Qualitative brief introduction to operational transfer path analisys and a tire noise application case

The Operational Transfer Path Analysis (OTPA) method is an alternative to classical TPA, applied mainly in automotive and aerospace industries in a NVH framework. OTPA provides sound and vibration transmission path contribution to the sound field, requiring less resources than traditional TPA, when it is properly performed. This paper reviews its theory basis where clear similarities are found with experimental modal analysis. The method is extended with the singular value decomposition method to reduce influences of noise. Boundary conditions in practical application are a remarkable issue to consider. An analysis on tire noise is included to illustrate this method strengths. RESUMEN El método de análisis de caminos de transmisión operativa (OTPA) es una alternativa al TPA clásico, empleado principalmente en las industrias de la automoción y la aeronáutica dentro del marco del ruido, vibraciones y molestia (NVH). OTPA proporciona la contribución de los caminos de transmisión del sonido y las vibraciones con menores requerimientos que un TPA tradicional, siempre que se ejecute correctamente. Este artículo revisa la teoría básica en la que se manifiestan claras semejanzas con el análisis modal experimental. El método se amplía con el método de descomposición en valores singulares para reducir la influencia del ruido. Las condiciones frontera es otro asunto importante a tener en cuenta. Se incluye un análisis de ruido de neumático para ilustrar las fortalezas del método. FIA 2018 XI Congreso Iberoamericano de Acústica; X Congreso Ibérico de Acústica; 49o Congreso Español de Acústica -TECNIACUSTICA’1824 al 26 de octubre INTRODUCTION Transfer Path Analysis(TPA) is and advanced and valuable methodology employed in industry when it comes to work out difficult problems in an NVH environment. Its need rises from the requirement to provide better noise and vibration products. TPA has been developed since the 60s from different points of view. Nowadays, the very theoretical first framework has been smoothed for practitioners and TPA techniques start being smart and affordable from a practical and daily basis point of view [1]. Operational transfer path analysis (OTPA), using cross talk cancelation (CTC) and singular value decomposition (SVD), is a signal processing method which finds the linearized transfer function (TF) matrix between a set of chosen input and output channels from a measurement. The inand output relations are determined such, that the transfer functions are linearly independent with respect to each other, hence the name CTC. The resulting transfer functions can be used in a transfer path analysis (TPA), determining a source’s propagation of noise and the resulting content in the response signal. The OTPA uses the singular value decomposition (SVD) algorithm to find independent principal components describing the transfer functions. In practice, the numerical operations involved often suffer from measurement noise. By rejecting smaller principal components, one reduces these influences on the TF estimates. Basically, OTPA is based on work of Bendat et al. [2]. The goal of this paper is to obtain a better understanding of the OTPA method, highlighting its capabilities and point of attention in its application. Besides, a case on tire noise OTPA analysis is included. OTPA vs CLASSICAL TPA Classical TPA which are based on Frequency Response Functions (FRF) measurements from different approaches can be classified as follows: A)TPA approach based on interface force [3]; B)The TPA based on matrix inversion method [4,5,6]; C)The mount stiffness TPA method [7,8]; D) The gear noise propagation (GNP) or component TPA method [9,10]. These methods basically consist of two steps. First, FRFs are determined between defined input/reference points and chosen output point. They are determined by use of impulse hammer/shaker if structural vibration is considered and/or by use of loudspeaker for air-borne. Secondly, these FRFs are combined with operational forces determined at the reference points to generate synthesized response signals. Those forces are determined in different ways depending on the method chosen. The synthesized output can thereafter be analysed, determining the contribution of each propagation path. The OTPA method uses a one-step approach and builds a model of a structure without FRF measurements by hammer, shaker or loudspeaker. Basically, the method uses a response to response transfer function matrix, also known as transmissibility matrix when accelerators are employed, to represent the propagation paths of the structure. All signals are collected from a measurement of the operating system, so that implicitly the operating excitations are used to determine the transfer paths. Compared to the FRF approaches one can make the following remarks: • The OTPA is very easy and fast to setup as it uses only an operational measurement. A large reduction in analysis time can therefore be achieved compared with FRF approaches. And so, operational influences are accounted for. • Air-borne noise has a spatially complex distributed sound field on the excitation source. It is difficult to reproduce this sound field with loudspeakers, yet OTPA uses the actual excitation source to determine the TF. • Careful design of the OTPA model of the analysed system is required. FIA 2018 XI Congreso Iberoamericano de Acústica; X Congreso Ibérico de Acústica; 49o Congreso Español de Acústica -TECNIACUSTICA’1824 al 26 de octubre OTPA METHOD INTRODUCTION The OTPA method tries to find the (linearized) transfer function (TF) matrix between a chosen set of input and output quantities from a measurement. These sets of input and output can best be seen as degrees of freedom (DoF) describing the measured object’s excitation (inputs) and the object’s responses (output) as a linear combination of the chosen/assumed excitations. Firstly, the OTPA theory with least-squares algorithm is introduced. Consider an arbitrary linearized system model described by a set of input and output DoF, represented as: (1) , where H(jω) is the complex frequency domain transfer function matrix that links input DoF x(jω) signals to the output DoF signals vector y(jω). In NVH problems, the measured signals are typically motions, denoted u(jω), forces f(jω) and sound pressures p(jω). The input and output vectors can thus in general be assembled from these quantities as: