Unveiling Probability Histograms from Random Signals using a Variable-Order Quadrature Method of Moments

Description

Random signals are crucial in chemical and process engineering, where industrial plants collect
and analyse big data for process understanding and decision-making. This necessitates unveiling
the underlying probability histogram from these signals with a finite number of bins. However,
finding the optimal number of bins is still based on empirical optimization and general rules of
thumb. In this contribution, we introduce an alternative and general method to unveil probability
histograms. Our method employs a novel variable-order QMOM, which adapts automatically based
on the relevance of the information contained in the random data. The number of bins used to
recover the underlying histogram increases with the information entropy. In this regard, an evolu-
tionary algorithm that optimally generates nodes and assigns probabilities to them is developed.
The algorithm terminates when no more significant information is available for assignment to newly
created nodes, up to a user-defined threshold. In conclusion, our method is a universal histogram
reconstruction technique that only requires enough number of moments to work. The method is
validated intensively using synthetic random signals and real-life problems.

Period	06 Jul 2025 → 09 Jul 2025
Event title	ESCAPE 35 - European Symposium on Computer Aided Process Engineering
Event type	Conference
Location	Gent, BelgiumShow on map