Systems Safety & Engineering (AI-augmented) · MARITIME-AI-01 · Version 1.0.0 · May 2026

PIER-VIBE

Predictive Intelligence Engine for Resonance, Vibration, and Integrity in Bridge Environments
A Critical Framework for Subsurface Scour Mechanics, Dynamic Wave-Structure Interaction,
and Resonance Fatigue Governance in Offshore and Riverine Bridges

"A bridge pier is not a static obstacle in water. It is a moving boundary-value problem
embedded in a continuously evolving hydrodynamic and geotechnical field. PIER-VIBE formalizes and governs
this evolution, enforcing structural integrity against subsurface scour, wave-structure resonance,
and fatigue accumulation in real time."

↗ View on GitHub 📦 PyPI Package 🔬 Zenodo DOI 🦊 GitLab Mirror

Real-Time Safety Governance

Four-Level BSHI Signal Classification

Every bridge operational state evaluated by PIER-VIBE receives a continuous safety signal with full scour, resonance, and fatigue diagnostics.

BSHI ≥ 0.85

🟢 STABILITY CERTIFIED

All scour, fatigue, and resonance constraints satisfied. Normal operation active — continuous PINN monitoring.

0.75 ≤ BSHI < 0.85

🟠 MONITORING PHASE — Level 1

Scour depth elevation or frequency drift detected. Reduced operations — PINN scour forecast issued.

0.65 ≤ BSHI < 0.75

🟠 MONITORING PHASE — Level 2

Load restriction recommended. Scour countermeasures and structural review issued.

BSHI < 0.65

🔴 STOP COMMAND

Bridge closure. Emergency inspection protocol activated. Full diagnostic: SSSE scour field, HSCE frequency analysis, EFGL fatigue report.

Governance Architecture

Three Modules · One Stress Field · Three AI Components

Fully coupled fluid-structure-soil simulation augmented by real-time AI inference. No decoupled scour-then-stability paradigm.

MODULE 01

SSSE — Sub-Surface Scour Engine

Scour RMSE: 0.075m

Computes scour depth evolution using Melville-Coleman equation with horseshoe vortex amplification. HEC-18 equilibrium depth prediction.

∂z_s/∂t = C_s·u*·f(d_s/d_50)·g(y/D_pier)·[1-D_s/D_s,max]
τ_b = ρ_F·u*² · α_v(Re, y/D)

MODULE 02

HSCE — Hydro-Structural Coupling Evaluator

F_face ≥ 1.25

Navier-Stokes fluid dynamics with k-ω SST turbulence. Morison wave forces. ALE fluid-structure interaction.

ρ_F[∂v/∂t+(v·∇)v] = -∇p + μ∇²v + ρ_Fg + f_FSI
F = ρ_F·C_m·A·du/dt + ½ρ_F·C_d·D·u|u|

MODULE 03

EFGL — Elastic Fatigue Governance Lock

D_fat < 0.80

Palmgren-Miner cumulative fatigue damage with rainflow counting. Goodman mean stress correction. S-N curves per detail category.

D(t) = Σ_i n_i(t)/N_i(σ_a,i)
σ_a,eq = σ_a / (1 - σ_m/σ_UTS)

AI COMPONENT 01

PINN — Scour Depth Forecaster

72h RMSE: ±0.08m

Physics-Informed Neural Network embedding Melville-Coleman scour equation as training constraint. Forecasts scour depth from sensor data.

L = λ_data·L_data + λ_phys·L_phys
λ_data=0.7 · λ_phys=0.3 · Update: 5s

AI COMPONENT 02

PINN — Fatigue Damage Forecaster

72h MAE: 2.8%

Physics-Informed Neural Network embedding Palmgren-Miner damage accumulation. Forecasts fatigue damage from strain gauge data.

L = λ_data·L_data + λ_phys·(dD/dt - Palmgren-Miner RHS)
λ_data=0.65 · λ_phys=0.35

AI COMPONENT 03

BSHI — Bridge Structural Health Index

Prec. 0.97 · Rec. 0.95

Composite safety index integrating scour, fatigue, and resonance. Weighted sum with calibrated thresholds.

BSHI = w_s·(1-D_s/D_crit) + w_f·(1-D_fat) + w_r·Δf_safe/Δf_crit
w_s=0.35, w_f=0.35, w_r=0.30

Experimental Validation

Six Canonical Benchmark Scenarios

Validated across sandy riverbeds, gravel riverbeds, offshore monopiles, jacket foundations, cable-stayed, and suspension bridges.

Case	Configuration	Scour RMSE	Fatigue MAE	BSHI Accuracy	Resonance Sens.
B1	Single pier — sandy riverbed	0.06 m	2.4%	97.2%	94.8%
B2	Twin pier — gravel riverbed	0.08 m	2.9%	96.5%	93.7%
B3	Offshore monopile — sand	0.07 m	2.6%	97.8%	95.1%
B4	Jacket foundation — rock-clay	0.09 m	3.1%	95.9%	92.8%
B5	Cable-stayed — composite deck	0.07 m	2.8%	96.8%	94.6%
B6	Suspension — deep-water pier	0.08 m	3.0%	97.1%	95.3%
MEAN	—	0.075 m	2.8%	96.9%	94.4%

D_s,crit = 4.2 m · δ_max = 45 mm · BSHI certification threshold = 0.85

Quick Start

Deploy Safety Governance in 60 Seconds

pip install pier-vibe-engine

from pier_vibe import BridgeGovernor

# Initialize with bridge configuration and water depth
governor = BridgeGovernor(
    bridge_config="configs/offshore_monopile.yaml",
    water_depth_m=25.0,
    sensor_stream="live"
)

result = governor.evaluate()

print(result.signal)          # "STABILITY_CERTIFIED" | "MONITORING" | "STOP_COMMAND"
print(result.bshi)            # Bridge Structural Health Index [0,1]
print(result.scour_depth_m)   # Current scour depth (metres)
print(result.fatigue_damage)  # Cumulative fatigue damage
print(result.frequency_drift_pct) # Natural frequency drift (%)
print(result.governance_level) # "none" | "level_1" | "level_2" | "stop"

from pier_vibe import BridgeGovernor
from pier_vibe.ai import PINNScourForecaster, PINNFatigueForecaster, BSHICalculator

governor = BridgeGovernor(
    bridge_config="configs/offshore_monopile.yaml",
    ai_modules={
        "scour_pinn":   PINNScourForecaster.from_pretrained("default"),
        "fatigue_pinn": PINNFatigueForecaster.from_pretrained("default"),
        "bshi":         BSHICalculator.from_pretrained("default"),
    }
)

result = governor.evaluate(forecast_hours=72)
print(result.scour_forecast_72h)   # Scour depth at T+72h (PINN)
print(result.fatigue_forecast_72h) # Fatigue damage at T+72h (PINN)
print(result.resonance_risk)       # "normal" | "elevated" | "critical"

from pier_vibe import BridgeGovernor
from pier_vibe.simulation import FloodScenario

scenario = FloodScenario(
    peak_velocity_mps=3.5,
    duration_hours=72,
    bridge_config="configs/single_pier_sand.yaml"
)

governor = BridgeGovernor(bridge_config="configs/single_pier_sand.yaml")
results = governor.run_transient(scenario, dt_hours=0.5, T_max_hours=120)

print(results.max_scour_depth)     # 2.8 m (equilibrium depth)
print(results.scour_warning_hours) # 48 hours before critical depth
print(results.bshi_min)            # Minimum BSHI during event

# Launch real-time Streamlit bridge safety dashboard
# Live scour hole heatmap · BSHI evolution · Fatigue damage · 🔴🟠🟢 signals

$ streamlit run examples/streamlit_live.py

# Dashboard at: http://localhost:8501
# Panels:
#   · Scour hole evolution heatmap (SSSE live output)
#   · Natural frequency drift plot (HSCE with PINN forecast)
#   · Cumulative fatigue damage chart (EFGL with rainflow)
#   · BSHI time-series with 0.85 threshold line
#   · 🔴🟠🟢 governance signal status panel
#   · PINN scour + fatigue forecasts at 24/48/72h
#   · JSON/CSV archive with SHA-256 checksums

Citation

Cite PIER-VIBE in Your Research

If PIER-VIBE contributes to your research, please use one of the citation formats below.

@software{baladi2026piervibe_pypi,
  author    = {Baladi, Samir},
  title     = {{PIER-VIBE}: Predictive Intelligence Engine for Resonance,
               Vibration, and Integrity in Bridge Environments},
  year      = {2026},
  version   = {1.0.0},
  publisher = {Python Package Index},
  url       = {https://pypi.org/project/pier-vibe-engine},
  note      = {Python package, MIT License,
               Systems Safety & Engineering (AI-augmented)}
}

@dataset{baladi2026piervibe_zenodo,
  author    = {Baladi, Samir},
  title     = {{PIER-VIBE}: Predictive Intelligence Engine for Resonance,
               Vibration, and Integrity in Bridge Environments —
               Research Paper and Simulation Data},
  year      = {2026},
  publisher = {Zenodo},
  version   = {1.0.0},
  doi       = {10.5281/zenodo.20390646},
  url       = {https://doi.org/10.5281/zenodo.20390646},
  note      = {Bridge Engineering Core · FSI · Systems Safety}
}

@misc{baladi2026piervibe_osf,
  author    = {Baladi, Samir},
  title     = {{PIER-VIBE} Framework: Pre-registered Study Protocol for
               AI-Augmented Structural Integrity Governance in
               Offshore and Riverine Bridges},
  year      = {2026},
  publisher = {Open Science Framework},
  doi       = {10.17605/OSF.IO/YKWEG},
  url       = {https://doi.org/10.17605/OSF.IO/YKWEG},
  note      = {OSF Preregistration}
}

@article{baladi2026piervibe,
  author  = {Baladi, Samir},
  title   = {{PIER-VIBE}: A Critical Framework for Subsurface Scour Mechanics,
             Dynamic Wave-Structure Interaction, and Resonance Fatigue
             Governance in Offshore and Riverine Bridges},
  year    = {2026},
  month   = {May},
  version = {1.0.0},
  doi     = {10.5281/zenodo.20390646},
  url     = {https://doi.org/10.5281/zenodo.20390646},
  note    = {Ronin Institute / Rite of Renaissance,
             Systems Safety & Engineering (AI-augmented)}
}

Baladi, S. (2026). PIER-VIBE: A Critical Framework for Subsurface Scour
Mechanics, Dynamic Wave-Structure Interaction, and Resonance Fatigue
Governance in Offshore and Riverine Bridges
(Version 1.0.0). Zenodo.
https://doi.org/10.5281/zenodo.20390646