**3. Source Location**

Methods of AE source location came from seismology and have been refined to meet demands for accuracy, speed, and robustness against false location [5,108–112]. Actually, the source location or localization problem is a general topic of interest to broad segments of science and engineering. See a comprehensive review in connection to signal processing [113]. The AE location methods also evolved with available computational capabilities, starting with table look-up and first-hit or zonal location, as described by Hutton in 1972 [114]. In 1991, Crostak [115] developed a directional sensing method with four-sensor arrays to simplify source location, allowing a source location using two sets of sensors. More recently, three-sensor arrays worked just as well, despite reducing the sensor count [116,117]. New localization methods are adapted to AE field as reported in, e.g., [112,118].

For typical AE applications, currently available 2-D and 3-D location algorithms satisfy their basic needs. The algorithms utilize time differences of arrival (TDOA) and seek the intersection of a set of hyperboloids assuming constant wave propagation speed, usually relying on iterative processes. However, there are more requirements developing in the SHM field for faster calculations and less sensor placements [14,119]. In particular, smaller sized PWAS have added a new dimension to source location strategy as these allow mode discrimination and provide directional information [14] and phased array concept is also a useful addition [120]. Automation of AE detection will enable broader uses of AE technology and Holford et al. [112] discussed some examples developed, focusing on fatigue problems that still menace critical structural elements.

One of newer approaches relies on exact closed form solutions, which can reach the source position efficiently and accurately. This analytical method obtains the AE source as the intersection of spheres, the radii of which are related to TDOA [121–124]. Some are introducing artificial intelligence concepts for source location, including Gaussian process, support vector machine and deep learning [125–127]. Earlier, neural networks and genetic algorithm were also used [128]. For AE source location on thin plates, Gorman [129–131] introduced the Lamb wave velocity variation due to S0 and A0 modes, although the dispersion behavior was used in sensor frequency selection earlier [33,114]. Others followed his approach and showed that, for linear location, only a single sensor is needed [132,133]. For anisotropic plates, Kundu et al. [117] developed a method without solving a system of nonlinear equations. This method relies on three-sensor arrays, allowing simpler orientation detection. For 2-D location, this method can also find velocity values by itself with improvements [134]. Other methods can also be used for anisotropic plates [135]. In some composite layups, complex velocity patterns develop and a generic method was devised for such cases [118]. In this best-matched point search method, a structure is represented by points defined relative to sensor network. TDOA values of an AE event are matched with those of the previously defined points, quickly yielding the position of the AE event. Another method with TDOA, named delta-T, has also been advanced since its inception and now incorporate several signal-processing methods, becoming more reliable in dealing with complex geometries [136]. These methods have a root, tracing back to the table look-up methods [114], but now are highly refined for today's AE applications.

Another new approach utilizes time reversal methods. This concept originated from the need to focus on the origin through inhomogeneous media [137–139]. A time reversal method was applied to the analysis of a ribbed composite plate where Lamb wave mode conversion occurs adding an extra mode to the initial two-mode propagation [140]. Here, a matched filter is created that maximizes the ratio of output amplitude to the square root of the input energy. For source location, a number of waveforms recorded by a single sensor containing the impulse response of the medium are used, aided by scattering, mode conversions, and boundary reflections of the medium. As it uses a virtual focusing procedure, no iterative algorithms are used and no prior knowledge of the properties or anisotropic wave speed is needed. See also Douma et al. [141] and Robert et al. [142].

Other special topics are of interest. Liu et al. [143] examined source location errors when thick-walled vessels are tested. Traditionally, the accuracy limit of source location was empirically thought to be the thickness of a structure [5]. They defined errors in three different ways and conducted experiments using large concrete blocks with the thickness of 150 to 600 mm and sensor spacing of 4 to 5.5 m. Errors were found to be 2% to 10%, while the absolute errors were 5% to 30% of the thickness. Thus, results indicate that empirical estimates were realistic considering errors coming from the uncertainties in TDOA. A related report is on the inspection of heavy wall radioactive waste containers [144]. This does show we have to deal with thick-walled containers. Ozevin et al. [145] presented a source location method for open structures, like trussed towers or beams. Each element is modeled in 1-D and these elements are combined for complex spaced structures. A 2-D truss was modeled and compared to a laboratory scale bridge, confirming their approach to be valid. However, the practicality of such an approach depends on the attenuation of flaw AE signals and noise generated at joints inevitably present in large truss structures.

Section 3 covered various approaches to locate the origin of an AE signal, often referred to as an AE event. Basic location method developed from concepts used in seismology about 50 years ago, and was adapted to available instrumentation over the years. With advances in data processing capacity, newer approaches have sprung up in the past 20 years or so. Representative works were collected with brief description in this section.
