Meaning
Complexity measure that quantifies the regularity or chaotic nature of a time series by analyzing ordinal patterns. Analysts calculate permutation entropy by mapping data sequences into rank ordered permutations and measuring their probability distribution. This tool is effective for identifying structural changes in noisy signals without requiring the data to follow a specific distribution.
Ordinal Mapping
Transforming raw values into ranks eliminates the influence of extreme outliers and focuses on the shape of the wave. Using permutation entropy allows for small windows of consecutive points to be compared to determine their relative order. These patterns represent the local dynamics of the system.
Entropy Calculation
Summing the probabilities of each unique permutation produces a single value between zero and one. A perfectly predictable signal yields low entropy because only one pattern ever appears. Completely random noise produces high entropy as every possible permutation occurs with equal frequency.
Signal Sensitivity
Detecting the transition from a stable state to a chaotic one is the primary use of this metric in industrial monitoring. Applying permutation entropy reacts to the loss of structural patterns before a simple threshold breach occurs. This early warning allows for maintenance before a total failure appears in the physical equipment.
