Open AccessWhite Noise Tests on the LSTM Model Trained with Double Pendulum
Author(s) -
Xisen Wang
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2137/1/012032
Subject(s) - randomness , chaotic , white noise , double pendulum , pendulum , series (stratigraphy) , mathematics , noise (video) , control theory (sociology) , statistical physics , representation (politics) , computer science , nonlinear system , statistics , artificial intelligence , physics , inverted pendulum , image (mathematics) , paleontology , control (management) , quantum mechanics , politics , political science , law , biology
This paper describes the intrinsic qualities of a simple double pendulum (DP), with a visual representation, a rigorous deduction of the Lagrangian equation, and a concrete factor analysis. LSTM model was utilized to simulate the double pendulum’s periodic and chaotic behaviors and evaluates the effectiveness of the model. The auto-correlation coefficients was calculated. Meanwhile, Box-Pierce test and Ljung-Box tests for various state-dependent time series were conducted to give various initial conditions to explore the DP system’s random characteristics. The research results are as follows: 1) Chaos did not lead to direct randomness; 2) seasonality could coexist with chaos; 3) the highly auto-regressive nature of DP’s time series data are found. Therefore, it can be concluded that the chaos in a double pendulum has particular patterns (such as the positive relationship with the likelihood of being a random white noise series) that could be further explored.