AE linear source location

Linear location is the simplest acoustic emission location method. Two sensors are placed a known distance L apart on the item — along a pipe run, a weld seam, a bolt line — and the only measurement needed is the difference in first-threshold-crossing time between them, Δt. Because the wave travels at the same speed in both directions, that time difference converts directly into a path-length difference Δx = c·Δt, and the source must sit half of that difference away from the mid-point, toward whichever sensor triggered first.

The distance from the first-hit sensor is d₁ = (L − c·Δt)/2. Note the whole method rests on one number the technician has to earn: the velocity. AE in plate and pipe wall does not travel at the bulk longitudinal velocity — it propagates as guided (Lamb) modes whose speed depends on wall thickness, frequency and mode. The extensional (S₀) mode in thin carbon steel runs at roughly 5300 m/s, the flexural (A₀) mode is slower and strongly dispersive, and a surface (Rayleigh) wave sits near 3000 m/s. Always establish the velocity on the actual structure with Hsu–Nielsen pencil-lead breaks before trusting any location.

Two limits bound the result. If |c·Δt| equals L, the source is at (or beyond) one of the sensors and the arrival difference saturates — anything outside the array collapses onto the end sensor and cannot be located. And the location error is roughly c·δt/2, so a 10 µs timing uncertainty on steel at 5300 m/s is already ±27 mm of position error before geometry is considered. Threshold crossing on a slow-rising flexural arrival can easily cost far more than that, which is why velocity checks and consistent threshold settings matter more than arithmetic precision here.

Δx = c · Δt
d₁ = (L − c·Δt) / 2   (from the first-hit sensor)
d₂ = L − d₁
Δt_max = L / c   (source at a sensor)
location error ≈ c · δt / 2