scholarly journals SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics

2020 ◽  
Vol 476 (2242) ◽  
pp. 20200279
Author(s):  
Kadierdan Kaheman ◽  
J. Nathan Kutz ◽  
Steven L. Brunton
Keyword(s):  
Nonlinear Dynamics ◽  
Measurement Data ◽  
Noisy Data ◽  
Rational Functions ◽  
Double Pendulum ◽  
Bz Reaction ◽  
Systems Models ◽  
Noise Robust ◽  
Pendulum Dynamics ◽  
Robust Variant

Accurately modelling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and simplified model for the Belousov–Zhabotinsky (BZ) reaction.

scholarly journals Semi-Supervised Manifold Alignment Using Parallel Deep Autoencoders

Algorithms ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 186
Author(s):  
Fayeem Aziz ◽  
Aaron S.W. Wong ◽  
Stephan Chalup
Keyword(s):  
Manifold Learning ◽  
Network Architecture ◽  
Image Data ◽  
High Dimensional ◽  
Double Pendulum ◽  
Manifold Alignment ◽  
Series Of Experiments ◽  
Underlying Manifold ◽  
Low Dimensional ◽  
Pendulum Dynamics

The aim of manifold learning is to extract low-dimensional manifolds from high-dimensional data. Manifold alignment is a variant of manifold learning that uses two or more datasets that are assumed to represent different high-dimensional representations of the same underlying manifold. Manifold alignment can be successful in detecting latent manifolds in cases where one version of the data alone is not sufficient to extract and establish a stable low-dimensional representation. The present study proposes a parallel deep autoencoder neural network architecture for manifold alignment and conducts a series of experiments using a protein-folding benchmark dataset and a suite of new datasets generated by simulating double-pendulum dynamics with underlying manifolds of dimensions 2, 3 and 4. The dimensionality and topological complexity of these latent manifolds are above those occurring in most previous studies. Our experimental results demonstrate that the parallel deep autoencoder performs in most cases better than the tested traditional methods of semi-supervised manifold alignment. We also show that the parallel deep autoencoder can process datasets of different input domains by aligning the manifolds extracted from kinematics parameters with those obtained from corresponding image data.

Partial state feedback sliding mode control for double-pendulum overhead cranes with unknown disturbances

2022 ◽  
pp. 095440622110520
Author(s):  
Qingrong Chen ◽  
Wenming Cheng ◽  
Jiahui Liu ◽  
Run Du
Keyword(s):  
Nonlinear Dynamics ◽  
State Feedback ◽  
Sliding Mode ◽  
Equilibrium Points ◽  
Sliding Mode Controller ◽  
Double Pendulum ◽  
The Novel ◽  
Overhead Cranes ◽  
Unknown Disturbances ◽  
Partial State

In this paper, a novel sliding mode controller which requires partial state feedback is proposed for double-pendulum overhead cranes subject to unknown payload parameters and unknown external disturbances. Firstly, it is theoretically proved that the hook and payload tend to their respective equilibrium points concurrently. Secondly, a decoupling transformation is performed on the original nonlinear dynamics of double-pendulum overhead cranes. The novel sliding mode controller that does not require the prior information and motion signals of the payload is designed based on the decoupled nonlinear dynamics. Then, the asymptotic stability of the equilibrium point of double-pendulum overhead cranes is proved by rigorous analysis. Finally, several simulations are conducted to validate the effectiveness and robustness of the proposed controller.

Nonlinear dynamics of a rotating double pendulum

2016 ◽  
Vol 380 (3) ◽  
pp. 408-412 ◽  
Author(s):  
Soumyabrata Maiti ◽  
Jyotirmoy Roy ◽  
Asok K. Mallik ◽  
Jayanta K. Bhattacharjee
Keyword(s):  
Nonlinear Dynamics ◽  
Double Pendulum

Data Rectification and Detection of Trend Shifts in Jet Engine Path Measurements Using Median Filters and Fuzzy Logic

2002 ◽  
Vol 124 (4) ◽  
pp. 809-816 ◽  
Author(s):  
R. Ganguli
Keyword(s):  
Detection System ◽  
Median Filter ◽  
Measurement Data ◽  
Noisy Data ◽  
False Alarms ◽  
Linear Filters ◽  
Data Set ◽  
Median Filters ◽  
Data Rectification ◽  
Path Measurement

Filtering methods are explored for removing noise from data while preserving sharp edges that many indicate a trend shift in gas turbine measurements. Linear filters are found to be have problems with removing noise while preserving features in the signal. The nonlinear hybrid median filter is found to accurately reproduce the root signal from noisy data. Simulated faulty data and fault-free gas path measurement data are passed through median filters and health residuals for the data set are created. The health residual is a scalar norm of the gas path measurement deltas and is used to partition the faulty engine from the healthy engine using fuzzy sets. The fuzzy detection system is developed and tested with noisy data and with filtered data. It is found from tests with simulated fault-free and faulty data that fuzzy trend shift detection based on filtered data is very accurate with no false alarms and negligible missed alarms.

A single and double closed-loop compound anti-sway control method for double-pendulum bridge cranes locating at random position

2021 ◽  
pp. 014233122110464
Author(s):  
Minghui Xia ◽  
Xiaokai Wang ◽  
Qingxiang Wu ◽  
Lin Hua
Keyword(s):  
Closed Loop ◽  
Control Method ◽  
Smooth Transition ◽  
Double Pendulum ◽  
Bridge Crane ◽  
Special Equipment ◽  
Pendulum Model ◽  
Bumpless Transfer ◽  
Random Position ◽  
Pendulum Dynamics

In the assembly workshops of some heavy special equipment, the bridge cranes for payload lifting often needs to be located frequently. However, the locating position is often determined by the operator, which is random and results in significant payload oscillation and difficulties in trolley positioning. Furthermore, in practice, the bridge crane always exhibits more complicated double-pendulum dynamics compared with single-pendulum crane. To solve these problems, this paper establishes the double-pendulum model of bridge crane. Derived from the proportional-derivative (PD) control, the single closed-loop is designed based on the hook oscillation during acceleration and transporting; when locating, the double closed-loop is presented by utilizing the position and the hook oscillation. Combining the two control methods, a single and double closed-loop compound anti-sway control (SDCAC) method for the bridge crane is proposed. On this basis, to improve the performance of the SDCAC system, the sequential quadratic optimization (SQP) method is adopted to optimize PD parameters. Besides, a novel bumpless transfer control method is proposed to realize the smooth transition between the two control modes. Finally, the simulations and experiments are conducted. The results demonstrate the effectiveness of the proposed method.

Noise Robust Video Super-Resolution Without Training on Noisy Data

2021 ◽  
pp. 353-365
Author(s):  
Fei Zhou ◽  
Zitao Lu ◽  
Hongming Luo ◽  
Cuixin Yang ◽  
Bozhi Liu
Keyword(s):  
Noisy Data ◽  
Super Resolution ◽  
Noise Robust
Sign in / Sign up

Export Citation Format

Share Document