Use of sound “Phonons” in the modelling and optimization of automo- tive acoustic systems in 3D

R.Morris-Kirby 1 Adler Pelzer Group Gmbh Advanced Acoustics Research Laboratory Padstow, Cornwall, England E.Harry 2 Adler Pelzer Group Gmbh Advanced Acoustics Research Laboratory Padstow, Cornwall, England

ABSTRACT Automotive manufacturers demand components with an ever higher acoustic performance combined with lower environmental impact, tuned to the emerging EV market, and are pres- sured into reducing lead times and prototype investment. Consequently, there is a desire for enhanced simulation techniques, utilizing advanced methods. The three-dimensional aspect of many palliative treatments can be shown to afford significant benefits to their acoustic perfor- mance, both in their transmission loss and random incidence absorption characteristics.

Virtual system engineering enables construction fundamentals to be created in CAD, but often acoustic treatments are chosen based on flat sample performance or simple power balance models. These do not tell the complete story. Current acoustic simulation techniques such as SEA, may present the model in a 3D environment to aid in visualization but, solving is done on a 2D matrix basis, and does not account easily for diffusion and refractive interaction caused by the complex shape of the component under investigation. BEM and FEM techniques are 3D based simulations but have a host of limitations due to mesh density and available processing power. Constructing models of individual palliatives such as wheel arch liners, dash insulations or carpets using such techniques may be of academic interest but of restricted use in the pres- sured world of component design and manufacture. It is not helped by the need to furnish the model with accurate, validated, material performance data. A modelling procedure was re- quired that could import component CAD from the product design team and rapidly create an acoustic model that could accurately predict its performance in both a transmission loss suite and associated random incidence “Alpha cabin” absorption test. Thus, short circuit the need for at least one if not more prototype test phases or enable quotations for new business to be formulated with a higher degree of clarity. Subsequently to export results from this model into a range of “full vehicle” modelling environments or compare to prototype test results. After considerable research the authors created and validated a toolbox approach using a com- bination of open-source code together with bespoke modifications and defined processing pro- cedures.

1 Rod.morris-kirby@adlerpelzer.com

2 Evan.Harry@adlerpelzer.com

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1. INTRODUCTION

The approach discussed in this paper can be considered similar to that of ray-tracing, however instead of sound rays, imaginary particles called Phonons are used to carry the energy, similar to Quantum mechanics. In the ray-tracing method, each sound beam carries an intensity whose amplitude decreases propor- tionally with the square of the propagation distance, thus simulating the acoustic radiation of a spher- ical source via geometrical dispersion. Whereas each Phonon carries an elementary energy ǫ, the amplitude of which does not vary as a function of the propagation distance. The physical phenomena likely to occur during propagation (reflection, absorption, diffusion, atmospheric absorption) are not considered in the same way in the two approaches. In the "sound rays" approach, these phenomena take the form of a weighting applied to the sound intensity carried by a ray. For example, in contact with an absorption coefficient wall α, the intensity of the radius after reflection will be weighted by the coefficient (1- α). In the Phonon approach, some of these physical phenomena can be considered probabilistically. In contact with a surface whose absorption coefficient is α, the Phonon may for example have a proba- bility (1- α) to be reflected, and a probability α to be absorbed. In the latter case, it disappears from the domain of propagation. One of the major advantages of the concept of Phonons lies, above all, in considering the diffuse reflections on the walls and the diffusion reflection by congested areas, such as inside a complex structure like an instrument panel or a wheelhouse or engine bay. In the sound ray methods, the reflection by the walls is determined by image-source methods that only allows "specular" type reflections, perfectly deterministic, and this prohibits considering the phenomena of "diffuse reflection". In the Phonon approach these diffuse reflections are considered in a probabilistic way and the reflex angle can be chosen according to a variety of arbitrary reflection laws, examples shown on figure 1. It was found that the Lambert reflection law was the most suitable for our automotive studies.

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Figure 1. Reflection Laws available. It is also the same in considering the diffusion by objects distributed in the medium of propagation (such as the power unit in an engine bay for example). In the "sound rays” approach, it is necessary to know exactly the shape and the position of the object to calculate in a deterministic manner the angle of reflection of a sound beam on the object. In the phonon approach, scattering objects can be considered statistically, with no knowledge other than their spatial distribution and mean shape,

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which significantly reduces the costs in terms of calculation and definition of the field of study. This statistical (or probabilistic) description, which can be generalized to most of the physical phenomena involved in the propagation of sound, is therefore the great strength of the “phonon" approach to the "sound rays" approach.

2. THE I-SIMPA GUI

The open-source code “ i-Simpa ” [2] enables the creation of an acoustic model using Phonons and this application also includes access to the Tetrahedral “mesher” and the SPPS solver executable. This powerful and well documented software can be configured with additional plug-ins written in Python to accommodate the users’ preferences and post processing activities. From an automotive perspective, full vehicle models have successfully been created and validated using relatively simple models. However, the authors have successfully modelled in i-Simpa using original high resolution CAD data from vehicle body systems via mesh conditioning in an intermediate application, also open source, called “Blender”. The flow diagram used for modelling is shown in figure 2. Typically, CAD for a vehicle dash or firewall contains over 1 million elements (or faces) and this would produce an unacceptable computational load on the tetrahedral volumetric mesh and SPPS solver applications executed by i-Simpa. It is also not necessary to maintain such a high mesh density due to the proba- bilistic nature of the solver. Blender enables the model to be simplified whilst still maintaining its 3D shape and significant spatial detail. The Tetrahedral mesh also requires a bounded propagation me- dium, and it is at this stage that items such as an anechoic test chamber, Noys box fixture and any associated hardware are added prior to transferring the model to i-Simpa.

Figure 2. Flow Diagram showing Modelling Sequence

2.1. Extending the dynamic range

Proof of concept studies using this method showed its overall usefulness but also that the maxi- mum transmission loss (STL) dynamic range was less than 60dB. For many models this would be sufficient but vehicle acoustic systems such as firewalls regularly exceed 60dB STL, especially when considering only the palliative component of the system and ignoring leakages. Figure 3 compares the available dynamic range of the SPPS solver with that expected from typical flat sample acoustic material lay-ups backed by steel metalwork. The limiting transmission loss of just below 60dB being insufficient for modelling high performance acoustic treatments. The solution was to use a material

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performance compression function (called a QFF) which acts in a similar way to that used in early high-performance tape recorders. The QFF forces the solver to work with materials whose transmis- sion loss performance is pre-conditioned by the value of the QFF to be lower than either their meas- ured or predicted performance. The values used for the QFF are chosen arbitrarily but have to ensure that no transmission loss above 60dB is applied to the solver as the result will not be accurate. It is possible to use such a function because each 3 rd octave band in the solver is a separate solution and does not infer anything from adjacent bands. After solving the resultant transmission loss is corrected by re-applying the QFF function across the response microphone array. Figure 4 shows that trans- mission loss results above 100dB can be successfully modelled.

Figure 3. Use of QFF Function to Extend the Dynamic Range.

2.2. Validation of flat material samples

The Proof-of-concept studies also included a series of validations starting with flat samples in both a transmission loss suite, described in more detail later and an Alpha cabin. Apart from spatially homogeneous samples which proved trivial to the solver these also included modelling flat samples that were spatially divided into areas of varying thicknesses. The SPPS solver provides sound pres- sure responses for microphones juxtaposed as per ISO 15186 test standards and the calculated trans- mission loss compared to traditional modelling software, see figure 4. A separate model of the ubiq- uitous “Alpha cabin” was constructed that allowed both flat samples to be laid on the floor of the cabin as well as vehicle systems that could be “virtually” suspended inside the cabin, see figure 5. A variety of acoustic parameters can be post processed including the reverberation time inside the cabin using Impulse response a nd Schroeder integration and figure 6 compares the predicted response of a fibre based flat sample using APG Protein (a TMM solver) with results from the SPPS solver.

3. CONDITIONING OF VEHICLE SYSTEM CAD

A significant number of proof-of-concept studies were carried out covering detailed double wall vehicle systems, HVAC ducting and pass-throughs which are not included in this paper but were essential to increase confidence with the method. Once these were completed the next phase was to model a complete dash system (firewall) directly from CAD. The CAD data encompassed both the body-in-white and the insulation thickness profiling.

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Figure 4. Transmission Loss Comparison of SPPS versus Pexmet for a tri-partite split flat Sample.

Figure 5. Model of an Alpha Cabin with a Flat Sample Installed.

Figure 6. Random Incidence Absorption Comparison of SPPS versus APG Protein.

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To enable a “blind validation” of the method, one set of the actual hardware was installed into a transmission loss chamber and tested to ISO 15186 and another installed in a small reverberation room (Alpha cabin) for measurement of the random incident absorption coefficient. Both modelling and testing was carried out by separate teams so that neither the model nor the test could be influenced by each other. The acoustic model was configured and solved in the UK with testing carried out in Italy.

Figure 7. CAD of Body Dash Figure 8. Thickness Profile Map of the Dash Insulation

The body-in-white CAD is shown on figure 7 and this was cropped at the tunnel as it would be in the transmission loss suite. The dash insulation thickness profile mapping is shown on figure 8 and was used to create a set of acoustic material characteristics. The acoustic model was constructed by installing the dash system into one side of a rigid non-transmitting cube, called a Noys box. The complete assembly was then placed into a large model of an anechoic chamber in order to provide a bounded environment for the tetrahedral mesher. Figure 9 shows the model inset into the cube show- ing the application of the average thickness profile and areas that were correspondingly overkilled in the test rig. The dash area contained 2205 individual faces. Figure 10 shows a transparent image of the model with the green dots as response microphones and the excitation source inside the Noys box as a red dot. The green lines emanating from each microphone location are used for intensity orien- tation purposes. The corresponding photographs of the dash system during testing are shown on fig- ures 11 and 12. The pass-throughs were overkilled using metal panels and additional insulation.

Figure 9. Layout of Acoustic Model Showing Average Thickness Zones.

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Figure 10. Acoustic Model Showing Response Microphone set and Excitation Source.

Figures 11 and 12. Photographs of Dash System Installed in the Transmission Loss Chamber. 3.1 Transmission loss validation Figure 13 compares the results of the model versus the test rig in both bare metal and when fitted with insulation treatment. The error bars in the chart represent spatial deviation across the model surface and those of the test rig, with the average transmission loss as solid lines for the model and dotted for the test rig. These results show acceptable validation of the model. The slight over predic- tion in the mid frequencies was considered acceptable bearing in mind the laboratory-to-laboratory deviation variability allowed in ISO 15186 of 2dB.

Figure 13. Comparison of Test versus Predicted Transmission loss.

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3.2 Random incidence absorption validation The second part of the validation procedure involved comparing measured versus predicted random incidence absorption of the dash insulation. The 3D nature of the dash insulation required it to be absorption tested using a fixture provided by the appropriate area of body-in-white. Ideally this would have had the fixture oriented as in the vehicle, but this was difficult in practice, so the dash system was laid down as shown in figure 14.

Figure 14. Photograph of the Dash System Installed in the Alpha Cabin.

Orientation was not compromised in the acoustic model and the dash system was suspended by virtual “sky hooks” inside the Alpha cabin as shown in figure 15. The orientation of the excitation source in the simulated alpha cabin allows only the insulation side facing the source to be included in the prediction. This is a useful feature and reduces the necessary complexity of this model.

Figure 15. Acoustic Model Installed in Simulated Alpha Cabin.

A comparison between predicted and measured random incident absorption is shown in figure 16. Considering the constraining effect of the dash system inside the actual alpha cabin the results of the validation were acceptable.

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3.3. Optimization algorithm

The final stage of the study considered modifying the thickness of the insulation decoupler, in this case Polyurethane foam, to achieve an increase in transmission loss. Modifications such as these must consider the strict packaging requirements of the dash system. One type of optimization, the “brute force” method would consist of varying each area of the model in turn within the packaging con- straints and re-solving. Whilst possible this would involve a massive computation, unless the model was very simplistic. The chosen optimization procedure involved a blending of the traditional power balance model with the Phonon model.

Figure 16. Comparison of Tested versus Predicted Random Incidence Absorption.

This was Carried out by extracting the spatial zone information (as shown in figure 9) together and forming a relatively straightforward 2D power balance model in MS Excel that was fed by a material database matrix that contained a wide variety of materials and thicknesses. Whilst this model did not have the 3D complexity of the Phonon model it can be manipulated very easily using the generalized reduced gradient non-linear solver inside MS Excel [3]. Appropriate constraints were applied to each zone. A least squares reduction was engaged which compared the baseline STL to the chosen target. Solutions proposed were evaluated and where acceptable these were introduced into the Phonon model for final validation. Whilst not a true optimization within the Phonon domain this proved a very efficient method, where only a handful of Phonon model “builds” had to be considered. Figure 17 shows the revised thickness map for each zone compared to the baseline solve following a requested 1dB increase in transmission loss by the optimizer. Figure 18 shows the corresponding transmission loss result.

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Figure 17. Optimized Decoupler Thickness for a 1dB Increase in STL.

Figures 18 and 19. Transmission loss and absorption after optimization As expected, increasing the transmission loss reduced the surface absorption and this is shown in figure 19. It would have been possible to optimize just for absorption, or transmission loss or a com- bination using this power balance approach depending on project requirements with the final proposal being solved in the Phonon model. 4. CONCLUSIONS

A method of modelling acoustic systems in 3D using Phonons has been described and validated firstly using simple flat samples then for a complete vehicle dash system directly from CAD. The validation results for both transmission loss and random incidence absorption were considered acceptable. It was then shown that an efficient optimization routine could propose modifications to the insulation thickness without the need for “brute force” solver iteration. This method allows detailed models of vehicle systems to be created with considerably more spatial detail than normally available with other modelling techniques. 5. REFERENCES

1. https://i-simpa-wiki.readthedocs.io

2. Dr J. Picaut of the “French Institute of Science and Technology for Transport, Development and

Networks (Ifsttar), Environmental Acoustics Laboratory (LA

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