General framework for transfer path analysis: History, theory and classification of techniques

Application of vibro-acoustic operational transfer path analysis

“…The individual path contributions using the TPA method [1,10] are synthesized from the FRF, which describes the system of interest, and the operational forces acting in the system: • Using a force transducer -requires mounting a force transducer at the interface, between the active and passive subsystems, and directly measuring the force. The drawback of this method is that it requires modifying the mounting, which is often not feasible in practice.…”

“…The noise, caused by 5 the engine, propagates to the position of interest through different paths, where each of them contributes differently. The path contributions cannot be measured directly; hence Transfer Path Analysis (TPA), introduced some decades ago [1], provided two experimental techniques for estimating the contributions indirectly. The first of the two, the mount-stiffness method can be only ap- 10 plied to structure-borne noise, whilst the second, which is often referred to as a matrix inversion method, can be applied to both structure-borne and air-borne problems.…”

“…The recent introduction of blocked forces 2 [6,7] and its application to TPA demonstrated that correct contributions can be obtained without disassembling the system into active and passive parts, which also allowed a significant reduction of the time necessary to conduct conven-30 tional TPA. An overview of existing methods addressing finding contributions from different sources and paths can be found in [1]. Nowadays, as electrical and hybrid vehicles are coming to the market, customers may experience new types of high frequency noise, which explains a renewed interest in the field [8].…”

“…where K is the diagonal matrix of mounts' stiffnesses, and {∆X} is the vector of mounts' deformations [1]. The drawback is that the mount stiffness data often is neither available nor very accurate.…”

“…The main issue with matrix inversion is that it requires a quite significant amount of indicators responses in order to avoid ill-conditioning. The rule of thumb is to have at least two times more responses than the number of paths [1,14].…”