04/06/2018

Estimation of Auto-Regressive models for time series using Binary or Quantized Data

R. Auber M. Pouliquen, E. Pigeon, M. M'Saad, O. Gehan  (LAC, Université de Caen, ENSICAEN, Bodycap)

In this talk, we first present an algorithm for the estimation of an Auto-Regressive model of time series using output data of a binary sensor.  This algorithm is based on the estimation of the autocorrelation of time series  for a threshold different from zero. The algorithm is then extended to time series with several quantization levels. Simulation results are given to show the effectiveness of the proposed approaches.

Parrallel Hammerstein System Identification using Exponential Sine Sweeps and Application to Structural Health Monitoring.

M. Rébillat, N. Mechbal (DYSCO team, PIMM laboratory, Arts et Métiers – CNRS – CNAM)

The process of implementing a damage monitoring strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM) and implies a sensor network that monitors the behavior of the structure on-line. A SHM process potentially allows for an optimal use of the monitored structure, a minimized downtime, and the avoidance of catastrophic failures. The SHM process classically relies on four sequential steps that are damage detection, localization, classification, and quantification. The key idea underlying this presentation is that structural damages may result in nonlinear dynamical signatures within inspected structures that are not yet used in SHM despite the fact that they can significantly enhance their monitoring. We thus propose to monitor these structural damages by identifying their nonlinear signature on the basis of a cascade of Hammerstein models representation of the structure. This class of models is here estimated at very low computational cost by means of the Exponential Sine Sweep Method which is especially suited for this application. This original identification method will be described in detail and compared with more classical ones such as Least Mean Squares. It will then be shown that based

on this richer nonlinear dynamical representation of the structure, efficient SHM algorithms dedicated to damage detection, classification and quantification can be derived.

 

How to infer prior knowledge in water distribution data-driven models ?

B. Brentan(CRAN)

The strategy of system identification can help the development of data- driven models of water distribution networks (WDN). The use of the available a priori knowledge is important to better design the models and to know their limitations. For physical elements of the WDN, which hydraulic laws are well known and can be used for modelling by gray-box approaches. But even if the physical laws are known, how to handle properly the data? To promote the discussions about the applications of the system identification tools to model the physical elements, a detailed example on a tank level estimation is presented. However, to model non-physical elements, such as the water demand, black- box modelling strategies are often used. But in this approach, how to use the empha priori knowledge? Or in other words, how to avoid the approach of the pure optimization of the model’s parameter that take into account only the fitting scores? Using the Reproducing Kernel Hilbert Spaces (RKHS), we discuss the possibilities to take the a priori knowledge in account, even in black- box models. The case-studies show that this kind of approach leads to better and more plausible prediction capabilities. 

Stochastic realization theory and its role in system identification

M. Petreczky (CR CNRS, CRYStAL, Ecole Centrale Lille/Université Lille/CNRS)

In this talk we present a tutorial on stochastic realization theory and its significance for system identification, in particular for subspace identification.  We will start by explaining the basics of stochastic realization theory for stochastic linear systems, including conditions for existence of a realization, minimality, existence of state-space representations in forward innovation form, uniqueness of minimal state-space representations in forward innovation form, and covariance realization algorithm. We then explain the relationship between stochastic realization theory and the covariance realization algorithms and subspace identification methods. If time permits, we will mention the recent extension of these results to stochastic LPV/bilinear systems.

On experiment design for local approach identification of LPV systems

K.M.D. Mochton, L. Etienne and S. Lecoeuche (URIA IMT Lille Douai)

The local approach for the estimation of a Linear Parameter-Varying (LPV) model consists in an interpolation of a finite number of Linear Time-Invariant (LTI) systems called local LTI systems. Each local LTI system is obtained by performing an identification experiment at a fixed constant value of the parameter describing the dynamic variation of the LPV model. This parameter is referred in the literature as scheduling variable and the fixed values of the scheduling variable are simply called operating points or scheduling points. In order to improve the accuracy of the local method for the identification of LPV systems, the choice of the scheduling points and the inputs used at each scheduling point for the identification of the local LTI systems is addressed in this paper. To deal with this problem, an accuracy measure is first introduced. This measure is shown to be a linear combination of the classic A-optimality accuracy measure of the local LTI systems. Using this result, an algorithm is finally proposed to solve the experiment design problem.