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The motivation for this article comes from our development of soft sensors for chemical processes where several challenges are encountered. For example, quality variables in chemical processes are often measured off‐line through laboratory analysis. Collection of samples and subsequent analyses inevitably introduce uncertain time delays associated with the irregularly sampled quality variables, which add significant difficulty in identification of process with multirate (MR) data. Considering the MR system with random sampling delays described by a finite impulse response (FIR) model, an Expectation–Maximization (EM)‐based algorithm to estimate its parameters along with the time delays is developed. Based on the identified FIR model, two algorithms are proposed to recover the approximate output error (OE) or transfer function model. Two simulation examples as well as a pilot‐scale experiment are provided to illustrate the effectiveness of the proposed methods. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4124–4132, 2013

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By using the stochastic martingale theory, convergence properties of stochastic gradient (SG) identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the SG algorithms consistently converge to the true parameters, as long as the information vector is persistently exciting (i.e., the data product moment matrix has a bounded condition number) and that the process noises are zero mean and uncorrelated. These results remove the strict assumptions, made in existing references, that the noise variances and high-order moments exist, and the processes are stationary and ergodic and the strong persistent excitation condition holds. This contribution greatly relaxes the convergence conditions of stochastic gradient algorithms. The simulation results with bounded and unbounded noise variances confirm the convergence conclusions proposed.