System Parameters Identification in a General Class of Non-linear Mechanical Systems (original) (raw)
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Lie series application to the identification of a multibody mechanical system
2008
Abstract:-A direct method of system identification and parameters monitoring is introduced for a general class of non-linear systems. The only requirement is that the system characteristics must be modeled by analytic or sufficiently smooth functions of the state variables, including the time parameter. The approach is based on the Lie operator representations and the corresponding Lie series solutions.
Current efforts towards a non-linear system identification methodology of broad applicability
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2011
A review of current efforts towards developing a non-linear system identification (NSI) methodology of broad applicability is provided in this article. NSI possess distinct challenges, since, even the task of identifying a set of (linearized) modal matrices modified ('perturbed') by non-linear corrections might be an oversimplification of the problem. In that context, the integration of diverse analytical, computational, and post-processing methods, such as slow flow constructions, empirical mode decompositions, and wavelet/Hilbert transforms to formulate a methodology that holds promise of broad availability, especially to systems with non-smooth non-linearities such as clearances, dry friction and vibro-impacts is proposed. In particular, the proposed methodology accounts for the fact that, typically, non-linear systems are energy-and initial condition-dependent, and has both global and local components. In the global aspect of NSI, the dynamics is represented in a frequency-energy plot (FEP), whereas in the local aspect of the methodology, sets of intrinsic modal oscillators are constructed to model specific non-linear transitions on the FEP. The similarity of the proposed methodology to linear experimental modal analysis is discussed, open questions are outlined, and some applications providing a first demonstration of the discussed concepts and techniques are provided.
NON-PARAMETRIC IDENTIFICATION OF A CLASS OF NON-LINEAR CLOSE-COUPLED DYNAMIC SYSTEM
A non-parametric identification technique for the identification ofarbitrary memoryless non-linearities has been presented for a class ofclose-coupled dynamic systems which are commonly met with in mechanical and structural engineering. The method is essentially a regression technique and expresses the non-linearities as series expansions in terms of orthogonal functions. Whereas no limitation on the type of test signals is imposed, the method requires the monitoring of the response of each of the masses in the system. The computational efficiency of the method, its easy implementation on analogue and digital machines and its relative insensitivity to measurement noise make it an attractive approach to the non-parametric identification problem. met with in mechanical and structural systems.?-For instance, a 'cubic spring' type non-linearity would require the determination of third-order kernels whose computation in practice becomes prohibitively expensive.20, In addition, the Wiener approach uses white noise inputs. It is often extremely difficult. if not impossible, to generate large enough inputs of this nature so as to drive large (and often massive) dynamic systems in their non-linear range of response. Applications of such techniques to large non-linear rnultidegree-of-freedom systems are few, if any. This paper presents a relatively simple non-parametric approach to the identification of a class of multidegree-of-freedom (MDF) close-coupled non-linear systems ). The method, following Graupe." is basically a rcgression technique. Masri and Caughey'" were the first to apply this technique to the identification of a single-degree-of-freedom oscillator, by expanding the restoring force in a series of Chebyshev polynomials.22 Herein, we extend the method to include a class of MDF systems, and further generalize it through the use of arbitrary orthogonal sets of functions. The technique has the advantage of being computationally efficient and simple to implement on analogue and digital machines. Unlike the Wiener Kernel approach, it is not restricted to 'white noise' type of inputs, and can be used with almost any type of test input. The choice of the class of models, M, has been governed by its wide usage in problems involving the dynamic response of: (i) full scale building structures, (ii) layered soil ma~ses,'~ (iii) mechanical eq~iprnent.'~. and (iv) machine components and subsystems in, for instance, the nuclear industry.26% " shown that even under extremely noisy measurement conditions, the method yields good results.
Time domain identification of non-linear systems
Proceedings of ISSE'95 - International Symposium on Signals, Systems and Electronics
A new method of non-linear system design, and non-linear subsystem modelling is presented. The method is based on identifying a non-linear model for each subsystem and combining the individual models to solve the entire system. Time domain modelling and simulation is used throughout the procedure but frequency domain characteristics are: also available. Modelling of non-linear subsystem is achieved by
On Algorithm of Identification of Nonlinear System Parameters
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Proceedings in applied mathematics & mechanics, 2016
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A state and parameter identification scheme for linearly parameterized systems
1998
This paper presents an adaptive algorithm to estimate states and unknown parameters simultaneously for nonlinear time invariant systems which depend affinely on the unknown parameters. The system output signals are filtered and re-parameterized into a regression form from which the least squares error scheme is applied to identify the unknown parameters. The states are then estimated by an observer based on the estimated parameters. The major difference between this algorithm and existing adaptive observer algorithms is that the proposed algorithm does not require any special canonical forms or rank conditions. However, an output measurement condition is imposed. The stability and performance limit of this scheme are analyzed. Two examples are then presented to show the effectiveness of the proposed schemes.
Parametric identification of non-linear systems
Proceedings of the IEEE INDICON 2004. First India Annual Conference, 2004., 2004
Parametric identification of a single degree-of-freedom (SDOF) nonlinear Duffing oscillator is carried out using a harmonic balance (HB) method. The parameters of the system are obtained using a harmonic input, for the case of periodic response. Problems of matrix inversion, due to poor conditioning are sometimes encountered in the computation. This may occur due to large differences in the relative values of inertia, damping and spring forces or dependence of these parameters on one another. The inversion problem may also occur due to a poor choice of the excitation signal frequency and amplitude. However there is limited choice of adjustable input parameters in this case. In this work, an extended HB method, which uses a combination of two harmonic inputs, is suggested to overcome the above problem.
Estimation of nonlinear systems parameters
International Journal of Robotics and Automation (IJRA), 2020
In this paper, an identification method is proposed to determine the nonlinear systems parameters. The proposed nonlinear systems can be described by Wiener systems. This structure of models consists of series of linear dynamic element and a nonlinearity block. Both the linear and nonlinear parts are nonparametric. In particular, the linear subsystem of structure entirely unknown. The considered nonlinearity function is of hard type. This latter can have a dead zone or with preload. These nonlinear systems have been confirmed by several practical applications. The suggested approach involves easily generated excitation signals.
Identification and Control of Mechanical Systems
Applied Mechanics Reviews, 2002
IDENTIFICATION AND CONTROL OF MECHANICAL SYSTEMS Vibration is a significant issue in the design of many structures including aircraft, spacecraft, bridges, and high-rise buildings. This book discusses the control of vibrating systems, integrating structural dynamics, vibration analysis, modern control, and system identification. Integrating these subjects is an important feature in that engineers will need only one book, rather than several texts or courses, to solve vibration/control problems. The book begins with a review of the fundamentals in mathematics, dynamics, and control that are needed for understanding subsequent materials. Chapters then cover recent developments in aerospace control and identification theory, including virtual passive control, observer and state-space system identification, and data-based controller synthesis. Many practical issues and applications are addressed, with examples showing how various methods are applied to real systems. Some methods show the close integration of system identification and control theory from the statespace perspective, rather than from the traditional input-output model perspective of adaptive control. This text will be useful for advanced undergraduate and beginning graduate students in aerospace, mechanical, and civil engineering, as well as for practicing engineers.