An approximate expectation maximisation algorithm for estimating parameters in nonlinear dynamic models with process disturbances

Karimi, Hadiseh; McAuley, Kimberley B.

doi:10.1002/cjce.21932

Cited by 11 publications

(30 citation statements)

References 52 publications

(146 reference statements)

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“…As explained in our previous work, AEM uses the mode of the expected value of the E step in the EM algorithm. 30 The results from this case study suggest that FLAEM uses a better approximation. Using CTSM, a successful parameter estimation was only obtained for 36 of the 100 Monte Carlo cases attempted for this scenario.…”

Section: Resultsmentioning

confidence: 88%

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

Karimi

McAuley

2013

Ind. Eng. Chem. Res.

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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., 1 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. 2 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. INTRODUCTIONMany chemical processes are modeled using ordinary differential equations (ODEs) or algebraic equations (AEs) arising from fundamental laws of physics and chemistry. 3−5 However, some chemical engineering processes are better modeled using stochastic differential equations (SDEs) that account for possible modeling imperfections and stochastic process disturbances. 3,6 Stochastic terms that are included in SDE models can result in improved model predictions due to decreased bias in parameter estimates. 3,7 Parameter estimates obtained using SDE models are suitable for online process monitoring applications because SDE models account for measurement errors and stochastic process disturbance, the two types of random errors that are accounted for by extended Kalman filters (EKFs) and related state estimators. 8,9 In this article, we consider a multi-input multi-output (MIMO) nonlinear SDE model of the following form:

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Section: Resultsmentioning

confidence: 88%

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

Karimi

McAuley

2013

Ind. Eng. Chem. Res.

Self Cite

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“…density and heat capacities in all streams. Based on material and energy balances on the reactor, we get the model (24) and (25):…”

Section: Numerical Examplementioning

confidence: 99%

“…Continuously stirred tank reactors (CSTR) are one of the widely studied benchmarks for nonlinear estimation and fault diagnosis. [24][25][26][27] In this paper, a CSTR process model is applied to check the effectiveness of the presented fault detection and diagnosis approach.…”

Section: Introductionmentioning

confidence: 99%

Fault detection for nonlinear systems with unreliable measurements based on hierarchy cubature Kalman filter

et al. 2017

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This paper is concerned with fault detection of a kind of nonlinear dynamic system. Based on the framework of hierarchy information processing, the scope of the fault is first located by use of the presented windowing cubature Kalman filter (WCKF), followed by point-by-point fault detection to locate the fault by use of the residuals of each moment within the suspected windows. Theoretical analysis and experiments show that the presented algorithm is more effective than the traditional point-by-point fault detection method that only uses the moment residuals. The presented algorithm has potential value in many application fields, such as fault detection, reliability evaluation, fault tolerant control, etc.

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“…The estimation of states and unknown inputs (UIs) is important in fault diagnosis and dynamic system control. [1][2][3][4][5] This problem is frequently encountered in power system exciters, [6,7] chemical processes, [8][9][10] state estimation of a battery, [11][12][13] navigation, [14,15] and earthquake damage estimation. [16] Over the last decade, many methods have been proposed for the simultaneous estimation of the UIs and states in a linear discrete-time system, [17][18][19][20][21][22] among which Gillijns and De Moor [22] present a valuable overview.…”

Section: Introductionmentioning

confidence: 99%

Distributed semi‐cooperative filter for a nonlinear multi‐agent system with heterogeneous and homologous unknown inputs

Liu

et al. 2020

Can J Chem Eng

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In this study, the simultaneous estimation of the states and unknown inputs for a nonlinear multi-agent system with homologous and heterogeneous unknown inputs is performed. The decentralized sub-filter is used to estimate the states and heterogeneous unknown inputs, whereas the distributed subfilter is used to estimate the homologous unknown inputs. The extended Kalman filter is used to solve the estimation problem for nonlinear systems. Compared with previous studies, the distributed solution is improved to relax the existence of the homologous unknown input sub-filter. Moreover, the updating method of the residual generator is improved to relax the heterogeneous unknown input sub-filter. The practical problem of estimating the state of charge and temperature of the battery pack is used to verify the effectiveness of the proposed filter.

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An approximate expectation maximisation algorithm for estimating parameters in nonlinear dynamic models with process disturbances

Cited by 11 publications

References 52 publications

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

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

Fault detection for nonlinear systems with unreliable measurements based on hierarchy cubature Kalman filter

Distributed semi‐cooperative filter for a nonlinear multi‐agent system with heterogeneous and homologous unknown inputs

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