AE planar location and sensor spacing

On a plate, vessel wall or tank floor an acoustic emission source is located by intersecting hyperbolae. For any one pair of sensors, the difference in arrival time fixes the difference in path length, and the locus of all points with a constant path-length difference is a hyperbola whose foci are the two sensors. One pair narrows the source to a curve; a third sensor gives a second hyperbola, and the intersection is the source. That is why planar location needs at least three sensors to hit on every event, and why an event detected by only two channels can never be located in two dimensions.

Written with the sensor pair on the x-axis and the origin at the mid-point, the hyperbola is x²/a² − y²/b² = 1 with a = c·Δt/2 and b² = (D/2)² − a², where D is the sensor separation. The vertex distance a is how far along the sensor axis the locus crosses; the asymptote angle atan(b/a) shows how quickly the curve opens out. When a approaches D/2 the hyperbola degenerates into a straight line running away from the near sensor — this is the geometric reason location accuracy collapses for events outside the array.

The other half of planning a planar array is attenuation. AE signals lose amplitude with distance through geometric spreading, material damping and — usually dominant on real plant — leakage into contents, coatings and attached structure. Measure it: run Hsu–Nielsen breaks at increasing distance and fit the dB/m slope. The detection radius is then simply the amplitude budget (source amplitude minus the detection threshold) divided by that slope. For an equilateral triangular array, the worst-case point for detection on three channels is at a sensor itself, at distance S from the other two, so the side length must not exceed the detection radius. For a square array the worst case is the diagonal, giving S ≤ R/√2.