Abstract
Transfer Path Analysis (TPA) is a test-based methodology used to analyse the propagation of noise and vibration in complex systems. In this paper we present a covariance based framework for the propagation of experimental uncertainty in classical, blocked force, and component-based TPA procedures. The presence of both complex and correlated uncertainty is acknowledged through a bivariate description of the underlying uncertainty. The framework is summarised by a series of equations that propagate uncertainty through the various stages of a TPA procedure i.e. inverse source characterisation, dynamic sub-structuring, and forward response prediction. The uncertainty associated with rank ordering of source contributions is also addressed. To demonstrate the proposed framework a numerical simulation is presented, the results of which are compared against Monte-Carlo methods with good agreement obtained. An experimental study is also presented, where a blocked force TPA is performed on an electric steering system. The proposed uncertainty framework requires no additional experimental effort over and above what is performed in a standard TPA and may therefore be readily implemented into current TPA practices.
Highlights
Transfer path analysis (TPA) is a diagnostic method used for analysing the propagation of noise and vibration in complex built-up structures, for example, ships, vehicles, trains, etc
Unlike classical or blocked force Transfer Path Analysis (TPA), which are typically used for diagnostic purposes, component-based TPA serves as a predictive tool, capable of predicting the noise and vibration in complex structures that do not necessarily exist, physically
Implementation of Eqs. (2) and (3) ( Eqs. (4) and (5)) requires measurement of the operational velocity vCb, the context mobility matrix YCbc, of a blocked force TPA, and the forward frequency response functions (FRFs) matrix HCrc, we are interested in the influence all of which are subject to some degree of this uncertainty on the estimate of the of uncertainty
Summary
Transfer path analysis (TPA) is a diagnostic method used for analysing the propagation of noise and vibration in complex built-up structures, for example, ships, vehicles, trains, etc. Termed ‘In-situ source path contribution analysis’ by Elliott et al [3], blocked force TPA offers 2 distinct advantages over classical TPA: 1) The active components are characterised independently This means that the same set of blocked forces can be used to excite a range of different assemblies, or be applied in the presence of a structural modification (i.e. they are transferable). Unlike classical or blocked force TPA, which are typically used for diagnostic purposes, component-based TPA serves as a predictive tool, capable of predicting the noise and vibration in complex structures that do not necessarily exist, physically This is achieved by combining blocked force TPA (the in-situ blocked force characterisation) with dynamic sub-structuring (DS) procedures [5]
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