arXiv subjects

Jean-Philippe Noël

Publications and source records attributed to Jean-Philippe Noël.

9 recordsLinked to original sources

arXiv2025

Inference and Learning of Nonlinear LFR State-Space Models

Estimating the parameters of nonlinear block-oriented state-space models from input-output data typically involves solving a highly non-convex optimization problem, which is prone to poor local minima and slow convergence. This paper presents a computationally efficient initialization method for nonlinear linear fractional representation (NL-LFR) models using periodic data. By first inferring the latent signals and subsequently estimating the model parameters, the approach generates initial estimates for use in a later nonlinear optimization step. The proposed method shows robustness against poor local minima, and achieves a twofold error reduction compared to the state-of-the-art on a challenging benchmark dataset.

eess.SY↗

arXiv2025

Feedback linearisation of mechanical systems using data-driven models

Linearising the dynamics of nonlinear mechanical systems is an important and open research area. A common approach is feedback linearisation, which is a nonlinear control method that transforms the input-output response of a nonlinear system into an equivalent linear one. The main problem with feedback linearisation is that it requires an accurate first-principles model of the system, which are typically hard to obtain. In this paper, we design an alternative control approach that exploits data-driven models to linearise the input-output response of nonlinear mechanical systems. Specifically, a model-based reference tracking architecture is developed for nonlinear feedback systems with output nonlinearities. The overall methodology shows a high degree of performance combined with significant robustness against imperfect modelling and extrapolation. These findings are demonstrated using large set of synthetic experiments conducted on a asymmetric Duffing oscillator and using an experimental prototype of a high-precision motion system.

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arXiv2022

An optimal open-loop strategy for handling a flexible beam with a robot manipulator

Fast and safe manipulation of flexible objects with a robot manipulator necessitates measures to cope with vibrations. Existing approaches either increase the task execution time or require complex models and/or additional instrumentation to measure vibrations. This paper develops a model-based method that overcomes these limitations. It relies on a simple pendulum-like model for modeling the beam, open-loop optimal control for suppressing vibrations, and does not require any exteroceptive sensors. We experimentally show that the proposed method drastically reduces residual vibrations -- at least 90% -- and outperforms the commonly used input shaping (IS) for the same execution time. Besides, our method can also execute the task faster than IS with a minor reduction in vibration suppression performance. The proposed method facilitates the development of new solutions to a wide range of tasks that involve dynamic manipulation of flexible objects.

cs.RO↗

arXiv2020

Experimental assessment of polynomial nonlinear state-space and nonlinear-mode models for near-resonant vibrations

In the present paper, two existing nonlinear system identification methodologies are used to identify data-driven models. The first methodology focuses on identifying the system using steady-state excitations. To accomplish this, a phase-locked loop controller is implemented to acquire periodic oscillations near resonance and construct a nonlinear-mode model. This model is based on amplitude-dependent modal properties, i.e. does not require nonlinear basis functions. The second methodology exploits uncontrolled experiments with broadband random inputs to build polynomial nonlinear state-space models using advanced system identification tools. The methods are applied to two experimental test rigs, a magnetic cantilever beam and a free-free beam with a lap joint. The respective models of both methods and both specimens are then challenged to predict dynamic, near-resonant behavior observed under different sine and sine-sweep excitations. The vibration prediction of the nonlinear-mode and state-space models clearly highlight the capabilities and limitations of the models. The nonlinear-mode model, by design, yields a perfect match at resonance peaks and high accuracy in close vicinity. However, it is limited to well-spaced modes and sinusoidal excitation. The state-space model covers a wider dynamic range, including transient excitations. However, the real-life nonlinearities considered in this study can only be approximated by polynomial basis functions. Consequently, the identified state-space models are found to be highly input-dependent, in particular for sinusoidal excitations where they are found to lead to a low predictive capability.

eess.SY↗

arXiv2018

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.

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arXiv2017

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.

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arXiv2016

Grey-box nonlinear state-space modelling for mechanical vibrations identification

In the present paper, a flexible and parsimonious model of the vibrations of nonlinear mechanical systems is introduced in the form of state-space equations. It is shown that the nonlinear model terms can be formed using a limited number of output measurements. A two-step identification procedure is derived for this grey-box model, integrating nonlinear subspace initialisation and maximum likelihood optimisation. The complete procedure is demonstrated on the Silverbox benchmark, which is an electrical mimicry of a single-degree-of-freedom mechanical system with one displacement-dependent nonlinearity.

eess.SY↗

arXiv2016

A nonlinear state-space approach to hysteresis identification

Most studies tackling hysteresis identification in the technical literature follow white-box approaches, i.e. they rely on the assumption that measured data obey a specific hysteretic model. Such an assumption may be a hard requirement to handle in real applications, since hysteresis is a highly individualistic nonlinear behaviour. The present paper adopts a black-box approach based on nonlinear state-space models to identify hysteresis dynamics. This approach is shown to provide a general framework to hysteresis identification, featuring flexibility and parsimony of representation. Nonlinear model terms are constructed as a multivariate polynomial in the state variables, and parameter estimation is performed by minimising weighted least-squares cost functions. Technical issues, including the selection of the model order and the polynomial degree, are discussed, and model validation is achieved in both broadband and sine conditions. The study is carried out numerically by exploiting synthetic data generated via the Bouc-Wen equations.

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arXiv2014

Royal Observatory of Belgium Gravitational balance

An astatized symmetrical vertical pendulum is monitoring torque Γ(M) resulting of gravitational attractions exerted by two external masses M moving up down. Local gravity field g produce the main pendulum restoring torque combined with a very weak variable torque Γ(c) induced by rotation of watch needles fixed to the pendulum. Transfer of fundamental units to calibrate the Γ(c) torques is obtained by a reference torque Γ(μ) resulting of precise displacements of a well known mass μ. We permanently monitored ratio between the gravitational effect Γ(M) and calibrated Γ(c) to determine G. Position of the pendulum is measured with a capacitive bridge. Bias voltages sent to two electrodes set-up at the bottom of the pendulum allows to feedback pendulum with a controlled electrostatic torque. We discuss potential interest of our prototype to design a multi pendulum system to check systematic effects for different geometries and various kinds of materials.

physics.ins-det↗