Artificial Intelligence-Enabled Crack Length Estimation From Acoustic Emission Signal Signatures

The motivation for this work lies within the aerospace industry. As in-service aircraft begin to age and fatigue, a method for evaluating the operational life they currently have and what they also have remaining comes into question.

These aircrafts are constantly undergoing complex repetitive stresses during flight, usually in the form of turbulence or other structural vibrations, pressurization, and depressurization during takeoff and landing, etc. Due to these repetitive stresses, the aircraft accumulates wear and tear. A large amount of this wear and tear is in the form of fatigue cracking, which is the product of these repetitive stresses [1]. Most cracks in metallic airframes grow from stress concentration around rivet holes (Fig. 1).

When the fatigue cracks grow, they release strain energy with associated “pops” called acoustic emissions. Acoustic emission (AE) is defined as “a phenomenon in which elastic or stress waves are emitted from rapid, localized change of strain energy in the material” [2]. In simpler terms, as the crack grows, the strain field that is around the tip of the crack collapses and releases energy due to the changing geometry. The released energy travels through the airframe as elastic waves that can be picked up by AE sensors. These AE waves contain a very small amount of energy when they are generated, and they have been compared to “ten orders of magnitude lower than that of the kinetic energy released from a mosquito landing on an AE sensor” [3].

Acoustic emission refers to the phenomenon in which elastic stress waves are emitted from a localized rapid change in the strain energy within a material [2]. The strain energy results from the interaction between the elastic properties of the material and a created strain field. During a failure event, the strain field collapses due to the changing geometry of the material, and the stored strain energy is reduced releasing energy in the form of multidirectional elastic waves.

Considerable research work has already been done worldwide in the art and the science of using acoustic emission signals to monitor the state of safety critical structures, as presented in Sec. 2. In our research group in the Laboratory for Active Materials and Smart Structures (LAMSS) at the University of South Carolina, we have focused attention on trying to understand the relation between the AE signatures and the geometric features of the physical structure in which the AE waves travel including the crack proximity and the structural boundaries. This journal article, which builds onto our previous AE work, has a twofold focus:

1. Create a reliable database of AE signals that contain AE signatures that can be directly related to fatigue crack length (CL) values

2. Develop an artificial intelligence (AI) neural network for estimating the crack length using AE signal signatures

The database of AE signals was created by conducting a large number of fatigue crack growth experiments on aluminum sheet specimens. The experiments were conducted over a period of several years. The AE signals collected during these experiments were generated either from “pops” at the crack tip during crack growth or rubbing/clapping of crack faying surfaces during noncrack growth cyclic loading. During these experiments, it was found useful to control the crack growth rate by modifying/reducing the loading level as the crack growth in an attempt to maintain constant the stress intensity factor (SIF) that controls the crack growth rate. In order to learn how to separate the AE signals due to crack growth from the AE signals due crack rubbing/clapping, a special set of specimens was constructed that consisted of hair-thin slits of predetermined lengths that permitted generation of AE signals that were generated only from cracks growing at tips of these slits.

The AI neural network developed to estimate the crack length from AE signal signatures was based on the GoogLeNet convolutional neural network (CNN) available in the matlab Deep Network Designer toolbox. The training of the GoogLeNet CNN was done of spectrogram images of the AE signals. These AE signal signatures were obtained by applying the Choi Williams transform (CWT) to the AE signals captured during the fatigue experiments. Several steps of signal processing were involved in preparing the datastore sets that were used as input for training, validation, and testing of our AE-length detection CNN. In spite of our extensive efforts to collect large numbers of AE signals with similar crack length, the datasets used in training our AE-length detection CNN were rather small when compared with the huge datasets typically used in training GoogLeNet networks. To compensate for this situation and to balance the training datasets, we augmented the datasets with synthetic data generated with the synthetic minority oversampling technique (SMOTE). The results presented in this article show that the resulting AE-length detection CNN was able to sort with good accuracy the AE signature datasets and predict the physical crack length with remarkable accuracy.

This article is organized as follows. After a short introduction, the article discusses the fatigue testing background necessary to understand the data and information presented in this article. Then, the article discusses in detail the fatigue testing experiments, AE collection process, and processing and organization of the AE signature datasets. Subsequently, the article describes the AI work conducted, and the use of SMOTE to augment the datasets, construction of the AE-length detection CNN and its training, validation, and testing results. The article finishes with a summary, conclusions, and suggestions for future work.

Monitoring of AE from the progressive fatigue damage is categorized as the passive online monitoring. The AE signals from the fatigue crack have always been an interest for the researchers. In recent decades, there have been significant advancements in the study of acoustic emissions, leading to a better understanding of their properties and behavior. Passive detection of fatigue cracks by acoustic emission sensing has attracted researchers’ attention for decades [4,5]. AE research has numerous applications, including source localization, material performance, and structural health monitoring (SHM). Within SHM, researchers use acoustic emissions to evaluate events and determine the location, magnitude, and characteristics of damage in structures. Commonly, AE is used to study structural health conditions surrounding erosive failure, welding quality, and fatigue failure.

AE has become a well-established nondestructive evaluation method [6–9] that is used in SHM by listening to the “pops” or “hits” generated by the energy released by an incremental crack growth [10–12]. Existing AE equipment identified such “hits” by setting a threshold on the recorded structural wave signals [9]. The threshold is set high-enough to discard “noise” signals originating from internal rubbing of crack faying surfaces or from the testing equipment and retain only the AE related to crack growth. Although being “the most crucial step in AE monitoring” [13], the setting of the “correct” AE threshold remains an “art form” strongly dependent of the subjective intuition of experienced AE technicians. As shown in Ref. [13], AE hits start to flow in large numbers only near the end of life when failure becomes imminent. The study by Barsoum et al. [14] indicates that the cumulative AE count has a slow linear growth for most of the fatigue life but suddenly tend to grow exponentially near the end when failure becomes imminent. The lack of an early-warning capability impedes the wide-spread use of AE methods in safety critical applications unless AE signals related to crack initiation can be collected. Hence, an early-warning capability, if existed, would greatly assist the effective management of structural fatigue in coordination with mission profile allocation and maintenance scheduling.

Several investigators have posited that the AE signals captured during the AE monitoring contain a wealth of information that is not properly exploited by an AE practice solely based on counting “hits.” In recent years, the analysis of AE signals has been intensified in order to extract more information about crack growth rate and even crack length. The analysis of AE signals can be basically carried out qualitatively and/or quantitatively. The meanings of qualitative AE analysis and of quantitative AE analysis are discussed next.

This subsection discusses qualitative AE analysis. In a qualitative analysis of acoustic emissions, signal features are calculated and stored in real time using dedicated hardware [15]. Signals features in common use are as follows:

• AE event count (and AE event rates): the number (and rates) of burst-type emissions

• averaged signal intensity of continuous-type emissions (e.g., rms of recorded signals)

• the peak amplitude value and distribution

• rise time and duration

• duration of burst emissions (defined with the threshold)

• the signal strength of burst emission (area of the signal envelope)

These features have been used to describe the temporal development of the AE activity and assign the acoustic emissions to either crack growth or process noise. It is hypothesized that the size of the strain field changes in accordance with the amount of energy required for crack growth to occur [2]. Specifically, larger cracks have smaller strain fields due to the lower amount of energy required for the crack to propagate. By analyzing the differences in energy associated with AE events, one could gain insights into the state of the material and the defect responsible for releasing the energy.

Frequency-based features have also been used. These include peak frequency, median frequency, spectral centroid (or mean frequency), and partial powers for various frequency bands. The power density spectrum or more commonly frequency spectrum and shape parameters of the signal waveforms can be utilized. Peak intensity and position in the frequency domain, shifts in dominant frequency over time, and rates of rise and decay of the waveform have been examined. Their values diminish when narrow-band sensors are used.

Fatigue crack length estimation from AE signal analysis had been reported [10,13,16–20]. Some methods of estimating crack length reported in the literature are based on parametric relationship between AE signals and fracture progression [16]. In such a data-driven approach, statistical signal processing is used to extract standardized signal features such as amplitude, rise time, duration, MARSE (measured area of the rectified signal envelop), counts, moments, kurtosis, and “signal energy.” The success of these methods still depends on being able to discard the AE signals not related to the crack growth. An attempt to use the statistical Bayesian approach to analyze the AE hits was reported in Ref. [21]. A method for fatigue crack length estimation method correlating the AE counts with the load level at which AE hits appear was reported in Ref. [18]. The method exploits the fact that stress intensity increases as crack growth occurs and hence AE hits appear at the diminishing load levels as growth progresses. AE signal features have also been used to construct artificial intelligence classifiers using pattern recognition analysis [12,22]. The aewin noesis software package offers pattern recognition and neural network capabilities [15].

This section discusses quantitative AE analysis. In quantitative AE analysis, the entire signal is evaluated in time and frequency domains. Quantitative AE analysis has been enabled by technological advances that permit the digital recording and storage of entire sets of AE signals. In quantitative analysis, the complete AE waveform is considered. Large data storage capabilities are required since tens and even hundreds of thousands of AE signals may be recorded in a typical high-cycle fatigue (HCF) situation. Quantitative AE analysis is a still developing discipline with prospects of breakthroughs using machine learning (ML) artificial intelligence approaches.

With recent technological advancements in sensing equipment and computing power, the collection and analysis of high-quality data have become increasingly accessible. One particular effective method of data analysis is through the utilization of machine learning algorithms. These algorithms have the ability to learn complex patterns within data and can do so in a short period of time. As a result, they can become experts in a specific type of data and be utilized at any time with a computer. These models have even been shown to outperform humans in data processing and pattern recognition. Given the data-driven nature of SHM and the multitude of signal types generated from various sources, machine learning has become an ideal approach for performing SHM within a given system. By attaching these models to passive sensor networks, they can continuously detect any signals that may be cause for concern. Machine learning has been used with a large amount of success when applied to multiple facets of acoustic emissions [23–25]. But this study is unique since it can both determine the size of a fatigue crack using discretized classes.

The LAMSS at the University of South Carolina has taken a physics-based approach to AE research. We have directed our attention to understanding the origin and causation of the wave signals recorded by the AE sensors and developing the computational models to assist this process. We have focused on trying to understand the relation between the AE signatures and the geometric features of the physical structure in which the AE waves travel including the crack proximity and the structural boundaries. Our work has been a judicious combination of analytical theory, finite element method (FEM) simulation, and carefully conducted experiments in which we developed our own AE sensors and experimental techniques. The long-term goal of our work has been to (a) identify a direct correlation between crack length and AE signal and (b) develop a methodology for extracting the crack length information from the AE signal waveform signatures.

The AE wave signals were collected with piezoelectric wafer active sensor (PWAS). The PWAS can convert mechanical strain into electricity, and these are highly sensitive sensors, which will allow for the collection of any AE on the testing specimen. Though PWAS transducers have both transmitting and receiving capabilities [26], in the present work, we only used them as receiver of AE wave signals. Previously reported comparative studies [27,28] have established that these relatively inexpensive sensors have as good performance as the conventional but more expensive AE sensors R15a, PICO, and S9225 [15].

There are two main mechanisms for generation of acoustic emission from a fatigue crack. One mechanism is when the crack grows and some of the energy at the crack tip is released in the form of acoustic emission [4]. The other mechanism is that when the crack resonated due to ambient vibration, the rubbing of the crack surfaces creates acoustic emissions [29].

In previous works [27,30–32], we identified two major categories of crack-related AE events that appear during fatigue test AE recording. One category of AE events is related to crack growth where the AE waves originate at the crack tip (Fig. 2). This AE event category is labeled type I. The other category of AE events is related to rubbing, clapping, and fretting of the crack faying surfaces, which meet and rub during the unloading portion of fatigue. This AE wave originates at various locations along the crack length. This AE event category is labeled type II. Figure 3 shows a type I signal corresponding to an AE event resulting from crack growth, while Fig. 4 shows a type II signal corresponding to an AE event resulting from crack rubbing and clapping. Crack face cohesion and fretting provide AE indication of the crack presence, especially under cyclic loading [11].

We posited that the AE waves traveling along the crack surface reflect at the other tip and establish a standing wave pattern between the two crack tips. This standing wave pattern contains characteristic frequencies that may be directly related to crack length [33] and are seen in the AE signal spectrum. In particular, we found that AE waveform contains information that can be related directly to crack length due to a process of local interaction between the emitted AE waves and the crack faying surfaces. We gleaned the possibility of extracting crack length information from the AE signatures [33,34] based on the fact that the energy released during an AE event can excite standing waves around the crack that manifest themselves as crack length-specific resonances in the AE signal [35]. This hypothesis was based on multiphysics FEM simulation confirmed by carefully conducted experiments [27,36]. Further experimental studies as well as theoretical developments using the moment tensor approach [31] have shown how the presence of the crack modifies the wave field by displaying standing wave pattern pinned on the crack tips (Fig. 5). The crack-pinned standing waves contribute their own frequencies in the overall AE signal received at the AE sensor (Fig. 6). It was also found that that the crack-related AE signal are of two fundamental types, one related to crack growth AE at the crack tip and the other related to the rubbing, fretting, and clapping of the crack faying surfaces during cyclic loading [30]. The crack rubbing/fretting can generate crack-related AE events even in the absence of fatigue loading such as during structural vibration [32]. Noncrack growth AE also appears when the stress intensity factor of the cyclic loading is below the crack propagation threshold [28]. More recent research has been focused on developing artificial intelligence methods to automatically classify AE signals such as to extract crack length information directly from the signature of the received AE signal without the need for historical AE information or other prior knowledge [37].

Collection of AE signals was performed on instrumented coupon specimens subjected to fatigue testing under cyclic loading. Fatigue testing is a type of destructive testing that is commonly used to determine the fatigue life of a material. Fatigue tests have been used by many researchers in trying to reproduce the wear and tear of in-service machinery and structures. This method has been widely used for over a century and aims to simulate real-world operating conditions for a material or specimen. Fatigue can be HCF of low-cycle fatigue (LCF). HCF is representative of most practical applications when fatigue failures happen after millions and tens of millions of cycles; however, some practical situations (e.g., as the fatigue of aircraft landing gear) may experience LCF when fatigue cracks may develop after tens of thousands of cycles, although this would happen well beyond the approved service life. LCF is most often used in laboratory testing when fatigue cracks are initiated more readily by applying larger-than-usual cyclic loads. In our work, we used higher-load LCF to initiate the crack and then lower-load HCF to grow the crack slowly under controlled conditions.

The experimental setup is presented in Fig. 7. The fatigue cyclic load was applied using an MTS-810 testing system along with its dedicated control software mts testware-sx running on a desktop computer. The test specimen was installed in the 4-in. hydraulic grips of the MTS-810 load-frame. A Basler camera was placed on a camera stand to monitor the crack initiation and crack growth in the specimen. The images captured by the Basler camera were viewed in real time on a laptop using the pylon viewer software. An Eddyfi Technologies eddy current probe and display instrument as well as a hand-help microscope were used to measure more precisely the crack initiation and crack growth in the specimen when the cyclic loading was stopped at predetermined intervals. The MISTRAS AE preamplifiers, AE collection instrument, and aewin real-time data acquisition and replay software were used to collect AE signals throughout the testing process. An Omicron Lab EMIS instrument connected to a laptop computer was used to periodically test the integrity of the PWAS instrumentation. Also apparent in Fig. 7 is a bridge-completion module that can be used for performing in situ load monitoring using strain gauges applied directly to the specimen.

A schematic of the fatigue specimens used in our work is given in Fig. 8. It consists of 100-mm wide, 300-mm long sheet-metal coupons made from 1-mm thin 2024-T3 aerospace-grade aluminum alloy. The fatigue specimens were of two types: (i) specimens with crack growing from a 1-mm hole crack initiator and (ii) specimens with crack growing from the tips of a hair-thin slit. Within the dataset used for the ML approach, only slit-type specimens were used, ranging from 10 to 12 mm, 12 to 14 mm, and 14 to 16 mm. Each class contained four different plates that were grown from the lower to upper limit of the classes range, resulting in a total of 12 fatigue specimens each of which were equipped with 4 PWAS.

The specimens with a 1-mm initiator hole in the center are similar to the specimens used in our previously reported works [27,28,30–37]. These specimens proved capable for successful collection of AE signals during fatigue crack growth experiments. This method allows for a fatigue crack to originate and spread outwards toward the edges of the plate. A crack would originate from the small 1-mm hole placed in the center of the specimen and then grow emitting AE signals. The crack would grow under HCF loading from a few millimeters to up to 20 mm with AE signals being synchronously captured.

However, the AE events recorded in these experiments occur both when crack growth happens and when crack faying surfaces rub and clap against each other [27,30]. It was also established that a cracked specimen would emit AE signals when transversally vibrated even if the crack does not grow [32]. The occurrence of noncrack growth AE signals was recorded in controlled SIF fatigue tests in which crack growth was inhibited by reducing the load to keep the SIF values below the crack propagation threshold [28]. Hence, careful analysis of the recorded signals was needed to differentiate between the AE signals due to crack growth and the AE signals due to crack faying surface interference.

In order to eliminate AE signals from the rubbing/clapping of faying surfaces and obtain AE signals due only to crack growth, a new specimen design was used. This new specimen design consisted of a coupon specimen having a hair-thin slit cut in the center instead of an actual fatigue crack. The hair-thin slit provides a site for fatigue cracks to initiate and propagate. Creating slits of this size usually involves expensive methods of manufacturing, but a novel method was developed involving a Dremel tool and a thin diamond saw disk of 0.005-in. (0.127-mm) thickness [37]. The Dremel tool was mounted in an ad hoc guiding devise that permitted the production of hair-thin slits precisely positioned onto the specimen. Subsequently, the slit was deburred with a diamond-floss tool, resulting in a clean hair-thin slit of 0.15-mm width. It was posited that such a hair-thin slit closely approximates the geometry of an actual crack but does not have the contact between the crack faying surfaces and thus does not produce AE signals associated with crack rubbing/clapping or fretting. It will not produce AE signals due to rubbing of the faying surfaces because these surfaces are sufficiently apart such as not to touch each other. Hair-thin slits were produced in various lengths as desired.

When subjected to cyclic fatigue loading, the hair-thin slit specimen experiences crack growth initiation and growth only at the tips of the narrow slit. Thus, this specimen produces AE signals only when crack propagation happens at either tip of the slit. This new specimen allowed us to differentiate between the AE signals due to crack growth and the AE signals from crack faying surface interference. This specimen allows our PWAS AE collection system to capture purely crack growth AE signals.

The instrumentation used for collecting the AE signals Fig. 7 consists of a PWAS array connected through MISTRAS preamplifiers to the MISTRAS AE instrumentation block run by the mistras aewin real-time data acquisition and replay software.

The AE wave signals were captured using PWAS transducers as receivers of AE wave signals. The PWAS were arranged in a four-PWAS linear array centered on the crack as shown in Fig. 8. On each side of the crack, one PWAS was placed at 5 mm from the crack and the other PWAS was placed at 25 mm from the crack. The four-PWAS sensing array allows one to use time-of-flight analysis to determine whether a collected AE signal comes from an actual AE event on the crack or is just AE noise from the grips.

The PWAS AE sensors were manufactured in situ from STEMINC SM412, 7-mm diameter 0.5-mm thick piezo wafers instrumented with connecting wires. Prior to installation on the specimen, the piezo wafers were sorted into similar capacitance groups using a bench instrument. The capacitance of the piezo wafers used in our tests was approximately 1.35 nF ± 0.03 nF. The piezo wafers were attached to the specimen with Micro-Measurements AE-15 epoxy adhesive, which is recommended especially for fatigue testing environments. Prior to PWAS bonding, the fatigue specimen undergoes a rigorous surface preparation process involving sandpapering, degreasing, and acid–base treatments.

After attachment to the specimen, the capacitance of the piezo wafers was checked again; any inconsistent capacitance reading was addressed either by carefully cleaning the adhesive residue around the sensor or by replacing the sensor. After passing the quality check, the PWAS terminals were soldered to shielded coaxial cables connected to the AE preamplifiers.

Throughout the experiment, the AE sensing PWAS instrumentation was thoroughly checked for integrity. This sensor integrity check was done with electromechanical impedance spectroscopy (EMIS). The EMIS frequency plot was checked for consistency throughout the fatigue test duration. Consistency among the four-PWAS transducers installed on the specimen was verified at the beginning of the fatigue testing. A consistent peak and valley pattern in both frequency and amplitude was expected. Any discrepancy was immediately addressed by microscopic inspection of the offending PWAS to determine cause and remedial action. At times, replacement of the PWAS and recalibration was warranted. The sensor integrity check was repeated at periodic intervals throughout the testing. If inconsistency was identified in one of the PWAS, then remedial action or replacement was applied.

As shown in Fig. 7, the specimen edges are covered with clay dams that create a nonreflective boundary (NRB). In our previous work [38], we developed a specific NRB profile that was proven very effective in dampening guided waves reflections at plate boundaries. In the present work, we applied the NRB principle to reduce the reflections of AE signals and minimize the interference from noise sources placed outside the NRB perimeter. The NRB is a crucial feature of our testing specimen. This is particularly important because the AE sensors placed on the specimen may be exposed to various elastic wave sources. In the absence of NRB protection, the AE waves originating from the crack may reflect off the edges of the testing specimen and, as they travel back, interfere with new AE waves resulting in a superposed collection at the AE sensor. Additionally, the grips holding the specimen during fatigue load cycling may generate fretting noise, which may also interfere with the AE signals coming from the crack. Therefore, the nonreflective clay boundary plays a critical role in ensuring the accuracy and reliability of our AE testing.

The MTS-810 is calibrated with a “dummy” plate that allows the machine to begin loading within an acceptable tolerance. The dummy plate is loaded between 60 and 100 pounds-force for five cycles. Once the cycles are completed, the dummy is removed from the hydraulic grips, and the test specimen is loaded in its place. The grips cover the entire 100 mm width of the plate and come 50 mm inwards on either end. The load adjustment was modified for every millimeter of crack growth. This process of loading and adjustment was repeated until a total crack growth of 2 mm was achieved. Once the desired crack length was reached, the specimen was unloaded at a rate of 100 pounds-force per second and then removed from the MTS-810 machine.

To ensure accurate loading curves during testing, a National Instruments (NI) cDAQ-9174 block was attached to the MTS-810 load cell to monitor its output. This NI block saved and displayed loading curves generated by the MTS machine. The MTS-810 consistently produced symmetric, constant loading cycles between the prescribed ranges, providing confidence in the SIF-controlled technique and accurate determination of crack growth events.

Key variables considered in fatigue testing include loading ratio R, loading frequency f, loading range, and amplitude variance. The loading ratio R is the ratio between the maximum and minimum load used, which has been found to determine the rate at which steady-state AE signals appear. Loading frequency is an important variable in fatigue testing. The fatigue test specifications for this experiment include a loading frequency of 4 Hz and an R value of 0.1, which were determined to be the most efficient and yielded the lowest noise when compared to other loading frequencies and R values.

Amplitude variance is also important. To conduct fatigue experiments for the purpose of AE collection, a modified version of variable amplitude fatigue loading was used. This approach allows for the amplitude of the load to change as the load increases, while the frequency and load ratio remain constant. Thus, we were able to control the crack growth rate and collect more AE signals for a given crack length.

Fatigue tests conducted under constant amplitude cyclic load yield exponential crack growth [14] with crack propagating very fast toward the final fracture and thus not allowing for the collection of sufficient AE signals at a given crack length value. But for our work on developing an AI model for predicting crack length from AE signal alone, we needed to collect a large number of AE signals at given crack length values. By decreasing the applied stress as the crack length increases, the crack growth rate could be linearized, which is preferable over exponential growth since a region of crack length can be accurately studied at a slow growth rate, as opposed to quick and uncontrolled growth through and beyond the specified region. Our previous work has shown that the AE signals may depend on the SIF, which varies drastically during the terminal phases of a constant-load fatigue experiment.

In previous works [28,30], both constant-load and constant-SIF fatigue testing were performed for AE signal comparison. In the current work, we used constant-SIF fatigue testing in order to slow down the crack growth and collect a sufficient number of AE signals at a given crack length. When hair-thin slit specimens were used, SIF control was applied under the assumption that the slit acts as a crack of the same length.

Accurate measurement of the crack length at each stage of fatigue testing is essential for making proper loading adjustments during the experiment. In our work, two methods were used to accurately measure the crack length. The first method involved the use of a pocket microscope and mm-labeled tape, which allowed for a visual inspection of the crack profile and easy readings of length. The second method utilized the eddy current testing system. This method uses eddy currents generated in the material to determine the length of any discontinuities in the material. The eddy current probe is run across the surface and induces eddy currents in the material, and it then detects when a discontinuity is present. These discontinuities are the crack itself since the empty space cannot easily carry a current. This method can detect when a crack is present even if not visible by the human eye. The eddy current testing was conducted with the EddyFi eddy current testing equipment. By using two methods, cross-validation of the results was possible, which increases the reliability and accuracy of the measurements. Therefore, the combination of these two methods provides a sufficiently accurate and precise approach to crack length measurement during fatigue testing.

Experimental methods for in situ crack measurement (eddy current probes and continuous video recording) were used to differentiate the received AE signals into (a) due to crack growth and (b) not due to crack growth though still emanating from the crack, i.e., due to crack rubbing, clapping, or fretting. The data collection process was strictly controlled to ensure precise labeling of the data. A visual check of the crack length and an eddy current scan of the crack were conducted every 500 cycles to make any necessary load adjustments to maintain a constant SIF.

The experiments with 1-mm hole crack initiator yielded a wide range of AE signals. However, these experiments took a long time for a crack to grow to larger lengths, and often, the target length is difficult to reach without overshooting. These 1-mm-hole specimens also tend to produce large amounts of type II AE from clapping and rubbing of the crack faying surfaces; these type II signals tend to overwhelm type I signals associated with crack growth. This situation may be acceptable unless type I signals are the desired target of the AE collection exercise.

The purpose of the hair-thin slit specimens was to collect AE signals that are mostly generated by crack growth instead of crack rubbing/clapping. The hair-thin slits were manufactured in various lengths. During fatigue testing, the slits would have small fatigue cracks growing from their tips. The crack growth at the slit tips was capped at 1 mm on either side in order to keep crack growth AE dominant in the recorded AE signals. During these slit experiments, the appearance of type II signals was significantly reduced; however, the type II signals still appear due to the cracks formed at either end of the slit tips. These fatigue cracks at either end of the slit were kept at a length of less than 1 mm per side to ensure type I signals had a larger appearance rate than type II.

A major difference between type I and type II AE signals resides in the location from which they originate, with a rubbing/clapping signal coming from an area within the crack profile, as opposed to coming directly from the crack tips. This location would be dependent on the individual fatigue specimens crack profile and be able to vary greatly between themselves.

In constant-SIF experiments, the clapping and rubbing will become the dominant source of AE emissions as the test progresses. This is due to the increased crack rubbing area that can be the source of type II signals, while the generative region for type I signals remains the same size but follows the crack tips. The type II rate of generation is also dependent on the loading frequency applied, and the higher the loading frequency, the higher the rate of type II appearance. This ultimately leads to a dataset composed of mostly type II AE signals.

By using a hair-thin slit that uses empty space where there would otherwise be crack rubbing surfaces, the amount of type II signals is significantly reduced and a sufficient amount of type I signals was collected at various crack/slit length values.

Another important characteristic of the collected AE signals is the changing of the frequency content in accordance with the length of the fatigue crack generating them. There is a clear shift in frequency peaks that occurs as the crack grows in size. These results are consistent with those previously reported in Refs. [30,31,36,37]. An illustration of how the frequency peaks shift with crack growth is given in Fig. 6, which presents the results of multiphysics FEM simulation using the ansys apdl software package [31,37]. This is shown in the following table for the 10, 12, 14 mm crack length spectra of Fig. 6:

The second and third peaks clearly decrease as the crack length increases. Please note that the first peak decreases from 115 to 102.5 kHz for the 10-mm and 12-mm CLs. The further decrease for 14-mm CL to a frequency below 100 kHz is not captured in the plot. In addition, please note that the fourth peak decreases from 765 to 667.5 kHz for the 12-mm and 14-mm CLs. The fourth peak was not captured for the 10-mm CL because it was too high to be detected by our band-limited equipment.

The apparent peak frequencies for a 10 mm crack source in Fig. 9 are observed at 94, 117, and 370 kHz. While these peaks are located close to the peaks found in FEM, they are not exact matches. These differences can be attributed to factors such as the nonperfect symmetry of the PWAS, as well as other conditions affecting the coupled system. Similar observations hold true for the 12 mm crack source signals shown in Fig. 10, with the peaks shifted toward higher frequencies. In Fig. 11, the 14 mm crack source response exhibits peaks at 96, 343, and 461 kHz, which again are similar, but not identical to the finite element analysis peaks in Fig. 10.

The type II AE signals that are derived from crack rubbing and clapping still contain valuable information regarding the crack length and display a similar pattern of frequency peak shifts in accordance with crack length. However, experimentally, it was found that as the fatigue testing continued, the amount of type II signals, as well as the variance between themselves, was changing. This could be due to the addition of new crack rubbing surfaces becoming available for new type II signals to spawn from.

There are two conclusions that can be made regarding the AE signals collected during these experiments. The first conclusion is that AE signals have different frequency content depending on the size of the fatigue crack they originate from. The second conclusion is that these similarities in waveform and frequency content were consistent throughout the experiments and allow for grouping of similar waveforms based on the crack length they originate from.

Machine learning methodologies involve two main components that are crucial to the success of implementation, which are the dataset and the model. The dataset serves as the fuel for the machine learning model, providing guidelines for the machine to learn from. A poor-quality dataset will lead to failed machine learning endeavors, as the saying goes, “Garbage in, Garbage Out.” The model, on the other hand, is the framework and approach used to learn the given material, and it directly controls what the model learns and predicts. Therefore, different models can greatly influence the performance of machine learning approach.

To enhance the quality of the dataset, several methods are used to improve the labeling procedure, manipulate class sizes, and optimize data format. The labels define what each data point is and what the machine learning will predict. In this experiment, the labels represent the range of crack length in increments of 2 mm, and labeling increments are carefully selected to provide sufficient data per label while remaining useful for application. Precise labeling is crucial to ensure accurate classification of each piece of data, and failure to do so can cause confusion during the training process.

Data format is also important and undergoes several transformations, such as the initial collection of time-series data, conversion to the frequency domain using fast Fourier transformation (FFT), transformation by the Choi-Williams Transform (CWT) process, and finally resizing into an acceptable image size and format. The data format chosen for this work is in the form of CW spectrograms, and these spectrograms allow for the usage of both the time and frequency domain into a single image. These images are a spectrogram with the time domain waveform on the X-axis and frequency domain on the Y-axis (Fig. 12). Within the spectrogram, the brighter regions are where the amplitude of both the time and frequency domain are larger, this locates regions where peaks are shared. By utilizing both time and frequency domain the features that are captured in a sample are maximized, allowing the computer to use the most possible information. Once the transformation is completed, a matlab code captures the CW spectrogram and saves it within a database for training and testing purposes.

It is essential to closely monitor these transformations to ensure homogeneity throughout the dataset. The software used also must be synchronized with variables such as the sampling rate, capture window, and noise-canceling applied.

The type of machine learning model used is specific to the problem set and desired results. There are two basic types of models: supervised and unsupervised. Unsupervised models use unlabeled data to cluster and determine patterns. In contrast, supervised models use labeled data as guidelines for training and have subcategories such as regression and classification. In this experiment, a classification model is used, but a regression model may be more useful due to small clusters of data forming during crack growth. A regression model can interpolate between class labels more accurately. The difficulty with creating a regression-based model is creating precise labels with enough finely labeled data to cover a large range.

AE-generating experiments do have limitations in the form of its reproducibility, these experiments have very sensitive environments, which can greatly affect results. Results from tests will vary even if a perfectly reproduced experiment is conducted, down to the specimen geometries, load settings, and amount of crack growth. There will never be two perfectly identical signals. These variations in testing results call for a method of signal analysis and interpretation that is not perturbed by these differences in data. The use of machine learning allows for the recognition of major patterns within the data without being slowed by the variations of data.

Acoustic emissions have previously been studied using machine learning using the AlexNet CNN model [39]. The study collected acoustic emissions data and labeled them as either crack related or noise (Fig. 13). This study was repeated using the GoogLeNet CNN model (Fig. 14). It was found that the GoogLeNet model performed just as well as the AlexNet model.

The resulting GoogLeNet model was able to accurately distinguish between the two categories with a perfect accuracy of 100%. While this is a promising starting point for using machine learning in SHM applications, this initial model lacked information related to the size of the crack and predictions about the state of the structural health. Therefore, the addition of a discretized crack length class within a machine learning model would allow for the better assessment of the structural health of a component by estimating the size of the fatigue crack present in the structure. With the ability to distinguish between smaller, less urgent cracks and larger, more urgent ones that indicate a shorter “life” left in the component, these models can be crucial in determining the length of an AE-generating crack and therefore the overall structural health of a component. By transferring these models onto an on-board computer, real-time diagnosis of health and fatigue cracks during flight becomes possible. This technology acts as a constant watchful eye for possible material fatigue, which would not otherwise be detectable.

The approach for the implementation of AE data into machine learning is done by first filtering the raw data gathered by the aewin software (Fig. 15). The filters operate with a series of simple logic tests that allow for only AE hits originating from the center of the plate to be included in the processing. These logic tests are as follows, the time of signal arrival should always be sooner for the PWAS closer to the crack, and the amplitude of the collected signals should be larger at the inner PWAS. Any signals that pass these two tests are processed, while any that do not follow this pattern are discarded. This filtering is conducted on all data collected and is a method for removing any signals, which did not originate from the area being studied. These signals can be generated by electrical humming or any other mechanical vibration on the testing sample. In the previous work [37], this was done manually using a text file reader and human operator, but by using a simple matlab script capable of reading .txt files and iteratively applying filters, the time it takes to discard unwanted signals becomes only seconds.

CNN models are extremely powerful and efficient tools, which are capable of the classification of sometimes hundreds of premade labels. The networks have complex structures and are a form of deep learning model where interconnected layers relay information through the model framework. CNN models have been found to be extremely compatible with the study of acoustic emissions and outperformed other typical ML models such as clustering methods, recurrent neural networks (RNN), and artificial neural networks (ANN) models [23]. However, these CNN models have a lengthy training time and high computation costs [23].

The GoogLeNet model is a pretrained, 22-layer machine learning model that has been suggested in the literature as suitable for small datasets [40]. Its framework involves stochastic gradient descent with a momentum of 0.9 and a fixed learning rate, making it a simple yet effective choice. This model was able to be interacted with within the matlab DeepLearningToolbox environment, which allows for direct manipulation of both the layers and training specifications of the model. The model used was slightly changed in order to be compatible with the data used in this experiment, the changes were simply changing the initial data input and final classification layers to operate with only three classes. Its final framework can be seen. This model framework was developed by researchers at Google for the LSVRC 2014 competition, GoogLeNet achieved first place. Its success in the competition set a new benchmark for CNN models in the field of data science.

Each class in this dataset contains between 208 and 220 samples. Each sample is a CWT spectrogram version of the original 300-ms waveform from the collected AE event. There are 646 total waveforms used for training, testing, and validation. This amount of data is considered a smaller size dataset for image classification since models are trained on thousands if not millions of images.

In this work, the chosen data format is CWT spectrograms (Fig. 12). These spectrograms include both time and frequency domain information and offer a higher spatial resolution when compared to a typical wavelet transformation. The frequency content in each AE signal is the main feature being studied in the dataset, so its inclusion in the data passed to the CNN model is a necessity. The time domain information in each CWT spectrogram allows for contributions to the dataset from the waveform patterns found in type I and type II AE signals. This creates a distinction that can be picked up by the model for type I and type II frequency content. It was decided to use an image classifier due to the complicated waveforms generated by AE events; these signals are difficult to parse for a human. But a computer would be able to determine the important features that a human might not be capable of. Image classifiers are ML models, which are capable of determining which features are important to focus on for learning, allowing for any features that may be correlated to crack length to be used. The use of an image classifier is also done in previous works at LAMSS [37], but the generation of images was done differently. In this work, the creation of CWT spectrograms was done automatically and iteratively for entire fatigue test data files. This is done by using matlab code to extract CWT spectrograms from generated figures (Fig. 15). Using an image processing technique that is done consistently is extremely important. If images were to be created manually, there is a chance that the operator may not crop to the same size or even introduce some other labeling problems. matlab is capable of applying the exact same image processing to the entire dataset, which reduces the error found from human interaction.

Previous AE-generating experiments also used only one PWAS for data collection [37], limiting the amount of data collected during the growth of a 2 mm crack. This method of crack generation is time consuming, especially when compiling an entire database of acoustic emissions. However, this experiment uses four bonded PWAS, all capable of the same quality of data collection, and signals from all four PWAS are added to the dataset, quadrupling the amount of data collected from a single specimen. The signals from PWAS 1 and 2 contain different time domain signals, but introducing a small-time delay corrects them, making their FFT signals similar to PWAS 3 and 4 signals (Fig. 16).

In many research fields, the cost and setup time required for signal analysis can be a significant bottleneck for development. To increase the efficiency of data collection, signal analysis and machine learning methods have been explored and implemented. However, in situ experiments often have limited datasets, which presents challenges for training and testing CNN models. In this experiment, only around 200 samples are collected per class, which requires extreme care when collecting and labeling data. Labeling data is labor intensive and involves assigning each AE signal with the corresponding crack length it originated from. Labeling becomes such an important task for a smaller dataset since a single mislabeled datapoint is much more influential.

One technique to address the lack of a large dataset is to generate synthetic data using the SMOTE. This method, adopted from Ref. [41], utilizes a k-nearest neighbor technique to mimic the patterns of the experimentally collected dataset, which helps to balance the dataset and reduce the majority class bias found in training. The generated data are the windowed signal located in the time domain, which is then transformed into the frequency domain via FFT (Fig. 17). These signals are found to be nearly identical to the signals collected during experimental work, but the changes introduced during SMOTE process creates AE that slightly alters each signal by a series of coefficients at each point, creating believable new data.

SMOTE is adept at synthesizing time-series data programmatically. This approach is an efficient way of using the already collected data in order to create new data. This is due to its methodology which roughly includes [42]:

1. You draw a random sample

2. For observations in this sample, identify nearest neighbors

3. Take one of the neighbors and identify vector between current and selected neighbor

4. Multiply vector with a number between 0 and 1

5. To obtain synthetic point, add value from (4) to current point

The data points generated by this technique include patterns in the frequency content similar to the experimentally collected ones. The SMOTE function in matlab [41] also has the bonus of generating synthetic data for all classes at once, cutting down data processing time.

Another important technique used to improve ML performance is the adjustment of class sizes to achieve balance. This balancing is done in order to avoid the appearance of a majority bias. This bias often arises when one class dominates the dataset, which can occur due to varying success rates in data collection. As a result, it is crucial to ensure that all labeled classes are balanced. For example, in the first case study, there was a single majority class with 100% more data than the other minority classes. The model learned to always predict the majority class, resulting in a loss of information about the minority classes. Although the dataset had many data points, the model's performance was limited by the class imbalance (Fig. 18(a)).

In contrast, the second case study had a perfectly balanced distribution among all classes. This allowed the model to learn about all three classes without developing a bias toward any one of them. By avoiding majority bias, even a small amount of data per class can lead to better ML performance. This is demonstrated in the second case, where the amount of data was the same as in the first case but distributed evenly among all classes (Fig. 18(b)).

Outlier detection in this dataset was done by hand since it was so small. The outliers found in data were often signals with frequency content that had been distorted or not matching the rest of the signals collected in the same test. These signals could arise due to either mechanical interference on the testing sample or by an error in the data acquisition system (DAQ) during the testing. By using the SMOTE function found within matlab [41], the balancing and synthetic data generation can be done in one step. The SMOTE function has the option to present multiple classes and generate data so that each class matches the size of the largest class creating balance. Deviation of the class sizes is difficult to completely eradicate, but by reducing it as much as possible, performance of the model in testing and training will increase.

The size of the classes is another crucial factor in using a machine learning model effectively. In general, larger amounts of data lead to better model performance, especially when the dataset is already considered small. In this particular experiment, the quantity of data collected will be constrained by the pace of in situ experimentation.

By using all the discussed methods on the AE dataset collected during testing, the raw class size and similarity between class size are greatly improved (Fig. 19). This dataset will perform at a higher level than the dataset was originally collected, without the running of additional experiments.

Postprocessing of testing and training results is a crucial step in creating a usable ML model. A training curve is often the first way to determine whether a model is viable (Fig. 20). In matlab's Deep Network Designer toolbox, training curves are updated in real time, displaying the validation, training (smoothed), and loss curves. These curves provide valuable information about how well the model is adjusting to training and whether it should mature further due to a lack of accuracy improvement.

To process testing results, confusion matrices are used to display the true and predicted values of the testing set in an easy-to-understand form. For a balanced model, a confusion matrix and basic accuracy calculations are acceptable methods of interpretation.

During the training of the GoogLeNet model with the four-PWAS dataset, a total of 30 epochs were run. An epoch represents the amount of time the data was passed through the entire network for training. The training accuracy reached 100% at around 23 epochs, taking a total of 37 min and 12 s. Although this training period was quite lengthy, it is typical for complex CNN models compared to other network types. The accuracy and validation curves showed some separation during training but never more than 10% for training accuracy, which is an acceptable level.

The confusion matrix for the GoogLeNet model and four-PWAS dataset (Fig. 21) shows a testing accuracy of 90.7%, which is considered an excellent classification model. This model was trained on 70% of the set as training, 20% as testing, and 10% validation.

The main objective of the work discussed in this article was to determine a correlation between fatigue crack growth and the acoustic emissions (AE) signal signatures.

A set of fatigue experiments were conducted using a thin aluminum sheet and two types of initiation defects: (a) 1-mm hole and (b) 150-µm slit of various lengths. Fatigue testing was performed under stress intensity factor control to moderate crack advancement. The AE signals were captured with piezoelectric wafer active sensors (PWAS) connected to MISTRAS instrumentation and aewin software. The four-PWAS array permitted the use of time-of-flight judgment for eliminating AE signals not connected to the crack. A nonreflective clay boundary was used to absorb reflections from specimen boundaries. Digital denoising was also applied. Scrutinous evaluation of the fatigue crack was done during experimentation to achieve a high accuracy of labeling the AE signals collected at various crack lengths.

The high-quality AE signals collected during the fatigue experiments were processed using automated filtering. The Choi Williams transform was applied to convert time domain AE signals into spectrograms. An image-preprocessing script was used to create datasets with AE signals recorded for various crack lengths. For example, we sorted to signals into three crack length groups (i) 10–12 mm; (ii) 12–14 mm; and (iii) 14–16 mm.

The image datasets were used to train a machine learning model based on the GoogLeNet CNN. To enhance the CNN's performance, we improved the dataset using the SMOTE as well as balancing the labeled classes. The dataset was partitioned into training, validation, and testing subsets. The performance of the CNN models was evaluated using the confusion matrix approach.

The results presented in this article showed a strong correlation between the fatigue crack length and the signatures of the AE signals. It was found that the frequency content of the AE signals shifts toward higher frequencies as the length of the fatigue crack increased. These experimental observations are in accordance with previously reported simulation results [33–37].

This correlation between AE signal signatures and crack length was successfully used to develop an AI-enabled crack length estimation method based on a large number of collected AE signals. It was possible to develop a matlab code for automating the signal processing, data generation, and labeling of the large number of collected AE signals. This greatly reduced the time needed to process the experimental AE data.

A GoogLeNet CNN was successfully trained on the AE signal image signatures. The usage of SMOTE to generate synthetic AE data was successfully applied to increase the CNN performance. The trained CNN was found capable of reliably determining the length of a fatigue crack in three distinct classes: (i) 10–12 mm, (ii) 12–14 mm, and (iii) 14–16 mm.

The trained GoogLeNet model showed a test accuracy of 91%, making it an excellent classifier of the AE data from the three classes. This is an improvement upon previous experimentation with AlexNet, which could determine whether a signal was AE, but incapable of determining the length of its source. This increase in performance is thought to be due partly to the inclusion of synthetic data, which increased the dataset size by 13%, as well as the balancing of each class to differ no more than 3% of the average class size.

By using all the implemented techniques, it was found that the GoogLeNet model outperformed the AlexNet model previously reported in Ref. [37].

In the future, the application of regression-based machine learning models to AE studies would be an interesting advancement. As the length of a fatigue crack is a continuous value, a regression-based model that can classify on a continuous scale would provide even greater insight. The current class labels span a range of 2 mm, which means that a 13.9 mm long fatigue crack could potentially be classified as a 12–14 mm crack without being identified as being extremely close to a 14 mm crack. This discrepancy could be resolved with the application of a regression model. However, labeling the crack and AE hit accurately is challenging. It may be possible to improve accuracy by coupling these two values using object detection machine learning models or other methods to precisely determine the point at which an AE event is captured.

In this work, NRB was used to ensure the captured AE signals are easily extracted without interference from the boundary reflections. The current research has shown to the scientific community that a clear correlation between the crack size and the acoustic emission signal signatures can be established. The current research is a baseline-free method that does not require prior knowledge of the pristine specimen. However, an NRB is unlikely to be feasible in real-life situations. The implementation of this method in real-life scenarios would require further research in which the effect of actual structural boundaries could be included. We believe that this issue can be resolved because the effect of structural boundaries is not affected by the crack length, and thus, structural boundaries are unlikely to affect the acoustic emission signal signatures. It is the authors’ hope that sustained research in this area will yield a feasible practical method for baseline-free SHM.

The work performed for this article was supported by the Office of Naval Research Grant N00014-21-1-2212, Dr. Ignacio Perez program manager.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

AE =

acoustic emission

CNN =

convolutional neural network

CWT =

Choi Williams transform

EMIS =

electromagnetic impedance spectrum

FFT =

fast Fourier transformation

HCF =

high-cycle fatigue

LCF =

low-cycle fatigue

LSTM =

long short-term memory

ML =

machine learning

MTS =

material testing systems

NRB =

nonreflective boundary

PWAS =

piezoelectric wafer active sensor

SHM =

structural health monitoring

SIF =

stress intensity factor

SMOTE =

synthetic minority oversampling technique