Multi-type damage localization using the scattering coefficient-based RAPID algorithm with damage indexes separation and imaging fusion

Abstract

Guided waves-based structural health monitoring (SHM) methods have potential for practical applications, since they are sensitive to small damages and are able to realize large area monitoring. Among these methods, the Reconstruction Algorithm for Probabilistic Inspection (RAPID), using a Piezoelectric transducer (PZT) sensor array, is one of the most widely used imaging algorithms to perform active damage monitoring and localization. However, since the sensing paths are distributed inside the sensor array with the non-uniform density, the RAPID algorithm can only localize damage when it is occurring inside of the array. If the damage occurs outside of the array or both inside and outside of the array, that is, multi-type damage, the performance of RAPID algorithm would not be satisfactory. In this paper, a scattering coefficient-based RAPID algorithm with damage indexes separation and imaging fusion is proposed. The amplitude of damage scattered signal at the corresponding time of fight is adopted as the weight in the probability distribution function, and damage indexes are then classified into two categories in the RAPID algorithm for the inside and outside damage localization respectively. Finally, an experiment on the complex composite plate, with the center large hole and surrounding bolt holes, is carried out to verify this proposed method. Experimental results show that this method can realize multi-type damage localization with errors less than 40 mm.

Keywords

Guided waves RAPID multi-type damage localization damage indexes separation imaging fusion

Introduction

In the last decades, composite materials have been extensively used in the aerospace structures, wind turbine blades, car bodies and the like, due to their superior characteristics.^1–3 However, this usage has posed several new challenges when it comes to the reliability of the mechanical design. In fact, composite structures suffer from the internal damage caused by low-velocity impact during the manufacture and service. Therefore, damage monitoring and localization is a very important task of structural health monitoring (SHM) for composite structures, which can ensure the safety and reduce the maintenance cost.^4–6

Among SHM methods, the guided waves-based damage imaging method, usually using the PZT sensor array, has been considered as a potential technique, because of the long-distance propagation and high sensitivity to a large variety of defects.^7–10 In addition, the sensor array-based guided waves methods can synthesize signals of multiple paths to enhance the damage effect and improve the signal-noise-ratio of guided waves, which have a high precision of damage localization, such as reconstruction algorithm for probabilistic inspection (RAPID),¹¹ delay and sum,^12,13 time reversal,^14,15 phased array,^16,17 multiple signal classification,^18–20 and so on.

RAPID algorithm usually adopts a sensor array, such as a circular array or rectangular array, which forms a certain number of sensing paths. For each sensing path, a baseline is acquired in the absence of any damage, which is stored and later compared to the subsequently acquired data during the damage monitoring. Then damage indexes of all sensing paths are computed as a function of the healthy baseline and the currently acquired data. A probability distribution function is then defined to describe the damage probabilities for each of the pixels of interest in the structure. Finally, a damage imaging of the structure can be properly built through the combined effects of damage indexes and damage probabilities for each sensing path and each pixel. Because of the easy implementation and straightforward interpretation of the RAPID algorithm, it has been gradually introduced and studied in guided waves-based SHM methods. Hay et al.²¹ and Lee et al.²² adopted the correlation between baseline and damage signals as the damage index, and then studied the implementation of RAPID algorithm for guided waves-based damage imaging. Monaco et al.²³ and Zhao and Rose²⁴ researched the performances of RAPID algorithm with different sensor arrays, including the rectangular array and circular array, which realized damage localization and ice detection on the aircraft wing. Teng et al.²⁵ and Gonzalez-Jimenez et al.²⁶ also researched the probability distribution function in the traditional RAPID to improve the damage imaging accuracy. For the crack monitoring on aluminum plates and fiber breakage monitoring on composite plates, Liu et al.,²⁷ Hettler et al.,²⁸ Ma et al.,²⁹ and Hwang et al.³⁰ studied the nonlinear features of guided waves-based RAPID algorithm.

However, when the RAPID algorithm is applied for practical applications of complex structures, there still exist some challenges. Firstly, the probability distribution function in the traditional RAPID provides the maximum weight for the points on the direct sensing path.^31,32 As a result, when the damage is located directly on the path or near a path intersection, the damage localization accuracy becomes better. However, when the damage is not on the path, the localization accuracy would decrease. And, once the damage is outside of the sensor array, the imaging result of RAPID algorithm would still be inside of the sensor array, which limits the monitoring area to the size of sensor array. Secondly, when multi-damage occurs both inside and outside of the sensor array, the inside damage must be close to some direct sensing paths and the outside damage is often far from the direct sensing path, resulting in the high scattered signal amplitude from inside damage and the relatively low scattered signal amplitude from outside damage.³³ In this case, the damage indexes corresponding to the inside damage are much larger than those of the outside damage. Then, the imaging maxima will tend to be drawn toward the inside damage, and the outside damage would be ignored.

To deal with these problems, a scattering coefficient-based RAPID algorithm with damage indexes separation and imaging fusion is proposed for multi-type damage localization in this paper. For each sensing path and each imaging pixel, this method adopts the amplitude of damage scattered signal at the corresponding time of fight as the weight in the probability distribution function, which could localize not only the inside damage but also the outside damage. In addition, the RAPID algorithm is improved with damage indexes separation and imaging fusion. The damage indexes are classified into two categories for each sensing path, according to whether the damage is near this direct sensing path or on its scattered sensing path. Then two imaging results based on two categories of damage indexes using the RAPID algorithm are fused, which could realize multi-type damage localization for both the inside and outside damage. Finally, an experiment of multi-damage localization on a carbon fiber panel with the center large hole and surrounding bolt holes is carried out to verify the proposed method. Experimental results show that this method successfully localizes multi-type damage with a high accuracy.

This paper is organized as follows: Section “Scattering coefficient based RAPID with damage indexes separation and imaging fusion” introduces the basic principle of scattering coefficient-based RAPID algorithm with damage indexes separation and imaging fusion for multi-type damage localization. In section “Experimental verification on complex composite structures,” damage localization experiments are performed on a complex composite structure. The multi-type damage localization results using the improved RAPID algorithm are depicted and compared with those of original RAPID algorithm. Finally, section “Conclusions” sums up the conclusions.

Scattering coefficient-based RAPID with damage indexes separation and imaging fusion

This paper proposes a scattering coefficient-based RAPID algorithm with damage indexes separation and imaging fusion for multi-type damage localization. The algorithm diagram is shown in Figure 1, and the specific process is introduced later in this section.

Theoretical description

Generally, to realize damage monitoring based on guided waves, a PZT sensor is actuated to generate the guided waves on the structure and another is used to receive, that is, the pitch-catch procedure. When guided waves are propagated on a structure surface, the damage in structures causes exclusive wave scattering. Thus, the structural health can be assessed through a proper statistical comparison of received guided waves of the healthy state with those of the current state, such as the damage index. Since the Pearson coefficient-based damage index is believed to provide the most satisfactory imaging results when dealing with guided waves-based SHM, it is selected as damage index to be implemented in the RAPID algorithm in this paper.³⁴ The corresponding damage index formulation is expressed in Equation (1).

DI = 1 - \frac{\sum_{i = 1}^{n} (S_{H, i} - \bar{S_{H}}) (S_{D, i} - \bar{S_{D}})}{\sqrt{\sum_{i = 1}^{n} {(S_{H, i} - \bar{S_{H}})}^{2}} \sqrt{\sum_{i = 1}^{n} {(S_{D, i} - \bar{S_{D}})}^{2}}}

(1)

Where S _H and S _D represent the guided waves corresponding to healthy state and damage state, respectively, and n is sampling length. Thus, the damage probability around this pitch-catch sensing path can be quantitatively estimated by the DI with a non-negative weight distribution function. The weight function is often measured by the positional relationship between the position (x, y) and the direct sensing path, which ranges from 0 to 1. Usually, the position (x, y) is closer to the direction path, the corresponding weight gets larger, as shown in Figure 2.

Moreover, to monitor the whole structure and improve the resolution, a sensor array is often needed, including a certain number of pitch-catch sensing paths. Through summing the damage probabilities of all pitch-catch sensing paths, the probabilistic inspection of damage can be reconstructed, expressed as Equation (2).

P (x, y) = \sum_{i = 1}^{N} P_{i} (x, y) = \sum_{i = 1}^{N} D I_{i} \cdot W_{i} (x, y)

(2)

where P _i(x, y) is the probability component derived from the ith sensing path at (x, y). DI_i denotes the DI value of the ith sensing path, and W_i is the corresponding weight.

Scattering coefficient-based probability distribution function

The probability distribution function in the traditional RAPID provides the maximum weight for the points on the direct path. As a result, when the damage is located directly on the path or near a path intersection, the damage localization accuracy becomes better. However, when the damage is not on the path, the localization accuracy would decrease. And, once the damage is outside of the sensor array, the damage cannot even be identified. To improve the localization accuracy of RAPID algorithm for the damage both inside and outside of the sensor array, a scattering coefficient-based weight function is proposed. In this method, the weight of each position is mainly decided by the amplitude of the scattered signal at the corresponding time of flight (TOF).

Firstly, the damage scattered signal of each sensing path is extracted, that is, the residual signals between acquired signals of the healthy state and those of the damage state. Since the complex Shannon wavelet is a function of the sinc function, and has excellent frequency localization ability due to its relatively small time decay property, which is considered to be an ideal passband filter to be used to extract the signal with a narrow bandwidth and obtain the signal envelope. Then, the envelope of damage scattered signal is used through the Shannon Wavelet Transform in this paper.³⁵

S_{i} (t) = abs (WT ({S_{H,}}_{i} (t) - {S_{D,}}_{i} (t)))

(3)

Assuming the damage is located at (x, y), the distance of damage scattered path can be expressed as

R_{i} (x, y) = \sqrt{{(x - x_{ai})}^{2} + {(y - y_{ai})}^{2}} + \sqrt{{(x - x_{si})}^{2} + {(y - y_{si})}^{2}}

(4)

where (x_ai, y_ai) and (x_si, y_si) are actuator and receiver coordinates of the ith sensing path. The corresponding TOF can be calculated as

t_{i} (x, y) = \frac{R_{i} (x, y)}{v}

(5)

where v is the propagation velocity of guided waves.

Then, the weight is decided as the amplitude of scattered signal at the corresponding TOF.

W_{i} (x, y) = S_{i} (t_{0} + t_{i} (x, y))

(6)

Here, t₀ is the time of excitation.

Improved RAPID algorithm for multi-type damage imaging

With the scattering coefficient-based weight function, damage can be accurately localized, even when damage is outside of the sensor array. However, when the damage happens both inside and outside of the sensor array at the same time, the inside damage must be close to some direct sensing path and the outside damage is often far from the direct sensing path, resulting in the high scattered signal amplitude from inside damage and the relatively low scattered signal amplitude from outside damage. In this case, the imaging maxima will tend to be drawn toward the inside damage, and the outside damage would be ignored. For this, an imaging fusion method using the damage index from direction sensing paths and scattered sensing paths respectively is proposed.

Firstly, the arrival time of the baseline and damage scattered signal are calculated, expressed as the Equations (7) and (8).

t_{i}^{H} = \arg max ({S_{H,}}_{i}^{'} (t))

(7)

t_{i}^{R} = \arg max (S_{i} (t))

(8)

where ${S_{H,}}_{i}^{'} (t) = abs (WT ({S_{H,}}_{i} (t)))$ . It can be judged that the damage is close to the ith direct sensing path or on its scattered sensing path through comparing $t_{i}^{H}$ with $t_{i}^{R}$ , as shown in Figure 3.

The damage index is then divided into two categories, that is,

\begin{matrix} DI 1_{i} = {\begin{matrix} 0 & abs (t_{i}^{R} - t_{i}^{H}) > Δ t_{ex} \\ D I_{i} & abs (t_{i}^{R} - t_{i}^{H}) \leq Δ t_{ex} \end{matrix} \end{matrix}

(9)

\begin{matrix} DI 2_{i} = {\begin{matrix} D I_{i} & abs (t_{i}^{R} - t_{i}^{H}) > Δ t_{ex} \\ 0 & abs (t_{i}^{R} - t_{i}^{H}) \leq Δ t_{ex} \end{matrix} \end{matrix}

(10)

where $Δ t_{ex}$ is the duration of excitation signal. If $abs (t_{i}^{R} - t_{i}^{H}) > Δ t_{ex}$ , the damage is considered to be on the scattered sensing path. Otherwise, the damage is close to the direct sensing path. According to Equation (9) and (10), DI1 denotes the case that the damage happens on the scattered sensing paths for every pitch-catch pair, that is, the outside damage. On another hand, DI2 denotes the case of inside damage.

Then, two imaging results can be obtained using DI1 and DI2 for the outside damage and inside damage, respectively, expressed as Equations (11) and (12).

P_{1} (x, y) = \sum_{i = 1}^{N} DI 1_{i} \cdot W_{i} (x, y)

(11)

P_{2} (x, y) = \sum_{i = 1}^{N} DI 2_{i} \cdot W_{i} (x, y)

(12)

Thus, multi-type damage can be localized through imaging fusion, expressed as Equation (13).

P = Normalized (P_{1}) + Normalized (P_{2})

(13)

where Normalized() denotes the normalization operation. Above all, the fused imaging result can realize multi-type damage localization.

Experimental verification on complex composite structures

To verify the effectiveness of scattering coefficient-based RAPID algorithm with damage indexes separation and imaging fusion, a multi-type damage localization experiment on the complex composite structure is carried out.

Experimental setup

Experimental setup includes an arbitrary waveform generator and data acquisition device (NI-USB6366), a multi-channel switch system, a computer and a complex composite plate with the center large hole and surrounding screw holes, as shown in Figure 4(a). NI-USB6366 is utilized to generate excitation signal and acquire signals output from PZT sensors. The multi-channel switch system is used to enhance the excitation signal and acquire guided waves of different pitch-catch pairs.³⁶ In the experiments, five cycle modified sine wave is used as the excitation signal with the amplitude of ±50V. Its central frequency is set to be 50 kHz to generate A0 mode dominated guided waves. In this case, the propagation velocity of guided waves is measured to be 1246.6 m/s, through obtaining the peak locations between excitation wave and arrival wave and then dividing the distance between sensors by the time difference of two peak locations.³⁷ The sampling rate is set to be 2MSPS and the sampling length is 2000.

The size of this composite plate is 500 mm × 500 mm × 2 mm, made of carbon fibers. The panel has 12 stacked layers and the thickness of each layer is 0.125 mm. The ply sequence is [45/0/−45/90/45/0] s. In addition, there is a large hole of Ø160 mm at the center and eight screw holes of Ø16 mm around. As shown in Figure 4(b), a circle sensor array is bonded with the diameter of Ø300 mm, which has 24 PZT elements, named from PZT 1 to PZT 24. In this experiment, PZT-5A piezoelectric elements are utilized, whose diameter and thickness are 8 mm and 0.48 mm, respectively. During the experiment, every PZT element is alternately used as an actuator to generate guided waves, and all other PZT elements receive guided waves. Thus, there are totally 276 pitch-catch pairs, shown as Table 1.

Table 1.

Pitch-catch pairs during the experiment.

Sensing path no.	Pitch-catch pair	Sensing path no.	Pitch-catch pair
1–23	PZT1-PZT2–24	211–221	PZT13-PZT14–24
24–45	PZT2-PZT3–24	222–231	PZT14-PZT15–24
46–66	PZT3-PZT4–24	232–240	PZT15-PZT16–24
67–86	PZT4-PZT5–24	241–248	PZT16-PZT17–24
87–105	PZT5-PZT6–24	249–255	PZT17-PZT18–24
106–123	PZT6-PZT7–24	256–261	PZT18-PZT19–24
124–140	PZT7-PZT8–24	262–266	PZT19-PZT20–24
141–156	PZT8-PZT9–24	267–270	PZT20-PZT21–24
157–171	PZT9-PZT10–24	271–273	PZT21-PZT22–24
172–185	PZT10-PZT11–24	274–275	PZT22-PZT23–24
186–198	PZT11-PZT12–24	276	PZT23-PZT24
199–210	PZT12-PZT13–24

To verify the effectiveness of proposed method, seven groups of damage are simulated on the composite structure. Among them, three damage sites are respectively manufactured at different positions inside of the sensor array in the first three groups. In this experiment, the wave-absorbing material with the size of 10 mm × 10 mm is bonded on the composite plate to simulate inside damage. Its stiffness is much smaller than that of the composite plate, so it could change the local stiffness of the structure. And the resulting stiffness discontinuity could cause guided waves scattering. In Groups 4 and 5, two damage sites of bolt loose are respectively manufactured outside of the sensor array. The coordinates of first five damage groups are denoted in Figure 5(a). In Groups 6 and 7, multiple damage sites are manufactured at the same time, including both the inside and outside damage, as shown in Figure 5(b) and (c).

Typical damage scattered signal

For the damage inside of the sensor array, 276 pitch-catch sensing paths can be classified into three categories. One category of sensing paths is that the damage is on or close to the direct sensing path. For example, the damage of Group 1 is close to the direct sensing path corresponding to PZT4-PZT22, as shown in Figure 6(a). In this case, the damage scattered wave is respectively obvious and its amplitude reaches up to 0.38V. Another category of paths is that the damage is on their scattered path, such as the pitch-catch pair of PZT2-PZT6, as shown in Figure 6(b). In this case, the amplitude of damage scattered wave decreases to about 0.03V. The last category of paths is that the damage is far from the sensing path, such as the pitch-catch pair of PZT10-PZT16, as shown in Figure 6(c). The monitoring signal is nearly the same with the baseline, and the residual signal between them is the background noise, whose amplitude is only 0.02V.

Above all, it can be obtained that the amplitude of damage scattered signal is much higher when the damage is on or close to the direct sensing path. The calculated damage indexes are also much higher, as shown in Figure 7. The maximum damage index reaches up to about 0.09, corresponding to the sensing path of PZT5-PZT22.

For the damage outside of the sensor array, since the bolt loose positions are not close to any direct sensing path, all paths are classified into the latter two categories. For example, the damage scattered signals of Group 4 are shown as Figure 8, including the sensing paths of PZT18-PZT22 and PZT7-PZT10. In Figure 8(a), the damage scattered wave can be extracted obviously and its amplitude reaches up to 0.15V. For PZT7-PZT10, as shown in Figure 8(b), the corresponding residual signal has also the background noise, which do not carry any damage information.

Then the damage indexes of Group 4 are plotted as Figure 9. Unlike those of the inside damage, the damage indexes become much smaller. The maximum damage index is only 0.03, corresponding to the sensing path of PZT18-PZT24.

When both the inside and outside damage happens, the damage scattered waves would be overlapped to varying degrees for different sensing paths. Figure 10 gives the acquired signals of PZT18-PZT22 and PZT4-PZT8 in Group 6, respectively. Among them, the inside damage is on the direct path of PZT18-PZT22 and the outside damage is on the scattered path of PZT4-PZT8. It can be obtained that the amplitude of scattered wave from inside damage reaches up to 0.7V, which is much larger than that from outside damage.

Correspondingly, the damage index of PZT16-PZT22 is very high, comparing with that of PZT4-PZT8, as shown in Figure 11(a). If these damage indexes are directly used in the RAPID algorithm, the imaging value of outside damage should be covered by the inside damage. As a result, the inside damage can be imaged and the outside damage cannot be identified. Through Equations (9) and (10), the damage indexes can be separated for inside damage and outside damage, as shown in Figure 11(b) and (c). Thus, the multi-type damage imaging can be realized using the separated damage indexes in the RAPID algorithm.

Damage imaging results

In this section, the signals of seven groups in section “Typical damage scattered signal” are used to realize damage imaging, and the corresponding localization results are compared with those of the original RAPID algorithm.

During the RAPID algorithm, the real scanning is discretized to have square pixels with dimensions 1 × 1 mm². The final dimensions of the imaging matrix are 500 pixels × 500 pixels. Figure 12 gives the imaging results of first three groups, that is, the single inside damage. For this type of damage, the imaging results using the original RAPID and improved RAPID algorithm respectively are nearly the same. According to the maximum value of imaging matrix, the localization results of original RAPID are (92 mm, 6 mm), (−29 mm, 117 mm) and (−82 mm, −107 mm) respectively, and those of the proposed method are (87 mm, −5 mm), (−14 mm, 108 mm) and (−82 mm, −105 mm) respectively. The localization errors of improved RAPID algorithm are 5.8 mm, 2.2 mm, and 5.8 mm, respectively.

Figure 13 gives the imaging results of Groups 4 and 5, that is, the single outside damage. In this case, the original RAPID algorithm is unable to localize damage accurately. The imaging results only provide the vague directions for outside damage of bolt loose. On another hand, through using the scattering coefficient-based RAPID algorithm, the outside damage could be localized with a high accuracy. In the same way, the localization results of Groups 4 and 5 can be obtained, (69 mm, −168 mm) and (−74 mm, 170 mm) respectively, according to the maximum value of imaging matrix. The corresponding localization errors are 18.8 mm and 15.3 mm, respectively.

Figure 14 gives the imaging results of Groups 6 and 7, that is, the multi-type damage, including both the inside damage and outside damage. From the left figures, it can be obtained that the original RAPID algorithm can only identify the single inside damage. This is because the damage index caused by inside damage is much larger than that of outside damage, which is covered during the damage imaging result. From the right figures, it can be obtained that the improved RAPID algorithm proposed in this paper could localize multi-type damage at the same time. In Group 6, the multi-type damage localization results are (−20 mm, −125 mm) and (58 mm, 208 mm), corresponding to the localization errors of 22.4mm and 29.8mm respectively. In Group 7, the multi-type damage localization results are (−15 mm, −117 mm) and (111 mm, −204 mm), corresponding to the localization errors of 15.1 mm and 38.9 mm, respectively.

Above all, Table 2 provides a detailed comparison of localization results between the original RAPID and improved RAPID algorithm. Particularly, some localization errors of improved RAPID algorithm are larger than those of the original RAPID algorithm in Groups 6 and 7. This is because the number of damage indexes for the inside damage reduce after separation. For example, the number of damage indexes for inside damage in Group 6 reduces from 276 to 83. In this case, the localization precision would be influenced. The improved RAPID algorithm can realize multi-type damage localization and the localization errors are less than 40mm.

Table 2.

Localization results of improved RAPID algorithm (unit: mm).

Damage type		Positions	Original RAPID		Improved RAPID
			Localization results	Error	Localization results	Error
Group 1	Inside simulated damage	(90, 0)	(92, 6)	6.3	(87, −5)	5.8
Group 2	Inside simulated damage	(−15, 110)	(−29,117)	15.7	(−14, 108)	2.2
Group 3	Inside simulated damage	(−85, −110)	(−82, −107)	4.2	(−82, −105)	5.8
Group 4	Outside bolt loose	(77, −185)	/	/	(69, −168)	18.8
Group 5	Outside bolt loose	(−77, 185)	/	/	(−74, 170)	15.3
Group 6	Inside simulated damage	(0, −115)	(−22, −114)	22.0	(−20, −125)	22.4
Group 6	Outside bolt loose	(77, 185)	/	/	(58, 208)	29.8
Group 7	Inside simulated damage	(0, −115)	(−2, −110)	5.8	(−15, −117)	15.1
Group 7	Outside bolt loose	(77, −185)	/	/	(111, −204)	38.9

Conclusions

In this paper, a scattering coefficient-based RAPID algorithm with damage indexes separation and imaging fusion is proposed, which realizes multi-type damage localization through using a scattering coefficient-based probability distribution function and a process of damage index separation and imaging fusion. Localization results of seven groups of multi-type damage on the complex composite structure show the effectiveness of the proposed method.

However, suffering from the dispersion of guided waves, resulting in the overlap of damage scattered waves and scattered waves from structural boundary, there still exist localization errors of the improved RAPID algorithm. Moreover, the current damage imaging method could only realize damage localization, whereas it is unable to estimate the damage shape. Further research is still worthy to address the dispersion compensation of guided waves and damage shape estimation for the RAPID algorithm.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by National Natural Science Foundation of China (Grant No. 52105152) and China Postdoctoral Science Foundation (Grant No. 2020M681680).

ORCID iDs

Qiao Bao

Kai Tao

Qiang Wang

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