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Monitoring of multi-bolt connection looseness using entropy-based active sensing and genetic algorithm-based least square support vector machine
Mechanical Systems and Signal Processing 136 (2020) 106507
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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Monitoring of multi-bolt connection looseness using entropybased active sensing and genetic algorithm-based least square support vector machine Furui Wang, Zheng Chen, Gangbing Song ⇑ Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA
a r t i c l e
i n f o
Article history: Received 15 May 2019 Received in revised form 15 August 2019 Accepted 6 November 2019
Keywords: Structural health monitoring Bolt looseness detection Piezoelectric transducer Multivariate multiscale fuzzy entropy Max-relevance and min redundancy Support vector machine
a b s t r a c t Looseness detection of bolted connections is an essential industrial issue that can reduce the maintenance and repair costs caused by joint failures; however, current loosening detection methods mainly focus on the single-bolt connection. Even though several methods, such as the vibration-based method and electro-mechanical impedance (EMI) method, have been employed to detect multi-bolt looseness, while they are easily affected by environmental issues. Therefore, the main contribution of this paper is to detect loosening of the multi-bolt connection through the PZT-enabled active sensing method, which has several merits including easy-to-implement, low cost, and good ability of anti-environment disturbance. Since the current indicator of the active sensing, namely the signal energy is insensitive to multiple damages, we developed a new damage index (DI) based on the multivariate multiscale fuzzy entropy (MMFE). Subsequently, the maximum relevance minimum redundancy (mRMR) was used to select significant features from the MMFEbased DI to construct the new datasets. After feeding the new datasets into the genetic algorithm-based least square support vector machine (GA-based LSSVM), we trained a classifier to detect loosening of the multi-bolt connection. Finally, repeated experiments were conducted to demonstrate the effectiveness of the proposed method, which can guide future investigations on bolt looseness detection. Published by Elsevier Ltd.
1. Introduction Across multiple industries such as aerospace engineering, mechanical engineering, and civil engineering, the bolted connection has been widely used to hold different components together, which induce severe structural nonlinearities [1,2], and their loosening and failures may lead to accidents if not detected in a timely manner. Moreover, detection of joint failures and maintenance of connection integrity are directly related to costs, particularly, under current strict requirements of safety and economy. For instance, over 20% of accidents in mechanical systems, which can induce great losses, are attributed to bolt looseness [3]. However, current methods, including human vision and percussion [4], are incompetent and costly, since the visible looseness is too late to ensure structural integrity and the percussion requires skilled personnel. Then, due to the rapid development of the image recognition technologies [5], several machine-vision methods [6,7] have been applied to detect bolt loosening, since they can mitigate the limitations such as boundary conditions, aging, sizes, and different working ⇑ Corresponding author. E-mail address: [email protected] (G. Song). https://doi.org/10.1016/j.ymssp.2019.106507 0888-3270/Published by Elsevier Ltd.
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cases. However, it is worth noting that the vision-based method focuses more on detection, rather than the monitoring. In other words, the vision-based method cannot grasp the real-time integrity of bolted connections during the entire working cycle. Moreover, visible rotation always means that bolts have lost most of their preloads, which may be too late for looseness detection in some cases. Therefore, in the past decades, remarkable progress has been developed to detect bolt loosening, particularly, based on various structural health monitoring (SHM) methods. The vibration-based method [8,9] and the electro-mechanical impedance (EMI) method [10,11], for instance, have demonstrated their effectiveness in bolt looseness detection. However, the vibration-based method is more suitable for global damage, rather than the bolt looseness that belongs to the local flaw, and the EMI method is affected by environmental conditions severely. Then, ultrasonic-based SHM methods [12,13] attract much attention, due to their high accuracy, convenient implementation, and excellent performance in avoiding environmental intrusions. Thus, some in situ bolt looseness monitoring methods based on the ultrasonic technology have been developed, including the linear ultrasound methods (e.g., the active sensing method [14–16]) and the nonlinear ultrasound methods including the subharmonic-based method [17], the higher-harmonics based method [18], and the modulated harmonics-based method [19,20]. Even though these methods perform well in bolt looseness identification; however, they all focus on single-bolt connection, whose applications are limited in real industries. Subsequently, to enhance the practical use of bolt looseness monitoring methods, several investigations on multi-bolt connections have been reported. For instance, by using the spectral element method to determine the electrical impedance changes of piezoceramic transducers under various conditions, the location and loosening extent of a multi-bolt joint could be quantitatively identified [21]. Park et al. [22] also verified the effectiveness of the EMI method in a pipeline structure, which is a typical multi-bolt connection. Moreover, employing the magneto-mechanical impedance as the indicator, Doyle et al. [23] estimated the integrity of a multi-bolt connection in a satellite structure. In Addition, the vibration-based method has also been investigated to detect bolt looseness [24–27]. Recently, with the rapid development of artificial intelligence techniques, their applications in SHM have been noticed, particularly, in bolt looseness monitoring. Based on EMI methods and neural network (NN)-based pattern analysis, Min et al. [28] detected the loose bolts in a bolted-joint beam. In their study, multiple frequency subranges from the EMI signals were extracted as the input to train the NN, and real damage types (i.e., bolted looseness) and severity were regarded as output. Similarly, Zhang et al. [29] identified the loosening of a multibolt plate based on the EMI method; however, the LibSVM, instead of the NN, was applied to locate the position of loose bolts. Liang et al. [30] applied a decision fusion system to develop a convenient vibration-based method for multi-bolt joint failures detection. However, the drawbacks of the vibration-based method and the EMI method have been mentioned earlier, and the application potential of ultrasound methods in detecting multi-bolt connections is overlooked. Fierro et al. [31] analyzed the linear and nonlinear acousto-ultrasound waves to evaluate the preload integrity in a multi-bolt structure, while their approach required prudent frequency selection, and some certain issues (e.g., the electronic equipment may induce nonlinear components in measured signals) also hindered practical applications. In addition, Meyer et al. [32] developed an impact modulation (IM) method to estimate the multi-bolt connection in a satellite structure; however, this method could not realize real-time monitoring due to its intrinsic characteristics. Thus, a new method is still required to achieve looseness detection of multi-bolt connections. Considering the merits such as insensitivity to the environment and easy to implement, we can expect that the active sensing method has great potential in detecting multi-bolt connections with the help of artificial intelligence techniques. However, previous investigations [14,15] have demonstrated that the current indicator (i.e., energy-based index) performs unsatisfactorily, particularly at the inception stage. Additionally, the energy attenuation caused by individual bolt looseness plays a small role in a multi-bolt structure, and the results may be confusing due to loose bolts in different positions. On the contrary, the nonlinear features of ultrasonic waves have proven their superiority for bolt looseness monitoring [17–20]. Therefore, to achieve loosening detection of multi-bolt connections through the active sensing method, a crucial problem that we face is how to develop a new indicator to quantify the defect-related nonlinear characters of received signals. In the past decades, we have witnessed the rapid development of entropy-based methods for nonlinear estimation, including the approximate entropy (ApEn) [33], the sample entropy (SampEn) [34], the permutation entropy (PE) [35], and the multiscale entropy (MSE) [36]. Notably, more advanced entropy-based algorithms perform well in analyzing nonlinear features (e.g., complexity) of signals in the fields of fault diagnosis [37–42] and the SHM [43–48], which may provide a useful reference for us to develop the new indicator. In this paper, based on the multivariate multiscale fuzzy entropy algorithm (MMFE) [49], a new indicator for the active sensing method was proposed to quantify the nonlinear features of received signals. Then, the max-relevance and min redundancy (mRMR) algorithm [50] was employed to select the first four important features from the obtained MMFE sets. Finally, by feeding the new datasets into the genetic algorithm-based least square support vector machine (GA-LSSVM) [51] that has proven its good performance in the field of SHM [52], we trained a classifier to identify loosening in a multi-bolt connection. The remaining sections of this paper are provided in the following manner. The theoretical background of the MMFE, the mRMR, and the GA-LSSVM are introduced in Section 2. Section 3 describes the experimental apparatus in detail. The results are discussed in Section 4 to demonstrate the effectiveness of the proposed method in this paper. Finally, the conclusions are drawn in Section 5.
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2. Theoretical background The overall framework of the proposed method in this paper is illustrated in Fig. 1. First, the data acquisition for training and testing is conducted by applying the active sensing method to a multi-bolt structure. Then, the MMFE is employed to quantify nonlinearity of received signals, which works as the damage index (DI) set. Subsequently, the first four significant features of each MMFE-based set are selected through the mRMR, and thus the new feature sets are conducted. Finally, the obtained new feature sets of the training data are fed into GA-based LSSVM to train a classifier, and the detection of different cases of bolt loosening is verified by using the new testing feature sets. 2.1. Multivariate multiscale fuzzy entropy Generally, systematic complexity can be reflected through the dynamical fluctuations of output signals, whose nonlinear features such as degrees of regularity can be quantified by using entropy-based methods (e.g., the ApEn [33], the SampEn [34], the PE [35]). Then, in 2002, Costa et al. [36] proposed the MSE algorithm to avoid the discrepancy of SampEn calculation, which can be attributed to the fact that only single temporal scale is considered during the entropy estimation process. Recently, the MSE has been extended to the multivariate multiscale entropy (MMSE) [53] by developing a multivariate sample entropy (MSampEn) algorithm, to achieve entropy analysis of multichannel data. However, both the MSE and the MMSE have a certain problem that holds back their performance, i.e., the similar degree between any two delay vectors is based on a Heaviside function. Analogous to a binary classifier, the boundary of the Heaviside function is solid, which will induce discontinuity. For instance, as depicted in Fig. 2, points 2 and 3 are regarded similar to original point 0 since they are within the boundary. Nevertheless, point 1 is still considered as dissimilarity, even though it is very close to point 2. Moreover, after enlarging the boundary to enclose point 1, the entropy estimation changes completely. In other words, the MSE and MMSE depend on the boundary (i.e., tolerance) severely. Therefore, based on the concept of fuzzy set theory [54], the Gaussian function that varies smoothly and continuously is employed to replace the Heaviside function and enhance robustness when different boundaries are applied. In this paper, guided by the concept of the MSE and the MMSE, we implemented the Multivariate multiscale fuzzy entropy (MMFE) [49], whose detailed procedure is presented as follows. We first denote a N time-series signal with p variable as xk;i i¼1 , where k ¼ 1; 2; ; p. (a) Composite delay vectors X m ðiÞ 2 Rm are conducted, where i ¼ 1; 2; ; N n; and n can be calculated as maxfMg maxfsg, where M ¼ m1 ; m2 ; mp 2 Rp is the embedding vector, and s ¼ s1 ; s2 ; ; sp is the time lag vector.
Fig. 1. Flowchart of the proposed method in this paper.
Fig. 2. Heaviside function and fuzzy function for entropy estimation.
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(b) Then, the local mean x0 ðiÞ ¼
Pm1 j¼0
xði þ jÞ=m is removed from each delay vector, that is
X m ðiÞ ¼ ½xðiÞ x0 ðiÞ; xði þ 1Þ x0 ðiÞ; ; xði þ m 1Þ x0 ðiÞ
ð1Þ
(c) The distance between two delay vectors is defined as the maximum norm [55], i.e., m
dij ¼ distance½X m ðiÞ; X m ð jÞ ¼ max fjxði þ l 1Þ xð j þ l 1Þjg l¼1;;m
ð2Þ
2 (d) By denoting a Gaussian function l dij ; r ¼ exp dij =2r2 as the fuzzy membership function, the similarity degree m Dm ij ¼ l dij ; r can be calculated, where r is the tolerance. Then, we define the function Nn Nn1 X m 1 X 1 B ðr Þ ¼ D N n i¼1 N n 1 j¼1;i–j ij
!
m
ð3Þ
(e) Extend the dimension m of delay vector in Step 1 to m þ 1, i.e., a p ðN nÞ vectors X mþ1 ðiÞ 2 Rmþ1 are obtained. mþ1 (f) Analogue to Step 4, the similarity degree Dmþ1 ¼ l dij ; r between two vectors can be calculated, and the function is, ij
Bmþ1 ðr Þ ¼
pðX NnÞ 1 1 pðN nÞ i¼1 pðN nÞ 1
pðNn XÞ1
! Dmþ1 ij
ð4Þ
j¼1;i–j
(g) Subsequently, the multivariate fuzzy sample entropy (MFSampEn), which is similar to MSampEn, can be calculated as,
" # Bmþ1 ðrÞ Bm ðr Þ
MFSampEnðM; s; r; N Þ ¼ ln
ð5Þ
(h) Finally, we can plot the MMFE as the MFSampEn versus various scale factor, which can assess nonlinear features of data. 2.2. Max-relevance and min redundancy The classification performance may deteriorate due to compromised accuracy or time-consuming computation when we apply over many extracted features. Therefore, it is important to minimize classification error by extracting the most important features of data, and several methods have been developed [56,57]. Amongst them, the most popular approach is the maximal relevance feature selection. However, direct implementation of maximal relevance feature selection may be unsatisfactory, particularly, in terms of features that have rich redundancy. Thus, to select proper features from MMFE sets in this paper, we employed the max-relevance and min redundancy (mRMR) method [50], whose procedure is presented as follows. (a) Given two random variables x and y with their corresponding probabilistic density functions pðxÞ and pð yÞ, and we can define the mutual information through the joint probabilistic density functions pðx; yÞ as,
ZZ Iðx; yÞ ¼
pðx; yÞlog
pðx; yÞ dxdy pðxÞpð yÞ
ð6Þ
(b) Then, we denote the mutual information between the feature x and target class c as Iðx; cÞ, and classification are implemented by selecting the features with max-relevance and min-redundancy to form a feature subset S, i.e.,
maxDðS; cÞ D ¼
1 X Iðxi ; cÞ; jSj x 2S i
minRðSÞ R ¼
1 2
jSj
X I xi ; xj
ð7Þ
xi ;xj 2S
where jSj is the total of features in the feature subset S. (c) According to the above criterion D and R, we can define the operators as follows,
maxUðD; RÞ U ¼ D R;
maxUðD; RÞ U ¼ D=R
ð8Þ
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(d) Finally, from the set fx Sm1 g, we can apply the mRMR to select mth feature by following criterions,
" max
xj 2xSm1
I xj ; c
# X 1 I xj ; xi ; m 1 x 2S i
m1
" max
xj 2xSm1
I xj ; c =
X 1 I xj ; xi m 1 x 2S i
# ð9Þ
m1
2.3. Genetic algorithm-based least square support vector machine Based on the statistical learning theory (SLT), the support vector machine (SVM) [58] belongs to a data-driven method, which can achieve linear classification through a hyperplane. As depicted in Fig. 3a, a hyperplane w x þ b ¼ 0 can separate the data into two classes (red circle and blue rectangle), and the margin 2=jjwjj between two boundary lines (i.e., jw x þ bj ¼ 1) should be maximized to ensure the best classification accuracy. Similarly, using a nonlinear mapping function /, we can apply the linear SVM to solve nonlinear classification problem, as shown in Fig. 3b. Subsequently, to enhance performance of the SVM such as the convergence rate, the least square support vector machine (LSSVM) was proposed [59], and its principle was briefly introduced as follows. A training data set as N
U ¼ fðxi ; yi Þ; xi 2 Rn ; yi 2 Rgn¼1 was denoted first, where xi is the input vector, yi represents the corresponding target value, N is the total number of samples. Then, the LSSVM model can be expressed as yðxÞ ¼ wT /ðxÞ þ b, where w 2 Rn ; b 2 R are modal parameters. The associated optimization problem is formulated as,
Minðw; b; eÞ ¼
N 1 T cX w wþ e2 ¼ Ew þ c ED 2 2 i¼1 i
ð10Þ
P where Ew ¼ ð1=2ÞwT w,ED ¼ ð1=2Þ e2i , c is the regularization parameter (penalty factor), and ei is the prediction error item. After using the Lagrange Multiplier to eliminate w and e, and solve the Eq. (10), we can obtain following matrix,
01n 0n1
11n P þ 1=c
b
a
¼
0 y
ð11Þ
where P ¼ K ðx; xi Þ ¼ /ðxÞT / xj is the Kernel function, according to the Mercer’s theory; a is the Lagrange multiplier. Finally, the LSSVM model can be rewritten as equation (12), and the radial basis function (RBF) [60] was employed as the Kernel function in this paper, since it has faster convergence speed and better generalization ability.
y ð xÞ ¼
N X i¼1
ai K ðx; xi Þ þ b; K ðx; xi Þ ¼ exp
k x xi k2
!
r2
ð12Þ
where r2 is the Kernel bandwidth parameter that can determine the radical range of the function. According to above introduction, we can find that proper selection of the regularization parameter c and the Kernel bandwidth parameter r2 is crucial to successful implementation of LSSVM, since c controls the trade-off between smoothness and minimized training error, and r2 determines the radical range of the function. In this paper, the genetic algorithm (GA) [61], which has demonstrated its effectiveness across multiple fields [62], was applied to optimize these two parameters, to overcome the high computational cost induced by traditional methods such as the cross validation and enumeration method. Typically, the GA modifies the population of solutions, which is also called as generation, with a repeated process, and it follows three main rules [63] to achieve iteration process: (1) selection; (2) crossover and (3) mutation. Moreover, in this paper the mean relative error (MRE) was defined as the fitness function, and the whole flowchart of the GA-LSSVM is given in Fig. 4.
Fig. 3. (a) SVM for linear classification (b) SVM for nonlinear classification.
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Fig. 4. Flow chart of GA-based LSSVM.
MRE ¼
N ^j 1X jyi y 100% N i¼1 yi
ð13Þ
^ is the prediction value. where N is the sample size, y 3. Experimental setup To verify the effectiveness of the proposed method in this paper, a set of experiments were conducted on two aluminum beams (size: 230 mm 40 mm 5 mm) integrated by three M8 bolts, and we denoted them as B1, B2, and B3, respectively. Since the proposed method is based on the active sensing method, the experimental setup consists of a computer equipped with a custom LabVIEW program, a NI multifunction DAQ system (NI USB-6363), and a power amplifier (Trek model 2100HF), as depicted in Fig. 5. Additionally, two PZT patches (namely, PZT A and B) were bonded on the surfaces of two beams. Through the NI DAQ system, a swept sine wave (100–300 kHz) with duration 0.01 s was generated and converted to an analog signal. To ensure enough signal power, we applied the amplifier to augment this analog signal fiftyfold and fed it into PZT A to generate stress wave, which would propagate across the bolted interface and be captured by PZT B. Subsequently, due to the piezoelectric effect, the captured waves were transformed to the analog signal again and converted to a digital signal by using the NI DAQ system (sampling rate: 1 MHz). Finally, the received digital signals under different cases were saved for next step process, i.e., the MMFE calculation. In this case, for convenience, each bolt has two status: complete looseness and perfect integration (60 Nm applied by using a digital torque wrench). Thus, there are 8 (23) cases in total, and each case has 20 data sets for training and 20 data sets for testing as shown in Table 1. Moreover, to further demonstrate the effectiveness of the proposed method, we have conducted this method on another multi-bolt joint derived from a space truss connection, which is a typical engineering structure. As depicted in Fig. 6, the specimen consists of two steel plates (size: 150 mm 150 mm 5 mm) held together by four M8 bolts. The experimental
Fig. 5. Experimental apparatus.
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F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507 Table 1 Detailed arrangement of the experimental cases. Case
B1
B2
B3
Total of training data
Total of testing data
1 2 3 4 5 6 7 8
Loose Tighten Loose Loose Tighten Tighten Loose Tighten
Loose Loose Tighten Loose Tighten Loose Tighten Tighten
Loose Loose Loose Tighten Loose Tighten Tighten Tighten
20 20 20 20 20 20 20 20
20 20 20 20 20 20 20 20
Fig. 6. Diagram of experimental setup.
Table 2 Arrangement of the cases in detail. Case
B1
B2
B3
B4
Case
B1
B2
B3
B4
1 2 3 4 5 6 7 8
Loose Tighten Tighten Tighten Tighten Tighten Tighten Tighten
Loose Loose Tighten Loose Loose Tighten Loose Tighten
Loose Loose Loose Tighten Loose Tighten Tighten Loose
Loose Loose Loose Loose Tighten Loose Tighten Tighten
9 10 11 12 13 14 15 16
Tighten Loose Loose Loose Loose Loose Loose Loose
Tighten Tighten Tighten Tighten Tighten Loose Loose Loose
Tighten Loose Tighten Loose Tighten Tighten Tighten Loose
Tighten Loose Loose Tighten Tighten Loose Tighten Tighten
apparatus and procedures are almost the same, and 16 cases are selected for training and testing with 20 data sets respectively, as presented in Table 2.
4. Results and discussion The received signals (in the time domain) under different cases are depicted in Fig. 7, and we can find that the relationship between received signal energy and eight pre-load cases of the multi-bolt connection is not straightforward, since several peaks exist in each received signal. This phenomenon may be due to two reasons: (1) different components of wave have different propagation velocities (typically, lower energy components have higher velocities and higher energy components have lower velocities); (2) wave components with lower energy may travel to the sensor directly, while higher energy components may reflect and scatter severely at the interface before reaching the sensor. Thus, we calculated and compared the signal energy under various cases as shown in Fig. 7, and the signal energy overall grow with more tightened bolts. This result conforms to prior investigation [14,15], which can be explained by the increscent true contact area when more preload is applied, since the transmitted wave energy is proportional to the contact area. However, it is worth noting that this growth is not monotonic (for instance, the energy under case 2, 5, 7 and 8 is almost the same), and thus we may not expect the potential of signal energy to work as a damage index (DI), particularly, for multi-bolt looseness detection.
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F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507
Fig. 7. Received signals and signal energy under different cases.
Prior investigation [49] has demonstrated that s ¼ 20 has the best performance during the computation of the MMFE, since overlarge s will induce calculating redundancy (additionally, the MMFE values remain almost unchanged when s is larger than 20), while too small s cannot reveal the characteristics of the signals adequately. Therefore, in this paper, the MMFE algorithm (with scale factor s ¼ 20) was used to analyze received signals to develop new DI that replaces the current indicator (i.e., signal energy), and results were shown in Fig. 8. Then, to demonstrate the robustness of the MMFE, each case in Fig. 8 consists of five testing results, and we can observe that the MMFE curves are almost consistent, which means that the MMFE is not affected by environmental conditions and thus suitable for on-line monitoring. The only exception is the case 1, and this phenomenon may be attributed to the reason that all bolts are loosening in this case, thus existing lowfrequency vibration of the connection due to the incentive effect of PZT patch. This vibration can induce severe nonlinearity of the received signals, which can be characterized by the entropy, and thus the results are much less consistent for case 1. Overall, the MMFE values tend to decrease when bolt loose, and this can be explained by the phenomenon of the contact
Fig. 8. MMFE values of received signals under different cases.
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acoustic nonlinearity (CAN) [64]. Due to the interfacial asperities, the bolted interface presents nonlinear features when stress waves traverse through the contact interface. With bolt preload decreases, the deformation of asperities eases, namely, the gap between two contact surfaces enlarges. Subsequently, the nonlinearity of received wave signal will increase and be reflected in entropy values, since entropy can estimate the complexity (i.e., nonlinearity) of signals. However, we should admit that the differences amongst cases with the same number of loose bolts are not obvious, for instance, cases 2/3/4 or cases 5/6/7. To enhance performance of the MMFE for loosening detection of the multi-bolt connection, we applied the mRMR method to select the first four significant features to reconstruct the new feature sets, which can be employed as input for next step, i.e., looseness identification through GA-LSSVM. In this paper, the determined feature sets with the most significance are s ¼ 17; 4; 20; 13. Additionally, to demonstrate the effectiveness of the mRMR method, we plotted the first three elements (i.e., s ¼ 17; 4; 20) of the new feature sets and compared them with feature sets that were randomly selected (e.g., s ¼ 1; 2; 3), as depicted in Fig. 9. It can be seen that all samples in the new feature sets cluster around their corresponding class centers and there was obvious distinction among eight cases. On the contrary, some samples in the randomly selected feature sets scatter from their class center, and there is no an obvious boundary amongst eight cases. Subsequently, a GA-based LSSVM classifier was trained by using input dataset matrix T j and the label matrix Lj , which take the following forms,
Fig. 9. Comparison between new feature sets and initial feature sets (left
s ¼ 17; 4; 20 right s ¼ 1; 2; 3).
Table 3 Classification accuracy of different methods. Method
The proposed method MMFE without mRMR Energy-based DI
Optimized model parameters
Accuracy (%)
c
r
Max
Min
Mean
20.8233 5.6794 12.5637
1.1355 0.9929 0.0448
90.44 83.34 66.11
88.33 80.20 60.58
89.39 81.65 63.06
2
Fig. 10. Comparison of classification accuracy for three methods.
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2
MMFEs¼17;1
6 MMFEs¼17;2 6 Tj ¼ 6 .. 6 4 . MMFEs¼17;i
MMFEs¼13;1
3
MMFEs¼4;1
MMFEs¼20;1
MMFEs¼4;2 .. .
MMFEs¼20;2 .. .
MMFEs¼13;2 7 7 7; .. 7 5 .
MMFEs¼4;i
MMFEs¼20;i
MMFEs¼13;i
2
l1
3
6l 7 6 27 7 Lj ¼ 6 6 .. 7 4.5
ð14Þ
li
where i ¼ 1; 2; ; 8 is the total number of cases, and j ¼ 1; 2; ; 20 is the number of training data sets. The regularization parameter c and the Kernel bandwidth parameter r2 are optimized through the GA algorithm under the maximum individual fitness (i.e., the best classification accuracy). Additionally, to demonstrate the advantage of the proposed method, the traditional energy-based DI and the MMFE features sets without the mRMR are also used to train the other two GA-based LSSVM models, and comparison results are given in Table 3. Meanwhile, 20 repeated training was conducted to avoid the randomness, as depicted in Fig. 10. It can be seen that the proposed method has the best classification accuracy (about
Fig. 11. Received signals with corresponding MMFE values under different cases.
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88.33–90.44%), which demonstrates its superiority. On the other hand, the MMFE without the mRMR has the moderate classification accuracy (about 80.20–83.34%), and the traditional energy-based DI has the lowest classification accuracy (about 60.58–66.11%). This phenomenon can be explain through three main reasons: (1) as discussed above, the received signal energy does not increase monotonically, i.e., the energy-based DI may be almost the same under some cases, which causes great difficulty in classification; (2) the stress waves presents nonlinear features when they traverse the contact interface, the MMFE that can quantify this nonlinearity outperforms the energy-based DI, since prior investigations have demonstrated that nonlinear features are more sensitive to linear counterpart (namely, signal energy); (3) due to the effectiveness of the mRMR method in selecting significant features with maximum relevance and min redundancy, the proposed method has better performance than the MMFE without mRMR. In addition, for the specimen with four bolts, we can obtain similar results. First, the received time-series signals and corresponding MMFE values (scale factor s ¼ 20) under different cases are illustrated in Fig. 11. We can see that the received signal energy has no obvious relationship with bolt preloads, while the MMFE values under different cases still present good consistency. The reasons of these phenomena have been discussed earlier. Then, after selecting the first four significant features through the mRMR, we can determine that the feature sets for this specimen are s ¼ 1; 17; 16; 4 and plot the first three elements (i.e., s ¼ 1; 17; 16) of the new feature sets to compare them with random feature sets (e.g., s ¼ 1; 2; 3), as depicted in Fig. 12. Using the GA, we can obtain the optimized regularization parameter c and the Kernel bandwidth parameter r2 , and then achieve the classification of different cases (i.e., multiple bolt loosening) through the LSSVM. To avoid randomness, we repeated the training and testing twenty times, and the results were given in Table 4 and depicted in Fig. 13. The proposed method proves its advantages, since it has better performance (95.14–98.55%) than the DI through the MMFE without the mRMR (85.93–89.10%) and the traditional energy-based DI (79.19–82.71%). It is worth noting that different bolted connections with various boundary conditions, size, and ages may cause different orders of s and various c and r2 , while it is acceptable for us to develop a data-base to address this issue. In other words, regarding different bolted connections with specific boundary conditions, size, and ages, we can apply trial-and-error or optimization to determine these uncertain parameters and import them into a data-base for real industrial application in the future. Finally, to demonstrate our statement, namely the insensitivity of the propose method to the environmental conditions such as temperatures, the authors repeated experiments on two specimens in a wide range of temperatures. As depicted in Fig. 14, a hair dryer was used to provide different temperatures, and an electronic thermometer (testo Quicktemp 825-T4) was employed to measure environmental temperatures. The comparison of classification results (mean accuracy %) among three methods under different temperatures are given in Table 5, and we can find that the classification accuracy remains almost unchanged, which indicates that the proposed method and even ultrasonic-based methods are insensitive to environmental temperatures.
Fig. 12. Comparison between new feature sets and initial feature sets (left
s ¼ 1; 17; 16 right s ¼ 1; 2; 3).
Table 4 Classification accuracy among three methods. Method
The proposed method MMFE without mRMR Energy-based DI
Optimized model parameters
Accuracy (%)
c
r2
Max
Min
Mean
5.2740 1.0089 3.4237
0.8021 0.0038 1.0354
98.55 89.10 82.71
95.14 85.93 79.19
96.69 87.49 81.44
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F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507
Fig. 13. Comparison of classification accuracy among three methods.
Fig. 14. Experimental apparatus for different temperatures.
Table 5 Comparison of classification results (mean accuracy %) among three methods under different temperatures. Method
Three-bolt connection
The proposed method MMFE without mRMR Energy-based DI
Four-bolt connection
25 1 C
35 1 C
45 1 C
25 1 C
35 1 C
45 1 C
89.39 81.65 63.06
88.72 83.16 64.11
88.30 82.56 61.98
96.69 87.49 81.44
95.43 85.36 80.78
97.39 87.16 82.63
5. Conclusions In this paper, by using the multivariate multiscale fuzzy entropy (MMFE), a new damage index was proposed for the PZTenabled active sensing method. Then, with the help of the max relevance and min redundancy (mRMR) and the genetic algorithm-based least square support vector machine (GA-based LSSVM), the improved active sensing method was employed to detect looseness of the multi-bolt connection. The experimental results demonstrated that the proposed method could effectively identify bolt looseness. The main contributions of this paper are summarized as follows: (1) the active sensing method was first applied to detect integrity status of the multi-bolt connection; (2) the MMFE was employed to develop a new DI for the active sensing method, and its superiority over current DI (i.e., signal energy) was verified; (3) the mRMR was introduced to choose significant features from the MMFE-based DI and thus enhance performance of classification. However, it is worth noting that only binary status (namely, loosening or not) of each bolt is considered in this preliminary investigation. In further studies, more advanced DIs and methods will be proposed to solve this issue and provide higher classification accuracy, which can guide further investigations on bolt loosening detection.
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Acknowledgement This research was partially supported by the China Scholarship Council (No. 201706060203), their financial support is appreciated.
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Contents lists available at ScienceDirect
Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Monitoring of multi-bolt connection looseness using entropybased active sensing and genetic algorithm-based least square support vector machine Furui Wang, Zheng Chen, Gangbing Song ⇑ Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA
a r t i c l e
i n f o
Article history: Received 15 May 2019 Received in revised form 15 August 2019 Accepted 6 November 2019
Keywords: Structural health monitoring Bolt looseness detection Piezoelectric transducer Multivariate multiscale fuzzy entropy Max-relevance and min redundancy Support vector machine
a b s t r a c t Looseness detection of bolted connections is an essential industrial issue that can reduce the maintenance and repair costs caused by joint failures; however, current loosening detection methods mainly focus on the single-bolt connection. Even though several methods, such as the vibration-based method and electro-mechanical impedance (EMI) method, have been employed to detect multi-bolt looseness, while they are easily affected by environmental issues. Therefore, the main contribution of this paper is to detect loosening of the multi-bolt connection through the PZT-enabled active sensing method, which has several merits including easy-to-implement, low cost, and good ability of anti-environment disturbance. Since the current indicator of the active sensing, namely the signal energy is insensitive to multiple damages, we developed a new damage index (DI) based on the multivariate multiscale fuzzy entropy (MMFE). Subsequently, the maximum relevance minimum redundancy (mRMR) was used to select significant features from the MMFEbased DI to construct the new datasets. After feeding the new datasets into the genetic algorithm-based least square support vector machine (GA-based LSSVM), we trained a classifier to detect loosening of the multi-bolt connection. Finally, repeated experiments were conducted to demonstrate the effectiveness of the proposed method, which can guide future investigations on bolt looseness detection. Published by Elsevier Ltd.
1. Introduction Across multiple industries such as aerospace engineering, mechanical engineering, and civil engineering, the bolted connection has been widely used to hold different components together, which induce severe structural nonlinearities [1,2], and their loosening and failures may lead to accidents if not detected in a timely manner. Moreover, detection of joint failures and maintenance of connection integrity are directly related to costs, particularly, under current strict requirements of safety and economy. For instance, over 20% of accidents in mechanical systems, which can induce great losses, are attributed to bolt looseness [3]. However, current methods, including human vision and percussion [4], are incompetent and costly, since the visible looseness is too late to ensure structural integrity and the percussion requires skilled personnel. Then, due to the rapid development of the image recognition technologies [5], several machine-vision methods [6,7] have been applied to detect bolt loosening, since they can mitigate the limitations such as boundary conditions, aging, sizes, and different working ⇑ Corresponding author. E-mail address: [email protected] (G. Song). https://doi.org/10.1016/j.ymssp.2019.106507 0888-3270/Published by Elsevier Ltd.
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cases. However, it is worth noting that the vision-based method focuses more on detection, rather than the monitoring. In other words, the vision-based method cannot grasp the real-time integrity of bolted connections during the entire working cycle. Moreover, visible rotation always means that bolts have lost most of their preloads, which may be too late for looseness detection in some cases. Therefore, in the past decades, remarkable progress has been developed to detect bolt loosening, particularly, based on various structural health monitoring (SHM) methods. The vibration-based method [8,9] and the electro-mechanical impedance (EMI) method [10,11], for instance, have demonstrated their effectiveness in bolt looseness detection. However, the vibration-based method is more suitable for global damage, rather than the bolt looseness that belongs to the local flaw, and the EMI method is affected by environmental conditions severely. Then, ultrasonic-based SHM methods [12,13] attract much attention, due to their high accuracy, convenient implementation, and excellent performance in avoiding environmental intrusions. Thus, some in situ bolt looseness monitoring methods based on the ultrasonic technology have been developed, including the linear ultrasound methods (e.g., the active sensing method [14–16]) and the nonlinear ultrasound methods including the subharmonic-based method [17], the higher-harmonics based method [18], and the modulated harmonics-based method [19,20]. Even though these methods perform well in bolt looseness identification; however, they all focus on single-bolt connection, whose applications are limited in real industries. Subsequently, to enhance the practical use of bolt looseness monitoring methods, several investigations on multi-bolt connections have been reported. For instance, by using the spectral element method to determine the electrical impedance changes of piezoceramic transducers under various conditions, the location and loosening extent of a multi-bolt joint could be quantitatively identified [21]. Park et al. [22] also verified the effectiveness of the EMI method in a pipeline structure, which is a typical multi-bolt connection. Moreover, employing the magneto-mechanical impedance as the indicator, Doyle et al. [23] estimated the integrity of a multi-bolt connection in a satellite structure. In Addition, the vibration-based method has also been investigated to detect bolt looseness [24–27]. Recently, with the rapid development of artificial intelligence techniques, their applications in SHM have been noticed, particularly, in bolt looseness monitoring. Based on EMI methods and neural network (NN)-based pattern analysis, Min et al. [28] detected the loose bolts in a bolted-joint beam. In their study, multiple frequency subranges from the EMI signals were extracted as the input to train the NN, and real damage types (i.e., bolted looseness) and severity were regarded as output. Similarly, Zhang et al. [29] identified the loosening of a multibolt plate based on the EMI method; however, the LibSVM, instead of the NN, was applied to locate the position of loose bolts. Liang et al. [30] applied a decision fusion system to develop a convenient vibration-based method for multi-bolt joint failures detection. However, the drawbacks of the vibration-based method and the EMI method have been mentioned earlier, and the application potential of ultrasound methods in detecting multi-bolt connections is overlooked. Fierro et al. [31] analyzed the linear and nonlinear acousto-ultrasound waves to evaluate the preload integrity in a multi-bolt structure, while their approach required prudent frequency selection, and some certain issues (e.g., the electronic equipment may induce nonlinear components in measured signals) also hindered practical applications. In addition, Meyer et al. [32] developed an impact modulation (IM) method to estimate the multi-bolt connection in a satellite structure; however, this method could not realize real-time monitoring due to its intrinsic characteristics. Thus, a new method is still required to achieve looseness detection of multi-bolt connections. Considering the merits such as insensitivity to the environment and easy to implement, we can expect that the active sensing method has great potential in detecting multi-bolt connections with the help of artificial intelligence techniques. However, previous investigations [14,15] have demonstrated that the current indicator (i.e., energy-based index) performs unsatisfactorily, particularly at the inception stage. Additionally, the energy attenuation caused by individual bolt looseness plays a small role in a multi-bolt structure, and the results may be confusing due to loose bolts in different positions. On the contrary, the nonlinear features of ultrasonic waves have proven their superiority for bolt looseness monitoring [17–20]. Therefore, to achieve loosening detection of multi-bolt connections through the active sensing method, a crucial problem that we face is how to develop a new indicator to quantify the defect-related nonlinear characters of received signals. In the past decades, we have witnessed the rapid development of entropy-based methods for nonlinear estimation, including the approximate entropy (ApEn) [33], the sample entropy (SampEn) [34], the permutation entropy (PE) [35], and the multiscale entropy (MSE) [36]. Notably, more advanced entropy-based algorithms perform well in analyzing nonlinear features (e.g., complexity) of signals in the fields of fault diagnosis [37–42] and the SHM [43–48], which may provide a useful reference for us to develop the new indicator. In this paper, based on the multivariate multiscale fuzzy entropy algorithm (MMFE) [49], a new indicator for the active sensing method was proposed to quantify the nonlinear features of received signals. Then, the max-relevance and min redundancy (mRMR) algorithm [50] was employed to select the first four important features from the obtained MMFE sets. Finally, by feeding the new datasets into the genetic algorithm-based least square support vector machine (GA-LSSVM) [51] that has proven its good performance in the field of SHM [52], we trained a classifier to identify loosening in a multi-bolt connection. The remaining sections of this paper are provided in the following manner. The theoretical background of the MMFE, the mRMR, and the GA-LSSVM are introduced in Section 2. Section 3 describes the experimental apparatus in detail. The results are discussed in Section 4 to demonstrate the effectiveness of the proposed method in this paper. Finally, the conclusions are drawn in Section 5.
F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507
3
2. Theoretical background The overall framework of the proposed method in this paper is illustrated in Fig. 1. First, the data acquisition for training and testing is conducted by applying the active sensing method to a multi-bolt structure. Then, the MMFE is employed to quantify nonlinearity of received signals, which works as the damage index (DI) set. Subsequently, the first four significant features of each MMFE-based set are selected through the mRMR, and thus the new feature sets are conducted. Finally, the obtained new feature sets of the training data are fed into GA-based LSSVM to train a classifier, and the detection of different cases of bolt loosening is verified by using the new testing feature sets. 2.1. Multivariate multiscale fuzzy entropy Generally, systematic complexity can be reflected through the dynamical fluctuations of output signals, whose nonlinear features such as degrees of regularity can be quantified by using entropy-based methods (e.g., the ApEn [33], the SampEn [34], the PE [35]). Then, in 2002, Costa et al. [36] proposed the MSE algorithm to avoid the discrepancy of SampEn calculation, which can be attributed to the fact that only single temporal scale is considered during the entropy estimation process. Recently, the MSE has been extended to the multivariate multiscale entropy (MMSE) [53] by developing a multivariate sample entropy (MSampEn) algorithm, to achieve entropy analysis of multichannel data. However, both the MSE and the MMSE have a certain problem that holds back their performance, i.e., the similar degree between any two delay vectors is based on a Heaviside function. Analogous to a binary classifier, the boundary of the Heaviside function is solid, which will induce discontinuity. For instance, as depicted in Fig. 2, points 2 and 3 are regarded similar to original point 0 since they are within the boundary. Nevertheless, point 1 is still considered as dissimilarity, even though it is very close to point 2. Moreover, after enlarging the boundary to enclose point 1, the entropy estimation changes completely. In other words, the MSE and MMSE depend on the boundary (i.e., tolerance) severely. Therefore, based on the concept of fuzzy set theory [54], the Gaussian function that varies smoothly and continuously is employed to replace the Heaviside function and enhance robustness when different boundaries are applied. In this paper, guided by the concept of the MSE and the MMSE, we implemented the Multivariate multiscale fuzzy entropy (MMFE) [49], whose detailed procedure is presented as follows. We first denote a N time-series signal with p variable as xk;i i¼1 , where k ¼ 1; 2; ; p. (a) Composite delay vectors X m ðiÞ 2 Rm are conducted, where i ¼ 1; 2; ; N n; and n can be calculated as maxfMg maxfsg, where M ¼ m1 ; m2 ; mp 2 Rp is the embedding vector, and s ¼ s1 ; s2 ; ; sp is the time lag vector.
Fig. 1. Flowchart of the proposed method in this paper.
Fig. 2. Heaviside function and fuzzy function for entropy estimation.
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(b) Then, the local mean x0 ðiÞ ¼
Pm1 j¼0
xði þ jÞ=m is removed from each delay vector, that is
X m ðiÞ ¼ ½xðiÞ x0 ðiÞ; xði þ 1Þ x0 ðiÞ; ; xði þ m 1Þ x0 ðiÞ
ð1Þ
(c) The distance between two delay vectors is defined as the maximum norm [55], i.e., m
dij ¼ distance½X m ðiÞ; X m ð jÞ ¼ max fjxði þ l 1Þ xð j þ l 1Þjg l¼1;;m
ð2Þ
2 (d) By denoting a Gaussian function l dij ; r ¼ exp dij =2r2 as the fuzzy membership function, the similarity degree m Dm ij ¼ l dij ; r can be calculated, where r is the tolerance. Then, we define the function Nn Nn1 X m 1 X 1 B ðr Þ ¼ D N n i¼1 N n 1 j¼1;i–j ij
!
m
ð3Þ
(e) Extend the dimension m of delay vector in Step 1 to m þ 1, i.e., a p ðN nÞ vectors X mþ1 ðiÞ 2 Rmþ1 are obtained. mþ1 (f) Analogue to Step 4, the similarity degree Dmþ1 ¼ l dij ; r between two vectors can be calculated, and the function is, ij
Bmþ1 ðr Þ ¼
pðX NnÞ 1 1 pðN nÞ i¼1 pðN nÞ 1
pðNn XÞ1
! Dmþ1 ij
ð4Þ
j¼1;i–j
(g) Subsequently, the multivariate fuzzy sample entropy (MFSampEn), which is similar to MSampEn, can be calculated as,
" # Bmþ1 ðrÞ Bm ðr Þ
MFSampEnðM; s; r; N Þ ¼ ln
ð5Þ
(h) Finally, we can plot the MMFE as the MFSampEn versus various scale factor, which can assess nonlinear features of data. 2.2. Max-relevance and min redundancy The classification performance may deteriorate due to compromised accuracy or time-consuming computation when we apply over many extracted features. Therefore, it is important to minimize classification error by extracting the most important features of data, and several methods have been developed [56,57]. Amongst them, the most popular approach is the maximal relevance feature selection. However, direct implementation of maximal relevance feature selection may be unsatisfactory, particularly, in terms of features that have rich redundancy. Thus, to select proper features from MMFE sets in this paper, we employed the max-relevance and min redundancy (mRMR) method [50], whose procedure is presented as follows. (a) Given two random variables x and y with their corresponding probabilistic density functions pðxÞ and pð yÞ, and we can define the mutual information through the joint probabilistic density functions pðx; yÞ as,
ZZ Iðx; yÞ ¼
pðx; yÞlog
pðx; yÞ dxdy pðxÞpð yÞ
ð6Þ
(b) Then, we denote the mutual information between the feature x and target class c as Iðx; cÞ, and classification are implemented by selecting the features with max-relevance and min-redundancy to form a feature subset S, i.e.,
maxDðS; cÞ D ¼
1 X Iðxi ; cÞ; jSj x 2S i
minRðSÞ R ¼
1 2
jSj
X I xi ; xj
ð7Þ
xi ;xj 2S
where jSj is the total of features in the feature subset S. (c) According to the above criterion D and R, we can define the operators as follows,
maxUðD; RÞ U ¼ D R;
maxUðD; RÞ U ¼ D=R
ð8Þ
F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507
5
(d) Finally, from the set fx Sm1 g, we can apply the mRMR to select mth feature by following criterions,
" max
xj 2xSm1
I xj ; c
# X 1 I xj ; xi ; m 1 x 2S i
m1
" max
xj 2xSm1
I xj ; c =
X 1 I xj ; xi m 1 x 2S i
# ð9Þ
m1
2.3. Genetic algorithm-based least square support vector machine Based on the statistical learning theory (SLT), the support vector machine (SVM) [58] belongs to a data-driven method, which can achieve linear classification through a hyperplane. As depicted in Fig. 3a, a hyperplane w x þ b ¼ 0 can separate the data into two classes (red circle and blue rectangle), and the margin 2=jjwjj between two boundary lines (i.e., jw x þ bj ¼ 1) should be maximized to ensure the best classification accuracy. Similarly, using a nonlinear mapping function /, we can apply the linear SVM to solve nonlinear classification problem, as shown in Fig. 3b. Subsequently, to enhance performance of the SVM such as the convergence rate, the least square support vector machine (LSSVM) was proposed [59], and its principle was briefly introduced as follows. A training data set as N
U ¼ fðxi ; yi Þ; xi 2 Rn ; yi 2 Rgn¼1 was denoted first, where xi is the input vector, yi represents the corresponding target value, N is the total number of samples. Then, the LSSVM model can be expressed as yðxÞ ¼ wT /ðxÞ þ b, where w 2 Rn ; b 2 R are modal parameters. The associated optimization problem is formulated as,
Minðw; b; eÞ ¼
N 1 T cX w wþ e2 ¼ Ew þ c ED 2 2 i¼1 i
ð10Þ
P where Ew ¼ ð1=2ÞwT w,ED ¼ ð1=2Þ e2i , c is the regularization parameter (penalty factor), and ei is the prediction error item. After using the Lagrange Multiplier to eliminate w and e, and solve the Eq. (10), we can obtain following matrix,
01n 0n1
11n P þ 1=c
b
a
¼
0 y
ð11Þ
where P ¼ K ðx; xi Þ ¼ /ðxÞT / xj is the Kernel function, according to the Mercer’s theory; a is the Lagrange multiplier. Finally, the LSSVM model can be rewritten as equation (12), and the radial basis function (RBF) [60] was employed as the Kernel function in this paper, since it has faster convergence speed and better generalization ability.
y ð xÞ ¼
N X i¼1
ai K ðx; xi Þ þ b; K ðx; xi Þ ¼ exp
k x xi k2
!
r2
ð12Þ
where r2 is the Kernel bandwidth parameter that can determine the radical range of the function. According to above introduction, we can find that proper selection of the regularization parameter c and the Kernel bandwidth parameter r2 is crucial to successful implementation of LSSVM, since c controls the trade-off between smoothness and minimized training error, and r2 determines the radical range of the function. In this paper, the genetic algorithm (GA) [61], which has demonstrated its effectiveness across multiple fields [62], was applied to optimize these two parameters, to overcome the high computational cost induced by traditional methods such as the cross validation and enumeration method. Typically, the GA modifies the population of solutions, which is also called as generation, with a repeated process, and it follows three main rules [63] to achieve iteration process: (1) selection; (2) crossover and (3) mutation. Moreover, in this paper the mean relative error (MRE) was defined as the fitness function, and the whole flowchart of the GA-LSSVM is given in Fig. 4.
Fig. 3. (a) SVM for linear classification (b) SVM for nonlinear classification.
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F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507
Fig. 4. Flow chart of GA-based LSSVM.
MRE ¼
N ^j 1X jyi y 100% N i¼1 yi
ð13Þ
^ is the prediction value. where N is the sample size, y 3. Experimental setup To verify the effectiveness of the proposed method in this paper, a set of experiments were conducted on two aluminum beams (size: 230 mm 40 mm 5 mm) integrated by three M8 bolts, and we denoted them as B1, B2, and B3, respectively. Since the proposed method is based on the active sensing method, the experimental setup consists of a computer equipped with a custom LabVIEW program, a NI multifunction DAQ system (NI USB-6363), and a power amplifier (Trek model 2100HF), as depicted in Fig. 5. Additionally, two PZT patches (namely, PZT A and B) were bonded on the surfaces of two beams. Through the NI DAQ system, a swept sine wave (100–300 kHz) with duration 0.01 s was generated and converted to an analog signal. To ensure enough signal power, we applied the amplifier to augment this analog signal fiftyfold and fed it into PZT A to generate stress wave, which would propagate across the bolted interface and be captured by PZT B. Subsequently, due to the piezoelectric effect, the captured waves were transformed to the analog signal again and converted to a digital signal by using the NI DAQ system (sampling rate: 1 MHz). Finally, the received digital signals under different cases were saved for next step process, i.e., the MMFE calculation. In this case, for convenience, each bolt has two status: complete looseness and perfect integration (60 Nm applied by using a digital torque wrench). Thus, there are 8 (23) cases in total, and each case has 20 data sets for training and 20 data sets for testing as shown in Table 1. Moreover, to further demonstrate the effectiveness of the proposed method, we have conducted this method on another multi-bolt joint derived from a space truss connection, which is a typical engineering structure. As depicted in Fig. 6, the specimen consists of two steel plates (size: 150 mm 150 mm 5 mm) held together by four M8 bolts. The experimental
Fig. 5. Experimental apparatus.
7
F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507 Table 1 Detailed arrangement of the experimental cases. Case
B1
B2
B3
Total of training data
Total of testing data
1 2 3 4 5 6 7 8
Loose Tighten Loose Loose Tighten Tighten Loose Tighten
Loose Loose Tighten Loose Tighten Loose Tighten Tighten
Loose Loose Loose Tighten Loose Tighten Tighten Tighten
20 20 20 20 20 20 20 20
20 20 20 20 20 20 20 20
Fig. 6. Diagram of experimental setup.
Table 2 Arrangement of the cases in detail. Case
B1
B2
B3
B4
Case
B1
B2
B3
B4
1 2 3 4 5 6 7 8
Loose Tighten Tighten Tighten Tighten Tighten Tighten Tighten
Loose Loose Tighten Loose Loose Tighten Loose Tighten
Loose Loose Loose Tighten Loose Tighten Tighten Loose
Loose Loose Loose Loose Tighten Loose Tighten Tighten
9 10 11 12 13 14 15 16
Tighten Loose Loose Loose Loose Loose Loose Loose
Tighten Tighten Tighten Tighten Tighten Loose Loose Loose
Tighten Loose Tighten Loose Tighten Tighten Tighten Loose
Tighten Loose Loose Tighten Tighten Loose Tighten Tighten
apparatus and procedures are almost the same, and 16 cases are selected for training and testing with 20 data sets respectively, as presented in Table 2.
4. Results and discussion The received signals (in the time domain) under different cases are depicted in Fig. 7, and we can find that the relationship between received signal energy and eight pre-load cases of the multi-bolt connection is not straightforward, since several peaks exist in each received signal. This phenomenon may be due to two reasons: (1) different components of wave have different propagation velocities (typically, lower energy components have higher velocities and higher energy components have lower velocities); (2) wave components with lower energy may travel to the sensor directly, while higher energy components may reflect and scatter severely at the interface before reaching the sensor. Thus, we calculated and compared the signal energy under various cases as shown in Fig. 7, and the signal energy overall grow with more tightened bolts. This result conforms to prior investigation [14,15], which can be explained by the increscent true contact area when more preload is applied, since the transmitted wave energy is proportional to the contact area. However, it is worth noting that this growth is not monotonic (for instance, the energy under case 2, 5, 7 and 8 is almost the same), and thus we may not expect the potential of signal energy to work as a damage index (DI), particularly, for multi-bolt looseness detection.
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F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507
Fig. 7. Received signals and signal energy under different cases.
Prior investigation [49] has demonstrated that s ¼ 20 has the best performance during the computation of the MMFE, since overlarge s will induce calculating redundancy (additionally, the MMFE values remain almost unchanged when s is larger than 20), while too small s cannot reveal the characteristics of the signals adequately. Therefore, in this paper, the MMFE algorithm (with scale factor s ¼ 20) was used to analyze received signals to develop new DI that replaces the current indicator (i.e., signal energy), and results were shown in Fig. 8. Then, to demonstrate the robustness of the MMFE, each case in Fig. 8 consists of five testing results, and we can observe that the MMFE curves are almost consistent, which means that the MMFE is not affected by environmental conditions and thus suitable for on-line monitoring. The only exception is the case 1, and this phenomenon may be attributed to the reason that all bolts are loosening in this case, thus existing lowfrequency vibration of the connection due to the incentive effect of PZT patch. This vibration can induce severe nonlinearity of the received signals, which can be characterized by the entropy, and thus the results are much less consistent for case 1. Overall, the MMFE values tend to decrease when bolt loose, and this can be explained by the phenomenon of the contact
Fig. 8. MMFE values of received signals under different cases.
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F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507
acoustic nonlinearity (CAN) [64]. Due to the interfacial asperities, the bolted interface presents nonlinear features when stress waves traverse through the contact interface. With bolt preload decreases, the deformation of asperities eases, namely, the gap between two contact surfaces enlarges. Subsequently, the nonlinearity of received wave signal will increase and be reflected in entropy values, since entropy can estimate the complexity (i.e., nonlinearity) of signals. However, we should admit that the differences amongst cases with the same number of loose bolts are not obvious, for instance, cases 2/3/4 or cases 5/6/7. To enhance performance of the MMFE for loosening detection of the multi-bolt connection, we applied the mRMR method to select the first four significant features to reconstruct the new feature sets, which can be employed as input for next step, i.e., looseness identification through GA-LSSVM. In this paper, the determined feature sets with the most significance are s ¼ 17; 4; 20; 13. Additionally, to demonstrate the effectiveness of the mRMR method, we plotted the first three elements (i.e., s ¼ 17; 4; 20) of the new feature sets and compared them with feature sets that were randomly selected (e.g., s ¼ 1; 2; 3), as depicted in Fig. 9. It can be seen that all samples in the new feature sets cluster around their corresponding class centers and there was obvious distinction among eight cases. On the contrary, some samples in the randomly selected feature sets scatter from their class center, and there is no an obvious boundary amongst eight cases. Subsequently, a GA-based LSSVM classifier was trained by using input dataset matrix T j and the label matrix Lj , which take the following forms,
Fig. 9. Comparison between new feature sets and initial feature sets (left
s ¼ 17; 4; 20 right s ¼ 1; 2; 3).
Table 3 Classification accuracy of different methods. Method
The proposed method MMFE without mRMR Energy-based DI
Optimized model parameters
Accuracy (%)
c
r
Max
Min
Mean
20.8233 5.6794 12.5637
1.1355 0.9929 0.0448
90.44 83.34 66.11
88.33 80.20 60.58
89.39 81.65 63.06
2
Fig. 10. Comparison of classification accuracy for three methods.
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F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507
2
MMFEs¼17;1
6 MMFEs¼17;2 6 Tj ¼ 6 .. 6 4 . MMFEs¼17;i
MMFEs¼13;1
3
MMFEs¼4;1
MMFEs¼20;1
MMFEs¼4;2 .. .
MMFEs¼20;2 .. .
MMFEs¼13;2 7 7 7; .. 7 5 .
MMFEs¼4;i
MMFEs¼20;i
MMFEs¼13;i
2
l1
3
6l 7 6 27 7 Lj ¼ 6 6 .. 7 4.5
ð14Þ
li
where i ¼ 1; 2; ; 8 is the total number of cases, and j ¼ 1; 2; ; 20 is the number of training data sets. The regularization parameter c and the Kernel bandwidth parameter r2 are optimized through the GA algorithm under the maximum individual fitness (i.e., the best classification accuracy). Additionally, to demonstrate the advantage of the proposed method, the traditional energy-based DI and the MMFE features sets without the mRMR are also used to train the other two GA-based LSSVM models, and comparison results are given in Table 3. Meanwhile, 20 repeated training was conducted to avoid the randomness, as depicted in Fig. 10. It can be seen that the proposed method has the best classification accuracy (about
Fig. 11. Received signals with corresponding MMFE values under different cases.
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F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507
88.33–90.44%), which demonstrates its superiority. On the other hand, the MMFE without the mRMR has the moderate classification accuracy (about 80.20–83.34%), and the traditional energy-based DI has the lowest classification accuracy (about 60.58–66.11%). This phenomenon can be explain through three main reasons: (1) as discussed above, the received signal energy does not increase monotonically, i.e., the energy-based DI may be almost the same under some cases, which causes great difficulty in classification; (2) the stress waves presents nonlinear features when they traverse the contact interface, the MMFE that can quantify this nonlinearity outperforms the energy-based DI, since prior investigations have demonstrated that nonlinear features are more sensitive to linear counterpart (namely, signal energy); (3) due to the effectiveness of the mRMR method in selecting significant features with maximum relevance and min redundancy, the proposed method has better performance than the MMFE without mRMR. In addition, for the specimen with four bolts, we can obtain similar results. First, the received time-series signals and corresponding MMFE values (scale factor s ¼ 20) under different cases are illustrated in Fig. 11. We can see that the received signal energy has no obvious relationship with bolt preloads, while the MMFE values under different cases still present good consistency. The reasons of these phenomena have been discussed earlier. Then, after selecting the first four significant features through the mRMR, we can determine that the feature sets for this specimen are s ¼ 1; 17; 16; 4 and plot the first three elements (i.e., s ¼ 1; 17; 16) of the new feature sets to compare them with random feature sets (e.g., s ¼ 1; 2; 3), as depicted in Fig. 12. Using the GA, we can obtain the optimized regularization parameter c and the Kernel bandwidth parameter r2 , and then achieve the classification of different cases (i.e., multiple bolt loosening) through the LSSVM. To avoid randomness, we repeated the training and testing twenty times, and the results were given in Table 4 and depicted in Fig. 13. The proposed method proves its advantages, since it has better performance (95.14–98.55%) than the DI through the MMFE without the mRMR (85.93–89.10%) and the traditional energy-based DI (79.19–82.71%). It is worth noting that different bolted connections with various boundary conditions, size, and ages may cause different orders of s and various c and r2 , while it is acceptable for us to develop a data-base to address this issue. In other words, regarding different bolted connections with specific boundary conditions, size, and ages, we can apply trial-and-error or optimization to determine these uncertain parameters and import them into a data-base for real industrial application in the future. Finally, to demonstrate our statement, namely the insensitivity of the propose method to the environmental conditions such as temperatures, the authors repeated experiments on two specimens in a wide range of temperatures. As depicted in Fig. 14, a hair dryer was used to provide different temperatures, and an electronic thermometer (testo Quicktemp 825-T4) was employed to measure environmental temperatures. The comparison of classification results (mean accuracy %) among three methods under different temperatures are given in Table 5, and we can find that the classification accuracy remains almost unchanged, which indicates that the proposed method and even ultrasonic-based methods are insensitive to environmental temperatures.
Fig. 12. Comparison between new feature sets and initial feature sets (left
s ¼ 1; 17; 16 right s ¼ 1; 2; 3).
Table 4 Classification accuracy among three methods. Method
The proposed method MMFE without mRMR Energy-based DI
Optimized model parameters
Accuracy (%)
c
r2
Max
Min
Mean
5.2740 1.0089 3.4237
0.8021 0.0038 1.0354
98.55 89.10 82.71
95.14 85.93 79.19
96.69 87.49 81.44
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F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507
Fig. 13. Comparison of classification accuracy among three methods.
Fig. 14. Experimental apparatus for different temperatures.
Table 5 Comparison of classification results (mean accuracy %) among three methods under different temperatures. Method
Three-bolt connection
The proposed method MMFE without mRMR Energy-based DI
Four-bolt connection
25 1 C
35 1 C
45 1 C
25 1 C
35 1 C
45 1 C
89.39 81.65 63.06
88.72 83.16 64.11
88.30 82.56 61.98
96.69 87.49 81.44
95.43 85.36 80.78
97.39 87.16 82.63
5. Conclusions In this paper, by using the multivariate multiscale fuzzy entropy (MMFE), a new damage index was proposed for the PZTenabled active sensing method. Then, with the help of the max relevance and min redundancy (mRMR) and the genetic algorithm-based least square support vector machine (GA-based LSSVM), the improved active sensing method was employed to detect looseness of the multi-bolt connection. The experimental results demonstrated that the proposed method could effectively identify bolt looseness. The main contributions of this paper are summarized as follows: (1) the active sensing method was first applied to detect integrity status of the multi-bolt connection; (2) the MMFE was employed to develop a new DI for the active sensing method, and its superiority over current DI (i.e., signal energy) was verified; (3) the mRMR was introduced to choose significant features from the MMFE-based DI and thus enhance performance of classification. However, it is worth noting that only binary status (namely, loosening or not) of each bolt is considered in this preliminary investigation. In further studies, more advanced DIs and methods will be proposed to solve this issue and provide higher classification accuracy, which can guide further investigations on bolt loosening detection.
F. Wang et al. / Mechanical Systems and Signal Processing 136 (2020) 106507
13
Acknowledgement This research was partially supported by the China Scholarship Council (No. 201706060203), their financial support is appreciated.
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