# An Omnidirectional Near-Field Comprehensive Damage Detection Method for Composite Structures
## 2 Ultrasonic Phased-Array Damage Imaging Method
### Near-Field Sampling Ultrasonic Phased-Array Damage Imaging Method
\[S_{\theta}=\max(\sum_{i,j=0}^{M-1}A_{ij}(\Delta t_{pij})) \tag{7}\]  
Using the ultrasonic phased-array technology, the position of damage can be determined using the angle \(\theta\) and radius \(r\), which can be calculated by using the signal arrival time \(\Delta t\) and Lamb wave velocity \(c\); the distance \(r\) of the damage from the coordinate system origin is given by:  
Figure 2: The principle of sampling near-field phased-array ultrasound imaging. \[r=\frac{\Delta t\cdot c}{2} \tag{8}\]  
The signal energy (amplitude) can be expressed as a function of its distance and direction, which represents a function of time and angle. Meanwhile, the scanning image can be obtained by displaying the energy of a synthetic signal, so the damage can be clearly displayed in the scanning image. To make the damage position more intuitive and easier to observe in the image, its polar coordinates, namely angle \(\theta\) and radius \(r\), are converted into Cartesian coordinates. Assuming that \(x\) and \(y\) are respectively the horizontal and vertical coordinates in the Cartesian coordinate system, the corresponding coordinates conversion relation is given by:  
\[\left\{ \begin{array}{l}x=r\cos\theta\\ y=r\sin\theta\end{array} \right. \tag{9}\]  
The advantages of near-field ultrasonic phased-array imaging technology are as follows: the detection area and position can be defined flexibly; and the fixed-point measurement can be realized, which is especially suitable for detecting the damage position. Also, due to the high detection accuracy, when a few detection errors occur, the entire detection image reconstruction will not be affected. The specific flowchart demonstrating near-field damage imaging monitoring is shown in Figure 3.  
The main shortcoming of near-field phased-array imaging is that in this method each polar angle \(\theta\) (the angle step is 1\({}^{\circ}\)) is used in data collection, which makes data collection laborious. Moreover, the problem of angle blindness and false images can also occur in one-dimensional phased-array ultrasonic monitoring. Thus, the key current problem is how to realize omnidirectional near-field damage monitoring quickly and efficiently. Through the experimental research, it has been found that the angle scanning realized by the time delay of the excitation signals of each array element in advance is as essential as the angle scanning realized by the time delay of the receiving signal of sensor elements in a later stage, which denotes the control of the initial phase of signals [12]. Figure 3: Flowchart of the near-field sampling ultrasonic phased-array damage imaging monitoring process. Therefore, in this work, we study the sampling phased-array data acquisition technology to improve data collection, where the viewpoints are not distinguished, and every piezoelectric element is used in the scanning process such that when one of the piezoelectric elements is in the incentive operating mode, the rest of the piezoelectric elements act as sensors. Then, using the already explained scanning principle and determination of the time delay of each of the elements, the overall sensing signal delay is determined. Sampling phased-array data collection is basically the same as traditional phased-array data collection but less time consuming and more efficient. In addition, the two-dimensional cruciform array can be used to realize the omnidirectional detection and solve the problem of angle blind areas and pseudo-images.