Non-Destructive Inspection of Bonded Components Using Singular Value Decomposition of Time-Series Temperature Variation Data ^†

Abstract

In the weld bonding used in automobiles, inspecting the adhesive areas is important to achieve the desired increase in rigidity. Active infrared thermography using flash lamp heating was applied to a weld-bonded specimen. Temperature differences were observed on the measurement surface depending on the presence or absence of adhesive, enabling the detection of the bonded areas. Furthermore, singular value decomposition (SVD) was applied to obtain time-series temperature variation data. SVD emphasizes the boundaries of the adhesive areas, improving the accuracy of inspections of the adhesive application areas.

1. Introduction

In order to improve fuel economy, automobiles are required to be lighter. While using high-strength steel plates can reduce a vehicle’s weight, using thinner steel plates reduces rigidity. Recently, a steel joining method called weld bonding has attracted attention for improving body rigidity. This method combines spot welding and adhesives to join steel plates together, compensating for the reduction in rigidity caused by the plates being thinned down. Since the stiffness-enhancing effect of this method depends on the adhesive areas being filled, these areas are an important inspection item. Conventional sampling inspection can only evaluate the cut surfaces, while the cut parts cannot be used; therefore, a method that enables non-destructive inspection is required. Rajic et al. [1] proposed principal component thermography (PCT), which uses singular value decomposition (SVD) on data obtained by active infrared thermography with flash lamp heating. They demonstrated that PCT provides high levels of thermal contrast for underlying structural flaws in composite materials. In this study, we focused on an analysis method using SVD to inspect bonding areas. Pulse heating with a flash lamp is applied to a weld-bonded specimen, and SVD is applied to the time-series temperature variation data to improve the accuracy of inspecting bonding areas.

2. Principle of SVD Analysis

The principle of SVD analysis is explained below. The infrared image data φ obtained by infrared thermography was a three-dimensional image matrix containing n_t frames of n_x × n_y infrared images. To perform SVD, the matrix A_k consisting of the n_x × n_y pixels of the kth frame shown in Equation (1) was reordered into the column vector x_k shown in Equation (2).

$$A_k=\left(\begin{array}{ccc}{a}_{11}& \dots & a_{1n_y}\\ ⋮& \ddots & ⋮\\ a_{n_{x}1}& \dots & a_{n_x{n}_y}\end{array}\right) k=\mathrm{1,2},\dots ,n_t$$

(1)

$$x_k=\left(\begin{array}{c}{a}_{11}\\ ⋮\\ a_{1n_y}\\ ⋮\\ a_{n_{x}1}\\ ⋮\\ a_{n_x{n}_y}\end{array}\right)k=\mathrm{1,2},\dots ,n_t$$

(2)

The column vectors of all frames were arranged as in Equation (3) to form matrix X. Singular value decomposition was then performed to obtain Equation (4).

$$X=\left(x_1,x_2,\dots ,x_{n_t}\right)$$

(3)

$$\begin{array}{cc}X=U\Sigma V^T\hfill & =\left[u_1{u}_2\dots u_M\right]\left[\begin{array}{ccc}{\sigma }_1& & 0\\ & \ddots & \\ 0& & {\sigma }_M\end{array}\right]\left[\begin{array}{c}\begin{array}{c}{v}_1^T\\ v_2^T\\ ⋮\end{array}\\ v_M^T\end{array}\right]\hfill \\ \hfill & =u_1{\sigma }_1{v}_1^T+u_2{\sigma }_2{v}_2^T+\dots +u_M{\sigma }_M{v}_M^T\hfill \end{array}$$

(4)

Each column u_k of matrix U is called an Empirical Orthogonal Function (EOF), and each row v_i^T of matrix V^T is called PC. PC waveform represents the characteristics of the time series. EOF is the intensity distribution per pixel for the corresponding PC waveform. In this study, SVD was applied to time-series temperature variation data. SVD was used to extract minute temperature fluctuations, improving the detection accuracy of the adhesive areas.

3. Experimental Method

In this study, a plate-joined specimen consisting of 0.7 mm and 2.3 mm thick automotive hot-dip galvanized steel sheets joined by adhesive and spot welding was used, as shown in Figure 1. Three spot welds were applied, one at the center of the specimen and the others at a position that was 15 mm from the center of the specimen. The specimen was covered with flat black paint to improve emissivity. The employed infrared camera was an FLIR SC7500, a product of Teledyne FLIR, Wilsonville, OR, USA. with an InSb MW infrared sensor. Xenon flashlamps (Hamamatsu Photonics, Hamamatsu, Japan)were used as a heating source. The infrared camera and the flashlamp were placed on the same side of the specimen. The specimen was heated by pulsed heating of the infrared measurement surface, and the time-series temperature fluctuations were captured by the infrared camera. Further SVD was applied to the obtained data.

4. Results

Figure 2 shows an infrared image taken at 0.5 s after pulse heating. Min-max normalization was applied to infrared intensity values. It was found that the spot weld was the lowest temperature. This is because steel plates have a higher thermal conductivity than adhesives and air, which allows heat to transfer quickly to the back plate. Next, low-temperature areas appear in a band-like pattern along the vertical axis of the steel plate. This is because the thermal conductivity of adhesives is higher than that of air, although not as high as that of steel plates, allowing heat to be transferred to the back plate quickly. The adhesive can be detected due to the localized low-temperature area. Figure 3 shows the results of applying SVD to time-series temperature variation data. Min-max normalization was applied to the EOF intensity values. The boundary between adhesive-applied and non-applied areas is clearer in the EOF image than in the infrared image. This indicates that applying SVD improves the accuracy of adhesive inspection.

5. Conclusions

Active infrared thermography using flash lamp heating was used to inspect the adhesive areas of a weld-bonded specimen. Due to the difference in thermal conductivity between the adhesive, the steel plate, and the air, heat is transferred differently to the back plate. As a result, the adhesive areas appear as low-temperature areas compared to the air areas, enabling the detection of the adhesive areas. Furthermore, SVD was applied to the time-series temperature variation data obtained via active infrared thermal imaging. SVD can be used to extract temperature fluctuations caused by adhesives, emphasizing the boundaries of the adhesive area and improving the inspection accuracy of the adhesive application area.