Acoustic Emission (AE) testing is an advanced non-destructive testing (NDT) technique that measures stress wave, or ultrasonic waves, that are generated by active flaws. AE testing is a passive technique that analyzes the stress waves emitted by structural defects activated during loading. Some common examples of AE in materials include fatigue crack growth in steel pressure vessels and fiber breaks in composite materials. The sudden release of energy caused by these phenomena generates elastic waves that propagate through the volume of the material and guided by the boundaries of the material. AE may travel through the bulk of a material as longitudinal and shear waves. Along the boundaries of the material, AE can be detected via measurement of guided and surface waves. Typically, stimuli such as mechanical loads, pressurization, thermal stresses and magnetic forces, can produce AE.
Figure 1 Acoustic emission hit showing first threshold crossing, peak amplitude, duration, and rise time features .
AE testing is widely used to detect and assess the severity of fatigue crack and fatigue crack growth rates in steel structures including fracture critical bridge structures and metallic pressure vessels. Compared to other NDT techniques, AE testing has several advantages over traditional NDT and even hydrotesting of pressure vessels: (i) in-service testing; (ii) no contamination due to humidity; (iii) remote inspection and (iv) sensitive to active flaws as they propagate. However, there are some important limitations associated with the technology as well: (i) controlled loading of the asset is required; (ii) flaw sizing is generally not possible; (iii) sophisticated instrumentation with operated by highly trained personnel is required; and (iv) only active defects are detected. In this article, the concepts of AE source location are introduced.
Figure 2 Schematic of the 1D linear location 
Source Location in AE testing
Source location is one of three basic objectives of an AE test, which are: (i) detecting AE activity; (ii) locating the source of the activity and (iii) evaluating the material defects causing the activity. Source location is also referred to location calculation in technical literature. Source location is perhaps the most important feature of AE testing since knowing the location of an event abets reduction in the number of source mechanisms that may be possible. This is because source mechanisms are dependent on particular geometric features and thus, accurate AE source location results can aid in inference of crack initiation and propagation.
In this article, the focal point is a class of source location techniques used in conjunction with AE testing for pressure vessels/cylinders. These techniques are (i) 1D linear location; (ii) 2D planar location and (iii) 3D location. They are based on the time difference of arrival (TDOA), wave speed and distance between the sensors. The two underlying assumptions for this class of source location methods are that (a) wave speed remains constant from the source to the sensor and (b) there is a direct wave path between the source and the sensor.
Linear Location (1D): Linear Location is most suited for vessels where the length is much larger than the diameter i.e., a rod-like shape. Figure 2 shows the schematic of the linear location setup.
Figure 2 Schematic of the 1D linear location 
The times when the signal arrives at sensors 1 and 2 are denoted by T1 and T2, also known as the arrival times. If the wave velocity is denoted by , and the difference of arrival times is computed as T2-T1 (or vice versa), then the distance between the AE source and the AE sensor 1 can be calculated using the equation:
In the above equation, D is the distance between the two sensors. Based on this equation, the location of the AE source can be known. From the above relation, it can be verified that if the AE source is in the exact middle of the two sensors, the difference in arrival times would be 0.
Planar Location (2D): If the diameter of the vessel is significant relative to its length, 2D planar location of an AE source has to be utilized. The schematic of the planar location is shown in Figure 3. The fundamental assumption is that the AE source is located in a uniform medium. The distance between the AE source and the sensor is now given by the Euclidean distance metric
Figure 3 Schematic of the 2D planar location 
The AE signal is produced at time To and is spread to any sensor at time Ti. Thus, we have the relationship
Measuring the value of To accurately is a challenge, thus the metric deltaT i-j = Ti - Tj is utilized. The resulting equation is
Given the above relationships, two analytical solutions can be obtained for the case when there are three AE sensors not located on the same line. Choosing the correct coordinates of an AE source would involve knowing the physics of the problem, or by increasing the number of sensors used to locate the source. Typically, an iterative algorithm is utilized in AE testing systems to obtain a numerical solution of a 2D planar location.
3D Location: The 3D location technique, shown in Figure 4, is used for vessels that are spherical in shape. Analogous to the 2D planar location technique, assuming the medium is uniform, the distance between the AE source and the sensor is now given by the equation:
Figure 4 Schematic of the 3D location of an AE source 
The time difference of arrival (TDOA) equation for any two sensors remains the same i.e.
Again, two analytical solutions can be obtained, but for 3D location, a minimum of AE four sensors would be required – and should not be on the same plane (note that for 2D location, they must not be on the same line). As before, an iterative algorithm is utilized in practice by AE testing systems to obtain a numerical solution. Also, as mentioned for 2D location, if an analytical solution is obtained, the correct solution would be chosen based on the physics of the problem at hand.
This article discussed the AE source location techniques used in conjunction with (but not limited to) AE testing of pressure cylinders/vessels. Source location is one of the three basic objectives of an AE test, and accuracy is of importance to make sound inferences about material defects. The source location techniques discussed in this article are (i) 1D linear location; (ii) 2D planar location and (iii) 3D location. They are based on the time difference of arrival (TDOA), wave speed and distance between the sensors. However, the medium is assumed to be uniform for these techniques, and that the wave speed is also constant between the AE source and the sensor. Academic literature on AE source location is focused on developing methods that can rectify these models for situations when the aforementioned assumptions do not hold true.
 Vallen AMSY-6 Software Operation Manual (2019) https://www.vallen.de/products/multi-channel-systems/