Modeling, goals

Besides the description of the position dependence, there is other important description level which has to be defined to formulate a model the model species. From this perspective, there are two main types of models those that consider all the significant compounds presented in the reactor as model species (multivariable models) and those that summarize different species into a small number of model species (in the more strict case only one variable and they are called as single-variable models). It is clear that the higher the number of species, the higher the complexity of the simulation. Hence, in the formulation stage it is important to study in detail what it is desired to model and to make a compromise as a function of our modeling goal between the optimum situation for the analysis of the process (many model species) and the optimum situation for the mathematical simulation (few model species). 

Chemical Modeling—Goals, Problems, Approaches, and Priorities... 

It is clear from this example that choosing templates and modeling goals is a process that takes some care and understanding of biological function. Automated procedures are less than satisfactory for the purposes described here. 

Modeling goals is particularly useful in RE. High-level business goals can be refined repeatedly as part of the elicitation process, leading to requirements that can then be operationalized. 

Minimal representations are known to have no redundant elements, therefore are of great importance. Based on the notions of performance and quality indices and measures for process systems, the paper proposes conditions for a process model being minimal in a set of functionally equivalent models with respect to a quality norm. Existing procedures to obtain minimal process models for a given modelling goal are discussed and generalized. The notions and procedures are illustrated and compared on a simple case study, on the example of a simple nonlinear fermentation process model. 

A process model is jointly determined by the process system it describes and by its modelling goal (Hangos and Cameron, 2001). In order to develop a formal description of the modelling goal of a process system, the notion of model indices should first be defined. 

Modelling goal The modelling goal is assumed to be given in terms of performance indices Xh X by setting acceptance limits for each of them in the form of inequalities... 

Performance indices for state-space models Model-based control is considered for this type of model as a modelling goal, where the requirements of a process system to satisfy the modelling goal is naturally given in terms of properties and/or parameters of a desired input-output behaviour. 

The above formal specification of the modelling goal can be used to define the notion of equivalent process models as follows. 

Functionally equivalent models When a set of admissible models is given together with a modelling goal defined in terms of performance indices as in Eq. (2), there is usually more than one model which can satisfy the modelling goal. Such models form a set of functionally equivalent models and they are defined as... 

Both functionally and algebraically equivalent models The above properties of equivalent state-space models raises the question What are the conditions of functionally equivalent process models that make them algebraically equivalent . It follows from the definitions that such models may be obtained in case of a modelling goal specified... 

It is important to note that two functionally equivalent process models Mi and M2 of equal quality with respect to some quality indices may or may not be algebraically equivalent. This depends on the invariance properties of the performance and quality indices with respect to algebraic transformation and also on the equality-inequality constraints in the formulation of the modelling goal. 

In case of algebraically different but functionally equivalent process models we aim at finding the simplest possible process model, a so called minimal model, for the given modelling goal. It follows from the ordering of process models that minimal models depend on the selection of the quality indices and their quality norm. Moreover, minimal models may or may not be algebraically equivalent. 

The definition of the minimality of process models assumes that we have a set of process models from which we determine the minimal one(s). There are, in principle, two different ways of obtaining minimal models satisfying a prescribed modelling goal ... 

Further assume that the reactor is operated in such a way that it starts from an initial volume Vo and a feed is fed to it until a prescribed final volume is reached. A possible choice for the modelling goal would be to estimate the reaction time Tm and the final concentrations of the biomass Xu and substrate 5m with a given precision, that is Xi= Mi X2 = Mi Su and the modelling goal is given in terms of inequalities like in Eq. (2). 

The modeling goal plays a vital role in the development of the model. Here we consider the most important general goals and describe briefly what is achieved. We make reference to the general process system illustrated in Figure 1. 

Computer scientists and engineers want to push the envelope of IT capabilities, and CTeate structures for efficient workflow and resource utilization. They need metadata from experimentalists in order to characterize the data and facilitate use of the data by others. They need an understanding of the physical basis of modeling goals, which are invariably the key to improving efficiencies. 

During the system analysis one focuses on the system itself, in order to investigate which physical-chemical phenomena take place and are relevant with respect to the modeling goal. One method that could be used is to find key mechanisms and key components, for example evaporation (phase equilibrium), mass diffusion or transport, heat convection, conduction or radiation, and liquid flow. The key variables could be, amongst others, temperature, pressure and concentration at a certain location. Also in this case, one should take into account the required level of detail, the hierarchy within the model and the required accuracy. 

The different applications of models and the different modeling goals have lead to many different model stmctures. Since models are used as a basis for further decisions, the knowledge should be presented in a usable form. The model should not be too complex, nevertheless it should give a sufficiently accurate description of the system. The following classifications can be made ... 

The level of detail is directly dependent on the modeling goal and has already an impact on the choices for the environmental model. The choices can be divided into the frequency domain or time domain one is interested in ... 

In case of the evaporator shown in Fig. 3.3, the modeling goal depends on the goal of the operation. 

The modeling goal is to investigate vapor flow behavior as a function of throughput variations. It is therefore not required to take fast pressure changes into account. The time scale of relevant changes is in the order of the residence time. 

The modeling goal is to investigate variations in the produced vapor flow as a function of variations in the steam pressure. The level of detail depends entirely on the speed of pressure variations. If pressure variations are fast, a detailed model should be developed. However, if the variations of fte pressure are limited, the level of detail is similar to the previous case. 

The intention is to give the reader an understanding of differences between models as reflected by the modeling goal. Which question is the model intended to answer ... 

Lind, M. Modeling Goals and Functions of Complex Industrial Plant, Applied Artificial Intelligence, 8 529-283, 1994. 

Jenne EA (1979) Chemical modeling-goals, problems, approaches and priorities. In Jenne EA (ed) Chemical modeling of aqueous systems I. Am Chem Soc Symp Ser 93, Washington DC, pp 3-24... 

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