Software Equation-Oriented

Two extremes are encountered in flowsheeting software. At one extreme, the entire set of equations (and inequalities) representing the process is employed. This representation is known as the equation-oriented method of flowsheeting. The equations can be solved in a sequential fashion analogous to the modular representation described below or simultaneously by Newton s method, Broyden s method, or by employing sparse matrix techniques to reduce the extent of matrix manipulations. Refer to the review by Evans and Chapter 5. ... 

It may be concluded that Sequential-Modular approach keeps a dominant position in steady state simulation. The Equation-Oriented approach has proved its potential in dynamic simulation, and real time optimisation. The solution for the future generations of flowsheeting software seems to be a fusion of these strategies. The release 11.1 of Aspen Plus (2002) incorporates for the first time EO features in the environment of a SM simulator. 

In Equation-Oriented (EO) approach the software architecture is close to a solver of equations. EO is more suited for dynamic simulation since this can be modelled by a system of differential-algebraic equations (DAE) of the form ... 

Figure 2.9 Software architecture of an Equation-Oriented simulator...

The development of trade software such as Aspen Dynamics or ProsimBatch proves the interest of manufacturers in the use of dynamic simulation for process design and operation. However, some specific process cases may lead end user to develop dedicated simulator of his own. In this context, a library of common building blocks which allows a modular modeling and an equation-oriented simulation of processes seems to be relevant and useful. Providing these software components is the main objective of PrODHyS. Developed in our research department, it results from the unification of works performed since several years in this domain (Jourda et al., 1996 Sargousse, 1999 Moyse, 2000 Hetreux et al., 2002 Ferret et al., 2002). 

Fiber orientation was determined by microradiography. The images of microradiographs were digitized and their orientational distribution determined by image processing software. The fiber orientation function was calculated from the following equation ... 

The main focus of this paper was on the pose estimation problem, which was to determine the position and object models, an algorithm based on a triangulation scheme was developed. The position of the object coordinate frame was found using a nonlinear kast-squares technique. Some of the problems with the software are the fact that only the position of the object is calculated versus both the position and orientation of the object, and that both the object to be grasped and the proximity sensor characteristics are modeled as spherical. This was done to make the equation development, and thus programming, simpler. 

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