StructuralVibration.jl

This Julia package is intended to provide a set of tools for generating vibration data either to validate new numerical methods or to serve as input data for solving inverse problems such as input state estimation via Bayesian filtering, Bayesian regularization, machine learning, etc.

The package is under active development. The package is developed as part of my research activities on source identification in structural dynamics and acoustics.

Installation

To install the package, you can use the following command:

(Yourenv) pkg> add StructuralVibration

Features

The package provides the following features:

Mechanical models

• Discrete models
  • Spring-mass-damper SDOF system
  • Spring-mass-damper MDOF system
  • FE models of bar, rod, strings and beams
• Continuous models
  • Longitudinal bars
  • Torsional bars
  • Strings
  • Beams
  • Rectangular plates
  • Rectangular membranes
• State space model
  • Continuous state-space representation
  • Discrete state-space representation
    • Zero-order hold (ZOH)
    • First-order hold (FOH)
    • Band-limited hold (BLH)
    • RK4

Vibration data generation

• Excitation signals
  • Rectangular wave
  • Triangular wave
  • Hammer impact
  • Smoothed rectangular wave
  • Sine wave
  • Half-sine pulse
  • Harversine pulse
  • Swept sine wave
  • Gaussian pulse
  • Colored noise
• Solution for SDOF systems
  • Free response
  • Forced response due to a harmonic force or a base motion
  • Forced response due to any external force or base motion (Duhamel's integral)
• Time-domain integration schemes for linear second order systems
  • Central difference scheme
  • RK4
  • Newmark-beta method
  • Linear acceleration method
  • Fox-Goodwin method
  • HHT
  • WBZ
  • Generalized-alpha
  • Mid-Point rule
• Frequency-domain calculations for linear systems
  • Frequency spectrum
  • Modal summation
  • Direct method
  • Frequency response function (FRF)
  • Modal summation
  • Direct method
• State-space solvers
  • Time domain
  • RK4 for continuous systems
  • ZOH, FOH, BLH, RK4 for discrete models
  • Frequency spectrum
  • Modal summation
  • Direct method
  • Frequency response function (FRF)
  • Modal summation
  • Direct method
• Measurement noise
  • Additive Gaussian white noise (agwn) with a prescribed SNR
  • Additive Colored noise (acn)
  • Multiplicative noise
  • Mixed - agwn + multiplicative noise

Signal Processing

• Measurement noise variance estimation algorithms from noisy data
  • Regularization-based estimation
  • D'Errico's method - [Link to the Matlab version](https://fr.mathworks.com/matlabcentral/fileexchange/16683-estimatenoise)
  • SNR estimation from estimated measurement noise variance
• Denoising algorithms
  • Regularization
  • Kalman filtering
• Detrending data using polynomial fit
• Gradient calculation using interpolation
• Signal estimation
  • Transfer functions estimation (H1, H2, H3, Hv)
  • Welch method (PSD, CSD, ESD, Autopower, Autopower linear)
  • Signal spectrum estimation

Modal extraction

• Modal extraction - SDOF methods
  • Peak picking method
  • Circle fit method
  • Least-squares fit method
• Modal extraction - MDOF methods
  • Least-squares complex exponential (LSCE)
  • Least-squares complex frequency (LSCF)
  • Polyreference least-squares complex frequency (PLSCF)
  • Stabilization diagram
• Analysis indicators
  • Modal Overlap Factor (MOF)
  • Mode overcomplexity value (MOV)
  • Mode Phase Collinearity (MPC)
  • Mode Complexity Factor (MCF)
  • Mean Phase Deviation (MPD)
  • Modal Assurance Criterion (MAC)
  • Coordinate Modal Assurance Criterion (COMAC)
  • Enhanced Coordinate Modal Assurance Criterion (ECOMAC)
  • Frequency Response Assurance Criterion (FRAC)
  • Complex Mode Indicator Function (CMIF)
  • Power Spectrum indicator function (PSIF)
• Modal synthesis
  • Estimation of the FRF residuals
  • Reconstruct FRF from modal parameters

Visualization

• Bode plot
• 2D and 3D Nyquist plot
• Waterfall plot
• General 2D plot