Improving the Positioning Accuracy of Acoustic Emission Events by Optimizing the Sensor Deployment and First Arrival Signal Picking

Acoustic emission (AE) source location is an effective method used to reveal the deformation and damage characteristics of materials. Improving the positioning accuracy of AE events is extremely important for both experimental research and engineering practice. An experiment was performed on a standard rock specimen to investigate the key factors that affect the positioning accuracy of an AE event, such as the computational combinations and spatial layout of the sensors and the picking accuracy of the first arrival signal. The results show that as the number of sensors involved in the positioning calculation increases, both the maximum and average positioning errors clearly decrease, and the positioning accuracy increases. Meanwhile, a better result is achieved when the number of sensors involved in the positioning calculation reaches three-fourths of the total number of monitoring sensors used. Under this condition, both the minimum positioning error and the error dispersion are sufficiently low, and the reliability of the positioning results is greatly improved. Furthermore, when different types of and deviations in the first arrival signal are used for the location calculation of the same AE event, the positioning results are quite different, and large errors are found. Finally, the accurate positioning of an AE event is realized by adjusting the number of sensors and improving the picking accuracy of the first arrival time of the signal. The maximum reduction in the positioning error achieved is 96.62%, and the minimum reduction is 57.61%. Hence, the positioning error decreases significantly. The investigation results can provide an important reference for the precise positioning of AE events involved in experimental research and engineering.


I. INTRODUCTION
As part of the irrecoverable energy dissipation due to the plastic straining of a stressed material, acoustic emission (AE) is highly associated with the material's failure. To date, AE source location has been successfully used for defect localization in many different materials, e.g., crack growth description in concretes or rocks [1]- [5], damage diagnosis for steels [6] and leakage detection from pipes [7]. The main purpose of AE localization is to confirm the spatial positions of internal seismic events induced by fracture initiation and propagation. By observing the abundant real-time AE events The associate editor coordinating the review of this manuscript and approving it for publication was Jenny Mahoney. during the microcrack fracturing process, the spatial scales and evolution features of the internal microcracks can be confirmed to provide rational, objective evaluation of the material breakage degree [8], [9]. However, the positioning accuracy of AE events is low, and the regularity and reliability are poor in many laboratory experiments and engineering practices [10]- [12]. Generally, a higher positioning accuracy can lead to a deeper understanding of the microcrack evolution in a material. Therefore, the positioning accuracy of AE events has become a notable geophysical parameter that determines the efficiency and reliability of AE monitoring.
Similar to natural earthquakes and mining-induced microseisms, AE phenomena belong to the category of passive seismic sources and have the characteristics of indeterminacy.
How to reduce errors in and improve the positioning accuracy of seismic sources has remained one of the core concerns in the field of passive seismic monitoring [13]- [15]. Most previous studies focused on improving the positioning algorithm of passive seismic sources with the purpose of enhancing the superiority of the algorithm (e.g., accuracy and timeliness). Schumacher et al. [16] emphasized that an important step in the quantitative analysis of AE is to estimate the locations of the stress wave sources. These authors introduced a novel holistic framework for the development of a probabilistic source location algorithm using Bayesian analysis with Markov Chain Monte Carlo simulation and posterior probability density functions. Based on the differences among the stress waves measured by six surface-bonded piezoelectric sensors, Ciampa and Meo [17] presented a new in situ structural health monitoring system that is able to identify the location of AE sources caused by low-velocity impacts and determine the group velocity in complex composite structures with unknown lay-up and thickness. The magnitude of the squared continuous wavelet transform modulus was employed for the identification of the arrival time of the flexural Lamb mode. Wang and Ge [18] demonstrated that the source location calculation at a mine site could be improved by a comprehensive source location approach, including digital filtering, reliability analysis, an absolute value-based optimization method and an advanced simplex location algorithm. Nagano et al. [19] developed an automatic algorithm of AE source location for AE measurement of subsurface cracks using the triaxial hodogram method. The P-wave arrival time was detected by analyzing the cross-correlation coefficients among three components of AE energy, and the P-wave direction was determined by the least-squares method. Niri and Salamone [20] proposed a probabilistic approach for AE source localization in isotropic plate-like structures based on an extended Kalman filter. Baxter et al. [21] described a novel solution for AE source location, ''Delta T'' source location, in complicated geometric structures, using an artificial source to record the differences in the arrival time information from a number of locations. In addition, a 5-step description of the process was provided. Xu et al. [22] developed a combined AE location algorithm based on the least-squares algorithm and the Geiger location algorithm and studied the temporal-spatial evolution process of microcracks in similarity experiments of pillar materials with the continuous AE technique. Ciampa and Meo [23] proposed an algorithm for AE source localization based on the differences among stress waves measured by surface-bonded piezoelectric transducers and developed an in situ impact detection monitoring system to identify the realtime AE source location. Kundu [24] presented a noniterative source location algorithm employing four AE sensors and found that the main error in source localization is caused by the arrival time calculation. To reduce the error in the AE signal arrival time calculation, different arrival time calculation methods were compared, and a comprehensive method was proposed. Hensman et al. [25] presented a method that ''learns'' the relationship between the time difference of signals and the damage location, using data generated artificially to stimulate AE, and found that the maps learned on a given structure could be effectively generalized to similar structures. Eaton et al. [26] carried out a detailed study on the use of a novel mapping technique for AE source localization in fiber-reinforced composite materials. The performance of the approach was assessed with artificial and realistic AE sources. It was found that the positioning accuracy could be considerably improved. Ohtsu [27] performed the moment tensor inversion analysis of AE sources to determine six independent tensor components and elucidate crack types and the orientations of AE sources. It was suggested that tensile cracks were generated first at weak seams and then shear cracking followed along opened joints.
As mentioned above, although efforts have been made to improve positioning algorithms, the spatial location of the passive seismic source cannot be accurately determined. This issue is attributed to the anisotropy of the medium in the seismic wave field. In most situations, the positioning algorithm obtains the most likely position of the seismic source [28], [29]. The difference between the most likely position and the actual position is the main concern. From studies on natural earthquakes, it is observed that the solution of passive seismic spatial positioning can only reduce the error to a certain degree, so optimization of and improvement in the algorithm is required to realize absolute accurate positioning. Hence, it is less significant to consider only the superiority of an algorithm. Under some circumstances, even if a so-called optimized algorithm is adopted, the positioning accuracy is only slightly improved, and no ideal result is achieved. It is difficult to realize the accurate positioning of the absolute spatial location of the seismic source. Furthermore, an optimized positioning algorithm cannot be applied to all types of AE events. Therefore, it is necessary to determine other factors, in addition to algorithm superiority, that play key roles in improving the positioning accuracy of AE sources. In this paper, AE simulation was performed on a standard limestone specimen, and a multichannel AE monitoring system was utilized. Furthermore, the influencing factors on positioning accuracy were analyzed, such as the computational combinations and spatial layouts of the sensors and the picking accuracy of the first arrival signal. Finally, the positioning error of the simulated AE events is reduced, and the reliability of the positioning is enhanced greatly.

II. POSITIONING ALGORITHM AND EXPERIMENT
A. POSITIONING ALGORITHM Compared with natural earthquakes and mining-induced microseisms, AE events occur at a smaller scale, in centimeter-scale materials. In view of the generality in AE sources, the positioning algorithm for natural seismic events can also be used for the location determination of AE events. VOLUME 8, 2020 In a Cartesian coordinate system, the distance (D n ) between the AE sensors and a specific AE event can be determined as follows [24], [30]: where x n , y n , z n , and t n (n = 1, 2, 3 · · · ) are the predetermined coordinates of the n-th AE sensor and the arrival time detected by each sensor, respectively; x 0 , y 0 , and z 0 are the coordinates of the AE event source location; v is the wave velocity; and t 0 is the origin time of the AE source. According to Eq. (1), the objective function can be established: where N is the number of the sensors. Generally, the wave velocity is assumed to be constant, so there are only four unknowns in Eq. (2), including the spatial coordinates of the AE event source and origin time of the AE source. By taking each sensor datum to Eq. (2), an equation can be obtained; four sensors correspond to four equations, which constitute a set of nonlinear equations. Therefore, a four-sensor array would be able to localize one AE event based on the time difference of arrival (TDOA) among sensors [24], [31], [32]. In this study, twelve sensors are arranged to eliminate potential errors.
According to Eq. (2), the closer the calculated position is to the actual position of the AE source, the smaller the result of the objective function. Hence, the process of inverse positioning of the AE source is the process of calculating the minimum value of the objective function. In Eq. (2), the positions of the AE sensors can be determined during the experimental setup. Therefore, reliable signal source location requires accurate determination of the arrival times picked by each sensor.
Therefore, it can be seen that the computational combinations and spatial layouts of sensors and the pickup accuracy of the signal first arrival will obviously affect the location result. An experiment will be implemented to investigate these factors for affecting the positioning accuracy of AE event.

B. EXPERIMENT
To analyze the influence of key factors other than the algorithm on the accuracy of AE source positioning, the artificial shock mode was applied in this study to generate the simulated AE sources. Since the practical spatial position of the impact point is known, it is convenient to compare it with the calculated position. In the experiment, the AE signals detected by the sensors were digitalized continuously with a sampling rate of 1250k samples per second through a high-speed data logger called SEMOS-lab (12 channels). The sensors were closely adhered to the surface of the standard cylindrical rock specimen with a diameter of 50 mm and height of 100 mm. The twelve AE sensors (Sen1 to Sen12) were orthogonally arranged in 4 columns and 3 rows at a spacing of 30 mm and were closely coupled with the rock specimen to synchronously and continuously monitor the seismic wave propagation after the artificial excitation. Meanwhile, one iron nail (In) and one iron rod (Ir), with black ink on their cusps, were taken and thrown from different directions and heights to generate 8 random active shot points (In1 to In4, Ir1 to Ir4) on the upper surface of the rock specimen. Instantaneous shock signals generated from the artificial excitation were recorded by the AE sensors in real time. With the black ink, the iron nail and iron rod accurately marked the striking positions, and the actual positions of the simulated AE event sources can be observed. This experimental scheme has the superiority that the actual spatial positions of the simulated AE events can be compared directly with those calculated from the positioning algorithm. This is convenient for verifying the reliability of the results and evaluating the positioning accuracy. The experimental devices and scheme are shown in Fig. 1. By considering the geometric center of the rock specimen as the origin of the Cartesian coordinate system, the spatial coordinates of the twelve AE sensors are summarized in Table 1.

A. SPATIAL COORDINATES OF THE AE SOURCES
Based on the experiment, the locations of eight AE events are recorded (Fig. 2). The spatial positions of these AE events are obtained by microscopic image analysis ( Table 2).

B. FIRST ARRIVAL TIME PICKING OF AE SIGNAL
A group of seismic signals (In2) are obtained from the experiment and are given in Fig. 3. Based on the relative rules of arrival time picking, the first arrivals of these recorded seismic waves in every channel are picked from the take-off points of the P waves (Table 3).

C. POSITIONING CALCULATION RESULTS OF AE EVENTS
When the computational combinations are twelve, the type of first arrival of signal adopts take-off point, deviation of first  Under the same experimental conditions, the error between the calculated position and the actual position of the eight simulated AE events is significant even if the same algorithm is used for positioning calculation and only the shock points are changed. The maximum error reaches 12.6410 mm (In2 event), while the minimum error is 1.0848 mm (Ir4 event). This finding indicates that the accuracy of the positioning is not completely dependent on the algorithms but is also highly dependent on other factors. The parameters involved in the positioning calculation mainly include the spatial coordinates of the sensors and the first arrivals of the P-waves. The sensor coordinates are fixed, and the sensors involved in the source location determination are selected. The first arrival times of the signals are artificially marked and selected. These factors are significantly affected by a few extrinsic factors, such as the noise, artificial judgment, sensor number and rock physical properties. The fact that the seismic source positioning is inaccurate does not necessarily result from an unreliable algorithm. In some situations, the inaccuracy is caused by the poor picking accuracy of the first arrival or the unreasonable selection of a senor. Changes in any factor will cause positioning errors to varying degrees and hence affect the reliability of seismic positioning calculations. Among the eight simulated AE events, In2 has the maximum positioning error. Therefore, to analyze the positioning error induced by multiple factors, the In2 event is taken as an example in this study. The same positioning algorithm is used, and the influences of computational combinations and spatial layout of the sensors, the first arrival time picking accuracy will be discussed.

IV. DISCUSSION
For passive seismic positioning, the accuracy of the calculation result depends on the positioning error. Error between the calculated position and the actual position always exists. Factors influencing the positioning error can be divided into two kinds: uncontrollable and controllable. Uncontrollable factors mainly include the positioning algorithm and material anisotropy, while controllable factors vary (e.g., the computational combination, sensor spatial layout, signal first arrival picking and sampling frequency). In the following context, taking the case of the In2 seismic source as an example, the influences of controllable factors on positioning accuracy will be analyzed.

A. IMPACT OF THE COMPUTATIONAL COMBINATIONS AND SPATIAL LAYOUTS OF SENSORS
Based on the Geiger ray positioning principle, the number of sensors used for the determination of the absolute source location should be no less than four. The total number of sensors in this experiment is twelve. Table 4    involved in the positioning calculation ranges from four to twelve, there are 3797 positioning results in total, as shown in Table 4. According to Table 4, a statistical analysis is performed on every quantitative combination, and the changes in positioning error with the increase in the number of sensors are presented in Fig. 6, including the maximum, minimum and average values of the positioning error. Fig. 6 shows that with the increase in the number of sensors involved in the positioning calculation, the maximum and average values of the positioning errors gradually decrease. When the number of sensors increases from four to twelve, the maximum positioning error changes from 100.472 mm (when Sen1, Sen4, Sen7 and Sen10 are employed) to 12.641 mm (when Sen1 to Sen12 are employed), which is a reduction of 60%, and the average positioning error changes from 24.328 mm to 12.641 mm, which is a reduction of 48%. It is indicated that the reliability of the positioning accuracy usually strengthens if more channels are used in the calculation. Therefore, more sensors are suggested when positioning passive seismic sources. This approach does not necessarily decrease the specific positioning error but often plays a key role in reducing the error in most situations.
Hence, a better result is achieved when the number of sensors involved in the positioning calculation is nine, accounting for three-fourths of the total number of monitoring sensors. Under this condition, both the minimum positioning error and the error dispersion are sufficiently low, and the reliability of the positioning results is greatly improved.
In addition, the spatial layout of the sensors is also a key factor affecting the reliability and effectiveness of AE event positioning. Based on the spatial layout of the AE sensors, the space in which the AE events may be localized is divided into two types. One region is the largest internal space covered by all sensors, which is called the sensor-controlled region. The other region is the space outside of the sensor-controlled region. The positioning accuracy is generally higher if the actual seismic source is in the sensor-controlled region. When the source locations of the AE events are calculated, it is often found that the variation in the source error in the threedimensional space is inconsistent.
In this research, the deviation in the positioning in the X and Y directions is limited but becomes obvious in the Z direction. This phenomenon is closely related to the spatial layout of the AE sensors in the experiment. Because the dimensions of the rock specimen are 50 mm in diameter and 100 mm in height, the spatial density and control range of the sensors in the X and Y directions are greater than those in the Z direction in this study, which easily ensures the positioning accuracy in the X and Y directions with the sensors in different locations. The extensions of the sensors in the Z direction are significantly smaller than those in the other two directions, which leads to weaker controllability of the sensors in this direction and higher deviation in the  positioning. Therefore, it is quite significant to optimize the spatial layout of the sensors in AE source positioning, and the sensors should be uniformly arranged as possible around the seismic source.

B. IMPACT OF THE PICKING ACCURACY OF THE FIRST ARRIVAL OF THE AE SIGNAL
The first arrival of the seismic wave signal is one of the key factors that affect the positioning reliability of AE events. The accuracy of the AE source positioning is closely related to the types and deviation in the picking of the first arrival. The types of first arrival usually include the take-off point, the first crest, the first trough, the first zero creep, the crosscorrelation point and the maximum energy point. On the other hand, the deviation in the picking of the first arrival is sensitive to the sampling interval.
For the eight simulated AE events presented in the study, if a consistent algorithm and related parameters are considered, the spatial locations of the shock points are repositioned when the first arrivals of different types and the deviations in every signal channel are chosen for calculation. Table 5 and Fig. 7 show the positioning errors of simulated AE events using the different types of the first arrivals considering that the deviation in the first arrival is the zero point. Table 6 and Fig. 8 present the maximum and minimum positioning errors and their percentage reduction from the maximum error to minimum error for AE events considering the different types of first arrivals.
It is seen that under different types of first arrivals for the same seismic event, the positioning results are quite different, and large errors are observed. Surprisingly, the greatest reduction percentage from the maximum error to minimum error can reach 73% for the same AE event (case Ir4), and the smallest reduction percentage is 32% (case In3).
Moreover, Table 7 and Fig. 9 show the positioning error of simulated AE events using the different deviations in the first arrival signal under the take-off point type of first arrival). Table 8 and Fig. 10 illustrate the maximum and minimum positioning errors and their percentage reduction from the maximum error to minimum error for AE events under the different deviations in the first arrival signal. It is found VOLUME 8, 2020 TABLE 6. The maximum and minimum positioning errors and their percentage reduction for different AE events considering the different types of first arrivals (deviation in first arrival: 0 point).

TABLE 7.
Comparisons of the positioning errors of simulated AE events using the different deviations in the first arrivals (type of first arrival: take-off point). that under different deviations in the first arrival signal, the positioning results are also extremely different. The greatest reduction prcentage from the maximum error to minimum error is 89% for the same AE event (case Ir4), and the smallest reduction percentage is 32% (case In2).
As mentioned above, when different types of and deviations in the first arrival signal are used for the source calculation of the same seismic event, the positioning results are quite different, and large errors are found. Taking the case In2 seismic source as an example, the positioning error reaches the minimum (8.2582 mm) if the first arrival deviation has no sampling interval and the cross-correlation point is used. However, the error increases by 2.12 times (17.5449 mm) when the first zero creep is used. The positioning error is minimal (9.3851 mm) under the condition that both the takeoff point and the sampling interval (−1 point) are applied, and the error increases by 1.45 times (13.5779 mm) as the sampling interval increases to 2 points.
Picking of the first arrival of the AE seismic waves seems simple but is quite difficult if high precision is needed. The local wave phase and morphology of every signal are different. It is unreliable to use uniform rules to determine the first arrival signal, especially without considering the effect of superimposition and dissimilation of multiple seismic wave phases. Therefore, accurate and reliable picking of the first arrival signal is an important prerequisite for improving the positioning accuracy of AE sources. In applications, it is necessary to suppress the noise and improve the signal quality so that the first arrival signal can be more accurately picked and that the positioning accuracy and reliability of the AE focal points can be further improved.

C. POSITIONING RECALCULATION RESULTS OF AE EVENTS
Based on the optimization and fine adjustment of the magnitude of the above influencing factors, under the condition that the spatial layout of the sensors remains the same, the positioning locations of the simulated AE events are repositioned, and the results are given in Fig. 11. All the positioning errors of these simulated AE events decrease greatly. It is found that all the positioning errors are less than 1 mm, which can meet the test requirements of the standard cylindrical rock specimen. The minimum and maximum errors are only 0.2519 mm and 0.7003 mm, respectively (the applied minimum grid scale is 1 mm). The calculated locations are extremely close to the actual impact points. This accuracy is much higher than those of other AE source location studies on rock materials, and the location error of previous studies usually reaches more than 10 mm for events inside the sensor array [31], [32].
Comparisons of the positioning errors of the initial condition and recalculation for different seismic sources are shown in Table 9 and Fig. 12. The maximum reduction in the positioning error reaches 12.2418 mm, which is a reduction of 96.62% (In2). The minimum reduction in the positioning error reaches 0.6249 mm, which is a reduction of 57.61% (Ir4). Therefore, the accurate positioning of the passive seismic source is realized by adjusting the number and spatial layout of the sensors and improving the picking accuracy of the first arrival of the signal.
In general, the number and spatial layout of the sensors involved in the positioning calculation have a direct impact on the AE positioning accuracy. As the number of sensors increases, the seismic positioning error tends to decrease gradually. A higher positioning accuracy is achieved if the spatial distribution of the sensors is more uniform. Currently, many passive seismic positioning algorithms are derived based on the modeling of a homogeneous medium. However, the structure of a medium is extremely complex and anisotropic in real situations. Energy absorption is intense, and the wave velocity decreases along some propagation paths. Due to the influence of an abnormal structure, the recorded first arrival signals are always different, even though there is no difference among the radial distances of the wave channels. Therefore, to improve the positioning accuracy and reliability of the passive seismic source, specific analysis and determination are necessary for the channels used according to the quality of the available signals. The use of more sensors in positioning does not always lead to better accuracy. On the premise that infinite channels are available, it is recommended to remove channels with large anomalous forms so that interference is avoided. The reliability of the positioning results tends to improve when signal channels with earlier first arrival are applied. This indicates that the location of the passive seismic source is relatively close to the measuring point and that the homogeneity of the medium along the wave propagation path is relatively higher than that for longer paths. Meanwhile, the sensors involved in positioning calculation can be multiplied and combined to obtain different positioning results. An optimal source location is then obtained through mutual verification.

V. CONCLUSION
1. Once the number of sensors involved in the positioning calculation increases, the maximum and average values of the positioning errors gradually decrease, and the positioning accuracy generally increases. As the number of sensors ranges from four to twelve, the maximum positioning error changes from 100.472 mm to 12.641 mm, which is a reduction of 60%, and the average positioning error changes from 24.328 mm to 12.641 mm, which is a reduction of 48%. 2. When the number of sensors ranges from four to nine, the minimum positioning error remains at 0.429 mm, and the minimum positioning error reaches 12.641 mm, which is 30 times greater, when the number of sensors increases to twelve. Hence, a better result is achieved when the number of sensors involved in the positioning calculation is nine, accounting for three-fourths of the total number of monitoring sensors used. Under this condition, both the minimum positioning error and the error dispersion are sufficiently low, and the reliability of the positioning results is greatly improved. 3. The positioning accuracy of the AE source is closely related to the types of and deviations in the first arrival signals. Considering the different types, the greatest reduction percentage from the maximum error to minimum error reaches 73% for the same AE event (case Ir4), and the smallest reduction percentage reaches 32% (case In3). On the other hand, with the different deviations, the greatest reduction from the maximum error to minimum error percentage reaches 89% for the same AE event (case Ir4), and the smallest reduction percentage is 32% (case In2). 4. The accurate positioning of an AE event is realized by adjusting the number of sensors and improving the picking accuracy of the first arrival of the signal. The maximum reduction in the positioning error reaches 12.2418 mm, a reduction of 96.62% (In2), and the minimum reduction in the positioning error reaches 0.6249 mm, a reduction of 57.61% (Ir4). Hence, the positioning error decreases significantly.