# An Image Processing Method for Extraction of the Stress Wave Reflection Period
## 1 Introduction  
Underground structures, such as foundation piles, anchor rods, and buried metal piles, play an important role in large civil engineering. The measurement and evaluation of their structural size and integrity are directly related to the safety of the engineered structures. The traditional method, i.e., pull-out testing, can accurately obtain the buried depth and integrity information of the column. However, it is slow in detection speed, low in efficiency, and it has a problem of secondary buried depth. Therefore, nondestructive testing (NDT) methods have been widely used in detecting size and structural health monitoring (SHM). As an NDT method, the stress wave reflection method has been successfully applied in the health monitoring of foundation piles [1], rock bolts [2; 3; 4], buried metal piles [5], and pipes [6]. The stress wave reflection method is based on the elastic vibration theory of wave propagation in one-dimensional rods [7]. After impacting upon the top of the pile, the stress wave will reflect when it meets a defector the end face of the pile in the process of propagation. By detecting and analyzing the travel time, the amplitude and phase characteristics of the reflected waves, as well as the length and damage location of the pile can be detected. The stress wave is usually produced by piezoelectric materials [8] or vibration hammers [9; 10]. Piezoelectric material, e.g., lead zirconate titanate (PZT), as a type of smart material, has attracted a lot of attention in the field of SHM for its small size, high stability, and good linearity. Because piezoelectric materials have direct and inverse piezoelectric effects, they can be used as both a vibrator and a sensor. PZT-based sensors have been successfully applied to detect metal cracks [11], bolt looseness [12; 13], pipelines length [14; 15], bond-slip monitoring of concrete structures [16], and so on. [PERSON] et al. [17] proposed using a single piezoelectric ceramic transducer to quantitatively evaluate the bolt connection status. [PERSON] et al. [18] used three PZT patches as sensors and actuators to form different detection processes to monitor the looseness of the steel strand. In addition, PZT-based stress wave communication in submarine environments may have greater potential than many conventional methods [19]. In this paper, the PZT sensor is used to collect the reflection signals after the hand-held hammer impacts the buried metal pile. The key to detecting the structural size or defect location by using stress wave reflection is the extraction of the reflection period. The traditional methods of reflection period extraction include the peak-peak method (PPM) and phase analysis method (PAM). The PPM finds the first two peaks of the reflected wave and takes the time interval between the two peaks as the reflection period; however, this method is only applicable to measurement signals with obvious periodic reflection. [PERSON] et al. [20] detected the amplitude of the signal after wavelet denoising to estimate the size and location of the disbond-type defect presented on glass fiber reinforced plastic material. However, when the cylinder is long, the stress wave energy leaks into the surrounding soil during the propagation, which makes the reflected signal too small to evaluate. On the other hand, PAM is widely used to detect bolt length due to the phase mutations only occurring at the end face or defect [21]. [PERSON] et al. [22] analyzed the instant phase of the stress wave to successfully detect the length of the anchor bolt and location of the density defect. However, the interpretation of data depends on skilled personnel and thus has limited objectivity. The self-correlation can make period extraction easier; however, the reflection signal is not obvious due to the energy attenuation and noise interference during wave propagation. The signal period is still difficult to evaluate, even after a single self-correlation. [PERSON] et al.