Power spectral entropy of acoustic emission signal as a new damage indicator to identify the operating regime of strain hardening cementitious composites

Cement and Concrete Composites 104 (2019) 103409

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Power spectral entropy of acoustic emission signal as a new damage indicator to identify the operating regime of strain hardening cementitious composites

T

Avik Kumar Das∗, Christopher K.Y. Leung Hong Kong University of Science and Technology (HKUST), Kowloon, Hong Kong

ARTICLE INFO

ABSTRACT

Keywords: Power spectral entropy Damage indicator SHCC Operating regime estimation Acoustic emission Cementitious materials

For strain-hardening cementitious composites (SHCCs) the knowledge of operating regime is important for maintenance planning and monitoring of the element. This paper presents a methodology of regime discrimination for SHCC from acoustic emission (AE) signals. From an AE signal, various damage indicators (DIs) can be derived. A new DI called Power Spectral Entropy (PSE) is developed in this paper. New benchmarks are developed to quantify possible effect of external factors on the measurement accuracy. Theoretical results indicate that the PSE is Signal to Noise Ratio (SNR) invariant, insensitive to the choice of subjective parameters and can be performed in real time. PSE was then obtained from the test result of SHCC with elastic behavior followed by strain hardening and softening. The test results indicate that the PSE varies with strain in a very similar way to the applied load. An approach to distinguish between different operating regimes of a SHCC component based on PSE is then proposed and validated. The practical applicability of PSE is hence demonstrated.

1. Introduction Infrastructure systems such as bridges, buildings, roads, pipelines and power grids are very important resources for the society. Given the vital role infrastructure plays in determining quality of life, it is important to maintain their operational conditions for a long period of time [1]. With aging of infrastructure and growing focus on durability all around the world, various monitoring techniques are being developed. Meanwhile, there is also growing impetus on the usage of advanced concrete materials to extend the lifetime of structures. One class of advanced materials, known as high performance fiber reinforced cementitious composites (HPFRCC) [2], have attracted a lot of interests. Common HPFRCC can be broadly classified into high strength cementitious composites (such as Ductal) and strain hardening cementitious composites (SHCCs). Ductal has high tensile strength of 12 MPa and a ductility (reflected by the tensile strain at ultimate tensile load) of 0. 2–0.6% [3], while SHCC typically exhibits a moderate tensile strength of 4–6 MPa but a much higher ductility of 3–5% [4,5]. The development approach for these two classes of materials is quite different. For Ductal, which can be traced back to the work of Bache [7], the approach is to employ a tightly packed dense matrix to increase both tensile and compressive strength of the material. Fiber is added to

∗

counteract the resulting high brittleness of the densified matrix. The dense matrix allows a strong bond with the fiber that results in a high post cracking strength as long as a fiber with high strength is utilized. For SHCCs, the approach is to create synergistic interactions between fiber, matrix and interface, to maximize the tensile ductility by development of closely spaced multiple micro-cracks while minimizing the fiber content (generally 2% or less by volume). This approach is based on micromechanics and is discussed in detail in Li [8] and Li and Leung [9]. The typical tensile stress-strain curves and crack distribution at various tensile strain for SHCCs is shown in Fig. 1. With large deformability/energy absorption and excellent crack width control, SHCCs can be employed for designing earthquake resistant structure and the structural elements that resists of water/chemical penetration thus, enhancing durability [10,11]. To take full advantage of the mechanical behavior of SHCC, it is often allowed to operate within the inelastic hardening regime during service condition, but crack localization (at the end of the hardening regime) should be avoided [12]. For a structural member made of SHCC, knowledge on which regime the material has reached is very useful for the condition/health monitoring and maintenance planning of the member. In the laboratory, the Load/ Stress vs Strain curve can be measured to distinguish these regimes. However, in the field, there is no reliable method for determining the

Corresponding author. E-mail address: [email protected] (A.K. Das).

https://doi.org/10.1016/j.cemconcomp.2019.103409 Received 26 April 2019; Received in revised form 1 September 2019; Accepted 3 September 2019 Available online 03 September 2019 0958-9465/ © 2019 Elsevier Ltd. All rights reserved.

Cement and Concrete Composites 104 (2019) 103409

A.K. Das and C.K.Y. Leung

To assess the condition of a structural component, the captured AE data (Signal) are correlated with damage according to either signal parameters or signal waveforms [13,22]. The former approach is referred to as parametric analysis while the latter is called waveform analysis [13,23]. Even though waveform analysis can provide more precise information of the AE Events (e.g., source discrimination, event localization), it is often not applied in real life monitoring due to computational complexity which requires a relatively long time to get the results [16,23]. Conversely, the advantages of parametric analysis, includes computational efficiency, ease of visualization and low storing capacity requirement, make AE parameters viable as damage indicators (DI) for severity assessment in practical applications. 1.1. AE parameters as DI and their limitations Fig. 1. Typical tensile behavior of strain-hardening cement-based composites adapted from [6].

For an AE Event, the basic AE parameters, including Count/Hit (rate), Peak Amplitude, Duration, Count to Peak, Rise Time (RT) and Rise Angle (RA) are commonly calculated. The determination of basic parameters for an Event is illustrated in Fig. 3. Other derived AE parameters are described in detail in [13]. Acoustic emission physically arises from the energy release associated with material cracking. For cementitious materials such as concrete, failure is caused by the formation and propagating of cracks under loading. AE is therefore commonly employed for monitoring the failure process of cementitious materials in both the laboratory and the field. In the literature, basic AE parameters have been used as DIs for detection of onset of damage in reinforced concrete (RC) beam [24–27], steel fiber reinforced concrete (SFRC) beams [28,29], RC columns [30], fiber reinforced concrete (FRC) under direct tension [31] and concrete under dynamic tensile testing [32]. However, to derive the numeric value for various DIs (or AE parameters), a threshold (as shown in Fig. 3) needs to be determined first. As the threshold is usually subjectively selected, variation is observed among different testing conditions and researchers. Due to such variation, the derived DIs might not be sufficiently accurate for engineers to make optimal real-time data driven decision. Even under laboratory condition, such a limitation can affect the reproducibility of experimental results. This aspect will be showcased quantitatively in Section 4.

stress in the material. Thus, there is a necessity to develop a monitoring technique which can successfully discriminate among the operating regimes. Structural health monitoring (SHM) is broadly described as a paradigm involving (a) data acquisition (in situ or remotely), (b) data feature extraction, and (c) mapping the extracted feature to the occurrence of performance deterioration (damage) to assess the condition of the structure. The acoustic emission (AE) system is a common SHM system that has been widely used for damage detection. Schematic of AE testing process is shown in Fig. 2. It relies on the passive detection of the waves (dynamic motion) generated by release of the strain energy associated with deterioration (such as cracking) of the structural element. Similar to any SHM system, the major objective of the AE approach is to provide useful information for monitoring deterioration of structures, by correlating detected AE signals with the evolution of fracture process or increasing deterioration [13]. AE data pre-processing (cleaning) is an important step before development of correlation function for damage. AE data cleaning (preprocessing) involves selection of appropriate filters to remove unwanted noise. This is as per the recommendation of RILEM technical committee [14] and also consistently found in the literature (for example: [13,15–20]). In adverse conditions i.e. operational acoustics lies within the same frequency interval as that of AE waveforms, filtered waveform might have to be processed before parameters are calculated. The process is elaborated with examples in Ohtsu et al. [21]. Since this paradigm is widely accepted, AE signals will refer to filtered waveforms in this paper.

1.2. DIs based on information entropy and their limitation Besides the conventional AE parameters described above, AE parameters based on information entropy (IE) have also been proposed. Information entropy (IE) (which is commonly known as Shannon's

Fig. 2. Schematic for AE monitoring. 2

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Fig. 3. An AE Event with Common AE parameters and their definitions.

time, which limits real world applications requiring decision making within a short time.

entropy) is first introduced in the context of communication theory as a measure of the information contained in the random letter from a receiver. In other words, entropy is the measure of the unpredictability or disorder in the information content [33]. Detailed discussion and results on information entropy can be found in Ref. [34]. Due to lucidity and ability of quantification of the uncertainty, the IE has been found useful in applications in physics [35], engineering [16,36–38] and mathematics [33,34]. The concept of information entropy has not yet been applied to cementitious materials in the context of damage monitoring, but researchers have employed the approach for metals. Amiri et al. [39] and Kahirdeh et al. [40] have conducted fatigue crack initiation and growth test on Aluminum Alloy (AA7075-T6) and Titanium Alloy respectively. Based on the Count of the AE waves, the information entropy was calculated. Since the entropy was calculated based on a conventional AE parameter, it is also susceptible to problems associated with common AE parameters described above. Unnthorsson et al. [41] applied information entropy to understand the fatigue damage in carbon fiber reinforced polymers. The IE was calculated from the probability distribution of amplitude and frequency every 5 min during testing. Due to the pre-defined time period, the results might vary based on the testing conditions and thus this method might not be reliable. Chai et al. [16] performed fatigue crack growth test under three point bending on a steel plate and the IE was calculated by first subjectively selecting a bin size (size of the intervals of a histogram) and then calculating the histogram of amplitude distribution in each AE waveform. A qualitatively positive correlation between crack growth and evolution of IE was obtained. It was suggested [16] that using this form of entropy can circumvent the uncertainty associated with predetermined time period [41]. Similarly, Sauerbrunn et al. [37] calculated IE from the amplitude distribution and found positive (qualitative) correlation between IE and fatigue damage in an aluminum alloy. Even though the entropy calculated from the amplitude distribution was not affected by the subjectively determined calculation time for the entropy, it is dependent on the manually determined bin size. Thus the method also has similar problem as that of basic AE parameters. The variation of entropy with bin size is illustrated in Fig. 4. For a typical AE wave (Fig. 4a) with entropy calculated for different bin size (Fig. 4b), the entropy is found to be more sensitive (showing higher values) for a lower bin size as compared to large bin size. In other words, for entropy to be an effective indicator for damage detection, the bin size has to be small. This translates into a longer computational

1.3. Research problem Deterioration of old concrete structures is a worldwide concern and the evaluation of structural condition by means of nondestructive testing (NDT) is therefore of great practical interest. Parameters obtained from waves captured by Acoustic Emission (AE) techniques have been employed as indicators of damage. In the laboratory, visual observation and complimentary data (such as loading, deflection or cracking) can be employed to correlate with the AE parameters, thus validating their applicability. However, for successful implementation of automated monitoring to discriminate various operating regimes and for data driven decision making in practice, it is crucial for an AE parameter to be insensitive to exogenous noise and manually determined parameters (such as the threshold applied on a wave, or selected noise filter). When deploying sensing system, it is important for the system to be robust even in extreme cases such as when the loading process is fast. A system which will not be adversely affected in these conditions is also expected to perform well in normal conditions. Thus, to design a monitoring technique for identification of various regimes of SHCCs , there is a necessity to develop a parameter which maintains the calculation efficiency of conventional parameters while curbing the necessity of manual intervention or subjective judgment for parameter derivation. To fill this gap, a novel damage indicator, Power Spectral Entropy (PSE), is introduced for cementitious materials. In the following sections, the precision, stability and value retention of PSE under various conditions will be presented in detail and compared with conventional AE parameters. The advantage of PSE over existing DIs (in terms of the insensitivity to noise and manually chosen parameters) is first demonstrated with realistic test data for a case with localized cracking. PSE is then applied to study the tension behavior in Pseudo Ductile Cementitious Composite (SHCC) members. Specifically, the use of PSE to discriminate between different regimes (which cannot be achieved with existing DIs) will be described in detail. 2. Proposed method 2.1. Formulation of information entropy Power Spectral Entropy (PSE), the new damage indicator to be 3

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A.K. Das and C.K.Y. Leung

Fig. 4. a) A typical AE Wave b) Entropy (from Amplitude Distribution) for AE wave (Fig. 4a) for different bin width.

developed in this work, is based on the concept of information entropy, which represents the uncertainty of information [33]. To illustrate this concept, one can assume that there are only two possible outcomes for an event, denoted as a and b. For case 1, the probability for each outcome is 50%. For case 2, the probabilities for outcomes a and b are 99% and 1% respectively. Case 1 is a case with high information entropy as it is not clear what the outcome will be, while for Case 2, it is almost certain (though not 100%) that the outcome is a, so the information entropy is low.The mathematical derviation of information entropy can be found in [33] and is briefly summarized here. Let A be a random discrete set with n elements i.e. A= [a1, a2, a3…. an] with probability of each element pi. Also, let B is a subset of A, B ⊂ A then P(B) is given by

P (B ) =

pi

selected segment T and = 2 f , with f being the frequency. Based on the definition of information entropy in the above, power spectral entropy (PSE) can be calculated from PSD (of each waveform) by treating the spectral power transmitted over different frequency bands as variables similar to the elements of set B (in Section 2.1). The calculated PSE will then represent the ‘uncertainty’ of the signal, which should be related to the physical mechanisms giving rise to the signal. If there is only one kind of physical mechanism behind a certain acoustic signal, the entropy should be low. On the other hand, if multiple mechanisms are present, higher entropy should be obtained. The PSE may hence be correlated to different operational regimes of a material if they are characterized by different physical damage mechanisms. To derive the PSE mathematically, we have to convert the PSD distribution to a complete probability space through normalizing. The normalized PSD distribution Sxx ( ni ) is calculated using Eq. (5).

(1)

i B

In all the equations in this paper, the small letter p is used to denote the proability of each element of the set while the big letter P is used when a full set is involved. Then, the information gained with knowledge of B a priori is defined as

G(B|A) = log2 [1/ P(B)] =

log2 [ P(B)]

Sxx ( ni ) =

n

H (Sxx ( ni)) =

(2)

p (i )

log 2p (i )

(3)

The Power Spectral Entropy is based on the Power Spectral Density (PSD) of a signal. Power Spectral Density consists of magnitude of the power transmitted in different frequency bands (i.e. PSD represents the variation of spectral power with frequency) and has previously been found to be very sensitive to the arrival of an acoustic wave [18]. The calculation of PSD is not straightforward due to ‘end effects’ of signal's segments. Such end effects can be reduced by selecting overlapping segments and tapering at the end (edge) of each segment. A good overview of various techniques for properly selecting segment length and overlap for PSD calculation can be found in Ref. [42]. After the proper segment is decided upon, PSD for the segment is then calculated using Eq. (4).

x (t ) e T

It should be noted that AE waves are narrow banded low frequency waves [18], so in the frequency domain, AE waveforms are observed as a narrow spike in PSD magnitude (Fig. 5B-C) in low frequency bands. Typically, in a AE signal, majority (> 90%) of the power is carried by the AE waveforms rather than noise [18]. Consequently, for other frequency bands, PSD magnitude is (very) low leading to the large extent of blank space in Fig. 5B-C. 3. Experimental investigation

2 j t dt

(6)

a) An AE wave (shown in Fig. 5a) is first selected. b) PSD magnitude is calculated using Eq. (4) and the result is shown in Fig. 5b. c) PSD magnitude is normalized using Eq. (5) to give the result in Fig. 5c. d) The database of normalized PSD magnitude corresponding to the frequency bundle is saved. e) PSE is calculated from the database using Eq. (6) and is plotted against the observed test time as shown in Fig. 5d.

2.2. Power spectral entropy

T

log2 Sxx ( ni )

The determination of PSE is illustrated by an example shown in Fig. 5a-d. The major calculation steps are as follows.

where n is the number of sets i ⊂ A and P(i) is the probability of the ith set.

1 Sxx ( ) = lim E T T

Sxx ( ni ) i=1

n i=1

(5)

Finally, the power spectral entropy is calculated with Eq. (6) using Eqs. (2), (3) and (5)

The information entropy in H(A) is given by

H (A ) =

Sxx ( i ) n S ( i) i = 1 xx

In the experimental setup, a multi-channel National Instrument AE system (NI-PXI 1042Q) was used to detect the acoustic waves in the material. Sampling frequency ( fs ) was set to 5 MHz using broadband

(4)

where, Sxx ( ) is power spectral density for AE signal x(t) within the 4

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Fig. 5. Calculation Process for PSE a) AE Wave b) PSD Magnitude c) Normalized PSD Magnitude d) PSE value.

piezoelectric sensor, and pre-amplifiers as described in [18]. Based on the external noise, detection threshold of the system was set to 0.002 V.

shielding the loading points and supports from machine vibration using rubber pads. Also, a low loading rate was employed. These measures, together with the selection of fiber content to ensure the formation of a single crack, are important for independent waveforms with high SNR value to be reliably obtained for theoretical study.

3.1. Point bending test To illustrate the applicability of the PSD based parameter to damage detection in concrete members, 4 pt Beam bending Test was performed on a steel fiber reinforced concrete (SFRC) beam. The mix proportion of the beam was Cement:Sand:Water = 1:2:0.5 with 1% (in volume) of steel fiber content. Based on preliminary tests, the employed fiber content will give rise to controlled cracking (rather than the sudden failure that occurs in a plain concrete member) but only a single crack will form so the possible overlapping of AE waves under multiple cracking is avoided. The beam dimensions, AE sensor locations and loading position are shown in Fig. 6. The span between supports at the bottom was 900 mm and the loading points was at 300 mm from each support. 8 piezoelectric transducers (PZT) were employed, with 2 on each opposing vertical side and 4 at the bottom of the beam (symmetrical about the center of the beam) (Fig. 6). During testing, the effect of exogenous noise was reduced by

3.2. Tension test for SHCC Table 1 shows the mix design of SHCC and samples of size 350 × 25 × 8mm (Fig. 7) were prepared for tensile testing. 4 samples were prepared and named as A,B,C,D respectively. CEM I 42.5 type Ordinary Portland cement, class F grade fly ash and specially graded fine sand with a maximum size of 0.16 mm [ASTM E11 mesh size 80] were used for the mix. Superplasticiser (SP) was added to give the appropriate rheology for optimal fibre dispersal and to avoid segregation. Kuraray™ K-II REC15 Polyvinyl alcohol (PVA) fibers were employed. To ensure sufficient length at the two ends for proper gripping of the specimen during testing, the middle gauge length is 150 mm. To detect acoustic signals during the test, two AE sensors were coupled 4 cm on each side from the center as shown in Fig. 7. During testing, an external linear variable displacement transducer (LVDT) was attached to one side of the middle part of the tensile specimen to measure the elongation(Fig. 7), for calculating the tensile strain. The tensile test was performed in a Lloyd-Ametek EZ50 (50 kN) testing machine, with a loading rate of 0.2 mm/min. The grips of the machine restrained the rotation and transverse displacements of the specimen both ends can be considered fixed.

Table 1 Mix design. Fig. 6. Dimension of the Beam (Note: The beam is shown in red lines, loading points in black lines, bottom support in blue lines, sensors as circle. Dimension are in mm). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 5

Sample

Fly Ash

Cement

Silica Fume

Sand

Water

Super Plasticizer

Fibers (PVA)

A-D

0.8

0.18

0.02

0.2

0.22

0.003

2%

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Fig. 7. Uniaxial Tension Test setup for SHCC.

4. Results and discussion

4.1. Precision

The results are divided into 4 sub-sections. The first 3 sub-sections on precision, value retention and filter sensitivity critically analyze the variation in the new PSE parameter in response to human intervention (e.g. selection of different thresholds, filters) and interlacing of extraneous noise. Using realistic AE waveform generated during the bending test, variations of PSE, AE Count and Duration are compared. As illustrated in Fig. 3, AE Count and Duration are the most basic parameters as other parameters (such as Energy, Rise Time, Rise Angle, Count to Peak) are derived from them. Variation in the value of these basic parameters will therefore also reflect the variation of the derived parameters. To understand the statistical stability of different DIs, the following benchmarks are defined:

Precision is defined as the change of a parameter value due to manual intervention. Since basic AE parameter depends on manual thresholding, the precision study focuses on thresholding alone. It is obvious that a parameter with higher precision would have less variation with change in thresholding value whereas a parameter with lower precision would show a high variation. In the following, the precision is compared between two common AE parameters and PSE as a function of the change in the thresholding level. For statistical accuracy, 10 different AE waves were used. The waves were normalized (as in Eq. (7)) such that the maximum amplitude is 1. This is done to ensure uniformity in the thresholding value. For all the waves, the average change in precision (ACp) for each parameter was calculated according to (Eq. (8)). The threshold was varied from 0.01 to 0.2 with steps of 0.01.

a) Precision: This benchmark is designed to understand the variation in numerical value of a DI for the same waveform, when a different threshold value is chosen since thresholding is a manual and subjective process. b) Value Retention: This benchmark is designed to understand the effect of exogenous noise on the changes in the derived value of a DI. Overlapped AE waves can be divided into intersected AE wave and intersecting AE wave. Due to overlapping, the intersecting wave would have a similar effect as a noise, so Value Retention can also help to understand overlapping effect of AE waves on the derived value of a DI. c) Filter Sensitivity: The prior filtration of an AE wave is an important step towards information extraction from AE waveforms. Due to difference in noise characteristics, adaptive filtration is often proposed. Thus, this benchmark is designed to understand the sensitivity of derived numerical value of the DI with the variation of the filtration technique among common choices.

Waven (i) =

Wave (i ) Max (Wave (i ))

(7)

where Waven(i) is the value of normalized wave of ith element

ACp =

1 n

n j=1

(Vi, j

V0.01, j ) V0.01, j

100

(8)

where, Vi, j is the value of parameter for the for jth wave at threshold i and ACp is average change in precision in percentage. The change is calculated using the case with threshold of 0.01 as reference. The procedure is as follows: a) b) c) d)

An AE wave is selected and normalized using Eq. (7). The threshold is varied and the different parameters are calculated. PSE is calculated with the methodology described in section 2. ACp is calculated using Eq. (8) for each AE parameter. The ACp results for different parameters as a function of the

6

Cement and Concrete Composites 104 (2019) 103409

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Fig. 9. Change of different parameter in response to change in SNR value.

Fig. 8. Change of different parameters in response to change in threshold value.

4.3. Filter sensitivity

threshold value is plotted in Fig. 8. Negative sign indicates reduction in value. The two conventional AE parameters (Duration and Count) decay in value by almost 75% whereas PSE stays unchanged. This observation can be attributed to the fact that the PSE derivation is independent of threshold whereas common AE parameter is very sensitive to the manual thresholding. On the average, when the threshold changes by 1% (0.01) (of Maximum Amplitude), the duration and Count change by approximately 4%. Thus, it can be concluded that the precision of the common AE parameters is far lower than that achieved by the new PSE parameter.

In this section, the sensitivity in relation to different filter selection is studied. In the literature, a low pass filter is commonly used for cleaning AE waves even though implementation details may vary [18,43]. To understand the variation in the parameter value, several common low pass filters reported in the literature, including (a) Equiripple, (b) Buttterworth (order 2 and 4), (c) Chebyshev Type I, (d) Chebyshev Type 2 and (e) Elliptic Filter [44], were studied here. In order to match the filter response the stop band (cutoff frequency fc) was kept constant for each AE wave. fc was determined from power characteristics of AE wave using Eq. (10) and Eq. (11) as given in [18]. Then, the different parameter values were calculated for the filtered wave and average change of filter sensitivity (ACfs) is obtained from (Eq. (12)).

4.2. Value retention Value retention is defined as the change in the value of the parameter associated with the same waveform under different SNR values. Similar to precision, a parameter with superior value retention would show little change in the inherited value for the same waveform over a wide range of SNR values. To obtain the value retention for different parameters, the following steps are followed:

f

Power (0,f) = 2 *

1 n

n j =1

(Vi, j

V100, j ) V100, j

100

(10)

99/100 ≤ Power(0,fc)/Power(0,fs/2) where, Sxx ( ) = Power Spectral Density and 2 f = quency and fs data acquisition rate

a) An AE signal is chosen randomly from Beam Bending Test. b) The SNR of the AE wave is calculated [18] for determining the power of the required white noise to reach a specified SNR value. c) White noise is added digitally [18] to get a Noised Wave. d) Step (c) is repeated 50 times for specified SNRs from 100 to 15 in step sizes of −5. e) The average change in value retention (ACvr) for each Noised Wave is calculated according to (Eq. (9)) for each parameter.

AC vr =

Sxx (2 f ) df 0

AC fs =

1 n

n j=1

(Vi, j

VNoFilter , j ) VNoFilter , j

*100

(11)

, fc is cutoff fre-

(12)

where Vi, j is the value of a parameter for jth wave under filter type i and ACfs is the average change of filter sensitivity in percentage of each parameter. To differentiate the filter sensitivity of the AE parameters, the following steps are followed: a) 20 AE waves are selected randomly b) The SNRs of the waves is calculated [15]. c) The duration and Count of the wave filtered through each of the filters are calculated, together with the PSE. d) The ACfs values for Duration, Count and PSE are calculated according to (Eq. (12)).

(9)

where, Vi, j is the value of parameter for jth wave at SNR i and AC is the average change in percentage. The Results of ACvr for different parameters as function of SNR is plotted in Fig. 9. Due to very high change in Count, its values are shown with a different axis on the right hand side of the figure. Examples of SNR 70 wave and SNR 20 wave are shown in Fig. 10a and Fig. 10b respectively. From Fig. 9, AE parameter Duration changes value for the same wave by approximately 50% and Count changes by approximately 5000% whereas the proposed parameter PSE does not change the retained value even for SNR as low as 25 and it only changed by about 3% for SNR value of 15. As a result PSE can be considered SNR invariant. In other words PSE retains the value of the waveform even when the waveform is degraded by noise. So, PSE is better Value Retainer as compared to other AE parameters.

Intuitively, a parameter which does not change in value for the same waveform under a particular noise filtration technique is filter insensitive, and is considered superior to a parameter whose value changes according to the choice of the noise filtration technique. The results are tabulated in Table 2: Following is inferred from Table 2: a) Filter selection is one of the most important parameters for consistency in the results when using conventional AE parameters. b) Common AE parameters such as Count and Duration show large and 7

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Fig. 10. a) Example of SNR 70 Noised AE Wave b) Same Wave Noised to SNR = 20 Note: For each wave, the calculated parameters are shown on the top of each figure.

studied by Li. et al. [45,46]. and it is characterized by three regimes: namely elastic (linear), strain hardening and strain softening. During the linear stage, microcraking in the matrix occurs but crack propagation is controlled by bridging fibers. The stable crack growth introduces little nonlinearity to the stress vs strain behavior so this regime can be considered to be approximately linear elastic. When the applied stress reaches a certain level, some microcracks will coalesce to form a through crack across the section of the member. This is referred to as first cracking, which marks the end of the linear stage. In the section where the first crack occurs, loading is carried completely by the fibers. In SHCC, the fibers can carry a higher stress than that at first cracking. Further straining is hence accompanied by increasing stress, which induces cracking at other sections of the member. The formation of multiple cracks under increasing strain results in a strain-hardening behavior similar to metals (though the mechanism is completely different). In a properly designed SHCC, the strain hardening regime can extend to strain levels of several percent, until deformation localizes into one particular crack which continues to open up widely. Strain softening behavior then occurs due to significant fiber pull-out and rupture at the localized crack. Recently, Paul et al. [47]. have studied the crack propagation in SHCC members using conventional AE parameters, i.e. amplitude and weighted peak frequency (which is calculated from the frequency spectrum). They attempted to characterize the evolution of weighted peak frequency with the evolution of different mechanisms (cracking of matrix, fiber pullout/rupture) and amplitude with propagation of failure. The results indicate that matrix cracking and fiber pullout/ rupture give rise to AE signals lying within different ranges of frequency whereas amplitude was found to increases as damage increases. Based on this information, it will be possible to distinguish between the linear regime (where there is little cracking), the strain hardening regime (with significant cracking) and softening regime (dominated by fiber pullout rupture). Test data on three different SHCC compositions indicated that the start of softening could be easily inferred for two compositions but hard to determine for one of them. As pointed out by the authors, their study has established the potential of the approach, but further work is still needed. In the present study, a different approach to distinguish between various regimes, based on the PSE of AE signal, will be demonstrated. While the advantage of PSE as a new AE

Table 2 Percent Change of different parameters in response of the Filter Type. Filter

SNR Range (Pre Filter) dB

ACfs (Count) (%)

ACfs (Duration) (%)

ACfs (PSE) (%)

No Filter Equiripple Butterworth (2nd order) Butterworth (4th Order) Chebyshev Type I Chebyshev Type II Elliptic

35–50 dB — —

0 −25.29 −25.35

0 0 0

0 0 0.03

—

−23.35

0

0.02

— — —

−25.13 −23.72 −53.33

−52.75 −0.1 −52.65

0 0.01 0.1

Note: 1. -ve sign indicate that the value is lower as compared to the case where No Filter was used. 2. A large variation among the values of AE parameter was observed for some AE waves.

unpredictable deviation when different filtration techniques are applied to the same AE waveform. c) For the same waveform, the proposed parameter PSE shows negligible changes in value for different filtration techniques, and can hence be considered filter Insensitive. In summary, the theoretical results validate that PSE is invariant to the level of noise and insensitive to manually determined parameters. This can be attributed to the fact the value of PSE is determined by the relative power carrying capability of various frequency bands. In addition, the calculation of PSE is relatively simple, and can be performed in real time (within 0.01s). The newly introduced PSE parameter which does not exhibit such drawbacks is hence better suited for practical applications. Table 3 shows the results of the comparison of various DIs for cementitious materials. 5. Failure discrimination of various regimes of SHCC in tension 5.1. Background Cracking behavior of SHCC specimens under direct tension was Table 3 Comparison among different DIs for cementitious materials. DIs

Precision Level

Value Retention

Filter Sensitivity

Computation Requirement

Damage Detection Ability

PSE Count Duration

Precise Imprecise Imprecise

Good Poor (very sensitive) Poor

Insensitive Sensitive Sensitive

Real Time Real Time Real Time

Accurate* (observed in laboratory investigation) Can be used in a controlled laboratory testing

8

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A.K. Das and C.K.Y. Leung

Fig. 11. Evolution of DIs with strain for SHCC in tensile failure a) PSE b) Amplitude c) Count. Note: For each graph, the measured load during the experiment is also shown.

parameter has been verified theoretically in the above, it is still necessary to show experimentally that it can provide more useful information for discriminating operating regimes than other parameters. To do so, other common parameter used in previous study of SHCCs/ FRCs in tensile test, including Amplitude [47] and Count [31], are also calculated. The testing and specimen details have been described in section 3.2. The AE data is processed using the method described in section 2 to calculate PSE values. The arrival time calculated using [18] is saved to match the parameters with corresponding load and strain values. The evolution of PSE and two conventional AE parameters, namely amplitude and count, as a function of strain, is shown in Fig. 11 (A-C) respectively. [Note: Event is not calculated as it has been shown in the previous section that its value is insensitive to degree of damage]. In Fig. 11 (A-C), the X axis is strain, whereas the left side Y axis is load in newton (N) and right side Y axis is the value of the parameter. In each plot in Fig. 11, the measured data are shown as dots, with each point in the diagram marking the PSE, amplitude or count for one hit of AE wave detected by one visually distinguish among 3 different regimes. Load is also shown in each of the figure at the corresponding strain to parameters (including PSE) over small changes in strain

resulting from unavoidable randomness of fracture process, 10 period (point) moving average (statistical variation of mean) is calculated for better visualization of the trend. In the elastic stage characterized by proportionality in load vs strain curve, there is a small number of hits due to micro-cracking. This section corresponds to low value in PSE and Amplitude however, very high values in Count are sporadically observed. This could be due to relatively low value of SNR. In the following strain-hardening stage, the load stays on a ‘plateau’ with small variation, but changes in moving average for both Amplitude and Count are not very pronounced in the hardening regime, so neither is sensitive to the ‘beginning’ of strain hardening regime. In contrast PSE starts to show much higher values at the beginning of the strain hardening regime, plausibly due to the multiple mechanisms of micro-cracking and fiber debonding/sliding, together with limited rupture of fibers at high inclination angles and pullout of fibers with very small embedded length on one side of a crack. In the strain hardening state, at around 0.25% strain, isolated values of high Amplitude and Counts are suddenly observed. At a higher strain of around 0.7%, high Amplitude values are consistently observed whereas no significant change is observed with Count. The variation of Amplitude is similar to the one reported by Paul et al. [47]. 9

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A.K. Das and C.K.Y. Leung

However, it does not seem to have correlation with the actual load vs strain behavior. On the other hand, the PSE correlates well with the load. Following the strain hardening stage is the strain softening stage with decreasing load (stress) due to damage localization at the major crack. A very high volume of activities within a small change in strain value is traced to this region which is caused by sudden release of energy associated with opening of the major crack. This region is undisguisable from the values of Amplitude and Count, but a wide range of lower values (relative to those at the hardening regime) is observed for PSE. One plausible explanation for the lower value of PSE is that the AE signal is dominated by fiber pull-out and rupture, which does not release as much energy as matrix cracking that occurs during the hardening stage. As a result, as damage progresses (strain softening regime progresses) a continuously decreasing trend is observed in the PSE (which is clearly visible in the moving average plot). While the results for only one specimen is shown in Fig. 11, the evolution trend of all AE parameters (PSE, Amplitude, Count) with strain and load for the other tested SHCC members are very similar, so they are not presented here. As discussed in section 1, load/stress curve has been ubiquitously used by researchers to identify the regimes. Thus, an AE parameter with statistical variation that is in correlation with the load curve is very useful for visually distinguishing various regimes. To summarize, our results show that both AE Amplitude and Count have very weak (or no) correlation with the load, while PSE shows similar trend as that of the load when strain is varied. The result is not surprising as PSE is a measure of the spectral power associated with the waveform (crack nucleation) during failure of SHCCs. In the initial linear region, the waveforms are due to microcracks with low average power thus PSE is low. During strain hardening the majority of the waveforms are due to matrix cracking (forming over full cross-sections) with some due to fiber debonding/sliding, which gives higher average PSE values. During softening, fiber rupture and pull out takes place which has lower acoustic power thus lower average PSE values. Therefore, the moving average (statistical behavior of the mean) of PSE is correlated with load development, and it can potentially be applied to distinguish among different regimes of cracking.

=

Vj Sj

(14)

COV = std (PSEi )/ µ F _Mu =

(15)

µj

F _rho =

µj

(16)

j j

COV _F =

(17)

COVj COVj

(18)

where std is the standard deviation, i represents the ith value and j represents the jth regime. The calculation process is illustrated by the three steps below: A Identify the PSE's, its volume (V) and strain (S) in each regime. (NOTE: Volume here is defined as total number of points observed) B Calculate µ, and COV in each regime (Eq. (13)–(15)). C Calculate F_Mu F_ rho and COV_F using (Eq. (16)–(18)) The results for 4 SHCC specimens namely A-D are shown in Fig. 12 a-d respectively. The results for all specimens are consistent among themselves without large inter-sample deviation in the shape, which indicates that these statistical parameters can be used to sufficiently distinguish the stochastic behavior of fracture processes of various regime. With this proposed benchmark, the various failure regimes (i.e initial/elastic region, strain hardening region and softening regions of SHCC in tensile failure) can be consistently and properly distinguished. To summarize, in this section we have presented the use of representative statistical parameters to distinguish various regimes in laboratory conditions. In the following section, the application of such parameters to inversely identify various regimes from limited AE data obtained for the same material in the field will be described in detail. 5.3. Inverse identification of correct regime with partial data collection

5.2. Quantitative classification of regimes

From the engineering point of view, it is important to know the regime at which the SHCC in a structural member is operating at. Specifically, in field application it is common to monitor structural elements over only a part of their lifetime. Consequently, only a partial section of the evolution of PSE would be available from the measured AE signals. Fig. 13 shows a typical evolution of PSE in various regime of SHCC and it is assumed that only the data within two black lines (in the region that is not greyed out) is available. To determine the regime based on such limited data is an inverse problem to be solved. To accurately solve such a problem we first calculate the sample characteristic (µs , COVs, s ) using Eqs. (13) and (14) &19.

In the previous section, we have shown that the acoustic emission behavior of various regimes is well captured qualitatively by the statistical behavior of PSE evolution. The theoretical basis of such behavior of PSE has also been discussed. However, for practical application of the PSE for decision making on the operation regime of a material, quantitative results are required. Fracture processes are inherently random and the temporal evolution of fracture is not smooth. For different specimens under the same loading regime, the fracture process is stochastically similar but not exactly the same. Consequently, the PSE significantly varies about the mean (as shown in Fig. 11A), possibly due to randomness in generation and evolution of the cracking process. The determination of each loading regime based on the mean of PSE alone, especially with the limited number of AE signals that can be obtained during field monitoring over a period of time, may not be sufficiently accurate. To this end, a simple method to quantitatively discriminate the various regimes using various statistical characteristics (parameters) µ, and COV (Eq. (13)–(15)) is proposed in this section. From the laboratory test data of load vs strain, the elastic, hardening and softening regimes can be identified. In each regime, the population characteristics can be calculated according to Eq. (13)–(15). Statistical parameters are then normalized as in Eq. (16)–(18) such that they are numerically comparable.

µ=

PSEi V

s

= Vs / T

(19)

where, Vs is the volume of emission during the measurement time T It should be noted that the laboratory test is carried out under displacement controlled (with rate r) so using the assumption of no slippage at the edge, time (T) is linearly related to strain through a scalar factor z which is related to strain (S) and gauge length for strain measurement (L). T = z*S;

(20)

z = L/r

(21)

Generally speaking, the number of AE samples taken during a certain monitoring period is less than the total number of signals generated within a certain regime. However, the calculated parameters (μ, COV and ρ) should be similar to those for the corresponding regime obtained from laboratory test data. Based on this idea, a similarity index SIj for

(13) 10

Cement and Concrete Composites 104 (2019) 103409

A.K. Das and C.K.Y. Leung

Fig. 12. Results of Quantitative Discrimination of various failure regime for SHCC in tension of samples A) A B) B C) C D) D.

the jth regime can be defined as:

Table 4 Classification result.

(22)

SI j = 1/ Ej where

Ej = µs

µj + COVs

COVj +

s

z

j

(23)

It is then possible to identify the correct regime by calculating SIj for all three possible regimes, using corresponding values of μj, COVj and ρj. The correct regime is the one that will give the maximum value of SIj. To validate the above approach, (µj , COVj, j ) for the three regimes are first determined from one of the SHCC specimens. Then, various sections are selected randomly from the PSE vs strain curve for any of the 4 tested SHCC samples, and SIj is calculated to see which regime the data should fall into. The predicted regime is then compared to the actual regime as observed from the load vs strain curve. This experiment was repeated 50 times with different sets of data. The results, which are shown in Table 4, indicate that the correct regime was obtained for approximately 90% of all cases. This shows the potential of this approach for practical cracking regime identification in SHCC members.

Regime

No of sections taken

Number of correct prediction

Hardening Softening Elastic

18 19 13

16 16 12

6. Conclusion Detection and analysis of acoustic emission signals is an effective approach to provide valuable information regarding the origin and importance of cracking damage in materials. It is of particular relevance to members made of cementitious materials, the failure of which is preceded by the formation and propagation of cracks. In this study, a new Damage Indicator (DI) called Power Spectral Entropy (PSE) is introduced. A quantitative (systematic) benchmarking study is performed to assess the effects of subjective parameters (threshold, filter) as well as exogenous noise on various DIs. The results show that that PSE is invariant to the level of noise and insensitive to manually determined

Fig. 13. An example of partial information problem. 11

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A.K. Das and C.K.Y. Leung

parameters, thus much more robust than DIs based on conventional AE parameters. For components made with pseudo-ductile cementitious composites (SHCC), elastic behavior is followed by strain hardening and then strain softening. The identification of which regime the material is operating at is useful for engineering decision making (e.g. need for maintenance) for SHCC based structural elements. This is a challenge for conventional DIs because the multiple cracking process in SHCC generate AE signal with high exogenous noise. Test results on SHCC show that PSE varies with strain in a very similar way to the load. With this finding, an approach to determine the operating regimes of a SHCC member based on PSE is proposed and verified with test data. The results of this study demonstrate the stability, feasibility and advantages of using PSE for conditional assessment of cementitious members with progressive damage, and provide benchmark for performance evaluation prior to real life deployment for non-destructive testing/monitoring. While the advantages of PSE over conventional AE parameters have been demonstrated, more laboratory investigations are needed to determine the performance of this new parameter under different test conditions (with different failure mechanisms) to provide guidelines for data interpretation in the field.

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