Alireza Fakhrizadeh Esfahani

Alireza Fakhrizadeh Esfahani, Philippe Dreesen, Koen Tiels et al.

Hysteresis is a highly nonlinear phenomenon, showing up in a wide variety of science and engineering problems. The identification of hysteretic systems from input-output data is a challenging task. Recent work on black-box polynomial nonlinear state-space modeling for hysteresis identification has provided promising results, but struggles with a large number of parameters due to the use of multivariate polynomials. This drawback is tackled in the current paper by applying a decoupling approach that results in a more parsimonious representation involving univariate polynomials. This work is carried out numerically on input-output data generated by a Bouc-Wen hysteretic model and follows up on earlier work of the authors. The current article discusses the polynomial decoupling approach and explores the selection of the number of univariate polynomials with the polynomial degree, as well as the connections with neural network modeling. We have found that the presented decoupling approach is able to reduce the number of parameters of the full nonlinear model up to about 50\%, while maintaining a comparable output error level.

Alireza Fakhrizadeh Esfahani, Johan Schoukens, Laurent Vanbeylen

Block oriented model structure detection is quite desirable since it helps to imagine the system with real physical elements. In this work we explore experimental methods to detect the internal structure of the system, using a black box approach. Two different strategies are compared and the best combination of these is introduced. The methods are applied on two real systems with a static nonlinear block in the feedback path. The main goal is to excite the system in a way that reduces the total distortion in the measured frequency response functions to have more precise measurements and more reliable decision about the structure of the system.

Deividas Eringis, John Leth, Zheng-Hua Tan et al.

In this paper we derive a PAC-Bayesian error bound for autonomous stochastic LTI state-space models. The motivation for deriving such error bounds is that they will allow deriving similar error bounds for more general dynamical systems, including recurrent neural networks. In turn, PACBayesian error bounds are known to be useful for analyzing machine learning algorithms and for deriving new ones.

Vera Shalaeva, Alireza Fakhrizadeh Esfahani, Pascal Germain et al.

In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a well-chosen temperature parameter. Second, the error bound also holds for training data that are not independently sampled. In particular, the error bound applies to certain time series generated by well-known classes of dynamical models, such as ARX models.