how-it-works.md

Overview of the GEDAD Algorithm

Here we provide a detailed explanation of the Gyroscope Euclidean Distance Anomaly Detection (GEDAD) algorithm, which initially developed for gyroscopes, and now it has been extended to 3-axis accelerometers while retaining its original name. The GEDAD algorithm consists of two core phases: learning and inference.

Data Acquisition and Pre-processing

The process begins with data acquisition. While vibration data is collected from a 3-axis accelerometer via I2C and stored in a circular buffer, later the data undergoes a linear transformation where it is multiplied by a coefficient $alpha$, and added with another coefficient $beta$.

Learning Phase

The objective of the learning phase is to establish a baseline template of normal vibration for the measuring device.

1. Template Generation: First, a $sample\ window$ of 3-axis acceleration data, sized to cover a complete normal operational cycle, is collected to serve as the template data.
2. Distance Calculation: The algorithm then randomly samples $N$ short data segments or named $chunks$ from identical positions within each channel of the template. Each chunk is then slid across the entire template of its corresponding channel with a defined $sliding\ step$, calculating the Euclidean (L2) distance at each position.
3. Threshold Calculation: Next, outliers are filtered from these distances (e.g., using the $3\sigma$ rule; specifically, values less than a given $\epsilon$). For each channel, the remaining distances are sorted to identify the $M$ smallest values. An average threshold is then computed for each channel from these $M$ distances, defining the boundary between normal and abnormal states.
4. Parameter Calibration: Finally, an additional parameter, $C$, is determined by finding the median counts of consecutive instances where the Euclidean distance is below the threshold during a subsequent comparison. This parameter is stored to enhance detection accuracy in the next phase.

Inference Phase

During inference, the algorithm compares real-time 3-axis acceleration data against the established template data to identify any vibrations that do not match the normal fingerprint.

The process is similar to training, but it uses real-time data segments for comparison instead of randomly sampled $chunks$.

• If the real-time data segment is sufficiently similar to a portion of the template (i.e., its Euclidean distance is below the threshold), the vibration is deemed normal.
• Conversely, if the distance remains above the threshold after comparison against the entire template, the system flags the vibration as an anomaly.

The actual computation is more complex, involving the fusion of anomaly scores across channels and the use of the parameter $C$.

Summary and Future Work

In summary, the algorithm's advantages include:

• Fast training speed
• Low computational overhead
• Suitability for low-power embedded devices
• Requires only a small amount of normal data for training

We are also exploring engineering optimizations, such as using Fast Fourier Transform (FFT) to analyze frequency components and considering time-frequency characteristics and average amplitude. Future work will focus on further enhancing the algorithm's accuracy, efficiency and robustness.