Identification of Complex Systems with the use of Interconnected Hammerstein Models (original) (raw)
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A Decoupling Derivative-Based Approach for Hammerstein System Identification
Proceedings of the 17th IFAC World Congress, 2008, 2008
This paper proposes a non iterative algorithm for the identification of Hammerstein model, using the sampled output data obtained from the step response, giving a continuoustime model for the linear part and a point-wise estimation of the nonlinear one. Key in the derivation of the results is the algebraic derivative method in the frequency domain yielding exact formula in terms of multiple integrals of the output signal, when placed in the time domain. By investigating the connection between such integrals and parameters to be estimated, a set of three linear regression equations is proposed. The first equation is used to estimate the structure of poles in the linear part, the second to estimate a point of the nonlinearity, the third to estimate the structure of zeros in the linear part. No a priori knowledge of the structure of the nonlinearity is required. The proposed algorithm is numerically robust, since it is based only on least squares estimation. Simulation results validate the proposed algorithm.
Identification of MIMO Hammerstein models using Singular Value Decomposition approach
International Journal of Computer Applications, 2012
In this paper, we present a new approach to identify multivariable Hammerstein systems based on the Singular Value Decomposition (SVD) method. The technique allows for the determination of the memoryless static nonlinearity as well as the estimation of the model parameters of the dynamic Auto-Regressive model with eXogenous input (ARX) part. First of all, an iteration procedure is proposed to identify the parameters of Multi-Input Multi-Output (MIMO) Hammerstein models by using the Recursive Least Squares (RLS) algorithm. Secondly, the obtained parameter estimates of the identification model include the product terms of the parameters of the original systems. So, to separate these parameters of the original parameters from the product terms, the singular value decomposition method is discussed. Finally, a simulation study is performed to demonstrate the effectiveness of the proposed method compared with the existing approaches.
Use of Hammerstein models in identification of nonlinear systems
AIChE Journal, 1991
The utility of the Hammerstein model, which is composed of a static nonlinear element in series with a linear dynamic part, was investigated to represent the dynamics of nonlinear chemical processes. Different methods to identify the parameters of Hammerstein models were tested. The methods were applied to the identification of simulated distillation columns and to an experimental heat exchanger process. The results show that the dynamics of such processes can be better represented by Hammerstein-type models than by linear models.
An identification algorithm for Hammerstein systems using subspace method
Proceedings of the 2011 American Control Conference, 2011
This paper describes a new algorithm for the identification of single-input single-output Hammerstein systems using the multivariable output error state space (MOESP) class of subspace identification algorithms. The algorithm consists of three main steps. First, the MOESP algorithm is used to determine the system order and estimate two of the state space model matrices. Second, a least squares problem is solved to minimize the prediction error. Finally, the global search optimization is needed to be used to estimate optimal values for the remaining parameters. Performance of the model was evaluated by simulating a model of ankle joint reflex stiffness, a well known Hammerstein system. The results demonstrate that the algorithm estimated the model parameters very accurately in the presence of additive, output noise.
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.
Parametric Identification of Parallel Hammerstein Systems
IEEE Transactions on Instrumentation and Measurement, 2000
This paper proposes a parametric identification method for parallel Hammerstein systems. The linear dynamic parts of the system are modeled by a parametric rational function in the zor s-domain, while the static nonlinearities are represented by a linear combination of nonlinear basis functions. The identification method uses a three-step procedure to obtain initial estimates. In the first step, the frequency response function of the best linear approximation is estimated for different input excitation levels. In the second step, the power-dependent dynamics are decomposed over a number of parallel orthogonal branches. In the last step, the static nonlinearities are estimated using a linear least squares estimation. Furthermore, an iterative identification scheme is introduced to refine the estimates. This iterative scheme alternately estimates updated parameters for the linear dynamic systems and for the static nonlinearities. The method is illustrated on a simulation and a validation measurement example.
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.
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.
18th IFAC World Congress, August 28, 2011 - September 2, 2011, 2011
This paper presents a two-step method for identification of the SISO Hammerstein model, which employs input autocorrelation and input-output cross-correlation functions as data for least-squares estimation. Using separable processes as input signals, the proposed method allows the linear block of a Hammerstein model to be identified up to a multiplicative constant, without a priori knowledge of the nonlinear model structure. Both ARX and ยต-Markov structures of the linear block are considered, where the main concern is the accuracy of pole and zero estimates. The correlation least-squares method is compared numerically with a wellknown nonlinear least-squares method, which shows that the correlation method is consistently accurate across different nonlinear model structures.