An approach for simultaneous estimation of reaction kinetics and curve resolution from process and spectral data

• Published in: Journal of chemometrics Vol. 30; no. 9; pp. 506 - 522
• Main Authors: Chen, Weifeng, Biegler, Lorenz T., Muñoz, Salvador García
• Format: Journal Article
• Language: English
• Published: Chichester Blackwell Publishing Ltd 01.09.2016; Wiley Subscription Services, Inc
• Subjects: Case studies; Collocation methods; Economic models; Kinetics; Mathematical models; multivariate curve resolution; Nonlinear programming; Optimization techniques; Parameter estimation; Parameters; Reaction kinetics; Spectra; Standard deviation
• ISSN: 0886-9383; 1099-128X
• DOI: 10.1002/cem.2808

Parameter estimation of reaction kinetics from spectroscopic data remains an important and challenging problem. This study describes a unified framework to address this challenge. The presented framework is based on maximum likelihood principles, nonlinear optimization techniques, and the use of collocation methods to solve the differential equations involved. To solve the overall parameter estimation problem, we first develop an iterative optimization‐based procedure to estimate the variances of the noise in system variables (eg, concentrations) and spectral measurements. Once these variances are estimated, we then determine the concentration profiles and kinetic parameters simultaneously. From the properties of the nonlinear programming solver and solution sensitivity, we also obtain the covariance matrix and standard deviations for the estimated kinetic parameters. Our proposed approach is demonstrated on 7 case studies that include simulated data as well as actual experimental data. Moreover, our numerical results compare well with the multivariate curve resolution alternating least squares approach. We present a unified framework for parameter estimation of reaction kinetics from spectroscopic data, based on maximum likelihood, nonlinear programming (NLP), and collocation methods for the differential‐algebraic model. An iterative procedure estimates the noise variance in state variables and spectral measurements. Then, concentration profiles and kinetic parameters are determined simultaneously by the NLP solver. Finally, NLP sensitivity recovers the covariance and standard deviations for the estimated kinetic parameters. Seven case studies demonstrate the advantages of the proposed framework.