Ultrasonic Array Imaging
This research project utilizes a maximum-likelihood estimation method for the detection and localization of single damage using sparse ultrasonic transducer arrays, commonly known as ultrasonic array imaging.
Experiment Setup
A total of six transmit-receive transducers are employed in this study, enabling the transmission and reception of ultrasonic guided waves. Waveform data are acquired by sequentially exciting each transducer while simultaneously recording received signals on the remaining transducers. As a result, a total of 15 pairs of waveform data are collected.
Assumption: single damage
Specimen: an aluminum plate
Baseline Subtraction
In the following analysis, we utilize different signals obtained through baseline subtraction, a traditional approach used to capture differences that characterize the scattering caused by the damage.
We consider that the damage is the sole distinguishing factor between the baseline and current signals. In other words, we assume that the environmental and operational conditions remain nearly identical before and after the introduction of the damage.
Wave Propagation
We separate the entire wave propagation in the following 3 sections.
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time before the arrival of any scattered wave from the damage
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the arrival of the first, directly scattered wave
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the subsequent echoes of the scattered wave from the structure’s geometric features.
After performing baseline subtraction, the direct incident wave is eliminated, leaving only the remaining first scattered waves and subsequent echoes.
Rayleigh Maximum-Likelihood Estimation
Known parts: feature matrix 𝑉
Each element of the feature vector is the magnitude of enveloped waves.
Unknown parts: the damage is centered at some location 𝒙 to be estimated.
Goal: Given 𝑉, we need to estimate 𝒙.
That is,
L(𝒙|𝑉) is an objective function that should be maximized and the final estimate of 𝒙 is corresponding to the maximum of L(𝒙|𝑉).
Assume: each element of 𝑉 follows Rayleigh distribution.
For more mathematical details, please refer to the following article.
[1] E. Flynn, M. Todd, P. Wilcox, B. Drinkwater, and A. Croxford, "Maximum-likelihood estimation of damage location in guided-wave structural health monitoring", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 467, no. 2133, pp. 2575-2596, 2011.
Rayleigh probability density distribution
Result Evaluation
The right figure displays the array imaging results, where each pixel represents a calculated value obtained from the likelihood function using different pairs of baseline and current signals. The circles represent the transducer locations, the triangle denotes the true damage location, and the white cross indicates the estimated damage location, corresponding to the highest calculated value from the likelihood function.
As can be seen from the figure, the RMLE method only works for the first four cases. However, for the remaining cases, accurate estimation of the true damage location is not possible. This is primarily due to the fact that the pairs of baseline and current signals were obtained under different temperature conditions, leading to a significant impact on the group velocity of incident waves, resulting in the deviation of the different signals from the Rayleigh distribution. Consequently, determining the true damage location becomes impossible.
