System identification of a class of Wiener systems with hysteretic nonlinearities

Existing works on Wiener system identification have essentially been focused on the case where the output nonlinearity is memoryless. When memory nonlinearities have been considered, the focus has been restricted to backlash like nonlinearities. In this paper, we are considering Wiener systems where the output nonlinearity is a general hysteresis operator captured by the well-known Bouc-Wen model. The Wiener system identification problem is addressed by making use of a steady-state property, obtained in periodic regime, referred to as hysteretic loop assumption'. The complexity of this problem comes from the system nonlinearity as well as its unknown parameters that enter in a non-affine way in the model. It is shown that the linear part of the system is accurately identified using a frequency method. Then, the nonlinear hysteretic subsystem is identified, on the basis of a parameterized representation, using a prediction-error approach.Postprint (author's final draft

Identification of Nonlinear Systems Structured by Wiener-Hammerstein Model

Wiener-Hammerstein systems consist of a series connection including a nonlinear static element sandwiched with two linear subsystems. The problem of identifying Wiener-Hammerstein models is addressed in the presence of hard nonlinearity and two linear subsystems of structure entirely unknown (asymptotically stable). Furthermore, the static nonlinearity is not required to be invertible. Given the system nonparametric nature, the identification problem is presently dealt with by developing a two-stage frequency identification method, involving simple inputs

Identification of the dynamic characteristics of nonlinear structures

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Detection and diagnostic of freeplay induced limit cycle oscillation in the flight control system of a civil aircraft

This research study is the result of a 3 years CIFRE PhD thesis between the Airbus design office(Aircraft Control domain) and TéSA laboratory in Toulouse. The main goal is to propose, developand validate a software solution for the detection and diagnosis of a specific type of elevator andrudder vibration, called limit cycle oscillation (LCO), based on existing signals available in flightcontrol computers on board in-series aircraft. LCO is a generic mathematical term defining aninitial condition-independent periodic mode occurring in nonconservative nonlinear systems. Thisstudy focuses on the LCO phenomenon induced by mechanical freeplays in the control surface ofa civil aircraft. The LCO consequences are local structural load augmentation, flight handlingqualities deterioration, actuator operational life reduction, cockpit and cabin comfort deteriorationand maintenance cost augmentation. The state-of-the-art for freeplay induced LCO detection anddiagnosis is based on the pilot sensitivity to vibration and to periodic freeplay check on the controlsurfaces. This study is thought to propose a data-driven solution to help LCO and freeplaydiagnosis. The goal is to improve even more aircraft availability and reduce the maintenance costsby providing to the airlines a condition monitoring signal for LCO and freeplays. For this reason,two algorithmic solutions for vibration and freeplay diagnosis are investigated in this PhD thesis. Areal time detector for LCO diagnosis is first proposed based on the theory of the generalized likeli hood ratio test (GLRT). Some variants and simplifications are also proposed to be compliantwith the industrial constraints. In a second part of this work, a mechanical freeplay detector isintroduced based on the theory of Wiener model identification. Parametric (maximum likelihoodestimator) and non parametric (kernel regression) approaches are investigated, as well as somevariants to well-known nonparametric methods. In particular, the problem of hysteresis cycleestimation (as the output nonlinearity of a Wiener model) is tackled. Moreover, the constrainedand unconstrained problems are studied. A theoretical, numerical (simulator) and experimental(flight data and laboratory) analysis is carried out to investigate the performance of the proposeddetectors and to identify limitations and industrial feasibility. The obtained numerical andexperimental results confirm that the proposed GLR test (and its variants/simplifications) is a very appealing method for LCO diagnostic in terms of performance, robustness and computationalcost. On the other hand, the proposed freeplay diagnostic algorithm is able to detect relativelylarge freeplay levels, but it does not provide consistent results for relatively small freeplay levels. Moreover, specific input types are needed to guarantee repetitive and consistent results. Further studies should be carried out in order to compare the GLRT results with a Bayesian approach and to investigate more deeply the possibilities and limitations of the proposed parametric method for Wiener model identification

Uma nova abordagem para representações e identificações de classes de sistemas dinâmicos não-lineares

In the last few years, the growth of the academic production about non-linear dynamic systems was noticed. Although the researches evolved, there are still topics that deserve a close analysis. One of them includes the study of mathematical models which represents many non-linear systems and will be the focus of this study. The purpose is to propose a new representation for non-linear dynamics system classes. It will combine models of interconnected blocks related concepts and base function. The parameters estimation for this model is done through frequency response techniques, based on harmonic balance concepts. To show and test the proposed model, systems with variable parameterization related to input signal amplitude will be utilized with numeric examples. In this work, it will be also presented concepts related to the modeling and linear and non-linear dynamic systems identification and parameters estimation.Nos últimos anos, o interesse pelo estudo de sistemas dinâmicos não-lineares, incluindo sua modelagem e identificação, tem sido crescente. Embora as pesquisas nesse sentido tenham evoluído, existem tópicos relacionados aos sistemas não-lineares que merecem uma análise mais detalhada. Um deles inclui o estudo de modelos matemáticos que representem algumas classes de sistemas não-lineares, o que constitui um dos objetivos desta dissertação. Este trabalho propõe uma representação nova para algumas classes de sistemas dinâmicos não-lineares. Ela utiliza uma combinação dos conceitos relacionados a modelos de blocos interconectados e a funções de base. A estimação de parâmetros dessa representação é efetuada por técnicas de resposta em freqüência, baseando-se no conceito de balanço harmônico. Com o objetivo de ilustrar e testar a representação proposta, sistemas que possuem parâmetros variáveis em função da amplitude do sinal de entrada são utilizados como exemplos numéricos. Os resultados obtidos são comparados com dados resultantes de outras técnicas conhecidas. Neste trabalho, são apresentados também conceitos relacionados à modelagem e à identificação de sistemas dinâmicos lineares, não-lineares e estimação de parâmetros

New Approaches in Automation and Robotics

The book New Approaches in Automation and Robotics offers in 22 chapters a collection of recent developments in automation, robotics as well as control theory. It is dedicated to researchers in science and industry, students, and practicing engineers, who wish to update and enhance their knowledge on modern methods and innovative applications. The authors and editor of this book wish to motivate people, especially under-graduate students, to get involved with the interesting field of robotics and mechatronics. We hope that the ideas and concepts presented in this book are useful for your own work and could contribute to problem solving in similar applications as well. It is clear, however, that the wide area of automation and robotics can only be highlighted at several spots but not completely covered by a single book

Connectionist Feedforward Networks for Control of Nonlinear Systems

The control of nonlinear systems is addressed from a new perspective, which makes use of several concepts and techniques developed in the area of Artificial Neural Networks. In particular, this work explores the potential of connectionist representations which consist of only feedforward connections of sigmoids or gaussian units. A unified review demonstrating the capabilities of these structures to approximate continuous nonlinear functions is given. The use of the Fourier transform and the properties of kernel functions are exploited in order to demonstrate some properties of gaussian networks. The adjustment of the different parameters plays a significant role in the relevance of these structures in control. For sigmoid networks a new learning algorithm is proposed, its main feature being the use of the forgetting factor and pseudoinverse. For gaussian networks several algorithms using different techniques, such as: the Fourier Transform, gradient approach, and/or clustering algorithm, are explored and compared. The representation of a dynamic system by means of a static nonlinear function, and consequently, by a connectionist representation, is addressed. Concepts such as controllability, observability, and invertibility, which are needed to develop any control structures, are put forward for the nonlinear case. Four control structures using connectionist models to generate the control signal are proposed, and its potential analysed. For each approach a simple example is presented to illustrate their performance. A summary of their main characteristics is also given. Two industrial applications have been tackled, and solutions developed, illustrating not only the differences between different techniques, but also the potential and limitations of the ideas pursued in this work. Finally, some suggestions are given, which may engender further research in the field of control and artificial neural systems

IDENTIFICATION OF NONLINEAR DYNAMIC SYSTEMS USING THE FORCE-STATE MAPPING TECHNIQUE

PhDThe identification of the dynamic characteristics of nonlinear systems is of increasing interest in the field of modal testing. In this work an investigation has been carried out into the force-state mapping approach to identification of nonlinear systems proposed by Masri and Caughey. They originally suggested a nonparametric identification technique based on curve fitting the restoring force in terms of the velocity and displacement using two dimensional Chebyshev polynomials. It has been shown that the use of Chebyshev polynomials is unnecessarily restrictive and that a simpler approach based on ordinary polynomials and special functions provides a simpler, faster and more accurate identification for polynomial and nonpolynomial types of nonlinearity. This simpler approach has allowed the iterative identification technique for multi-degree of freedom systems to be simplified and a direct identification approach, which is not subject to bias errors, has been suggested. A new procedure for identifying both the type and location of nonlinear elements in lumped parameter systems has been developed and has yielded encouraging results. The practical implementation of the force-state mapping technique required the force, acceleration, velocity and displacement signals to be available at the same instants of time for each measurement station. In order to minimise the instrumentation required, only the force and acceleration are measured and the remaining signals are estimated by integrating the acceleration. The integration problem has been investigated using several approaches both in the frequency and time domains. An analysis of the sensitivity of the estimated parameters with respect to any amplitude and phase measurement errors has been carried out for single-d.o.f. linear systems. Estimates are shown to be extremely sensitive to phase errors for lightly damped structures. The estimation of the mass or generalised mass and modal matrices required for the identification of single or multi-d.o.f. nonlinear systems respectively, has also been investigated. Initial estimates were obtained using a linear multi-point force appropriation method, normally used for the excitation of normal modes. These estimates were then refined using a new technique based on studying the sensitivity of the mass with respect to the estimated system parameters obtained using a nonlinear model. This sensitivity approach seemed promising since accurate results were obtained. It was also shown that accurate estimates for the modal matrix were not essential for carrying out a force-state mapping identification. Finally, the technique has been applied experimentally to the identification of a cantilevered T-beam structure with stiffness and damping nonlinearity. The cases of two well separated and then two fairly close modes were considered. Reasonable agreement between the behaviour of the nonlinear mathematical model and the structure was achieved considering inaccuracies in the measurement set-up. Conclusions have been drawn and some ideas for future work presented.Scientific Studies and Research Centre of Syri