# EMD-Shannon Entropy-Based Methodology to Detect Incipient Damages in a Truss Structure
## 5 Results
Based on ANOVA results and Figures 7 and 8, the EMD method fused with SEI is capable of identifying incipient damage; the other two EMD methods (EEMD and CEEMD methods) can be discarded for this task because they are more computationally-intensive, as mentioned in Section 2. In this way, the computational load used in the proposed methodology is kept at a minimum. Therefore, the IMF 1 in the x-direction (Ax), obtained using the EMD method, is selected as the most discriminant IMF. Figure 7: Distribution of the estimated SEI values for the healthy (H) and the incipient damage condition for each bay (B) using the IMF 1 for Ax, Ay, and Az, and the (**a**) EMD, (**b**) EEMD, and (**c**) CEEMD methods, respectively. Once selected as the most useful method for evaluating the structure condition, it is used to verify its efficiency under other levels of damage such as moderate, high, and severe, which are represented by a reduction of diameter in the bar element of 3 mm, 5 mm, and 8 mm, respectively. Figure 9 illustrates the distribution of the SEI values estimated by using the IMF1 and Ax for healthy condition and for all the damage levels of corrosion treated in this work (1 mm (I: incipient), 3 mm (L: light), 5 mm (M: moderate), and 8 mm (S: severe) of reduction in the bar element diameter). Observing this figure, the obtained SEI values for the healthy condition and different levels of damage are completely separated, allowing us to identify different levels of damage regardless of its location. Figure 8: Distribution of the estimated SEI values for the healthy and the incipient damage condition joining all the estimated SEI values for all the bays using the IMF 1 for Ax, Ay, and Az, and the (**a**) EMD, (**b**) EEMD, and (**c**) CEEMD methods, respectively. Figure 9: Distribution of the estimated SEI values using IMF 1 and Ax for healthy condition (H) and for the four levels of corrosion, joining all SEI values estimated by all bays (1 mm (I: incipient), 3 mm (L: light), 5 mm (M: moderate), and 8 mm (S: severe) of reduction in the bar element diameter). Finally, once all SEI values for the 5 conditions (healthy and four damage levels) have been estimated, and based on one-way ANOVA, two intervals of analysis are established and introduced to the DTC for the automatic evaluation of the structure condition. Interval 1 (healthy condition): \(8.4\leq\text{SEI}\leq 8.65\) and interval 2 (damage condition): \(8.69\leq\text{SEI}\leq 9.8\). Table 2 presents the classification results in form of a confusion matrix, showing that the proposed methodology is efficient and reliable for assessing the structure's condition, because 100% accuracy is obtained. It is important to mention that the proposed method can become a useful tool for evaluating the condition of civil structures because (a) it can be considered of low computational complexity, allowing the implantation in hardware such as field-programmable gate arrays (FPGAs), digital signal processors (DSPs), etc, (b) it requires only a sensor to determine the structure's condition, and (c) it detects the presence of incipient damage in the structure regardless of its location, overcoming the recent work proposed by [PERSON] et al. [58] and [PERSON] et al. [5], where their proposals are only capable of identifying damages starting from a moderate level; in addition, they require more than one sensor.