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In acoustic emission measurement, the information of the arrival time is very important for event location, event identification and source mechanism analysis. Manual picks are timeâ€‘consuming and sometimes subjective, especially in the case of large volumes of digital data. Various techniques have been presented in the literature and are routinely used in practice such as amplitude threshold, analysis of the LTA/STA (Long Term Average / Short Term Average), high order statistics or artificial neural networks.
A new automatic determination technique of the first-arrival times of AE signals is presented for thin metal plates. Based on Akaike's information criterion, proposed algorithm of the first arrival detection uses a specific characteristic function, which is sensitive to change of frequency in contrast to others such as envelope of the signal. The approach is applied to data sets of three different tests. Reliable results show the potential of our approach.
Keywords: acoustic emission, first arrival, Akaike's information criterion, thin metal plates
PACS: 43.40.+s, 43.60.+d
The precise determination of the arrival time of transient signals like AE, seismograms or ultrasound signal is one of the fundamental problems in non-destructive testing and geophysics. The information of this time is very important for event location, event identification and source mechanism analysis.
The accurate first arrival determination is carried out visually by an operator or automatically by an algorithm and it depends on the first arrival definition itself. It can be described as the moment when the first energy of a particular phase arrives at a sensor or as a point where the difference from the noise occurs first . These descriptions are also requirements to reliable automatic picker.
With some modification, the methods used in seismology can be applied to AE. The number of recorded AE signals can be up to several thousands during one test. It represents huge amounts of data, which call for automatic determination of first arrival without human intervention by sophisticated approaches. The reason is simple, manual picks are timeâ€‘consuming and sometimes subjective, especially in the case of large volumes of digital data.
Allen  described picker as an algorithm, which is used to estimate the arrival time a phase, and described detector as an algorithm, which is used to detect a phase ( phase means e.g. longitudinal, transversal or Lamb wave). We refer to this convention in this paper. In our case, the proposed picker is designed to determinate the arrival time of first phase in AE signal (it means first-arrival time).
In the past few years, several approaches were used for first arrival determination. An amplitude threshold-picker is the simplest one of them. However, the signals with low signal-to-noise ratios (SNR) are not suitable for a pure threshold approach . Baer and Kradolfer  published a widespread approach based on short-term average to long-term average ratio (STA/LTA) for purpose of usage in seismology. It was not applied on the raw signal but on the characteristic function, which is defined as an envelope of the signal. The STA measures the instant amplitude of the signal and LTA contains information about the current average noise amplitude. The result is defined as time in which the STA/LTA function reaches predefined threshold level. Earle and Shearer  chose a similar approach with a different envelope function. Unfortunately, in AE the signal and noise can be often found in same frequency range 20 kHz - 1 MHz, STA/LTA picker would not be enough accurate .
Wang and Teng  used artificial neural network for real time seismology. The network is trained by STA/LTA time series. The output of network sets the threshold level for STA/LTA function. Dai and MacBeth  also used artificial neural network, but it is trained by noise and P-wave segments. The modulus of the windowed segment of the signal is passed to the network. The output of the network consists of two values, which are parameters of a function that highlights difference between the actual output and ideal noise. Long calculation time and suitable selection of learning data are two main problems of this approach.
An approach based on high-order statistics (HOS) was successfully tested by Saragiotis  on real seismic data. Lokajicek and Klima  proved that the HOS can also be successfully used in the determination of the first-arrival time on AE data. This approach is applicable when the recorded signal converts from a random distribution to non-random one. On the other hand, this approach is not suitable for determination of arrival time of multi-path signals, since only first arrival time can be determined, and times of following arrivals would be very probably hidden in the tail of the previous signal.
Modeling the signal as an autoregressive process (AR) is another approach for onset time determination. It is based on the assumption that the signal can be divided into locally stationary segments and the intervals before and after onset are two different stationary processes . On the basis of this assumption, an autoregressive Akaike Information Criterion (AR-AIC) has been used to detect P and S phases [11-13] in seismology. For AR-AIC picker, the order of the AR process must be specified by trial and error and the AR coefficients have to be calculated for both intervals. In contrast, Maeda  calculated the AIC function directly from signal, without using AR coefficients. However, the AIC picker does not perform well, if the signal-to-noise ratio is low and the arrival is not evident. Further, for AIC picker to identify the proper arrival a limited time window of the data must be chosen .
In our case, the signal is characterized by a specific function, which is used as input information for AIC picker. This characteristic function is sensitive to change of frequency in contrast to others such as envelope of the signal, which indicates only change in amplitude of a signal. The approach was applied to data sets of three different tests. It will be shown that our two-step AIC picker is a reliable tool to identify the arrival time for AE signals of varying signal-to-noise ratios.
Previous AIC Pickers
As mentioned above, standard AR-AIC approach supposes that a signal can be divided into locally stationary segments each modeled as an AR process. The intervals before and after the arrival time are premised on two different stationary time series .
AIC Pickers in Seismology
Sleeman and van Eck  divided the time series into deterministic (forward and backward prediction models) and non-deterministic part, see Fig. 1a. The AR coefficients of forward and backward models are computed in corresponding deterministic term. The variances of prediction errors of models are computed for every point of non-deterministic part and are used in the calculation of the AIC. For fixed order AR process the point where the AIC is minimized determines the separation point of the two times series (noise and signal). This approach is known as AR-AIC picker [11, 12]. The AIC of two-interval model for signal x of length N is represented as a function of merging point k
where M is the order of an AR process fitting the data, and ³ F2 and ³ B2 indicate the variance of the prediction errors of forward and backward model. To realize AR-AIC picker, the order of the AR process must be specified by trial and error, and then AR coefficients can be determined by the Yule-Walker equations.
Maeda  calculated the AIC function directly from seismogram without using the AR coefficients. For signal x of length N, the AIC is defined as
where k is range through all samples of signal and var(x[1,k]) indicates the variance of corresponding interval from 1 to k of signal x.
The AIC global minimum determines the arrival time. If the time window, which considers the signal segment of interest, is chosen properly, the AIC picker is likely to find arrival time accurately. Zhang et al.  applied this AIC picker to multiple scales, which are decomposed by wavelet transformation. By comparing the consistency among the picks at different scales, they could determine whether there is an arrival in the current time window or not.
AIC Pickers in Acoustic emission
AE and seismograms are quite similar to each other. However, there also exist several differences. In seismology the signal and noise are usually located in different frequency range. AE signal and noise are often in the same frequency range and also signal-to-noise ratio is generally not constant during experiment.
Kurz et al.  successfully applied an adapted automatic AIC picker based on Maeda's relation to AE from concrete and used the complex wavelet transform and Hilbert transform as characteristic function instead of the signal. Both these transforms lead to a certain envelope of the signal. Firstly Kurz et al. use squared and normed envelope for prearranging the onset by a constant threshold value, as can be seen in Fig. 1b. A window of several hundred sampled points, before (Nbefore) and after (Nafter) this onset, is cut off the signal. The signal onset is determined by AIC picker, which is applied on this window (Fig. 1b). The advantage of the envelope by wavelet transformation is that it can be calculated only for one frequency, while most of the noise of the signal is found in different frequencies. However, if two or more signals of different amplitude and frequency superpose each other, the envelope calculated by the Hilbert transform should be used.
New Two-Step AIC Picker
In AE measurements noise and signal are in same frequency range 20kHz - 1MHz. Low frequency noise or high frequency noise can be eliminated by analog or numerical filters. If suitable mathematical function is chosen, the characteristic function can improve resolution level between noise and AE signal for picking algorithm.
Choice of Characteristic Function
The performance of the picker depends on characteristic function strongly. The arrival time can be indicated by a change in the frequency, or amplitude, or both, in the time series. Characteristic function should enhance the change .
The absolute value function CF(i) = |x(i)| is easy to compute and the most widely used (amplitude threshold picker). The square function CF(i) = x(i)2 enhances the amplitude changes. Envelope of the signal calculated by Hilbert transform characterizes the original shape of the signal. We found that these functions do not fit proposed AIC picker. Naturally, the characteristic functions based on amplitude of signal are not sensitive to periodic changes of signal, and are only sensitive to changes in amplitude.
We realized that and tried frequency-sensitive function by Allen for seismogram threshold picker,
where K ( x(i) - x(i -1) )2 represents changes in frequency. The parameter K is a weighting constant that varies with sample rate and station noise characteristics .
This characteristic function is sensitive to change of frequency and amplitude, but it gives the quite similar results as envelope of the signal calculated by Hilbert transform, if it is applied on our picker. We suppose that Allen's function (3) can not pose the signals with low signal-to-noise ratios due to that it is a square function. So, we modified this function into following form,
where R is constant specified by trial and error, for our case R = 4. The best results were obtained by using this characteristic function.
Algorithm of AIC Picker
During one experiment, AE measurement system can recognize and record up to several thousands AE signals. The length of one AE signal and threshold level is defined by researcher in advance Figure 2 presents visual description of individual stages of our algorithm.
The proposed algorithm is two-step process. Firstly the characteristic function (4) is computed (Fig. 2a). The algorithm shortens the time interval of the original time window, which can be seen in Fig. 2b. . The AIC function, Maeda's relation(2), is sensitive to choice of correct time window. If the time window is chosen properly, the AIC picker provides good results, otherwise it provides poor results. The procedure of shortening is based on asumption that the time window should start in noise and should end just after maximum value of the signal amplitude. After this time there are only ending part of AE event, its reflections and noise in the signal and they influent the results of AIC function. Figure 3 shows an example of this behaviour and our solution.
The start of the time window is set to the beginning of original signal and is presumed as non-informative part. The algorithm shortens the time interval of the original time window, which can be seen in Fig. 2b. The end of the time window is set to the time, after maximum value of characteristic functon on time tMAX +€ „tAM , where tMAX is time of global maximum of CF and time delay „tAM is specified by trial and error and depends on metrial under the test. We set the „tAM = 20 s. The AIC picker based on Maeda's relation (2) is applied on this new time interval. The global minimum of AIC function determines the first estimation of the arrival time (Fig. 2c).
In second step, we focus on the neighborhood of first estimation (Fig. 2c). The time interval is changed to start at „tFB before first estimation and to end at „tFA after first estimation. For our case, „tFA = 10 s and „tFB = 30 s were found by trial and error. The AIC picker is applied once again on CF in this shortened time interval (Fig. 2d). The global minimum of recalculated AIC function defines the arrival time of AE event, as can be seen in Fig. 2e.
The first step of our proposal can be applied on most of AE signals and its results of first arrival determination provide good accuracy. Nevertheless, there are exceptions with poor accuracy. In some signals, the amplitude of the first incoming wave is very small compare to amplitudes of the following incoming waves. In such signal, accuracy of first arrival determination is limited by AIC function due to the choice of time window. The second step is used to eliminate this limitation. It focuses on neighborhood of first estimation with shortened time window, which gives better information about first-arrival time.
Figure 4 shows an example, when the second step is needed. The prediction of first AIC function is inaccurate and is used as estimation for second prediction, which is more successful. Their comparison is presented in fig. 4 b. The second step was designed to prove or to improve the first estimation.
AE is one of methods that describe behavior and properties of material under various conditions. Considering the nature of AE, many spurious events can occur during an experiment and represent the potential errors in final conclusions. In our case, the localization is used to eliminate this possible error.
The approach was applied to data sets of three different tests. Figure 5 presents measurement set-ups of these three experiments, tensile test of 25-layered SPCC/SUS420J2 thin plate of the overall dimensions 165 x 20 x 0.95 mm3, tensile test of silicon-manganese steel specimen of the overall dimensions 230 x 20 x 0.5 mm3 and four point bending test of silicon-manganese steel rod of the overall dimensions 36 x 5 x 4 mm3. The both tensile tests were measured with four sensors and bending test was measured by two sensors. The AE sensors were located in one line. The location of AE event is estimated by one-dimensional hyperbolic localization by times of first arrival.
AE measurement system called Continuous Wave Memory  was used to recognize the events by 15 mV threshold and to store every event in 100 s time length. Continuous Wave Memory sampled data at a rate of 10MHz by 12bit A/D converter. The data were filtered numerically by 4th order Butterworth high-pass filter with cut-off frequency 100 kHz.
Results and discussion
Three data sets were in our interest. For tensile tests, 100 AE events and, for bending test, 200 AE events were chosen from center region of corresponding specimen for comparative investigation. It represents 1200 AE signals in three tests. Arrival times of these AE signals were determined manually as well as automatically using our approach and Kurz's approach with envelope calculated by Hilbert transform . Signal amplitude and the signal-to-noise ratio (SNR) of the chosen event varied according to the test stage when the individual event occurred.
In the tensile test of 25-layered SPCC/SUS420J2 thin plate, the arrival times determined by two-step AIC picker are in close proximity to times picked manually. The distribution of deviation of first arrival is presented in Fig. 6. The deviation of first-arrival times is less than 0.5 s in 88.8% signals and greater than 2.5 s in 1.8% only. Kurz's AIC picker is not as successful as our proposal (Fig. 7). The arrival times obtained by Kurz's way are different greater than 2.5 s in 12.5% signals and are different less than 0.5 s in 78% in comparison to times picked manually. It results in fact that the localized events by Kurz's AIC picker are not in such proximity to manually picked events (Fig. 8) as events localized using two-step AIC picker (Fig. 9). Using Kurz's AIC picker the 14 % localizations were determined with deviation greater than 5 mm, but in case of two-step AIC picker it is only 2% localizations. The examples of first arrival determination for varying signal-to-noise ratios are shown in Fig. 10.
In the tensile test of silicon-manganese steel specimen, the signal-to-noise ratios of AE signals were generally lesser than in the previous test. Figure 11 shows the distribution of deviation between manual picks and Kurz's AIC picker. The 55.5% deviations of arrival times are less than 0.5 s, and 31% deviations are greater than 2.5 s (Fig. 11). In case of our approach (Fig. 12), 83% deviations of arrival times are less than 0.5 s, and 6.5% deviations are greater than 2.5 s. The localization errors of our approach (Fig. 13), 18% deviations of localization vector greater than 5 mm, are relative lesser than errors of Kurz's approach (Fig. 14), 46% deviations of localization vector greater than 5 mm. The examples of first arrival determination for varying signal-to-noise ratios in second test are shown in Fig. 15.
In the four point bending test of silicon-manganese steel rod, the only two sensors were used. The signal-to-noise ratios of AE signals in this test were lesser in comparison to previous tests. The two-step AIC picker showed good accuracy also in this test. Figure 16 presents that the 87.5% deviations of first arrival are less than 0.5 s and 3.5% deviations are greater than 2.5 s. According to this fact, only 5% deviations of localization vector are greater than 5 mm, as can be seen in Fig. 17. In case of Kurz's AIC picker (Fig. 18), 71.5% deviations of first arrival are less than 0.5 s and 8.5% deviations are greater than 2.5 s. The 13.5% deviations of localization vector are greater than 5 mm (Fig. 19). Figure 20 shows examples of first arrival determination in the third test.
For each test and for each automatic picker, the standard deviation was computed for time differences between manual picks and first-arrival times, which were determined by corresponding AIC picker. Figure 21 presents the schematic comparison for all tests. The standard deviations of our proposal are almost three times lesser than standard deviations of Kurz's approach in the three tests.
The summary of all tests also shows that 86.4% first-arrival times were determined by two-step AIC picker with deviation less than 0.5 s in compare to 68.3% by Kurz's approach. On the other hand, 6% first-arrival times were determined by our proposal with deviation greater than 2.5 s in compare to 17.3 % by Kurz's approach.
The presented results show that our proposal gives better information about first-arrival time than Kurz's approach since these approaches are not so different in principles. Both of them calculate the first estimation to find close neighborhood of first-arrival time, and than use same Maeda's relation for final determination of arrival time.
For first estimation, Kurz et al. use constant threshold. This is not as suitable as AIC picker for signals of low signal-to-noise ratios. The AIC picker can be applied only due to the shortening of original length of the signal, which was described in detail before and was successfully applied in our proposal. Nevertheless, we suppose that the choice of characteristic function is crucial factor for first-arrival detection by AIC pickers. The approaches differ in characteristic functions mainly. Kurz's function is sensitive to changes in amplitude of the signal, but our function is sensitive to changes in amplitude and in frequency also.
For all three tests, we computed the standard deviations for time differences between manual picks and first step of our proposal, which we marked as one-step AIC picker. Figure 22 presents that only one-step shows the great improvement in comparison to Kurz's technique. The two-step improves results of one-step, slighlty. It corresponds to purpose of second step to prove or to improve the first step.
A new automatic determination technique of the first-arrival times of AE signals is presented in thin metal plates. Based on Maeda's relation, proposed algorithm of the first arrival detection uses the specific characteristic function. This characteristic function (CF) is sensitive to change of frequency in contrast to others such as envelope of the signal.
The proposed algorithm computes the characteristic function of an AE signal and shortens its time window so that it ends in informative part of the signal. Then the AIC picker is applied. The global minimum of AIC function determines the first estimation of the arrival time. The time window is shortened again and focused on the neighborhood of first estimation. The AIC picker is applied once again on characteristic function in this shortened time interval. The global minimum of recalculated AIC function defines the arrival time of the AE event.
The approach was applied to data sets of three different tests, tensile test of 25-layered SPCC/SUS420J2 thin plate, tensile test of silicon-manganese steel specimen and four point bending test of silicon-manganese. From each test, amount of AE events were chosen. Arrival times of these chosen events were determined manually as well as automatically using our approach and Kurz's approach.
The standard deviations of time differences between manual picks and automatic determined first-arrival times were computed for all three tests. The comparison of standard deviations shows (Fig. 21) that two-step AIC picker gave better information about first-arrival time than Kurz's AIC picker. The comparative investigation also shows that 86.4% arrival times of all analyzed signals were determined by two-step AIC picker with deviation less than 0.5 s and 92.7% arrival times of all analyzed signals were determined by two-step AIC picker with deviation less than 1 s. It shows that the two-step AIC picker is a reliable tool for automatic identification of the arrival times for AE signals of varying signal-to-noise ratios.
Our proposal can be applicable also for other materials in AE measurement. Its advantages are easy implementation and settings of three parameters „tFA€¬€ „tFB€ € and€ „tAM.
The present research was conducted as the part of the LISM (Layer-Integrated Steels and Metals) Project funded by Ministry of Education, Culture, Sports, Science and Technology of Japan. Also, this research has been supported by Japan Society for the Promotion of Sciences (JSPS).