Distribution of Relaxation Times Library (DRT_Lib)

Python implementation of different algorithms for calculating electrochemical impedance distribution of relaxation times.

Installation

pip install -i https://test.pypi.org/simple/ DRT-Lib==0.0.4

or

npm install @giangtle/drt_lib@1.0.1

or

"@giangtle/drt_lib": "1.0.1"

Code Credits

Major credit to Liu and Ciucci source codes (GitHub Page, Deep-Prior DRT, Gaussian Process DRT). Two algorithms for calculating DRT are based straight of their works & open-source codes.

Methods Included

• Deep-Prior Distribution of Relaxation Times (Liu and Ciucci, 2020)
• Gaussian Process Distribution of Relaxation Times (Liu and Ciucci, 2020)
• Tikhonov Regularization/Ridge Regression Distribution of Relaxation Times (Saccoccio et al., 2014)

Quick Start

Checkout Example.ipynb file with jupyter notebook for more details.

import DRT_Lib
import numpy as np
from math import pi

# Frequency range:
N_freqs = 81
freq_vec = np.logspace(-4, 4, N_freqs)

# Create sample electrochemical impedance spectra (EIS) of a ZARC element with noise:
# Parameters:
R_inf = 10
R_ct = 50
phi = 0.8
tau_0 = 1.
C = tau_0**phi/R_ct
# Exact impedance:
Z_exact = R_inf + 1./( 1./R_ct + C*(1j*2.*pi*freq_vec)**phi )
# Add noise to make synthetic experiment impedance data:
rng = np.random.seed(214975)
sigma_n_exp = 0.1
Z_exp = Z_exact + sigma_n_exp*( np.random.normal(0, 1, N_freqs) + 1j*np.random.normal(0, 1, N_freqs) )

# Compute Tikhonov Regularization/Ridge Regression Distrubution of Relaxation Times:
gamma, R_inf = DRT_Lib.TR_DRT(freq_vec, Z_exp, display=True)

# To caclulate EIS from DRT results:
Z_cal = DRT_Lib.calculate_EIS(freq_vec, gamma, R_inf)

License

Released under the MIT License.