Principal component analysis of kinetic models

S.V/ajda, P. Valkd and T. Tur3nyi, Principal component analysis of kinetic models, Int. J. Chem. Kinet. 17 (1985) 55-81. 

Vajda, S., Valko, P. Godfrey, K. R. (1987). Direct and indirect least squares methods in continuous-time parameter estimation. Automatica, 23, 707-18. Vajda, S., Valko, P. Turanyi, T. (1985). Principal component analysis of kinetic models. Int. J. Chem. Kinet., 55-81. 

It can be noted that the kinetic law (18) actually involves the group of three determining parameters k = kj3(kj2/kj5). Consequently, if, during experiments, only the rates of appearance of the main products BH and m have been measured, only the value of the global constant k can be determined, and not of the individual constants kj2j k k 5. The existence of links between the parameters of a model can be demonstrated by the principal component analysis of a suitable objective function. 

A more systematic approach for reducing the reaction kinetic model using the sensitivity analysis method, known as the method of principal components analysis, was developed by T. Turanyi and co-workers [56,57]. This method is applicable after calculation of the local sensitivity array and the compiling of the approptiate matrix from the normalized sensitivities... 

Based on selected data array on the sensitivity of species concentrations for the rate constants of steps at the reaction time 5-10 s, E.P. Dougherty, J.T. Hwang, H.G. Rabitz [69] determined both the dominant and imimportant steps of the reaction mechanism, as presented in Table 3.3. Further, using a more systematic method to analyze data on the sensitivity of concentrations [56] and rate-of-production of the reaction species [28], with respect to variations of the step rate constants (the method of principal components analysis) S. Vajda, P. Valko, T. Turanyi [56] ranked the role of steps for the reaction mechanism of gas-phase oxidation of formaldehyde in the presence of carbon oxide (II). They succeeded also in separating the minimal reaction mechanism involving 13 steps, which gives the same results, accurate to within 2% (for the reaction time of 5 10 s), as the initial kinetic model consisiting of 25 steps (see Table 3.5). 

When a preliminary extended version of the kinetic model is used to identify the B-Zh reaction mechanism, frequently classical approximation methods are used, such as the ratedetermining step and the quasi-steady state approximations (see, for example [22,24-26]). However T. Turanyi and S. Vajda [29], applying the sensitivity analysis method, more precisely the method of the principal components analysis selection, specified numerically a base mechanism that comprise only 9 steps for the B-Zh reaction (see table 8.1), from the conventional model of Edelson-Field-Noes (EFN), which includes 32 steps. In this case, the... 

Very often in DCS-operated batch polymer reactors the primary process variables such as pressure, temperature, level, and flow (Section 12.2.1-12.2.4) are recorded during the batch as well as the quality variables at the end of the batch. However, it may be very difficult to obtain a kinetic model of the polymerization process due to the complexity of the reaction mechanism, which is frequently encountered in the batch manufacture of specialty polymers. In this case it is possible to use advanced statistical techniques such as multi-way principal component analysis (PCA) and multi-way partial least squares (PLS), along with an historical database of past successful batches to construct an empirical model of the batch [8, 58, 59]. This empirical model is used to monitor the evolution of future batch runs. Subsequent unusual events in the future can be detected during the course of the batch by referencing the measured process behavior against this incorrective action during the batch in order to bring it on aim. 

To close this chapter, it is noted that the radiation pattern and the equivalent force models of the dipole and the double-couple are not essential to study the source characterization of AE waves. The important result is the fact that kinetics of AE source is recovered by the deconvolution analysis, while kinematics can be represented by the moment tensor. The equivalent force models and the radiation patterns just show us the principal components of the moment tensor. 

BP processing of stripping analysis responses allowed the quantitative determination of heavy metals in the presence of interferences, and selectivity coefficients of berberine-selective electrodes were predicted satisfactorily. o BP networks were used to analyze piezoelectric crystal data to simultaneously determine sulfur dioxide concentration and relative humidity. 2 A BP network was used to model properties of materials. 2 x vo studies described the modeling and recognition of flow injection patterns. " Compared to principal components regression and partial least squares (PLS), BP provided a better method for multicomponent kinetic determinations. BP... 

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