NOTES¶

Detection — Determine if Structural Damage Exists

Compare current modal parameters against baseline. Outputs damage index [0, 1] and flagged metrics.

Algorithm¶

Compare three metrics, taking the maximum change across modes:

Thresholds and the combined damage index:

Metric	Threshold	Physical meaning
Frequency shift	> 5%	Significant stiffness loss
MAC loss	> 15%	Significant shape change
Damping change	> 100%	Significantly increased damping

\[ \text{DI} = \frac{1}{3} \left(\frac{\Delta f_{max}}{15\%} + \frac{MACloss_{max}}{30\%} + \frac{\Delta \zeta_{max}}{300\%}\right) \]

Verdict: DI > 0.5 or >= 2 metrics exceed thresholds → damaged = true

Data Structure¶

typedef struct {
    bool  damaged;     // damage detected?
    float index;       // damage index [0, 1]
    int   flags;       // bitmask: bit0=freq, bit1=MAC, bit2=damping
} tiny_damage_detect_t;

Design Deep Dive¶

1. Threshold Selection¶

The thresholds come from statistical experience with civil structures:

Metric	Threshold	Rationale	False positive
Frequency	5%	Normal temperature variation < 3%; 5% excludes environmental drift	~5%
MAC	0.15 loss	Typical measurement uncertainty for 5-ch systems	~2%
Damping	100%	Damping measurement error ~±30%; doubling confirms change	~10%

2. Damage Index Design¶

Denominators 15%/30%/300% represent "certain damage" levels for each metric. When one metric reaches certainty: DI ≈ 0.33. Two metrics: DI ≈ 0.67. Three: DI ≈ 1.0.

3. Flags Bitmask¶

Compact representation: bit 0 = freq, bit 1 = MAC, bit 2 = damping. Enables batch checks like (out->flags >= 2).

4. Edge Computing¶

All stack-allocated, O(20) float ops, < 1μs. No dynamic allocation. Runs in real-time on ESP32.