Sensors

A sensor converts physical phenomena into a measurable digital signal, which can then be displayed, read, or processed further^[1]. According to the physical characteristics of sensor sensing, common sensors include temperature sensors that sense temperature, acceleration sensors that sense motion information, infrared sensors that sense infrared information, etc. According to the way of sensing signals, sensors can be divided into active sensors and passive sensors. Active sensors need an external excitation signal or a power signal. On the other hand, passive sensors do not require any external power and produce an output response. LiDAR is an example of an active sensor, as it requires an external light source to emit a laser. By receiving the returned beam, the time delay between emission and return is calculated to determine the distance to an object. Passive sensors, such as temperature sensors, acceleration sensors, and infrared sensors, do not require external excitation and can directly measure the physical characteristics of the system being monitored. A wide variety of sensors are used in different industries and have greatly increased the productivity of society.

Time Series Sensor Data

The time series of length $n$ observed by the sensor can be expressed as

where the data point $x_t$ is the data observed by the sensor at moment $t$. When $\mathbf{x}$ is univariate time series data, $x_t$ is a real value and $x_t\in \mathbb{R}$. When $\mathbf{x}$ is multivariate {time series} data, $x_t$ is a vector and $x_t\in \mathbb{R}^d$, where the $d$ indicates the dimension of $x_t$. Much of the time series data collected in practical applications are multivariate data that may be obtained from multiple attributes of a sensor or multiple sensors. For example, in the fault diagnosis of rolling bearings, an acceleration time series of three axes XYZ can be obtained simultaneously by a single accelerometer. Another example is in fault diagnosis of power plant thermal system, where multidimensional time series data are obtained simultaneously by using multiple sensors, such as temperature sensors, pressure sensors, flow rate sensors, etc.

This entry is adapted from the peer-reviewed paper 10.3390/s22155507