A Decoupling Derivative-Based Approach for Hammerstein System Identification (original) (raw)
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Hammerstein system identification using LS-SVM and steady state time response
2016 European Control Conference (ECC), 2016
In this paper a new system identification approach for Hammerstein systems is proposed. A straightforward estimation of the nonlinear block through the use of LS-SVM is done by making use of the behavior of Hammerstein systems in steady state. Using the estimated nonlinear block, the intermediate variable is calculated. Using the latter and the known output, the linear block can be estimated. The results indicate that the method can effectively identify Hammerstein systems also in the presence of a considerable amount of noise. The well-known capabilities of LS-SVM for the representation of nonlinear functions play an important role in the generalization capabilities of the method allowing to work with a wide range of model classes. The proposed method's main strength lies precisely in the identification of the nonlinear block of the Hammerstein system. The relevance of these findings resides in the fact that a very good estimation of the inner workings of a Hammerstein system can be achieved.
Automatica, 2009
The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of Hammerstein systems. It is essentially based on a particular formulation of Hammerstein systems in the form of bilinearly parameterized linear regressions. This paper has been motivated by a somewhat contradictory fact: though the optimality of the TSA has been established by Bai in 1998 only in the case of some special weighting matrices, the unweighted TSA is usually used in practice. It is shown in this paper that the unweighted TSA indeed gives the optimal solution of the weighted nonlinear least-squares problem formulated with a particular weighting matrix. This provides a theoretical justification of the unweighted TSA, and also leads to a generalization of the obtained result to the case of colored noise with noise whitening. Numerical examples of identification of Hammerstein systems are presented to validate the theoretical analysis.
Combined parametric-nonparametric identification of Hammerstein systems
Ieee Transactions on Automatic Control, 2004
A novel, parametric-nonparametric, methodology for Hammerstein system identification is proposed. Assuming random input and correlated output noise, the parameters of a nonlinear static characteristic and finite impulse-response system dynamics are estimated separately, each in two stages. First, the inner signal is recovered by a nonparametric regression function estimation method (Stage 1) and then system parameters are solved independently by the least squares (Stage 2). Convergence properties of the scheme are established and rates of convergence are given.
Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, 2013
This paper describes a novel method for the identification of Hammerstein systems with time-varying (TV) static nonlinearities and time invariant (TI) linear elements. This paper develops a linear parameter varying (LPV) state-space representation for such systems and presents a subspace identification technique that gives individual estimates of the Hammerstein components. The identification method is validated using simulated data of a TV model of ankle joint reflex stiffness where the threshold and gain of the model change as nonlinear functions of an exogenous signal. Pilot experiment of TV reflex EMG response identification in normal ankle joint during an imposed walking task demonstrate systematic changes in the reflex nonlinearity with the trajectory of joint position.
Hammerstein System Identification by a Semi-Parametric Method
2000
A semi-parametric algorithm for identification of Hammerstein systems in the presence of correlated noise is proposed. The procedure is based on the non-parametric kernel regression estimator and the standard least squares. The advantages of the method in comparison with the standard non-parametric approach are discussed. Limit properties of the proposed estimator are studied, and the simulation results are presented.
Identification of Hammerstein systems without explicit parameterisation of non-linearity
International Journal of Control, 2009
This article proposes a new approach to identification of Hammerstein systems, where a non-linearity precedes a linear dynamic system, driven by piece-wise constant inputs. The proposed approach does not require an explicit parameterisation of the non-linearity. Moreover, the non-linearity does not have to be static, but could be the one with finite memories like backlash. By exploiting input's piecewise constant property, the denominator of the linear system described by an ARX model is consistently identified from the information of the output only; next, a subspace direct equalisation method estimates the unmeasurable inner signal based on the resulted denominator estimate and output measurements. Contrary to the existing blind approaches, the numerator of the linear system is not required, which leads to a significant improvement of removing an error propagation. On the basis of the estimated inner signal, the measured input and output, the non-linearity and linear system are obtained separately. The proposed approach is validated and compared with two existing blind approaches through numerical and experimental examples.
Hammerstein system identification through best linear approximation inversion and regularisation
International Journal of Control, 2017
Hammerstein systems are composed by the cascading of a static nonlinearity and a linear system. In this paper, a methodology for identifying such systems using a combination of least squares support vector machines (LS-SVM) and best linear approximation (BLA) techniques is proposed. To do this, a novel method for estimating the intermediate variable is presented allowing a clear separation of the identification steps. First, an approximation to the linear block is obtained through the BLA of the system. Then, an approximation to the intermediate variable is obtained using the inversion of the estimated linear block and the known output. Afterwards, a nonlinear model is calculated through LS-SVM using the estimated intermediate variable and the known input. To do this, the regularisation capabilities of LS-SVM play a crucial role. Finally, a parametric re-estimation of the linear block is made. The method was tested in three examples, two of them with hard nonlinearities, and was compared with four other methods showing very good performance in all cases. The obtained results demonstrate that also in the presence of noise, the method can effectively identify Hammerstein systems. The relevance of these findings lies in the fact that it is shown how the regularisation allows to bypass the usual problems associated with the noise backpropagation when the inversion of the estimated linear block is used to compute the intermediate variable.
An adaptive approximation method for Hammerstein systems identification
2012 IEEE International Conference on Control Applications, 2012
This paper aims to describe a new identification method for Hammerstein systems relying on the framework of basis functions approximation in order to obtain an adequate model for the nonlinear static component. The specific coefficients of the basis functions approximation and also the parameters of the linear dynamic component are estimated using a nonlinear least squares method based on a modified version of Gauss-Newton algorithm. An algorithm is introduced based on wavelet multiresolution analysis that returns a low complexity approximation of the nonlinear component built on a grid hierarchy using adaptive bases. Such bases provides a powerful means to detect local singularities and often lead to quite simple refinement strategies. Finally, we present some numerical results for our method that show its efficiency.
A New Identification Approach of MIMO Hammerstein Model with Separate Nonlinearities
Advances in Science, Technology and Engineering Systems Journal
A new coupled structure identification of Multi-Input Multi-Output (MIMO) Hammerstein models with separate nonlinearities is proposed. It is based on the use of the Recursive Least Squares (RLS) algorithm. A comparative study between a decoupled and coupled structures identification of MIMO Hammerstein models is discussed. A quadruple-tank process is used to illustrate the e ectiveness of the new structure.
New results for Hammerstein system identification
1995
Abstract A novel approach is presented for the analysis and design of identification algorithms for Hammerstein models, which consist of a static nonlinearity followed by an LTI system. The authors examine two identification problems. In the first problem, the system is excited with white noise and the LTI system is FIR, and they find a simple explicit solution for the optimal parameter estimate and show that for sufficiently large data lengths a standard iterative technique globally converges to this optimal value.