Contents
Chapter 7 Monitoring with weld image information
7.5 Image rendering using fractal theory
7.5.2 Method II
In this method, the algorithm proposed by Katz (1988) is used to estimate the FD.
This algorithm applies to 2D waveforms and cannot be applied directly to images.
Therefore, the information available in the image is first converted to 2D waveforms in terms of GLD of the image with respective pixel index by converting the RGB images to grey images. Three fixed locations on the top surface of the grey images are selected for
Monitoring of FSW process with weld image information
the extraction of grey distributions. Two locations at the two extremities of the weld zone and one at the center of the weld zone are selected. GLDs against each zone are extracted using MATLAB software package (MATLAB 2017b). Among the three locations, grey distributions obtained from the middle of the weld zone show more variations. Hence, these distributions from all the images are considered for this study. Fig. 7.4 shows a particular case of GLD along the line of extraction on the image. This characteristic distribution is the indicator of the surface irregularities on the top surface of the image and hence reflects the process condition.
(a) (b)
Fig.7.3 Variation of ultimate tensile strength with (a) computed fractal dimension (b) process parameters
Fig. 7.4 Grey level distribution of image with location of extraction
The computed FD is correlated to the process parameters to investigate the effect of these on the FD. Fig. 7.5a-b shows the variation of FD with the process parameters.
The trend in the computed FD through this method is the same as observed in the variation of FD computed through Method I. At low tool rotational speed, the irregularities on the surface of the welds are high, which generates more variations in the obtained GLDs of image, resulting in high FD values. The same is again valid for high
Chapter 7
tool rotational speed and welding speed values which also generate GLDs with more variations. Whereas, at a moderate level of these two parameters (tool rotational speed and welding speed), GLDs of the images contain fewer variations as compared to other cases and results in less FD. The same conclusions cannot be drawn for the variations of FDs with welding speed as all the data set does not lead to a similar trend. The correlation coefficient between the FDs computed from Method II, and UTS of the joints are found to be -0.91. The variation of computed FDs with UTS of the joints is shown in Fig. 7.3a. The clear decreasing trend of UTS with an increase in the FDs from this method is an indication that FDs of GLD of weld images can be a better candidate to monitor process outcome than process parameters.
(a) (b)
Fig. 7.5 Variation of fractal dimensions computed from Method II with (a) tool rotational speed and (b) welding speed
Grey values of an image depend on the source, the device used to capture the image and the software used for the conversion of RGB image to grey image. For the present case, the images are captured though a photographic camera keeping the elevation of the image, magnification of the image and light intensity of the image fixed for all the images. The images are captured using a regular photographic camera so that the process can be kept as simple as possible. MATLAB software package (MATLAB 2017b) is used for the conversion of captured RGB image to grey scale image. In this software package, there are dedicated tools available for converting the RGB colour image to grey scale image. For the conversion of the image, the algorithm used weighted values of , , components which is given by Eq. 7.1 where , and represents intensity levels against at pixel for red, green and blue components and represents grey intensity at the respective pixel of the image.
Monitoring of FSW process with weld image information
(7.1) The weights for the formulation is fixed and the grey values computed from the image merely depends on the , , components of the individual image. Moreover, in the study, the grey images are not used directly. The intensities from the middle of the grey image along a line are extracted and plotted, where abscissa represents the pixel index and ordinate represents the grey intensities. This plot, as it follows trends, and can be defined as a function of pixel index and intensity content. This idea motivates to treat the intensity distribution as a signal, sampled over different pixel number or index within the same image. This is performed for all the captured images and all the other values, i.e., position of the line of interest against which grey distributions are sampled are fixed for every case. Thus, changes in the images, captured under same environment are bound to yield grey distribution more or less similar to the ones reported in Fig. 7.4. The changes in the images are due to the profiles generated in the top surface of the welds due to the combined action of the tool rotation and traversing of the tool over the top surface. At various combinations of tool rotational speed and welding speed the characteristics semicircular rings or profile generated in the top surface will be different from one sample to another. Thus, this will make grey level distributions unique for each image, meaning information contained in the grey distributions plots is unique for a particular set of process parameters. Fractal dimension algorithm is implemented to these plots, to find out the characteristics of the distributions in terms of FDs those are correlated to UTS of the joints. The idea of implementing fractal theory to images is to find the fractal nature of the object (image in this case). The more precise software packages, more sophisticated image acquisition tools obviously lead to more precise information of the image, but this research work is all about to present the concept of weld quality modelling with FD utilizing the available resources and not deviating from the key concept of developing a simple, yet effective modelling technique for the prediction of weld quality. The images are enlarged and the same methodology is implemented to extract the grey level distribution from the grey images. For all the grey distributions from all the images gives the FD consistent up to second decimal point.