# Review on Structural Health Evaluation with Acoustic Emission
## 2 Signal Attenuation
### Attenuation Measurements on Large Metallic Structures  
[PERSON] and [PERSON] [33] reported in 1975 the first quantitative study of AE signal attenuation on pressure vessels, showing that signal amplitude (expressed in dB scale) decreased linearly with distance of propagation, except near the signal source where the slope of the decrease was steeper. The frequency they examined was 100 to 850 kHz and the wall thickness of the pressure vessels was 100-130 mm. Thus, the signals examined were Rayleigh waves. Selected data was replotted against distance (in the logarithmic scale) as shown in Figure 1. Of the five plots, the data at 100 and 200 kHz followed the inverse square root distance dependence, indicating absorption loss was negligible. For the two higher frequency cases at 400 and 600 kHz, additional attenuation term of 1.7 or 2.1 dB/m accounted for the observed deviation from the 1/\(\surd\)x dependence. Data at 850 kHz was inadequate, but it seems to show even higher attenuation. For a given plate thickness, a limiting frequency exists, below which Rayleigh waves do not exist. For the 100-mm thick steel, it is 82 kHz, as shown in the Appendix A.  
[PERSON] [34] reported AE signal attenuation for 30-kHz signals on a pipeline of nearly 300-m length. A replot of this data (with blue + symbols) in Figure 2a exhibits the same 1/\(\surd\)x behavior (indicated by a black line) with small additional attenuation of 0.17 dB/m. Data points for the 1/\(\surd\)x plus 0.17-dB/m attenuation are shown by red circles. Here, Lamb waves propagated on a relatively thin pipe wall (of a few cm thickness). [PERSON] [35] reported attenuation data for large gas cylinders. These cylinders were 12-m length, 0.6-m diameter, and 14.3-mm wall thickness and made of heat-treated 4130 steel (quenched and tempered after fabrication). His data for a 3 AAX tube at 150 kHz is plotted in Figure 2b. Most data points fit the 1/\(\surd\)x behavior except a few points deviated lower, suggesting possible effects of signal absorption at large distances. In these two studies, dispersion loss was minimal.  
More attenuation measurements have been published recently. The data of [PERSON] et al. [36] for 30-kHz signals on a pipeline up to 100-m length are shown in Figure 2c. Their results are similar to the [PERSON] case with a slightly higher attenuation of 0.34 dB/m. [PERSON] et al. [37] tested 150-kHz signals from pencil-lead breaks on steel sheet and plate, getting only the 1/\(\surd\)x behavior since the maximum distance was 2 m. Their cylindrical block did exhibit attenuation of 17 dB/m in addition to the 1/\(\surd\)x behavior. Thus, these observations fit with the theory and early experiments [20; 24].  
Figure 1: Attenuation data (amplitude in dB vs. distance in m) on steel pressure vessels at five frequencies from Graham-Alers [33]. From top to bottom: 100 kHz (blue), 200 kHz (red), 400 kHz (purple), 600 kHz (orange), and 850 kHz (green). Signal source was a white noise generator. Lines drawn represent 1/\(\surd\)x dependence.  
Two other works were outside the above framework. CETIM group [38] examined large penstocks in a hydropower plant covering the length of 40 m. Their low and medium frequency attenuation studies resulted in the inverse-distance behavior. This may be due to many thick flanges for these particular penstocks that appear different from the common design of long pipe sections. [PERSON] [39] reported Lamb wave attenuation on a steel plate, but his signal energy values decreased with \(1/\surd\)x, implying negative amplitude attenuation. It is likely that his energy data was already converted to amplitude values.