NOTES¶
Severity — Estimate Stiffness Loss and Damage Level
Estimate stiffness loss from frequency shifts and classify severity.
Algorithm¶
Frequency → Stiffness¶
\[ f \propto \sqrt{\frac{k}{m}} \implies \frac{\Delta k}{k} \approx -2 \cdot \frac{\Delta f}{f} \]
Classification¶
| Level | Stiffness loss | Code | Confidence |
|---|---|---|---|
| Healthy | < 5% | DMG_NONE | 30% |
| Mild | 5-20% | DMG_MILD | 60% |
| Moderate | 20-50% | DMG_MODERATE | 80% |
| Severe | > 50% | DMG_SEVERE | 90% |
Design Deep Dive¶
1. Stiffness-Frequency Derivation¶
\[ f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \implies \frac{\Delta k}{k} \approx -2 \cdot \frac{\Delta f}{f} \]
Assuming mass is unchanged (damage typically only affects stiffness).
2. Frequency Increase Handling¶
Frequency increases (Δf > 0 → dk < 0) are clamped to 0. These typically come from temperature changes or sensor replacement, not structural improvement.
3. Skipping Unchanged Modes¶
Changes < 0.1% are skipped to avoid numerical noise in the average.
4. Confidence Design¶
| Level | Confidence | Rationale |
|---|---|---|
| Healthy | 30% | Normal environmental drift ~3% possible |
| Mild | 60% | Clear freq shift but weather-interference possible |
| Moderate | 80% | Multiple modes shift; high confidence |
| Severe | 90% | Large-scale damage, near-impossible from environment |
Confidence grows asymmetrically—severe damage is much easier to confirm than mild.