Acoustic Emission Crack Localization: 2D Grid-Search Inversion

Crack Event

Material & Sensors

Wave speed c 5000 m/s

Attenuation α 0.50 Np/m

Sensor timing jitter 0.3 μs

Playback speed 1.0×

Live Readouts

Elapsed time

0.0 μs

Sensors fired

0 / 4

Localization error (grid-search)

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How it works

This is the 2D companion to the 3D acoustic-emission simulator, computed independently rather than a flattened render of the 3D scene. It keeps the same real time-difference-of-arrival (TDOA) multilateration physics, but adds two effects the 3D version doesn't model — amplitude decay of the elastic burst and a resulting detection-latency bias — and locates the source with a genuinely different algorithm: a coarse-to-fine brute-force grid search instead of the closed-form 3×3 linear solve.

amplitude:   A(r) = A₀·e^(−αr) / √r        (2D cylindrical spreading + attenuation)
threshold crossing:  δ(r) = τ·(A_thresh / A(r)),  clamped to [0, τ]
measured arrival:    t_i = r_i/c + δ(r_i) + jitter_i

A weaker, more attenuated arrival takes longer to climb past the sensor's fixed detection threshold, so farther or more attenuated sensors report a later-than-true arrival — a systematic bias, distinct from the random timing jitter, that a plain arrival-time model can't see. Push attenuation high enough and a sensor's peak amplitude falls under the threshold entirely: it never fires (dropout), and the source must be located from whichever three (or more) sensors remain.

grid search:  for every candidate (x,z),
  residual(x,z) = Σᵢ [ (t_i−t_ref)_measured − (rᵢ−r_ref)/c ]²
  minimise over a coarse grid, then re-search a shrinking box
  around the best point through several finer passes

Click anywhere on the plate or press Trigger Random Crack to fire an event; the expanding ring shows the true wavefront, fading with the modelled amplitude decay.
Each sensor flashes orange once its measured (delay- and jitter-corrupted) arrival is reached; a sensor that never crosses threshold stays grey — a dropout.
Once at least three sensors have fired, the grid search solves for the source (green marker); the gap to the true source (red marker) is the localization error.
The strip below the map plots each fired sensor's measured arrival time against its true distance from the source, with the ideal noiseless t=r/c line — the vertical gap above that line is the detection-latency bias, and it grows with distance exactly as the α slider predicts.

Real acoustic-emission structural-health-monitoring systems face this same problem: onset-picking algorithms must separate genuine propagation delay from amplitude-dependent trigger bias, and a single dropped sensor (signal too weak, or blocked by damage) is common enough that localization has to work with three good arrivals, not always four.

Click the plate to place a crack

Sensor Sensor — dropout True source Grid-search source Wavefront