PIER-VIBE — Documentation | AI-Augmented Bridge Pier Safety Framework

📖 Overview

"Structural integrity is not negotiated with the sea — it is enforced through real-time physics, adaptive intelligence, and principled constraint design."

PIER-VIBE (Predictive Intelligence Engine for Resonance, Vibration, and Integrity in Bridge Environments) is a fully coupled, AI-augmented hydro-structural continuum mechanics framework that treats bridge structural safety as a continuously governed dynamic invariant — not a static design property frozen at the completion of a finite element run.

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.

🏗️ 3-Module + 2 AI Architecture

Module 01 — SSSE (Sub-Surface Scour Engine)

Computes scour depth evolution using Melville-Coleman equation with horseshoe vortex amplification. HEC-18 equilibrium depth prediction. Real-time bed shear stress monitoring.

Melville-Coleman Scour Rate + HEC-18

∂z_s/∂t = C_s·u*·f(d_s/d₅₀)·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)

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

Navier-Stokes + Morison Equation

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)

Palmgren-Miner cumulative fatigue damage with rainflow counting. Goodman mean stress correction. S-N curves per detail category (A, B, C, D, E).

Palmgren-Miner + Goodman

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

Physics-Informed Neural Network embedding Melville-Coleman scour equation as training constraint. Forecasts scour depth at 24/48/72 hour horizons from sensor data.

PINN Loss Function

L = λ_data·L_data + λ_phys·L_phys
λ_data=0.65 · λ_phys=0.35 · 72h RMSE: ±0.08m

AI Component 02 — PINN Fatigue Damage Forecaster

Physics-Informed Neural Network embedding Palmgren-Miner damage accumulation. Forecasts fatigue damage at 72 hour horizon from strain gauge data.

PINN Fatigue Loss

L = λ_data·L_data + λ_phys·(dD/dt - Palmgren-Miner RHS)
λ_data=0.65 · λ_phys=0.35 · 72h MAE: 2.8%

BSHI — Bridge Structural Health Index

Composite safety index integrating scour, fatigue, and resonance. Weighted sum with calibrated thresholds. Continuous real-time safety certification.

BSHI Formula

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 · Threshold: BSHI ≥ 0.85

📐 Core Equations

Eq. 1 — Scour Rate (SSSE)

∂z_s/∂t = C_s·u*·f(d_s/d₅₀)·g(y/D_pier)·[1 - D_s/D_s,max]

Melville-Coleman scour rate with horseshoe vortex amplification

Eq. 2 — Bed Shear Stress

τ_b = μ ∂v_x/∂z |_{z=z_bed} = ρ_F u*²

Shields parameter θ_cr = τ_cr/[(ρ_s-ρ_F)g d₅₀] ≈ 0.047

Eq. 3 — Navier-Stokes (HSCE)

ρ_F[∂v/∂t+(v·∇)v] = -∇p + μ∇²v + ρ_Fg + f_FSI

Incompressible NS with k-ω SST turbulence closure

Eq. 4 — Morison Wave Force

F = ρ_F·C_m·A·du/dt + ½ρ_F·C_d·D·u|u|

Wave-induced inertia and drag forces on pier

Eq. 5 — Fatigue Damage (EFGL)

D(t) = Σ_i n_i(t)/N_i(σ_a,i)

Palmgren-Miner linear cumulative damage

Eq. 6 — BSHI Composite Index

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

Weighted composite of scour, fatigue, and resonance

⚙️ BSHI Governance Protocol

Signal	Condition	Action	Governance Level
🟢 STABILITY CERTIFIED	BSHI ≥ 0.85	Normal operation — continuous PINN monitoring	None
🟠 MONITORING PHASE — Level 1	0.75 ≤ BSHI < 0.85	Reduced operations — PINN scour forecast issued	Level 1
🟠 MONITORING PHASE — Level 2	0.65 ≤ BSHI < 0.75	Load restriction — scour countermeasures required	Level 2
🔴 STOP COMMAND	BSHI < 0.65	Bridge closure — emergency inspection protocol	Stop

📦 Installation

bash — pip install

pip install pier-vibe-engine

# From source
git clone https://github.com/gitdeeper12/PIER-VIBE.git
cd PIER-VIBE
pip install -e .

# Quick test
python -c "from pier_vibe import BridgeGovernor; print('PIER-VIBE ready')"

🔧 API Reference

python — main interface

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"
)

# Run full PIER-VIBE pipeline
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 D(t)
print(result.frequency_drift_pct)  # Natural frequency drift (%)
print(result.governance_level)     # "none" | "level_1" | "level_2" | "stop"

BridgeGovernor Parameters

Parameter	Description	Default	Domain
bridge_config	Path to bridge configuration YAML file	—	string
water_depth_m	Water depth at pier location (m)	25.0	0–200 m
sensor_stream	Sensor source ("live" or file path)	"live"	string
ai_modules	Dictionary of AI module instances	None	dict

📊 Validation Summary

Scenario	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%

👤 Author

🌉

Samir Baladi

Principal Investigator — AI-Augmented Bridge Safety

Samir Baladi is an interdisciplinary researcher at the intersection of computational physics, biomedical AI, and engineering systems safety. Affiliated with the Ronin Institute and the Rite of Renaissance research program, his work spans three converging themes: the governance of dissipative AI systems (ENTRO-DASA), causal discrimination in data-driven models (COREX), and AI-augmented enforcement of structural safety constraints (DAMS-SLIP, TUNNEL-SHIELD, PIER-VIBE).

PIER-VIBE is the third project in the MARITIME-AI series (MARITIME-AI-01), applying cybernetic safety principles from aviation and aerospace to bridge pier scour and resonance governance.

📧 gitdeeper@gmail.com 🔗 ORCID: 0009-0003-8903-0029 🐙 GitHub 🦊 GitLab

📝 Citation

@software{baladi2026piervibe, author = {Samir Baladi}, title = {PIER-VIBE: Predictive Intelligence Engine for Resonance, Vibration, and Integrity in Bridge Environments}, year = {2026}, version = {1.0.0}, publisher = {Zenodo}, doi = {10.5281/zenodo.20390646}, url = {https://doi.org/10.5281/zenodo.20390646}, note = {MARITIME-AI-01, Systems Safety \& Engineering (AI-augmented)} }

"Structural integrity is not negotiated with the sea — it is enforced through real-time physics, adaptive intelligence, and principled constraint design." — PIER-VIBE v1.0.0

PIER-VIBE Documentation