Athena Visual Studio

This book will acquaint the reader with some of the important tools and strategies now available for investigating chemical processes and systems on personal computers. We present some useful mathematical models, numerical methods for solving them, and statistical methods for testing and discriminating candidate models with experimental data. The software package Athena Visual Studio, obtained from www.AthenaVisual.com, will enable you to do these computations and view the results on your personal computer screen, print them and transmit them. Familiarity with Microsoft Windows (1998 or later) is required, but little knowledge of Fortran, since Athena converts equation statements directly into Fortran code as described in the Athena tutorial on your computer s desktop. 

The object code for DDAPLUS and its dependencies is provided in the software package Athena Visual Studio, which is available at www.AthenaVisual.com. 

All the subroutines described in this appendix can be created automatically by Athena Visual Studio in ANSI standard FORTRAN-77. Since FORTRAN-90/95 is compatible with this standard, there should be no difficulty in using the package under FORTRAN-90/95. The user needs only to supply the (1) model equations, (2) the initial conditions, and (3) any pertinent data. The user input is decribed in more detail in the Help menu of Athena Visual Studio, by clicking Book Examples and then Appendix B and finally selecting the appropriate example. 

The code DDAPLUS is normally called via Athena Visual Studio. For very detailed control of the available options, DDAPLUS may be called as follows from a user-provided MAIN program for the given problem ... 

The following Athena Visual Studio code solves this test example by calls to DDAPLUS and tabulates the four state variables as functions of time. 

The following Athena Visual Studio code sets up this problem and solves it by calls to DDAPLUS. The chosen absolute tolerance, ATOL=l.D-10, is satisfactory until f = 1.00 hr, after which ui and g attain much smaller values. Careful nesting of the multiplications and divisions proved necessary to avoid underflows in the calculations of /g, fg, and fig note the placement of parentheses in those lines of the UModel Equations section. 

The following Athena Visual Studio code sets up this problem and solves it by call to DDAPLUS. The Athena nomenclature for the state and sensitivity functions is given by the following ... 

The package GREGPLUS, included in Athena Visual Studio, tests user-provided models against data on one or more observed response types and assists sequential planning of experiments. Nonlinear and overparameterized models are handled directly. The following types of information can... 

This example uses a subroutine MODEL that computes only the values fu e) of the expectation function in Eq. (C.6-1). Input values DEL(i)=-lD-2 are used, with IDIF=1 so that GREGPLUS uses forward-difference approximations of the derivatives dfu 0)/d0j. To make these approximations accurate, the elements DEL(I) are refined by GREGPLUS in each iteration, using Eq, (6.B-7). Abbreviated output is requested by using LISTS = 1. Finally, an additional event condition is selected from five candidates, to minimize the volume of the three-parameter HPD region. Details of the implementation of this example in Athena Visual Studio can be found by running the software and selecting Book Examples under the Help menu item. 

The user-written Athena Visual Studio code given below was compiled and linked, giving the executable code to run this problem. The numerical results are shown below. Noteworthy features are (1) the rapid convergence of S 6) and the parameter vector 6, (2) the closeness of the final parameter estimates to the true values 1, 2, and 3 of Eq. (G.6-2), (3) the narrowness of the 95% HPD intervals for the individual parameters, and (4) the probabilistic assessment of goodness of fit, which is more informative than the customary pass/fail decision based on a particular significance level. 

Athena Visual Studio Code for Example C.l Appendix C Example C.l... 

The user-written Athena Visual Studio code and results are shown below. The results agree closely with those of the previous example, except that the number of calls of MODEL is reduced from 17 to 8. The number of iterations needed is unchanged. 

The user-written Athena Visual Studio code is shown below. It expresses the observations as / = InT. , where It is the hydrogen uptake rate in Ib-mols per hour per lb of catalyst, adjusted to a standard level of catalyst activity. Weights are assigned to these adjusted observations according to the formula... 

The Athena Visual Studio code for this example is shown below. The array lOBS is set to show which locations in OBS contain data. NBLK is set to 1 to put the three responses in one block, and the elements of YTOL are... 

The Athena Visual Studio code and the output with LISTS = 1 are shown below, The results are similar to those of Example C.4, except that the number of function calls for the estimation phase is reduced from 15 to 8. 

Abbreviated numerical output for this problem is shown explixitly for each model. The summary comparison can be accessed from Athena Visual Studio by selecting Discrimination and lack-of-Fit from the View menu. Remarkably, Models 2, 4, and 5 reduce to Model 1 as the estimation proceeds. Model 3 yields an additional estimated reaction parameter, but the penalty for this addition outweighs the very modest improvement obtained in S. Model 1 (which generated the data used here) is the most probable in this candidate set, and its goodness of fit probability Pr(A4 > Mh]) of 0.71 is very satisfactory, as noted in the first example of this section. 

Athena Visual Studio is a state-of-the-art software package that encapsulates the theoretical concepts presented in the chapters of this book in an integrated manner via a Windows interface. Athena Visual Studio can be downloaded for a free trial from www.AthenaVisual.com. 

Figure 10.23. An example of a steady-state isothermal CSTR m Athena Visual Studio.

In Athena Visual Studio, the selection of tasks (modelling, estimation or optimization) is combined with an option to select a variety of mathematical models (Figure 10.24). 

Figure. 10.24. Selection of tasks in Athena Visual Studio.

Figure. 10.25. Specification of the model details in Athena Visual Studio.

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