Six recently proposed methods for analyzing copolymerization composition data have been compared to a nonlinear least‐squares analysis to ascertain the precision of the six methods in determining reactivity ratios. Data used were simulated for five hypothetical monomer pairs with three different types of experiment design and contained error structures similar to those observed experimentally. The results of the comparisons suggest that retrospective analyses of existing copolymerization data should only be done with a nonlinear least‐squares analysis. For new data, the design of experiments is of great importance, and when done properly allows the use of some of the linear least‐squares methods of analysis.
IntroductionThe detection and diagnosis of abnormal situations in the operation of industrial processes is a problem of considerable challenge that is attracting wide attention in both academe Ž . and industry. Nimmo 1995 showed that the U.S.-based petrochemical industry alone could save up to $10 billion per year if abnormal situations could be detected, diagnosed, and appropriately dealt with. The consequences of not being able to detect such abnormal situations range from increased operational costs to costly plant shutdowns.Industrial processes often present a large number of process variables, such as temperatures, pressures, flow rates, compositions, which are typically sampled at a frequency of one minute. Identifying and troubleshooting abnormal operating conditions simply by observation are difficult tasks with such a large amount of data, particularly since the process Ž variables are usually highly correlated MacGregor et al.,. 1991 . However, the sampled data have embedded within them information for revealing the state of the process operation.
Two empirical strategies for open‐loop on‐line optimization are developed as alternatives to the use of mechanistic process models. These strategies are based on on‐line identification of dynamic multi‐input single‐output (MISO) and multi‐input multi‐output (MIMO) models. The steady state gain of these models provides information for steady state optimization. Desirability functions, originally developed for multi‐objective optimization, are utilized as objective function modifiers for constrained on‐line optimization. The integration of dynamic model identification and desirability functions results in an on‐line optimizer which combines fast optimizing speed with the ability to predict future encroachments on constraint boundaries. Corrections to the search direction are based on these predictions, reducing the probability of actual constraint violation.
The optimization strategies are tested by simulation on nonlinear multivariable interacting systems at two levels of complexity: a CSTR supporting a multiple reaction and a fluid catalytic cracker. Both methods were effective in avoiding violation of constraints but the MIMO strategy required fewer steps to reach an optimum and was less prone to generate a nonfeasible optimization step.
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