Regularized LTI system identification in the presence of outliers: A variational EM approach

Lindfors, Martin; Chen, Tianshi

doi:10.1016/j.automatica.2020.109152

Cited by 13 publications

(6 citation statements)

References 19 publications

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“…Using ∫ 𝜒 𝜀 = 1, an isolated value u 𝜈 can thus be approximated by c 𝜈 𝛿 𝜈 = (T s u 𝜈 )𝛿 𝜈 , suggesting that, for a small sampling period T s (= 𝜀), only large input deviations can significantly affect the estimation process. This yields the impulsive model with (n, q) = (5, 2): (1) , y (1) , y (2) , y (3) ] 𝜃…”

Section: Numerical Simulationmentioning

confidence: 99%

“…In a linear discrete time (DT) setting, system identification in the presence of impulsive disturbances has been studied in References 1‐4. These approaches, based on nonsmooth optimization (e.g.,

{l}_1

norm minimization), are generally developed in a batch mode and the reader may consult the survey paper 5 for a complete and comprehensive description of these optimization techniques.…”

Section: Introductionmentioning

confidence: 99%

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Online continuous time system identification in the presence of impulsive terms

Belkoura

2022

Adaptive Control & Signal

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Online parameters estimation algorithms are proposed for continuous time systems subject to structured perturbations. Using a distribution framework, a matrix pencil structure, whose polynomial order is characterized by the nature of the singularities describing the impulsive effects, is proposed for the modeling of perturbed systems with different disturbance types. Then, using an appropriate projection subspace, the rectangular pencils are reformulated as square generalized eigenvalue problems subject to linear constraints, from which unperturbed regression are derived. This approach allows for the implementation of recursive estimation schemes, free of penalty terms. An identifiability analysis is also conducted, and theoretical results are illustrated with experimental and simulated data.

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Section: Numerical Simulationmentioning

confidence: 99%

{l}_1

norm minimization), are generally developed in a batch mode and the reader may consult the survey paper 5 for a complete and comprehensive description of these optimization techniques.…”

Section: Introductionmentioning

confidence: 99%

Online continuous time system identification in the presence of impulsive terms

Belkoura

2022

Adaptive Control & Signal

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“…As shown in Fig 3, we denote z(t), h(t) and y(t) as the input, hidden state and output of the time step t, respectively. The behavior of this RNN layer can be described by (23) where W i , W h and W o represent the weight matrix of the input layer, hidden layer and output layer, respectively, and σ is the activation function. The Hessian should be Unfold Fig.…”

Section: Hessian Computationmentioning

confidence: 99%

“…A framework for identifying the governing interactions and transition logics of subsystems in cyber-physical systems was presented in [46] by using Bayesian inference and pre-defined basis functions. A variational expectation maximization approach to SYSID when the data includes outliers was developed in [23]. Two approaches to SYSID using Bayesian networks were proposed in [2].…”

Section: Introductionmentioning

confidence: 99%

Sparse Bayesian Deep Learning for Dynamic System Identification

Zhou¹,

Ibrahim²,

Zheng³

et al. 2021

Preprint

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This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification problems. First, DNNs are known to be too complex that they can easily overfit the training data. Second, the selection of the input regressors for system identification is nontrivial. Third, uncertainty quantification of the model parameters and predictions are necessary. The proposed Bayesian approach offers a principled way to alleviate the above challenges by marginal likelihood/model evidence approximation and structured group sparsity-inducing priors construction. The identification algorithm is derived as an iterative regularized optimization procedure that can be solved as efficiently as training typical DNNs. Furthermore, a practical calculation approach based on the Monte-Carlo integration method is derived to quantify the uncertainty of the parameters and predictions. The effectiveness of the proposed Bayesian approach is demonstrated on several linear and nonlinear systems identification benchmarks with achieving good and competitive simulation accuracy.

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“…A comprehensive survey on the kernel design for the LTI system can be found in the work of Chen. 22 The GPRbased identification method has been an effective practice for estimating the impulse response, and it has been applied to the estimation of Volterra series, 23 Hammerstein systems, 24 system with outliers, 25 and other nonlinear processes. 26 This study extends the GPR-based identification method to the identification of batch process.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric Identification Based on Multi-inherited Gaussian Process Regression for Batch Process

Chen

Zhao

et al. 2020

Ind. Eng. Chem. Res.

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This study presents a multi-inherited Gaussian process regression (GPR)-based nonparametric identification method for batch process. In the GPR framework, the impulse response of each time point consists of two parts: one is the inheritance part for utilizing the model information of previous time points, in which a Gaussian prior is imposed over the unknown inheritance weight, and the other is the residual impulse response, which is interpreted as a zero-mean Gaussian process. Following the empirical Bayes approach, we derive the joint estimation of the inheritance weight and the residual impulse response. The hyperparameters are determined by maximizing the marginal likelihood. As the correlation of process dynamics at adjacent time points is considered by model inheritance, the proposed method can effectively improve the estimation accuracy. Finally, we demonstrate the superiority of the proposed identification method in two case studies.

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Regularized LTI system identification in the presence of outliers: A variational EM approach

Cited by 13 publications

References 19 publications

Online continuous time system identification in the presence of impulsive terms

Online continuous time system identification in the presence of impulsive terms

Sparse Bayesian Deep Learning for Dynamic System Identification

Nonparametric Identification Based on Multi-inherited Gaussian Process Regression for Batch Process

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