Hammerstein-Wiener System Research Articles

NONLINEAR SYSTEM IDENTIFICATION OF WPC TERRACE WALL WITH HAMMERSTEIN-WIENER MODEL USING AMBIENT VIBRATION

Today, many advances in engineering field have been and are being made. Especially the predictions of the strengths and behavior of the models designed against external factors are of great importance. Elimination of negative effects and necessary updates on the model or in other words, strengthening works play the biggest role in the design stages. In addition to all these, the dynamically influenced situations of existing structures should be revealed. New methods have been developed for this and similar reasons. System identification is one of these methods. System identification is simply the estimation of the mathematical model of the building from the input and output vibration data obtained through the structures. Thanks to the predicted mathematical model, the reactions of the building to dynamic effects can be predicted. The aim of this study is to reveal the mathematical model of the WPC terrace wall with the nonlinear system identification method. Finally, nonlinear system identification of the WPC terrace wall results demonstrated that fit to estimation data was nearly 100 % and it can be concluded that Hammerstein–Wiener system identification method is efficient and accurate in identifying mathematical model of the WPC terrace wall.

Modeling and simulating dynamics of lithium-ion batteries using block-oriented models with piecewise linear static nonlinearity

The article deals with the research of the efficiency of modelling the dynamics of voltage change in lithium-ion rechargeable batteries in charging/discharging modes using nonlinear block-oriented systems. Drawing on experimental data, a structural and parametric identification of the Hammerstein, Wiener and Hammerstein-Wiener models with a polynomial structure of the linear dynamic block and piecewise linear static nonlinearities was performed. It has been established that the best modelling accuracy was ensured by using the Hammerstein-Wiener system with a linear model having the 6th order of the numerator and denominator polynomials and an input delay of 3 samples. It showed 15.67% and 6.2% higher accuracy compared to the Wiener and Hammerstein systems, respectively. The application of those models in battery management systems will make it possible to improve the control quality for battery assemblies of solar and wind power plants in the context of the variable nature of the charging/discharging processes due to the variability of weather conditions and fluctuations in power consumption during a 24-hour period. This will ensure a wider introduction of renewable power generation into existing power systems, which is currently the leading way to ensure sustainable development of the energy sector.

Block-oriented system identification for nonlinear modeling of all-solid-state Li-ion battery technology

The high energy density characteristic of the all-solid-state battery technology makes it one of the promising competitors of current liquid electrolyte-based lithium-ion batteries. However, due to the low ionic conductivity of solid materials and existing issues in active material-solid electrolyte interfaces, all-solid-state batteries show strong nonlinear behavior when the amplitude of input current is relatively high. In this paper, we have developed a methodology based on block-oriented nonlinear systems that can detect, quantize, and model the battery behavior, accurately. For this purpose, two solid-state coin cells, which have different ionic conductivity at the cathode interface are manufactured and excited with multisine input current. The Best Linear Approximation (BLA) method has been used to separate linear frequency response function (FRF) from nonlinear distortion. Then, a Hammerstein-Wiener system has been developed and parametrized to model the nonlinear distortions caused by ionic conductivity variation of the solid electrolyte at the cathode layer. Furthermore, the developed model has been utilized to detect possible faults in the electrode-electrolyte interface based on the nonlinearity level of the measured voltage.

Improved Intelligent Identification of Hammerstein-Wiener Systems by Particle Swarm Optimization and K-Means Clustering

This paper considers the robust identification of Hammerstein-Wiener systems in the presence of Gaussian or non-Gaussian noises. An improved intelligent identification scheme is exploited by combining particle swarm optimization (PSO) and K-means clustering. The proposed scheme has strong ability to keep the balance between exploration and exploitation. Its procedure is about “global particle swarm optimization search — K-means clustering — local particle swarm optimization search”. The proposed scheme can identify the parameters of the general Hammerstein-Wiener system with dead zone and saturation characteristics, and obtain a more accurate model for the actual production process. Relative to other improved particle swarm optimization methods, the accuracy of parameter estimation is improved by nearly 53 % at data length L=2000. In particular, the method can better model nonlinear dynamics and facilitate the precise implementation of control in chemical production.

Multi-model predictive control of Hammerstein-Wiener systems based on balanced multi-model partition

ABSTRACTModel analysis of Hammerstein-Wiener systems has been made, and it is found that the included angle is applicable to such systems to measure the non-linearity. Then, a dichotomy gridding algorithm is proposed based on the included angle. Supporting by the gridding algorithm, a balanced multi-model partition method is put forward to partition a Hammerstein-Wiener system into a set of local linear models. For each linear model, a linear model predictive controller (MPC) is designed. After that, a multi-MPC is composed of the linear MPCs via soft switching. Thus, a complex non-linear control problem is transformed into a set of linear control problems, which simplifies the original control problem and improves the control performance. Two non-linear systems are built into Hammerstein-Wiener models and investigated using the proposed methods. Simulations demonstrate that the proposed gridding and partition methods are effective, and the resulted multi-MPC controller has satisfactory performance in both set-point tracking and disturbance rejection control.

Parameter estimation of Hammerstein–Wiener nonlinear system with noise using special test signals

In this paper, an identification procedure of Hammerstein–Wiener nonlinear system with process noise using special test signals is presented. Special test signals that contain separable signal and uniformly random multi-step signal are employed to separate the identification problems of the linear dynamic part and the output static nonlinear part from that of the input static nonlinear part, and then correlation analysis method is applied to estimate the parameters of the output static nonlinear part and linear dynamic part. Moreover, a filter is embedded to form extended Hammerstein–Wiener system to calculate the noise correlation functions by the information of zeros and poles of the extended system, further an error compensation term which consists of the noise correlation functions is added to least square estimation to compensate the error caused by process noise. Therefore, the unbiased estimation of model parameters can be derived by error compensation based recursive least square method. Simulation results demonstrate that proposed approach can effectively identify parameters of Hammerstein–Wiener nonlinear system in the presence of process noise.

Recursive identification for multi-input–multi-output Hammerstein–Wiener system

ABSTRACTIn this paper, an identification method based on the recursive auxiliary variable least squares algorithm is proposed for a multi-input–multi-output Hammerstein–Wiener system with process noise. In the proposed identification method, the system is converted into the multivariate regression form under the condition that the nonlinear block in the output part is invertible. Then, the auxiliary variable is constructed, the parameters of the regression equations are identified, and the system parameter matrices can be obtained by matrix composition of the parameter product matrix. A theoretical analysis showed that the proposed method has uniform convergence when the process noise is white and has a finite variance. The effectiveness of the proposed method is validated through the experiments.

Data-Driven Predictive Control with Nonlinear Compensation for Performance Management in Virtualized Software System

This paper deals with data-driven predictive control for relative performance management in virtualized software system. The system dynamics are characterized in Hammerstein-Wiener structure to capture nonlinear and linear characteristics. The proposed control approach is the implementation of Subspace-based Predictive Control with the integration of nonlinear compensation. The compensator functions are inverse static input and output nonlinearity models from the Hammerstein-Wiener system identification. The subspace predictors are formulated from the linear model input and output of Wiener block. The experimental results from three scenarios of performance objectives show the reliability of Subspace-based Predictive Control to manage the virtualized software system.

Recursive parameter estimation for Hammerstein-Wiener systems using modified EKF algorithm

This paper focuses on the recursive parameter estimation for the single input single output Hammerstein-Wiener system model, and the study is then extended to a rarely mentioned multiple input single output Hammerstein-Wiener system. Inspired by the extended Kalman filter algorithm, two basic recursive algorithms are derived from the first and the second order Taylor approximation. Based on the form of the first order approximation algorithm, a modified algorithm with larger parameter convergence domain is proposed to cope with the problem of small parameter convergence domain of the first order one and the application limit of the second order one. The validity of the modification on the expansion of convergence domain is shown from the convergence analysis and is demonstrated with two simulation cases.

Design and experiment of data-driven modeling and flutter control of a prototype wing

This paper presents an approach for data-driven modeling of aeroelasticity and its application to flutter control design of a wind-tunnel wing model. Modeling is centered on system identification of unsteady aerodynamic loads using computational fluid dynamics data, and adopts a nonlinear multivariable extension of the Hammerstein-Wiener system. The formulation is in modal coordinates of the elastic structure, and yields a reduced-order model of the aeroelastic feedback loop that is parametrized by airspeed. Flutter suppression is thus cast as a robust stabilization problem over uncertain airspeed, for which a low-order H∞ controller is computed. The paper discusses in detail parameter sensitivity and observability of the model, the former to justify the chosen model structure, and the latter to provide a criterion for physical sensor placement. Wind tunnel experiments confirm the validity of the modeling approach and the effectiveness of the control design.

Recursive identification for Hammerstein–Wiener systems with dead-zone input nonlinearity

A new recursive algorithm is proposed for the identification of a special form of Hammerstein–Wiener system with dead-zone nonlinearity input block. The direct motivation of this work is to implement on-line control strategies on this kind of system to produce adaptive control algorithms. With the parameterization model of the Hammerstein–Wiener system, a special form of model estimation error is defined; and then its approximate formula is given for the following derivation. Based on these, a recursive identification algorithm is established that aims at minimizing the sum of the squared parameter estimation errors. The conditions of uniform convergence are obtained from the property analysis of the proposed algorithm and an adaptive setting method for a weighted factor in the algorithm is given, which enhances the convergence of the proposed algorithm. This algorithm can also be used for the identification of the Hammerstein systems with dead-zone nonlinearity input block. Three simulation examples show the validity of this algorithm.

Hierarchical Least Squares Estimation Algorithm for Hammerstein–Wiener Systems

This letter focuses on identification problems of a Hammerstein-Wiener system with an output error linear element embedded between two static nonlinear elements. A hierarchical least squares algorithm is presented for the Hammerstein-Wiener system by using the auxiliary model identification idea and the hierarchical identification principle. The major contributions of the present study are that the identification model is formulated by using the auxiliary model identification idea (the estimate of the unknown internal variable is replaced with the output of an auxiliary model) and that the bilinear parameter vectors in the identification model are estimated by using the hierarchical identification principle. The proposed hierarchical identification approach is computationally more efficient than the existing over-parametrization method.

Identification of Hammerstein-Wiener Systems

This work introduces a new formulation of the Hammerstein-Wiener system for identification purpose. Two methods to calculate the estimates are implemented: the overparametrization approach, and the iterative approach. The good performance obtained by both methods is shown with a simulation example.

Two-stage refined instrumental variable method for identifying Hammerstein-Wiener continuous-time models in closed loop

The continuous-time model identification problem of closed-loop Hammerstein-Wiener system with unknown controller and different noise situations is studied. A two-stage approach is proposed, based on the refined instrumental variable method. With the assumption of monotonic nonlinear function, the closed-loop non linear model is iteratively estimated as an over-parameterized MISO LTI model. To obtain an accurate model in the closed-loop case, the identification is implemented in two stages: 1) identification between the input and the reference signal, which produces estimate of the noise-free input, 2) identification between the output and estimated noise-free input signal. Monte Carlo simulation analysis is carried out to illustrate the effectiveness of the proposed method, in both output and process noise circumstances.

A Kalman Pre-filtered IV-Based Approach to Continuous-Time Hammerstein-Wiener System Identification

This paper studies the identification problem for a class of Hammerstein-Wiener continuous-time systems, with a monotonic nonlinear function for the Wiener part. Based on the previously developed simplified refined instrumental variable method, and by making use of an adaptive observer for data filtering, a combined approach, referred to as the Kalman pre-filtered instrumental variable based method, is proposed. By taking the advantages of the two aforementioned methods, the new method is faster and has a naturally stabilized filter, as well as keeps a high estimation accuracy in most cases. Monte Carlo simulation analysis is used to illustrate the performances of the proposed methods.

Three-Tone Characterization of Nonlinear Memory Effects in Radio-Frequency Power Amplifiers

A stepped three-tone measurement technique based on digitally modulated baseband signals is used in characterizing radio-frequency power amplifiers (PAs). The bandwidths of the stepped measurement were 8.8 MHz for the input signal and 26.4 MHz for the output signal. A PA designed for third-generation mobile telecommunication system was analyzed. The amplitude and phase of the third-order Volterra kernel were determined from the identified intermodulation products. The properties of the Volterra kernel along certain paths in the 3-D frequency space were analyzed and compared to some box models for nonlinear systems. The main symmetry of the third-order Volterra kernel of this PA was found to be of the type given by the cascaded quadratic nonlinearities with a linear filter in between (a Hammerstein-Wiener system), and frequency dependence, i.e., memory effects, was found to be due to the effects at the baseband.