Inverse Approach to the Reconstruction and Quantification of Vibratory Sources

Abstract

Vibratory analysis allows us to interpret the fundamental conditions of rotating machines. This interpretation is useful in the diagnosis of faults. In practice, the vibratory measurements made by sensors come from a mixture of vibratory sources corresponding to different machine components. Thus, it becomes hard to conduct state interpretation for each individual component. This fact leads us to consider the inverse problem, reconstruction of the vibratory sources based on measurements. However, the inversion is unfortunately unstable. To limit the instability, previous studies proposed use of a large number of sensors and the processing of measurements using regularization methods. However, regularization requires estimation of the regularization parameter, which is a hard task. In addition, regularization can remove some vibratory sources. Moreover, the sensor positions are “random”, but the stability is significantly influenced by the sensor positions and by the mixture properties described by modal analysis. This article proposes to link modal analysis and stability. This link allows us to reduce the number of sensors and to avoid regularization methods. Thus, two complementary approaches are developed to determine optimal sensor positions: A numerical approach with a numerical updated model and an experimental approach using modal analysis. Thanks to the use of these optimal positions, stability is improved and vibratory sources are correctly reconstructed.

Keywords

Vibratory sources inverse problems modal analysis

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