System identification using an over-parametrized model class-improving the optimization algorithm

McKelvey, Tomas; Helmersson, Anders

doi:10.1109/cdc.1997.657905

Cited by 33 publications

(30 citation statements)

References 11 publications

(12 reference statements)

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“…However, optimisation methods are known to exhibit poor convergence properties when they are used to minimise an identification problem which relies on a pseudo-canonical parametrisation [17]. More specifically, we showed in a recent study that the pseudo-canonical LMFD can sometimes lead to a numerical locking of the convergence.…”

Section: New Model Parametrisation Of Transfer Functionsmentioning

confidence: 91%

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New developments for experimental modal analysis of aircraft structures

Vayssettes

Mercère

2015

MATEC Web of Conferences

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Abstract. This article presents an identification algorithm dedicated to the modal analysis of aircraft structures during flighttests. More specifically, this algorithm was designed to process short duration tests carried out with multi-input excitations. The identification problem is solved in the frequency domain and the limit effects are considered so as to avoid transient effects with short data sequences. To minimise the effects of the noise, a non-linear gradient-based optimisation method is used. Its performance is improved by the use of an appropriate over-parametrised matrix fraction descriptions. Because the cost function to be minimised is non-convex, this method is however sensitive to the initialisation. For this reason, an iterative instrumental variable method is used to find an initial estimate. This one gives a value of the cost-function sufficiently close to its global minimum so as to ensure a fast convergence of the optimisation. Thus, the algorithm presented in this article is a combination of two iterative methods that gives accurate mode estimations even with high level of noise, as shown on an illustrative example.

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Section: New Model Parametrisation Of Transfer Functionsmentioning

confidence: 91%

“…As shown for state-space representation in [17], using a representation with a higher number of parameters improves the performance of gradient-based optimisation methods when this choice is combined with search dimension reductions at each iteration of the optimisation. As we will see in Sect.…”

Section: New Model Parametrisation Of Transfer Functionsmentioning

confidence: 99%

New developments for experimental modal analysis of aircraft structures

Vayssettes

Mercère

2015

MATEC Web of Conferences

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“…However, this is taken care of in most quasi-newton solvers to ensure that the minimum is reached in a numerically stable way. The over-parametrization can also help the algorithm numerically, see McKelvey and Helmersson (1997).…”

Section: Lemma 1 For a Matrix A That Is Hurwitz It Holds Thatmentioning

confidence: 99%

Model reduction using a frequency-limited -cost

Petersson

Löfberg

2014

Systems & Control Letters

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We propose a method for model reduction on a given frequency range, without the use of input and output filter weights. The method uses a nonlinear optimization approach to minimize a frequency limited H 2 like cost function. An important contribution of the paper is the derivation of the gradient of the proposed cost function. The fact that we have a closed form expression for the gradient and that considerations have been taken to make the gradient computationally efficient to compute enables us to efficiently use off-the-shelf optimization software to solve the optimization problem.

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“…This method determines the directions in the parameter space that do not change the cost function, and does not update the parameters in this direction by using an appropriate projection for the gradient in (5). The method is based on ideas used for identification of linear and linear parameter-varying state space systems by McKelvey and Helmersson (1997), Lee and Poolla (1999), and Verdult and Verhaegen (2000).…”

Section: Problem Descriptionmentioning

confidence: 99%

Identification of composite local linear state-space models using a projected gradient search

Verdult¹,

Ljung²,

Verhaegen³

2002

International Journal of Control

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An identification method is described to determine a weighted combination of local linear state space models from input and output data. Normalized radial basis function are used for the weights, and the system matrices of the local linear models are fully parameterized. By iteratively solving a nonlinear optimization problem, the centers and widths of the radial basis functions and the system matrices of the local models are determined. To deal with the nonuniqueness of the fully parameterized state space system, a projected gradient search algorithm is described. It is pointed out that when the weights depend only on the input, the dynamical gradient calculations in the identification method are stable. When the weights also depend on the output, certain difficulties might arise. The methods are illustrated using several examples that have been studied in the literature before.

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System identification using an over-parametrized model class-improving the optimization algorithm

Cited by 33 publications

References 11 publications

New developments for experimental modal analysis of aircraft structures

New developments for experimental modal analysis of aircraft structures

Model reduction using a frequency-limited -cost

Identification of composite local linear state-space models using a projected gradient search

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