Modeling blackbox

Level 3 Blackbox Models Environment models Operator Task models HCI models Blackbox functional models Interface specifications Analysis plans and results. Subsystem Hazard Analysis... 

The model learned is usually a blackbox and does not provide any insight into the physical phenomena and events influencing the process outputs. 

The model induced via the decision tree is not a blackbox, and provides explicit and interpretable rules for solving the pattern classification problem. The most relevant variables are also clearly identified. For example, for the data in Table I, the value of the temperature are not necessary for obtaining good or bad quality, as is clearly indicated by the decision tree in Fig. 22. 

From a simulation viewpoint units SO, S6 and S7 may be considered blackboxes. On the contrary, SI to S5 are simulated by rigorous distillation columns, as sieve trays. In the steady state all the reactors can be described by a stoichiometric approach, but kinetic models are useful for Rl, R2 and R4 in dynamic simulation [7, 8]. As shown before, the reaction network should be formulated so as to use a minimum of representative chemical species, but respecting the atomic balance. This approach is necessary because yield reactors can misrepresent the process. 

In practice, one is often faced with choosing a model that is easily interpretable but may not approximate a response very well, such as a low-order polynomial regression, or with choosing a black box model, such as the random-function model in equations (l)-(3). Our approach makes this blackbox model interpretable in two ways (a) the ANOVA decomposition provides a quantitative screening of the low-order effects, and (b) the important effects can be visualized. By comparison, in a low-order polynomial regression model, the relationship between input variables and an output variable is more direct. Unfortunately, as we have seen, the complexities of a computer code may be too subtle for such simple approximating models. 

Hence, there are subtle but important differences between modeling and simulation. Modeling looks back in time, whereas simulation looks forward. Simulation is used to answer What if..., whereas modeling is used to answer What happened Modeling requires data, simulation requires models that may or may not be built on data. Both M S are sensitive to their assumptions and any blackbox aspects in their use, both of which may lead to criticism of a M S exercise. Furthermore, both M S can be used to identify important variables and can be used to summarize and understand complex systems. 

A mobile or stand-alone unit which would controllably convert food waste into ethanol at a busy cafeteria or restaurant would be attractive if the economics were favorable. Using a blackbox model, several eomponents are considered important for monitoring the conversion into ethanol (Fig. 1). 

Nevertheless, as discussed previously, the physical model for a crystallizer is an integro-partial differential equation. A common method for converting the population balance model to a state-space representation is the method of moments however, since the moment equations close only for a MSMPR crystallizer with growth rate no more than linearly dependent on size, the usefulness of this method is limited. The method of lines has also been used to cast the population balance in state-space form (Tsuruoka and Randolph 1987), and as mentioned in Section 9.4.1, the blackbox model used by de Wolf et al. (1989) has a state-space structure. 

Crew Station/equipment characteristics The crew station design module and library is a critical component in the MIDAS operation. Descriptions of discrete and continuous control operation of the equipment simulations are provided at several levels of functiontil deteiil. The system can provide discrete equipment operation in a stimulus-response (blackbox) format, a time-scripted/ event driven format, or a full discrete-space model of the transition among equipment states. Similarly, the simulated operator s knowledge of the system can be at the same varied levels of representation or can be systematically modified to simulate various states of misunderstanding the equipment function. 

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... 

Note that the impedance model, the actuation model, and the reduced model are all expressed in terms of fundamental physical parameters of IPMC and thus are geometrically scalable. On the other hand, the resulting models are amenable to system analysis and control design. Such physics-based, control-oriented models effectively bridge the gap between PDE-based physical models and low-order black-box models. For blackbox models, the parameters have no physical meanings and have to be re-identified empirically whenever the actuator dimensions are changed. 

The reason for calling a time-dependent concentration a capacitance has already been explained in Section 2.3 in context with the relaxation behaviour of the blackbox membrane model. Let us assume that the concentration c. of a molecule of kind i is given as a unique function of its chemical potential c. = c. (y. ). Taking the time derivative and making use of the associated reference direction we then obtain... 

In the present section, let us now discuss the simplest possibility of representing a pore model in terms of bond-graph network elements and ask whether the results obtained from that network essentially differ from those of the blackbox model of Section 2.3. In Section 5.4 we shall then consider the simplest network realizations of carrier mechanisms. Our starting point is the assumption that a limited number of pores is present in the membrane. The pores are represented by a material capacitance with concentration X of numbers or moles of pores per membrane area. From either side of the membrane a neutral molecule with concentration c, c, respectively, can selectively jump into an empty pore thus forming a molecule-pore complex with concentration Y. Clearly, this jump process will be represented by a 2-port reaction element like that in (4.27) where the reactants 1 and 2 on the forward side will be replaced by the molecule in the adjacent solution... 

Commercial finite element codes are often called upon to simulate the behaviour of tyres in real-world applications. These numerical codes are mostly used as blackboxes , and the validity of the results is rarely questioned, even though they might provide a decisive argument in favour of, or against, the viability of a given tyre model. 

A second class of methods is instead based on the knowledge of the electron density in a theoretical framework similar to that of the DPT. In DPT the effects of the exchange and of the electronic correlation are included by the so-called exchange-correlation (xc) functional, which is obtained by an empirical fit of experimental data or by imposing some physical constrains based on the behavior of some limit model systems [44]. Por the excited states, the TD-DPT [17,18] recently emerged as a very effective tool, since, when coupled to suitable density functionals, it often reaches an accuracy comparable to that of the most sophisticated (but expensive) post-Hartree-Fock methods [45-59], with a much more limited computational cost As a consequence in the last years an increasing number of TD-DPT applications have appeared in the literature, also because this method can be used as a blackbox and is thus also easily accessible to nonspecialists. 

Most of the literature in control of continuous crystallizers is based on a singleinput single output (SISO) control structure. Different controlled variables and manipulations have been suggested based on the relative ease and accuraey of on-line measurements and their efficiency in effectively addressing set-point tracking and disturbance rejections. Both linearized physical models and blackbox models have been suggested for the controller design, as reviewed by Sheikh (1997) as follows. 

The Hammerstein-Wiener model can be used as a blackbox model structure since it prepares a flexible parameterization for nonlinear models. It is possible to estimate a linear model and try to improve its quality by adding an input or output nonlinearity to this model. 

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