Transfer Path Analysis (TPA) is widely used to identify individual path contributions and to solve Noise, Vibration and Harshness (NVH) issues in different industries. However, the complexity and ...technical burden of the conventional TPA calls for alternative, faster techniques. One such alternative is the Operational Transfer Path Analysis (OTPA), which uses only operational data to estimate the contributions. However, this approach has its own limitations; in some situations, the OTPA results may be affected, which can lead to the wrong engineering decisions. This paper presents an alternative formulation of OTPA, in application to structure-borne noise: Operational Transfer Path Analysis – Difference (OTPA-D). The theoretical considerations and analytical model showed that OTPA-D solves one of the crucial issue regarding the OTPA technique. The paper provides theoretical considerations behind OTPA-D; also, a laboratory model is set up to compare the results of three versions of OTPA with the results of TPA. It is shown that two experimental OTPA versions matched TPA better compared to the traditional OTPA method.
Structure borne noise induced by vibrating systems is considered as a major contribution to the noise generated inside vehicles and can be assessed using Transfer Path Analysis (TPA) methods. Their ...theoretical formulation requires the mobility of either the vibrating system, the receiving structure or the assembly of the two components according to all Degrees of Freedom (DoFs). However, rotational and in-plane DoFs cannot be measured easily and their determination may result in a more complex experimental set-up or an increase in measurement uncertainties. The need for assessing the full mobility matrices thus deserves to be investigated. In this work, the robustness of multiple TPA methods dedicated to the design and validation phases of aircraft light equipment is investigated numerically according to the mobility matrices completeness and by considering several configurations of assemblies (i.e., different active source properties, different numbers of contact points). Numerical models have been developed to simulate a source with controlled vibratory behavior and the spatial averaged mean-square velocity on the receiving structure is used as an objective indicator of the method’s robustness. For proper predictions accuracy, it is shown that the required completeness should account for the terms of highest amplitude and thus depends on the (i) TPA method, (ii) active behavior of the source and (iii) coupling configuration. A completeness involving all the DoFs is generally required for TPA methods based entirely on the mobility of the decoupled components. Otherwise, the omission of rotational or in-plan DoFs could be suitable for TPA methods based on the mobility of the assembly.
•All Degrees of Freedom (Dofs) are not required for accurate predictions provided by the Transfer Path Analysis (TPA) methods.•The required Dofs depend on the TPA method considered and on the active and passive dynamic behavior of the structures.•Component-Based TPA (CB-TPA) without Dynamic Substructuring (DS) methods only requires the consideration of the translational Dofs.•Aeronautical structures may be characterized considering only a quarter of the Dofs for accurate predictions provided by the CB-TPA methods with DS.
Transfer Path Analysis (TPA) designates the family of test-based methodologies to study the transmission of mechanical vibrations. Since the first adaptation of electric network analogies in the ...field of mechanical engineering a century ago, a multitude of TPA methods have emerged and found their way into industrial development processes. Nowadays the TPA paradigm is largely commercialised into out-of-the-box testing products, making it difficult to articulate the differences and underlying concepts that are paramount to understanding the vibration transmission problem. The aim of this paper is to derive and review a wide repertoire of TPA techniques from their conceptual basics, liberating them from their typical field of application. A selection of historical references is provided to align methodological developments with particular milestones in science. Eleven variants of TPA are derived from a unified framework and classified into three categories, namely classical, component-based and transmissibility-based TPA. Current challenges and practical aspects are discussed and reference is made to related fields of research.
•In this paper a general framework for Transfer Path Analysis is presented.•The vibration transfer problem is derived conceptually, based on the admittances of the active and passive subsystems.•Eleven methods are derived and classified into classical, component-based and transmissibility-based TPA.•The evolution of historical developments to practical TPA methodologies is presented.•Several practicalities are discussed that may be important when conducting a TPA.
•We introduce the novel concept of decomposing the FRFs into paths.•The concept is based upon the FRFs, not upon transmissibilities as in GTDT.•The methodology can realize clear visualization of the ...contents of the FRFs.•It can evaluate the contributions of paths to the FRFs quantitatively.•The presented approach will promise to solve NVH problems.
Frequency response functions (FRFs) lie within the framework of the linear response theory in elastic structures. In FRFs, the inputs/outputs relationships are strictly determined, but there is no way of knowing how waves are propagated and converted from the input signals into the output signals. Thus, the wave propagation between the inputs and outputs cannot be clearly understood by the FRFs. In this study, we succeeded in visualizing the contents of these FRFs by decomposing them into geometric paths using a signal flow graph. Moreover, we succeeded in quantitatively evaluating the contributions of the paths to these FRFs. In terms of application, when the noise or vibration of industrial products is loud and unpleasant, this analytical methodology can help identify the cause behind such nuisance by using paths in contribution to FRFs. This methodology is expected to pave the way for taking quantitative countermeasures on the basis of analytical results.
•Reduction of interior noise in helicopters.•Helicopter inside cabin acoustic.•General framework for transfer path analysis: history, theory, and classification of techniques.•Numerical and ...experimental analysis on helicopter’s main rotor transmission for predicting structure-borne noise (SBN) using CB-TPA methods.•General framework for dynamic substructuring: history, review, and classification of techniques.
The noise prevailing inside the helicopter’s cabin always presents a problem for the operators of this vehicle. It is a source of annoyance and represents a pressing problem in the helicopter industry, causing manufacturers to constantly seek new technologies and solutions to reduce noise. This article aims to present a component-based transfer path analysis method (CB-TPA) and its application to the prediction of structure-borne noise transmitted into the cabin of a helicopter due to its main gearbox. The approach characterizes the source using a laboratory test bench and uses various CB-TPA methods to couple the blocked force to the dynamics of the receiving structure. The article details the used methods, their main assumptions, the experimental test configurations, and discusses the results compared to the classical in situ CB-TPA method. The effects of important parameters such as the completeness of the input and transfer mobility matrices are also discussed. It is shown that the presented methodology can correctly and accurately capture the noise in the cabin from a decoupled characterization of the source and the receiving structure.
This paper presents an efficient approach to select the reference sensor position in active control of road noise by considering the vibro-acoustic transfer path of a passenger car. To ensure ...sufficient noise attenuation in active road noise control, the reference signals should be correlated with vehicle interior noise signals. To achieve this aim, the vibro-acoustic transfer path delivers promising options. An appropriate number of reference signals have generally been obtained by principal component analysis. Then reference sensor positions have been determined by evaluating a large number of candidate locations on a car from a coherence perspective. However, this task is time-consuming and inefficient in the actual vehicle development process. Furthermore, in practice, it is challenging to obtain a highly coherent reference signal for road noise with broadband noise characteristics without understanding the characteristics of the road noise transmitted to the interior of the vehicle. In this study, a structural transfer path analysis was conducted to derive the primary vibro-acoustic paths of structural road noise, and the optimum positions of the reference sensors were determined through the analysis of path contribution and vibro-acoustic transfer function. A practical active noise control system was implemented with the remote microphone technique based on a vehicle audio system to validate the noise attenuation performance. The experiments demonstrated an average attenuation of 3.4 dB at the driver and rear right-hand-side seat positions for up to 400 Hz frequencies. This approach is expected to increase the efficiency in developing active road noise control systems based on adaptive feedforward control systems.
In noise and vibration engineering, a structure’s passive dynamic properties are often evaluated in terms of its frequency response functions (FRFs). The typical FRF measurement campaign consists of ...controlled structure excitation and the capturing of its response. However, exploiting operational excitation for FRF acquisition is not feasible, with many sources simply too complex to model or measure directly. In the present paper, an alternative approach is proposed for an indirect FRF estimation of a system in operation, in which the source is characterized independently of the final assembly. To overcome the issue of the unmeasurable excitation force, transfer path analysis (TPA) methods are proposed. TPA replicates the source excitations using the set of equivalent or pseudo forces that are an inherent property of the source. The assembly’s FRFs are then evaluated on the basis of receiver responses and pre-determined pseudo forces for independent operational load cases at the source. Thus, a single source description can be applied to estimate the FRFs of any assembly with an identical source and arbitrary passive side.
•Indirect FRF estimation for operational assemblies using internal source excitations.•Source structure is characterized independently using dedicated laboratory test-bench.•FRFs for any assembly with the same source are obtained from response measurement.
•Gearbox fault diagnosis using BFNCC is proposed for nonstationary condition.•The method can remove the effect of the structure transfer paths.•The proposed method is robust to the location of ...measuring points.•Method shows potential for a machinery with complicated structure transfer paths.
The main challenges in gearbox condition monitoring and fault diagnosis are the heavy noises caused by harsh operating environments and the complicatednonstationary condition during the runtime. It is extremely difficult and even impossible to obtain sensitive faultcharacteristics through direct measurements. Thus, it is ofgreat significance of faultcharacteristic inversion based on the structure vibration transfer paths for complicated mechanical systems fault diagnosis. This paper proposes a gearbox fault diagnosis method under nonstationary condition through using nonlinear chirp components extracted from bearing force (BFNCC). In the proposed method, the bearing dynamic forces are first identified based on the vibration transfer function matrix, and the intrinsic signal components are then decomposed through a nonlinear chirp mode decomposition method. The proposed method improved the quality of vibration signals by removing the effect of the structure vibration transfer paths. In comparison with order tracking, the BFNCC is capable of clearly reflecting the magnitude increase phenomenon under gear fault condition. Numerical simulation and experimental studies show that the proposed method is effective for gear fault diagnosis under nonstationary condition. The proposed method is demonstrated to be superior to the existing approaches and robust to the location of measuring points, and thus shows potential in machinery fault diagnosis under the interference of complicated structure transfer paths.
•The vibration characteristics of steering wheel were measured and analyzed.•The vibration at the engine ignition frequency is the largest at the idle condition.•The dominant contribution paths are ...identified using transfer path analysis.•The main causes leading to the vibrations are identified.•The vibrations are improved by modifying the mounting structure using finite element modal analysis.
The demands on improving the noise, vibration and harshness of passenger vehicles are growing rapidly. Low-frequency vibration of steering wheel is one of the most important factors leading to the discomfort of drivers. This study proposes a systematic analysis methodology to reduce the low-frequency vibration of steering wheel using classical transfer path analysis (CTPA). The theoretical basics of TPA using dynamic stiffness approach and inverse matrix approach are briefly introduced, and then the experimental apparatus and analysis procedures in performing the TPA are introduced. The static forces in the rubber mounts of the powertrain system are calculated, the dynamic stiffness of the rubber mounts are estimated, and the operational forces are determined. The contributions of different transfer paths to the vibration of steering wheel are analyzed and compared, and the predominant causes are identified. The results show that the vibration of steering wheel along the X direction is protruded at the engine ignition frequency, and the vibration of the exhaust system along the X direction contributes most to the vibration because of large frequency response function. The mounting structure of the exhaust system is modified based on modal analysis results using finite element method to reduce the vibration of steering wheel.
•Neural network model was developed for operational transfer path analysis.•Complex-valued learning algorithm was established to derive the reliable transfer functions.•Neural network-based OTPA ...method was more accurate than operational TPA method.•Noise contribution analysis was successfully conducted using only operational data.
Noise, vibration, and harshness (NVH) issues induced by vibrating source to receivers are sensitive concerns in the automotive industry, significantly determining the product quality. Transfer path analysis (TPA) serves as a crucial tool in addressing these concerns. However, classical and component-based TPA methods necessitate the measurement of all transfer functions associated with the NVH phenomenon, causing high experimental costs; moreover, operational TPA (OTPA) involves matrix inversion processes that may result in the loss of important information. In this study, a neural network-based OTPA (NOTPA) method is proposed that eliminates the need for a matrix inversion process and utilizes only operational measurement. To derive the physical meaning of transmissibility obtained from the trained neural network model, the learning algorithm for NOTPA was developed, and appropriate learning rules were applied to the model. In the general neural network model, training was performed using real-valued parameters. However, the phase of the signal is crucial information in the theoretical formulation of TPA; thus, a complex-valued propagation algorithm was established. Furthermore, an appropriate activation function was chosen to derive the actual transfer mechanism from the trained complex-valued parameters. To experimentally verify the NOTPA method, a testbed resembling automotive vehicle structure was constructed. Estimation of sound pressure and noise contribution analysis were conducted using the NOTPA method and compared with conventional TPA methods. The proposed method demonstrated higher accuracy compared to the conventional OTPA method and successfully identified the main transfer path compared to the classical TPA. Furthermore, by comparing the estimated sound pressure according to the architecture of the model, the consistency of the proposed model was verified.
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