Time Domain Modal Estimation Documentation¶

A Python package for extracting modal parameters from time-domain response data using the Complex Exponential Algorithm (CEA) and Eigensystem Realization Algorithm (ERA).

Overview¶

This package implements time-domain modal estimation techniques for identifying modal parameters (natural frequencies, damping ratios, and mode shapes) from measured response data. Two primary methods are implemented:

Complex Exponential Algorithm (CEA) - for free decay response data
Eigensystem Realization Algorithm (ERA) - for impulse response data

Both methods are derived from:

Fahey, S. O’F., & Pratt, J. (1998). Time domain modal estimation techniques. Experimental Techniques, 22(6), 45-49.

Features¶

Complex Exponential Algorithm (CEA): Extract modal parameters from free decay response
Eigensystem Realization Algorithm (ERA): Extract modal parameters from impulse response via Hankel matrices and SVD
Automatic pole identification: Find system poles from characteristic polynomial or eigenvalues
Modal parameter extraction: Calculate natural frequencies, damping ratios, and mode shapes
Response reconstruction: Validate identified models by reconstructing the original response
Stabilization diagrams: Assist with model order selection

Quick Start¶

import numpy as np
from time_domain_modal_estimation import complex_exponential_algorithm

# Generate synthetic response data
dt = 0.01  # Time step (seconds)
t = np.arange(0, 5, dt)
f = 5.0  # Frequency (Hz)
zeta = 0.03  # Damping ratio
omega_n = 2 * np.pi * f
y = np.exp(-zeta * omega_n * t) * np.cos(omega_n * np.sqrt(1 - zeta**2) * t)

# Apply CEA algorithm
results = complex_exponential_algorithm(y=y, dt=dt, n_modes=1)

print(f"Estimated frequency: {results['frequencies'][0]:.4f} Hz")
print(f"Estimated damping: {results['damping_ratios'][0]:.4f}")

Installation¶

From source:

git clone https://github.com/daleas0120/time_domain_modal_estimation.git
cd time_domain_modal_estimation
pip install -e .

With documentation dependencies:

pip install -e ".[docs]"

Contents¶

Additional Information