structural-health-monitoring

name	structural-health-monitoring
description	Structural health monitoring (SHM) — damage detection methods (Lamb waves, AE, strain, modal), sensor networks, damage indices, guided wave propagation, PZT transducers, aerospace/civil SHM.
metadata	{"priority":7,"promptSignals":{"phrases":["structural health monitoring","SHM","Lamb wave","acoustic emission SHM","damage detection","guided wave"],"minScore":3}}

Structural Health Monitoring — Complete Skill

SHM Levels (Rytter Hierarchy)

1. Detection: damage present? (yes/no)
2. Localization: where is the damage?
3. Classification: what type of damage?
4. Quantification: how severe (size, growth rate)?
5. Prognosis: remaining useful life?

Guided Wave (Lamb Wave) Methods

Wave Modes

Symmetric (S₀) mode: in-plane particle motion; fast; slightly dispersive at low frequency-thickness (f×h) Antisymmetric (A₀) mode: out-of-plane (bending); slower; strongly dispersive

Dispersion equation (symmetric): tan(qh/2) / tan(ph/2) = -4k²pq / (q²-k²)² p² = ω²/c_L² - k²; q² = ω²/c_T² - k² c_L = √(E(1-ν)/(ρ(1+ν)(1-2ν))); c_T = √(G/ρ)

Group velocity (f×h < 1 MHz·mm): S₀: c_g,S0 ≈ √(E/(ρ(1-ν²))) (plate wave speed; slightly frequency-dependent) A₀: c_g,A0 ≈ 1.84 (f×h×c_T²/c_L)^(1/4) (strongly dispersive)

Pitch-Catch and Pulse-Echo

Pitch-catch: transmit at one PZT; receive at another Damage between them → scatter, attenuation, mode conversion Damage index: DI = 1 - C_damaged/C_healthy (correlation coefficient ratio)

Pulse-echo: same PZT transmits and receives (different time windows) Damage appears as reflected wave between transmitted wave and boundary reflection

Time of Flight (ToF) Localization

Multiple sensor pairs → triangulation t_arrival at sensor i: t_i = d_i / c_g System of equations from N sensors → solve for damage coordinates (x_d, y_d)

Acoustic Emission (AE)

Transient elastic stress waves from sudden energy release (crack growth, fiber break, delamination)

AE features: Peak amplitude, ring-down count, energy, rise time, duration, frequency centroid Pattern recognition → classify source (matrix crack: low freq; fiber break: high freq)

Threshold: detection above background noise floor (typically 40–60 dB AE threshold) Kaiser effect: AE only emitted above previous maximum load → loading history detectable Felicity ratio: F_AE / F_previous (F_AE = load at AE onset) → damage indicator

Source location (2D): Δt = t₂ - t₁ from two sensors; Δt × c = difference in distance Hyperbola locus; multiple sensor pairs → intersection = source

Vibration-Based Methods

Modal parameters change with structural damage:

Natural frequency shift: ω_n² = (EI × k / m) → damage reduces local EI → reduces ω_n Sensitivity: first few modes show ~1–5% frequency shift for moderate damage

Mode shape change: more sensitive to local damage; compare MAC (Modal Assurance Criterion) MAC(i,j) = |{φᵢ}ᵀ{φⱼ}|² / (({φᵢ}ᵀ{φᵢ})×({φⱼ}ᵀ{φⱼ})) MAC < 0.9 between healthy and damaged → significant change

Curvature damage index: φ''(x) = (φᵢ-₁ - 2φᵢ + φᵢ₊₁) / h² (finite difference) Increase in curvature at damage location → identify and localize

Statistical process control: Mahalanobis distance from feature vector to healthy baseline distribution D² = (x - μ)ᵀ Σ⁻¹ (x - μ) → control chart with threshold

Strain-Based SHM

Fiber Bragg Grating (FBG): Bragg wavelength: λ_B = 2 n_eff Λ (n_eff = effective index, Λ = grating period) Strain: Δλ_B / λ_B = (1 - p_e) ε (p_e = photo-elastic constant ≈ 0.22) Sensitivity: ~1 pm/με; simultaneously temperature (ΔT shifts λ_B by 10 pm/°C)

FBG advantages: immune to EM interference; multiplexable (wavelength division); lightweight

PZT Electromechanical Impedance (EMI)

PZT bonded to structure → measure electrical admittance Y(ω) = 1/Z_mech + j ω C₀ Damage changes local mechanical impedance → changes Y(ω) spectrum RMSD (root mean square deviation): RMSD = √(Σ(Y_damaged - Y_healthy)²/Σ Y_healthy²) RMSD > threshold → damage detected

High frequency range (30–400 kHz): sensitive to local damage near PZT (λ_Lamb ≈ 5–20 mm)

Aerospace SHM (USAF, Boeing)

AW-SHM (Airworthiness SHM): AC 20-189 (FAA); enable extended inspection intervals Typical for metallic structure: demonstrate Pd > 90% (probability of detection) at critical crack size ROI: reduce maintenance hours; enable condition-based maintenance

Wing/fuselage: Lamb wave networks; AE for landing gear; strain monitoring for fatigue

Civil Infrastructure SHM

Bridge monitoring: accelerometers for modal parameters; strain for traffic loads; corrosion sensors Offshore: ultrasonic thickness monitoring; cathodic protection monitoring

Wireless sensor networks: Zigbee, LoRa, WiFi; battery or energy harvesting (vibration, solar) Data aggregation at gateway → cloud → analysis

Output

Provide: sensor type and placement (spacing [mm], array pattern), wave mode recommendation (S₀/A₀), frequency range [kHz], damage index threshold for alert, localization accuracy [mm], probability of detection (POD) curve basis, inspection interval recommendation.