Partially coupled gradient estimation algorithm for multivariable equation‐error autoregressive moving average systems using the data filtering technique

Liu, Qinyao; Ding, Feng; Xu, Ling; Yang, Erfu

doi:10.1049/iet-cta.2018.5541

Cited by 21 publications

(27 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…10,11 Parameter estimation and state filtering are basic for system control and system analysis. 12,13 Many parameter estimation methods, such as hierarchical identification methods, 14,15 Newton identification methods, [16][17][18] and coupled identification methods, 19,20 have been widely studied. In the literature, Waschburger and Galvão investigated a method to estimate the input delays of a discrete-time state-space model by utilizing the standard least squares methods to minimize a quadratic cost function of the prediction error of the system states within a given time range.…”

Section: Introductionmentioning

confidence: 99%

Adaptive parameter estimation for a general dynamical system with unknown states

Xiao

Ding

2020

Intl J Robust & Nonlinear

Self Cite

132

View full text Add to dashboard Cite

Summary This paper is concerned with the design of a state filter for a time‐delay state‐space system with unknown parameters from noisy observation information. The key is to investigate new identification algorithms for interactive state and parameter estimation of the considered system. Firstly, an observability canonical state‐space model is derived from the original model by linear transformation for the purpose of simplifying the model structure. Secondly, a direct state filter is formulated by minimizing the state estimation error covariance matrix on the basis of the Kalman filtering principle. Thirdly, once the unknown states are estimated, a state filter–based recursive least squares algorithm is proposed for parameter estimation using the least squares principle. Then, a state filter–based hierarchical least squares algorithm is derived by decomposing the original system into several subsystems for improving the computational efficiency. Finally, the numerical examples illustrate the effectiveness and robustness of the proposed algorithms.

show abstract

Section: Introductionmentioning

confidence: 99%

Adaptive parameter estimation for a general dynamical system with unknown states

Xiao

Ding

2020

Intl J Robust & Nonlinear

Self Cite

132

View full text Add to dashboard Cite

show abstract

“…8 Therefore, many research works have focused on the parameter estimation of multivariate systems. 9,10 In the literature, Pan et al studied the identification problem of a multivariate system disturbed by the moving average noise and developed a data filtering based multi-innovation stochastic gradient (MISG) algorithm for parameter estimation. 11 Wang et al combined the maximum likelihood identification method with the least squares principle and proposed a recursive maximum likelihood identification algorithm for a multivariable controlled autoregressive system.…”

Section: Introductionmentioning

confidence: 99%

The innovation algorithms for multivariable state‐space models

Ding

Xiao

2019

Adaptive Control & Signal

Self Cite

116

View full text Add to dashboard Cite

This paper derives the input-output representation of the dynamical system described by a linear multivariable state-space model and the corresponding multivariate linear regressive model (ie, multivariate equation-error model). A projection identification algorithm, a multivariate stochastic gradient identification algorithm, and a multi-innovation stochastic gradient (MISG) identification algorithm are proposed for multivariate equation-error systems by using the negative gradient search and the multi-innovation identification theory. The convergence analysis of the MISG algorithm indicates that the parameter estimation errors converge to zero under the persistent excitation condition. Finally, a numerical example illustrates the effectiveness of the proposed algorithms.

show abstract

“…It is difficult to obtain an accurate long-term prediction of PM2.5 concentration because PM2.5 comprises typical complex nonlinear time-series data [3], where the vector field of state dynamics is a nonlinear function of state variables. In the literature, the estimation and prediction of air quality are often based on mathematical models, the predicted models can be established through some parameter estimation methods [4][5][6][7], some have used input-output representations [8][9][10][11], and others have used state-space models [12,13].…”

Section: Introductionmentioning

confidence: 99%

Integrated Predictor Based on Decomposition Mechanism for PM2.5 Long-Term Prediction

et al. 2019

View full text Add to dashboard Cite

Featured Application: This work can be used in the intelligent system for the smart city, smart agriculture, etc.Abstract: It is crucial to predict PM2.5 concentration for early warning regarding and the control of air pollution. However, accurate PM2.5 prediction has been challenging, especially in long-term prediction. PM2.5 monitoring data comprise a complex time series that contains multiple components with different characteristics; therefore, it is difficult to obtain an accurate prediction by a single model. In this study, an integrated predictor is proposed, in which the original data are decomposed into three components, that is, trend, period, and residual components, and then different sub-predictors including autoregressive integrated moving average (ARIMA) and two gated recurrent units are used to separately predict the different components. Finally, all the predictions from the sub-predictors are combined in fusion node to obtain the final prediction for the original data. The results of predicting the PM2.5 time series for Beijing, China showed that the proposed predictor can effectively improve prediction accuracy for long-term prediction. Appl. Sci. 2019, 9, 4533 2 of 14 models [14] and vector auto-regression (VAR) [15]. ARIMA is a linear modeling method that provides accurate predictions for approximate linear relationships. However, its prediction performance is not good enough for nonlinear prediction problems.To capture the complex nonlinearity of PM2.5, a back propagation (BP) neural network has been widely applied in time-series data prediction [16][17][18]. Other shallow nonlinear networks based on a machine-learning mechanism such as the improved gray neural network model [19] and the radial basis function (RBF) neural network [20] have also been used to predict time-series data. Xu et al. [3] proposed a supplementary leaky integrator echo state network (SLI-ESN), which added the historical state term of the historical moment to the calculation of a leaky integrator reservoir. Compared with an echo state network (ESN), a leaky integrator ESN (LI-ESN), an extreme learning machine (ELM), a hierarchical ELM (H-ELM), a stacked auto-encoder (SAE), and a traditional SLI-ESN, the proposed SLI-ESN of Xu et al.[3] could achieve good prediction results, but its long-term predictions were not satisfactory.As a shallow network still cannot effectively extract the complex nonlinearity of the data, decomposition must be used; that is, the data must be decomposed into multiple components to reduce its complexity, and then multiple sub-models are used to improve the prediction performance. For example, García et al. [21] decomposed a long-term data series into smaller seasonal component patterns. Jesús et al. [22] divided a pollen-concentration data series into seasonal and random parts, used partial least-squares regression (PLSR) to fit the residuals, and established an airborne pollen time-series model to predict the daily pollen concentration. Ming et al.[23] extracted accurate seasonal signals, a...

show abstract

Partially coupled gradient estimation algorithm for multivariable equation‐error autoregressive moving average systems using the data filtering technique

Cited by 21 publications

References 56 publications

Adaptive parameter estimation for a general dynamical system with unknown states

Adaptive parameter estimation for a general dynamical system with unknown states

The innovation algorithms for multivariable state‐space models

Integrated Predictor Based on Decomposition Mechanism for PM2.5 Long-Term Prediction

Contact Info

Product

Resources

About