## 4 Results
### Sparse Array NDT  
As mentioned at the end of the previous section, to increase flaw detection reliability, a sparse array of optical fiber sensors could be situated at different circumferential and/or axial locations along the pipe. This would allow detection of a flaw at any location along a pipe, because if it is close to one sensor it will also be sufficiently far from other sensors to allow for reliable detection. Several sparse arrays were simulated by moving the optical fiber sensors to different locations on the test pipe. An optical fiber sensor was located at 0 feet, 3 feet, 6 feet and 9 feet from the sending collar on the top, left, bottom, and right sides at each of those axial locations. Data was collected at two locations at a time until data from all 16 locations was collected. Data from multiple positions is then combined to allow for an assessment of a variety of sensor array geometries. In the present work, two optical fiber sensor arrays are considered. Both spiral down the pipe so that there is one sensor located on the top, right, bottom, and left sides of the pipe, each at a different axial location. Group 1 contained sensors on the left, bottom, right, and top, and group 2 contained sensors on the right, top, left, and bottom of the pipe at axial locations of 0 feet, 3 feet, 6 feet and 9 feet, respectively. This is shown schematically in Figure 9. These groups were selected such that group 1 had sensors directly in front of the two flaws, while the sensors closest to the flaws in group 2 are on the opposite side of the pipe (and therefore those two sensors are not expected to easily detect the flaws). Note that the flaws are located on the top and right sides of the pipe at 10 feet and 7 feet from the sending collar, respectively. To combine the four waveforms collected via the four FBGs in each array into a single \"group waveform\", the individual waveforms are processed by suppressing known position-dependent signals including the dead zone, the direct wave arrival, and the reverse pipe end reflection. When these events are present in the signals, the amplitude is reduced to a value of 20 mV, chosen because it is close to the noise level. The amplitude envelope of each of the four waveforms is also shifted in time to correspond to their respective positions along the pipe axis. After time-shifting, the waveforms are added, and the average is calculated. Flaws are more easily detectable in the group waveform than in any individual waveform from a single FBG. Additionally, the combined waveform is more robust than data from a single location since we are unlikely to miss a flaw due to a particular flaw position relative to a single sensor. Note that in general, the arrival times of these suppressed features would be known _a priori_ since the sensor locations are known. This suppression algorithm also adds a jaggedness to the waveforms, as the suppression is applied as a step function. For the data shown in Figure 10, this jaggedness occurs for the approximate length of the initial wave pulse (1 foot) as the wave passes each sensor location: 1-2 ft, 3-4 ft, 6-7 ft and 9-10 ft. Figure 10 shows F-Scans of the processed group waveforms for both (a) group 1 and (b) group 2 fiber optic sensor arrays over 30 to 100 kHz frequencies generated with the SMS collar. The combined  
Figure 10: F-Scans of the processed group waveforms for both (a) group 1 and (b) group 2 fiber optic sensor arrays. Flaws (red ovals) are clearly detected at 7 feet and 10 feet from the sending collar across a wide range of frequencies. The far pipe end reflection is detected at 18 feet. Note that groups 1 and 2 both detect the flaws even though group 2 has multiple sensors near flaws in non-ideal locations for efficient flaw detection. Figure 9: Schematic showing sensor locations for array groups 1 (**above**) and 2 (**below**). Fiber optic sensors are indicated by green rectangles and the optical fiber is indicated by the blue line. Dashed lines indicate the optical fiber and sensor on the far side of the pipe.