Investigation of a directional warning sound system for electric vehicles based on structural vibration

Warning sound systems for electric vehicles with advanced beamforming capabilities have been investigated in the past. Despite showing promising performance, such technologies have yet to be adopted by the industry, as implementation costs are generally too high and the components too fragile for implementation. A lower cost solution with higher durability could be achieved by using an array of inertial actuators instead of loudspeakers. These actuators can be attached directly to the body of the vehicle and thus require minimal design modifications. A directional sound field can then be radiated by controlling the vibration of the panel via adjustments to the relative magnitude and phase of the signals driving the array. This paper presents an experimental investigation of an inertial actuator-based warning sound system. A vehicle placed in a semi-anechoic environment is used to investigate different array configurations in terms of the resulting sound field directivity and the leakage of sound into the cabin. Results indicate that the most efficient configuration investigated has the actuators attached to the front bumper of the vehicle. Using this arrangement, real-time measurements for different beamformer settings are performed to obtain a thorough picture of the performance of the system across frequency and steering angle.

Warning sound systems for electric vehicles with advanced beamforming capabilities 1 have been investigated in the past. Despite showing promising performance, such 2 technologies have yet to be adopted by the industry, as implementation costs are 3 generally too high, and the components too fragile for implementation. A lower cost 4 solution with higher durability could be achieved by using an array of inertial actua- The advent of electric and hybrid electric vehicles has been encouraged due to the search 19 for sustainable transportation globally, but has also sparked concern over potential hazards 20 in road safety that it may create as a new technology. With particular relevance to the field 21 of acoustics, there have been studies focusing on the increased risk Electric Vehicles (EVs) 22 and Hybrid Electric Vehicles (HEVs) may pose to vulnerable road users such as pedestrians 23 and cyclists due to their silent operation 1,2 .

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Compared to an internal combustion engine, an electric motor produces low levels of 25 noise emissions when in operation. The internal combustion engine is the main noise source 26 at speeds below approximately 30 km/h. Above this limit, the noise generated by the 27 interaction between the tyres and the road and the aerodynamics of the vehicle begin to 28 dominate 3 . Therefore, EVs and HEVs are comparatively quiet at low speeds, meaning that 29 they offer little auditory warning of their presence and direction of travel in situations such 30 as cornering, parking manoeuvres, and low speed city traffic 4 . This potential safety issue 31 has led to the issuing of regulations on a global scale 5-7 , which dictate guidelines on the use 32 of artificial warning sounds, or Acoustic Vehicle Alert Systems (AVAS), that aim to ensure 33 that EVs and HEVs can be detected aurally. The inclusion of warning sounds is mandatory 34 for the aforementioned speeds below 30 km/h, as beyond that limit noise produced by other 35 sources in the vehicle is considered sufficient to provide the necessary auditory warning. 36 This relatively new requirement has sparked research focusing on the design of such warn-37 ing sounds, with the objective of generating a detectable signal that can be readily associated 38 3 JASA/Sample JASA Article with a vehicle, and is also indicative of its velocity and acceleration. This information is 39 valuable to vulnerable road users, such as cyclists and pedestrians, but particularly the vi-40 sually impaired 8 . Factors such as annoyance and intrusiveness in the sonic environment are 41 also considered in this design process 9-12 , with the objective of minimizing these parameters 42 in order to counteract arguments against the use of warning sounds citing the increase in 43 noise pollution 13 .

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Balancing the warning sound requirements may lead to a decrease in their effectiveness, 45 and therefore, it may prove beneficial to seek a solution that is able to limit the resulting 46 noise pollution through controlling the spatial aspects of the warning sound. For exam-47 ple, by focusing the radiated sound field towards the direction of vehicle motion, or even 48 individual vulnerable road users, and minimising its output in all other directions, it may 49 be possible to provide a sufficiently audible warning whilst keeping noise pollution to a 50 minimum. Such directional warning sound systems have been proposed and investigated, 51 using highly directional parametric loudspeakers 14 , low-cost single loudspeaker solutions 15 52 and loudspeaker arrays capable of beam-steering to direct sound at identified targets 16-18 . 53 However, due to limitations in their effective bandwidth and beamforming capabilities 15 , 54 or the increased cost of production and maintenance that comes with higher performance 55 solutions 14, [16][17][18] , so far none of the above systems have been adopted for widespread use by 56 the automotive industry.

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Loudspeaker array-based systems have been proven capable of generating highly direc-58 tional, controllable sound fields across a significant bandwidth and have been implemented 59 in hi-fidelity applications 19,20 . A difficulty to be overcome with the implementation of a 60 4 JASA/Sample JASA Article loudspeaker array as a vehicle warning sound system, however, is the necessity for signif-61 icant design modifications to be made to existing structures in order to accommodate the 62 loudspeakers and enable them to radiate sound efficiently. This might significantly raise the 63 cost of production and potentially even interfere with other systems in the vehicle. Another 64 issue to consider is the exposure of the fragile loudspeaker cones to adverse environmental 65 conditions such as wind, dust, water and temperature variation. to existing panels or structures. Secondly, since inertial actuators radiate via the structure 80 to which they are attached, such an array design offers increased durability because the 81 actuators are not exposed to the external environment. The potential downside of a struc-82 5 JASA/Sample JASA Article tural actuator-based array is the more irregular frequency response, but this is unlikely to 83 be extremely critical for warning sound generation.

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This paper investigates the implementation of an inertial actuator-based directional sound 85 system in a vehicle as a potential warning sound system. Different array arrangements on 86 the body of a commercial vehicle are investigated to determine which components can be 87 utilized to produce a controllable sound field within the frequency range from 100 Hz to 88 5 kHz, which is the bandwidth of warning sounds required by current legislation 5,6 . The structure. Following this previous work, this section will present the principles of operation 106 of the actuator-based system by identifying the key parameters that affect performance and 107 the differences when compared to conventional loudspeaker arrays. In addition, a strategy 108 for achieving control over the resulting sound field directivity through the acoustic contrast 109 maximization process is outlined.  The sound field radiated from by a vibrating structure driven by an actuator array has 120 some key differences and additional parameters when compared to conventional loudspeaker 121 systems. One of the benefits of using such a system is an improved high frequency limit com-122 pared to a loudspeaker array. This is due to the effective interpolation of the array sources  The control strategy used for the proposed system is the acoustic contrast maximization 148 strategy, which attempts to maximize the difference between the average sound pressure 149 levels within designated bright and dark zones in the far field 28 . Figure 1 Taking the above into account, the acoustic contrast is defined at a given frequency as the 156 ratio of the mean of the squared pressures in the bright zone and the dark zone, which can 157 be expressed as where the H superscript indicates the conjugate transpose operator.

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In addition to the acoustic contrast, it is also important to consider the electrical power signal required from a single element at the centre of the array to produce the same mean 167 square pressure in the bright zone, u m . This has the form Both acoustic contrast and array effort, as defined in Eqs. (2) and (3), are dimensionless 169 quantities, usually expressed in decibels with their level defined as 10 log 10 AC, or 10 log 10 AE 170 respectively.

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The input signals required to achieve the maximum acoustic contrast at a specific fre- where λ 1 and λ 2 are the positive real values of the Lagrange multipliers. Seeking the mini-178 mum solution of this Lagrangian has been shown 29 to lead to the relation The optimal solution in this case can be obtained from the eigenvector corresponding to

B. Control strategy implementation 228
The directivity of the sound field resulting from the vibration of the vehicle structure is 229 controlled by adjusting the relative phase and amplitude between the actuators of the array, 230 two properties that are contained in the complex input vector, u, introduced in Section II B.

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In practice, this can be achieved by filtering the base signal of the warning sound to be 232 emitted through appropriate filters, and driving the actuator array with the filtered signals.    Utilizing this method, a real-time implementation would require a number of pre-defined 260 filter sets to be stored, each corresponding to a specific steering angle, that could be imple-261 mented in order to control the direction to which the beamformer is focused.  of loudspeaker arrays, but also from the previous work on actuator-based arrays 25 .

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For the forward-steered setting, shown in Fig. 6 A, the bumper configuration is consis-301 tently the most effective out of the four configurations considered here, and it is capable of 302 an average contrast above 10 dB when using four or more actuators. Due to the orienta- achieve an average contrast of over 10 dB in the forward direction ( Fig. 6 A), and three or 331 four actuators would be required per door to yield a relative improvement in performance 332 (Fig. 6 C) at higher steering angles. Such a configuration would employ ten or twelve 333 actuators in total, and would be ultimately outperformed by a six actuator bumper array, 334 which is capable of higher contrast in the forward direction, and similar levels at higher 335 angles. Moreover, the cost of implementing more distributed systems with higher numbers 336 of actuators is unlikely to be acceptable for the automotive application.

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Overall, it has been shown that the most efficient configuration, when taking into account 338 the number of actuators used, has the array placed on the front bumper of the vehicle.

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Although the hood has enough area to accommodate larger arrays, its orientation in relation array, nor is the orientation appropriate for a forward aimed sound field, which is expected 343 to be the most commonly required steering angle.

B. Sound leakage into the vehicle interior 345
Another factor that is key to evaluating the suitability of the proposed system for practical 346 implementation, and can be readily investigated in this study, is the separation between the 347 resulting external and internal sound fields. The system is intended to convey a warning 348 sound to vulnerable road users in the path of the vehicle, but it should not be intrusive to 349 the driver and passengers. Therefore, it is important to ensure that the sound radiated from In order to obtain a more in-depth view of the performance of the system, it is useful to 398 examine the directivity as a function of frequency. Figure 10 shows the acoustic contrast fre-

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The array effort across frequency for the bumper configuration is shown in Fig. 11. These

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The acoustic contrast across the investigated frequency range for different steering angles 422 is presented in Fig. 12 for the six-actuator bumper array. Excluding the low frequency 423 region up to 200 Hz, these results demonstrate that the system is capable of high directivity 424 performance for different steering angles. Particularly within the 1 kHz to 2 kHz region, the 425 acoustic contrast is calculated to be greater than 15 dB, although it drops to 10 dB when 426 steered at a high angle. This is consistent with the off-line simulations presented in Sec. IV A.

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The average contrast achieved within the 200 Hz to 5 kHz bandwidth is consistently above 428 10 dB, which is comparable to the performance of loudspeaker-based systems 17 .

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This bandwidth sufficiently covers the frequency requirements set by regulations 5,6 , with