Variable-Order Springpot Model Tuning via Cross-Entropy Method

SpringpotTune: Variable-Order Springpot Model Tuning via Cross-Entropy Method is a Matlab package designed to fit variable-order springpot models (fractional rheological elements) using the Cross-Entropy (CE) method for global optimization. With simple adaptations, the SpringpotFit framework can be extended to optimize other variable-order fractional models in rheology and time-dependent systems, offering a versatile and robust approach to parameter identification.

SpringpotTune uses as optimization tool the package CEopt - Cross-Entropy Optimizer, which can be downloaded at https://ceopt.org.

Table of Contents

• Overview
• Features
• Usage
• Documentation
• Reproducibility
• Authors
• Citing FracTune
• License
• Institutional support
• Funding

Overview

SpringpotTune was developed to fit variable-order springpot models for rheological systems by addressing nonconvex optimization problems using the Cross-Entropy (CE) method. The underlying results are reported in the following publication:

• J. G. Telles Ribeiro and A. Cunha Jr, Advanced creep modeling of polypropylene: A variable-order fractional calculus approach, 2025 (under review)

Preprint available here.

Features

• Implements the Cross-Entropy method for fitting variable-order springpot models
• Transparent "gray-box" optimizer offering intuitive control over key parameters
• Robust and scalable for moderately complex fitting problems in rheological systems
• Demonstrated versatility and effectiveness through case studies of variable-order fractional models

Usage

To get started with SpringpotTune, follow these steps:

1. Clone the repository:

   git clone https://github.com/americocunhajr/SpringpotTune.git

2. Navigate to the code directory:

   cd SpringpotTune/SpringpotTune-1.0

3. To calibrate the Springpot model, execute the main file:

   Main_VOSpringpot_Calibration1

This package includes the following files:

• Main_VOSpringpot_Calibration1.m --- Calibrates the variable-order springpot model parameters (elastic modulus, viscosity, initial & asymptotic fractional orders, characteristic time, deformation rate) to experimental creep data
• Main_VOSpringpot_Calibration2.m --- Performs a second calibration stage using a phenomenological equation to capture the load-dependent behavior of the mechanical properties. This script uses the CEopt black-box package (without exposing the internal CEopt code) and compares the calibrated phenomenological curve against reference values obtained from the first calibration
• Main_VOSpringpot_StrainCurves.m --- Computes and plots the strain evolution curve for a chosen material (PP or PVC) and load using the calibrated variable-order springpot model. The script reads the experimental data from CSV files, automatically discovers the available loads, and then filters the data for the selected load value
• CEopt.m -- Cross-entropy solver
• CreepDataPP.csv: Contains creep test data for polypropylene (PP) with columns for load (MPa), time (days), and strain (%) CreepDataPVC.csv: Contains creep test data for polyvinyl chloride (PVC) with columns for load (MPa), time (days), and strain (%)
• PlotSemilogx2.m -- Auxiliary function to plot two curves from given datasets in semilogx scale
• PlotLoglog2.m -- Auxiliary function to plot two curves from given datasets in loglog scale
• Plot2.m -- Auxiliary function to plot two curves from given datasets in linear scale

Documentation

The routines in SpringpotTune are well-commented to explain their functionality. Each routine includes a description of its purpose, inputs, and outputs.

Reproducibility

Simulations done with SpringpotFit are fully reproducible, as can be seen on this CodeOcean capsule.

Authors

• José Geraldo Telles Ribeiro
• Americo Cunha Jr

Citing SpringpotTune

We ask the package users to cite the following manuscript in any publications reporting work done with our code or data:

• J. G. Telles Ribeiro and A. Cunha Jr, Advanced creep modeling of polypropylene: A variable-order fractional calculus approach, 2025 (under review)

@article{TellesRibeiro2024SpringpotTune,
   author  = {J. G. {Telles Ribeiro} and A. {Cunha~Jr}},
   title   = "{Advanced creep modeling of polypropylene: A variable-order fractional calculus approach}",
   journal = {Under Review},
   year    = {2025},
   volume  = {~},
   pages   = {~},
   doi    = {~},
}

License

SpringpotTune is released under the MIT license. See the LICENSE file for details. All new contributions must be made under the MIT license.

Institutional support

Funding