Continuous-time Hammerstein system identification

A continuous-time Hammerstein system, i.e., a system consisting of a nonlinear memoryless subsystem followed by a linear dynamic one, is identified. The system is driven and disturbed by white random signals. The a priori information about both subsystems is nonparametric, which means that functional forms of both the nonlinear characteristic and the impulse response of the dynamic subsystem are unknown. An algorithm to estimate the nonlinearity is presented and its pointwise convergence to the true characteristic is shown. The impulse response of the dynamic part is recovered with a correlation method. The algorithms are computationally independent. Results of a simulation example are given     

Continuous-time Hammerstein system identification from sampled data

A continuous-time Hammerstein system driven by a random signal is identified from observations sampled in time. The sampling may be uniform or not. The a-priori information about the system is nonparametric, functional forms of both the nonlinear characteristic and the impulse response are completely unknown. Three kernel algorithms, one offline and two semirecursive are presented. Their convergence to the true characteristic of the nonlinear subsystem is shown. The distance between consecutive sampling times must not decrease too fast for the algorithms to converge.     

Continuous-time system identification using shifted Chebyshev polynomials

A new instrumental-variable-based identification procedure is introduced to estimate linear and nonlinear continuous-time models using a shifted Chebyshev basis in the presence of noise.     

Continuous-time system identification of a smoking cessation intervention

Cigarette smoking is a major global public health issue and the leading cause of preventable death in the United States. Toward a goal of designing better smoking cessation treatments, system identification techniques are applied to intervention data to describe smoking cessation as a process of behaviour change. System identification problems that draw from two modelling paradigms in quantitative psychology (statistical mediation and self-regulation) are considered, consisting of a series of continuous-time estimation problems. A continuous-time dynamic modelling approach is employed to describe the response of craving and smoking rates during a quit attempt, as captured in data from a smoking cessation clinical trial. The use of continuous-time models provide benefits of parsimony, ease of interpretation, and the opportunity to work with uneven or missing data.     

Subspace based approaches for Wiener system identification

We consider the problem of Wiener system identification in this note. A Wiener system consists of a linear time invariant block followed by a memoryless nonlinearity. By modeling the inverse of the memoryless nonlinearity as a linear combination of known nonlinear basis functions, we develop two subspace based approaches, namely an alternating projection algorithm and a minimum norm method, to solve for the Wiener system parameters. Based on computer simulations, the algorithms are shown to be robust in the presence of modeling error and noise.     

Continuous-time system identification of the steering dynamics of a ship on a river

In this study, we consider the parameter estimation problem of a ship dynamics model. We consider two possible approaches to identify a continuous-time model from real data obtained on a river, where the presence of disturbances is a key issue. The first approach is identification through optimisation using a disturbance observer. The second approach corresponds to the refined instrumental variable method for linear parameter varying systems. In addition, we evaluate the accuracy of the parameter estimation through a sensitivity analysis. The obtained results show an improvement in the parameter estimates compared to identification procedures that do not consider the river disturbances. The application of the model for track-keeping control is also illustrated.     

Parameter identification of fractional-order Wiener system based on FF-ESG and GI algorithms

Fractional-order calculus has broad application scenarios in engineering and physics. Unlike integer-order calculus, fractional-order calculus has the ability to analyze nonclassical phenomena in science and engineering. For industrial processes with strong nonlinear characteristics, nonlinear models such as the Wiener model have become research hotspots. This paper studies the parameter identification of the fractional-order Wiener system. In this paper, the forgetting factor extended stochastic gradient (FF-ESG) algorithm and the gradient iterative (GI) algorithm are proposed to identify the parameters of the fractional-order Wiener system. Then, the convergence of the FF-ESG algorithm for the fractional-order Wiener system is analyzed. Both proposed algorithms can obtain exact parameter estimates, which are verified by a numerical example and a case study of a fluid control valve.     

Frequency domain identification of Wiener models

This paper proposes a frequency domain algorithm for Wiener model identifications based on exploring the fundamental frequency and harmonics generated by the unknown nonlinearity. The convergence of the algorithm is established in the presence of white noise. No a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric.     

Recursive identification of continuous-time Wiener systems

Recursive algorithms to identify both subsystems of a continuous-time Wiener system are presented. The system is driven and disturbed by Gaussian white random signals. The impulse response of the linear dynamic subsystem is recovered with a correlation method. It is shown that the inverse of the non-linear characteristic of the other subsystem is a regression function. Then, to recover the inverse, two estimates are presented. The algorithms converge to the unknown impulse response, and the inverse of the characteristic, respectively. Convergence rates are presented. Moreover, results of simulation examples are given.     

Maximum likelihood identification of Wiener models

The Wiener model is a block oriented model, having a linear dynamic system followed by a static nonlinearity. The dominating approach to estimate the components of this model has been to minimize the error between the simulated and the measured outputs. We show that this will, in general, lead to biased estimates if there are other disturbances present than measurement noise. The implications of Bussgang’s theorem in this context are also discussed. For the case with general disturbances, we derive the Maximum Likelihood method and show how it can be efficiently implemented. Comparisons between this new algorithm and the traditional approach, confirm that the new method is unbiased and also has superior accuracy.     

Recursive identification of errors-in-variables Wiener systems

This paper considers the recursive identification of errors-in-variables (EIV) Wiener systems composed of a linear dynamic system followed by a static nonlinearity. Both the system input and output are observed with additive noises being ARMA processes with unknown coefficients. By a stochastic approximation incorporated with the deconvolution kernel functions, the recursive algorithms are proposed for estimating the coefficients of the linear subsystem and for the values of the nonlinear function. All the estimates are proved to converge to the true values with probability one. A simulation example is given to verify the theoretical analysis.     

Continuous-time model identification for closed loop control performance assessment

The paper describes a system identification procedure for continuous-time transfer function models and demonstrates how it can be used for control performance assessment. Two normalized indices are derived for detecting oscillations and sluggish performance. The methods are designed for single-input single-output (SISO) control loops that experience periodic setpoint changes. An advantage of the system identification procedure is that it can operate on irregularly sampled data. The paper presents results from simulation tests and from tests on an heating, ventilating, and air-conditioning (HVAC) system serving a large commercial office building.     

On identification of Hammerstein and Wiener model with application to virtualised software system

This paper proposes a system identification method for estimating virtualised software system dynamics within the framework of a Hammerstein–Wiener model. Building on the authors’ previous work in identification and control of the software systems, the approach utilises frequency sampling filter structure to describe the linear dynamics and B-spline curve functions for the inverse static output nonlinearity. Furthermore, the issue on parameter selection for B-spline model approximation of scatter data is addressed by using a data clustering method. An experimental test-bed of virtualised software system is established to generate real observational data which are used to confirm the performance of the proposed approach. The identification results have shown that the model efficacy is increased with the proposed approach because the dimension of the nonlinear model can be significantly reduced while maintaining the desired accuracy.     

Continuous-time system representation with exact macro-difference expressions

A macro-difference equation representation is proposed which is a mixture of finite-difference quotients and integrals over finite time intervals. The choice of the micro or sampling interval length (for the numerical integration accuracy and representation bandwidth) and the choice of the macro interval length (for numerical conditioning/accuracy of the difference quotients and of the resulting equations) are independent. This approach does not need the assumption (which in practical situations is quite unnatural) of zero initial conditions.     

An integro-differential formula on the Wiener kernels and its application to sandwich system identification

It is well known that a nonlinear system with a white Gaussian noise input can be characterized in terms of kernels using the celebrated Wiener theory. In a practical use of the method, however, one may encounter difficulty in obtaining higher order kernels except for the first few because of, for instance, the excessive computational requirement. In this paper, we give an integro-differential formula on the kernels and as its application, an algorithm to identify a cascade system of a linear, a memoryless nonlinear, and linear subsystems, which we call a sandwich system as a whole. According to the formula, kernels up to the second order for different power levels of the input noise are required to identify the subsystems. Impulse response functions of the two linear subsystems can be obtained under appropriate normalization conditions, while the nonlinear subsystem is estimated in the form of a truncated Hermite polynomial expansion. As illustrated examples, two such systems are identified using the algorithm.     

Recursive identification for Wiener systems using Gaussian inputs

The recursive algorithms are given for identifying the single‐input single‐output Wiener system which consists of a moving average type linear subsystem followed by a static nonparametric nonlinearity. The input is defined to be a sequence of mutually independent Gaussian random variables. The estimates for coefficients of the linear subsystem as well as for f(v) at any v are proved to converge to the true values with probability one. A numerical example is given, justifying the theoretical analysis. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Strong consistence of recursive identification for Wiener systems

The paper concerns identification of the Wiener system consisting of a linear subsystem followed by a static nonlinearity f(·) with no invertibility and structure assumption. Recursive estimates are given for coefficients of the linear subsystem and for the value f(v) at any fixed v. The main contribution of the paper consists in establishing convergence with probability one of the proposed algorithms to the true values. This probably is the first strong consistency result for this kind of Wiener systems. A numerical example is given, which justifies the theoretical analysis.