Regularized Nonparametric Volterra Kernel Estimation

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

Identification of human joint impedance using a wearable powered knee exoskeleton

Joint impedance is the mechanical property that describes the dynamical relationship between joint angle and torque. It provides a description of the neuromechanical behavior of a joint and it is regulated according to the surrounding environment to promote a stable interaction with it. Joint impedance has been shown to be successfully estimated using system identification techniques on humans experimentally1 . Estimation of joint impedance is critical in post-stroke individuals particularly when they are in the chronic state of the pathology (after six months from onset). After this time, the affected limbs commonly show signs of increased resistance to movements. This condition of altered joint impedance is clinically described as joint hyper-resistance2 . The presence of hyper-resistance provokes pain, restricts the range of motion of the affected joints, limits the achievement of functional tasks, and might lead to health complications, not including worsening of the quality of life.Peer ReviewedPostprint (published version

Best Linear Approximation of Nonlinear Continuous-Time Systems Subject to Process Noise and Operating in Feedback

In many engineering applications the level of nonlinear distortions in frequency response function (FRF) measurements is quantified using specially designed periodic excitation signals called random phase multisines and periodic noise. The technique is based on the concept of the best linear approximation (BLA) and it allows one to check the validity of the linear framework with a simple experiment. Although the classical BLA theory can handle measurement noise only, in most applications the noise generated by the system -- called process noise -- is the dominant noise source. Therefore, there is a need to extend the existing BLA theory to the process noise case. In this paper we study in detail the impact of the process noise on the BLA of nonlinear continuous-time systems operating in a closed loop. It is shown that the existing nonparametric estimation methods for detecting and quantifying the level of nonlinear distortions in FRF measurements are still applicable in the presence of process noise. All results are also valid for discrete-time systems and systems operating in open loop.Comment: Accepted for publication in IEEE Transactions on Instrumentation & Measuremen

Electrochemical impedance spectroscopy beyond linearity and stationarity - a critical review

Electrochemical impedance spectroscopy (EIS) is a widely used experimental technique for characterising materials and electrode reactions by observing their frequency-dependent impedance. Classical EIS measurements require the electrochemical process to behave as a linear time-invariant system. However, electrochemical processes do not naturally satisfy this assumption: the relation between voltage and current is inherently nonlinear and evolves over time. Examples include the corrosion of metal substrates and the cycling of Li-ion batteries. As such, classical EIS only offers models linearised at specific operating points. During the last decade, solutions were developed for estimating nonlinear and time-varying impedances, contributing to more general models. In this paper, we review the concept of impedance beyond linearity and stationarity, and detail different methods to estimate this from measured current and voltage data, with emphasis on frequency domain approaches using multisine excitation. In addition to a mathematical discussion, we measure and provide examples demonstrating impedance estimation for a Li-ion battery, beyond linearity and stationarity, both while resting and while charging

Frequency-Domain Least-Squares Support Vector Machines to deal with correlated errors when identifying linear time-varying systems

A Least-Squares Support Vector Machine (LS-SVM) estimator, formulated in the frequency domain is proposed to identify linear time-varying dynamic systems. The LS-SVM aims at learning the structure of the time variation in a data driven way. The frequency domain is chosen for its superior robustness w.r.t. correlated errors for the calibration of the hyper parameters of the model. The time-domain and the frequency-domain implementations are compared on a simulation example to show the effectiveness of the proposed approach. It is demonstrated that the time-domain formulation is mislead during the calibration due to the fact that the noise on the estimation and calibration data sets are correlated. This is not the case for the frequency-domain implementation

An LTV approach to identifying nonlinear systems - With application to an RRR-Robot

Nonlinear systems are appearing in all engineering applications. Deriving models for these systems is important for instance for prediction and control. The goal of this paper is to estimate models of a class of nonlinear systems, from experimental data. When considering slowly varying setpoints, nonlinear systems can be approximated by linear time-varying models. That is, the nonlinear system is linearised around a trajectory of setpoints. The approach followed in this paper formulates the identification problem of a nonlinear system as an exploration through the relevant range of setpoints, which are identifiable by using tools for linear time-varying systems. This approach is demonstrated on an idealised simulation example, and on a real-life robotic application