# Vibration Isolation of a Surveillance System Equipped in a Drone with Mode Decoupling
## 3 Experimental Vibration Characterization
### Modal Testing  
Experiments were performed to measure vibration data to characterize the transmissibility between the drone rotors and a surveillance camera system. The mobile surveillance system was comprised of a drone, gimbal, optical camera, and auxiliary system. A drone (DJI M600, Nanshan, China) was used as a crewless aerial vehicle owing to its large payload capacity, 5.5 kg, excluding its own weight. This drone has been widely used for various purposes, including the monitoring and diagnosis of enormous facilities, such as transmission facilities, and 3D mapping of environments [20]. A high-resolution camera (See3 CAM_CU135, San Jose, CA, USA) was used as surveillance equipment, which acquires optical images with a resolution of 1280 by 960 pixels. An optical camera was installed underneath the drone body with a gimbal, which was self-produced using a 3D printer (Ultimaker S5, ED Utrecht, Netherlands) to minimize the payload, because the flight time of a drone is critical, and it is inversely proportional to the drone's weight [21].  
Modal testing was performed with an impact hammer to identify vibration characteristics and transmissibility of the original and proposed systems. Specifically, 2 three-axisaccelerometers (PCB 356A16, Depew, NY, USA, sensitivity: 100 mV/g) were used to measure the vibrations (Figure 2). One was installed on the base, i.e., on a drone body, to measure vibration from rotors, and the second on a receiving part, i.e., on the surveillance system consisting of a camera, microprocessor, and power supply. A direction of X in the three-axis accelerometers corresponds to a drone's front head (the direction of the green arrow in Figure 2). The direction of the front head is important from an operation perspective because an operator requires a frontal view of a drone. Note that a front view should always be secured, even if a drone is operated in an autopilot mode, because a drone is manually controlled during emergencies [21]. Hereafter, it is defined as a fore-after direction. Directions Y and Z in the three-axis accelerometers correspond to side-by-side and vertical drone coordinates, respectively. Note that both the directional vibrations--side-by-side and vertical--in a drone coordinate are important because they significantly influence the camera tremble in the horizontal and vertical directions. On the contrary, the fore-after direction only affects the distance between a camera and an object. Therefore, the side-by-side and vertical directions are of main interest in this study.  
An impact hammer (PCB 086E80, USA, sensitivity: 24.0 mV/g) with a steel tip was used to exert an impulse force to the base. Impulse force in the time domain has a flat amplitude spectrum in the frequency domain; therefore, the entire frequency range was excited with the impulse force [22]. Specifically, the coherence function (Equation (24)) during the modal testing showed that coherence was above 0.8 until 160 Hz. This implies that the frequency range of 0-160 Hz has a high correlation for vibration measured between the drone body and surveillance system. The M600 drone was hung using six fishing lines as the drone's six arms replicating the actual operational conditions. The impulse responses were measured using Pulse 3050-A-060 (B&K, Narum, Denmark). Furthermore, the frequency response function was calculated using Equation (19) with input and output accelerations using parameter sets as follows: input acceleration in a base (the drone body), the output acceleration in a payload (the surveillance system), sampling frequency at 1024 Hz, resolution at 0.25 Hz, and the number of averages at 5.