IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 4, APRIL 2014
923
Smooth Nonnegative Matrix Factorization for Defect Detection Using Microwave Nondestructive Testing and Evaluation Bin Gao, Member, IEEE, Hong Zhang, Student Member, IEEE, Wai Lok Woo, Senior Member, IEEE, Gui Yun Tian, Senior Member, IEEE, Libing Bai, and Aijun Yin, Member, IEEE Abstract— This paper addresses the interpolation issue of current spectral estimation methods in microwave-based nondestructive testing and evaluation. We developed a spatialfrequency feature extraction algorithm for defect detection with an open-ended waveguide system using smooth Itakura-Saito nonnegative matrix factorization. In addition, the mathematical models of spatial-frequency characteristics for both defects and nondefects areas are derived. The newly developed algorithm has two prominent characteristics, which benefit the detection system. First, it is scale-invariant in the sense that spatialfrequency features that are characterized by large dynamic range of energy can be extracted more efficiently. Second, it imposes smoothness constraint on the solution to enhance the spatial resolution of defect detection. To evaluate the proposed technique, we demonstrate the efficacy of the proposed method by performing extensive experiments on four samples: four defects in an aluminum plate with different depths, a steel plate with 15-mm coating thickness, one tiny defect on steel and one natural defect. Experimental results have unanimously demonstrated the capabilities of the proposed technique in accurately detecting defects, especially for shallow and coated samples with high resolution. Index Terms— Defect detection, nondestructive testing and evaluation (NDT&E), nonnegative matrix factorization, openended waveguide, smoothness, source separation.
I. I NTRODUCTION ONDESTRUCTIVE testing and evaluation (NDT&E) for defects detection is the science and practice of evaluating material properties variation without compromising its utility.
N
Manuscript received April 29, 2013; revised September 10, 2013; accepted September 17, 2013. Date of publication November 20, 2013; date of current version March 6, 2014. This work was supported in part by the National Natural Science Foundation of China under Grant 51105396 and Grant 51377015 and in part by International Paint, and partially funded by Sichuan Science and Technology Department (Grant No. 2013HH0059). The Associate Editor coordinating the review process was Dr. Sergey Kharkovsky. B. Gao and H. Zhang have contributed equally to this work. B. Gao and L. Bai are with the School of Automation Engineering, University of Electronic Science and Technology of China, Sichuan 611731, China (e-mail:
[email protected]). H. Zhang and W. L. Woo are with the School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. G. Y. Tian is with the with the School of Automation Engineering, University of Electronic Science and Technology of China, Sichuan 611731, China, and also with the School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. A. Yin is with the School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K., and also with The State Key Laboratory of Mechanical Transmission; College of Mechanical Engineering, Chongqing University, Chongqing 400044, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2013.2287126
The demands for NDT&E methods are required for lowcost, noncontact, fast detection, and imaging of even small defects [1]. There are many well established and standard NDT&E methods available such as ultrasonic [2], [3], eddy current [4], [5], magnetic method [6], radiography [7], pulse eddy current [8] and thermography based NDT [9] etc. Micro or millimeter frequency signals can penetrate lowloss dielectric coating materials to inspect the surface of target metal. Such advantages include the fact that these methods are noncontact, one-sided, do not require a couplant to transmit the signal into the material under test, and enable images to be obtained with high spatial resolutions in the near-field [10], [11]. Therefore, the microwave and millimeter-wave-based NDT techniques have already been widely used [12], and have achieved good performance. Such techniques include: openended waveguide [13], [14], coaxial probes [15], subsurface sensing, and thickness evaluation of dielectric slabs [16]. The potential of using microwave NDT for defect detection has also been demonstrated [17]. In addition, measurement parameters such as frequency, bandwidth, polarization, phase, and magnitude information (coherent properties) and probe properties can be optimized for a particular application [18], [19]. From a signal processing point of view, many works have already been performed for spectral estimation and image reconstruction including, but not limited to Fourier-based, correlation-based, and superresolution methods [20]. In the literature, spectral estimation or image reconstruction for samples under test has been limited to interpolation [21] in Fourier-based methods [22], and the inverse fast Fourier transform [23]. Furthermore, these methods only manually or use some criteria to select specific frequency band for analysis of defect, therefore, it lacks of deeply mining the informative from the whole frequency band. The proposed method bypasses the above problems. We estimate the spectral basis for both defect and nondefect areas. These are obtained globally across the whole X-band frequency range and therefore avoid the interpolation issue faced by conventional spectral estimation methods. In addition, we separate the power spatial-frequency spectrum (PSS) and reconstruct the defect and nondefect areas individually. Therefore, the proposed method enhances the overall image resolution. This paper presents the design and experimental testing of an open-ended waveguide operating in the X-band for defect detection. We have proposed an efficient nonnegative matrix factorization (NMF) algorithm to analyse the frequency
0018-9456 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
924
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 4, APRIL 2014
spectrum characteristics of the reflected signal between the defect and nondefect areas. In addition, the mathematical bridge to model both defects and nondefects characteristics in PSS domain is given. The smooth Itakura-Saito NMF (SISNMF) has the unique property of scale-invariant whereby the lower energy components in the PSS domain can be treated with equal importance as the higher energy components. This property is highly desirable since it enables the spatialfrequency components with low energy to be estimated with significantly higher accuracy than other cost functions such as least square (LS) distance and Kullback–Leibler divergence [24], which only favor the high-energy components but neglect the low-energy components. In addition, the smoothness constraint is imposed to effectively extract the spatial-frequency features, which enhance the performance of defect detection. Guided by this analysis and other empirical design equations, a microwave scanning system was designed for good sensitivity, penetration depth, and spatial resolution in the evaluation of test samples. This paper is organized as follows. Section II describes the mathematical bridge generation between the physical parameter characteristics and source separation model. In addition, the proposed detection method based on S-ISNMF is demonstrated. The experimental setup is given in Section III. Measurement results and discussion of the proposed method and comparison with other matrix factorization methods is presented in Section IV. Finally, Section V concludes this paper. II. B RIDGING THE G AP B ETWEEN M ATHEMATICAL AND P HYSICAL M ODELS A. Microwave NDT The problem of transmission and reflection of microwaves in a multilayer dielectric medium has been investigated by many researchers [25]. An incident signal is transmitted into the layered medium (coating and steel layers) and once reflected by the conducting plate, the magnitude and phase difference between the reflection coefficients for coating samples becomes related to the thickness and the permittivity (ε) of the sample under test. The lift-off here is known as air layer thickness, which is the distance between the waveguide and sample surface. Specifically, there should be a small air gap (noncontact) between the probe and the sample surface (which is termed as lift-off) to have a smooth, simple movement of the waveguide. Calculation of the effective reflection coefficient for metal defect detection involves the derivation of the forward and backward travelling electric and magnetic field components based on a known incident field and the application of appropriate boundary conditions. The broad and narrow transverse dimensions of the waveguide are represented by a and b. Hence, for TE10 mode, the incident wave whose electric and magnetic fields are given by [26] π x − jβ1 z e (1) E iy = sin a −1 π x − jβ1 z e Hxi = sin (2) η1 a
where β1 = k02 − (π/a)2 , k0 = 2π/λ0 , η1 = k0 η0 /β1 , and √ η0 = μ0 /ε0 and where λ0 , k0 , η0 , and μ0 are the freespace wavelength, wavenumber, permittivity, and permeability, respectively. η0 and η1 are the free-space and waveguide intrinsic impedances, respectively. The reflected wave in the waveguide, due to the defect, is given by π x jβ1z e a π x jβ1z sin e a
E ry = A10 sin Hxr =
A10 η1
(3) (4)
where A10 is the unknown coefficients to be determined. The complete set of solutions for the field components for nearfield open-ended waveguide NDT is constructed in [27]. The complex reflection coefficient is given by =
E ry E iy
(5)
where E ry is the electric field strength of the reflected wave and E iy denotes the electric field strength the incident wave. It is clear that the reflection coefficient is different when the defect is present (as when there is no defect, the incident wave will be totally reflected). Thus, this difference can be used for defect detection. Macroscopically, when there is a defect under these coated metal samples, they exhibit surface discontinuities. Because of the difference of the natural physical properties, these discontinuities affect through the microwave changes in attenuation or absorption in metal. In principle, the reflected signals are more pronounced from abrupt, large changes in material properties. Small continuous changes create little or no variation. These reflected signals can then be detected and the defect information (such as size and location, etc.) can be deduced from these signals [28]. For test samples without coating layer, the model can simply consider the coating layer as the air layer. This model benefits from simplicity since the attenuation from coating layer will not apply. B. Mathematical Spatial-Frequency Mixing Modeling Section II-A refers to the case where there are differences in the reflected frequency spectrum between the nondefect and defect areas. Once the raster-like relative motion of waveguide probe scans the area of the surface, the scan area may contains both nondefect and defect parts, thus, this process can be considered as a mixing spatial-frequency spectrum which can be visualized as follows. The visualized entity of Fig. 1 can be considered as a tensor representation of mixing spatial-frequency spectrum observation Y, which is the combination of nondefect and defect spatial-frequency spectrum, respectively Figure 2 shows the mathematic explanation of tensor observation. In Y, the frequencies are given by f = 1, 2, . . . , F and F represents the total frequency units. The tensor observation can be unfolded in matrix format as Y = [vec(Y(1)), vec(Y(2)), . . . , vec(Y(F))]T , where Y( f ) denotes the spatial-frequency spectrum matrix with dimensional Nx × N y of the f th slice of Y. Subsequently, the
GAO et al.: SMOOTH NONNEGATIVE MATRIX FACTORIZATION
Fig. 1.
925
Fig. 2. (a) Tensor representation of the image sequences Y. (b) f th frame of Y. (c) Visual explanation of vec(Y( f ))T .
Microwave NDT C-scan progress.
mixing spatial-frequency spectrum observation at each spatialfrequency point becomes Y ( f, s) = X ndefect ( f, s) + X defect ( f, s)
(6)
where Y ( f, s) is the mixed spatial-frequency spectrum components and X i ( f, s) denotes the source (nondefect or defect) spatial-frequency spectrum component, which can be obtained by applying Fourier transform. Here, the space slots are given by s = 1, 2, . . . , S, where S = Nx × N y . Note that in (6), each component is a function of s and f . The PSS is defined as the squared magnitude of (5) Y ( f, s)2 ≈ X ndefect ( f, s)2 + X defect ( f, s)2 (7) where |X i ( f, s)| and |X j ( f, s)| are assumed nonoverlaping are assumed to be each other. Thus, a matrix representation of (7) considering the residual noise to be small, this gives .2 ndefect 2 defect 2 + X Y ≈ X (8) where
.2 Y = Y ( f, s)2 f =1,2,...,F s=1,2,...,S 2 f =1,2,...,F ndefect 2 ndefect X = X ( f, s) s=1,2,...,S defect 2 X = X defect ( f, s)2 f =1,2,...,F s=1,2,...,S
are 2-D matrices (row and column vectors represent the spatial slots and frequencies, respectively), which denotes the PSS representation of (6) and the superscript “·” is an elementwise operation. The identification of the spatial-frequency characteristics of nondefect and defect given by observation |Y |.2 can be considered as matrix factorization problem. This is a commonly used technique in understanding the latent structure of the observed data. There are many forms of matrix factorization and to name a few, these are principal component analysis (PCA), independent component analysis (ICA) [29], and NMF [30]. Comparing with PCA and ICA, NMF gives a part-based decomposition and is unique under certain conditions making it unnecessary to impose the constraints in the form of orthogonality and statistical independence. It also gives physical meaning when factorizing the power spectrum data. Given the mixing power spectrogram of |Y |.2 , NMF
factorizes this matrix into a product of two nonnegative matrices as .2 Y ≈ DH (9) K × , H ∈ ×L with K and L representing the where D ∈ + + total number of rows and columns in matrix Y, respectively. The matrix D can be compressed and reduced to its integral components such that it contains a set of basis, and H is a activation code matrix, which its element describes the amplitude of each basis at each time (or space) point. Later, Lee and Seung [31] developed the multiplicative update (MU) algorithm to solve the NMF optimization problem based on the LS distance and KLD. Other families of parameterized cost functions such as the beta divergence has also been presented.
C. Smooth Itakura-Saito (IS) Divergence-Based NMF Method 1) Relation Between Itakura-Saito and β Divergence: The β-divergence was introduced in [32], which is defined as ⎧
β
1 ⎪ a + (β −1)bβ −βabβ−1 β ∈ \ 0, 1 ⎨ β(β−1)
dβ (a|b) = a log a − log b + b − a β = 1 ⎪ ⎩a a b − log b − 1β = 0 (10) The term β is defined as the divergence choice, which has been used for optimization of NMF. It is interesting to note that for β = 2, we obtain the Euclidean distance expressed by Frobenius norm and for β = 1 the generalized KLD is defined. For β = 0, this results in the IS divergence. As noted in [32], a noteworthy property of the β-divergence is its behavior with to respect to scale, as the following equation holds for any value of β : (11) dβ (γ a|γ b) = γ β dβ (a|b) It implies that factorizations obtained with β > 0 (such as with the Euclidean distance or the KL divergence) will rely more heavily on the largest data values and less precision is to be expected in the estimation of the low-power components, i.e., dLS (γ a|γ b) = γ 2 dLS (a|b) and dKL (γ a|γ b) = γ dKL (a|b). For the case of β = 0, this results in the IS divergence which is scale invariant, i.e., dIS (γ a|γ b) = dIS (a|b) and is the only one in the family of β-divergences to possess this property.
926
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 4, APRIL 2014
TABLE I S MOOTH ISNMF
The IS divergence [33] was mainly used as a measure of the goodness of fit between the two spectra and has proven to be quite efficient especially in terms of obtaining the good perceptual properties of the reconstructed sources. Recently, IS divergence has picked up renewed interest in NMF. The IS divergence leads to desirable statistical interpretations of the NMF problem [34]. Most significantly, NMF with IS divergence can provide scale invariant property, which enables low energy components of |Y |.2 to bear the same relative importance as high energy ones. This is relevant to situations in which the coefficients of |Y |.2 have a large dynamic range such as in short-term spectra. This property, in particular, can effectively separate the mixture and will be detailed in Section IV-B. 2) Majorization-Minimization (MM) Algorithm for Smooth IS Divergence: The un-penalized IS divergence NMF algorithm is based on surrogate auxiliary functions (local majorizations of the cost function). The MM algorithm can be derived by optimizing these auxiliary functions, which result in efficient MUs. The monotonicity of the cost function can be proven by leveraging on techniques in [35]. For conve
nient, we define v f,s = |Y |.2f,s , v f,s = [DH] f,s , z f,s =
−2
−1 th f d f,i v f,s v f,ts , and q f,s = f d f,i v f,s . d f,i is the ( f, i ) element of D. The form of the auxiliary function for IS divergence is [36]. The smoothness constraint is encoded in the form of Markov chains, namely p (H) =
Ns S
p h i,s h i,(s−1) p h i,1
(12)
i=1 s=2
where the Markov kernel p(h i,s |h i,(s−1) ) is a probability density function defined on the nonnegative orthant, with mode at h i,(s−1) and the specific update steps are summarized in Table I. III. E XPERIMENTAL S ETUP The experimental setup is shown in Fig. 3. An X-band (from 8.2 to 12.4 GHz) open-ended rectangular waveguide is mounted with an X–Y scanner. The probe is a standard WR-90 waveguide with the aperture dimensions of 22.86 × 10.16 mm (a × b). The sample under test is placed under the waveguide with a certain lift-off. This lift-off is set as 1.5 mm. A vector network analyser (Agilent PNA E8363B) is employed here to provide signal source and obtain the frequency spectrum information of the reflected signal. The waveguide is connected with the vector network analyser through a coaxial cable. A control PC here is used to control and acquire the measurement data from the vector network analyser through IEEE-488 general purpose interface bus (GPIB). The X–Y scanner is controlled by X–Y scanner controller. This controller is connected with the parallel port of the control PC. A MATLAB program is designed and used to control vector network analyser and X–Y scanner. During the measurement, the frequency range is set from 8.2 to 12.4 GHz. A linear sweep is applied over this frequency range (frequency resolution is ∼0.02 GHz with 201 linear swept points). This whole reflected frequency spectrum is
Fig. 3.
Open-ended waveguide system experiment setup.
obtained using linear sweep frequency technology with vector network analyser. Four test samples are described from Tables II–Table IV. Fig. 4 shows the experimental architecture of the microwave detection system based on waveguide probe (a is broad dimension of the open-ended rectangular waveguide aperture, b is narrow dimension of the open-ended rectangular waveguide aperture, W is defect width, and L is the defect length). To reduce the influence from the long leads before measurement, an Agilent E-Cal unit is used to calibrate our waveguide system. The E-Cal modules are transfer standards capable of transferring the factory calibration accuracy to the network analyzer. They are characterized by Agilent using
GAO et al.: SMOOTH NONNEGATIVE MATRIX FACTORIZATION
927
TABLE II PARAMETERS S ETTING FOR M ICROWAVE NDT (A LUMINUM AND T INY C RACK S TEEL )
Fig. 4.
Schematic of the aluminum sample and probe scanning direction.
TABLE III PARAMETERS S ETTING FOR M ICROWAVE NDT (S TEEL W ITH H OLE )
Fig. 5. Schematic of the steel sample with 19-mm diameter hole (left) and coating layer (right). TABLE IV PARAMETERS S ETTING FOR M ICROWAVE N ATURAL S TEEL (NDT)
a precision calibration technique (similar in accuracy to TRL) that is traceable to the National Institute of Standards and Technology. Each calibration module’s unique S-parameter data is stored in the module’s memory. During calibration, ECal uses this data to calculate the error terms for the network analyzer. For this aluminum sample, line-scanning is performed with the same lift-off. For the coated steel testing, one steel sample (300-mm length, 300-mm width, and 10-mm thickness) with man-made defects was measured with our proposed Microwave NDT measurement system. Fig. 5 shows one steel sample with a 19-mm diameter hole. To verify our proposed method, one tiny defect (0.45-mm width and 0.43-mm depth) on a steel bar (Fig. 6) and two natural defects with corrosion and small defects (Fig. 7) on pipline have been measured.
Fig. 6.
One tiny defect under measurement.
Fig. 7.
Schematic of the steel sample with two natural defects.
IV. R ESULTS AND D ISCUSSION The S-ISNMF for the NDE application was tested by evaluating its ability to extract the spectral basis and activation spatial basis for both defect and nondefect areas for an aluminum sample with four defects (for location and width estimation) and coated steel samples with a hole (for location and shape estimation).
928
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 4, APRIL 2014
Fig. 8. Reflection PSS of line-scan aluminum sample under test with 1.5-mm lift-off (bottom).
Fig. 9. Simulation for aluminum sample with four different depth cracks and the magnitude results of reflected coefficients and the selected frequency point for defects under different depth situation.
Fig. 10. Experimental detection results by selecting frequency spectrum according the simulation results for different depth of defect.
Fig. 11. IS-NMF estimation results of an aluminum sample with four defects of 1.5-mm lift-off. (a) Spectral basis of the nondefect area. (b) Spectral basis of the defect area. (c) Activation basis of the nondefect area. (d) Activation basis of the defect area.
A. Aluminum Sample Under Test 1) Estimation of Spectral and Activation Spatial Information: As it can be observed from Fig. 8, several abnormal are present due to the differences of spatial-frequency spectrum characteristic between the nondefect and defect areas. However, it is difficult to clearly display the shallow defect (as marked by the red dotted box) as well as measuring the widths of defects. This indicates that the reflection spectrum is unable to provide specific measurements as to: 1) the differences of the frequency spectrum characteristic between the nondefect and defect areas and 2) how to precisely locate and estimate the width of the defect areas (especially for low depth defects). To validate the proposed method, the CST Microwave Studio 2012 software is employed to simulate the attenuation of reflection coefficient. We have used the standard method [37] to manually select one frequency (whose magnitude attenuation decrease the lowest, which marked by rectangular box) and compare it with the proposed method. Fig. 9 shows the simulation result of the magnitude of reflected coefficients for both nondefect and defect situations. As observed in Figs. 9 and 10, if only specific frequency spectrum has been selected for defect detection, it lacks the ability to mine the whole band information such as the worse detection results (none of the selected frequency spectrum can display the detection of all defects). This is clearly shown in the plot where each frequency spectrum fails to detect one
or two depth defects as marked with red box. By applying S-ISNMF algorithm, it is now possible to find the solutions for above issues. Fig. 11 shows the S-ISNMF factorization results. NMF factorizes the observation matrix into a product of basis matrix and activation matrix, where the observation matrix is obtained by scanning the whole testing sample, which consist of both defect and nondefect areas. This is revealed by Fig. 11 shows the factorization results. Here, we use the basis matrix to characterize the defect and nondefect spectral basis. Fig. 11 left panels, and activation matrix Fig. 11 right panels to estimate the defect location, width and inference of depth information. Fig. 11 right panels are the factorized activation matrices for the nondefect spectral basis matrices. As we can observe in the Fig. 11 right panels (top), when the activation peaks reduce in magnitude, this implies that the nondefect spectral basis matrix at that spatial position (this position actually refers to defect position) is not active. This is because the characteristics of the frequency spectral between the nondefect and defect areas are different. In other words, the activation peaks should increase in magnitude at the same position in Fig. 11 right panels (bottom) where activation peaks increase for the defect spectral basis matrix. It is observed that for all defects, the S-ISNMF has successfully estimated both the defects location as well as the
GAO et al.: SMOOTH NONNEGATIVE MATRIX FACTORIZATION
929
Fig. 13. Simulation for coated sample with 10-mm hole and the magnitude results of reflected coefficients and the selected frequency point for defect. Fig. 12. sample.
Difference of spectral basis between nondefect and defect of test
width from the mixing PSS (more analysis will be detailed in Section IV-D). Notwithstanding the above, it is worth pointing out that the estimated activation basis has indicated the trend of defects’ depth according to attenuation except the last one, which should be with the deepest depth. For the 2–6mm defects, the trend of depth information can be predicted with the proposed method. For 8-mm depth defect, it is still detectable. However, the peak of trend for 8-mm depth is shorter than 6-mm depth. The reason the 8-mm depth defect attenuates less than the 6-mm depth defect can be attributed to the 8-mm depth being too deep and is beyond the system range (8.20–12.40 GHz). Therefore, the microwave signal is unable to correctly predict the 8-mm defect depth as the attenuation of the reflected signal decreases shorter than that of the 6-mm depth defect. This has been confirmed and clearly indicated by the proposed algorithm. 2) Spectral Analysis Between the Nondefect and Defect Areas: Once the estimation of spectral basis for both nondefect and defect areas are obtained, one can measure the degree of differences of the spectral basis between these two areas. Fig. 11 show the estimated spectral basis results and it implies that any defect will scatter and change the reflection of energy through the material [38] due to the irregularity of defects compare with sound area. Therefore, this potential can be used to automatically identify defect and nondefect areas using their difference characteristic of spectral basis. To efficiently quantify the differences between the nondefect and the defect spectral basis, the relative two norm is employed [39]. The formula of relative two norm is given 2 F defect − D Dndefect f f R2 -norm =
f =1
2 F Dndefect f
× 100%.
(13)
f =1
In (13), to obtain fairly comparison, all elements in vector Dndefect and Ddefect are scaled within the range between 0 and 1. This can be implemented as (Dndefect− min(Dndefect )/max(Dndefect ) − min(Dndefect )) and (Ddefect − min(Ddefect )/max(Ddefect ) − min(Ddefect )) where min(•) and
max(•) calculate the minima and maxima value of the vecis the component from the nontor, respectively. Dndefect f is the component from the defect spectral basis and Ddefect f defect spectral basis that are obtained using IS-NMF method. ndefect − Ddefect )2 of the Fig. 10 shows the difference (D f f spectral basis between the nondefect and defect areas. Because of the sample’s dimensions, discontinuity, separation, and contrast in properties of defects, this results in the characteristics difference between the defect and the nondefect areas [40]. From Fig. 10, the differences between the nondefect and the defect spectral basis are Roverall 52% denotes the results calculated using all frequency elements, namely f = 1, . . . , F. the amplitude of defect spectral component is sharply decreasing since the 9.5 GHz. Thus, we further divide both the nondefect and defect spectral basis into two frequency blocks and then calculate R≤9.5 GHz and R>9.5 GHz . The term R≤9.5 GHz denotes the results calculated using frequency elements which are below 9.5 GHz, namely f = 8.2 GHz, . . . , 9.5 GHz and R>9.5 GHz denotes the results calculated using frequency elements beyond 9.5 GHz, frequency bins, namely f = 9.5 GHz, . . . , 12, 4 GHz, respectively. The lower frequency region R≤9.5 GHz gives only a small level of R-2norm with averaged 8% while the higher frequency region R>9.5 GHz shows a much larger difference with 82%. This implies that the amounts of differences of spectral basis between the nondefect and the defect areas are significantly higher in the higher frequency region and this will undoubtedly enhance identification rate of defect area by just comparing the higher frequency parts of spectral basis between the nondefect and defect areas. B. C-Scan for Coated Sample Under Test 1) Estimation of Spectral and Activation Spatial Information: For coated sample the simulation results are given in Fig. 13. Fig. 14 shows the testing results for the coated sample with operation frequencies by manual selection. As can be observed with selected operation frequency, the location and shape of the defect area is difficult to be identified. Fig. 15 shows examples of the factorization results about test realizations by sweeping all operation frequencies (from
930
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 4, APRIL 2014
Fig. 14. Experimental detection results by selecting frequency spectrum according the simulation results for coated defect. Fig. 17. Estimation results of activation spatial (aluminum sample) using the different NMF algorithms.
Fig. 15. IS-NMF estimation results of coated steel sample with hole. (a) Spectral basis of the nondefect area. (b) Spectral basis of the defect area. (c) Activation basisof the nondefect area. (d) Activation basis of the defect area.
Fig. 18. Estimation results of activation spatial (coated steel sample) using the different NMF algorithms. (a) ISNMF. (b) KLNMF. (c) LSNMF.
28.7% and similar with the previous results. As shown in Fig. 12, the amplitude of defect spectral component is sharply decreasing from the 9.5 GHz point. C. Discuss the Impact of IS Divergence
Fig. 16. sample.
Difference of spectral basis between nondefect and defect of test
8.2 to 12.4 GHz). When compared with the manually selected results, it is observed that the S-ISNMF has successfully estimated both the location and shape of the defect from the coated test sample. Fig. 16 shows the difference (Dnondefect − Ddefect )2 of the spectral basis between the f f nondefect and the defect areas. In the overall, the differences between the nondefect and the defect spectral basis are Roverall
In the following, experiments are conducted to evaluate the efficiency of the NMF algorithm under different cost functions. Here, we consider the IS divergency, LS distance and KL divergence. Figs. 17 and 18 shows how different cost functions have impacted the factorization performance. It is clearly observed that the both LS-NMF and KL-NMF algorithms fail to determine the correct activation spatial basis of each defect. The middle and bottom panels show a considerable level of mixing ambiguities, which have not been accurately resolved. On the other hand, the IS-NMF algorithm has successfully extracted all activation spatial with high accuracy. This is evidenced by the fact that the IS divergence holds a desirable property of scale invariant so that low energy components can be precisely estimated and they bear the same relative importance as the high energy ones. On the contrary, factorizations obtained with the LS distance and KL divergence tends to favor the high energy components at the expense of disregarding the low energy ones. In the mixing PSS, the dynamic range of the mixture signal can be considerably large such that the dominating source at a
GAO et al.: SMOOTH NONNEGATIVE MATRIX FACTORIZATION
Fig. 19. Comparison results between ISNMF and S-ISNMF for an aluminum test sample.
931
Fig. 20. Comparison results between ISNMF and S-ISNMF for the coated test sample.
particular spatial-frequency spectral unit can manifest either as low or high energy components. In addition, when either LS distance or KL divergence is used, clusters with low energy tend to be ignored in favor of the high energy ones. This leads to mixing ambiguities especially for low energy ones in which case when they are subsumed together leads to significant loss of spectral spatial information of the sources. D. Discussion on the Impact of Smoothness During the experiments, the setting for smoothness parameter of S-ISNMF is λ = 100 where the best image resolution for a defect can be obtained. The separation methods using ISNMF consider mixing power spectrum at each spatial point as an individual observation. However, this mixing power spectrum usually has a temporal structure along with spatial points, and the defect spectrum characteristics vary slowly as a function of spatial point. On the other hand, the noise signal will be removed due to their random spectrum characteristics. The following figures show the comparison results of estimating activation spatial between the ISNMF and the S-ISNMF. Fig. 19 compares the experimental data on defect width. The dotted line shows the actual defect width with X-band waveguide. When the scanning direction is normal to the defect lips, the probe observes a nonnormal reflection coefficient for a distance b + W (where b is the narrow dimension of the open-ended rectangular waveguide aperture, W is defect width), where the received signal is not constant. During the measurement, the scanning direction of waveguide is along the defect width, the obtained width (as the red dash line shown in the Fig. 19) of the defect is about b + W = 10.16 + 4 = 14.16 mm. It can be observed from Fig. 19, with S-ISNMF, the location of defect is much easier to obtain. In other words, the sensitivity of microwave system will increase with S-ISNMF compared with ISNMF. In addition, the 2-mm depth defect is very difficult to visually detect using ISNMF as marked with black dot circle. Similarly in testing coated steel sample with one hole defect, Fig. 20 shows the results obtained from the preliminary analysis of the coated steel sample. The defect can be obtained clearly using S-ISNMF. The black dotted line shows the actual defect area with around 19-mm diameter and the S-ISNMF
Fig. 21. Simulation for tiny defect and the magnitude results of reflected coefficients for both defect and nondefect situations across all frequency band.
estimates 23 mm with an accuracy of 82.6% (the K means clustering algorithm with setting K = 3 will be used to segment the defect area), with S-ISNMF and the defect area is easier to obtain. However, for ISNMF, the image resolution contains a high degree of noise and the defect area is too noisy to visualize and the K means clustering algorithm fail to segment the defect area. As the signal characteristics between the above two regions are totally different and that the defect region displays a stronger part-based property, the NMF [41] can successfully extract these characteristics and shows unique results. The task to separate different types of defect is significantly more difficult than just detecting the defect and the nondefect components. The uniqueness results in sizing and separating different types of cracks can be improved by introducing sparsity constraints [42], different cost function, and incorporating prior knowledge where this can be obtained using the simulation work to get prior knowledge of different types of crack. E. Discussion on the Impact of Detecting Tiny Defects In this section, the experiment focuses on the detection of a tiny defect (0.45-mm width and 0.43-mm depth), as shown in Fig. 6. Using the CST software, Fig. 21 shows the simulation results and the magnitude of reflected coefficients for both nondefect and defect situations.
932
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 4, APRIL 2014
Fig. 22. Measured PSS of tiny steel defect with 1.5-mm lift-off across all frequency bands.
Fig. 23. Comparison of detection results between the selected frequency method and the S-ISNMF when testing the tiny defect sample.
From Fig. 21, the magnitude results between the nondefect and defect situations are too similar. This is because the tiny defect is too small as the defect with dimension 0.45-mm width and 0.43-mm depth already touches the boundary of X-band waveguide detective range. We consider to use standard method where we manually select one frequency (whose magnitude attenuation decrease the lowest) and compare it with the proposed method. We first plot the scanned results of the real sample. In Fig. 22, there are no significant differences between the defect and nondefect areas (the defect area is highlighted by the red dotted line). We follow the standard method to choose 12.1 GHz (we cannot choose 12.114 GHz, because Xband from 8.2 to 12.4 GHz and the minimum gap between each band is 0.02 GHz). Fig. 23 shows the real experimental detection results by selecting frequency spectrum according to the above simulation results for the tiny defect and the detection results using the proposed method. Fig. 24 shows the defect detection results by manually selecting the original single frequency reflection signal based on simulation results and using the proposed method, respectively. There is a significant difference between manually selecting the spatial-frequency spectrum (12.1 GHz) and the estimated activation basis using the S-ISNMF. As can be observed, by manually selecting the spectrum, it is not feasible to find the abnormal pattern and hence the defect location is not detectable. On the other hand, because of the unique property of scale-invariant (whereby low energy components of PSS to bear the same relative importance as high energy ones) the proposed S-ISNMF algorithm is able to detect the
Fig. 24. Measurement results for natural defects. (a) Spectral basis of the non-defect area. (b) Spectral basis of the defect area. (c) Activation basis corresponding to the nondefect area. (d) Activation basis corresponding to the defect area.
abnormal pattern of tiny defect as marked with red color in the figure. In addition, these results clearly show that when the size of defect exceeds the waveguide aperture, the reflected signal only registers very tiny variation. The noise-like feature associated with the signal may cover these tiny variations due to the attenuation of long coaxial cable and the intemal noise of the PNA. As the defect begins to appear within the waveguide aperture, the amplitude experiences a rapid magnitude change in the reflection coefficient at the aperture. The same phenomenon occurs when the defect leaves the waveguide aperture. The resolution of waveguide system can be found from [43]: ρ ≈ λ/Dx,y L, where Dx,y denotes the length of the aperture in the corresponding direction, λ the wavelength, and L the distance between the object and aperture (lift-off). For X-band, with 12.4 GHz and 1.5-mm lift-off, 1.58 mm is the minimum size of defect can be obtained with this waveguide. F. Discussion on the Impact of Detecting Natural Defects As observed in Fig. 7, one steel unflat sample with two deep cracks with corrosion around as well as roughness (small defects and cracks) is used for testing. It can be observed from Fig. 25(d) that the area (dark color parts) of two deep cracks have been clearly detected. The area (red colored parts) around the two deep cracks is still a defect because it corresponds to the natural crack; in addition there are corrison, small cracks, and roughness due to the un-flated surface of the sample. In this sample, it is not feasible to carry our simulation, therefore, we can only manually choose four frequency spectrum [we use the maximum frequency minus the minmum frequency and divide by four to choose (12.4– 8.2)/4 = 1.05 the specific frequency for comparison. These gives 9, 10.1, 11.2, and 12.2 GHz, which already cover the low, middles and high frequency bands). The results are shown in Fig. 25. As can be observed in Fig. 25, for manually selected results, it is difficult to choose one result, which can fully determine the crack position. In addition, the corrosion as well as small defect parts is undetectable. However, using the proposed method, both deeper crack and normal defects are detected.
GAO et al.: SMOOTH NONNEGATIVE MATRIX FACTORIZATION
Fig. 25. Measurement results of using the selected frequency point for natural defects. (a) PSS of 9 GHz. (b) PSS of 10.1 GHz. (c) PSS of 11.2 GHz. (d) PSS of 12.2 GHz.
V. C ONCLUSION In this paper, a novel S-ISNMF-based microwave NDT system for defect detection is presented. This system uses an X-band rectangular waveguide with a vector network analyser for nondestructive testing and evaluation. The efficient spatialfrequency feature extraction algorithm for defect detection and analysis has been proposed using S-ISNMF method, which holds two desirable properties of scale invariant and smoothness constraint. In addition, this paper generates the mathematic bridge, which incorporates physical characteristics into a source separation model. The influence factors such as defect spectrum characteristics, width, and location have been studied and the proposed system has been verified using aluminum sample, coated steel sample, tiny crack, and natural cracks steel samples. These findings suggest that in general this method has the potential for the system to detect and analyse the characteristic of defects with given known host objects. Particularly, it has demonstrated that not only manmade defects but natural cracks can be detected and visualised using the proposed efficient spatial-frequency feature extraction algorithm. In further work, these studies can be used for unknown defects 2- and 3-D reconstruction and classification. Moreover, to increase the range of the applicability of the proposed approach, a further study needs to be considered to lift-off influence, asses defects under various thick coated metals and QNDE for multiple layered structure. ACKNOWLEDGMENT A. Yin would like to thank the Chinese Scholar Council (CSC) for allowing him to undertake one year of visiting study at Newcastle University and Y. He for assistance with the experimental studies during his visit. R EFERENCES [1] G. C. Giakos, L. Fraiwan, N. Patnekar, S. Sumrain, G. B. Mertzios, and S. Periyathamby, “A sensitive optical polarimetric imaging technique for surface defects detection of aircraft turbine engines,” IEEE Trans. Instrum. Meas., vol. 53, no. 1, pp. 216–222, Jan. 2004. [2] R. Ludwig and D. Roberti, “A nondestructive ultrasonic imaging system for detection of flaws in metal blocks,” IEEE Trans. Instrum. Meas., vol. 38, no. 1, pp. 113–118, Feb. 1989. [3] L. Bechou, D. Dallet, Y. Danto, P. Daponte, Y. Ousten, and S. Rapuano, “An improved method for automatic detection and location of defects in electronic components using scanning ultrasonic microscopy,” IEEE Trans. Instrum. Meas., vol. 52, no. 1, pp. 135–142, Feb. 2003.
933
[4] T. G. Yun, “Design and implementation of distributed measurement systems using fieldbus-based intelligent sensors,” IEEE Trans. Instrum. Meas., vol. 50, no. 5, pp. 1197–1202, Oct. 2001. [5] A. Bernieri, L. Ferrigno, M. Laracca, and M. Molinara, “Crack shape reconstruction in eddy current testing using machine learning systems for regression,” IEEE Trans. Instrum. Meas., vol. 57, no. 9, pp. 1958–1968, Sep. 2008. [6] G. Betta, L. Ferrigno, and M. Laracca, “GMR-based ECT instrument for detection and characterization of crack on a planar specimen: A handheld solution,” IEEE Trans. Instrum. Meas., vol. 61, no. 2, pp. 505–512, Feb. 2012. [7] B. Jin, N. Park, K. M. George, C. Minsu, and M. B. Yeary, “Modeling and analysis of soft-test/repair for CCD-based digital X-ray systems,” IEEE Trans. Instrum. Meas., vol. 52, no. 6, pp. 1713–1721, Dec. 2003. [8] D. Vasic, V. Bilas, and D. Ambrus, “Pulsed eddy-current nondestructive testing of ferromagnetic tubes,” IEEE Trans. Instrum. Meas., vol. 53, no. 4, pp. 1289–1294, Apr. 2004. [9] B. Gao, L. Bai, G. Y. Tian, W. L. Woo, and Y. Cheng, “Automatic defect identification of eddy current pulsed thermography using single channel blind source separation,” IEEE Trans. Instrum. Meas., IEEE Early Access Articles. [10] M. A. Abou-Khousa, S. Kharkovsky, and R. Zoughi, “Novel near-field millimeter-wave differential probe using a loaded modulated aperture,” IEEE Trans. Instrum. Meas., vol. 58, no. 5, pp. 1273–1282, May 2009. [11] M. T. Ghasr, D. Pommerenke, J. T. Case, A. McClanahan, A. Aflaki-Beni, M. Abou-Khousa, et al., “Rapid rotary scanner and portable coherent wideband Q-band transceiver for high-resolution millimeter-wave imaging applications,” IEEE Trans. Instrum. Meas., vol. 60, no. 1, pp. 186–197, Jan. 2011. [12] S. Kharkovsky and R. Zoughi, “Microwave and millimeter wave nondestructive testing and evaluation—Overview and recent advances,” IEEE Instrum. Meas. Mag., vol. 10, no. 2, pp. 26–38, Apr. 2007. [13] N. N. Qaddoumi, W. M. Saleh, and M. Abou-Khousa, “Innovative near-field microwave nondestructive testing of corroded metallic structures utilizing open-ended rectangular waveguide probes,” IEEE Trans. Instrum. Meas., vol. 56, no. 5, pp. 1961–1966, Oct. 2007. [14] G. D. Dester, E. J. Rothwell, and M. J. Havrilla, “Two-iris method for the electromagnetic characterization of conductor-backed absorbing materials using an open-ended waveguide probe,” IEEE Trans. Instrum. Meas., vol. 61, no. 4, pp. 1037–1044, Apr. 2012. [15] H. Maftooli, H. R. Karami, S. H. H. Sadeghi, and R. Moini, “Output signal prediction of an open-ended coaxial probe when scanning arbitrary-shape surface cracks in metals,” IEEE Trans. Instrum. Meas., vol. 61, no. 9, pp. 2384–2391, Sep. 2012. [16] M. T. Ghasr, D. Simms, and R. Zoughi, “Multimodal solution for a waveguide radiating into multilayered structures—Dielectric property and thickness evaluation,” IEEE Trans. Instrum. Meas., vol. 58, no. 5, pp. 1505–1513, May 2009. [17] C. Y. Yeh, and R. Zoughi, “Sizing technique for slots and surface cracks in metals,” Mater. Evaluat., vol. 53, no. 4, pp. 496–501, 1995. [18] A. M. Yadegari, R. Moini, S. H. H. Sadeghi, and F. Mazlumi, “Output signal prediction of an open-ended rectangular waveguide probe when scanning cracks at a non-zero lift-off,” NDT E Int., vol. 43, no. 1, pp. 1–7, Jan. 2010. [19] N. Qaddoumi, E. Ranu, J. D. McColskey, R. Mirshahi, and R. Zoughi, “Microwave detection of stress-induced fatigue cracks in steel and potential for crack opening determination,” Res. Nondestruct. Evaluat., vol. 12, no. 2, pp. 87–104, Jun. 2000. [20] S. Barbarossa, L. Marsili, and G. Mungari, “SAR super-resolution imaging by signal subspace projection techniques,” Archiv Elektron. Ubertragungstechnik, vol. 50, no. 2, pp. 133–138, 1996. [21] M. Craig, “Analytic signals for multivariate data,” Math. Geol., vol. 28, no. 3, pp. 315–329, Apr. 1996. [22] K. Gröchenig and T. Strohmer, “Numerical and theoretical aspects of nonuniform sampling of band-limited images,” in Nonuniform Sampling, F. Marvasti, Ed. New York, NY, USA: Springer-Verlag, 2001, pp. 283–324. [23] K. Abbasi, S. Ito, and H. Hashizume, “Prove the ability of microwave nondestructive method combined with signal processing to determine the position of a circumferential crack in pipes,” Int. J. Appl. Electromagn. Mech., vol. 28, no. 4, pp. 429–439, Dec. 2008. [24] R. Kompass, “A generalized divergence measure for nonnegative matrix factorization,” Neural Comput., vol. 19, no. 3, pp. 780–791, 2007. [25] R. Zoughi and S. Bakhtiari, “Microwave nondestructive detection and evaluation of disbonding and delamination in layered-dielectric slabs,” IEEE Trans. Instrum. Meas., vol. 39, no. 6, pp. 1059–1063, Dec. 1990.
934
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 4, APRIL 2014
[26] D. M. Pozar, Microwave Engineering, 4th ed. Hoboken, NJ, USA: Wiley, 2012. [27] Y. Chin-Yung and R. Zoughi, “A novel microwave method for detection of long surface cracks in metals,” IEEE Trans. Instrum. Meas., vol. 43, no. 5, pp. 719–725, Oct. 1994. [28] R. Zoughi and S. Kharkovsky, “Microwave and millimetre wave sensors for crack detection,” Fatigue Fract. Eng. Mater. Struct., vol. 31, no. 8, pp. 695–713, Aug. 2008. [29] B. Gao, W. L. Woo, and S. S. Dlay, “Single channel source separation using EMD-subband variable regularized sparse features,” IEEE Trans. Audio, Speech Lang. Process., vol. 19, no. 4, pp. 961–976, May 2011. [30] B. Gao, W. L. Woo, and S. S. Dlay, “Variational Bayesian regularized two-dimensional nonnegative matrix factorization,” IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 5, pp. 703–716, May 2012. [31] D. D. Lee and H. S. Seung, “Learning the parts of objects by nonnegative matrix factorization,” Nature, vol. 401, no. 6755, pp. 788–791, Oct. 1999. [32] C. Févotte, N. Bertin, and J. L. Durrieu, “Nonnegative matrix factorization with the Itakura-Saito divergence: With application to music analysis,” Neural Comput., vol. 21, no. 3, pp. 793–830, Feb. 2009. [33] F. Itakura and S. Saito, “Analysis-synthesis telephony based upon the maximum likelihood method,” in Proc. 6th Int. Congr. Acoustics, vol. 2. 1970, pp. 17–20. [34] B. Gao, W. L. Woo, and B. W.-K. Ling, “Machine learning source separation using maximum a posteriori nonnegative matrix factorization,” IEEE Trans. Cybern., 2013, to be published. [35] C. Févotte, “Majorization-minimization algorithm for smooth ItakuraSaito nonnegative matrix factorization,” in Proc. IEEE ICASSP, pp. 1980–1983, May 2011. [36] C. Févotte and J. Idier, “Algorithms for nonnegative matrix factorization with the β-divergence,” Neural Comput., vol. 23, no. 9, pp. 2421–2456, Mar. 2011. [37] C. Yeh and R. Zoughi, “Microwave detection of finite surface cracks in metals using rectangular waveguides,” Res. Nondestruct. Evaluat., vol. 6, no. 1, pp. 35–55, Jan. 1994. [38] N. Ida, Microwave NDT. Boston, MA, USA: Kluwer, 1992. [39] G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD, USA: The Johns Hopkins Univ. Press, 1996. [40] K. Belkebir, R. E. Kleinman, and C. Pichot, “Microwave imaginglocation and shape reconstruction from multifrequency scattering data,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 4, pp. 469–476, Apr. 1997. [41] H. Laurberg, M. G. Christensen, M. D. Plumbley, L. K. Hansen, and S. H. Jensen, “Theorems on positive data: On the uniqueness of NMF,” Comput. Intell. Neurosci., vol. 2008, pp. 1–9, Mar. 2008. [42] B. Gao, W. L. Woo, and S. S. Dlay, “Adaptive sparsity non-negative matrix factorization for single channel source separation,” IEEE J. Sel. Topics Signal Process., vol. 5, no. 5, pp. 989–1001, Sep. 2011. [43] S. S. Ahmed, A. Schiessl, F. Gumbmann, M. Tiebout, S. Methfessel, and L. Schmidt, “Advanced microwave imaging,” IEEE Microw. Mag., vol. 13, no. 6, pp. 26–43, Oct. 2012.
Hong Zhang (S’11) received the bachelor’s degree from joint program between Nanjing Normal University, Nanjing, China, and Northumbria University, Newcastle, U.K., in 2009, and the master’s degree in communication and signal processing from Newcastle University, Newcastle, U.K., in 2010. He is currently pursuing the Ph.D. degree with the School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne, U.K. His current research interests include electromagnetic nondestructive testing, digital signal process, and communication science and technology. Wai Lok Woo (SM’09) was born in Malaysia. He received the B.Eng. (Hons.) degree in electrical and electronics engineering and the Ph.D. degree in statistical signal processing from Newcastle University, Newcastle upon Tyne, U.K. He is currently a Senior Lecturer and the Director of operations with the School of Electrical and Electronic Engineering, Newcastle University. He has an extensive portfolio of relevant research supported by a variety of funding agencies. He has published over 250 papers on these topics on various journals and international conference proceedings. His current research interests include the mathematical theory and algorithms for nonlinear signal and image processing, machine learning for signal processing, blind source separation, multidimensional signal processing, signal/image deconvolution, and restoration. Dr. Woo is an Associate Editor of several international journals and has served as a Lead-Editor of journals’ special issues. He is a member of the Institution Engineering Technology. He received the IEE Prize and the British Scholarship. Gui Yun Tian (M’01–SM’03) received the B.Sc. degree in metrology and instrumentation and the M.Sc. degree in precision engineering from the University of Sichuan, Chengdu, China, in 1985 and 1988, respectively, and the Ph.D. degree from the University of Derby, Derby, U.K., in 1998. He was a Lecturer, Senior Lecturer, Reader, Professor, and the Head of the Group of Systems Engineering, University of Huddersfield, Huddersfield, U.K., from 2000 to 2006. Since 2007, he has been with Newcastle University, Newcastle upon Tyne, U.K., where he has been a Chair Professor of sensor technologies. Currently, he is with the School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, China. He has coordinated several research projects from the Engineering and Physical Sciences Research Council, Royal Academy of Engineering and FP7. On top of this, he also collaborates with leading industrial companies such as Airbus, Rolls Royce, BP, nPower, and TWI. Libing Bai received the B.S. degree from the University of Electronic Science and Technology of China, Chengdu, China, in 2008, where he is currently pursuing the Ph.D. degree. His current research interests include measurement and control technology and instrument.
Bin Gao (M’12) received the B.S. degree in communications and signal processing from Southwest Jiao Tong University, Chengdu, China, in 2005, the M.Sc. (Hons.) degree in communications and signal processing and the Ph.D. degree from Newcastle University, Newcastle, U.K., in 2011. He was a Research Associate with Newcastle University from 2011 to 2013 on wearable acoustic sensor technology. Currently, he is an Associate Professor with the School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu. His current research interests include sensor signal processing, machine learning, data mining for nondestructive testing, and evaluation. Dr. Gao is a very active reviewer for many international journals and long standing conferences.
Aijun Yin (M’13) received the B.S. degree in mechatronics engineering and the M.S. and Ph.D. degrees from Chongqing University, Chongqing, China, in 2001, 2003, and 2006, respectively. He is currently an Associate Professor with the College of Mechanical Engineering, Chongqing University. His current research interests include machine vision and image processing, intelligent test and instruments, nondestructive testing and evaluation, modern signal analysis and processing, and fault detection and diagnosis.
