Improving accuracy of damage quantification based on two-level consistency control of PZT layers

Yuanqiang REN, Qiuhui XU, Shenfang YUAN

Research Center of Structural Health Monitoring and Prognosis, State Key Lab of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

KEYWORDS Consistency control;Guided waves;PZT layer;Quantitative damage diagnosis;Structural health monitoring

Abstract Structural health monitoring-based quantitative damage diagnosis technique plays a key role in real-time condition monitoring.Among the current research,piezoelectric(PZT)sensor and Guided Wave(GW)based damage quantification methods are promising,which normally establish a calibration model between GW feature and damage degree by experiments on batch specimens,and then conduct the calibration model on the monitored specimen.However, the accuracy of PZT and GW based damage quantification is affected by dispersion introduced by sensor network performance, structural material, and damage propagation among the adopted batch specimens.For improving the accuracy of damage quantification, this paper adopts PZT layer as sensor network and creatively implements theoretical and experimental research on batch PZT layers consistency control.On one hand, a two-level consistency control method based on multidimensional features-Euclidean distance is proposed to ensure the performance consistency of PZT layers placed on different specimens.On the other hand,experimental research on typical aircraft lug structures is also carried out to evaluate the requirement on performance consistency of PZT layers when performing quantitative damage diagnosis, and further verify the proposed two-level consistency control method.Experimental results show that the accuracy of damage quantification raises by 38%when the dispersion of different PZT layers is controlled within 5%.

1.Introduction

The condition monitoring technique is developed to ensure the full life potential of in-service aircraft under the premise of flight safety for each aircraft by enabling condition-based maintenance strategies.1–2In order to realize condition monitoring, the Structural Health Monitoring (SHM) technique has been widely implemented in aeronautical engineering for real-time structural condition monitoring based on feedback information from sensors installed on the structure during its service life.3–5It can realize the monitoring of metal crack,corrosion, composite delamination, and other damages in key parts of the aircraft by taking advantage of piezoelectric(PZT) sensors6–8, strain sensors9, optical fibers10, smart coating sensors11, comparative vacuum monitoring sensors12, etc.By conducting quantitative damage diagnosis, the results can be used as the basis for the evaluation of the aircraft service life.Therefore,improving the accuracy of the damage quantification is of great significance to the service life monitoring and prediction of the aircraft structure.

Among the existing SHM methods, the PZT sensor and Guided Wave (GW)-based SHM method has been proved to be one of the most promising and effective methods due to its advantages including sensitivity to small damage and ability of regional monitoring,etc.13–14In recent years,many promising methods have been developed for quantitative damage diagnosis using GW-based SHM, including Reconstruction Algorithm for Probabilistic Inspection of Damage(RAPID)15–16, Multiple Signal Classification (MUSIC)17–18,Artificial Neural Network (ANN)19, Gaussian Process(GP)20, and other methods.Among them, for the quantitative diagnosis of metal cracks, Lim et al.19established an ANN model between nonlinear ultrasonic GW features and crack length trained by experiments on batch plate-like structures.Yuan et al.20used GW features and crack length dataset obtained from a total of six aircraft lug specimens to train a GP model and realized the online quantitative diagnosis of the fatigue crack.Gao et al.21developed a probabilistic averaging model trained by datasets acquired from five aluminum plates to realize crack size quantification under hierarchical uncertainties.It can be seen that basically,a normal procedure of damage quantification based on GW is establishing a calibration model between GW signal feature and damage degree by experiments on batch specimens and then conducting the calibration model on the monitored specimen.

However, the accuracy of PZT and GW based damage quantification can be affected by dispersion arising from the variations in sensor network performance, structural properties (geometry, material, surface finish, etc.), and flaw morphology (flaw type, shape, orientation, growth rate, depth,location,etc.).22Among the above influencing factors,the dispersion of the PZT sensor network performance will directly lead to the dispersion of the output GW signal features, and ultimately reduce the accuracy of damage quantification.Therefore, it is crucial to perform consistency control of the PZT sensor network performance.Consistency evaluation and control methods of PZT sensor performance are attracting more and more attention.The steady-state and transient features of the PZTs are investigated for consistency control.Correlation methods such as covariance and correlation coefficient method, slope method, and morphological characteristic method are usually used to calculate the similarity of PZT signal curves.23–25However,the studies mentioned above are just preliminary performance control research for a single PZT sensor.The application scenario of damage quantitative diagnosis, in which PZT sensor networks are usually arranged on batch specimens, is not considered.Therefore, in order to improve the accuracy of quantitative diagnosis, further research on consistency control of the PZT sensor network is needed.

In recent years,to improve the consistency of the PZT sensor network performance, Chang and Lin26proposed a distributed sensor network, called the PZT layer, which packs PZT sensors in a flexible interlayer with a certain technology to form the sensors network, using printed circuits instead of ordinary wire connections, and finally outputting through a standard interface.Aliabadi27and Qiu28et al.adopted PZT Layer into their experimental or practical research to enhance the consistency of the PZT sensor network performance,showing that PZT layers have good application prospects for damage monitoring of aircraft structures.However,when the PZT layer is used for damage quantification, it is necessary to arrange multiple same PZT layers on the batch specimens.The current research is aimed at a single structure, ensuring the consistency of PZT sensor performance within a single PZT network,and there is a lack of research on the consistency control of batch PZT layers for quantitative damage diagnosis.

In order to solve the above problems in the process of quantitative damage diagnosis, this paper creatively implements theoretical and experimental research on batch PZT layers consistency control.The requirements of PZT layers consistency for damage quantitative diagnosis are studied,and a two-level consistency control method is proposed to realize consistency control.On one hand, a two-level consistency control method based on Multidimensional Features-Euclidean Distance(MF-ED)is proposed to ensure the performance consistency of PZT layers placed on different specimens.This method first extracts the impedance at typical multi-frequencies of PZTs to construct the Multidimensional Features Vector (MFV) and performs the first-level control of PZTs according to the distance between MFVs.Then,PZT layers can be manufactured based on the PZTs after the first-level control.The MFVs of PZT layers are extracted and combined with the consistency Threshold(TH)to achieve the second-level control.On the other hand, experimental research on typical aircraft lug structures is also carried out to evaluate the requirement on performance consistency of PZT layers when performing quantitative damage diagnosis and to verify the proposed two-level consistency control method.

The rest of the paper is organized as follows: Section 2 introduces the basic principle and process of GW based quantitative damage diagnosis.Section 3 carries out theoretical research on two-level consistency control of PZT layers performance, followed by experimental research on the requirement of consistency in quantitative diagnosis in Section 4.The effectiveness of the proposed two-level consistency control method is also verified on aircraft lug structures in Section 4.Section 5 gives conclusions.

2.Basic principle of GW based quantitative damage diagnosis

Taking the quantitative monitoring of fatigue crack growth of typical aircraft lug structure as an example, the basic damage quantification process using the GW-based method is shown in Fig.1, where S1, S2，...，Snare the names of n specimens respectively.GWF represents GW features and a represents the crack length.f(.) represents the calibration model.a(Tn)represents the crack length at the current monitoring time Tn.The basic damage quantification process mainly includes two parts: offline calibration model establishment process and online damage quantification process.

Fig.1 Damage quantification process.

Part 1:offline calibration model establishment process.First,make batch specimens with the same material and geometric characteristics as the target monitored structure.A specific PZT layer designed for the aircraft lug is placed on each of the batch specimens, respectively.Then, fatigue cracks are expanding during the fatigue experiment.During crack growth,acquire GW signals and extract the GWFs at different crack lengths of every specimen.After the fatigue experiment of the batch specimens,the training dataset of the crack length and the GWF is obtained.Based on the dataset, a calibration model can be established by different algorithms, as shown in Eq.(1).

where GWF represents GW features and a represents the crack length.f(.) represents the calibration model.

Part 2: online damage quantification process.First, arrange the same PZT layer as the training specimen on the target monitored structure.Then, fatigue crack propagates under fatigue load.During crack growth, obtain the GW signal of the monitored specimen and extract the GWF(Tn) at the current monitoring time Tn.In combination with the calibration model,the crack length can be quantitatively output as shown in Eq.(2).

where a(Tn)represents the crack length of the monitored structure at the current monitoring time Tn.

The GW signals output of the batch PZT layers on batch specimens are the basis for calibration model establishment,so the performance consistency of batch PZT layers is crucial for the accuracy of damage quantification.The consistency of batch PZT layers can be affected by two main sources:(A)The dispersion of the PZTs.During the production process,the dispersion of doped elements and element ratios will directly affect the dielectric properties and piezoelectric properties of the PZTs.29The dispersion of temperature and electric field intensity during the polarization process will also affect the performance of the PZTs.30–31(B) The dispersion in the manufacturing process of the PZT layers.In summary, the dispersion of the PZT layers performance will directly affect the output GW signal features of batch specimens, and ultimately reduce the accuracy of damage quantification.Therefore, it is necessary to perform consistency control of the PZT layers.

3.Theoretical research on consistency control of PZT layers performance

In this section, theoretical research on consistency control of PZT layers performance is conducted.Based on the research,a two-level consistency control method is proposed to ensure the performance consistency of PZT layers for quantitative damage diagnosis.

3.1.Basic principle of consistency control

In circuits, impedance is usually represented by Z(Z = A + Bi), which is a complex number, the real part A is called resistance, and the imaginary part B is called reactance.The relationship between the output equivalent voltage Veqand equivalent impedance Zeqis shown in Eq.(3).

where ω is the excitation frequency.Ieqis the equivalent current.

Fig.2 shows the equivalent circuit diagram of the receiving PZT during GW based damage monitoring.It can be seen that the impedance of the PZT sensor affects the voltage of the output signal.Therefore,controlling the consistency of impedance characteristics can achieve performance consistency control of PZT.The impedance varies with the frequency, and the relationship between the impedance and frequency can be derived and calculated from the equivalent circuit diagram32.

According to the research mentioned above, the performance consistency between different PZTs can be evaluated by comparing their impedances.Since the impedance of PZT varies with frequency, the performance of PZT is different at different frequencies.Therefore, it is not enough to consider only one frequency.Instead, multiple impedance characteristics corresponding to typical frequencies are needed to construct the MFV for controlling the consistency of PZT sensors.By measuring the similarity (i.e.distance) between the MFVs of different PZTs,consistent control of PZT performance can be achieved.In this paper, Euclidean Distance(ED), which is a classic similarity measuring method, is used to calculate the similarity between different MFVs, due to its advantages in measuring the regular distance between two points in space.The ED value c between two n-dimensional vectors X1(x11,x12,...,x1n)and X2(x21,x22,...,x2n)is defined as Eq.(4).

3.2.MF-ED based two-level consistency control method

Combined with the above research, a two-level consistency control method based on MF-ED is proposed to ensure the performance consistency of PZT layers placed on different specimens.This method first extracts the impedance values at typical multiple frequencies of PZTs to construct the MFV and performs the first-level control of PZTs according to the ED value of the MFV.Then, PZT layers can be manufactured based on the selected PZTs after the first-level control.The MFV of PZT layers can be constructed and combined with a consistency threshold TH to achieve the second-level control.The flow chart of the MF-ED based two-level consistency control method proposed in this paper is shown in Fig.3, where Zifkrepresents the impedance at frequency fkof the i-th PZT.Diis the ED between the MFVifrom the coordinate origin.TH represents the consistency control threshold.The detailed implementation process of the method is introduced as follows.

3.2.1.First-level consistency control of PZT layers

Due to the dispersion of PZTs in the production process, the first-level control is mainly to improve the consistency of PZTs performance.The first-level consistency control process mainly includes the following steps:deleting the PZTs with impedance curve distortion, MFV extraction, consistency classification,and consistency control.

(1) Deleting the PZTs with impedance curve distortion

In this step, the impedance curves of all PZTs manufactured from the same batch are first measured using an Impedance Analyzer.Then, delete the PZTs whose impedance curves are abnormal.As an example,Fig.4(a)shows the impedance curves of 100 PZTs made from the same batch.It can be seen that the impedance curves of 4 PZTs are abnormal compared with others.After deleting the 4 PZTs, the remaining impedance curves are shown in Fig.4(b).

(2) Extracting MFV of PZTs

For the i-th PZT, extract the impedance at K typical frequencies (f1, f2,..., fk,..., fK) to construct the MFVi:

Fig.2 Equivalent circuit diagram of the receiving PZT during GW based damage monitoring.

Then, sort in descending order of Di.After sorting, the PZTs with similar ED values are classified into one category.On the one hand, because there will be multiple PZTs located in the PZT layer, PZTs need to be divided into multiple categories.The number of categories is the same as the number of PZTs in each PZT layer.A separate group is required for each PZT location.On the other hand, in order to ensure the consistency of PZT performance at the same position on the batch PZT layers, the number of PZTs in each category is determined according to the number of PZT layers.Meanwhile,because a second level consistency control is required, the number of PZTs in each category should be more than the number of PZT layers finally used.

For example, if there are 5 PZTs in each PZT layer and 6 batch PZT layers need to be made eventually, it is necessary to divide the PZTs into 5 categories of at least 10 PZTs each according to the ED, as shown in Fig.6.Those of the same color in Fig.6 are classified into one category.

(4) Controlling Consistency by threshold.

Calculate the mean value and range of the PZTs impedance of each category.The dispersion of PZTs in category c in frequency fk(k = 1, 2,..., K) is defined as Eq.(7).

where Zmaxand Zminrespectively represent the maximum and minimum values of the impedance of PZTs at frequency fk,and mean(Z) represents the mean value.

Fig.3 Flow chart of MF-ED based two-level consistency control method.

Fig.4 Batch PZTs with impedance curve distortion removed.

Fig.5 Extract the impedance at 3 typical frequencies.

Set the consistency threshold TH and TH can be determined by experimental studies of batch specimens.The determination of the consistency threshold TH value mainly considers the trade-off between the accuracy of damage quantification and the economy of engineering application.If the TH value is set too high,the consistency of PZT layers performance will be low, resulting in a high error of damage quantitative diagnosis results.If the TH value is set too low,it needs to be selected from a large number of PZT sensors and PZT layers to meet the threshold, resulting in a low utilization rate of sensors, time-consuming and laborious, and not conducive to practical engineering applications.

Fig.6 Consistency classification by ED.

In this paper, the method of determining the TH value mainly includes the following steps.First, measure the impedance dispersion of batch PZT layers without consistency control, i.e.the value of TH0.Second, according to TH0, the lower TH values are set at equal intervals.Third, the dispersion of GW signals under different TH values is investigated respectively.The variability of the signals caused by small damage is compared with the dispersion of the GW signals under different TH values.Finally, by ensuring that the variability of the signals under the selected TH value is smaller than that caused by damage, a reasonable TH value can be determined.If Ec> TH, delete the PZT with the largest relative deviation in category c.Perform this operation repeatedly until Ec< TH is satisfied, and finally, select PZTs with good consistency.

3.2.2.Second-level consistency control of PZT layers

In addition, the performance of the PZT layers is also dispersed due to the dispersion of the manufacturing process when welding the PZTs to the smart layers.Therefore, a second-level consistency control is performed to reduce the dispersion of the PZT layers.

The second-level consistency control process mainly includes the following steps: manufacturing PZT layers,MFV extraction, and consistency control.

(1) Manufacturing PZT layers

Manufacture batch PZT layers based on the PZTs after the first-level consistency control.To control the consistency of the PZTs in the same position of different PZT layers,the PZTs in the same category must be used for welding at the same position on the PZT layers.

(2) Extracting MFV of PZT layers

In this step, the impedance curves of the PZTs at all locations on the PZT layers are first measured using an Impedance Analyzer.Then, according to Eq.(5), extract the impedance values of the PZTs at typical multi-frequencies at the same position of different PZT layers to construct the MFV.

(3) Controlling Consistency by threshold

Set the consistency threshold TH and TH can be determined by experimental studies of batch specimens.The method of determining the TH value is the same as that in Section 3.2.1.The performance dispersion of the PZTs at the location l(0 TH, delete the PZT layer with the largest relative deviation of performance parameters at position l.Perform this operation many times until El< TH is satisfied,and finally select PZT layers with good consistency.

4.Experimental research on quantitative damage diagnosis

In this section, experimental research on damage quantification of aircraft lug structures is carried out.The influence of the dispersion of PZT layers on damage diagnosis is investigated, and the dispersion threshold TH of the PZT layers is determined.Finally, after the consistency control of PZT layers, the damage quantification of the lug structures is performed.Compared with the damage quantification results of PZT layers without consistency control, the effectiveness of the method proposed in this paper is verified.

4.1.Experimental setup

The aircraft lug specimen shown in Fig.7(a)is adopted to perform experimental research, which is an important aircraft structure and is usually used as the interconnecting piece of critical components such as the undercarriage and wing spar.The specimen is made of LY12 aluminum alloy,and the thickness is 5 mm.The layout of the PZT network is shown in Fig.7(b), which contains 5 PZTs, labeled as PZT 1 to PZT 5.The location of PZTs on the lug specimen is selected based on the layout optimization result,which is obtained by the following steps.

(1) Through the crack propagation simulation based on ABAQUS and FRANC3D, the key damage parts and crack propagation path are determined to provide guidance for the PZT layout.The simulation results show that the crack initiates on both sides of the lug hole,marked as Key part 1 and Key part 2 in Fig.7(b), and propagates perpendicular to the loading direction.

(2) For crack monitoring of the Key part 1, through the guided wave damage monitoring simulation based on COMSOL, the positions of PZT 1, PZT 3, and PZT 4 are determined.Among them, pitch-catch Channel 1–4 pass through the crack initiation position to monitor the crack initiation of Key part 1, and Channel 1–3 is located in the propagation path to monitor the crack propagation of Key part 1.

(3) Considering the crack monitoring of Key part 2, PZT 2 and PZT 5 are symmetrically arranged to form the final PZT optimized layout.

Based on the above PZT layout optimization research, the location of PZTs shown in Fig.7(b) is finally determined.

Fig.7 Aircraft lug specimen and layout of the PZT network.

In order to reduce the influence of bonding of the PZT layer to the substrate,a co-curing method is adopted.By controlling the temperature and pressure in the curing process, this method can realize the consistency of the adhesive layer when the PZT layer is coupled with the structure, so as to minimize the influence of bonding of the PZT layer to the substrate.In this experiment, three groups of batch lug specimens with different consistency TH values of batch PZT layers are prepared.The details of the three groups of batches specimens denoted as Group 1,Group 2,and Group 3,are shown in Table 1.Different consistency TH values of PZT layers are set in these three groups of experiments, mainly for the following purposes: (A) To investigate the requirements of consistency in quantitative diagnosis through experimental research, and finally determine the value of TH in the two-level consistency control process;(B)To verify the effect of the proposed consistency control method in improving the accuracy of damage quantification.As shown in Table 1, each group has six lug specimens,where the first five specimens are used for establishing a calibration model and the last one is used for quantitative damage diagnosis.

The fatigue experimental setup is shown in Fig.8(a).The SUNS-890 electro-hydraulic servo material test system in Fig.8(a) is employed to apply the random fatigue load for crack initiation and propagation.Fig.8(b) shows the variable amplitude load spectrum.The load spectrum is based on Fighter Aircraft Loading STAndard for Fatigue and Fracture(FALSTAFF) standard load sequence spectrum33.A digital microscope is used to observe the crack length along with scale lines on the lug surface during the fatigue test.The integrated multi-channel monitoring system is adopted for GW exciting and acquisition.The excitation waveform is adopted as the 3-cycle Hanning-windowed sine burst with the amplitude of±70 V.Two typical frequencies, 70 kHz and 170 kHz are mainly chosen as the excitation frequencies of the GW considering that different GW modes have different sensitivity to different damages.

4.2.Experimental research on consistency control of PZT layer

In this section, firstly, the dispersion of the PZTs and the output GW signals of the batch PZT layers are examined without consistency control.Secondly,the effects of PZT layers dispersion and crack propagation on GW signals are compared,highlighting the necessity of PZT layers consistency control.Thirdly,the dispersity of batch PZT layers is controlled within TH1 and TH2 using the two-level consistency control method proposed in this paper, respectively.Finally, the consistency control requirements of PZT layers on damage quantification are determined.

The experimental setup for testing the impedance curve of the PZT is shown in Fig.9.The Precision Impedance Analyzers WK6500B is for testing the impedance curves of the PZTs.The values of PZTs impedance dispersion at five PZT positions in 70 kHz and 170 kHz without consistency control are shown in Fig.10.As can be seen from Fig.10,the impedance dispersion of batch PZT layers without consistency control is within 15 %, i.e.TH0 = 15%.

When the PZT layers consistency is not controlled,baseline S0 mode direct waves in channel PZT 1–3 of 170 kHz acquired from the five testing specimens in Group 1 are shown in Fig.11(a), where S1, S2,...,S5 represent five specimens respectively.Taking typical specimen TH0-S1 as an example, the S0 mode direct waves of 170 kHz under different crack lengths are shown in Fig.11(b).The influence of PZT layers dispersion and crack growth on S0 direct waves are shown in Table 2.It can be seen that when the crack propagates 3 mm,the amplitude of the S0 direct wave changes to 254 mV.The change in GW signal features caused by damage is smaller than that caused by the dispersion of PZT layers.Therefore, the influence of small damage on the signal may be masked, resulting in early small damage that cannot be monitored.This also illustrates the importance of consistent control of PZT layers.

To have a judgment on the requirements of PZT layers consistency control,this paper studies the determination of TH of PZT layers.The experimental setup for the first-level consistency control is shown in Fig.9.The impedance curves of all the PZTs manufactured from a uniform batch are measured.The impedance curve measurement results are shown in Fig.12(a).It can be seen from Fig.12(a) that there is dispersion in the impedance curves due to the dispersion during the processing and manufacturing of PZTs.The results of MFVs extraction are shown in Fig.12(b),where MFV(1)indi-cates the impedance value at 70 kHz and MFV(2)indicates the impedance value at 170 kHz.Since the consistency without control in Group 1 is about 15%, it is considered to set the TH1 in Group 2 and TH2 in Group 3 to 10% and 5% when performing consistency control, respectively, to compare the effects under different consistency control thresholds.

Table 1 Details of the three batches of specimens.

Fig.8 Fatigue experimental setup and load spectrum.

Fig.9 Experimental setup for testing the impedance performance of the PZT.

Fig.10 Impedance dispersion of batch PZT layers without consistency control (TH0 = 15%).

Then,calculate the ED of MFVifrom the coordinate origin according to Eq.(6).The results of the ED are then sorted in descending order.Considering that there are five PZTs on each PZT layer and 6 batch PZT layers need to be made eventually.In order to ensure the consistency of PZT performance at the same position on different PZT layers, it is eventually necessary to divide the PZTs into 5 categories of 10 pieces each according to the ED.The first-level consistency control results are shown in Fig.13, where the same color is one category.

As shown in Fig.14(a), manufacture 10 batch PZT layers based on the PZTs after the first-level consistency control.To control the PZT consistency of the same position on different PZT layers,the same category PZTs must be used for welding at the same position on the PZT layers.The impedance curves of the PZTs at all locations on the PZT layers are measured according to the experimental setup shown in Fig.14(b).Delete the PZT layer with the largest relative deviation of impedance values.Eventually,six PZT layers with consistency within TH1 = 10% could be selected and cured on butch lug specimens for damage monitoring experiments.The impedance dispersion of batch PZT layers within TH1=10%in Group 2 after second-level consistency control is shown in Fig.15(a).Likewise, following the same steps as above, the dispersion of the PZT layers is controlled within TH2 = 5% in Group 3 and the impedance dispersion of five PZTs on batch PZT layers within TH2 = 5% is shown in Fig.15(b).

The S0 mode direct waves of baseline signals acquired from channel PZT 1–3 of 170 kHz are shown in Fig.16(a)-Fig.16(b)when TH1 = 10% and TH2 = 5%.

The dispersion of GW signal amplitudes of batch specimens is defined as Eq.(8).

Fig.11 Influence of PZT layers dispersion and crack growth on GW signals.

Table 2 Influence of PZT layers dispersion and crack growth on S0 mode direct waves.

Fig.12 Impedance curve measurement results and MFV extraction.

where Vmaxand Vminrespectively represent the maximum and minimum values of the amplitude of the GW signals in batch specimens and mean(V) represents the mean value of the amplitude.

Table 3 shows the comparison of the consistency of the S0 mode direct wave under different THs.It can be seen that setting more stringent (smaller) TH can effectively improve the consistency of the direct signals.As shown in Table 3, the change in GW signal features caused by damage is smaller than that caused by the dispersion of PZT layers when TH1=10%.This suggests that setting a consistency threshold of TH1 = 10% is not sufficient, and the effect of damage on GW still has the potential to be masked by the dispersion of batch PZT layers.However, when TH2 = 5%, the maximum change in the amplitude of the S0 direct wave is 137 mV.The amplitude change caused by the 3 mm crack propagation is 254 mV, which is larger than the influence caused by the 5%dispersion of the PZT layers.The influence of damage on the signal will not be masked, and the diagnosis of small cracks can be realized.Therefore, it is finally determined that TH = 5% is the dispersion requirement of the PZT layers for crack monitoring of the aircraft lug structure.

4.3.Quantitative diagnostic results

In this paper, two GW features called Damage Indexes (DI)with high crack detection sensitivity are extracted, and they are denoted as DI1and DI2, respectively.

DI1mainly describes changes in amplitude of signals34, as shown in Eq.(9).

DI2can be used to describe changes both in amplitude and phase of signals35, as shown in Eq.(10).

where b(t) and m(t) represent baseline signal and monitoring signal respectively,t0and t1are the start and stop times corresponding to the selected signal segment.

Then DI1and DI2are summed and averaged to obtain DIFuse,which is used to fully characterize the damage information of the lug structure.After the fatigue test of the batch specimens,the training dataset of the crack size and the DIFuseis obtained.Based on the dataset, the polynomial model as shown in Eq.(12) is obtained by the least square method to establish a calibration model between the DIFuseand the crack length a.

where β0,β1, β2,...,βpare polynomial fitting parameters.p is the polynomial order.

As can be seen from Section 4.2,it is finally determined that TH =5% is the dispersion requirement of the PZT layers for crack monitoring of the aircraft lug structure.Therefore, the damage quantification results of the following two groups of batch specimens are finally compared: (A) Group 1, without consistency control of PZT layers (TH0 = 15%); (B) Group 3, with two-level consistency control of PZT layers(TH2 = 5%).

Fig.14 Fabrication of PZT layers and experimental setup for second-level control.

Fig.15 Impedance dispersion of batch PZT layers after two-level consistency control.

Fig.16 S0 mode direct waves of baseline signals with two-level consistency control.

Table 3 Effects of damage and PZT layers dispersion on S0 mode direct wave.

Fig.17 Typical GW signals acquired at different crack lengths without consistency control in Group 1.

Typical S0 mode direct waves acquired from channel PZT 1–3 of 170 kHz under different crack lengths without consistency control in Group 1 are shown in Fig.17.With the crack propagation, the S0 mode direct wave tends to amplitude decrease and phase delay.Then, the DIs and the corresponding crack length obtained from the first five training specimens in Group 1 without consistency control of PZT layers are used to train a calibration model.The training data and calibration model are shown in Fig.18(a).According to the calibration model above,after the monitoring GW signal of the monitored specimen is obtained, the newly extracted DI can be input to obtain the crack length.The actual crack length and diagnosis results of the monitored specimen are shown in Fig.18(b).The absolute error range of the crack quantification is ± 2.0 mm,and the Root Mean Square Error (RMSE) is 1.3 mm.

Fig.19 shows the typical S0 mode direct waves acquired from channel PZT 1–3 of 170 kHz accompanying the crack propagation with two-level consistency control in Group 3.When the two-level consistency control is performed,the training data and calibration model are shown in Fig.20(a).Based on the calibration model,the actual crack length and diagnosis results of the monitored specimen are shown in Fig.20(b).The absolute error range of the crack quantification is ± 1.1 mm,and the RMSE is 0.8 mm.

Table 4 shows the comparison of the accuracy of the damage quantification whether the two-level consistency control is carried out or not.It can be seen that consistency control can effectively improve the accuracy of damage quantification,and the accuracy of damage quantification has increased by 38%.

5.Conclusions

For improving the accuracy of quantitative damage diagnosis,theoretical and experimental studies are carried out on the influence of the performance consistency of PZT layers on damage quantification.The main work and conclusions of this paper are summarized in points as follows.

(1) A two-level consistency control method based on MFED is proposed to ensure the performance consistency of PZT layers placed on different specimens.

(2) The experimental research on typical aircraft lug structures is also carried out to evaluate the requirement on performance consistency of PZT layers when performing quantitative damage diagnosis.It is finally determined that the dispersion threshold TH = 5% is the consistency requirement of the batch PZT layers for damage monitoring.

(3) The proposed two-level consistency control method of PZT layers is finally verified on the typical aircraft lug structure.Experimental results show that the accuracy of damage quantification raises by 38%when the dispersion of different PZT layers is controlled within 5%.

However,since this paper mainly focuses on the theoretical and experimental research of the PZT layer consistency control, there still exist some issues that need to be addressed in the ongoing research.

Fig.18 Crack quantification without consistency control in Group 1.

Fig.19 Typical GW signals acquired at different crack lengths with two-level consistency control in Group 3.

(1) Aiming at the realization of automatic implementation of the proposed damage quantification approach, the automation research will be carried out in the next stage of research.

(2) Considering the uncertain influence of temperature and loads on the GW signal, the applicability of the proposed method will be investigated under the influence of time-varying environmental factors such as varying temperature and loads in the future work.

Table 4 Comparison of damage quantification error results.

(3) In view of the lack of research on the aging of the system, the quantification of the aging of the system will be investigated in future research.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

Fig.20 Crack quantification with two-level consistency control in Group 3.

This work is sponsored by the National Natural Science Foundation of China (Nos.51921003 and 51905266), the Natural Science Foundation of Jiangsu Province,China (No.BK20190418), the China Postdoctoral Science Foundation(No.2019M661819),the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures,China (Nanjing University of Aeronautics and Astronautics,No.MCMS-I-0521K01), the Priority Academic Program Development of Jiangsu Higher Education Institutions of China, the Postgraduate Research & Practice Innovation Program of Jiangsu Province,China (No.KYCX22_0347), the Interdisciplinary Innovation Fund for Doctoral Students of Nanjing University of Aeronautics and Astronautics,China(No.KXKCXJJ202208).