Extension of Modal Analysis to Linear Time-Varying Systems

Liu, Kefu

doi:10.1006/jsvi.1999.2286

Cited by 61 publications

(44 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If system matrixÂðkÞ has been derived, the identification of the time-varying modal parameters (i.e., pseudo-modal parameters) of the satellite can be implemented. 16,21) The eigenvalue decomposition of system matrixÂðkÞ at time k is:…”

Section: Identification Of Time-varying Modal Parametersmentioning

confidence: 99%

Identification of Time-varying Frequencies and Model Parameters for Large Flexible On-orbit Satellites Using a Recursive Algorithm

Tan

2016

Trans. Japan Soc. Aero. S Sci.

View full text Add to dashboard Cite

Today, the primary identification methods in time domain for spacecraft are based on singular value decomposition (SVD), such as the eigensystem realization algorithm (ERA) or stochastic subspace identification (SSI), which requires significant computation time. However, some control problems, such as self-adaptive control, need the latest modal parameters to update controller parameters online. To improve computational efficiency, the fast approximated power iteration (FAPI) recursive algorithm, which avoids SVD, is applied as an alternative method to identify the time-varying frequencies of large flexible satellites. Moreover, an improved recursive form is also proposed to obtain the time-varying input matrix in a state-space model by rewriting the relation of the input and output data. In numerical simulations, the time-varying model of the Engineering Test Satellite-VIII (ETS-VIII) is established. The results illustrate that this recursive algorithm can implement time-varying parameter online identification and it has a better computational efficiency than the SVD-based methods.

show abstract

Section: Identification Of Time-varying Modal Parametersmentioning

confidence: 99%

Identification of Time-varying Frequencies and Model Parameters for Large Flexible On-orbit Satellites Using a Recursive Algorithm

Tan

2016

Trans. Japan Soc. Aero. S Sci.

View full text Add to dashboard Cite

show abstract

“…The modal parameters are directly extracted from the matrix () Ak and they are called respectively pseudo-damping factors and pseudo-damped natural frequencies [11,12]. For simplicity, they are usually renamed as damping factors and natural frequency, as in the linear time-invariant case.…”

Section: Time-varying Frequenciesmentioning

confidence: 99%

Experimental Dynamic Analysis of Nonlinear Beams under Moving Loads

Bellino

Marchesiello

Garibaldi

2012

Shock and Vibration

View full text Add to dashboard Cite

Abstract.It is well known that nonlinear systems, as well as linear time-varying systems, are characterized by non-stationary response signals. In this sense, they both show natural frequencies that are not constant over time; this variation has however different origins: for a time-varying system the mass, and possibly the stiffness distributions, are changing over time, while for a nonlinear system the natural frequencies are amplitude-dependent. An interesting case of time-varying system occurs when analyzing the transit of a train over a railway bridge, easily simulated by the crossing of a moving load over a beam. In this case, the presence of a nonlinearity in the beam behaviour can cause a significant alteration of the modal parameters extracted from the linearized model, such that the contributions of the two effects are no more distinguishable.For this study, some reinforced concrete beams have been tested in the framework of a vast project: these beams show a clear softening nonlinear behaviour, well detectable when the excitation is produced by a hammer (free response). If the passage of a carriage is considered, moreover, the variation of natural frequencies is always larger than expected because of this softening nonlinearity.The article first analyzes theoretically the two effects on the natural frequencies of a simply supported beam, then a numerical and an experimental tests are presented. The identification procedure is conducted with a linear algorithm called ST-SSI, which has been demonstrated to be appropriate for the analysis of non-stationary signals, in particular in presence of moving masses. The article shows that the nonlinear contribution can be well estimated by using this linear tool but, on the contrary, when also moving masses are present, it is difficult to separate the nonlinear effects from the time varying ones.

show abstract

“…In [9][10][11][12], efforts have been undertaken to extend the subspace identification approach [13] to the LTV case by introducing the idea of repeated experiments. As pointed in [14], most subspace-based results developed thus far, even if significant, give state space realizations that are topologically equivalent from an input and output standpoint, but are not n Corresponding author.…”

Section: Introductionmentioning

confidence: 99%

“…Recursive algorithms such as recursive least squares (RLS), recursive instrumental variable and recursive predictive error [3,4] have also been widely investigated. For the class of rapidly time-varying systems, the functional expansion techniques have been suggested in manifold works [5][6][7][8].In [9][10][11][12], efforts have been undertaken to extend the subspace identification approach [13] to the LTV case by introducing the idea of repeated experiments. As pointed in [14], most subspace-based results developed thus far, even if significant, give state space realizations that are topologically equivalent from an input and output standpoint, but are not n Corresponding author.…”

mentioning

confidence: 99%

A new SSI algorithm for LPTV systems: Application to a hinged-bladed helicopter

Jhinaoui

Mevel

Morlier

2014

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

a b s t r a c tMany systems such as turbo-generators, wind turbines and helicopters show intrinsic time-periodic behaviors. Usually, these structures are considered to be faithfully modeled as linear time-invariant (LTI). In some cases where the rotor is anisotropic, this modeling does not hold and the equations of motion lead necessarily to a linear periodically timevarying (referred to as LPTV in the control and digital signal field or LTP in the mechanical and nonlinear dynamics world) model. Classical modal analysis methodologies based on the classical time-invariant eigenstructure (frequencies and damping ratios) of the system no more apply. This is the case in particular for subspace methods. For such time-periodic systems, the modal analysis can be described by characteristic exponents called Floquet multipliers. The aim of this paper is to suggest a new subspace-based algorithm that is able to extract these multipliers and the corresponding frequencies and damping ratios. The algorithm is then tested on a numerical model of a hinged-bladed helicopter on the ground. IntroductionMost existing identification techniques in mechanical and civil engineering work under the assumption that the underlying system can be modeled by a linear time-invariant (LTI) model. Unfortunately, structures that exhibit intrinsically time-varying behaviors are increasingly used in industry. For accurate analysis of such structures, that assumption is not satisfied. The time-varying aspect must be taken into account for a whole and reliable description of the system dynamics.The extension of the well-known identification techniques to the linear time-varying (LTV) systems is an ongoing active topic of research. A wide range of methods have been suggested in the literature. Among them, one can cite the frozen-time approach introduced first in [1,2] which deals with the identification of slowly time-varying systems (the frozen-time approach consists in modeling the slowly time varying system as a sequence of LTI systems, called frozen-time systems). Recursive algorithms such as recursive least squares (RLS), recursive instrumental variable and recursive predictive error [3,4] have also been widely investigated. For the class of rapidly time-varying systems, the functional expansion techniques have been suggested in manifold works [5][6][7][8].In [9][10][11][12], efforts have been undertaken to extend the subspace identification approach [13] to the LTV case by introducing the idea of repeated experiments. As pointed in [14], most subspace-based results developed thus far, even if significant, give state space realizations that are topologically equivalent from an input and output standpoint, but are not n Corresponding author. Tel.: þ33 2 99 84 73 25; fax: þ 33 2 99 84 71 71.

show abstract

Extension of Modal Analysis to Linear Time-Varying Systems

Cited by 61 publications

References 14 publications

Identification of Time-varying Frequencies and Model Parameters for Large Flexible On-orbit Satellites Using a Recursive Algorithm

Identification of Time-varying Frequencies and Model Parameters for Large Flexible On-orbit Satellites Using a Recursive Algorithm

Experimental Dynamic Analysis of Nonlinear Beams under Moving Loads

A new SSI algorithm for LPTV systems: Application to a hinged-bladed helicopter

Contact Info

Product

Resources

About