Identification Of Output Error Model Research Articles

Pattern-Moving-Based Parameter Identification of Output Error Models with Multi-Threshold Quantized Observations

This paper addresses a modified auxiliary model stochastic gradient recursive parameter identification algorithm (M-AM-SGRPIA) for a class of single input single output (SISO) linear output error models with multi-threshold quantized observations. It proves the convergence of the designed algorithm. A pattern-moving-based system dynamics description method with hybrid metrics is proposed for a kind of practical single input multiple output (SIMO) or SISO nonlinear systems, and a SISO linear output error model with multi-threshold quantized observations is adopted to approximate the unknown system. The system input design is accomplished using the measurement technology of random repeatability test, and the probabilistic characteristic of the explicit metric value is employed to estimate the implicit metric value of the pattern class variable. A modified auxiliary model stochastic gradient recursive algorithm (M-AM-SGRA) is designed to identify the model parameters, and the contraction mapping principle proves its convergence. Two numerical examples are given to demonstrate the feasibility and effectiveness of the achieved identification algorithm.

Parametric identification of output error model for sampled systems with integer‐type time delay subject to load disturbance with unknown dynamics

In this paper, a bias-eliminated output error (OE) model identification method is proposed for single-input-single-output sampled systems with integer-type time delay subject to load disturbance with unknown dynamics. By viewing the load disturbance response as a time-variant parameter, an iterative least-squares identification algorithm is established to estimate the rational model parameters together with an integer-type delay parameter, while the disturbance response could be simultaneously estimated. To overcome the adverse effect of stochastic noise involved with output measurement, an auxiliary model is constructed to predict the noise-free system response. Moreover, a set of adaptive forgetting factors is introduced to expedite the convergence rate of model parameter estimation and the tracking performance of load disturbance response, respectively. In addition, a monotonically rising profile for evaluating the delay parameter is proposed for implementing the above iterative least-squares algorithm, in order to avoid the occurrence of multiple local minima of the loss function for model fitting. The asymptotic convergence on estimating the rational model parameters together with the delay parameter is analysed with a proof. An illustrative example is given to demonstrate the effectiveness and advantage of the proposed method.

Improvement Instrumental Variables Method for Output Error Model

The identification of parameters system can be done in multiple ways by alternating methods (Least Squares, Instrumental Variables) and models (ARX, OE). The Ordinary Least Squares method which was presented in several research papers gives biased estimates for Output Error model. For example, the interpretation results in the first order OE model, the autocorrelation function shows that the residuals are not white noise, and the LS estimator is well biased, and it is not a suitable estimator for identification of output error model. In this paper, we will present a detailed study of Recursive Instrumental Variables method and its instruments choice to identify the parameters of Output Error model with unbiased estimates. The idea is simultaneously to identify the parameters system similar to an ARX model with Least Squares method. It is a successfully applied to identify with unbiased estimates parameters of a second order system based on whitening error prediction, and we showed that, if the instruments are weak, then the estimator may be biased and confidence intervals and hypothesis tests unreliable. Also, for every data observation set, the estimates parameters can be compared with those originally generated by MATLAB functions. Finally, a numerical example illustrates the efficiency and performances of the proposed method.

Multi-innovation based Identification of Output Error Model with Time Delay under Load Disturbance

In this paper, a robust output error model identification method is proposed for industrial processes with time delay subject to load disturbance. By viewing the load disturbance response as a time-variant parameter to be estimated, an extended recursive least-squares (RLS) identification method is established to simultaneously estimate the model parameters and the disturbance response, based on a multi-innovation fitting strategy. The integer type time delay parameter is determined by using a one-dimensional searching approach. An auxiliary model is used to estimate the noise-free output against stochastic noise. Besides, two adaptive forgetting factors are introduced to improve the convergence rates of estimating the time-invariant model parameters and the time-variant disturbance response, respectively. The effectiveness and merit of the proposed method is demonstrated by an illustrative example.

Iterative identification of output error model for industrial processes with time delay subject to colored noise

To deal with colored noise and unexpected load disturbance in identification of industrial processes with time delay, a bias-eliminated iterative least-squares (ILS) identification method is proposed in this paper to estimate the output error model parameters and time delay simultaneously. An extended observation vector is constructed to establish an ILS identification algorithm. Moreover, a variable forgetting factor is introduced to enhance the convergence rate of parameter estimation. For consistent estimation, an instrumental variable method is given to deal with the colored noise. The convergence and upper bound error of parameter estimation are analyzed. Two illustrative examples are used to show the effectiveness and merits of the proposed method.

Iterative Identification of Output Error Model with Time Delay

In this paper an iterative identification method is proposed to simultaneously estimate the parameters of an output error model together with a delay parameter for industrial processes with time delay, to facilitate model based control design. An extended observation vector is constructed to establish a negative-gradient based iterative identification algorithm. An auxiliary model is established to estimate the unknown noise-free output of the system for consistent estimation. Moreover, a variable forgetting factor (VFF) is introduced to enhance the convergence rate and identification accuracy against measurement noise. The convergence of the proposed algorithm is analyzed with a strict proof. An illustrative example is shown to demonstrate the effectiveness of the proposed identification method.

Adaptive Input Design for Identification of Output Error Model with Constrained Output

Optimal input design for system identification is an area of intensive modern research. This paper considers the identification of output error (OE) model, for the case of constrained output variance. The constraint plays a very important role in the process industry, in the reduction of degradation of product quality. In this paper, it is shown, in the form of a theorem, that the optimal input signal, with constrained output, is achieved by a minimum variance controller together with a stochastic reference. The key problem is that the optimal input depends on the system parameters to be identified. In order to overcome this problem, a two-stage adaptive procedure is proposed: obtaining an initial model using PRBS as input signal; application of adaptive minimum variance controller together with the stochastic variable reference, in order to generate input signals for system identification. Theoretical results are illustrated by simulations.

Prediction error identification of linear systems: A nonparametric Gaussian regression approach

A novel Bayesian paradigm for the identification of output error models has recently been proposed in which, in place of postulating finite-dimensional models of the system transfer function, the system impulse response is searched for within an infinite-dimensional space. In this paper, such a nonparametric approach is applied to the design of optimal predictors and discrete-time models based on prediction error minimization by interpreting the predictor impulse responses as realizations of Gaussian processes. The proposed scheme describes the predictor impulse responses as the convolution of an infinite-dimensional response with a low-dimensional parametric response that captures possible high-frequency dynamics. Overparameterization is avoided because the model involves only a few hyperparameters that are tuned via marginal likelihood maximization. Numerical experiments, with data generated by ARMAX and infinite-dimensional models, show the definite advantages of the new approach over standard parametric prediction error techniques and subspace methods both in terms of predictive capability on new data and accuracy in reconstruction of system impulse responses.