assumed to be the truth. Consequently, the experimental design chosen should reflect doubt in the validity of the model by allowing for model lack-of-fit to be tested. 

In practice, it generally will be found that one-dimensional models are entirely adequate for optimization, provided that they are validated in some kind of pilot-scale tubular reactor. Validation comprises the adjustment of parameters in the reactor model equations so that observed and predicted temperature and concentration profiles match as closely as possible. Typical parameters are the relative catalyst activity factors Bj and, if necessary, the overall heat-transfer coefficient, U. A statistically-designed set of experiments in the pilot-plant is invaluable for model validation, and such a set was used in this project. 

Annaswamy, A. M., M. Fleifil, J. W. Rumsey, R. Prasanth, J.P. Hathout, and A. F. Ghoniem. 2000. Thermoacoustic instability Model based optimal control designs and experimental validation. IEEE Transactions on Control Systems Technology 8(6). 

Further experiments may be added to a D-optimal design to validate the model (laek of fit) and... 

For each of these interactions, a model complex was designed the BSSE-corrected MP2 interaction potential energy surface (IPES) was calculated then the CHARMm IPES was validated against the MP2 one. If the CHARMm force field cannot produce a satisfactory IPES, the force field will be reparameterized using an automatic least square optimization program OPTMM written by G.D. in C language [24]. 

Cross-validation, in which objects are eliminated and only the excluded objects are predicted from the resulting model to check its stability and validity (see chapter 5.3 for a detailed description), seems to be a too crude instrument to (automatically) decide on the validity of a QSAR regression equation. Cross-validation may be applied to relatively large data sets. But if only few compounds are included in the QSAR equation, if a certain parameter is mainly based on a single data point, or if the compounds have been selected according to a rational design procedure, e.g. a D-optimal design (chapter 6), cross-validation may incorrectly indicate a lack of validity of the QSAR model. 

Chapter 9 shows how compartmental models may be used to describe physiological systems, for example, pharmacokinetics. The production, distribution, transport, and interaction of exogenous materials, such as drugs or tracers, and endogenous materials, such as hormones, are described. Examples of both linear and nonlinear compartmental models are presented, as well as parameter estimation, optimal experiment design, and model validation. 

Dow has developed a pultrusion simulation modeling (PSM) service designed to help fabricators achieve higher levels of productivity and reliability. Process variables such as pull speed, part and die temperature, heater output and pulling force can affect the quality of pultruded components. The PSM tool allows fabricators to predict processing performance for specific applications, and is accurate to within 10% of actual performance. The tool has been validated in customer trials and allows the pultrusion process to be optimized quickly. 

If the enqrirical model is validated, we can then calculate the response studied at each point of the experimental domain. If the number of factors is big. it is not very easy to extract all of the existing information. There are tools that facilitate this interpretation (canonical analysis, study of optimal design, gr rhic representations. etc.) (9,12). 

Within the framework of component development, CFD is used for scientific modeling and model validation in addition to the classical engineering parameter studies and optimization processes. Both approaches are based on the use of HPC calculation capacity. Within the framework of modeling and vahdation, HPC facilitates a complex representation of the physical phenomena with fine space and time discretization. With the aid of such submodels and appropriate laboratory experiments, models for nozzles, heat transfer phenomena, two-phase flow, and so on can be derived and vahdated. CFD models thus selected and validated form the basis for the CFD-based design and optimization of flow systems. The classical engineering problem of parameter variation and optimization requires a large number of simulation calculations and therefore leads to an extremely high cost of computation. HPC allows the parallelization of individual simulations, which in turn makes it possible to calculate several simulations simultaneously and thus enables comprehensive parameter studies and flow optimizations to be completed in an acceptable time frame. In the ATR 10 development process, CFD simulations were conducted on up to 16 cores of the JuRoPA supercomputer simultaneously. This meant that when two simulation... 

From the above simple discussion, it is clear that the pseudohomogeneous model is simply a heterogeneous model but with t = 1.0 [or at least r] = constant (i.e., it is not changing along the length of the reactor)]. Therefore, when rj approaches 1.0, the pseudohomogeneous models are valid for design, operation, and optimization of catalytic... 

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