## 3 Materials and Methods
### Data Collection  
The cloud-based condition monitoring system represented in Figure 1 consists of an IP-66 class multi-mode sensor that inherits a MEMS (Micro-Electro-Mechanical System) 3-axial accelerometer, an ultrasound, and a temperature sensor. The 3-axial MEMS accelerometer has a bandwidth of 1.75 kHz provided by a sampling rate of 4.5 kHz, having a full range of +/ - 16 g and producing a typical Root Mean Square (RMS) noise of approximately 7 mg. The ultrasound sensor, on the other hand, covers a total bandwidth of 70 kHz provided by a sampling rate of 180 kHz, producing acoustic data with a signal-to-noise ratio (SNR) of 64.3 dB at a total harmonic distortion of 0.20%. The data collected at equal time intervals (decided by the user) is then transferred via a 20 cm cable to the transmitter, which also stands as an embedded system. The pre-processing step of estimating peak, peak-to-peak, and RMS acceleration for each axis and ultrasound, as well as ISO 10816-3 vibration velocity (mm/s) and higher-order statistics (HOS) such as kurtosis, takes place at the battery-powered transmitter. The time-window length (duration) of the signals collected depends solely on the rotational speed of the machine being monitored. To capture all possible periodic events, comparatively longer-duration vibration signals (approximately 3-4 s) are collected from machines rotating under 600 rpm (10 Hz), and relatively shorter-duration signals (approximately 0.5 to 1 s) are read from machines rotating over 600 rpm by the MEMS sensor. As the ultrasound sensor is located beneath the multi-mode unit to transmit and receive sound waves propagating perpendicular to the mounting surface, creating only longitudinal waves in a non-dispersive medium where plane waves are transmitted [68], and since the speed of sound and attenuation are frequency-dependent to avoid interference from noise generated by nearby machinery, the scope of the presented study is delimited to cover only the highest frequency-band ultrasound RMS levels. The ultrasound signal that has a bandwidth of around 70 kHz, standing as a feature here, is collected within a time window as short as 20 microseconds. The raw vibration and ultrasound signals collected by the AC-coupled sensors are subject to averaging (simply a low-pass filter) to suppress Gaussian noise and possible normally distributed environment noise, after removing possible trends (mean) and normalizing with the standard deviation. The estimated metrics are then compressed into a data package and sent to a LoRa-WAN (Long Range-Wide Area Network) gateway (with a range of 200 m), which routes the estimated time series trend data to a cloud server or the factory's automation system, as depicted in Figure 1[69]. The data examined in this paper were collected from an industrial coupled suction (radial) fan that nominally rotates at 3000 rpm at 50 Hz, collecting the dust from the production process to exhaust it to the atmosphere, as can be seen in Figure 2. Since there is a driver-controller (typical PID) that adjusts the rotation speed of the motor according to the amount of dust to be collected (i.e., load), the rotation speed, as will be shown in forthcoming sections, is time-varying. The rotation speed is estimated by detecting the peak with the greatest magnitude around a given rotation speed range, typically [3000, 4200] rpm ([50, 70] Hz) in the velocity spectrum. This method is subject to a certain level of error that can be neglected given the methods employed in this work. The sensor is attached to the drive end (DE) of the motor with a double-sided industrial tape, allowing the capture of information-rich signals related to rotor imbalance, rotor blade faults, bearing (6313 ZZ/C3) defects, and possibly loose or abrasive bearing housing. Figure 1: The cloud-based condition monitoring system. (**a**) Interconnected devices communicating to a central server. (**b**) The collection and processing of data from a multi-mode sensor mounted on machinery and transmitting it to a remote server.