Design Using Eigenvectors

In this chapter, we have presented the application of CPMs to the most common pieces of distiUation equipment, absorbers/stripping towers, and simple cohitims. The versatility of the CPM method can already be seen even in these baric structures. 

DESIGN OF SIMPLE COLUMNS USING COLUMN PROFILE MAPS 

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Dominant correlations of data are usually captured by a small number of initial eigenvectors. A simple orthogonal decomposition is accomplished by partitioning U = [UmU/j] and A = [Am A ] where M designates the number of initial dominant modes to be used for approximation while R stands for the remaining N — M) modes or the residual. Data matrix becomes Y = JM- M + R- R = Ym + Yr. For a successful approximation, YM captures significant variability trends and Yr simply represents residual random noise. Transformation in the form Y Ym uses M N + K) data entries and provides [1 — M N + K)/ NK)]100 % data compression. 

Figure 2.5 demonstrates the Mathcad document designed to form all the vectors and matrices necessary for solving the direct kinetic problem. The built-in function e igenvals should be used to find eigenvalues of a constant rate matrix. A matrix of eigenvectors is calculated with the help of eigenvecs. 

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