I. Introduction

Pass-By Noise (PBN) is airborne substantially with high energy at about 500 Hz - 2000 Hz. Thus, it is sensitive to human ear and regarded as a serious environmental problem. Particularly it does matter in European cities with high population density and correspondingly the related regulation has been strengthened. The latest regulation, Economic Commission for Europe (ECE) R51-03,^[1] requires that PBN meet 68 dB for a newly manufactured vehicle entering markets since 2024, and now manufacturers should consider noise emitted from a vehicle at constant speed as well as in acceleration condition by the revised measurement method, ISO 362-1:2015.^[2] Most of the vehicle manufacturers have already studied PBN for long time,^[3,4] of which approaches were normally limited to experimental works.

Meanwhile, as an Electric Vehicle (EV) is becoming important, the noise radiated from an internal combustion engine decreases and tire-induced noise becomes a great concern reversely. Consequently, it seems that PBN studies are also focused on the EV and one can imagine that most of the noise of the EV is responsible for tires. The most effective way to reduce tire-induced PBN may be to control directly the emission from the tire itself. However, recent studies show that the maximum difference of tire-radiated noise is up to about 2 dB for the Close-ProXimity (CPX) trailer test^[5] and 6 dB for the chassis dynamo test^[6] even for the tires with the same noise label. Such uncertainty of the noise source implies that countermeasures only on the source may not be enough and probably additional countermeasures are required. In this context, path contribution studies are often considered. One example of the case shows that an acoustic panel under the powertrain can be a possible solution for PBN reduction.^[7]

It should be noticed that they are carried out mostly by experiment approaches. Nevertheless, it is clear that a simulation-based method can be a convenient alternative compared to experiments in several aspects. In this regard, one previous study^[8] shows that the experimental work with the application of acoustic treatments to reduce acoustic transfer function experiences a lot of time and cost, and use of simulation can reduce such resources. In terms of source, establishing a simulation model for a tire may also need to be considered. Although there are several methods are known including Finite Element (FE) tire and wave-guide FE tire,^[9,10] it seems that the accuracy to cover PBN or long calculation time remains to be overcome. This is because dynamic modelling of non-linear characteristics when rubber contacting the ground is very difficult and the exact mechanism of noise radiation from the contacting area is not fully understood yet.

Considering studies mentioned above, it may be an efficient approach using a simulation model comprising acoustic treatments combined with experimental source data. Fortunately, practically useful studies to define tire source by experimental approaches are known,^[11,12,13] which will be recalled later. The simulation study in this paper is based on the previous study^[8]dealing with acoustic transfer function, but takes it one step further to estimate PBN itself in the framework of simulation and also to find efficient countermeasures.

This paper largely consists of four parts. First, some theoretical backgrounds are explained to quantify the strength on a tire as acoustic source. Second, how to quantify the source from experiments and a simulation model to give exterior acoustic transfer function are introduced. Third, the simulated results are verified and then PBN is predicted by multiplying source and transfer function. Experimental work was also accompanied, whose results are used as basic information for simulation and for validation. Finally, countermeasures using acoustic absorption treatments are studied from the viewpoint of simulation as well as test. A mid-sized electric Sport Utility Vehicle (SUV) was taken into account.

II. Theory for pass-by noise estimation

The most difficult task in this study is how to define the strength of acoustic radiation from a tire as a source. Although one of straightforward methods will be to use an appropriate simulation model of a tire, it seems that there are still some limitations as mentioned above. Therefore, an indirect approach deducing source strength is chosen in this study instead of directly making a simulation model.

In this context the short cut may be to utilize experimental data already existing because measuring tire noise has been tried for long time. Also there have been studies to identify acoustic source strength by inverse method.^[11,12]

For estimation of tire source, two steps are carried out in this study. Those procedures to quantify source strength are the same as explained in the reference^[13] and this paper only gives some equations to help readers understand this study.

First, the number and the position of monopoles will be chosen by an optimization algorithm, so-called Lasso algorithm.^[14,15] Acoustic pressure at the reference microphones in the nearfield generated by equivalent monopoles will give a relationship in a matrix form as^[13]

where H is an acoustic transfer function matrix of a tire,

is the pressure at the positions of reference microphones with the number of reference microphones M, and

is the strength (i.e. volume velocity) of monopoles with the number of monopoles N.

For all frequency points considered, the Lasso algorithm for optimization will be defined as^[9]

where p_near is acoustic pressure measured at the reference microphones in operating conditions, ω_k is angular frequency at frequency point k,

and τ is a regularization parameter for the Lasso optimization.

Note that Eq. (5) is mixed ℓ1,2 norm of Q containing volume velocity vectors q. Using Eqs. (4) and (5) the total strength of volume velocities can be distributed along the monopole sources in the frequency range considered. The Lasso algorithm tries to minimize the squared difference under the constraint that the overall ℓ1,2 norm does not exceed a given τ. If τ is lower, the algorithm will take a smaller number of non-zero equivalent sources, which leads to identification of the best position to minimize the squared difference. The results will be shown in the following section.

Second, after the positions of monopoles are fixed, the strengths of the monopoles can be determined by the regularization problem as^[11,12,13]

Instead of directly finding q by minimizing error matrix e, another approach using an alternative definition of the cost function to be minimized is suggested, which is so-called Tikhonov regularization as

where β is a regularization parameter for the Tikhonov regularization. If β is bigger, the optimization process will penalize the solution more, which means the solution q is high in a relative sense. Then the solution for the Tikhonov regularization will be as follows.^[11]

where Γ is a pseudo-diagonal matrix, V, U are unitary matrix, H means the Hermitian. Note that the diagonal elements of Γ will be like σ/(σ² + β), and thus β will increase any small singular value σ in particular, which leads to the stabilized matrix inversion. Parameter β is basically obtained by trial and error to give minimum error seen in Eq. (7).

Finally, PBN can be obtained by

where p_PBN is acoustic pressure indicating pass-by noise calculated by acoustic transfer function of a vehicle T and strength of monopoles previously calculated q. Note that T is obtained by simulation strength of monopole being unit, which will be explained later.

III. Modelling of sources and transfer functions

It can be said that the advantage of simulation is that separation of design variables is relatively convenient and one can easily try them if the performance meets the target. This study thus tries to separate source and path corresponding to experiment and simulation respectively. They are strength of monopoles q and acoustic transfer function of a vehicle T. That is, they are evaluated and either one or both is investigated instead of investigating PBN itself. In this manner, a target may be achieved efficiently.

3.1 Defining tire sources

It is assumed that the whole noise radiated from a single tire can be made up of many monopole sources along the tire circumference. An initial placement of such monopole sources is shown in Fig. 1 (left), where 16 monopole sources are placed. Initially, the number of monopole sources was investigated between 16 and 31, which resulted in no meaningful difference. Thus, the minimum number is chosen for rapid calculation. Volume velocity of the monopole can be inversely deduced from sound pressure measured microphones (i.e. reference microphones, see Fig. 1 right) placed in the nearfield of acoustic radiation. Sound pressure on the reference microphones can be measured under the prescribed conditions either in the indoor test in the semi-anechoic room with chassis dynamo or in the outdoor test which is the case in this study.

Fig. 1.

(Color available online) Candidates of monopole sources (left) and set-up of reference microphones in the acoustic nearfield of tire (right).

Once acoustic transfer function H for a tire from reference microphones to monopoles is measured, volume velocity of the monopole under real driving condition can be deduced from the measurement of the reference microphone under the same driving condition.

As explained in the previous section, the number of monopoles is chosen by a mathematical optimization, the Lasso optimization. Fig. 2 (left) shows the selected monopoles from the initial configuration. On the right, how the monopoles are selected is shown. Yellow bar means the source is turned on at some 𝜏, a regularization parameter and blue bar means turned off. In this manner, 8 sources are selected basically by trial and error^[13] and it is expected that modelling of tire source becomes easier and calculation efficiency is enhanced with smaller numbers of monopoles.

Fig. 2.

(Color available online) Selected monopoles from the candidates of the front tire (left) and selection of monopoles by parameter 𝜏 (right).

Then the strength of the selected monopole is calculated by Tikhonov regularization as in Eqs. (7) and (9). Fig. 3 shows one example of the strength calculated at monopole No. 1 of the front tire. The data are shown in frequency domain as well as in vehicle position as they are inversely calculated pressure measured in the driving condition. One can notice that the strength is in similar level with respect to the position, which means the vehicle is running in the constant speed.

Fig. 3.

(Color available online) Strength of monopole No. 1 at the front tire in the constant speed 50 KPH.

It should be noted that the front and the rear tires are separately identified using the same procedure explained above. However, the left and right tires are assumed to be the same. This is fairly acceptable as the exterior configuration of the vehicle is symmetric and there is no asymmetric contribution in terms of acoustic radiation from the EV.

3.2 Modelling of exterior cavity for acoustic transfer function

Use of acoustic treatment outside the vehicle can be a practical countermeasure to reduce PBN, while reduction of source itself will be relatively difficult. In addition, measuring T is convenient but measuring with various acoustic treatments is bothersome and takes long time. On the other hand, using simulation to get T must be faster and easier. Ranking the effectiveness of different treatments will be even more advantageous once the model is ready. Thus, this study aims to use simulation-based acoustic transfer functions of a vehicle.

Fig. 4 (left) presents the exterior CAD of the vehicle that is used for modelling an exterior cavity for simulation. The simulation model is also shown in Fig. 4 (right), where the exterior cavity is made of 2 layers. Meshes in cyan are modelled for nearfield acoustic cavity and magenta layer, so-called Adaptive Perfectly Matched Layer (APML), for infinite acoustic field respectively. A commercial software MSC.Actran is used. The acoustic cavity covering the vehicle exterior was carefully made where the vehicle’s exterior skin is assumed to be watertight. The skin is basically rigid but comprises plastic trims, which are the wheel house liners and the panel under the e-motor. The shape of the front and rear tires was captured when suppressed by the vehicle weight. There are acoustic gaps between a tire and vehicle boundary such as wheel house. They are also modelled as acoustic elements, which can be converted to absorptive materials (sound packages) for design study.

Fig. 4.

(Color available online) CAD of the vehicle (left) and the simulation model for exterior acoustic cavity (right).

As the sources are quantified and the acoustic transfer functions are available, PBN will be obtained by multiplying them as in Eq. (10).

IV. PBN test and validation

4.1 Validation of acoustic transfer function

PBN outdoor test was carried out at Autoneum proving ground in Biel, Switzerland (Fig. 5). Weather including climate was taken into account and tests were repeatedly carried out to secure minimum test deviation. The microphone placed in the center line (0.0 m position) of the test track is to measure PBN. The other microphones in this figure are just to get some additional data. PBN is actually measured from –10.0 m to + 15.0 m positions when the vehicle moves along the test track as seen in the later section in this paper.

Fig. 5.

(Color available online) PBN testing at the proving ground in Biel, Switzerland.

Before combining source and transfer function, it is essential to check the accuracy of the simulated acoustic transfer functions. Two curves of acoustic transfer functions of the vehicle, measured in the outdoor test and calculated by simulation with respect to 1/3 Octave bands, are compared in Fig. 6. Only from monopole sources No.1 and 16 of the front right tire to PBN microphone are shown here. They are in good agreement with maximum difference of 1.6 dB in 500 Hz ~ 2000 Hz and simulation accurately estimates acoustic transfer functions.

Fig. 6.

(Color available online) Comparison of acoustic transfer function of the vehicle with respect to 1/3 Octave bands {upper, source at the front Right-Hand (RH) tire No.1; lower, source at the front RH tire No. 16 as shown in Fig. 1. Blue, outdoor test; brown, simulation}.

4.2 Reconstructed PBN using a hybrid approach

PBNs measured directly in the outdoor test and calculated one as in Eq. (10) are compared in Fig. 7. The horizontal axis in the figure means the longitudinal distance between the vehicle and the PBN microphone. The maximum difference of two curves is less than 0.5 dB and they are in excellent agreement for both driving conditions. Especially note that the curve pattern of the hybrid method follows well the experimental curve. Thus it can be said that the hybrid approach tried in this study is reasonable and the simulation model can be conveniently used to minimize acoustic transfer function of a vehicle.

Fig. 7.

(Color available online) PBN curves measured directly in the outdoor test and reconstructed by a hybrid method. Acceleration test (upper) and constant speed test (lower). Red dot, outdoor test; sold black, hybrid method.

In addition to the accuracy, one can notice that there are two smooth but clear peaks just before and after 0 m. That is, just before and after passing the PBN microphone (0.0 m position) PBN increases. As PBN mainly comes from tires of the moving vehicle, it seems that the acoustic radiation parallel with the moving direction is larger than in the normal direction. Such founding that most contribution lies in the parallel direction of the vehicle is known in the reference.^[16] Meanwhile, the reason why the second peak for the acceleration condition is larger is not clear. One possible reason is the larger contribution from the rear tire, where there are no particular undercover unlike front tire area equipped with the under panel as seen in Fig. 4. More study investigating this reason may be necessary.

V. Design study

As already mentioned, the hybrid method should be efficient to find countermeasures for PBN reduction. This study considered acoustic absorption treatment, so-called sound packages attached to the underbody. Sound packages may be attachable on under the e-motor, under the floor, and inside the wheel house, and they are categorized into 4 representative packages for convenience as shown in Fig. 8. Stating the details of material properties of the sound packages is beyond this study but it can be said that usual Biot’s parameters are used.^[17]

Fig. 8.

(Color available online) Treatment of sound packages outside the vehicle.

Each package case is investigated using simulation, and then PBN reduction is confirmed with experimental results. Fig. 9 shows that PBN is improved by attaching sound packages. It can be seen that difference between experimental and reconstructed results is less than 0.5 dB. Thus, the approach proposed in this study may be particularly useful with good accuracy when only a simulation model is available before a physical vehicle is produced at very early design stages.

Fig. 9.

(Color available online) PBN reduction obtained by the hybrid method and the outdoor test due to sound package treatment.

Noise reduction is maximum when sound packages are attached on the whole area (Maximum package case). It is natural that a larger area of the acoustic treatment achieves more noise reduction. However, because it may be true that the noise reduction efficiency differs dependent on the treatment location, such a characteristic is further compared by investigating noise reduction normalized by the area. The corresponding result is shown in Fig. 10. It is interesting that the closest area to tires, Wheel Outer Liner (WOL) only, is not enough in terms of reduction efficiency. The most effective treatment comes from Near Tire case that also covers bottom areas close to the tires. This implies that area around the tires should be properly taken into account. Indeed, this is often ignored by development engineers.

Fig. 10.

(Color available online) PBN reduction normalized by the corresponding area. The PBN reduction as in Fig. 9.

VI. Conclusions

This study investigated to find an effective method to countermeasure PBN meeting European regulation. A novel hybrid method, combining experimental tire source and simulated exterior acoustic transfer functions, was suggested.

Numerical methods to give equivalent strength of tire source using combination of monopoles are applied, which cover the Lasso algorithm and Tikhonov regularization.

Exterior acoustic transfer functions are calculated using a simulation model, which is made of finite elements for nearfield cavity and Adaptive Perfectly Matched Layer (APML) for infinite field. The accuracy is validated in good agreement by comparison with test results.

It was shown that the suggested hybrid approach can be a good method to predict PBN properly with maximum error of 0.5 dB. Thanks to the convenience of simulation, various design cases with respect to sound packages could be investigated easily. When the results of hybrid method compared with the experimental ones, it can be seen that the reduction of PBN can be accurately predicted by means of the reduction of acoustic transfer function.

The efficiency of acoustic treatment was investigated using the suggested hybrid approach. The study shows that the treatment only around tires is not efficient but covering bottom area close to the tires can enhance the efficiency in terms of PBN reduction.