Microphone array processing for sparse equivalent source representations of tyre noise

Abstract

The estimation of pass-by noise indoors, using a rolling road and a microphone array, has advantages over outdoor measurements in terms of the repeatability and robustness to the environmental conditions of the measurements. It also has the advantage of estimating the individual source contributions to pass-by noise, by placing additional microphone arrays close to each source. The in situ contribution of tyre noise is characterised here by discretising the tyre into a few equivalent sources, which are quantified using the measured near field spectra in an inverse problem and then used in a forward problem to synthesise the pressure in the far field. While the inverse method yields estimates of the source strengths acting simultaneously, the number and the position of the equivalent sources need to be known a priori. In this thesis, different techniques are investigated to choose the number and positioning of the equivalent sources for tyre noise synthesis using the sparsity promoting properties of the `1 norm regularisation. In the first instance, the methods are formulated and tested in a 2D tyre model, which models the tyre vibration up to 1 kHz. Two different `1 norm regularisation techniques are investigated, using frequency - dependent and frequency - averaged source positions. The `1 norm regularisation techniques are then used with the spectra measured from a rolling tyre at 50 km/h. While the frequency-dependent `1 norm regularisation delivers good representations of the directly measured far field spectra, an `2 norm regularisation is also needed when using a higher number of sources, to avoid ill-conditioning. Additional formulations of the `1 norm regularisation are also investigated, particularly a power-based approach for the frequency - averaged `1 norm regularisation, which gives good synthesised far field pressures with only 2 equivalent sources, near the leading and trailing edges of the tyre. The frequency - averaged `1 norm regularisation is then used to analyse the spectra measured from a tyre as it is accelerated, on a rolling road, from 5 to 60 km/h. Different cases are considered, where only tyre noise is present and where fully operational conditions are considered for an electric vehicle. It is shown that, in both cases, the regularisation can predict the number and position of the equivalent sources that give good representations of the measured far field spectra, which are valid for different acceleration rates. The power-based approach is also investigated in this case, again showing good results with only 2 equivalent sources. Omitting the phase and coherence information thus has advantages in reducing the number of equivalent sources needed for tyre noise synthesis.

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Identifiers

ORCID for Athanasios Papaioannou: orcid.org/0000-0003-1682-1412

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