CE 540 • Structural Dynamics • Spring 2025

Structural Response Prediction using LSTM (Linear 3-DOF + Nonlinear Bouc-Wen SDOF)

Trained an LSTM to map ground acceleration time-series → displacement response for both a linear multi-DOF building model and a nonlinear hysteretic system (Bouc-Wen).

Project Overview

This project evaluates whether an LSTM network can approximate structural dynamics by learning a sequence-to-sequence mapping from excitation to response.

  • Linear 3-DOF building: input = ground acceleration, output = story displacements (u1, u2, u3).
  • Nonlinear SDOF: Bouc-Wen hysteresis, input = ground acceleration + parameters, output = displacement u(t).
  • Goal: accurate time-history prediction + ability to reproduce hysteresis behavior (F–u loop).
3-DOF building schematic

3-DOF lumped-mass building model (schematic).

LSTM Structural Dynamics Time Series Bouc-Wen Nonlinear Hysteresis

Method (What I Built)

Linear System

  • 3-DOF lumped-mass model
  • Rayleigh damping (5% for first two modes)
  • 500 synthetic samples (Gaussian white noise)
  • Train/Val/Test split: 70/15/15

Nonlinear System

  • SDOF with Bouc-Wen hysteresis
  • 200 random parameter sets × 5 excitations = 1000 samples
  • Train/Val/Test split: 70/15/15
  • Validated displacement + hysteresis loop (F vs u)
LSTM Architecture: Input → LSTM (128 units) → Dense output layer Adam optimizer, MSE loss, 50 epochs, batch size 16.
LSTM network architecture diagram

LSTM sequence-to-sequence architecture used for response prediction.

Key Results

Linear 3-DOF

R² ≈ 0.97–0.99

Across all 3 stories (test)

Linear 3-DOF

RMSE ≈ 6.85e-4–9.43e-4

Per-story test RMSE

Nonlinear SDOF

R² ≈ 0.98–0.99

Representative test samples

Linear system: predicted vs true displacement
Linear system: predicted vs. true displacement time history (test sample).
Nonlinear system: predicted vs true displacement
Nonlinear system: predicted vs. true displacement time history (test sample).

Generalization Insight

When tested on real earthquake records, the LSTM followed the overall trend but underpredicted peak amplitudes when the excitation exceeded the training distribution. This suggests training should include a wider range of strong motions (beyond Gaussian noise).

Generalization on real earthquake records

Generalization test on real ground motions (example): trend captured, peaks may be underpredicted if outside training range.

Future Work

  • Train on broader excitation types (real earthquake records + varying intensity).
  • Add multi-output prediction (velocity, acceleration, internal forces) after stable displacement prediction.
  • Apply explainability (LRP) to identify which time windows/frequencies drive the LSTM predictions.

Tools & Skills Used

  • MATLAB / numerical simulation (linear & nonlinear dynamics)
  • Python / deep learning workflow concepts
  • LSTM sequence-to-sequence regression
  • Model evaluation: RMSE, R², waveform comparison
  • Interpretation: hysteresis loop reproduction (F–u)
MATLAB Python ML Dynamics