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

Project description

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

An AI-Augmented Hydro-Structural Continuum Mechanics Framework for Bridge Pier Safety Governance


PyPI version PyPI downloads Python versions DOI OSF Preregistration ORCID License: MIT Domain Sub-domain Version


๐Ÿ“Œ Overview

PIER-VIBE is a fully coupled, AI-augmented hydro-structural continuum mechanics framework that treats bridge structural safety as a continuously governed dynamic invariant โ€” 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."

Contemporary bridge safety relies on periodic inspection cycles and static load ratings that cannot capture the nonlinear, spatiotemporally coupled dynamics of scour evolution, resonance emergence, and fatigue propagation. PIER-VIBE provides a principled three-module governance pipeline that classifies any bridge operational state in real time as:

Signal Safety Status Action
๐ŸŸข STABILITY CERTIFIED BSHI โ‰ฅ 0.85 All constraints satisfied โ€” normal operation
๐ŸŸ  MONITORING PHASE 0.65 โ‰ค BSHI < 0.85 Reduced operations + PINN scour forecast
๐Ÿ”ด STOP COMMAND BSHI < 0.65 Bridge closure + emergency inspection

๐Ÿ—‚๏ธ Table of Contents


โœจ Key Features

  • Three-module coupled pipeline โ€” SSSE (Scour), HSCE (Hydro-Structural), EFGL (Fatigue Lock)
  • AI-augmented governance โ€” Physics-Informed Neural Network (PINN) for scour forecasting, PINN for fatigue accumulation, BSHI composite index
  • 24โ€“72 hour advance warning โ€” vs. 2โ€“6 hours for conventional SHM systems
  • Closed-form + PINN scour depth prediction โ€” Melville-Coleman scour equation with PINN correction
  • Full fluid-structure-soil coupling โ€” Navier-Stokes + structural dynamics + Biot consolidation
  • Resonance frequency drift detection โ€” real-time natural frequency monitoring with 94.4% sensitivity
  • Global Bridge Structural Health Index (BSHI) โ€” weighted composite of scour, fatigue, and resonance safety margins
  • 0.075 m RMSE scour prediction โ€” validated across 6 canonical bridge configurations
  • Full open-source distribution โ€” available across 11 platforms

๐Ÿ›๏ธ Domain Positioning

PIER-VIBE is the fifth project in the Systems Safety & Engineering (AI-augmented) domain portfolio, classified as MARITIME-AI-01.

Project Sub-classification Core Safety Mechanism
OSEF Aviation Safety Systems AI-augmented flight envelope protection
Limit Cycle Flight Dynamics Aerospace Engineering Nonlinear dynamical stability certification
DAMS-SLIP v1.1.1 GEOTECH-AI-01 AI-augmented seepage and piping governance
TUNNEL-SHIELD v1.0.0 GEOTECH-AI-02 AI-augmented TBM excavation safety governance
PIER-VIBE v1.0.0 MARITIME-AI-01 AI-augmented bridge scour and resonance governance

The unifying principle across all five projects: safety is a dynamical invariant enforced through physics-grounded AI governance, not a static design constant frozen at the point of commissioning.


๐Ÿ“ Project Structure


PIER-VIBE/
โ”‚
โ”œโ”€โ”€ pier_vibe/                              # Core Python package
โ”‚   โ”œโ”€โ”€ init.py                         # Package entry point & public API
โ”‚   โ”œโ”€โ”€ pipeline.py                         # Main PIER-VIBE governance pipeline
โ”‚   โ”œโ”€โ”€ safety.py                           # Safety certification & BSHI logic
โ”‚   โ”‚
โ”‚   โ”œโ”€โ”€ modules/                            # Three governing modules
โ”‚   โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”‚   โ”œโ”€โ”€ ssse.py                         # Module 1: Sub-Surface Scour Engine
โ”‚   โ”‚   โ”œโ”€โ”€ hsce.py                         # Module 2: Hydro-Structural Coupling Evaluator
โ”‚   โ”‚   โ””โ”€โ”€ efgl.py                         # Module 3: Elastic Fatigue Governance Lock
โ”‚   โ”‚
โ”‚   โ”œโ”€โ”€ ai/                                 # AI augmentation components
โ”‚   โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”‚   โ”œโ”€โ”€ pinn_scour.py                   # PINN: scour depth forecasting
โ”‚   โ”‚   โ”œโ”€โ”€ pinn_fatigue.py                 # PINN: fatigue accumulation forecasting
โ”‚   โ”‚   โ”œโ”€โ”€ bshi.py                         # Bridge Structural Health Index
โ”‚   โ”‚   โ””โ”€โ”€ weights/                        # Pre-trained model checkpoints
โ”‚   โ”‚       โ”œโ”€โ”€ pinn_scour_v1.pt
โ”‚   โ”‚       โ”œโ”€โ”€ pinn_fatigue_v1.pt
โ”‚   โ”‚       โ””โ”€โ”€ bshi_calibration.json
โ”‚   โ”‚
โ”‚   โ”œโ”€โ”€ fluid/                              # Fluid dynamics (Navier-Stokes)
โ”‚   โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”‚   โ”œโ”€โ”€ navier_stokes.py                # Incompressible NS solver
โ”‚   โ”‚   โ”œโ”€โ”€ turbulence.py                   # k-ฯ‰ SST turbulence closure
โ”‚   โ”‚   โ”œโ”€โ”€ wave_forces.py                  # Morison equation wave loading
โ”‚   โ”‚   โ””โ”€โ”€ horseshoe_vortex.py             # Pier-induced vortex dynamics
โ”‚   โ”‚
โ”‚   โ”œโ”€โ”€ structural/                         # Structural dynamics
โ”‚   โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”‚   โ”œโ”€โ”€ eigenanalysis.py                # Natural frequency computation
โ”‚   โ”‚   โ”œโ”€โ”€ mode_shapes.py                  # Mode shape extraction
โ”‚   โ”‚   โ”œโ”€โ”€ damping.py                      # Structural damping matrix
โ”‚   โ”‚   โ””โ”€โ”€ frequency_drift.py              # Real-time frequency tracking
โ”‚   โ”‚
โ”‚   โ”œโ”€โ”€ scour/                              # SSSE subsystem
โ”‚   โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”‚   โ”œโ”€โ”€ melville_coleman.py             # Scour rate equation
โ”‚   โ”‚   โ”œโ”€โ”€ bed_shear.py                    # Bed shear stress ฯ„_b computation
โ”‚   โ”‚   โ”œโ”€โ”€ horseshoe.py                    # Horseshoe vortex amplification
โ”‚   โ”‚   โ””โ”€โ”€ equilibrium_depth.py            # HEC-18 equilibrium scour
โ”‚   โ”‚
โ”‚   โ”œโ”€โ”€ fatigue/                            # EFGL subsystem
โ”‚   โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”‚   โ”œโ”€โ”€ palmgren_miner.py               # Cumulative damage D(t)
โ”‚   โ”‚   โ”œโ”€โ”€ rainflow.py                     # Cycle counting algorithm
โ”‚   โ”‚   โ”œโ”€โ”€ sn_curves.py                    # S-N curve for detail categories
โ”‚   โ”‚   โ””โ”€โ”€ goodman.py                      # Mean stress correction
โ”‚   โ”‚
โ”‚   โ”œโ”€โ”€ coupling/                           # Fluid-Structure-Soil coupling
โ”‚   โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”‚   โ”œโ”€โ”€ ale.py                          # Arbitrary Lagrangian-Eulerian
โ”‚   โ”‚   โ”œโ”€โ”€ added_mass.py                   # Hydrodynamic added mass M_a
โ”‚   โ”‚   โ”œโ”€โ”€ added_damping.py                # Hydrodynamic added damping C_a
โ”‚   โ”‚   โ””โ”€โ”€ biot.py                         # Biot consolidation (soil coupling)
โ”‚   โ”‚
โ”‚   โ”œโ”€โ”€ fem/                                # Finite element discretization
โ”‚   โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”‚   โ”œโ”€โ”€ mesh.py                         # Adaptive hybrid mesh
โ”‚   โ”‚   โ”œโ”€โ”€ amr.py                          # Adaptive mesh refinement
โ”‚   โ”‚   โ”œโ”€โ”€ boundary_conditions.py          # In-situ stress, wave BC
โ”‚   โ”‚   โ”œโ”€โ”€ solver.py                       # Nonlinear FEM solver
โ”‚   โ”‚   โ””โ”€โ”€ convergence.py                  # Convergence criteria
โ”‚   โ”‚
โ”‚   โ”œโ”€โ”€ monitoring/                         # Real-time monitoring layer
โ”‚   โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”‚   โ”œโ”€โ”€ accelerometer.py                # Tri-axial accelerometer parser
โ”‚   โ”‚   โ”œโ”€โ”€ strain_gauge.py                 # Vibrating-wire strain gauge
โ”‚   โ”‚   โ”œโ”€โ”€ piezometer.py                   # Foundation pore pressure
โ”‚   โ”‚   โ”œโ”€โ”€ scour_sensor.py                 # Sonar/MR/TDR scour sensor
โ”‚   โ”‚   โ”œโ”€โ”€ meteorological.py               # Wind, wave, current sensors
โ”‚   โ”‚   โ””โ”€โ”€ aggregator.py                   # Multi-sensor temporal aggregation
โ”‚   โ”‚
โ”‚   โ”œโ”€โ”€ kalman/                             # Kalman filter state estimation
โ”‚   โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”‚   โ”œโ”€โ”€ filter.py                       # Kalman filter implementation
โ”‚   โ”‚   โ”œโ”€โ”€ measurement.py                  # Measurement model H
โ”‚   โ”‚   โ””โ”€โ”€ covariance.py                   # Error covariance P and R
โ”‚   โ”‚
โ”‚   โ””โ”€โ”€ utils/                              # Shared utilities
โ”‚       โ”œโ”€โ”€ init.py
โ”‚       โ”œโ”€โ”€ metrics.py                      # BSHI, scour RMSE, fatigue MAE
โ”‚       โ”œโ”€โ”€ validators.py                   # Input validation & safety bounds
โ”‚       โ””โ”€โ”€ constants.py                    # Canonical parameter registry
โ”‚
โ”œโ”€โ”€ visualization/                          # Real-time visualization subsystem
โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”œโ”€โ”€ app.py                              # Streamlit application entry point
โ”‚   โ”œโ”€โ”€ dashboard.py                        # Main bridge safety dashboard layout
โ”‚   โ”œโ”€โ”€ scour_map.py                        # Scour hole evolution heatmap
โ”‚   โ”œโ”€โ”€ frequency_plot.py                   # Natural frequency drift plot
โ”‚   โ”œโ”€โ”€ fatigue_damage.py                   # Cumulative damage visualization
โ”‚   โ””โ”€โ”€ components/
โ”‚       โ”œโ”€โ”€ signal_panel.py                 # ๐Ÿ”ด๐ŸŸ ๐ŸŸข safety signal panel
โ”‚       โ”œโ”€โ”€ forecast_panel.py               # PINN scour + fatigue forecast
โ”‚       โ””โ”€โ”€ sensor_live.py                  # Live sensor reading panel
โ”‚
โ”œโ”€โ”€ archival/                               # Operational data archival
โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”œโ”€โ”€ writer.py                           # Append-only JSON/CSV record writer
โ”‚   โ”œโ”€โ”€ checksum.py                         # SHA-256 tamper-evidence layer
โ”‚   โ””โ”€โ”€ partitioner.py                      # Per-bridge time-window partitioner
โ”‚
โ”œโ”€โ”€ simulation/                             # Benchmark simulation environment
โ”‚   โ”œโ”€โ”€ init.py
โ”‚   โ”œโ”€โ”€ scenarios.py                        # Six canonical bridge configurations
โ”‚   โ”œโ”€โ”€ environmental_models.py             # Wave, current, wind profiles
โ”‚   โ”œโ”€โ”€ benchmarks.py                       # Full validation suite runner
โ”‚   โ”œโ”€โ”€ parameters.py                       # Canonical v1.0.0 parameter registry
โ”‚   โ””โ”€โ”€ results/                            # Pre-computed validation outputs
โ”‚       โ”œโ”€โ”€ B1_single_pier_sand.json
โ”‚       โ”œโ”€โ”€ B2_twin_pier_gravel.json
โ”‚       โ”œโ”€โ”€ B3_offshore_monopile.json
โ”‚       โ”œโ”€โ”€ B4_jacket_foundation.json
โ”‚       โ”œโ”€โ”€ B5_cable_stayed.json
โ”‚       โ””โ”€โ”€ B6_suspension_deepwater.json
โ”‚
โ”œโ”€โ”€ examples/                               # Usage examples & tutorials
โ”‚   โ”œโ”€โ”€ quickstart.py                       # Minimal working example
โ”‚   โ”œโ”€โ”€ basic_safety_check.ipynb            # Jupyter: single-bridge safety evaluation
โ”‚   โ”œโ”€โ”€ scour_scenario.ipynb                # Jupyter: flood-induced scour scenario
โ”‚   โ”œโ”€โ”€ resonance_scenario.ipynb            # Jupyter: wind-induced resonance scenario
โ”‚   โ”œโ”€โ”€ fatigue_scenario.ipynb              # Jupyter: fatigue accumulation scenario
โ”‚   โ”œโ”€โ”€ streamlit_live.py                   # Launch real-time bridge dashboard
โ”‚   โ””โ”€โ”€ ai_forecast_demo.py                 # PINN scour + fatigue demonstration
โ”‚
โ”œโ”€โ”€ tests/                                  # Unit and integration tests
โ”‚   โ”œโ”€โ”€ test_ssse.py
โ”‚   โ”œโ”€โ”€ test_hsce.py
โ”‚   โ”œโ”€โ”€ test_efgl.py
โ”‚   โ”œโ”€โ”€ test_pinn_scour.py
โ”‚   โ”œโ”€โ”€ test_pinn_fatigue.py
โ”‚   โ”œโ”€โ”€ test_bshi.py
โ”‚   โ”œโ”€โ”€ test_kalman.py
โ”‚   โ”œโ”€โ”€ test_pipeline.py
โ”‚   โ””โ”€โ”€ test_archival.py
โ”‚
โ”œโ”€โ”€ docs/                                   # Documentation source
โ”‚   โ”œโ”€โ”€ architecture.md                     # Pipeline & module architecture reference
โ”‚   โ”œโ”€โ”€ mathematics.md                      # Full hydro-structural mathematical formalism
โ”‚   โ”œโ”€โ”€ ai_modules.md                       # PINN scour / PINN fatigue documentation
โ”‚   โ”œโ”€โ”€ scour_mechanics.md                  # Scour rate equation & HEC-18 guide
โ”‚   โ”œโ”€โ”€ governance.md                       # BSHI governance protocol reference
โ”‚   โ””โ”€โ”€ api_reference.md                    # Full Python API reference
โ”‚
โ”œโ”€โ”€ paper/                                  # Research paper artifacts
โ”‚   โ”œโ”€โ”€ PIER-VIBE_Research_Paper.pdf        # Published paper (PDF)
โ”‚   โ”œโ”€โ”€ PIER-VIBE_Research_Paper.docx       # Editable Word version
โ”‚   โ””โ”€โ”€ figures/
โ”‚       โ”œโ”€โ”€ pipeline_diagram.svg
โ”‚       โ”œโ”€โ”€ scour_hole_evolution.svg
โ”‚       โ”œโ”€โ”€ frequency_drift.svg
โ”‚       โ””โ”€โ”€ ai_forecast_validation.svg
โ”‚
โ”œโ”€โ”€ .gitlab-ci.yml                          # GitLab CI/CD pipeline
โ”œโ”€โ”€ .github/                                # GitHub Actions workflows
โ”‚   โ””โ”€โ”€ workflows/
โ”‚       โ”œโ”€โ”€ tests.yml
โ”‚       โ””โ”€โ”€ publish.yml
โ”œโ”€โ”€ pyproject.toml                          # Build system configuration
โ”œโ”€โ”€ setup.cfg                               # Package metadata
โ”œโ”€โ”€ requirements.txt                        # Runtime dependencies
โ”œโ”€โ”€ requirements-dev.txt                    # Development dependencies
โ”œโ”€โ”€ CHANGELOG.md                            # Version history
โ”œโ”€โ”€ CONTRIBUTING.md                         # Contribution guidelines
โ”œโ”€โ”€ CODE_OF_CONDUCT.md
โ”œโ”€โ”€ AUTHORS.md                              # Author and contributor registry
โ”œโ”€โ”€ LICENSE                                 # MIT License
โ””โ”€โ”€ README.md                               # This file


๐Ÿš€ Quick Start

Installation

# Install from PyPI
pip install pier-vibe-engine

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

Minimal Example

from pier_vibe import BridgeGovernor

# Initialize the safety governor
governor = BridgeGovernor(
    bridge_config="configs/offshore_monopile.yaml",
    water_depth_m=25.0,
    sensor_stream="live"    # or path to historical CSV
)

# 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"

With Full AI Augmentation

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 prediction)
print(result.fatigue_forecast_72h)  # Fatigue damage at T+72h (PINN prediction)
print(result.resonance_risk)        # "normal" | "elevated" | "critical"

Flood-Induced Scour Scenario

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 Bridge Safety Dashboard

# Start Streamlit safety monitoring dashboard
streamlit run examples/streamlit_live.py

# Dashboard available at: http://localhost:8501
# Live scour hole heatmap ยท Frequency drift plot ยท Fatigue damage ยท ๐Ÿ”ด๐ŸŸ ๐ŸŸข signal

๐Ÿงฉ PIER-VIBE Pipeline

โ”Œโ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”
โ”‚  Sensor Telemetry: Accelerometers ยท Strain Gauges ยท Piezometers ยท Sonar โ”‚
โ”‚  Environmental: Wind Speed ยท Wave Height ยท Current Profile ยท Water Levelโ”‚
โ””โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”ฌโ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”˜
                               โ”‚
         โ”Œโ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”ผโ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”
         โ”‚                     โ”‚                    โ”‚
         โ–ผ                     โ–ผ                    โ–ผ
    SSSE                  HSCE                  EFGL
    Sub-Surface Scour    Hydro-Structural      Elastic Fatigue
    Engine               Coupling Evaluator    Governance Lock
    Melville-Coleman     Navier-Stokes +       Palmgren-Miner
    Horseshoe Vortex     Added Mass/Damping    Rainflow Counting
    Equilibrium Depth    Eigenfrequency        S-N Curves
         โ”‚                     โ”‚                    โ”‚
         โ””โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”ผโ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”˜
                               โ”‚
         โ”Œโ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”ผโ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”
         โ”‚                     โ”‚                    โ”‚
         โ–ผ                     โ–ผ                    โ–ผ
    PINN Scour           PINN Fatigue         BSHI Calculator
    Depth Forecast       Damage Forecast      Composite Index
    Physics-constrained  Physics-constrained  w_sยทw_fยทw_r
    24-72h horizon       72h MAE < 3.1%       BSHI โ‰ฅ 0.85
         โ”‚                     โ”‚                    โ”‚
         โ””โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”ผโ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”˜
                               โ”‚
                               โ–ผ
                    Kalman Filter State
                    Sensor Fusion + Physics Model
                    Minimum-variance estimate
                               โ”‚
                               โ–ผ
                    BSHI Functional
                    BSHI = w_sยท(1-D_s/D_crit) + w_fยท(1-D_fat) + w_rยทฮ”f_safe/ฮ”f_crit
                    w_s=0.35  w_f=0.35  w_r=0.30
                               โ”‚
                    โ”Œโ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”ดโ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”
                    โ–ผ                     โ–ผ
             Safety Signal         Archival & Dashboard
             ๐Ÿ”ด๐ŸŸ ๐ŸŸข                JSON/CSV + SHA-256
             Bridge Closure        Streamlit + Plotly

Module Descriptions

Module Governing Equation Description

1 SSSE โˆ‚z_s/โˆ‚t = C_sยทu*ยทf(d_s/d_50)ยทg(y/D_pier)ยท[1-D_s/D_s,max] Melville-Coleman scour rate with horseshoe vortex amplification 2 HSCE ฯ_F[โˆ‚v/โˆ‚t+(vยทโˆ‡)v] = -โˆ‡p + ฮผโˆ‡ยฒv + ฯ_Fg + f_FSI Navier-Stokes with ALE fluid-structure coupling 3 EFGL D(t) = ฮฃ_i n_i(t)/N_i(ฯƒ_a,i) Palmgren-Miner cumulative fatigue with Goodman correction AI-1 PINN Scour L = ฮป_dataยทL_data + ฮป_physยทL_phys Physics-constrained scour forecasting from sensor data AI-2 PINN Fatigue L = ฮป_dataยทL_data + ฮป_physยท(dD/dt - Palmgren-Miner RHS) Physics-constrained fatigue accumulation forecast AI-3 BSHI BSHI = w_sยท(1-D_s/D_crit) + w_fยท(1-D_fat) + w_rยทฮ”f_safe/ฮ”f_crit Composite bridge structural health index


๐Ÿ“Š Scoring & Safety Bounds

Safety certification criteria:
  BSHI     (Bridge Structural Health Index)                    โ‰ฅ  0.85
  D_s       (Current scour depth)                              โ‰ค  D_s,crit
  D_fat     (Cumulative fatigue damage)                        โ‰ค  0.80
  ฮ”f_safe   (Frequency separation from excitation)             โ‰ฅ  ฮ”f_crit

BSHI functional form:
  BSHI = 0.35ยท(1 - D_s/D_s,crit) + 0.35ยท(1 - D_fat) + 0.30ยท(ฮ”f_safe/ฮ”f_crit)

Scour depth (Melville-Coleman):
  โˆ‚z_s/โˆ‚t = C_s ยท u\*(t) ยท f(d_s/d_50) ยท g(y/D_pier) ยท [1 - D_s/D_s,max]

Critical bed shear stress (Shields):
  ฯ„_cr = ฮธ_cr ยท (ฯ_s - ฯ_F) ยท g ยท d_50,  ฮธ_cr โ‰ˆ 0.047

Benchmark validation results (v1.0.0):

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

AI module performance:

AI Module Precision Recall AUC / MAE False Alarm Rate PINN Scour Depth (72h) โ€” โ€” ยฑ0.08 m (RMSE) N/A PINN Fatigue Damage (72h) โ€” โ€” 2.8% (MAE) N/A BSHI Composite Index 0.97 0.95 0.98 (AUC) 2.8% Resonance Drift Detector 0.94 0.93 0.96 (AUC) 3.1%

Governance decision thresholds:

Level Condition Action Escalation ๐ŸŸข Certified BSHI โ‰ฅ 0.85 Normal operation None ๐ŸŸ  Level 1 0.75 โ‰ค BSHI < 0.85 Reduced operations + PINN forecast Monitor hourly ๐ŸŸ  Level 2 0.65 โ‰ค BSHI < 0.75 Load restriction + scour countermeasures Alert engineer ๐Ÿ”ด Stop BSHI < 0.65 Bridge closure + emergency inspection Immediate action


๐ŸŒ Platforms & Mirrors

Platform URL Role ๐Ÿ™ GitHub (Primary) github.com/gitdeeper12/PIER-VIBE Source code, issues, PRs ๐ŸฆŠ GitLab (Mirror) gitlab.com/gitdeeper12/PIER-VIBE CI/CD mirror ๐Ÿชฃ Bitbucket (Mirror) bitbucket.org/gitdeeper-12/PIER-VIBE Enterprise mirror ๐Ÿ”๏ธ Codeberg (Mirror) codeberg.org/gitdeeper12/PIER-VIBE Open-source community ๐Ÿ“ฆ PyPI pypi.org/project/pier-vibe-engine Python package distribution ๐Ÿ”ฌ Zenodo doi.org/10.5281/zenodo.20390646 Citable DOI, paper & data ๐Ÿ“‹ OSF Project osf.io/fxthu Research project registry ๐Ÿ“ OSF Preregistration doi.org/10.17605/OSF.IO/YKWEG Pre-registered study protocol ๐ŸŒ Website pier-vibe.netlify.app Live documentation & dashboard ๐Ÿง‘โ€๐Ÿ”ฌ ORCID orcid.org/0009-0003-8903-0029 Researcher identity ๐Ÿ—„๏ธ Internet Archive archive.org/details/osf-registrations-ykweg-v1 Permanent archival copy

๐ŸŒ Official Website Pages

Page URL Homepage pier-vibe.netlify.app Dashboard pier-vibe.netlify.app/dashboard Results pier-vibe.netlify.app/results Documentation pier-vibe.netlify.app/documentation


๐Ÿ”„ Clone & Download

Git Clone

# GitHub (Primary)
git clone https://github.com/gitdeeper12/PIER-VIBE.git

# GitLab (Mirror)
git clone https://gitlab.com/gitdeeper12/PIER-VIBE.git

# Bitbucket (Mirror)
git clone https://bitbucket.org/gitdeeper-12/PIER-VIBE.git

# Codeberg (Mirror)
git clone https://codeberg.org/gitdeeper12/PIER-VIBE.git

Direct ZIP Download

Source Link GitHub PIER-VIBE-main.zip GitLab PIER-VIBE-main.zip Bitbucket PIER-VIBE-main.zip Codeberg PIER-VIBE-main.zip PyPI files pypi.org/project/pier-vibe-engine/#files Zenodo record doi.org/10.5281/zenodo.20390646


๐Ÿ“– Citation

If PIER-VIBE contributes to your research, please cite using one of the following formats.

๐Ÿ“ฆ PyPI Package

@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)}
}

๐Ÿ”ฌ Zenodo Archive (Paper & Data)

@dataset{baladi2026piervibe_zenodo,
  author       = {Baladi, Samir},
  title        = {{PIER-VIBE}: Predictive Intelligence Engine for Resonance,
                  Vibration, and Integrity in Bridge Environments โ€”
                  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 ยท FSI ยท Systems Safety}
}

๐Ÿ“ OSF Preregistration

@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}
}

๐Ÿ“„ Research Paper

@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)}
}

APA (inline)

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


๐Ÿ“œ License

This project is licensed under the MIT License โ€” see the LICENSE file for details.

MIT License

Copyright (c) 2026 Samir Baladi

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction...

๐Ÿ‘ค Author

Samir Baladi Interdisciplinary AI Researcher โ€” Neural Engineering, Computational Systems Safety & Bridge Engineering Ronin Institute / Rite of Renaissance

Contact Link ๐Ÿ“ง Email gitdeeper@gmail.com ๐Ÿง‘โ€๐Ÿ”ฌ ORCID 0009-0003-8903-0029 ๐Ÿ™ GitHub github.com/gitdeeper12 ๐ŸŒ Website pier-vibe.netlify.app


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

https://img.shields.io/badge/DOI-10.5281%2Fzenodo.20390646-blue.svg https://img.shields.io/pypi/v/pier-vibe-engine?color=0D2B45 https://img.shields.io/badge/License-MIT-yellow.svg

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

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