Parameter reduction in nonlinear state-space identification of hysteresis

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.Comment: 24 pages, 8 figure

Grey-box state-space identification of nonlinear mechanical vibrations

The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure

Learning, Identifying, Sharing

This article argues that a cooperatively-built, well-organized, shared knowledge base is a new – and, from certain viewpoints, optimal – kind of support (refining and integrating other kinds of supports) for three complementary tasks: learning about living entities (and how to identify them), supporting their identification, and sharing knowledge about them. This article gives the ideas behind our prototype, and argues that knowledge providers can be not solely specialists, but also amateurs. In essence, for these three tasks, it argues for the (re-)use of much more semantically organized and interconnected versions of semantic wikis or scratchpads

Accelerated storage testing of freeze-dried Pseudomonas fluorescens BTP1, BB2 and PI9 strains

Freeze-dried cultures of Pseudomonas fluorescens are used in agriculture and microbiological industry. However, P. fluorescens is very susceptible to damage during freeze-drying and subsequent storage and it would be useful to increase culture viability during storage. The viability of freeze-dried P. fluorescens strains (BTP1, PI9 and BB2) was evaluated by using the Arrhenius model. This model was described by measuring the reaction rate constants (D or k) and temperature sensitivity of rate constant (z or Ea). The freeze-dried P. fluorescens strains were stored in glass tubes at 60, 37 and 4°C for 8 h, 28 days and two months, respectively. D value decreased or k increased with an increase of the storage temperature. By comparing their decimal reduction time (D), we observed that BB2 strain was more resistant than BTP1 and PI9 at 37 and 60°C. The activation energy of all P. fluorescens strains were not significantly different and thermal inactivation may occur by the same mechanism. Thus, it was possible to compare rate constants of survival for the freeze-dried P. fluorescens strains. These results will be useful to the development of improved reference materials and samples held in culture collections.Key words: Arrhenius model, accelerated storage testing (AST), freeze-drying, storage stability

Identification of complex nonlinearities using cubic splines with automatic discretization

One of the major challenges in nonlinear system identification is the selection of appropriate mathematical functions to model the observed nonlinearities. In this context, piecewise polynomials, or splines, offer a simple and flexible representation basis requiring limited prior knowledge. The generally-adopted discretization for splines consists in an even distribution of their control points, termed knots. While this may prove successful for simple nonlinearities, a more advanced strategy is needed for nonlinear restoring forces with strong local variations. The present paper specifically introduces a two-step methodology to select automatically the location of the knots. It proposes to derive an initial model, using nonlinear subspace identification, and incorporating cubic spline basis functions with fixed and equally-spaced abscissas. In a second step, the location of the knots is optimized iteratively by minimizing a least-squares cost function. A single-degree-of-freedom system with a discontinuous stiffness characteristic is considered as a case study