# EMD-Shannon Entropy-Based Methodology to Detect Incipient Damages in a Truss Structure
## 6 Conclusions  
This paper proposes a new methodology to perform the SHM in truss-type civil structures. It consists of the integration of the EMD method coupled with SEI to analyze the vibration structure response in order to obtain the features that can determining a given structure's condition. In this regard, a statistical analysis using the one-way ANOVA is performed to determine the IMF number as well as the axis that has the most discriminate features. The IMFs obtained using three EMD-based methods (EMD, EEMD, and CEEMD) are compared. From Figure 6 and Table 1, it is shown that the three methods estimate very similar results, being also necessary to select the method that has the lowest computational burden [64]. In this way, EMD is the one that uses the fewest resources; therefore it is chosen as the signal processing technique in this proposal. In this way, the computational resources employed are kept at a minimum. On the other hand, the SEI was shown to be an effective and reliable index to detect damage, since an effectiveness of 100% was obtained using a low-complexity DTC. From Table 1, it is seen that IMF 1 has all the information required to detect damage, regardless of its severity. It should be pointed out that IMF 1 is a high-frequency mode; thus, failure is found in the high-frequency region.  
The obtained results show that the proposal can detect a reduction of 1 mm in the bar diameter, which is a useful advantage in SHM applications. On the other hand, if the ADC resolution is increased, a more detailed signal can be acquired, which for noisier signals, can be useful; this can allow us to better estimate features using the SEI, possibly resulting in a lower \(p\)-value. Further, it must be noted that the proposed method can detect damage regardless its location, which is also a desirable feature, as it can be used in situations where the number of sensors is limited. Thanks to the moderate usage of computational resources, a real-time signal processing platform, such as a field programmable gate array, can be used to implement the proposal, as efficient implementations of the EMD and Shannon entropy methods have been developed [65; 66], allowing for the development of the proposed strategy for the continuous assessment of truss structure integrity, by executing the proposal in specific time  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Structure Condition**} & **Healthy** & **Corrosion** & **Effectiveness (\%)** \\ \hline \multirow{4}{*}{Corrosion} & Healthy & 100 & 100 & 100 \\  & incipient (1 mm reduction) & & & \\  & Light (3 mm reduction) & & & \\  & Moderate (5 mm reduction) & & & \\  & Severe (8 mm reduction) & & & \\ \hline \multicolumn{2}{c}{Total Effectiveness} & & 100\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of the DTC (confusion matrix) based on the estimated intervals using ANOVA of the estimated SCI values for all bays.  
intervals, and comparing the obtained results with previous ones. Hence, the results presented allow us to affirm that the proposal can be considered as a solid alternative for SHM-based methodologies, where computational resources as well as the number of sensors are limited.  
Methodology: A.M.-G. and C.A.P.-R.; Experiments and Analyzed: M.V.-R., O.C.-A. and A.D.-G. Guided the research, Conception, and Revision: J.P.A.-S.  
This work was supported in part by the Mexican Council of Science and Technology (CONACyT) by the scholarship 304844 and by the SEP-CONACyT CB-2015/254697 project.  
The authors declare no conflict of interest.