An Approximate Expectation Maximization Algorithm for Estimating Parameters, Noise Variances, and Stochastic Disturbance Intensities in Nonlinear Dynamic Models

• Published in: Industrial & engineering chemistry research Vol. 52; no. 51; pp. 18303 - 18323
• Main Authors: Karimi, Hadiseh, McAuley, Kimberley B
• Format: Journal Article
• Language: English
• Published: American Chemical Society 26.12.2013
• Subjects: Algorithms; Approximation; chemistry; data collection; differential equation; Disturbances; dynamic models; Dynamical systems; engineering; Mathematical models; Maximization; Noise measurement; Nonlinear dynamics; statistical analysis; variance
• ISSN: 0888-5885; 1520-5045; 1520-5045
• DOI: 10.1021/ie4023989

An algorithm is proposed for simultaneous estimation of model parameters, process disturbance intensities, and measurement noise variances for nonlinear dynamic systems that are described by stochastic differential equations. The proposed fully-Laplace approximation expectation maximization (FLAEM) algorithm uses an iterative approach wherein, in the first step, the model parameters are estimated using the approximate maximum likelihood estimation objective function developed by Varziri et al., assuming that disturbance intensities and noise variances are known. In the second step, process disturbance intensities and measurement noise variance estimates are updated using expressions that rely on the fully-Laplace approximation in the expectation maximization algorithm. The proposed FLAEM method is illustrated using a nonlinear two-state continuous stirred tank reactor (CSTR) example. The effectiveness of the FLAEM algorithm is compared with a maximum-likelihood based method proposed by Kristensen et al. For the CSTR example studied, FLAEM provides more accurate parameter estimates and is more robust to poorly known initial guesses of parameters and to smaller data sets.