Categories of Models

Quantitative models for predicting quality can be classified into two categories (1) fundamental process models, which are based on physical and chemical events that occur in the autoclave, and (2) regression-type models, which are based on a statistical fit of the observed product quality to the input raw material properties and the process conditions used. 

When available, fundamental process models are preferred. For many complex processes such as composite manufacturing in general and autoclave curing in particular, however, these models are often not available. This lack of availability is due to an inadequate understanding of the complex events that take place during the process. A fundamental process model is occasionally available, but it is still unsuitable for on-line model predictive control application due to the extensive computing time required to solve the model s equations. This lack of 

For continuous process systems, empirical models are used most often for control system development and implementation. Model predictive control strategies often make use of linear input-output models, developed through empirical identification steps conducted on the actual plant. Linear input-output models are obtained from a fit to input-output data from this plant. For batch processes such as autoclave curing, however, the time-dependent nature of these processes—and the extreme state variations that occur during them—prevent use of these models. Hence, one must use a nonlinear process model, obtained through a nonlinear regression technique for fitting data from many batch runs. 

Traditional regression-type models have been linear and quadratic regression models. Linear and quadratic regression models unfortunately impose further constraints upon the nature of the process nonlinearity as such, these models are limited in the range of their applicability. A relatively new nonlinear regression-type model—the Artificial Neural Network (ANN)—is not as limited, and is worthy of additional discussion. 

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Development of Process (Matfiematical) Models Constraints in optimization problems arise from physical bounds on the variables, empirical relations, physical laws, and so on. The mathematical relations describing the process also comprise constraints. Two general categories of models exist ... 

In routine comparisons of X and Y data for spectroscopic analysis, when X and Y denote a comparison of the reference analytical results (X) versus instrument response (Y), at least three main categories of modeling problems are found ... 

Several categories of models appear as the basis for the study of molecular electronics in general, and molecular transport junctions in particular. These are the geometrical (or molecular), Hamiltonian, and transport analysis models. 

Various models have been proposed to describe the facilitated mass transfer phenomena, although five basic categories of models have mostly been reported in the literature [29]. The same models can essentially be applicable for Type II facilitated transport. 

In this category of models the animal learns a performance, typically to abstain from a behavior that it would normally display according to its natural and current tendency. For example, in the so-called Vogel test a partly water-deprived and thirsty rat learns that, during a signaled period, every lick at the water spout will be followed by a mild electric foot-shock. This sequence induces anxiety and an untreated (control) animal will abstain from drinking. However, animals pretreated with anxiolytic drugs will overcome their inhibition and tolerate at least some of the shocks and drink even when punished. 

It is assumed that before we start OF-FMEA an adequate environment to support the work has been set up. Part of this environment is object-oriented models of the system of interest. Of particular interest are two categories of models ... 

When a model is validated it does not mean that it is considered to be true, which is consistent with Box s previously stated dictum. Validation is most often defined as the evaluation of the predictability of the model developed (i.e., the model structure and form together with the model parameter estimates) and estimated from a learning or index data set when applied to a validation (test) data set not used for model building and parameter estimation. Thus, for validation, we are concerned with the predictive performance of a PM model (28). This addresses the issue of transportability of the PM model. That is, ascertaining whether predicted values from a developed PM model are likely to accurately predict responses in future subjects not used to develop the model (1). There are two broad categories of model validation, external and internal, and these will be discussed next. 

In order to calculate the diffusive flux, a suitable mass transfer model must be assumed. T vo categories of models exist (1) interactive models (due to Krishna and Standart [206] and Toor [207]), and (2) noninteractive models, known also as effective diffusivity models. For the interactive models, the diffusion flux j b is... 

Through this step and based on experimental evidence we try to develop the appropriate model to describe the test chamber kinetics. As was anticipated in the introduction of this Chapter, from a conceptual point of view, two broad categories of models can be developed empirical-statistical and physical-based mass transfer models. It should be emphasized that, in several cases, even the fundamentally based mass transfer models are indistinguishable from the empirical ones. This happens because the mass transfer models are generally very complex in both the physical concept involved and the mathematical treatment required. This often leads the modelers to introduce approximations, making the mass transfer models not completely distinguishable from some empirical models in terms of both functional formulations and descriptive capabilities. Considering the current status of models which have been developed to describe VOC emissions (and/or sink processes), we could define the mass transfer models as hybrid-empirical models. 

The mathematical complexity increases considerably from steady state to dynamic simulation, changing from algebraic to differential-algebraic equations. From mathematical viewpoint we may distinguish between two categories of models ... 

This refers to a category of models that describe the flow of information and the process performed on information through a system. It is useful for determining the consequences of failures in THERP... 

Further research has produced a category of models that attempt to describe the jump feature of asset prices and interest rates. Observation of the markets confirms that many asset price patterns and interest rate changes do not move continuously from one price (rate) to another, but sometimes follow a series of jumps. A good example of a jump movement is when a central bank changes the base interest rate when this happens, the entire yield curve shifts to incorporate the effect of the new base rate. There is a considerable body of literature on the subject, and we only refer to a small number of texts here. 

Several qualitative models have been proposed to explain porous Si formation but none of them allow full explanation of the rich variety of morphology exhibited by porous Si and, in particular, the formation of the duplex layers (nano -I- macroporous). In addition, they possess very little predictive power. A majority of the models focussed on the pore propagation, whereas the mechanism of pore initiation received very little attention. A comprehensive review of the various models proposed to explain pore formation is found in excellent review articles by Smith and Collins [5], Parkhutik [12], and Chazalviel and coworkers [13]. Two main categories of models have been proposed. The first one is basically electrostatic in nature, based on the consideration that physical effects associated with the SCR play a major role in the pore-formation mechanism. The second category is based on computer simulations. 

A category of models has developed for use in two-dimensional cases employing a curvilinear (natural) coordinate system. The curvilinear coordinate system recognizes the natural channel curvature which almost always exists in natural streams of any length. In addition, even in rather straight channels, irregularities in the channel bottom due to structures, sediment deposition, and the like may... 

To model the uptimes and downtimes, different assumptions are made depending on how the components are believed to be deteriorating. For some components it is reasonable to assume no deterioration, while others are likely to show strong aging effects. Two basic categories of models are used for this purpose ... 

Another variation on the manipulated distillate scheme is to use a setpoint for the steam/feed ratio to establish the separation power base. Generally, the feed flow rate signal should be lagged with an 8 to 20 min capacitance lag (filter), so the steam flow is proportional to a trailing average of the feed rate. Sometimes, this falls into the category of model-based predictive control because the McCabe-Thiele model, or a computer simulation model shows that the separation power base can be established by the steam/feed ratio as shown in Table 3.3. 

The fidelity of the modeling was speeified on a detailed equipment level, based on the user requirements, with the most stringent requirement governing. Three categories of modeling were defined, i.e. ... 

Table 21.2 lists the key assumptions on which each category of models is based, as well as representative models of the category. Additional assumptions specific to each model are listed in Table 21.3. Table 21.4 examines the validity of some of these assumptions (either the generic assumptions of a category or the additional assumptions of a specific model). 

In the chemical and process industry, there exist three broad categories of models... 

In this category of models, the water molecules are localized. They may either be in their normal position (in which case we would have substoichiometric hydrates of the limited hydrate S,( + p) H2O), or in an interstitial position, in which case we are dealing with an overstoichiometric hydrate of the inferior hydrate S,... 

One can distinguish different types of fiizzy models, each having their own stmctuie and area of application. The Mamdani models are a category of models of the linguistic type. They... 

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