Enhanced data-driven monitoring of wastewater treatment plants using the Kolmogorov–Smirnov test

Kini, K. Ramakrishna; Harrou, Fouzi; Madakyaru, Muddu; Sun, Ying

doi:10.1039/d3ew00829k

Cited by 1 publication

(1 citation statement)

References 39 publications

(57 reference statements)

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“…The choice of the K-S test was motivated by its nonparametric nature, which means that it does not make assumptions about the underlying distribution of the data, making it suitable for analyzing complex dynamical systems where the distribution is often unknown or difficult to model parametrically. Additionally, the K-S test is widely used in various scientific fields for comparing distributions and detecting deviations from a hypothesized distribution [e. g. [33][34][35], further justifying its application in our analysis. We employed SciPy's stats module [15] to conduct an automated K-S test.…”

Section: Methodsmentioning

confidence: 97%

Reappraising Double Pendulum Dynamics across Multiple Computational Platforms

Herho,

Fajary,

Herho

et al. 2024

Preprint

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This study presents the complexity and sensitivity of chaotic system dynamics in the case of the double pendulum. It applied detailed numerical analyses of the double pendulum in multiple computing platforms in order to demonstrate the complexity in behavior of the system of double pendulums. The equations of motion were derived from the Euler-Lagrange formalism, in order to capture the system's dynamics, which is coupled nonlinearly. These were solved numerically using the efficient Runge-Kutta-Fehlberg method, implemented in Python, R, GNU Octave, and Julia, while runtimes and memory usage were extensively benchmarked across these environments. Time series analyses, including the calculation of Shannon entropy and the Kolmogorov-Smirnov test, quantified the system's unpredictability and sensitivity to infinitesimal perturbations of the initial conditions. Phase space diagrams illustrated the intricate trajectories and strange attractors, as further confirmation of the chaotic nature of the double pendulum. All the findings have a clear indication of the importance of accurate measurements of the initial condition in a chaotic system, contributing to an increased understanding of nonlinear dynamics. Future research directions are faster simulations using Numba and GPU computing, stochastic effects, chaotic synchronization, and applications in climate modeling. This work will be useful for understanding chaos theory and efficient computational approaches in complex systems of dynamical nature.

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