# Acoustic Emission Monitoring in Prestressed Concrete:
## 5 Aggregation of Results and Discussion
underlying data, the limits of a 95 % confidence interval are introduced, using the standard errors of the coefficients (SEs) associated with the wire break events \(SE(\bar{\beta}_{\text{wb}})\):  
\[\bar{\beta}^{\prime}_{\text{orm}}=F\cdot\bar{\beta}_{\text{orm}}\pm 1.96\cdot SE( \bar{\beta}_{\text{wb}}). \tag{6}\]  
The transfer factor is determined using the medians of the attenuation coefficients of the time-domain features for the wire breaks and the rebound hammer measurements on the bridges and is approximately the same for both features:  
\[\frac{\bar{\beta}_{\text{wb}}}{\bar{\beta}_{\text{rbh}}}=\frac{4.3\,\text{dB/ m}}{3.6\,\text{dB/m}}=1.2. \tag{7}\]  
The standard errors of the coefficients of the wire breaks were determined during the data processing, but were not documented in detail. They range between 0.1 and 0.6 dB/m and are similarly distributed for both time-domain features and frequency bands. To account for the scattering, the 95 % quantile value of the standard errors is determined at approximately 0.51 dB/m, resulting in the transfer factor  
\[\bar{\beta}^{\prime}_{\text{orm}}=1.2\cdot\bar{\beta}_{\text{orm}}\pm 1.0 \,(\text{dB/m}). \tag{8}\]  
In case ORMs are not feasible, the statistical overview obtained suggests that the attenuation coefficient in the longitudinal direction should be chosen to be at least around 6 dB/m. Figure 13 underscores the observation that higher frequencies experience significantly greater attenuation than lower frequencies. For wire breaks and rebound hammer impulses on the girders, median values in the 0-10 kHz frequency band range from approximately \(-4.7\) to \(-5.0\) dB/m, increasing to about \(-10.3\) dB/m in the 40-50 kHz band. This trend is consistent across bridges in both the longitudinal and transverse directions, suggesting a clear preference for focusing measurements within the low-frequency range. The results discussed align well with the observations made by other researchers, as mentioned briefly in Section 2. Specifically, [PERSON] reported attenuation coefficients in the range of 220-250 dB/m at 1 MHz for mortar specimens, with a predominantly linear relationship observed within the attenuation spectra [27; 28]. Based on these findings, it's feasible to make an approximate extrapolation to the lower frequency range, which is the focus of this study. From this extrapolation, attenuation coefficients are estimated to be between 11.0 and 12.5 dB/m at a frequency of 50 kHz, demonstrating a reasonably good consistency with the established data. Notably, on the girders, the attenuation coefficients derived from time-domain features generally exhibit lower medians compared to those from frequency bands. For bridges there is an overlap between these two data sets for both types of excitation sources. As discussed in Section 4.2, this discrepancy is likely attributable to the data processing approach, wherein only the signal's onset was cut for frequency band analysis, and less than the entire transient was used. This could allow for larger-amplitude occurrences in the residual part of the transient, thus affecting the analysis' outcome. The validity of the results presented assumes that the sensors utilized in the respective applications have similar sensitivity compared to those employed in this study. It is essential that the sensors' response spectra predominantly cover frequencies below 100 kHz. Moreover, when calculating attenuation coefficients using regression analysis, the trend in amplitude changes is crucial. In certain instances, particularly at larger distances during rebound hammer tests on bridges, nonlinear relationships were observed. Such nonlinearity can lead to distortions and potential underestimation of the attenuation coefficients, necessitating careful consideration and evaluation in specific applications. Additionally, it is important to acknowledge that the bridges were not uniformly represented in the study.