Abstract
Abstract
This paper compares two optimization strategies for three-dimensional acoustic emission
(AE) source localization in cylindrical shell structures with base plate: the Trust-Region
Reflective (TRF) method with Huber loss function and adaptive initial seeding, and
Particle Swarm Optimization (PSO). Piezoelectric sensors mounted exclusively on the
cylindrical shell were used to localize pencil-lead-break sources placed on both the shell
and the base plate, the latter representing a geometrically challenging case in which the
wave must traverse two distinct surfaces to reach the sensors. Five detection thresholds
(0.25%–5% of the peak signal voltage) were evaluated across both methods and both
surface domains.
Twenty repetitions were acquired at each source position, and the differences between
methods were assessed with paired Wilcoxon signed-rank tests, bootstrap 95% confidence
intervals, and Cliff’s delta effect sizes. For shell sources, PSO achieved the lowest average
localization error (0.189 m, 95% CI [0.153, 0.229] m) at a 0.5% threshold and was
significantly more accurate than adaptive TRF across thresholds, a shell advantage that
persists under correction for multiple comparisons. For base-plate sources the two methods
were statistically comparable: their errors were nearly equal at a 1% threshold (PSO
0.079 m; adaptive TRF within 0.02 m) and each reached its lowest value at the highest
threshold (≈ 0.056 m for PSO and ≈ 0.074 m for adaptive TRF), the paired differences
being either non-significant at the mid-range thresholds or of small effect and mixed
direction elsewhere. In the unrestricted localization scenario, where neither method was
constrained to a surface a priori, the best results were 0.199 m (PSO, shell sources, 0.5%
threshold) and 0.107 m (PSO, base sources, 1% threshold). The lowest threshold was the
worst choice for both surfaces; beyond it, the optimum was
surface-dependent—intermediate thresholds were best for shell sources, whereas base-plate
accuracy improved toward higher thresholds.
The results demonstrate that localizing AE sources on a surface not instrumented with
sensors is feasible with the minimum sensor count required for three-dimensional
localization, provided the geometric propagation model correctly accounts for
multi-surface paths and the detection threshold is tuned to a mid-range value. With
formal statistical testing, PSO emerges as the more robust single choice across both
surfaces: it is clearly superior for shell localization owing to its global search capability,
and at least as accurate as adaptive TRF for base-plate sources, where adaptive TRF
nonetheless remains a competitive alternative.