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

Bouc-Wen class models

Model file	Description
bw_model.py	Standard Bouc-Wen model. Simulates symmetric hysteresis with softening/hardening.
bw_analysis.py	Sensitivity analysis of the parameters of the standard Bouc-Wen model.
mbwbn_model.py	Modified Bouc-Wen-Baber-Noori model. Simulates pinched hysteresis, stiffness degradation, and strength degradation.
hys-sym-deg-pinc.py	Generates figures for the modified Bouc-Wen-Baber-Noori model (mbwbn_model.py).
gbw_model.py	Generalized Bouc-Wen model. Simulates asymmetric hysteresis.
fsbw_model.py	Flag-shape Bouc-Wen model. Simulates flag-shaped hysteresis.
bw_citation_evolution.py	Displays the evolution of the citations of the Bouc-Wen class model across the years.

Other hysteresis behaviors

File name	Description
hys-s-shaped.py	S-shaped hysteresis.
hys-backslash-like.py	Backslash-like hysteresis.
hys-butterfly.py	Double loop hysteresis.
hys-lonely-stroke.py	Hysteresis with lonely-stroke.

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.
sindy_hys_02.py	Case 2: Linear-time growth external force.
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.
pnorm.py	Plots for the l0-norm, l1-norm, and l2-norm.
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.
pareto_front.py	A mockup to ilustrate the Pareto curve.

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.
outputs	Contains .txt outputs from the SINDy implementation.
results_data	Contains data generated from hysteresis simulations using Bouc-Wen (BW) models.
results_plots	Contains plots from BW simulations, hysteresis behaviors, and complementary figures.
scopus	Contains citation data for the Bouc-Wen class model.
scopus_plots	Contains plots showing the evolution of the Bouc-Wen class model over the years.
sindy_plots_1	Contains plots for Case 1 (exponential growth external force), including single and composed libraries.
sindy_plots_1c	Contains plots for Case 1 with control.
sindy_plots_2	Contains plots for Case 2 (linear-time growth external force).