This paper presents a method for estimating a linear time-varying approximation of a general class of nonlinear time-varying systems. It starts from noisy measurements of the response of the nonlinear time-varying system to a special class of periodic excitation signals. These measurements are subject to measurement noise, process noise and a trend. The proposed method is a two-step procedure. First, the disturbing noise variance is quantified. Next, using this knowledge, the linear time-varying dynamics are estimated together with the nonlinear time-varying distortions. The latter are split into even and odd contributions. As a result, the signal-to-nonlineardistortion ratio is quantified. It allows one to decide whether or not a linear approximation is justifiable for the application at hand. The two-step algorithm is fully automatic in the sense that the user only has to choose upper bounds on the number of basis functions used for modeling the response signal. The obtained linear time-varying approximation is the best in the sense that the difference between the actual nonlinear response and the response predicted by the linear approximation is uncorrelated with the input. Therefore, it is called the best linear time-varying approximation (BLTVA). Finally, the theory is validated on a simulation example, and illustrated on two measurement examples: the cristallographic pitting corrosion of aluminum, and copper electrorefining.
In this paper, the regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modelled as Volterra series. The kernels of order higher than one, representing higher dimensional impulse responses in the series, are considered to be realizations of multidimensional Gaussian processes. Based on this, prior information about the structure of the Volterra kernel is introduced via an appropriate penalization term in the least squares cost function. It is shown that the proposed method is able to deliver accurate estimates of the Volterra kernels even in the case of a small amount of data points.
Despite the increasing interest in using powered ankle-foot orthoses for assistive purposes, their development and benchmarking still present core challenges. Powered orthoses have to be safe and provide adequate torque while keeping limited size and weight. The discordance of these requirements is a challenge for the development of these devices. This paper describes the control strategy and characterization of a compact variable stiffness actuator, to be used in an assistive ankle-foot orthosis for impaired subjects. The results of the characterization experiments show the advantageous behavior of the actuator and its performance in providing different relevant assistive torque profiles, with different actuator stiffnesses, during emulated walking experiments. However, some divergences in the results obtained in different testing conditions highlight the need for more general benchmarking techniques. Towards this objective, the paper also proposes a novel performance indicator that can be used to better evaluate the performance of robotic actuators both in quasi-static and in dynamic conditions. The article concludes with a call for research on new benchmarking techniques, to understand more in-depth series elastic's actuators behavior under dynamic conditions.
Inspired by the recent promising developments of Bayesian learning techniques in the context of system identification, this paper proposes a Transfer Function estimator, based on Gaussian process regression. Contrary to existing kernel-based impulse response estimators, a frequency domain approach is adopted. This leads to a formulation and implementation which is seamlessly valid for both continuous-and discrete-time systems, and which conveniently enables the selection of the frequency band of interest. A pragmatic approach is proposed in an output error framework, from sampled input and output data. The transient is dealt with by estimating it simultaneously with the transfer function.Modelling the transfer function and the transient as Gaussian processes allows for the incorporation of relevant prior knowledge on the system, in the form of suitably designed kernels. The SS (Stable Spline) and DC (Diagonal Correlated) kernels from the literature are translated to the frequency domain, and are proven to impose the stability of the estimated transfer function. Specifically, the estimates are shown to be stable rational functions in the frequency variable. The hyperparameters of the kernel are tuned via marginal likelihood maximisation.The comparison between the proposed method and three existing methods from the literature -the regularised finite impulse response (RFIR) estimator, the Local Polynomial Method (LPM), and the Local Rational Method for Frequency Response Function estimation -is illustrated on simulations on multiple case studies.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.