Volume 48, pp. 435-449, 2018.

Frequency-dependent reconstruction of imbalances

Jenny Niebsch and Ronny Ramlau


Imbalances in rotating machines cause vibrations of the system and may lead to an early wearout of the machine. In this paper, we consider the development of an algorithm for the detection (and subsequent correction) of imbalances from vibrational measurements at certain nodes of the system. Since, e.g., modern wind turbines operate with variable speed, the vibration data are usually collected during changing rotational speed. Based on a mathematical model that connects the measured vibrations at different rotational speeds with the imbalance distribution, we propose an algorithm for its reconstruction. The reconstruction algorithm is based on a tensor product formulation of the forward model. Test examples with artificial data are used to verify our approach.

Full Text (PDF) [869 KB]

Key words

integral equation, Kronecker product, inverse problem, tensor product, regularization

AMS subject classifications

65N21, 47A52, 15A05

Links to the cited ETNA articles

[16]Vol. 38 (2011), pp. 233-257 Stefan Kindermann: Convergence analysis of minimization-based noise level-free parameter choice rules for linear ill-posed problems
[17]Vol. 40 (2013), pp. 58-81 Stefan Kindermann: Discretization independent convergence rates for noise level-free parameter choice rules for the regularization of ill-conditioned problems
[26]Vol. 46 (2017), pp. 89-106 Jenny Niebsch, Ronny Ramlau, and Kirk M. Soodhalter: Solution of coupled differential equations arising from imbalance problems

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