## 5 Case Study  
To verify the feasibility of the proposed prediction model for SLS, experiments are carried out on a SLS machine, and the used material is coated in sand. The equipment and experimental scene are shown in Figure 8. Three pairs of parts were printed independently with different laser powers. The first pair was printed at a power of 35 W, the second was printed at a power of at 40 W, and the third was printed at a power of at 45 W. During the sintering process of each part, about 40,000 images of the temperature field were produced by the infrared thermal imager. Therefore, there were 80,000 images for each level of laser power. Figure 7: Variation curve of metrics with gamma at C = 10. (The red curve represents accuracy, while the blue curve represents the F value). The used infrared camera is \"VarioCAM hr research 480\" produced by InfraTec. The camera and its software can measure the surface temperature of the targets in the image area, based on the thermal radiation of those targets. Generally, the thermal radiances are various when referring to different kinds of materials; even for the same material, the thermal radiance will be variable while the temperature of the material changing. The infrared camera simplified this issue by providing a setup option of the thermal radiances of the target material. In this experiment, we set the thermal radiance of coated sand to be 0.95, which is based on the suggestions from material professionals and some of the literature. Assuming the temperature of the target area is 400 \({}^{\circ}\)C, then the energy captured by the camera will be 380 \({}^{\circ}\)C; as result of the setup of the thermal radiance, the final temperature shown on the interface of the software will be 400 \({}^{\circ}\)C again, which is calculated by 380/0.95. Actually, the measurement uncertainty exists in any measurement system. The measured temperature values given out by the infrared camera may still not be the real temperatures of the target area. However, the measurement bias will not influence the analysis based on the proposed method, which focuses on the difference between temperatures at different times, instead of the actual values of them. As illustrated, the key features of the temperature field are extracted from those images, and their values are expressed by matrixes. Then, all 240,000 matrixes are divided into three groups: the training group, validation group, and test group, as shown in Figure 9.  
Using the PCA algorithm, the high-dimensional features of the temperature field are reduced to seven features, and the values are represented by an array with seven cells. Some arrays are produced by the SLS process with 35-W and 40-W laser power and are called negative samples; other arrays are produced by the process with 45-W laser power, and they are called positive samples. Set Y = 1 for positive samples and Y = -1 for negative samples; then, an SVM model can be built to determine the hyperplane function, which can divide all the arrays into two categories. Finally, for any value of the array, the SVM model can tell us the actual laser power of the process that produces the array; the laser power can be predicted in process based on the key feature values of the temperature field. Based on the matrixes of the training group, an initial SVM model is built based on the data set of \(\mathrm{X}_{\mathrm{training}}\) and \(\mathrm{Y}_{\mathrm{training}}\); then, the validation group is used to optimize the parameters (gamma and C), using the meshing search method described in Section 4. In this experiment, the optimal value of gamma is 0.1, and the optimal value of C is 10.