White box model

The advanced process control strategies that are most applicable to the optimization of the distillation process are usually based on white-box modeling, where the theoretical dynamic models are derived on the basis of the mass, energy, and momentum balances of this well-understood process. Although the optimization techniques described here can improve productivity and profitability by 25%, this goal will only be achieved if the distillation process is treated as a single and integrated unit operation and the variables, such as flows, levels, pressures, etc., become only constraints, and the controlled and optimized variables are productivity and profitability. 

Fig. 5.1 A schematic drawing of the proposed modeling approach, leading from in-vitro biochemistry to an in-vivo understanding. In step 1, in-vitro experiments are carried out to determine the mechanisms of the involved reactions, and to determine estimates of the corresponding kinetic parameters and concentrations. In step 2, this information is collected into a mechanistic white-box model, which might also be adjusted to agree with the observed in-vivo behavior (gray-box modeling). In step 3, this model is simplified (step 3b) to a smaller model that is identifiable (step 3a) with respect to the in-vivo data, and has the same basic features as the original model. This is the core model, and an alternative way is to formulate it directly from...

The traditional approach used in engineering design and modeling is based on the assumption that the entire system/process can be described by mathematical equations. This type of model is called a white box model. Such a model is based on the first engineering principles, i.e., physical, chemical, biological, or economic laws. No ejqierimental data is needed. 

The grey box model approach, i.e., a combination of the black box and white box model is proposed for remaining useful hfe prediction. Use of expert judgement is suggested to compensate for lack of operating ejqrerience and operational data. 

Current modeling work on IPMC actuators typically falls into three categories, with progressively increased level of complexity and fidelity blackbox models, gray-box models, and white-box models. Black-box models... 

In this section, a physics-based and control-oriented actuation model for IPMC actuators is presented. The model combines the seemingly incompatible advantages of both the white-box models (capturing key physics) and the black-box models... 

Physics-based and control-oriented actuation model was presented that combines the seemingly incompatible advantages of both the white-box models (capturing key physics) and the black-box models (amenable to control design). This modeling approach provides an interpretation of the sophisticated physical processes involved in IPMC actuation from a systems perspective. Also, an empirical model for mechanical simulations was described that can be implemented for complex mechanical systems when physical model using partial differential equations is too complicated for numerical simulation. 

The models can be white box, gray box, and black box. White box models are derived using physical laws and principles. Their parameters are identified from experimental data. However, these models are overly complex and usually not realistic to build and use. Gray box models which are partially based on physical laws and principles use the experimental data to complete the rest of the model and subsequently validate them. On the other hand, a black box model which is the most commonly used model structure describes an output-input relationship, without explaining the physical phenomena behind the identified model. 

This list includes all kinds of development work. We have already discussed model frameworks and template packages, which can be valuable to an enterprise. They are white-box assets What you see is what is they offer. By contrast, an executable piece of software, delivered without source code, can perform a useful and well-defined function and yet not be open to internal inspection. Software vendors prefer such black-box components. 

The box model amounts to a system of N boxes, into which one randomly and successively throws white (A) and black (B) balls, with the total numbers of thrown balls a and b equal to one another at any instant (apart from a single ball). In the absence of annihilation the colour of a ball has no... 

White-box or first-principle modeling. A dynamic model for well-understood processes derived from mass, energy, and momentum balances. 

Gray-box modeling. ANNs can learn complex functional relations by generalizing from a limited amount of training data. When part of the process is well understood, white- and black-box models can be combined and called gray-box modeling. 

There are a number of important issues and possible trade-offs to be discussed in this section that, in principle, do not stand against each other but, in reality, often do, such as the balance between the interpretability versus robustness or predictability of the derived model, that is, transparent versus opaque models, white versus black box models, a well as whether to derive local versus more global models for a particular target in question. For a recent review of statistical methods, see Ref. [80]. 

GV150013 has shown activity in a number of animal models of anxiety. In the mouse black/white box test GV150013 increased the time that naive mice remain in a brightly illuminated section of an activity box The effect was dose related and significant increases were measured at 0.1, 0.3 and l. Ong.kg 1.Similar anxiolytic effects were seen in the rat social interaction test and the marmoset human threat test [25]. The ED50 values are given in table 5. 

FIGURE 1.1 A box model for the Earth System, showing some of the major reser voirs and the interactions (white arrows) between them. 

Figure 25 The middle layer of the model enzyme used by Bagdassarian and coworkers to examine the role of vibrations in promotion of catalysis. C is the catalytic subunit, and S the substrate. Molecular dynamics simulations were used to assess the catalytic efficiency of enzymes that varied in the number of flexible and stiff linkages between neighboring subunits in the white box. P (phantom) and N (neutral) subunits were not varied during the simulation. Reproduced with permission from G. S. B. Williams A. M. Hossain S. Shang D. E. Kranbuehl C. K. Bagdassarian, J. Theor. Comput.

Fig. 5 Scheme of model for calculating relative aquatic concentrations (RAC). The soil compartment and the river model are connected through the flux (fsw) from soil to the first box of the river model. The river model consists of flowing water (shaded boxes), stagnant water (white boxes) and an underlying river sediment (not shown). Reprinted with permission from [8], p 2446. (2007) American Chemical Society... 

Fundamental models (white/gray box models) i.e., models based on the physical and chemical fundamentals of the processes (e.g. E=mc ). 

Protein sequence based on intron/exon modeling performed by Todd Richmond (hHp //cellwall. stanford.edu/php/structure.php). Black boxes = putative transmembrane domains White boxes = conserved U domains Grey boxes = hydrophobic regions manually. 

Finally the system is a major consideration in modeling because of the various ways the real system can be represented by the model M of that system. Numerous forms of the model M are available. They can have a structure based on capturing fundamental phenomena from physics and chemistry ( white box ... 

Figure 6.18 Projection images of a rat lung at three magnification levels. The white dashed box on the left image encloses the middle image and the solid white box on the middle image encloses the right image. The small white rectangles designated by the arrows are the boxes across which the line scans were taken for vessel diameter estimation in the respective lower panels. The solid lines in the lower panels indicate a model fit to the line scan data obtained from the vessel cross section.

For system applications of soft materials, it is important to analyze and model the responses. Some models of the sensor function of IPMCs were studied fi om the viewpoint of the black/gray box modeling (Newbury and Leo 2003 Bonomo et al. 2006) and the white box (physical and chemical) modeling (Farinholt and Leo 2004). 

Nica et al. [16] propose a method for combining debugging, testing and mutants to reduce the set of possible fault candidates. Contrary to our work, they use white-box methods by mutating the faulty code, they try to find mutants behaving correctly, while we mutate the correct model, trying to find mutants that show the same faulty behavior as the implementation. 

---