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한국항공대학교 항공 모빌리티 및 공력음향학 연구실
Summary
Background
Multirotor noise and the identification of the characteristics and sources of this noise have been the key research focus. The spectral characteristics indicated that the BPF harmonics noise of the blade is the primary source of noise in a quadcopter, and a certain unsteadiness exists in the noise signatures. The unsteadiness in the flow induces unsteady acoustic signatures, corresponding to frequency modulation in the frequency domain, caused by the change in the angular speed during multirotor operation.
Although many studies have illustrated the characteristics of multirotor tonal noise, most of them were performed with the assumption of static conditions. In general, in the case of a multirotor, the angular speed is varied by the control system in response to the continuously changing operating conditions, and it has significant effects on the multirotor noise. Frequency modulation and fluctuation strength owing to the change in the angular speed considerably influence the annoyance corresponding to multirotor noise. To alleviate this noise problem, the variation effect of the angular speed variation on the multirotor noise must be quantified.
Objective
The change in the angular speed is modeled as uncertainty and the effect of the angular speed uncertainty is quantified. Because the angular speed is the only control variable in the multirotor and reacts instantaneously to the environmental changes, it can be assumed that operation uncertainty directly affects the angular speed uncertainty. Therefore, the angular speed uncertainty of a hovering multirotor according to the operation uncertainty can be quantified and predicted. Effects of the angular speed uncertainty on each rotor were also quantified with single rotor stochastic experiments and simulation.
Contribution
Uncertainty quantification of multirotor noise based on defined validation hierarchy
Compare the RPS and SPL uncertainty of multirotor and single rotor in hovering flight
Validate the single rotor stochastic prediction in terms of noise and thrust prediction
[Quadrotor noise spectrogram (NASA experiment)]
Method
Experimental multirotor noise measurements
When a multirotor is in hovering motion, the main cause of the angular speed change (shown in terms of the BPF in STFT) is the RPS difference among the rotors due to the change in the pitch or roll angle rather than the thrust change.
Pitching and rolling can be considered as tilt angle changes. Moreover, it is assumed that the tilt angle variation of the hovering multirotor due to the disturbance and RPS of the rear and front rotors can be expressed in terms of the mean value and change in the RPS. Therefore, the CoV of the RPS can be quantified as a change in the tilt angle.
The CoV of the RPS, according to the variation in the tilt angle, was calculated through a Monte Carlo simulation, performed over 10,000 samples for each case of the tilt angle variation.
Experiments on the multirotor with payload were conducted considering the maximum payload capacity to identify the maximum limit of the CoV of the RPS. It was noted that the CoV of the RPS obtained experimentally according to the tilt angle variation exhibits the same trend as in the calculated results.
The angular speed variation of the hovering multirotor can be predicted considering the maximum tilt angle of the multirotor. In this study, a CoV of RPS of 2–8% was considered in the single rotor analyses.
[Relation of RPS variation and the multirotor motion]
Results
Comparison of single rotor noise with multirotor noise
The spectral characteristics of the single rotor with the stochastic RPS are similar to those of the multirotor noise instead of those of the single rotor with the steady RPS, especially near the BPF harmonics.
The RPS variation considerably influences the BPF higher harmonics, and these tonal components spread out to the overall mid-frequency region. Therefore, the overall mid-frequency SPL increases similar to broadband noise.
The comparison of the multirotor and single rotor frequency spectra shows that the effects of the rotor tip speed variation can be described by the single rotor with the stochastic RPS.
[Comparison of measured SPL spectrum of the multirotor and single rotor]
The CoV of the OASPL against the CoV of the RPS were compared for a single rotor and multirotor. According to the multirotor UAV experiment results, as the weight increases, the mean and standard deviation of the RPS increase, thereby changing the CoV of the RPS.
The single and multirotor CoV of the OASPL exhibits the same slope, although the magnitude of the single rotor CoV of the OASPL is smaller.
The CoV of the 1st BPF SPL of the multirotor shows a similar value with the single rotor experiment and analytical results. Moreover, the single rotor numerical results and experimental results match at a low and high mean RPS, respectively.
[Comparison of CoV of SPL of the multirotor and single rotor]
Conclusion
A single rotor stochastic analysis with uncertainty quantification was performed to predict the angular speed variation effects of each rotor on the multirotor noise in the hovering condition. The key results can be summarized as follows:
The angular speed and SPL of the hovering multirotor noise can be modeled as uncertainty variables with a normal distribution. Furthermore, the angular speed uncertainty of a hovering multirotor can be predicted considering the maximum tilt angle of the multirotor, which can be used as the input for the single rotor experiments and prediction.
SPL and Thrust uncertainty of the single rotor can be quantified for the input RPS uncertainty. In the proposed single rotor with the RPS uncertainty method, the result shows that the CoV of SPL according to the BPF harmonics components and thrust is linearly related to the RPS uncertainty. Besides, a stochastic simulation technique is suggested to predict the SPL and thrust uncertainty, and it is validated with the analytical scaling law results.
Although there are some limitations in considering aerodynamic phenomena such as wake interaction, the SPL uncertainty and spectral characteristics for the hovering multirotor could be quantified by the single rotor with RPS uncertainty condition.
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