Statistical Energy Analysis Model Research Articles

Derivations of transfer functions for estimating ship underwater radiated noise from onboard vibrations

The adverse impacts of underwater radiated noise (URN) from marine vessels on marine life are increasingly recognized. URN estimation and subsequent monitoring could be used to track URN and take measures to reduce it in sensitive environments (e.g., a marine life protected area). Two common analytical radiated noise power approximations and two empirical methods are assessed for URN estimation. The assessments were carried out by testing the methods on data from acoustic range measurements of an ORCA-class training vessel of the Royal Canadian Navy, named Patrol Craft Training (PCT) Moose and a DAMEN Combi Freighter 3850, named Heinz G. The analytical approximations are called equivalent radiated power and power from volume velocity; both are used to estimate URN directly from the onboard ship vibration measurements. The empirical methods are based on the correlations of onboard vibrations with measured URN, from which the derived transfer functions. The analytical and empirical transfer functions are compared. A statistical energy analysis model of PCT Moose is also used to estimate onboard vibrations from the ship’s engine, generator, and propeller specifications for URN estimation at the design stage.

The effect of furniture on room acoustic parameters and its dependence on different suspended ceilings' sound absorptive properties

In ordinary public rooms such as classrooms and offices, the base line of acoustical treatment is an absorbent suspended ceiling. Due to the non-uniform distribution of the absorptive material, the scattering as well as the absorption properties of furniture will have a significant influence on room acoustic parameters such as reverberation time, speech clarity and sound strength. In particular, the absorption of the sound scattered energy will depend on the absorbing efficiency of the suspended ceiling. This effect is not accounted for in classical diffuse field models such as Sabine's formula. Measurements were conducted in the reverberant room with varying degrees of furnishing for several ceiling treatments ranging from highly reflective to highly absorptive. Using Sabine's formula and the Statistical Energy Analysis model, this paper discusses the scattering effect of furniture on room acoustic parameters such as reverberation time, speech clarity and sound strength as well as how the equivalent scattering absorption area is related to the absorbing efficiency of the suspended ceiling. It is concluded that a novel method for the quantification of furniture is needed to include both absorption and scattering effects of furniture on reverberation time and its dependence on the suspended ceilings' absorptive properties.

Acoustic performance of a multi-layer vehicle interior trim sound-absorbing material

This paper investigated the acoustic properties of a multi-layer vehicle interior trim acoustic material. In this study, a thin fiber layer was inserted between the vehicle carpet and the porous sound-absorbing material layer, and backed by the vehicle floor. The theoretical prediction method was based on the Johnson-Champoux-Allard (JCA) model, and the sound absorption coefficient of the multi-layer vehicle interior trim acoustic material was calculated by using the transfer matrix method (TMM). An impedance tube was used to measure the normal incidence sound absorption coefficient of the vehicle interior trim with different combinations of acoustical materials. The comparison of the theoretical and the experimental results showed that the sound absorption coefficient curves predicted using the JCA model are consistent with the measurement data across the mid and high-frequency range (500-6400 Hz). In addition, a car cabin Statistical Energy Analysis (SEA) model was developed and used to predict the effect of the acoustic properties of the multi-layer vehicle interior trim acoustic material. The results presented in this paper, are useful for enhancing vehicle interior acoustic design and refining vehicle cabin sound quality in future vehicles.

Engineering process for eVTOLs interior sound predictions

Urban Air Mobility (UAM) is quickly developing with the objective to transport passengers and cargos at lower altitudes in urban areas using automated aircrafts. Noise is one of the important challenges facing engineers developing these aircrafts as they will be operating in cities and are thus subjected to noise regulations. In addition, customers will be expecting similar interior noise performance as in luxury automotive vehicles. This paper presents an engineering process developed to predict the acoustic performance inside Electric Vertical Take-off and Landing (eVTOL) aircrafts. The process starts with Computational Fluid Dynamics (CFD) simulations to calculate the noise sources generated by the propellers. A Boundary Element Model (BEM) is then used to propagate these sources around the aircraft and calculate the pressure distribution on the fuselage exterior, which is then applied, in the last step, as excitation in a Statistical Energy Analysis (SEA) model to predict the interior noise. The paper uses a demonstrator model to illustrate the process and results. This process is now available to support engineers when optimizing their eVTOL design for costs, weight and interior noise performance without the need for physical prototypes.

A Comparative Study of a Hybrid Experimental–Statistical Energy Analysis Model with Advanced Transfer Path Analysis for Analyzing Interior Noise of a Tiltrotor Aircraft

The excessive noise present within an aircraft cabin during flight operations constitutes a notable origin of fatigue, stress, and communication impediments for both pilots and passengers. Ensuring the comfort, well-being, and safety of passengers and crew members necessitates the accurate anticipation of noise levels. This study concerns the computation of structure-borne noise levels within the cabin of a tiltrotor aircraft. This investigation employed two distinct methodologies: advanced transfer path analysis (ATPA) and statistical energy analysis (SEA). To assess the results obtained with the ATPA approach, the acquired outcomes were compared with empirically measured sound pressure levels during airplane mode operations. The contributions of air-borne and structure-borne noises were calculated with the ATPA methodology. On the other hand, the structure-borne noise was calculated with a hybrid experimental–SEA model with ACTRAN software, and its results were compared with those of the ATPA method. The results show a good agreement between these methods at high frequencies, while at low frequencies, certain adjustments or modifications to the SEA model are necessary to predict the noise levels.

Comparison of Clustering-Based Virtual SEA Subsystem Generation Models

Building a valid Statistical Energy Analysis (SEA) model is far from straightforward in real life applications because it has to comply with certain requirements. Since intuition-based SEA subsystems do not always entirely meet these, more advanced methods such as clustering techniques have been proposed for model building. This paper focuses on the comparison of different clustering techniques from SEA model validity point of view in the case of a simplified car body model. Besides the compliance with the SEA theory, each obtained model is compared to a reference finite element simulation to assess its accuracy.

Assessment of a Statistical Energy Analysis model to perform automotive acoustic comfort subjective evaluation

Saint-Gobain is currently developing Statistical Energy Analysis models in order to predict the mid-high frequency airborne interior noise generated by the wind excitations on vehicles. Our objective is to assess the possibility of using the predictions of this model to perform subjective evaluation of the acoustic comfort inside the cabin. This way, as a tier-one supplier of automotive glazing, Saint-Gobain could investigate psycho-acoustic evaluations earlier in its design process. A car equipped with several sets of glazing was exposed to an in-lab representative excitation to record an experimental set of sounds. Concurrently, those car configurations were simulated using the model and a numerical set of sounds was auralized. Both sets were compared through two jury testing campaigns. The campaigns highlighted that the participants gave similar evaluations of sounds regardless of their origin set. However, the ratings were not exactly the same between measurement and simulation. The definition of the glazing inside the model and/or its interaction with elements linked to it, like the window seals, might be the cause of those rating differences. More investigations were thus conducted to assess the influence of the window seals on the acoustic insulation performances of the glazing.

Vibroacoustic response of a high-speed train extruded profile under fluid-induced vibration

The wall pressure fluctuation caused by a turbulent boundary layer is an important source of noise and vibration in high-speed trains. Considering that railway vehicles are usually made of extruded profiles, a simple and reliable model is needed to predict the vibroacoustic characteristics of extruded profiles excited by a TBL in the early stages of design. A hybrid finite element and statistical energy analysis model is established for computing the vibroacoustic response of finite-sized panels excited by a TBL. In the hybrid model, the wall pressure fluctuation of the TBL is modelled in the wavenumber domain. The panels are modelled using FEs, and acoustic waves in the fluid space below the panels are modelled using SEA. The TBL wall pressure acting on the top surface of the panels is resolved into equivalent nodal forces with discretization of the structure using FEs, achieved by calculating the cross-spectrum matrix of the wall pressure in the spectral domain and using jinc functions with smooth boundary and symmetric properties as shape functions. The reciprocity between direct and reverberant fields couples the acoustic fields to the structure. Once the response of the hybrid model is determined, sound transmission through the panels can be calculated. By following the procedures outlined in this paper, the range of wall pressure model selection for TBL has extended and reduced computational time and provides a basis for the acoustic optimization design of extruded profiles.

Analysis of the effect of combined noise reduction measures of trapezoidal sleeper and sound barrier on elevated line

In this paper, a noise test on the viaduct of a city in China was conducted to analyze the effect of trapezoidal sleepers, sound barriers, and the combination of trapezoidal sleepers and sound barriers on the spatial distribution characteristics of overall noise. A statistical energy analysis model was established to analyze the influence of these sound barrier configurations. The results show that at the speed of 60 km/h, the trapezoidal sleeper track can reduce the overall noise by 2.0 dB to 6.0 dB. The upright-type sound barrier can reduce the overall noise by 10.3 dB to 13.2 dB, with the most significant frequency band of noise reduction above 800 Hz; the combination of the trapezoidal sleeper and sound barrier has a significant noise reduction effect above 31.5 Hz, and the overall noise reduction can reach 13.8 dB to 23.1 dB. The high-frequency wheel-rail noise decays faster with distance, while the low-frequency bridge structure noise decays slowly with distance. When sound barriers are set up on both sides of the viaduct, the sound pressure level at the near field point is further reduced by 3.3 dB to 5.2 dB compared with sound barriers on only one side. Compared with a section with no sound barriers, the noise inside the sound barriers is about 1.2 dB higher than when the sound barriers are set on one side or both sides of the viaduct.

Experimental and numerical study on vibration and structure-borne noise of composite box-girder railway bridges

ABSTRACT This paper adopts a proficient approach to evaluate vibration and structure-borne noise and makes up for the steel-concrete composite (SCC) box girder vacancy in the SCC structure. First, the dynamic equation of the train-rail system is established, the pseudo-response of the system in the frequency domain is appropriately assessed by pseudo excitation method (PEM), and the frequency spectra of the wheel-rail force as well as the forces transmitted to the bridge are obtained. Next, applying the force to the finite element method (FEM), boundary element method (BEM), and statistical energy analysis (SEA) model. The vibration and structure-borne noise of the SCC box girder are calculated in the frequency domain. Then, the effectiveness of the method and model is verified through the comparison of the field experimental results. Finally, the effect of the ground reflection in the SEA model is considered using the sound ray-tracing method for the first time.

Fast statistical energy analysis modelling of periodic box-like structures

This paper proposes a fast way to create a base Statistical Energy Analysis (SEA) model for periodic box-like structures, for which further refining and modification can be conducted with simplicity. A novel numbering system is introduced which enables the model builder to build, locate and change the property of each subsystem as well as to specify the connections between different subsystems in a 3D coordinate system. Two numerical SEA models are studied with the aid of the new method. It greatly decreases the time in model building and increases the simplicity of studying the acoustic attenuation by changing the properties of different subsystems. The results show that when increasing the internal loss factors (ILF) of all structural elements from 0.015 to 0.12, a 13.5 dB sound insulation improvement can be observed for the 2-room system at 1000 Hz and that for the 24-room system is 10.9 dB. This method serves as a promising way to investigate the acoustic transmission in heavily damped periodic box-like structures.Article HighlightsA fast SEA model building method is proposed.A 3D coordinate based numbering system is developed for subsystem location and identification.Application of damping on structural elements results in better sound insulation.

Pyroshock Response Prediction of Spacecraft Structure in Wide Frequency Domain Based on Acceleration FRF

The initiating explosive shock environment of an aerospace mission has the characteristics of instantaneity, high amplitude and a wide frequency domain. An improved method based on the acceleration frequency response function (FRF) and virtual mode synthesis method (VMSS) is proposed to predict the pyroshock response of a spacecraft structure in a wide frequency domain. Firstly, the statistical energy analysis (SEA) model of the spacecraft structure was established, and the FRF and modal density of the model were obtained. Then, the paper explains how, due to the small number of modes in the low-frequency band, the calculation results of the SEA method in the low-frequency band were not accurate enough. The FRF of the SEA model in the low-frequency band was modified by an FRF test of the structure. Finally, the shock response spectrum (SRS) was obtained based on the VMSS and the modified FRF. A shock experiment on the spacecraft structure was conducted by using the shock experiment system, which is based on a light-gas gun. The accurate shock force function and acceleration response results were obtained. The numerical results based on the improved method are in line with those in the experiment. This verifies that the novel method can better grasp the response characteristics of the structure in the broadband domain. The novel method effectively improves the response prediction accuracy of the SEA model in the relatively low-frequency band. While ensuring the computational efficiency, more accurate shock response results in a wide frequency domain were obtained. The novel method presented in this paper provides support of numerical analysis for pyroshock response prediction of spacecraft structure in a wide frequency domain.

Sound transmission paths through a statistical energy analysis model of mechanically linked aircraft double-walls

Sound transmission loss (TL) through mechanically linked aircraft double-walls is studied with a statistical energy analysis method. An overview of the method is given with details on acoustic and structural transfer path analysis. The studied structure is composed of a thick composite sandwich panel representative of a skin panel, lined with an acoustic insulation layer (glass wool), and structurally connected via vibration isolators to a thin composite sandwich lining panel representative of a trim panel. Two types of vibration isolators are considered: a soft and rigid mechanical link. Various experimental methods were used to assess the accuracy of this model. This study shows the robustness of the simple four-pole modeling of isolators, which depends mainly on the importance of correctly determining the experimental dynamic stiffness of typical aircraft vibration isolators. The prediction of the TL while acceptable was, however, found less satisfactory for the soft configuration. This is traced to the uncertainties on the used coupling loss factor. Finally, a transfer path analysis is performed to identify the contribution of each transmission path in the entire frequency range of interest. Results show that non-resonant airborne transmission dominates in low frequencies, the airborne radiation is significant in the critical frequency region of the panels, while the structure-borne radiation increases the noise transmitted in the mid- and high-frequency ranges.

Finite element method and dynamical energy analysis in vibro-acoustics - A comparative study

Future aircraft concepts utilizing innovative lightweight structures and novel propulsion concepts are a necessity for long term sustainable air travel. These concepts pose new challenges for the vibro-acoustic assessment of cabin structures and the associated noise impact on passengers. Finite Element (FE) models derived from aircraft pre-design data are not optimized for use in acoustic analyses, i.e. the mesh is too coarse to provide meaningful results while setting up Statistical Energy Analysis models for this specific purpose is adding another time-consuming step. A possible alternative, Discrete Energy Analysis (DEA), is evaluated. This method allows to calculate the acoustic behavior of thin-walled structures in higher frequency ranges simply using existing FE meshes. In this paper an experimental lightweight aluminum structure and its respective FE model is investigated for a frequency range up to 5000 Hz. A comparison in terms of vibrational energy between DEA, FE and measurement results are presented. Finally, a lower-bound frequency range is identified in which DEA and FEM correlate and thus allow a substitution for further simulations at higher frequencies.

Psycho-acoustic evaluation of the automotive acoustic comfort using vibro-acoustic prediction methods

In the automotive industry, the acoustic comfort is considered as a selling point of utmost importance. To help the OEMs improve the acoustic comfort in cars, as a one-tier supplier of automotive glazing, Saint-Gobain is currently working on the acoustic comfort within the cabin in order to propose the right set of glazing consistent with the OEMs' specifications. The characterization of the acoustic comfort mostly relies on physical demonstrators required for carrying out the relevant measurements. It is however not available early in the project phase, delaying the subjective analysis late in the development phase. To have the opportunity to develop effective solutions, the acoustic comfort has to be investigated as early as possible in the design process. Saint-Gobain is thus currently developing relevant acoustic models in order to predict the mid-high frequency airborne interior noise generated by the wind excitations. The subjective acoustic comfort has then to be assessed using the predicted interior sound pressure levels converted into audio soundtracks for the auralization purposes. In this paper, we briefly present the Statistical Energy Analysis model developed by Saint-Gobain. The psychoacoustic methodology deployed to evaluate its reliability for the subjective evaluation of the automotive acoustic comfort is detailed.

An Energy Model for the Calculation of Room Acoustic Parameters in Rectangular Rooms with Absorbent Ceilings

The most common acoustical treatment of public rooms, such as schools, offices, and healthcare premises, is a suspended absorbent ceiling. The non-uniform distribution of the absorbent material, as well as the influence of sound-scattering objects such as furniture or other interior equipment, has to be taken into account when calculating room acoustic parameters. This requires additional information than what is already inherent in the statistical absorption coefficients and equivalent absorption areas provided by the reverberation chamber method ISO 354. Furthermore, the classical diffuse field assumption cannot be expected to be valid in these types of rooms. The non-isotropic sound field has to be considered. In this paper, a statistical energy analysis (SEA) model is derived. The sound field is subdivided into a grazing and non-grazing part where the grazing part refers to waves propagating almost parallel to the suspended ceiling. For estimation of all the inherent parameters in the model, the surface impedance of the suspended ceiling has to be known. A method for estimating the scattering and absorbing effects of furniture and objects is suggested in this paper. The room acoustical parameters reverberation time T20, speech clarity C50, and sound strength G were calculated with the model and compared with calculations according to the classical diffuse field model. Comparison with measurements were performed for a classroom configuration. With regard to all cases, the new model agrees better with measurements than the classical one.

Study on sound transmission loss modeling through simplified sealing specimens and an automotive door sealing system

An imperfect sealing system would be the main path of the noise propagating into the interior compartment of a high-speed vehicle. The study on the sound insulation modeling of automotive door sealing systems, which involve complicated threedimensional sealing structures and gap cavities, has attracted more and more attention. This study employs hybrid finite element–statistical energy analysis (FE-SEA) models to predict the sound transmission loss of three simplified sealing specimens and an actual automotive door sealing system. For the actual sealing system under compression, a three-dimensional FEmodel is built to simulate the nonlinear compression, which can acquire the compressed geometries and pre-stress modal results of the seals for further prediction of the sound transmission loss. The hybrid FE-SEA method is firstly verified by the experimental result of a double plate vibro-acoustic system and another numerical method. Several factors concerning the modeling, including the boundary conditions, the equivalent elastic modulus for the hyper-elastic rubber, the specimen length, and the structural grid size, are considered to study their impacts on the sound transmission loss. The effects of using shell elements and using solid elements to model the sealing rubber layers are also compared. The results of this study can provide guides regarding the trade-off between the modeling efficiency and accuracy, so that it has significance for engineering modeling, as well as the design and optimization of automotive door sealing systems.

First models for structural energy transmission decoupling in the high frequency regime under aerodynamic excitations

In the wind tunnel facility, a test structure is often used for measuring its vibrational response to the aerodynamic excitation. A support is needed to sustaining the structure and it is mandatory that this support does not influence the vibrational energy to be measured. To this aim, the maximum amount of energy decoupling between the structure and the support is desired. This work is focused around a quick method to estimate this decoupling by using simplified models for the Turbulent Boundary Layer (TBL) excitation and for the structural response. Specifically, the Equivalent Rain-on-the-roof excitation is invoked with a Statistical Energy Analysis model for the structure. Some simple design rules are proposed and based on little information leading to foresee the difference of vibrational velocity levels between the two structural systems. A simplified test-case is used for the first investigations and a complex structure is finally conceived thinking to vibroacoustic measurements in a large wind tunnel facility. Although some results are largely expected, the global approach is promising.

Rapid Acoustic-vibration Modelling Methods of Solar Arrays in Satellites

Large components outside satellite body are extremely sensitive to the sound field. As the entire satellite acoustic-vibration (hereinafter referred to as acoustic) model is very complex, computationally intensive and time-consuming, the feasibility of only modelling these large components when they are just concerned deserves to be investigated. In this paper, an entire satellite model, a finite element (FE) model a statistical energy analysis (SEA) model of the solar array were firstly established, and then their results and time needed were compared in order to explore the fastest and most efficient modelling method of large components outside satellite body. The results demonstrate that modelling only solar array not the entire satellite is feasible when only it is concerned. The FE model of solar array should be used if the responses at each point are necessary, while the SEA model is recommended if not.

Vibration responses of a satellite subjected to acoustic excitation at launch stage

Acoustic-vibration prediction at early stage of satellite development can contribute to their structural and layout design. In this paper, numerical models of a practical satellite subjected to acoustic excitation at launch stage were established. Then, the effect of acoustic condition was further analyzed. The results demonstrate that it is difficult to predict all-frequency-band acoustic response of complex satellites by an individual method, so a combined method was proposed in this paper. The damping loss factor model of panels with equipment was introduced to resolve the issue of on-board equipment modelling in the statistical energy analysis model. The service modules are extremely sensitive to acoustic excitation of about 354∼2828Hz, which should be highlighted when carrying a rocket with a high sound pressure level at this frequency band.