# An Improved Hilbert-Huang Transform for Vibration-Based Damage Detection of Utility Timber Poles
## 1 Introduction
Additionally, the testing data obtained from practical field are often non-stationary and non-linear since the patterns of acquired data frequently changes with time which means frequency components also changes over time. Consequently, pole assessment results vary ominously from the practical condition of tested poles. Regarding this problem, advanced signal processing techniques play a significant role in the condition assessment of timber poles. The conventional Fourier transform can be effective; however, it transforms the data from time to frequency domain resulting into complete loss of time information. Due to this deficiency, time-frequency analysis has attracted numerous researchers for analyzing field tested broadband signal. Among all the time frequency analysis techniques, Wavelet Transform (WT) and Wavelet Packet Transform (WPT) are widely adopted by researchers to deal with such signals which yielded acceptable outcomes [8; 11; 31]. In this technique, original broadband signal was first decomposed into several narrow band signals and then the reconstructed signal was obtained for each band using WT or WPT from which features can be extracted. Usually, resolution and decomposition capability is better for WPT than that of WT while considering a discrete signal [31]. WT can only be used for decomposing the original signal in low frequency components, whereas WPT can decompose the same signal in both low and high frequency components. As a result, WPT can process a signal in more details than WT [31]. However, selection of proper mother wavelet is crucial for both WT and WPT. Features that are extracted in vibration based method using signal processing techniques include resonance frequency [7], power spectral density [32], continuous wavelet transform coefficient [8; 9], short kernel coefficient [9] and auto-regressive coefficient, energy value, and energy coefficient [11]. The signal processing techniques that are used includes fast Fourier transform [7], continuous wavelet transform [9], short kernel method [9], wavelet packet transform [11], empirical mode decomposition [11], and auto-regressive models [11] in order to extract the above mentioned features. However, these features solely cannot distinguish between serviceable and unserviceable condition poles. Recently, another time-frequency analysis method named Hilbert-Huang Transform (HHT) has become more popular for analyzing nonstationary and nonlinear signals [33]. HHT has been adopted for the condition assessment of timber poles using stress wave propagation technique with satisfactory results [34; 35]. The key part of HHT is empirical mode decomposition (EMD) that can decompose field captured broadband signals into subcomponents or mono-component signals denoted as intrinsic mode function (IMFs). Later, Hilbert transform is applied to those IMFs to obtain instantaneous amplitude and instantaneous frequency, thus Hilbert spectrum can be derived representing full energy-time-frequency distribution. EMD process does not require any convolution [36]. Compared to the Wavelet transform, the computation time for EMD is also less. Moreover, it is noteworthy to mention that the concept of the frequency and time resolution is not included in HHT [37]. Instantaneous frequency obtained from HHT has a meaning only for mono-component signals and signals obtained from field are not mono-component but multicomponent. Hilbert transform of IMFs (generated from EMD process) lead to physically meaningful instantaneous frequencies. However, in practice, HHT suffers from a number of deficiencies. First of all, the EMD process generates some unwanted IMFs in the low frequency range that can be misleading during data interpretation of the data [36]. Secondly, depending on the analysed signal, the first IMF may cover broad range of frequency in the high frequency range as well which cannot satisfy the mono component property of IMF [36]. Accordingly, WPT and HHT are employed together in this paper to overcome the aforementioned challenges.