High-Precision Time-of-Flight Extraction of Ultrasonic Echoes from Ring Arrays Using a Physics-Informed Neural Network

Installation eccentricity of an in-pipe ring array changes the water-layer propagation path and degrades time-of-flight (TOF) extraction in small-diameter thin-walled tubes. This study proposes an array-level physics-informed neural network (PINN) that jointly processes an azimuth-ordered 16 × M echo matrix. A shared temporal encoder and circular-topology feature-fusion module exploit periodic inter-element correlations, while an analytical eccentric-geometry prior and a coordinate-conditioned acoustic-wave-equation residual constrain the solution. A two-dimensional water–pipe-wall finite-element model in COMSOL 6.3 generates 16-channel echo sets under multiple eccentricities and directions. For the representative +x channel and eccentricities from 0.00 to 0.90 mm, the proposed method achieves a TOF mean absolute error (MAE) of 2.33 ns, a root-mean-square error (RMSE) of 2.37 ns, and a maximum absolute error of 3.03 ns. Under the two added noise levels (20 and 10 dB), its TOF MAEs are 1.62 and 1.53 ns, respectively. Within the two-dimensional simulation assumptions and investigated eccentricity range, the corresponding wall-thickness MAE is approximately 0.007 mm and the maximum absolute error is approximately 0.0095 mm. These values quantify algorithmic error under the modeled eccentric propagation and waveform distortion only; they do not represent the total uncertainty of a practical measurement system.