Hammerstein Systems Research Articles

Identification of fractional Hammerstein systems with the conformable fractional derivative

SummaryIn this article, we study parameter estimation problems for fractional commensurate Hammerstein systems utilizing the conformable fractional derivative. Two algorithms are investigated: first, the Poisson moment functions (PMF) method, aiming to transfer the fractional derivative of the measurement signal into PMF using the fractional Laplace transform and convolution; second, a proposed new instrumental variable algorithm, which is based on the conformable fractional derivative. Both algorithms have been analyzed and shown to be consistent. A comprehensive complexity analysis is provided for each algorithm. Furthermore, a kind of special time‐varying systems are discussed under the conformable fractional derivative. Finally, an example is given to illustrate the effectiveness of the proposed algorithms.

Iterative parameter identification for Hammerstein systems with ARMA noises by using the filtering identification idea

SummaryIn practical applications, many processes have nonlinear characteristics that require nonlinear models for accurate description. However, constructing such models and determining their parameters are a challenging task. This article explores filtered identification methods for estimating the parameters of a particular type of nonlinear Hammerstein systems with ARMA noise. An auxiliary model‐based least squares algorithm is developed for such systems based on the auxiliary model identification idea. A hierarchical least squares algorithm that utilizes the hierarchical identification principle is proposed to enhance computational efficiency. Additionally, a key term separation technique is employed to express the system output as a linear combination of parameters, allowing the system to be decomposed into smaller subsystems for more efficient estimation of parameters. Simulation results demonstrate the effectiveness of these proposed algorithms.

Parameter learning of multi‐input multi‐output Hammerstein system with measurement noises utilizing combined signals

SummaryIn this article, the parameter learning scheme for the multi‐input multi‐output (MIMO) Hammerstein nonlinear systems under measurement noises is studied, which is derived by exploiting the correlation analysis and data filtering technique. The coupled MIMO Hammerstein system presented involves a static nonlinear subsystem modeled by neural fuzzy model (NFM), and a dynamic linear subsystem established by autoregressive moving average with extra input (ARMAX) model. To learn the unknown parameter of the MIMO Hammerstein system, the combined signals are designed to realize that identification of the nonlinear subsystem is separated from that of linear subsystem. First, the correlation properties of separable signals in a nonlinear system are analyzed, then the parameters of the linear subsystem are estimated utilizing correlation analysis, which can deal with the issue of unmeasured intermediate variable in the Hammerstein system. Second, the data filtering technique is introduced to derive the data filtering‐based recursive least squares technique for learning the nonlinear subsystem parameter, which can reduce the impact of the moving average noise and improve the precision of parameter estimation. Finally, the effectiveness and feasibility of the proposed identification scheme is proved by numerical simulation and nonlinear pH process.

Self-error learning framework-based algorithm for parameter recovery of extended Wiener–Hammerstein systems subject to quantised measurements

In this study, a novel estimation scheme is proposed for identifying extended Wiener–Hammerstein systems with hysteresis nonlinearity subject to quantised measurements. The proposed scheme is established in a self-error learning framework to achieve high-performance parameter estimation compared with classic error feedback learning estimation algorithms. Initially, the useful identification data can be extracted from contaminated system data by introducing an adaptive filter. Then, with the help of the filtered data, the identification error expression used to establish the estimator is derived. Subsequently, an online compensation estimation error variable is proposed to eliminate the effect of the regression vector on the convergence performance. A new adaptive law is designed with adaptive recursive gain, considering the compensation estimation error data and parameter initial error data. Under general persistent excitation (PE) condition, the PE condition of the regressor information is verified online, and the estimator convergence is strictly proven. Finally, the statistical results of two illustrated examples and a real-word example are provided to validate the positive features and effectiveness of the proposed estimation scheme.

Fixed-Time Adaptive Parameter Estimation for Hammerstein Systems Subject to Dead-Zone

The Hammerstein model has proven its ability for modeling many industrial servo systems, but the corresponding parameter estimation remains as a challenging problem, especially for the purpose of achieving fast convergence. This paper presents a fixed-time (FxT) adaptive parameter estimation scheme for Hammerstein systems with an asymmetric dead-zone to ensure the convergence of estimated parameters in fixed-time. A continuous piecewise linear (CPL) function is adopted to model the nonlinear dead-zone dynamics to remedy the use of intermediate variable. To avoid using the system state information, a K-filter is used to construct a relationship between the unknown system parameters and the input/output signals. Then a new adaptive law based on the parameter error and the FxT scheme is developed to online estimate the lumped unknown parameters and ensure the fixed-time convergence, where an online updated auxiliary variable of regressor is suggested to eliminate the impact of the regressor on the convergence performance. Both numerical simulations and experimental results are given to demonstrate the effectiveness of proposed methods.

Online identification of Hammerstein systems with B‐spline networks

SummaryNonlinear systems widely exist in real‐word applications and the research for these systems has enjoyed a long and fruitful history, including the system identification community. However, the modeling for nonlinear systems is often quite challenging and still remains many unresolved questions. This article considers the online identification issue of Hammerstein systems, whose nonlinear static function is modeled by a B‐spline network. First, the identification model of the studied system is constructed using the bilinear parameter decomposition model. Second, the online recursive algorithms are proposed to find the estimates using the moving data window and the particle swarm optimization procedure, and show that these estimates converge to their true values with a low computational burden. Numerical examples are also given to test the effectiveness of the proposed algorithms.

Probability-Based Identification of Hammerstein Systems With Asymmetric Noise Characteristics

Probability-Based Identification of Hammerstein Systems With Asymmetric Noise Characteristics

Recursive Identification of Nonlinear Hammerstein Systems With FIR Linear Parts Under Impulsive Noise With Model Selection and Order Determination

Recursive Identification of Nonlinear Hammerstein Systems With FIR Linear Parts Under Impulsive Noise With Model Selection and Order Determination

Discrete Second Order Sliding Mode Control for Fractional Order Hammerstein System

This study explores the control of discrete fractional order Hammerstein systems using first-order sliding mode control (FOSMC) and improves its performance by integrating second-order sliding mode control (2SMC). Two simulation examples are presented to assess the effectiveness of these techniques. Results indicate that 2SMC performs better than FOSMC, demonstrating its superiority in controlling these complex systems and offering promising advancements in control strategies.

Decentralized sliding mode control using an event-triggered mechanism for discrete interconnected Hammerstein systems

Decentralized sliding mode control using an event-triggered mechanism for discrete interconnected Hammerstein systems

Identification of switched dynamic system for electric multiple unit train modeling

A new iterative algorithm is proposed to identify the high-speed train model which is described as a switched dynamic system including a fast switched nonlinear static subsystem followed by a non-switched linear dynamic subsystem. The non-switched property of the linear part leads to a more complex dynamics of the whole system, compared to the switched Hammerstein system which linear part switches synchronously with its nonlinear part. The proposed iterative algorithm alternates between identifying the switched nonlinear static subsystem and the linear dynamic subsystem. The switched nonlinear subsystem identification incorporates a quadratic error bound constraint with respect to nominal values of model parameters, and is formulated as a second-order cone program. Properties of convergence and asymptotic unbiasedness of the obtained estimates are proved under some necessary assumptions. With real data and simulation examples, the proposed iterative algorithm produces convergent and asymptotically unbiased estimates. In the simulation results, incorporating the quadratic error bounds results in a fast convergence rate in the presence of a small noise variance, and also produces a smaller identification error in the presence of colored noises with a non-zero mean and a large variance.

Robust adaptive algorithm for widely-linear Hammerstein system and its application

The Hammerstein model is a crucial model frequently employed in the field of signal processing. This paper focuses on the widely-linear (WL) complex-valued adaptive filtering and proposes a WL Hammerstein system model. Firstly, a cost function which minimizes the complex correntropic loss criterion is constructed. Subsequently, by extending the alternate direction method of multipliers (ADMM) optimization and non-convex projection method to the WL model, and leveraging the special structure of the autocorrelation matrix in the WL Hammerstein system, a robust recursive adaptive filtering algorithm for the WL Hammerstein system is proposed, along with its simplified version. More importantly, the performance analysis is studied, in which the convergence performance and the mean-square performance are provided. Simulations about system identification and stereophonic acoustic echo cancelation (SAEC) are carried out to validate the theoretical analysis and demonstrate the superior performance of the algorithms in this paper.

Frequency Domain Identification of Continuous-Time Hammerstein Systems With Adaptive Continuous-Time Rational Orthonormal Basis Functions

In this paper, we propose a new identification method for continuous-time Hammerstein systems. This method is based on the adaptive generalized rational orthonormal basis functions. In particular, we use the strategy in which poles of basis functions are selected one by one in terms of a criterion. By doing this, we not only take advantage of the variability of the generalized orthogonal basis functions, but also reduce the computational burden. The proposed algorithm is adaptive. Meanwhile, convergence analysis is performed with considering the sampling frequency, noise level, sampling length, and terms of basis functions. The obtained results guarantee the convergence of the whole Hammerstein system. Finally, a numerical example is presented to illustrate the usefulness of the proposed identification algorithm.

Maximum likelihood gradient‐based iterative estimation for closed‐loop Hammerstein nonlinear systems

AbstractThis article studies a new iterative method for a class of closed‐loop Hammerstein systems. The new iterative method solves the crossproducts between the parameters of the linear block and the nonlinear block by using the key term separation technique, decomposes a system into two subidentification models by utilizing the hierarchical identification principle for reduced computational complexity, and maximizes the maximum likelihood cost function by using the input and output data with a data window for improved parameter estimation accuracy. A numerical simulation example and a continuous stirred tank reactor experiment are presented to demonstrate that the proposed algorithm can work effectively.

Adaptive Regulation for Hammerstein and Wiener Systems with Event-Triggered Observations

Adaptive Regulation for Hammerstein and Wiener Systems with Event-Triggered Observations

Bias-Correction Errors-in-Variables Hammerstein Model Identification

In this paper, a Bias-Correction Least-Squares (BCLS) algorithm is proposed for identifying block-oriented Errors-In-Variables nonlinear Hammerstein (EIV-Hammerstein) systems. Due to both the input and output of the EIV-Hammerstein system are observed with additive white noises, the estimation bias of traditional LS algorithm is introduced. The estimation bias is derived from a consistency point of view, which is a function about noises variances and monomial of noiseless system input-output measurements. A bias-estimation scheme based only on the available noisy measurements is then proposed for consistent identification of the monomial of noiseless system input-output measurements in a recursive form. In particular, a specific algorithm based on minimizing the output prediction error is given to find out the unknown noise variances for practical applications. Such that the noise effect can be eliminated and the consistent estimated parameters are obtained. The effectiveness of the proposed method is demonstrated by a simulation example and an experimental prototype of wireless power transfer system.

Fault Detection for Nonlinear Dynamic Systems With Consideration of Modeling Errors: A Data-Driven Approach.

This article is concerned with data-driven realization of fault detection (FD) for nonlinear dynamic systems. In order to identify and parameterize nonlinear Hammerstein models using dynamic input and output data, a stacked neural network-aided canonical variate analysis (SNNCVA) method is proposed, based on which a data-driven residual generator is formed. Then, the threshold used for FD purposes is obtained via quantiles-based learning, where both estimation errors and approximation errors are considered. Compared with the existing work, the main novelties of this study include: 1) SNNCVA provides a new parameterization strategy for nonlinear Hammerstein systems by utilizing input and output data only; 2) the associated residual generator can ensure FD performance where both the system model and its nonlinearity are unknown; and 3) with consideration of modeling-induced errors, the quantiles are invoked and used to provide a reliable FD threshold in situations where only limited samples are available. Studies on a nonlinear hot rolling mill process demonstrate the effectiveness of the proposed method.

Payload symbol-based nonlinear RF fingerprint for wireless QPSK-OFDM devices

Radio Frequency (RF) fingerprinting is one physical-layer authentication method for wireless communication, which uses the unique hardware characteristic of the transmitter to identify its true identity. To improve the performance of RF Fingerprint (RFF) based on preamble with fixed duration, a nonlinear RF fingerprinting method based on payload symbols is proposed for the wireless OFDM communication with the bit mapping scheme of QPSK. The wireless communication system is modeled as a Hammerstein system containing the nonlinear transmitter and multipath fading channel. A parameter separation technique based on orthogonal polynomial is presented for the estimation of the parameters of the Hammerstein system. The Hammerstein system parameter separation technique is firstly used to estimate the linear parameter with the training signal, which is used to compensate the adverse effect of the linear channel for the demodulation of the successive payload symbols. The demodulated payload symbols are further used to estimate the nonlinear coefficients of the transmitter with the Hammerstein system parameter separation technique again, which is used as the novel RFF for the authentication of the QPSK-OFDM device. Numerical simulations have verified the proposed method, which can also be extended to the OFDM signals with other bit mapping schemes.

Identification of series–parallel systems composed of linear and nonlinear blocks

AbstractMost works on system identification of block‐oriented nonlinear systems were devoted to Wiener and Hammerstein systems. This article is focused on a more general, and so more complex, nonlinear model structure. Specifically, the system under study is a series connection of two subsystems each one being constituted of linear dynamic block and a nonlinear static block coupled in parallel. Clearly, this system structure generalizes those of Wiener and Hammerstein systems. Interestingly, the linear blocks can be parametric or not and are allowed to be of unknown structure. We develop a two‐stage frequency‐type identification method that provides accurate estimates of the all system parts. The proposed identification method enjoys the simplicity and the consistency of developed estimators. Furthermore, the parameters of linear dynamic blocks can be easily decoupled without any further experiments. The performances of the proposed identification method are highlighted by several simulation results. As perspectives, one or the two nonlinearities can be considered non‐static, for example, of backlash type.

On the combined estimation of the parameters and the states of fractional-order systems

In this article, we propose an approach for system identification for a class of discrete-time fractional-order Hammerstein systems using only input–output data. Using a combined state and parameter estimation approach, we develop an algorithm serving to estimate simultaneously, the system parameters, the system orders, and the system states. By minimizing the defining criterion, which is non-convex and nonlinear in the parameters, the model parameters are estimated using the recursive least squares and the Levenberg–Marquardt algorithms. Next, the system states are estimated using the Luenberger observer. Then, the convergence analysis of the proposed algorithm is proved. Finally, the Monte Carlo simulation analysis and an application to Ultracapacitor system are used to demonstrate the effectiveness of the suggested method.