Fault Identification, Diagnosis, and Prognostics Based on Complex Signal Analysis
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Guannan Wu, Chao Xu, Fei Du, Weidong Zhu, "A Modified Time Reversal Method for Guided Wave Detection of Bolt Loosening in Simulated Thermal Protection System Panels", Complexity, vol. 2018, Article ID 8210817, 12 pages, 2018. https://doi.org/10.1155/2018/8210817
A Modified Time Reversal Method for Guided Wave Detection of Bolt Loosening in Simulated Thermal Protection System Panels
Abstract
In this work, a modified time reversal method is proposed for guided wave detection and localizing loosened bolt in a complicated multiboltjointed structure. Different from the traditional time reversal guided wave method, the response signal due to a tone burst input received at the healthy state is time reversed and recorded as a standard reemitting signal. In the detection process, this recorded standard signal is used for all damage cases to yield time reversalfocalized reconstruction signals. This largely improves the sensitivity of the focalized signal to damage state. In this paper, the peak amplitude of the focalized wave packet in the reconstructed signal is calculated and utilized as tightness index. By bonding PZT transducers at different joint locations inside the structure, multiple tightness indices, where each tightness index presents the correlation between the current joint condition to its healthy condition at the joint, can be obtained. To analyze a large number of tightness indices, a principle component analysis method is introduced, and a neural networkbased loosening detection method is proposed. The proposed method is experimentally validated in a simulated doublelayer boltjointed thermal protection system panel. Experimental results illustrate that the proposed method is effective to identify and localized the bolt loosening in complicated multiboltjointed structure. The detection and identification of the location of multibolt loosening is realized.
1. Introduction
In aerospace engineering, a thermal protection system (TPS) is necessary for protecting an aerospace vehicle from harsh heating due to high reentry temperatures. It plays a critical role in keeping structural integrity and safety. A typical TPS design is a multilayer configuration, where a cover panel made of hightemperature material, such as carboncarbon composite, is attached to the main airframe panel of the aerospace vehicle through mechanically bolted joints. The extreme thermal, vibration, and shock excitations during the flight may cause the pretightened bolts to loosen, which further cause detachment gap in a TPS. Then, hot air can penetrate through the gap and cause catastrophic results. Therefore, the detection of loosening in bolted joints plays an underlying role to ensure a TPS functionality, integrity, and reusability.
Structural health monitoring (SHM) is referred as the process of implementing a damage detection and characterization strategy for structures [1]. In the past decade, a number of SHM approaches have been developed to detect bolt loosening in TPS structures. At the early stage, the SHM methods based on experimental modal analysis were proposed to realize the objective. For example, Vandawaker et al. [2] proposed to detect damage in a TPS tile by comparing mode shapes and frequencies from healthy and damaged structures. However, since highfrequency vibration modes are difficult to obtain in practice, the modal analysisbased methods mainly rely on the lowfrequency vibration modes, which only represent the properties of the whole structure. Like Todd et al. [3] pointed out an assembled structure which consists of many bolts and one or less number of loosened bolts cannot cause the whole structural properties to change significantly. Consequently, the modal analysisbased methods are relatively insensitive to detect local bolt loosening for a complicated jointed structure.
To detect local and small structural damage, a number of local SHM methods have been developed. Among them, electromechanical impedancebased and guided wavebased methods are very popular [4, 5]. Basically, the electromechanical impedancebased method monitors variations in mechanical impedance due to damage, which is coupled with electrical impedance of a piezoelectric transducer (PZT) [6, 7]. A lowcost miniaturized impedance measurement device was developed by Peairs and Inman [8] for detection of bolt loosening. A system that includes PZTs and a wireless impedance device for data acquisition and communication was built by Mascarenas et al. [9] to detect bolt preload loss. Recently, an electromechanical impedance method for health monitoring of aircraftbolted joints was presented by Kuznetsov et al. [10]. While the previous studies have shown the feasibility of using impedancebased approaches for detection of bolt loosening, the effective detection area of a transducer is very small and a large number of transducers are required for detecting a structure with thousands of bolts.
Guided wavebased SHM techniques have been intensively developed over the last two decades. They are very attractive and commonly utilized due to their ability to inspect a large structure over long distance with a small number of transducers. In recent years, several guided wavebased SHM methods have been proposed for bolt loosening detection. Yang and Chang [11] developed a guided wavebased method to identify bolt loosening in a TPS panel. In their study, a piezoelectric (PZT) embedded smart washer was developed to generate and acquire ultrasonic wave signals. The features of wave energy dissipation (WED) and specific damping capacity were extracted. However, a large number of smart washers are required in applying the detection method to a TPS with hundreds of bolts, because each bolt should be installed with a smart washer. Similar wave energy dissipationbased methods were studied by Montoya and Maji [12] and Wang et al. [13]. It is known that the nonlinear contact mechanics on the joint interface can cause nonlinear transmission of guided waves. The SHM method based on nonlinear ultrasonic wave phenomenon was proposed by Doyle et al. [14] to localize loosened bolts in a satellite panel. In their work, the acoustoelastic behavior due to the joint was used as an indicator of structural integrity. Furthermore, the feature of contact acoustic nonlinearity in bolted joints was utilized for preload monitoring [15–20]. Amerini and Meo [15] studied both linear and nonlinear ultrasonic methods and proposed several tightening state indices, including the firstorder acoustic moment, highharmonic generation, and sideband modulation indices. Bao et al. [16] established a nonlinear contact element model to simulate the strip lap joint specimen. On this basis, the highharmonic generationbased index was studied by Shen et al. [17]. After that, Zhang et al. [18] proposed to use subharmonic resonance to detect bolt looseness, and Zhou et al. [19] utilized nonlinearmodulation method to detect bolt looseness in frame structure. Zhang et al. [20] carried out a comparative study of the WEDbased method and the vibroacoustic modulationbased method and found that the sensitivity of WEDbased methods is closely related to the wave energy transmitted across joints.
In recent years, new guided wave detection methods based on the time reversal principle in modern acoustics have been developed and the effectiveness was demonstrated. Fundamentally, the time reversal concept lies in reconstruction of an input signal at an excitation point, while a response signal measured at another point is reemitted to the original excitation point after being reversed in time domain, taking into account that there is no damage in the wave path. As a result, changes between the reconstructed signal and the input signal can be inferred as presence of damage in the wave path. Wang et al. [21] carried out an experimental work to study the applicability of the time reversal concept to guided waves in plates. Then, Park et al. [22] utilized the time reversal technique to improve the detect ability of local defects in composite plate. A detailed theoretical investigation on the effect of multimodel and reflections on time reversal progress was given in [23]. It was pointed out that narrowband input signal can enhance time reversal progress. In recent years, the technique of time reversal guided wave SHM has been applied to a variety of structures, such as metallic plates [24], composite plates [25], and rebarreinforced concrete beams [26]. Mustapha and Ye proposed a very effective and innovative time reversalbased imaging algorithm to detect debonding in sandwich composite plates [27] and then extended it to detect multiple debonding in complex tapered composite sandwich panels [28]. However, the time reversal guided wave method has not been widely used for detection of bolt loosening, except the works done by Tao et al. [29] and Parvasi et al. [30], where only very simple single bolt lapjointed structures were considered. In their work, the aim is to identify the preload loss in single bolt. The problem of detection of loosening in a multiboltjointed structure was not considered.
In this paper, a modified time reversal (MTR) guided wave method is proposed to detect bolt loosening in TPS panels. The conventional time reversal process is modified, and a new implemented process is proposed to localize loosening bolts in a complicated multiboltjointed structure. In the proposed method, a standard remitted signal which recorded for a nominal healthy structure is used for all damage cases. The peak amplitude of the refocused wave packet obtained by the MTR method is normalized and utilized as the tightness index. By bonding PZT sensors at different joint locations inside the structure, multiple tightness indices can be obtained, where each tightness index presents the correlation between the current joint condition to its healthy condition at the joint. To analyze a large number of tightness indices, a principle component analysis method is introduced, and a neural networkbased loosening detection method is proposed. The feasibility and effectiveness of the proposed method to identify and localize bolt loosening is experimentally investigated in a simulated TPS structure.
2. Theory Background
2.1. The Conventional Time Reversal Guided Wave Method
Figure 1 shows the work principle of the conventional time reversal guided wave method in a simple lap joint. First, a tone burst input is applied to transducer A, which acts as an actuator and activates wave propagation in the structure. A wave response signal is captured by the transducer B. The response signal at the transducer B can be defined as where is the impulse response function (IRF) of the structure between points A and B; denotes the convolution. After that, the recorded response signal is reversed in time domain before reemitted at transducer B. Thus, the reemitted signal is
After the signal is reversed in time domain, the wave packets that arrive at transducer B early will be reemitted late, and the wave packets that arrive at transducer B late will be reemitted early. Therefore, wave packets in the timereversed signal arrive at transducer A at the same time and overlap to a focalized wave packet. Note that, in practical applications, the reversed signal is amplified before feeding it into PZT B. The reconstructed signal received at the transducer A can be written as where is a autocorrelation function and also called the time reversal operator. gets its maximum value at time point and is equal to the energy of IRF of the structure between points A and B. It is noted that the energy of IRF is decided by the wave energy transmits through the joint interface. Bolt loosening causes the decrease of contact area and consequently transmitting wave energy and the IRF energy decreases. Thus, the peak amplitude of reconstructed signal is proportional to the IRF energy, and the peak amplitude of can be extracted as a tightness index (TI) to detect bolt loosening.
This principle is used by Tao et al. [29] and Parvasi et al. [30] for detecting preload loss in a single bolted lap joint. However, the results show that a saturation phenomenon of the TI happens when the preload reaches to a critical value [29, 30]. The reason is that the feature of peak amplitude is related to the IRF and the wave energy transmitted across joint, which are determined by the contact area. When the preload is high, the contact area changes very little due to the change of preload. Thus, in this situation, the IRF nearly holds constant. This causes the conventional time reversal guided method which has a low sensitivity at the early stage of loosening.
2.2. The Modified Time Reversal Guided Wave Method
The basic idea of the MTR method is to introduce a “standard” reemitted signal (SRS) for all damage cases, where damage is referred to bolt loosening in this work. As shown in Figure 2, the timereversed reemitted signal (the symbol ③ signal in Figure 1) recorded at the nominal healthy structure is chosen as the “standard” reemitted signal for all damage cases. When the SRS is reemitted back to the structure, damage affects the reconstructed signal in extensive patterns comparing to the conventional time reversal method. Thus, additional damage information that can be extracted to reveal the extent of damage is contained in the reconstructed signal. The detailed explanation of the proposed modified method is presented below.
Fundamentally, when a SRS is reemitted back to the structure, if the bolt in the wave path is not loosened, which means the structure can be regarded as the same as the nominal healthy structure, the MTR is therefore equal to the TR method. The velocities for every wave packet in the SRS keep the same and a focalized wave packet can be obtained by the backward travelling of SRS, due to the inphase overlapping of wave packets in the SRS. However, if the bolt in the wave path is loosened, the wave velocity for each wave packet may also be changed. According to Zagrai et al. [31], the main reason of the change of wave velocity is due to acoustoelastic effect. With the change of bolt preload, the static stress level changes and the wave speed of the transmitted guided wave signals changes. Therefore, the inphase overlapping of wave packets in the SRS cannot be realized to a focalized wave packet. This indicates that in the MTR method, not only the transmitted wave energy is related to the peak amplitude of the reconstructed signal, but also the impaired focalizing ability of SRS can cause the decrease of the peak amplitude.
If the IRF of the healthy structure between a actuator and a sensor is , therefore, as the same as (1), the “standard” reemitted signal can be written as
This signal is recorded and used for all damage cases. If there exists damage in the wave path, it is obvious the IRF changes. It is assumed that the IRF of the damaged structure is , and then the reconstructed signal due to the SRS can be obtained, defined as where is a crosscorrelation function of and and represents the degree of the correlation of and . gets its maximum value at the time instant . Comparing (5) to (3), it can be seen that the MTR method actually modifies the time reversal operator. In the conventional time reversal method, the autocorrelation function of the IRF is used, while in the modified time reversal method, by introducing a reference IRF, the crosscorrelation function is used as the time reversal operator. Meanwhile, it can be found that in (5), similar to (3), the peak amplitude of the focalized wave packet is proportional to the maximum value of . Therefore, the principle of the proposed method is to change the time reversal operator from the autocorrelation function of structural states to the crosscorrelation function of structural states.
It should be noted that in the conventional time reversal method, for any signal path, both transducers need to work as actuators and sensors. This often means a large number of hardware, such as PZT amplifier and wiring are required. In [25], a simplified time reversal method is proposed, which can largely reduce the hardware requirement by using only one transducer A to actuate signals and another transducer B to act as a sensor for a signal path. The underlying reason is that the impulse response function (IRF) of the structure from point A to B is assumed the same as that from point B to A. In this paper, the same simplified technique is used to reduce hardware requirement and experimental cost.
2.3. Loosening Localization Method for Multibolt Structures
It is noted that the aboveproposed principle uses a single bolt loosening detection problem as an example. However, the proposed method can be easily extended to a multibolt structure. In this paper, the aim is to detect the loosening location for a multibolt TPS structure. To this end, each joint with attached bolts is considered as a possible loosening location. At each possible loosening location, a PZT sensor is bonded to act as a wave signal receiver. In addition, a PZT transducer boned at the central location of bottom panel is used to generate wave signal to sensors. The detailed sensor configuration is given in the next section.
In this paper, the peak amplitude of the reconstructed focalized wave packet is extracted as a TI for detection of bolt loosening in a multiboltjointed TPS structure. The TI can be written as where is the peak amplitude of reconstructed signal received by sensor at the current structure, and is the peak amplitude received by sensor at the healthy structure. By installing PZT sensors around every possible loosening bolts, predictive variables s can be defined. Each represents the correlation coefficient of a structural state of a joint to its healthy state. For instance, bolt loosening happening at joint 1 changes the IRF of actuator to sensor 1 significantly; according to (5) and (6), the corresponding is therefore significantly decreased. On the other hand, the loosening at joint 1 has less effect to the IRF of actuator to sensor 2 which is far from joint 1. Hence, the corresponding to sensor 2 shows a smaller change than when loosening occurs at joint 1. Depending on this feature, the bolt loosening in the structure can be detected by using predictive variables s.
To implement the proposed MTR method, each bolt joint location needs one sensor to form a signal path. Hence, in real application, a great number of transducers may be needed, and a lot of variables need to be processed, correspondingly. However, too many predictive variables cause the difficulty in the visual description of detection results. Therefore, it is important to keep the independence of each predictive variable for the proposed method. In this paper, dimension reduction of predictive variables before the establishment of damage index database is performed. The principal component analysis (PCA) [32] is used for dimension reduction of . First, should be scandalized to mean equals to zero and the standard deviation equals to one. Assuming is a vector and is the number of data. D is the matrix composed by , where is the number of the predictive variable. Then, the normalized matrix X can be obtained by where index “−1” means calculating inverse, is the means of , and is a matrix of standard deviation, defined as where is the standard deviation of . Calculating the covariance matrix of X, and we can get the eigenvalues and eigenvectors of . Then, the number principal component can be obtained by
The number of principal component can be determined by the data variation ratio that the obtained can explain. Generally, 90% of data variation should be explained by the principal components, that is, where is the data variation explained by and .
Finally, the SKohonen neural network [33] is used in this work for clustering analysis of the known data and classifying of the unknown data. The SKohonen neural network is an extended Kohonen neural network (KNN) that contains an added output layer. As shown in Figure 3(a), a typical KNN contains an input layer and a competitive layer, the node number of input layer equals to the predictive variables, and the competitive layer is a 2D array that usually contains much more nodes than the target variables. Furthermore, the SKohonen network has an added output layer after the competitive layer to connect target variables directly to the clustering result. By performing the above steps, a loosening detection flow can be built, as shown in Figure 3(b).
3. Experimental Study
3.1. The Simulated TPS Structure
As shown in Figure 4, a simulated multiboltjointed TPS structure is considered for validating the proposed MTR method. A Q235 steel thin plate simulating the cover panel is attached to a Q235 steel thin base plate to simulate the airframe panel via four steel brackets. M6 bolts are used as fasteners. The dimension of the base plane is and the upper plane is . PZT patches are used to actuate and receive wave signals. One PZT actuator is bonded on the center of the base plate, and each bracket is bonded with one sensor. The PZT sensor location and the bolt numbers are shown in Figure 4.
(a)
(b)
Considering the allowable tensile load of M6 bolt and the yielding strength of Q235 steel, is selected as the standard bolt torque. For each bracket, totally, 6 bolt loosening cases are taken into account as shown in Table 1. During the experiments, each bolt loosening case is repeated four times to get reliable results. In this work, the bolt loosening means a totally loose condition. In each bolt loosening detection experiment, the TPS panel specimen is assembled to the normal tightening condition firstly, and then it is adjusted to a bolt loosening case by loosening corresponding bolts. A standard assembly sequence is regulated to guarantee experimentally repeatability. Each bolt is tightened to 70% standard torque firstly and then tightened to 100% in sequence to prevent unnecessary internal stress.

3.2. Experimental Setup
Figure 5 gives the experimental setup. The multifunction data acquisition (DAQ) system NI USB6366 is used to generate and receive guided wave signals. Before the input signal is sent to PZT actuator, a signal amplifier PINTEK HA400 is used to amplify the signal amplitude to 50 Vpp (peak to peak). A LabVIEW program is coded and runs on the computer to control the DAQ system. In addition, the structure is placed on a foam support.
A 5cycle tone burst is used as the original input of MTR process. The central frequency of the input is chosen as 150 kHz based on the group velocity dispersion plot of 3 mm steel plate, as shown in Figure 6. It can be seen that at 150 kHz, only the first symmetrical mode and antisymmetrical mode are generated, and the velocity dispersion of these modes is minimized. Response signals of the tone burst input at each sensor in the healthy structure are recorded. After reversed in time domain, they are saved as SRSs. The generated and recorded signals in the MTR method for the healthy state are shown in Figure 7. To reduce the effect of noise, each recorded signal is the average of 32 measurements. Moreover, a highpass filter is used to cut off the lowfrequency noise; the lowpass cutoff is set to 10 kHz. It can be clearly found that a focalized wave packet occurs in the reconstructed signal.
(a)
(b)
(c)
(d)
4. Results and Discussion
4.1. Validating the Modified Time Reversal Process
By implementing the proposed time reversal method, the reconstructed signals recorded at each bracket sensor for the healthy structure are given in Figure 8(a). It can be seen for the healthy state that each sensor received a clear reconstructed signal with a focalized wave packet. This result corresponds with the conventional time reversal guided wave method. However, it can be found that the peak amplitudes of the focalized wave packet for each sensor are slightly different. This is due to the structural assembly error and the deviation of bonding condition of PZT patches.
(a)
(b)
The reconstructed signals in Figure 8(b) were normalized by the corresponding reconstructed signals for the healthy structure. Then, the peak amplitudes of the reconstructed signals for the healthy structure were normalized to 1. Figure 8(b) shows the comparisons of normalized peak amplitudes for damaged and healthy structures at different PZT locations. It is found that a focalized wave packet still exists in the reconstructed signal for each sensor, but the peak amplitude of reconstructed wave packet at each sensor changes obviously. Since the loosening of bolt 2 in bracket 2 has changed the wave propagation behavior of the whole structure significantly, the peak amplitude of each PZT patch is affected by different extents. It can be seen in Figure 8(b) that the peak amplitude decreases the largest at the PZT patch bonded on bracket 2 compared to the other three results.
4.2. Predictive Variables
The predictive variables for each bracket at different bolt loosening cases are calculated and shown in Figure 9. First, it can be seen that in each bolt loosening case, each is less than 1, and the loosening bracket corresponding is smaller than the other . Therefore, based on , the bolt loosening location can be identified by directly comparing the values of predictive variable. Second, the robustness of the MTR method is examined by three repeating experiments at each bracket. It can be seen that at each bolt loosening case, the predictive variable at each bracket appears similar character, and from three repeating experiments, good repeatability of the measurement can be observed.
(a)
(b)
(c)
(d)
In addition, it can be seen that the mismatched of the loosening bracket is nearly unchanged at each case, but the corresponding changes with the change of case number. On the one hand, comparing the results of case 1/2/3, it can be found that the loosening of bolt 3 has the most significant influence to the corresponding . On the other hand, the change of becomes more distinct with the increase of the number of loosening bolt. Checking on Figure 4, it can be found that the bolt 1 is the farthest bolt to the PZT sensor, and bolt 2 is the nearest one. Since the actuator PZT patch is bonded on the base plate, the loosening of bolt 1 and bolt 3 has direct influence to the wave propagation path, comparing to bolt 2 which connects the bracket with the cover plate. Overall, considering these factors, the reason of why bolt 3 has the most significant influence to can be explained: (1) the loosening of bolt 1 and bolt 3 can directly affect the wave propagation path, and (2) bolt 3 is more closer to the PZT sensor than bolt 1.
4.3. Clustering Results
The PCA of is performed in this step. The correlation of is shown in Figure 10, and it can be seen that predictive variables and show the same correlation with each other. For instance, the values of and are high when the bolt loosening happens at bracket 3 and bracket 4, and when it happens at bracket 1 and bracket 2, and get a low value, respectively. The scatter diagram of and appears a curvilinear correlation with the loosening at different positions. Furthermore, it can be found that this relationship is kept in the correlation of other predictive variables. Since a same curvilinear correlation is found between any two , it indicates that the PCA method can be performed properly to extract principal components.
This study got 96 s from 4 repeating experiments of 6 bolt loosening cases at 4 brackets, respectively. The 72 data from the first 3 times repeating experiments were used to establish a database, and the last 24 data were utilized as test. The PCA for the 72 data was performed, and the covariance matrix was calculated. Then, the eigenvalues and eigenvectors of were calculated as , , , and . Based on (10), it can be found that when , the principal components can explain 89.47% of the data variation. A 3D scatter plot of principal components and is shown in Figure 11; it can be found that the data at the same loosened bracket is close to each other and the distance of data from different loosening brackets is large. This distribution of data guarantees the accuracy of the clustering analysis and the possibility for bolt loosening locating.
4.4. Tests of the Loosening Detection Database
Figure 12 shows the distribution of winning nodes at the competitive layer of the 72 s data in one running result of SKohonen neural network. Accordingly, the node number of input layer is 3, and the node number of competitive layer is 4 × 4 = 16. The learning rate is set to [0.01, 0.1], and the learning diameter is set to [0.4, 2]; number of cycles is 1000. In Figure 12, the symbol represents bolt loosening cases at bracket 1, the symbol ② represents bolt loosening cases at bracket 2, and the rest can be done in the same manner. The blank represents the node not belonging to any cluster. It can be seen that the winning nodes distribute as blocks; the effect of clustering analysis is good.
Based on (9), the last 24 s data can be transferred to s. The classifying results of SKohonen network is shown in Figure 13. The node number of the output layer is 4, and learning rate between the output layer and the competitive layer is [0.5, 1]. It can be seen that all of the 24 data have been classified correctly; the accuracy is 100%. Therefore, it can be concluded that the proposed MTR method can correctly recognize the bolt loosening location and the recognizing accuracy is extremely high.
5. Conclusion
The problem of detecting bolt loosening for a complicated multiboltjointed structure is investigated. To this end, a modified time reversal guided wave method is proposed in this paper. Different with the conventional time reversal guided wave method, the response signal due to a tone burst input received at the healthy structure is time reversed and saves as standard reemitting signal. The peak amplitude of the focalized wave packet in the reconstructed signal due to the SRS is extracted as tightness index. By bonding PZT sensors at different joint locations inside the structure, multiple tightness indices can be obtained, where each tightness index presents the correlation between the current joint condition to its healthy condition at the joint. To analyze a large number of tightness indices, a principle component analysis method is introduced, and a neural networkbased loosening detection method is proposed.
Experiments at a simulated TPS panel are conducted to verify the feasibility and effectiveness of the MTR method for bolt loosening identification. Different bolt loosening cases are considered, and repeating experiments have been done. Conclusions can be extracted from the analysis of experiment results. It is found that the proposed modified time reversal method can be used to identify and localize the bolt loosening in a simulated TPS panel. By analyzing principal componentss, the loosened bracket can be found out. Moreover, the change of becomes more distinct with the increase of the number of loosening bolt. This work can be extended to similar bolt loosening detection problems in variety multiboltjointed structures.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
The authors wish to acknowledge the financial support from the China NSAF Project (Grant no. U1530139), China Science Challenge Project (Grant no. TZ2018007), and National Natural Science Foundation of China (Grant no. 51705422).
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Copyright © 2018 Guannan Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.