Experimental statistical energy analysis in the time domain

<div class="htmlview paragraph">Automotive interior noise at mid and high frequencies is typically dominated by the airborne noise from acoustic sources that are spatially distributed around a vehicle. Each source is typically spatially compact (for example, a tire contact patch) but the source radiates sound that then propagates across the entire exterior surface of the vehicle. To characterize a source it is therefore necessary to know both the sound pressure level in the vicinity of the source and also the way in which sound from the source diffracts around the vehicle. The former depends on the details of the source, the latter typically depends on the overall vehicle geometry. When creating Statistical Energy Analysis (SEA) models of interior noise, the diffraction of airborne loads around a vehicle is often measured experimentally. Since SEA deals with averaged quantities, it is typically only necessary to obtain an approximate estimate of the space and frequency averaged sound pressure level across various surface regions of the vehicle (rather than a very detailed narrowband prediction of the diffraction).</div> <div class="htmlview paragraph">This paper provides a numerical investigation of the diffraction of typical acoustic sources around a vehicle using the Fast Multipole Boundary Element Method (FMM BEM). In particular, the paper investigates the sensitivity of the space and frequency averaged diffracted field to various modeling details (for example, geometric detail, mesh density/quality, surface impedance, frequency resolution etc.). The objective of the study is to investigate how much “detail” is needed in an FMM BEM model in order to get accurate predictions of the exterior acoustic loads for use in Statistical Energy Analysis (SEA) models. Significant reductions in computational expense can be obtained by matching the level of detail in the FMM BEM model to the level of detail required in the input results for an SEA model (and therefore avoiding “over computing” results that are subsequently frequency and space averaged).</div>

The use of statistical energy analysis (SEA) for the solution of vibroacoustic problems that occur with the operation of machinery, has only recently become practicable. This paper charts the developments that led from the early ideas of energy accountancy (EA) to the current SEA modeling techniques. The basic concept of EA, which was conceived to show the influence of the overall design parameters on the radiated noise, is explained and its limitations discussed. The paper then goes on to describe how the various practical difficulties preventing the application of SEA were overcome to the point where it could be used as a practical tool. Finally, a case history is presented in which an experimental SEA model is used to determine input (exciting) powers, power flow and sensitivity of the noise to parameter changes. In addition, the use of an optimization algorithm for driving the noise level down to a target spectrum within parameter and weight constraints is also demonstrated.

Prediction of structure-borne sound transmission on built-up structures at audio frequencies is well-suited to Statistical Energy Analysis (SEA) although the inclusion of periodic ribbed plates presents challenges. This paper considers an approach using Advanced SEA (ASEA) that can incorporate tunneling mechanisms within a statistical approach. The coupled plates used for the investigation form an L-junction comprising a periodic ribbed plate with symmetric ribs and an isotropic homogeneous plate. Experimental SEA (ESEA) is carried out with input data from Finite Element Methods (FEM). This indicates that indirect coupling is significant at high frequencies where bays on the periodic ribbed plate can be treated as individual subsystems. SEA using coupling loss factors from wave theory leads to significant underestimates in the energy of the bays when the isotropic homogeneous plate is excited. This is due to the absence of tunneling mechanisms in the SEA model. In contrast, ASEA shows close agreement with FEM and laboratory measurements. The errors incurred with SEA rapidly increase as the bays become more distant from the source subsystem. ASEA provides significantly more accurate predictions by accounting for the spatial filtering that leads to non-diffuse vibration fields on these more distant bays.

This paper introduces the interval perturbation method into the sensitivity analysis of statistical energy analysis (SEA) models. The damping loss factors and coupling loss factors are treated as the design parameters, while the modal energy of each subsystem is considered as the decision-making target. The variation of the design parameter is characterized by an interval form, and the ratio between different interval widths is used to represent the sensitivity of the decision-making target to the design parameter. Then the sensitivity factor matrix that can help a designer find the design parameters giving the greatest benefit in noise and vibration reduction is provided. The presented interval approach is verified through simulated studies for a two-plate coupling system and a three-plate coupling system. The work of this paper can enrich and develop the theory of the sensitivity analysis of SEA models.

<div class="htmlview paragraph">Statistical Energy Analysis (SEA) models were created and analyzed of the Gulfstream Aerospace Corporation (GAC) G100 mid-cabin and G150 wide-cabin, high speed business jets to assist in the design efforts of the G150 cabin interior development program. The G100 was used as a model validation platform due to the existence of extensive test data. Once satisfied that the modeling technique and material properties were adequately characterizing the G100 aircraft, a G150 model was created and predictions were made. Additionally, optimization was performed successfully on the G150 SEA model to reduce the weight of the thermal / acoustic package without adversely affecting the acoustic performance. This analytical modeling effort was the first of its kind to be used at Gulfstream during an early development phase in helping to design and optimize a GAC lightweight interior thermal / acoustic package. This paper describes the specifics of analytical modeling as part of the G150 interior development effort by rendering an overview of the SEA models, constructs used to develop the models, applied loads, response of the models, and correlation of results to test data. Cambridge Collaborative Inc.'s SEA software SEAM3D and Engineous Software's optimization code iSIGHT were used in this analysis effort.</div>

<div class="htmlview paragraph">A process is implemented to propagate uncertainties inherent to the Statistical Energy Analysis (SEA) modeling practice to variance in predictions. A Monte Carlo based approach is scripted for the VA-One environment to account for uncertainties in gross parameters of SEA model subsystems. The variance module of the commercial software is used to estimate possible variations in local modal properties. A first-order expansion solution is applied to integrate uncertainties in the power inputs of the system. The impact of each type of source is assessed in computing overall variance in predictions. The process is applied to analysis of in-flight interior cabin noise predictions using a simplified aft fuselage section SEA model.</div>

<div class="section abstract"><div class="htmlview paragraph">Prediction of flow induced noise in the interior of a passenger car requires accurate representations of both fluctuating surface pressures across the exterior of the vehicle and efficient models of the vibro-acoustic transmission of these surface pressures to the driver’s ear. In this paper, aeroacoustic and vibro-acoustic methods are combined in order to perform an aero-vibro-acoustic analysis of a Mercedes-Benz A-class. The exterior aero-acoustic method consists of a time domain incompressible Detached Eddy Simulation (DES) and an acoustic wave equation. The method is extended in this paper to account for convection effects when modelling the exterior sound propagation. The interior vibro-acoustic model consists of a frequency domain Finite Element (FE) model of the side glass combined with a generalized Statistical Energy Analysis (SEA) model of the interior cabin. The method is extended in this paper to account for additional geometric details that affect the direct and reverberant fields within the cabin. The overall approach is presented and validated against vibro-acoustics tests and wind tunnel measurements for two separate mirror designs. The aero-vibro-acoustic method achieves very good results and accurately predicts the change in interior noise resulting from an exterior body design change.</div></div>

<div class="htmlview paragraph">The high-frequency performance of automotive sound packages may be predicted by combining transmission loss and absorption calculations with statistical energy analysis (SEA) models. Vehicle SEA modeling therefore requires analytical tools that accurately describe the acoustic properties of layered structures such as trim panels. While widely accepted prediction models for fibrous materials exist, less work has been done on foam layers. This paper presents a numerical calculation of sound transmission through layered structures using a direct global matrix (DGM) solution. This numerical technique is used to compare several models for acoustic propagation in foams. Predictions are compared to transmission loss measurements for several panel configurations. A rigid porous model compares well with data up to 1 kHz for the foams studied, while foam elasticity appears to be important at higher frequencies.</div>

A statistical energy analysis (SEA) model of a 510 l capacity refrigerator is used to calculate the sound pressure level generated in a reverberation room. This is a reliable indicator of the vibroacoustic performance of the refrigerator, and it is in some countries as a pre-commercialization test. The main contributions of the SEA model are the characterization of the refrigerator structure (three-layer: HIPS, polyurethane foam and steel) and the modelling of important components such as internal chambers or ventilation gratings. The simulation results are successfully compared with laboratory measurements. The SEA model is then used to understand the vibroacoustic behaviour of the refrigerator and to establish the most critical transmission paths and radiation mechanisms.

A modelling approach for the vibroacoustic behaviour of aluminium extrusions used in railway vehicles

<div class="section abstract"><div class="htmlview paragraph">Many sources and paths cause interior cabin noise. Some noise from an electric vehicle is unique and different from a vehicle with an internal combustion engine. Especially, whine noise occurs due to the particular orders of the electromagnetic force of an electric motor and transmission gears, which is tonal and usually reaches high frequencies. This paper covers structure-borne (SB) and airborne (AB) aspects to estimate whine, and the difference between the two characteristics is distinguished. The focus lies mainly on the process of virtual vehicle development and application for performance improvement. First, to predict SB whine, an e-powertrain is modeled as a finite element model (FEM), and electromagnetic (EM) forces are calculated. A vehicle model is also modeled as an FEM, in which interior sound packages are carefully modeled as they play an important role in the medium-frequency region. The e-powertrain and vehicle models (being simulated separately) are combined to obtain cabin noise up to 1.5 kHz. Design studies show that the stiffness of mount insulators and the panel stiffness of the vehicle can be substantial design variables to reduce the SB whine. Second, the study highlights a simulation method to predict interior airborne whine up to 8 kHz by combining the FEMs of the e-powertrain and the vehicle’s exterior cavity with a statistical energy analysis (SEA) model of a vehicle. Path contribution can be identified by defining source strength and acoustic transfer function of airborne paths. Design modifications, including encapsulation of the e-powertrain, show this simulation process could be practically useful to reduce the airborne whine at high frequencies.</div></div>

Military rotorcraft must adhere to internal noise standards to minimize hearing loss during operation and enable effective voice communication in noisy environments. This study predicted the internal noise levels and suggested noise reduction of a coaxial rotorcraft under high-speed maneuvering conditions to ensure compliance with these standards. To achieve this, Statistical Energy Analysis(SEA) models for helicopters were validated, and a new SEA model specific to the high-speed coaxial rotorcraft was suggested. Also, frequency spectrum of internal noise sources such as coaxial rotor, engines, and main gear box was scaled for the coaxial rotorcraft in high-speed maneuvering. As the sources were scaled for a high-speed coaxial rotorcraft, the internal noise levels at cockpit and cabin was predicted to exceed the design limit. This study proposed sound-proof panel modeling and position to satisfy the design limit.

<div class="htmlview paragraph">A series of tests have been performed on a production vehicle to determine the characteristics of the external turbulent flow field in wind tunnel and road conditions. Empirical formulas are developed to use the measured data as source levels for a Statistical Energy Analysis (SEA) model of the vehicle structural and acoustical responses. Exterior turbulent flow and acoustical subsystems are used to receive power from the source excitations. This allows for both the magnitudes and wavelengths of the exterior excitations to be taken into account - a necessary condition for consistently accurate results. Comparisons of measured and calculated interior sound levels show good correlation.</div>

This study investigates the influence of in-plane vibration on the construction of statistical energy analysis (SEA) models of flexural vibration in plate structures. A simple system is used that consists of two flat plates connected in an L-shaped configuration. For two SEA models, the loss factors related to flexural vibration are calculated by the finite element method, both with and without the in-plane vibration being taken into consideration. Differences occur in the flexural vibration loss factors in the frequency bands corresponding to the natural frequencies of the in-plane vibration in the unconnected plates. The subsystem energy, averaged over frequency and space, also shows the influence of in-plane vibration. As a result, a new method is developed to evaluate the effects of in-plane vibration on constructed SEA models of flexural vibrations. It is demonstrated that the method is useful in identifying the frequency bands affected by in-plane vibration and in determining under- or over-estimation of the loss factors.

<div class="htmlview paragraph">Each time a new vehicle is developed, engineers face the challenge to develop the ideal sound insulation package. The goal is to attenuate powertrain, wind and road/tire noise from entering the vehicle while complying with cost, weight and packaging constraints. The design process is greatly facilitated if the engineer has effective tools to rapidly quantify how various sound insulation components contribute to the overall NVH performance of the vehicle.</div> <div class="htmlview paragraph">This paper discusses how an interactive vehicle acoustical design tool can be developed that assists the designer in making rapid decisions as to how to balance the performance of the various sound package components. The acoustical design tool is unique for each vehicle, and must take into account design decisions such as type of powertrain, body style, and numerous other factors in order to correctly predict the performance of the total package. Any good modeling tool must also take into account inputs from a reasonable range of operating conditions.</div> <div class="htmlview paragraph">A very good model for the acoustical behavior of the vehicle can be developed using data from measurements made while operating a sample vehicle at the target operating conditions. The authors will present a method for utilizing measurements together with some simple equations to predict the result when components of different designs are exchanged. The process of generating the needed data for this method from experiments on a vehicle is admittedly time consuming, if all of the possible design variations are to be considered. An alternative that the authors present in this paper is for the case in which a correlated Statistical Energy Analysis (SEA) model exists for the vehicle being considered [<span class="xref">1</span>]<sup><span class="xref">1</span></sup>. A great time savings is realized when the same acoustical behavior information about the vehicle can be extracted by running analytical experiments in the SEA model. The authors assert that even if an SEA model must be developed from scratch and correlated, this approach is preferable over the experimental approach.</div> <div class="htmlview paragraph">Once developed, an interactive design tool of the type being discussed has ongoing benefit to product development engineers by giving them a handy way to asses future design changes. If sound insulation components are later sacrificed in the interest of reducing vehicle costs or weight, the model can accurately portray the implication of the changes on sound levels in the vehicle. A case study is presented that demonstrates the use of this tool and its accuracy.</div>