Steps in model building

Part I comprises three chapters that motivate the study of optimization by giving examples of different types of problems that may be encountered in chemical engineering. After discussing the three components in the previous list, we describe six steps that must be used in solving an optimization problem. A potential user of optimization must be able to translate a verbal description of the problem into the appropriate mathematical description. He or she should also understand how the problem formulation influences its solvability. We show how problem simplification, sensitivity analysis, and estimating the unknown parameters in models are important steps in model building. Chapter 3 discusses how the objective function should be developed. We focus on economic factors in this chapter and present several alternative methods of evaluating profitability. 

The crucial step in model building is model formulation, since the mathematical modeling is intended to represent a large network of multiple biochemical reactions, controlled by complex regulatory processes that... 

The book includes model formulation, i.e. how to describe a physical/chemical reality in mathematical language, and how to choose the type and degree of sophistication of a model. It is emphasized that this is an iterative procedure where models are gradually refined or rejected in confrontation with experiments. Model reduction and approximate methods, such as dimensional analysis, time constant analysis, and asymptotic methods, are treated. An overview of solution methods for typical classes of models is given. Parameter estimation and model validation and assessment, as final steps, in model building are discussed. The question What model should be used for a given situation is answered. 

Indeed, the description of the process is recognized as the rst step in the building of the mathematical modelling of a process. The result obtained here is recognized as a descriptive model or model by words. During this step, dependent and independent process variables resulting from the identification of the actions and interactions of the elementary phenomena that compose the state and evolution of the investigated process will be listed. At the same time, the effect of each independent variable on each dependent variable must be described. 

The coupling of the general mathematical model with the evolution of the material and spatial conditions is given by its association with the investigated conditions of univocity of the process. This is the basis of the third step in the building of the mathematical model of a process. At the end of this step, we will have a particularized mathematical model. This step will be specified for each one of the decomposed models of the parts i.e. for each of the particular devices in a unit. For this particularization, we use the following conditions of univocity ... 

Figure 3.4 Steps in the building of a mathematical model for a concrete case.

The run time of a specific model depends on the complexity of the model, the converging algorithm, the chosen software, and the amount of data. In many situations, it is the run time that is the rate-limiting step of model building. The following are some approaches that can be adopted to decrease the duration of or to enable one to cope with long run times. 

In the following, a real case study will be given to practically demonstrate how the chamber kinetics of VOCs can be modelled by applying mathematical theory to handle experimental data resulting from experiments performed in test chambers. Through this case study, the different steps of model building and model validation processes will be clearly identified and thoroughly discussed. 

Because reaction rates between minerals and solutions are directly proportional to the interfacial area between the phases, it is necessary to quantify this area for rate models. There are various methods to measure the interfacial area, but a useful first step for model building is to develop idealized reference models for reacting surfaces. Idealized surface area models neglect important surface features in a trade-off for simplicity. As such they provide a handy approximation of the relationship between surface geometry and reaction rates. 

The first step in the building the atmospheric distillation unit is entering the composition of the crude in order to generate the necessary hypothetical components for model. For the purposes of this simulation, we will consider the crude assays given in Table 2.5 to Table 2.8. It is important to remember that that we may have to remove extraneous details from the distillation curve to avoid unusual column behavior. We use the TB P distillation, density distribution and overall bulk density to define this system in Figure 2.14. 

Iteration of the steps, descriptor selection, model building, and model validation in combination with an optimi ation algorithm allows one to select a descriptor subset having maximum predictivity. 

The abbreviation QSAR stands for quantitative structure-activity relationships. QSPR means quantitative structure-property relationships. As the properties of an organic compound usually cannot be predicted directly from its molecular structure, an indirect approach Is used to overcome this problem. In the first step numerical descriptors encoding information about the molecular structure are calculated for a set of compounds. Secondly, statistical methods and artificial neural network models are used to predict the property or activity of interest, based on these descriptors or a suitable subset. A typical QSAR/QSPR study comprises the following steps structure entry or start from an existing structure database), descriptor calculation, descriptor selection, model building, model validation. 

The general procedure in a QSPR approach consists of three steps structure representation descriptor analysis and model building (see also Chapter X, Section 1.2 of the Handbook). 

Model building consists of three steps training, evaluation, and testing. In the ideal case the whole training data set is divided into three portions, the training, the evaluation set, and the test set. A wide variety of statistical or neural network... 

Backbone generation is the first step in building a three-dimensional model of the protein. First, it is necessary to find structurally conserved regions (SCR) in the backbone. Next, place them in space with an orientation and conformation best matching those of the template. Single amino acid exchanges are assumed not to affect the tertiary structure. This often results in having sections of the model compound that are unconnected. 

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