| 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)
- Detection: damage present? (yes/no)
- Localization: where is the damage?
- Classification: what type of damage?
- Quantification: how severe (size, growth rate)?
- 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.
