Procedure variable assignment

There are at least three ways to "work around" this problem caused by "horizontal" and "vertical" arrays. One way is to use a loop to write the elements of the array to individual worksheet cells in a column (Figure 15-7), instead of using the more convenient procedure of assigning the array variable to a range of cells in the worksheet. 

Randomization is the procedure of assigning the experimental units to various treatments in a purely chance manner. It is also used for arrangement of the experiments in random order. It is intended to balance out the effect of uncontrollable variables. Because bias errors are not confused with the effect of the factors, the quality of data is improved and statistical inferences are made possible. 

A structured approach to modeling involves a systematic analysis to determine the number of degrees of freedom and a procedure for assigning them. The steps in the degrees of freedom analysis are summarized in Table 2.2. In Step 4 the output variables include the dependent variables in the ordinary differential equations. 

Data is passed between levels of recursive procedures in variables cited in the CALL statement for the procedure. As indicated in the section on programming issues, care must be taken in assigning names to the data variables so that values returning from a recursive CALL do not overwrite the values in variables within the calling procedure. Note the difference between the variable names in the SUBROUTINE statement of... 

A basic use of a process model is to analyse experimental data and to use this to characterise the process, by assigning numerical values to the important process variables. The model can then also be solved with appropriate numerical data values and the model predictions compared with actual practical results. This procedure is known as simulation and may be used to confirm that the model and the appropriate parameter values are "correct". Simulations, however, can also be used in a predictive manner to test probable behaviour under varying conditions, leading to process optimisation and advanced control strategies. 

Q, the procedure body, is any nonempty list of assignment instructions, test instructions and CALL instructions, involving as variables only the formal parameters and local variables of the procedure, such that START Q STOP is a program scheme with CALLs. 

To each procedure F we assign two inductive assertions pA and pB which are written solely in terms of the formal parameters of procedure F flat is, the only free variables in pA and pB are the formal parameters of F. ... 

In this section, the numerical solutions of the MINLP-model and of the MILP-model as presented in Sections 7.4 and 7.5 are compared with respect to their solution quality (measured by the objective values) and the required solution effort (measured by the computing time). In order to compare the MILP-solution with the MINLP-solution, the optimized values for the start times of polymerizations tn, the recipe assignments W, and the total holdups Mnr are inserted into the MINLP-model and the objective is calculated. To guarantee comparability of the results, the models were stated with identical initial conditions, namely t° = 0, = 2 Vk, pf = 0 Vs, and ra = 0.4 Vs (i.e., the variables defined at the beginning of the corresponding time axes are fixed to the indicated values). For the algorithmic solution procedure, all variables were initialized by 1 (i.e., the search for optimal values starts at values of 1 ), and none of the solvers was specifically customized. 

In this chapter, the mathematical formulation of the variable classification problem is stated and some structural properties are discussed in terms of graphical techniques. Different strategies are available for carrying out process-variable classification. Both graph-oriented approaches and matrix-based techniques are briefly analyzed in the context of their usefulness for performing variable categorization. The use of output set assignment procedures for variable classification is described and illustrated. 

Romagnoli and Stephanopoulos (1980) proposed a classification procedure based on the application of an output set assignment algorithm to the occurrence submatrix of unmeasured variables, associated with linear or nonlinear model equations. An assigned unmeasured variable is classified as determinable, after checking that its calculation may be possible through the resolution of the corresponding equation or subset of equations. 

The output set assignment is not unique however, this does not affect the result of the classification. As Steward (1962) has shown, if there is no structural singularity, the determinable unmeasured variables are always assigned independently of the obtained output set assignment. The classification of the unmeasured variables allows us to define the sequence of calculation for these variables. That is, expressions are obtained to solve them as functions of the measurements. The expressions are also used in the classification of the measured variables and in the formulation of the reconciliation equations. After the reconciliation procedure is applied to the measurements, these equations are used to find an estimate of the unmeasured determinable variables in terms of the reconciled measurements. 

Formulation of expressions for the unmeasured variables in terms of the measured ones (see Appendix 3-B), using the sequence of calculations that is obtained as a by-product of the assignment procedure. 

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