a case study for predicting wind noise inside a car

A case study for predicting wind noise inside a car compartment using a multi-disciplinary CFD and Acoustic approach

R. Hallez1, K. Vansant

1

1 Simulation and Test Solutions, Siemens Industry Sector, Siemens Industry Software NV

Interleuvenlaan 68 B-3001 Leuven (Belgium)

e-mail: [email protected]

Abstract Environmentally conscious OEMs are making cars ever more efficient by using lightweight steel and

composite materials. The weight reduction exercise highlights the benefits of powertrain energy resource

optimization, but being lighter can also present a challenge for in-vehicle acoustic performance. The body

panels, such as windows, floor, roof and doors, should be designed and mounted in such a way that yields

sufficiently high transmission loss for exterior noise sources. Wind noise is such an external noise source

which forms an important contributor to the total in-vehicle noise at higher vehicle speeds, especially if

the vehicle is electrically powered.

This paper examines the acoustic performance of a car model when subjected to hydrodynamic wind loads

typical of high speed operation. The sound transmission through a glass window loaded by turbulent flow,

caused by the wind interaction with the A-Pillar, were measured and simulated on a simplified car model

in collaboration with Hyundai.

For the simulation study, the turbulent field is first captured by a transient CFD analysis. The noise

sources are captured using compressible CFD. These pressure results on the window are applied as

loading on a vibro-acoustic model to predict cabin Sound Pressure Level up to high frequencies (4 kHz)

using LMS Virtual.Lab Acoustics. As the pressure loads are caused by the turbulent flow phenomena they

are to some extent random in nature. Depending on the stochastic characteristics of the pressure loading,

different approaches to pre-process and to apply the load data are presented. Each approach is evaluated

on its accuracy and performance and based on this recommendations are provided. Finally the effects of

flow speed and yaw angle on the interior noise are investigated demonstrating the potential for mature

industrial applications.

1 Introduction

Windnoise is considered as a very important noise component for automotive cabin comfort. This is

especially true in the context of electrical and hybrid vehicles where less or no masking by an ICE engine

is observed. There is a clear need from automotive OEMs to get insight into noise mechanisms related to

windnoise in order to reduce it and improve cabin comfort. Simulation can help addressing these

challenges and avoid long and expensive test campaigns in windtunnels.

The modelling methodology for assessment of aerodynamic noise typically consists of two important

aspects - first to capture transient noise sources accurately and second to propagate these external noise

sources into the passenger compartment. The objective of this paper is to focus on the second step and to

provide guidelines on how to best model the turbulence loading obtained from CFD and apply it as a

boundary condition for the vibro-acoustic problem. As turbulence-related phenomena are stochastic in

nature, their treatment in a numerical model is not straightforward. Various methods to decompose the

301

stochastic load into uncorrelated components or to pre-process the data so that it can be used in a

deterministic vibro-acoustic solver are available. The objective of this paper is to describe each method

and to investigate its performance in terms of accuracy of prediction and computational efficiency.

A test case and global modeling approach are first presented. Each method for defining the random load is

then described and results are compared for each method on a simplified test case. Conclusions on the best

modeling strategy are then drawn and applied on a full test case used for validation against experimental

data.

2 Test case and modeling approach

2.1 HSM test case

The windnoise analysis is performed on a model built and tested by Hyundai Motor Company called the

HSM (Hyundai Simplified Model). It corresponds to an idealized vehicle made out of a stiff aluminum

frame and 3 glass panels representing the side windows and windscreen of the vehicle. As the model does

not contain any side mirror, windnoise is assumed to be generated by turbulences around the vehicle,

especially around the A-pillars. The size of the HSM is representative for a typical vehicle cabin at scale ½

(length=2m, height= 1m), see figure 1. The windows are made of 4 mm single layer glass material and the

aluminum body is 12 mm thick. Glass panels are connected to the body by a silicone sealer and 3mm

urethane spacers.

Figure 1: sketch of HSM model

Measurements have been performed by putting the HSM into an acoustic wind tunnel for two wind speeds

(110 km/h and 130 km/h) and two yaw angles (0 deg yaw and 10 deg yaw). Window vibrations as well as

acoustic pressure inside the cabin have been measured and will be compared to simulation results.

302 PROCEEDINGS OF ISMA2014 INCLUDING USD2014

2.2 Transient CFD Simulation

A CFD model has been created to solve the turbulent flow around the vehicle, which is assumed to be

rigid. Commercial software EXA Powerflow has been used to solve the model. It is using the Lattice-

Boltzmann approach which intrinsically assumed the fluid to be compressible. Figure 2 shows the

boundary conditions used in the model. The mesh is strategically refined around the HSM body to

accurately capture the wind noise sources.

Figure 2: Boundary Conditions of the CFD model

The wind noise assessment is carried out for two yaw positions (0 and 10 degree yaw) of the HSM and

two inlet air speeds (110 km/h and 130 km/h). It is important to capture the turbulent structures

downstream of the left A-pillar for accurate windnoise predictions. A physical time of 1s has been solved,

pressure fluctuations are exported every time step (2.3e-5s) for a physical time of about 0.5 s. The analysis

time is about 24 hours per case using 204 cores on Linux Xeon X5680 cluster with 114 GB of RAM.

Figure 3 shows the comparison between measured and simulated surface pressure results at a location in

the middle of the left hand side window. Agreement is excellent up to 4 KHz after which the CFD under-

predicts the pressure fluctuations. This demonstrates the ability of the CFD model to accurately capture

turbulence loading on the flexible windows.

Figure 3: Validation of the CFD surface pressure results for 110 km/h and 0 deg yaw (left) and 110 km/h

and 10 deg yaw (right)

AEROACOUSTICS AND FLOW NOISE 303

2.3 Vibro-Acoustic Simulation

A vibro-acoustic model is built in commercial software LMS Virtual.Lab [1]. Strong coupling is assumed

between the structure and the acoustic model so the vibration and acoustic results are obtained by solving a

direct vibro-acoustic model with surface pressures obtained from CFD (converted from time to frequency

domain by a Fourier transform) as loading.

In order to have an accurate modeling of the structural dynamics of the HSM, a structural FE model is first

built to correlate the FRFs for a few points on the windows with measurements and make sure that the

constraints and material properties are correctly defined. The structural mesh contains 27000 nodes and

56000 elements. Shell elements are used to model the glass windows and body whereas solid elements are

used to model the silicon sealer and urethane spacers.

Figure 4 shows the structural mesh with refined zones on the flexible windows and a comparison between

measured and computed structural FRFs for an excitation and response point as seen by the yellow dot in the

left picture. The agreement between the measured and simulated FRF is excellent although the measured

model seems to be slightly more damped.

Figure 4: Validation of the CFD surface pressure results for 110 km/h and 0 deg yaw (left) and 110 km/h

and 10 deg yaw (right)

Noise transmission is assumed to happen only through the vibration of the glass windshield and side

windows. Given the broad range of frequencies excited by windnoise phenomenon and the desire to

investigate noise transmission up to 4 KHz, it is necessary to use a very efficient modeling technique. Using a

conventional Finite Element approach would lead to prohibitive computation time for these frequencies. An

innovative technique available in LMS Virtual.Lab software is used here, called FEMAO (Finite Element

method with Adaptive elements Order). This technique is based on a finite element method with coarse

elements whose interpolation order is automatically adapted at each frequency [2]. While in a conventional

FEM approach, linear or quadratic elements are used (corresponding to element order 1 and 2 respectively),

in the FEMAO solver, higher-order element shape functions are used (up to order 10) to capture the acoustic

field (pressure, and pressure gradients) at the desired frequency. This allows to greatly reduce the total

computation time and memory requirements for the complete frequency range.

Figure 5 shows the mesh which is used for the validation case. It can be seen that mesh is refined on the

windows where vibration boundary conditions are imposed whereas coarse elements are used on other

surfaces and inside the cavity. The acoustic mesh contains 36 000 nodes and is valid up to 4000 Hz.


Figure 5: Window acceleration and FEMAO mesh cut

Since the CFD is compressible, it is assumed to capture both hydrodynamic (incompressible component) as

well as acoustic pressure (compressible component), therefore the surface pressure fluctuation from CFD can

directly be applied as structural loading in the vibro-acoustic model. Although acoustic pressure is typically

much less energetic than hydrodynamic pressure, it is usually observed that it has the tendency to couple

more efficiently with the bending modes of the structure.

3 Random vibro-acoustic response computation approaches

Turbulence-related phenomena such as windnoise are typically assumed to be stochastic by nature.

Different modeling approaches can be used to compute the response of a system submitted to such

stochastic loads. Following approaches are discussed here:

1. Computation of the response PSD (Power Spectral Density) using transfer vectors

2. Decomposition of the excitation PSD into (uncorrelated) pseudo-load cases using Singular

Value Decomposition

3. Decomposition of the excitation PSD into random load cases using a randomly reduced

Cholesky Decomposition

4. Averaging of the excitation spectrum in the FFT algorithm

5. Time segmentation of the excitation load.

The objective is to find amongst the above mentioned methods, these ones which provide the best balance

between accuracy of results and feasibility of the computations.

Indeed, for vibro-acoustic problems with stochastic input data, the quality and reliability of the stochastic

response is depending on how accurately the loading is represented by means of stochastic functions. The

latter can be a challenge. For cases in which no theoretical model can be used as approximation of such

loading, typically long time histories are required to capture the true coherence between the loads acting

on different load application points. This coherence has an influence on the stochastic response. Not only

the coherence between responses (which is of lesser interest to us) is affected by it, but also the auto-

spectral densities (or auto powers) of the individual responses depend on it.

To understand the severity of the need for long time histories better, we consider the case of an attached

turbulent flow, for which approximate analytical models are available (Corcos). A spectral Singular Value

Decomposition (SVD) analysis, which allows to decompose such a stochastic load into its constituting

orthogonal (deterministic) loads, principal components, and their importance as singular or principal

values, shows a very large number of only very slowly decreasing singular values. This means that a lot of

principal components are almost equally important, and it is not straightforward to say how small the

singular values of components should be to make it justified to remove them from the decomposition and

yet retain a sufficiently accurate (decomposed) description of the stochastic excitation. Therefore also for


wind noise, in which not only attached but also detached flow is expected, but which shows to some

extend many similarities with TBL loading, we expect that a decomposition of the stochastic loads will

need to keep a large number of principal components.

It can be shown that the maximum number of singular values that can be obtained when applying the SVD

on a PSD, is the number of averages that was used to derive that PSD using Digital Signal Processing

(DSP) methods. This means in the end that we should aim for an as high as possible number of averages,

to make sure the resulting PSD captures correctly the stochastic loads’ constituting components (principal

components) and their respective importance (principal values). However, the more averages used for a

given time history of input load signals, the shorter the time in each of the time segments becomes and the

more coarse the resulting frequency resolution in the obtained PSD. The only way to solve this is to use

long time histories, which is however also not always evident as the results in the presented case are

obtained using a transient compressible CFD analysis.

Assuming the obtained time histories are sufficiently long, the stochastic loads, also expressed on a large

number of loading points, represent a large set of data. Working with such large data sets can be tedious.

On the one hand there are the DSP operations (windowing, Fourier transforms and computing averages) to

be carried out on the core time data, which can take some time. On the other hand, depending on the

approach taken to compute the stochastic response, the stochastic loads, now represented by PSD matrices

covering all loading nodes and at all frequencies of interest, might need to be decomposed into their

constituting orthogonal components. In the latter case the loading components are applied as deterministic

loads before recombining their individual deterministic responses again into a meaningful stochastic

response result. Such a decomposition of large PSD matrices on many frequencies can be also quite costly.

This chapter further discusses the different approaches supported in LMS Virtual.Lab Acoustics, keeping

in mind the considerations laid out above.

3.1 Vibro-acoustic Transfer (VATV) Approach

The PSD matrix of responses is given by

T

XXYY HSHS .. (1)

where XXS is the PSD of the excitations and YYS is the PSD of the responses and H is the transfer

matrix. In the case of vibro-acoustic problem, H is called Vibro-acoustic Transfer Vectors (VATVs) and

relates the acoustic pressure Y (or YYS

as PSD) at the response microphones to the structural pressure

loading X (or XXS as PSD) on the nodes of the structural FEM model.

In order to obtain a converged, "smooth" PSD estimate from a given time series, the Welch's method is

used, which consists in performing separate Fourier transforms of partial segments dividing the initial time

series (usually with some overlap), and then using Real-Imaginary averaging the PSDs. This averaging

process is important as already mentioned above: it is the only way to converge as close as possible to the

actual stochastic content of the loading which will result later on in an accurate prediction of the stochastic

response. Assuming a statistically steady time signal, a smooth amplitude spectrum can be obtain in this

way, however with a lower frequency resolution, since each segment is naturally shorter than the initial

complete time series. The Vibro-Acoustic Transfer approach requires nothing more than the DSP

operations (including averaging) on the loading side. No decomposition of PSD XXS is required.

However, the approach requires for H to be known. For the case where the loads are applied on a large

number of surface elements, like on a car side window, computation of the transfer matrix H can be

prohibitive: hundreds, thousands of load cases would need to be computed to populate this transfer matrix.


However, if the number of response points is small, like a few microphones inside the car compartment,

and if only acoustic pressure results are desired, then the transfer matrix can be computed very efficiently

using the reciprocity principle [3,4].

3.2 Singular Value Decomposition

The previous approach is very efficient in the case where the number of response point is limited and only

acoustic pressure results are desired. A more generic approach consists in decomposing the input PSD into

principal components, then computing the response for each component, to finish with a re-combination of

deterministic response results to get the total stochastic acoustic response in the end.

Using a Singular Value Decomposition (SVD), the PSD of the excitation can be written as:

T

qqXX XSXS~

..~ (2)

where *~

X is the matrix of principal components or pseudo load cases (i.e. complex conjugate of the

singular vectors) and qqS is a diagonal matrix containing virtual autopowers (these are the singular values

in SVD terminology). The SVD used in equation (2) can actually be truncated to use only a reduced set of

principal components (the most important ones). The error made by truncating the SVD is directly

controlled by the last principal component kept. In the following simulations, a truncation ratio of 1% has

been used.

The response PSD YYS can then be written as:

T

qqYY YSYS~

..~ (3)

Where *~

Y is the deterministically computed response of the system, each column presenting the response

to one (kept) principal component.

Whereas it is not needed to know the vibro-acoustic transfer vectors in this approach, an extra

computational burden is found in the computation of the excitation PSD decomposition. The time

performance of the deterministic vibro-acoustic response computations (*~

Y ) will depend not only on the

size of the models (DOFs) used, but also on the number of load cases, principal components, to be applied.

To keep this to an acceptable level, the Principal Component Analysis approach allows us fortunately to

keep only the most relevant principal components. This keeps the computations feasible from a time

perspective, but we do have to give away some accuracy for this, albeit in a well-controlled manner.

3.3 Randomly reduced Cholesky decomposition

As explained earlier, the SVD decomposition given by equation (2) can be quite expensive especially for

PSD matrices representing excitation phenomena with small correlation lengths .i.e. when a large number

of principal components have to be retained. For such phenomena (e.g. Turbulent Boundary Layer),

almost all principal components have to be retained to capture the biggest part of the energy. In such

cases, a Cholesky Decomposition can be performed which is less expensive than an SVD but does not

provide any ranking information on the vectors of the resulting basis:

TLLSXX

* (4)

L is a lower triangular matrix. (Standard Cholesky decomposition leads to H

LLSXX in which case, one

can replace L by its complex conjugate).


Using only the non-zero vectors of L and writing HLY

the response obtained using those vectors as

excitation, becomes:

T

YY YYS

(5)

The Cholesky decomposition does not give any information on the relative importance of each of the

vectors. This means that, in theory, all of vectors have to be used by opposition to the truncated SVD that

allows reducing the number of RHS (right hand sides).

However, random sampling techniques allow reducing the number of excitations to be taken into account.

The approach consists in reducing the number of RHS to m using a random process:

LζX (6)

where ζ is a n*m complex matrix formed using random phases:

mnn

m

ii

i

iii

ee

e

eee

m

,1,

1,2

,12,11,1

21

1

ζ

(7)

where ]1,1rand[, ji . The m vectors X are often called realizations or random samples. They

represent possible snapshots of the loading.

Without random sampling the stochastic loads can be represented as the combination of randomly

(random phase) contributing Cholesky components (vectors in L), each of which are equally important.

T

LILSXX *

If we would measure the loading in time, and carry out a DSP on one time segment (no averaging) of

measured data, we can represent the obtained loads with a specific combination (specific set of phase

angles, one for each component) of the Cholesky components. However, when repeating the experiment,

we would find another specific combination, as in fact the Cholesky components are randomly

contributing for any measurement done. We could also construct the PSD of loads and find (again) that

only by averaging over the different measurements we will find the real stochastic nature of the loads.

This process of ‘measuring’ or taking ‘samples’ and averaging, can also be introduced mathematically.

XXSLLLξξLXX TTTT ****

(8)

(8) shows that , instead of representing the loads with all randomly contributing components, we can also

make random combinations of the components, as long as we take enough random samples. In case

enough random samples are chosen (m should be large enough but remain substantially smaller than the

number of Cholesky components, n, to provide the computational performance advantage), the forced

response can be rewritten,

TTTT

T

HSHHLξξLHYY XX

*****

(9)

The advantage of this approach is that the Cholesky decomposition is significantly faster than a

conventional SVD, and that the response computation is accelerated by using a reduced number of

components. However, there is no rule of thumb to know a-priori how many random samples should be

used to get good accuracy. This makes the error introduced less controlled and more depending on

application experience.


3.4 Averaging of input spectrum

Also in this approach, Welch's method is applied to the sources. The source time series is divided into

Nseg segments (overlapping or non-overlapping), a Fast Fourier Transform is applied to each segment,

and the Nseg deterministic source spectra are averaged to yield a unique smoothened deterministic source

spectrum: the acoustic response to this source spectrum is then obtained using the conventional

deterministic forced response system equations. This approach has the advantage that only a single

deterministic vibro-acoustic response problem has to be solved.

However, this loads averaging approach provides only spectrum magnitudes for the loads, and does not

consider averaging the phases. Considering that the phases of Fourier components of a quasi-random

turbulence signal may vary with uniform distributions in the [-π;+ π] range, the averaged phases would in

any case eventually converge towards zero, bringing all distributed loads exactly in phase with each other,

which is not physical. An ad-hoc solution is to consider that the phase of the Fourier components obtained

from the first segment are representative of the other segments, and patch this phase to the averaged

source spectrum. This is already more physical, but can still be far from accurate. At each frequency, the

resulting spectrum still assumes perfect coherence and constant phase angles between the loads at all

points. Such fixed phase difference is not to be expected for a stochastic loading acting on a large set of

points, for which many point pairs can be considered to be relatively (with respect to the correlation length

of the stochastic load) far away from each other. Consider two loads at two points, each generating the

same contribution on their own to a microphone receiver. In the approach explained here, the second load

can add up to 6dB SPL on top of the SPL caused by the first load or even cancel it, since the loads are

coherent. In case however the loads would be purely random, only 3dB SPL would be added by the

second load and it cannot cancel the contribution of the first load.

Nevertheless, this approach was retained as one of the methods to test, as it clearly will score well on

computation time. Again, only a single deterministic response is required. This approach has to be seen as

the more extreme shift to computational feasibility on the balance with the computational speed on the one

side and accuracy on the other. Therefore a comparison with Test results is needed to judge whether the

possibly limited amount of accuracy sacrificed justifies the shortcuts taken.

3.5 Time segmentation of input load

Another approach consists in postponing or transferring the averaging operations towards the acoustic

response side. The source time series is divided into Nseg segments (overlapping), a Fast Fourier

Transform is applied to each segment, and the acoustic response is calculated for each corresponding

source spectrum, then the responses of the Nseg acoustic spectra are averaged together in an energetic

(RMS) sense. Following equations clarify this approach further.

Suppose the response array Y containing the responses for only a single microphone but for all time

segments.

xNseg

yy121 Y

(10)

Suppose H the matrix of transfer functions and X the matrix of k excitations

NsegkNsegk

xk

x

x

xx

hh

,,

1,2

2,11,1

121

XH (11)


With (10) and (11), the average squared response in a single microphone response y can be written in

matrix form as

H'X'XHY'Y

NsegNsegMS

11 (12)

Here Y' represents the complex conjugate transpose of Y . When writing this matrix multiplication

explicitly as a sum with its terms, this yields

Nseg

t

k

i

k

ij

ititjjjtjtii

Nseg

t

titi

k

i

*

ii

Nseg

t

*

tt

hxxhhxxhNseg

xxhhNseg

yyNseg

MS

1

1

1 1

**

,,

**

,,

1

*

,,

1

1

11

1

(13)

In (13), we can clearly recognize a first term stemming from the excitations’ averaged auto-spectral

density and a second term representing the averaged result of the excitations’ cross-spectral density. In

fact this second term can/should be interpreted as the response of the excitation’s averaged cross-spectral

density. This second formulation contains a small but important nuance. For pure random loads, this term

will eventually vanish for sufficiently large Nseg . For partially coherent excitations this term will never go

to zero and thus it contributes to the mean square SPL results. Therefore (13) shows that even when we

average on the response side, we also should catch the contribution of the averaged, and therefore

converged, auto-spectral and cross-spectral densities. Finally the root of (13) can also be taken to obtain

the amplitude of simulated response in Pascal.

The advantage of this approach is that there is no need to compute all the products and terms as shown the

second line of (13). We can simply use the implementation as given in the first line of (13) using only the

microphone responses of the different time segments. This allows to avoid storing a large input PSD

matrix XXS . Moreover, no decomposition of any PSD is required and also no set of transfer vectors H

needs to be computed upfront.

3.6 Comparison of all methods

All methods presented above have been applied to the HSM case for which only the left window is

excited and for the case 110 km/h – 0 deg yaw. This allows to compare accuracy and performance of each

method on a simplified case. Conclusions drawn in this section will be applied on the full test case with

all excited windows and all flow conditions and compared to measurement data.

Since time data is available for about 0.5s and 20 000 time steps, averaging and time segmentation is

performed on blocks of 1071 time steps, corresponding to a frequency resolution of 40 Hz. An overlap of

50% is chosen which leads to a total number of 38 data blocks.

Figure 6 shows the SPL obtained at the driver’s ear for 3 simulation approaches: VATV, SVD and time

segmentation of input load. It can be seen that results are almost identical for each approach. It can be

noted that using 1% truncation error for the SVD leads to very accurate predictions. In this case, the rank

of the decomposition remains equal to the number of averaged blocks (38), all principal components are

above the chosen threshold.

As expected, these three methods have similar level of accuracy, however, it is expected that they will

have different performance results.


Figure 6: Comparison of SPL results obtained with approaches leading to no accuracy loss

Figure 7 shows the SPL obtained at the driver’s ear for 3 simulation approaches leading to loss of

accuracy. 10 random samples have been used (out of 38 Cholesky components) for the randomly reduced

Cholesky decomposition. It can be seen that the approach based on randomly reduced Cholesky

decomposition leads to moderate loss of accuracy with a slightly less smooth spectrum and a maximum

deviation of 4 dB compared to the SVD approach considered as reference. Considering the moderate

accuracy loss, this approach is seen as very attractive given the fact that performance improvements are

expected both on the decomposition phase and also on the vibro-acoustic response phase (number of load

cases reduced by a factor 4).

Approach based on averaging of input spectrum leads to more inaccurate predictions with a deviation up

to 28 dB at some frequencies compared to the SVD approach. The spectrum clearly appears as less

smooth which is due to the lack of phase averaging associated with this approach (phase of first block is

retained, only the amplitude is averaged). Although a huge performance gain is expected with this

approach, it is not considered as accurate enough and is therefore not recommended.

Figure 7: Comparison of SPL results obtained with approaches leading to accuracy loss


Table 1 shows the performance associated to each computation approach. It can be seen that storage space

for methods using a PSD matrix as input (VATV, SVD and Cholesky decomposition) is very important

with 20 GB of disk space required. In this model, only nodes from the left window are loaded (4319

nodes), therefore the PSD matrix has a size of (4319*4319). In the case where all windows would be

loaded, the storage requirements for the PSD matrix would be even higher. The time to compute this

matrix is not indicated here as it is negligible compared to the other steps. Approaches based on input

spectrum averaging and time segmentation require much less disk space (less than 0.3 GB) as only based

on vector data.

The time for decomposition is significantly reduced by using a Cholesky approach compared to SVD,

going from 40 minutes to 3 minutes. This makes the Cholesky decomposition very attractive. However,

there is no ranking of components in this case, which makes the error introduced by the random sampling

approximation less controlled.

VATV SVD Randomly reduced Cholesky

Averaging of input spectrum

Time Segmentation

Storage space for Input Data (PSD

matrix or Vectors) 20 GB 20 GB 20 GB 0.01 GB 0.3 GB

Time for decomposition

- 40min 3min - -

Time for solving 1h20 1h34 1h25 1h12 1h34

Table 1: performance results for each computation approach

The number of load cases to be solved in the Vibro-acoustic analysis depends the method used (38 for the

SVD approach and Time segmentation approach, 10 for the randomly reduced Cholesky approach, 2 for

the VATV approach with 2 field points and 1 for the input spectrum averaging. It can be noticed that this

had little impact on the solving time. This can be explained by the fact that the MUMPS solver used here

is a direct solver which very efficiently handles multi-load case analyses [5].

Comparing the two excitation PSD decomposition approaches, using SVD and Cholesky, it should be

mentioned that the Cholesky has proved to outperform the SVD on the wind noise cases the authors

examined so far. Cholesky therefore is preferred over SVD. Still however, in order to keep the

computations limited and feasible, a reduction of load cases is required, which can be achieved using the

random sampling technique. Since there are no clear heuristics available to know how many random

samples should be taken, this remains to be discovered by the engineer by building experience per

application by carrying out some convergence studies.

In order to avoid the decomposition of excitation PSD matrix XXS , which represents clearly an important

contribution to the total simulation time and feasibility, there are three methods left.

The averaging of the input spectrum as deterministic spectra will clearly be the best performing with

respect to computation time, but it appeared from the test case that we have not enough guarantees when

it comes to accuracy.

The vibro-acoustic transfer approach remains interesting whenever the response is required in only a few

microphone points, as in such cases the transfer matrix can be computed in an elegant reciproque way.

As the system transfer is known from this point onwards, the methods also allow to easily apply a new set

of wind loads, for instance after a change in vehicle speed or (yaw) angle with respect to the mean

direction of the approaching wind. Given these considerations, and under assumption that the

computation (DSP and averaging) and storage of the excitation PSD is not an issue, the authors point out

the vibro-acoustic transfer approach as one of the better methods.


The time segmentation method turned out to be promising as well, as it preserves the accuracy that can be

obtained from a given time series, yet doesn’t require any lengthy or tedious operations on the large

excitation PSD matrix. Because of its simplicity in implementation – in fact we are carrying out a

standard NVH response scenario for Nseg time segments –, the computational advantages that the latter

brings, and because of its preservation of accuracy (inherent to the length of the given time series of CFD

results), the authors advise to use the time segmentation approach, and favor it over the other approaches.

4 Validation of the best approach on the full test case

Above analysis indicated that time segmentation of the input spectrum is the recommended approach for

handling windnoise loading as it shows best compromise between accuracy and performance. This

approach will now be used to validate the full simulation process on the HSM model loaded on all three

glass panels and results will be compared to wind tunnel measurement data.

Figure 8 shows the HSM model which is solved and some results at a given frequency in terms of window

vibrations and interior SPL on a plane field point mesh. The model is solved using the approach described

above. The CFD pressure loading on all glass panels is pre-processed by creating time segments of 1071

samples and 50 % overlap which leads to 38 blocks. After converting these time blocks into the frequency

domain, the vibro-acoustic response is computed for each of these 38 load cases and the global response is

then computed by averaging the results in a RMS sense.

Figure 8: HSM simulation model with vibrating windows and computed SPL in cabin.

Figure 9 shows the comparison between simulated and measured SPL in the cabin for the case of 110

km/h and 10 deg yaw in third octave bands. The trend and absolute level as a function of frequency are

well captured by the simulation model. Given the complexity of the problem, the accuracy is considered to

be extremely good. The performance with respect to memory consumption is also considered to be good

with a disk storage less than 1 GB and also the time performance is good with a computation time of less

than 4 hours from 100 Hz to 4 kHz with a frequency step of 40 Hz on a 4-core Intel Xeon E5-1903 2.8

GHz machine with 64 GB of RAM.


Figure 9: SPL result for the 10 deg yaw 110 km/h

An increase of SPL by changing the yaw angle from 0 to 10 deg is shown in Figure 10. It can be observed

that the trend is well captured by simulation although a slight over-estimation of the SPL is noticed. Figure

10 also shows the increase of SPL for a flow speed increase from 110 km/h to 130 km/h. Both trend and

absolute levels are well captured by the simulation, especially at frequencies above 500 Hz.

Figure 10: Left: effect of Yaw angle at 110 km/h – Right: effect of the flow speed at 10 deg yaw

5 Conclusions

In this paper, different modeling approaches have been investigated to predict automotive windnoise with a

stochastic nature. Unsteady pressure loading is provided by a transient CFD analysis. The surface pressure

fluctuation is then applied as structural loading on flexible glass windows. It was shown that the approach

based on time segmentation of the input data is the recommended approach as it is the best compromise

between accuracy and performance. This method was applied and validated on a scaled simplified model and

compared with measurements obtained in a wind tunnel. The agreement between simulation and

measurement is very good in terms of absolute noise level but also to capture to effect of yaw angle and flow

speed. This demonstrates the ability of such simulation process to accurately capture windnoise phenomenon

on realistic cases.


References

[1] LMS Virtual.Lab Revision 13.1 User’s manual

[2] T. ten Wolde, J.W. Verheij and H.F. Steenhoek, Reciprocity method for the measurement of

mechano-acoustical transfer functions, J. Sound Vib. 42, 49-55 (1975).

[3] B.-K. Kim, J.-G. Ih, In-situ estimation of an acoustic source in an enclosure and prediction of

interior noise by using the principle of vibro-acoustic reciprocity, J. Acoust. Soc. Am. 93(5), 2726-

2731 (1993).

[4] Vansant K. (2012), Latest developments in solving large simulation models in view of pass-by noise,

AIA-DAGA Conference 2012.

[5] P.R. Amestoy, I.S. Duff, J.-Y. L’Excellent, Multifrontal parallel distributed symmetric and unsymmetric solvers, Computational Methods for Applied Mechanical Engineering, (2000) 184, pp. 501-520.


a case study for predicting wind noise inside a car

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