A state-of-the-art review of the Bouc-Wen model and hysteresis characterization through sparse regression techniques

This repository contains the code used in my master thesis.

Table of contents

1. Auxiliary functions
2. Bouc-Wen models and hysteresis behaviors
3. SINDy implementation
4. Complementary figures
5. Folders structure

Auxiliary functions

File name	Description
functions.py	Helper functions for plotting and data management.
dynamics_functions.py	Functions for hysteresis simulations.
sindy_implementation_functions.py	Functions for SINDy implementation in hysteresis identification.

Bouc-Wen models and hysteresis Behaviors

Model file	Description
bw_analysis.py	Sensitivity analysis of the parameters of the standard Bouc-Wen model.
bw_fsbw_model.py	Flag-shape Bouc-Wen model. Simulates flag-shaped hysteresis.
bw_gbw_model.py	Generalized Bouc-Wen model. Simulates asymmetric hysteresis.
bw_mbwbn_model.py	Modified Bouc-Wen-Baber-Noori model. Simulates pinched hysteresis, stiffness degradation, and strength degradation.
bw_model.py	Standard Bouc-Wen model. Simulates symmetric hysteresis with softening/hardening.
hys--backslash-like.py	Backslash-like hysteresis.
hys--butterfly.py	Double loop hysteresis.
hys--lonely-stroke.py	Hysteresis with lonely-stroke.
hys--s-shaped.py	S-shaped hysteresis.
hys--sym-deg-pinc.py	Generates figures for the modified Bouc-Wen-Baber-Noori model (bw_mbwbn_model.py).
hysteresis_plots.py	Generates all the figures with the adecaute format presented in the final document.

SINDy implementation

The sparse identification of nonlinear dynamics (SINDy) technique is used for hysteresis characterization. The implementation can be found in the following files:

File name	Description
sindy_hys_01.py	Case 1: Exponential growth external force. Single and Composed feature library.
sindy_hys_02.py	Case 2: Linear-time growth external force. Single feature library.
sindy_hys_01_control.py	Control implementation for Case 1 (exponential growth external force).

Complementary figures

The following codes are used to generate complementary figures for the thesis:

File name	Description
2d_damped_oscillator.py	2D damped oscillator simulation.
abs_smooth_approximation.py	Smooth approximation of the absolute value.
pareto_front.py	A mockup to ilustrate the Pareto curve.
pnorm.py	Plots for the l0-norm, l1-norm, and l2-norm.
publication_trends.py	Displays the evolution of the citations of the Bouc-Wen class model aand the SINDy algorithm across the years.
sign_approx_tanh.py	Plots the approximations used for the SINDy implementation, including smooth absolute value and sign approximations.
terms_growth.py	Presents how the increase in the order of a polynomial feature library leds to a exponential growth tendency.

Folders structure

The results and data used are organized into the following folders:

Folder Name	Description
data	Contains data used in the generation of hysteresis models.
hysteresis_plots	Contains the plots of the different hysteretic behaviors.
outputs	Contains .txt outputs from the SINDy implementation.
publication_registry	Contains citation data for the Bouc-Wen class model and the SINDy algorithm.
publication_trends_plots	Contains plots showing the evolution of the Bouc-Wen class model and the SINDy algorithm over the years.
results_data	Contains the data to create the hysteresis_plots, from Bouc-Wen simulations and shared data.
results_plots	Contains some Bouc-Wen simulations and the complementary figures.
sindy_hys_01_composed	Contains plots for SINDy simulation for Case 1 with control.
sindy_hys_01_control	Contains plots for SINDy simulation for Case 1 with composed feature libraries.
sindy_hys_01_single	Contains plots for SINDy simulation for Case 1 with single feature libraries.
sindy_hys_02_single	Contains plots for SINDy simulation for Case 2 with single feature libraries.
zz_screenshots	Some figures to present in this README.md