# An Improved Hilbert-Huang Transform for Vibration-Based Damage Detection of Utility Timber Poles
## 5 Results and Discussion
### Improved HHT
#### 5.3.3 Instantaneous Frequency Analysis Using Improved HHT  
In order to overcome the deficiencies of original HHT, improved HHT is employed on the same inspected signal from A90C1 sensor that has been used for analysing original HHT in Section 5.2. First, EMD is performed on the reconstructed signal of A90C1 sensor at (5,0) node from Figure 14. After decomposing this reconstructed signal through EMD, screening technique based on correlation coefficients value is applied to obtain the dominant IMFs. A threshold value of 0.1 is selected for the correlation coefficient in order to avoid accidental removing of some low amplitude but relevant IMFs. After applying improved HHT, 5 dominant IMFs are obtained whereas in case of original HHT applied on the same acceleration data, there were 13 IMFs which can be misleading. Figure 15 demonstrates the dominant IMFs after EMD operation for A90C1. Later, instantaneous frequencies of these dominant IMFs are calculated by Equation (5), and energy-frequency-time distribution of these dominant IMFs, designated as Hilbert spectrum, is shown in Figure 16. In Figure 16, some sharp noisy peaks are observed at both ends of the instantaneous frequency plot. This is known as edge effect which occurs due to the approximation in the EMD process [36]. These sharp peaks at the edges will be avoided for data interpretation. Figure 14: Example of reconstructed signal considering A90C1 at (5,0) node. Figure 15: Dominant IMFs after Empirical Mode Decomposition (EMD) operation for A90C1 Serviceable Pole 1 using improved HHT. One noteworthy behaviour is observed from the Hilbert spectrum of IMF1, A90C1 Serviceable Pole 1. Figure 17 demonstrates the Hilbert spectrum of all IMF1 for A90C1, Serviceable Pole 1 including all 4 tests. From this figure, sudden change and a sharp increase in frequency is observed around 0.02 sec which is very consistent for all the IMF1s. Signal after 0.02 s is related to noise and other uncertainties from field testing. Similar behaviour is noticed for all IMF1s of A90C2 for Serviceable Pole 1 and Serviceable Pole 2 including all four tests. The results look very consistent irrespective of the fact that all these IMF1s have different energy values due to different hammer strikes in each test. Therefore, signal up to 0.02 sec will be considered for data interpretation. Additional significant finding here is that the improved HHT is able to recover low frequency and low energy components. Considering the signal up to 0.02 sec in Figure 16, it is observed that instantaneous frequency of IMF5 is almost constant at 55 Hz. This is the possible fundamental frequency/natural frequency of that particular pole. Similarly, 105 Hz and 250 Hz frequencies are observed for IMF4 and IMF3, respectively, which are believed to be higher order fundamental frequencies. Since the condition of this pole is believed to be healthy, there are not much sudden changes in the instantaneous frequency of IMF3, IMF4, and IMF5 and very slight changes are observed for IMF2. Similar analysis has been performed for 12 accelerometer data of 3 serviceable poles and 3 unserviceable poles obtained from all 4 tests in order to check the repeatability and consistency of the results. After that, frequency range of dominant IMFs, average frequency of each dominant IMF and standard deviation are calculated. Figures 18 and 19 demonstrate the frequency range of dominant IMFs, average frequency of each dominant IMF and standard deviation for Serviceable Pole 1 and Unserviceable Pole 3, respectively, considering all the accelerometer data. Both the poles are from same species and their strength class and durability class are also same. Frequency range of dominant IMFs for Serviceable Pole 1 are found to be in a similar range with good consistency considering the variability and uncertainty can exist in any field testing (Figure 18). On the other hand, frequency ranges of dominant IMFs for  
Figure 16: Instantaneous frequencies of dominant IMFs for A90C1 Serviceable Pole 1 using improved HHT.