# Analysis of a Sound Signal for Quality Monitoring in Laser Microlap Welding
## 4 Results and Discussion
To extract valuable features for joint-bonding-strength monitoring, RMS and standard deviation (STD) for each section were calculated first. Average values of RMS and STD were obtained from 20 samples for each section (Figure 10). The difference between the cases with high- and low-joint-bonding strengths was observed for both RMS and STD features. Sections 6 and 7 had the highest level of difference. However, on analyzing the level difference of these two features for each sample (Figure 11) in each section, we found that the results were not in agreement with the presented observations in Figure 10. For Sections 2, 6, and 7, presented in Figure 11, the RMS feature level refers to two joint-bonding strengths tangled with each other from sample to sample. This means that these three features cannot be considered proper features for developing a monitoring system, although the average of the RMS feature from all samples had the potential to separate different joint strengths at the feature level. The RMS value of the first section was considered the better choice for identifying low joint strengths. By investigating STD features on the sample base (Figure 12), data from Sections 6 and 7 revealed no promising capabilities in identifying low-joint-bonding strength. Conversely, the STD feature of the first section demonstrated the capability of distinguishing between the high- and low-joint-bonding strength cases. To extract more reliable features from the aforementioned analysis, the STD of each section was divided using RMS values to create a new feature. Values of created STD/RMS ratio features for each section are illustrated in Figure 13. The STD-to-RMS ratio in the second section is a promising feature for identifying the joint-bonding condition. Figure 8: Eight sections of sound signals for analysis. Figure 4:0 Root-mean-square (RMS) values of full-length sound signals for 20 samples with normal joint strength, and 20 samples with low joint strength. Figure 4:1 Average of RMS values and standard deviations (STDs) for 20 samples: (**a**) RMS and (**b**) STDs. Figure 4:2 Time-domain sound signal for each selected section with high- and low-joint-bonding strengths (10 samples for each case): (**a**) first section; (**b**) second section; (**c**) third section; (**d**) fourth section; (**e**) fifth section; (**f**) sixth section; (**g**) seventh section; (**h**) eighth section. Figure 4:3 RMS values for each selected section with high- and low-joint-bonding strengths: (**a**) first section; (**b**) second section; (**c**) third section; (**d**) fourth section; (**e**) fifth section; (**f**) sixth section; (**g**) seventh section; (**h**) eighth section. Figure 4:4 STDs for each selected section with high- and low-joint-bonding strengths: (**a**) first section; (**b**) second section; (**c**) third section; (**d**) fourth section; (**e**) fifth section; (**f**) sixth section; (**g**) seventh section; (**h**) eighth section. To quantify the capability level of each feature for identifying the joint condition, scatter index \(J\) was calculated on the basis of the ratio of between-class to in-class distribution for the three aforementioned features for each section. Results presented in Figure 14 showed that RMS values and STDs in the first section, and the STD-to-RMS ratio in the second section had the highest \(J\) values and could be considered optimal candidates as inputs for the classifier. To evaluate selected features for monitoring the low joint strength caused by the gap generated between metal sheets in laser microlap welding, an HMM-based classifier was implemented with selected features [17]. Observation sequence levels are listed in Figure 4:5 The model was developed using 10 sets of data that were obtained from 10 samples and evaluated by 10 other sets of data. A 100% classification rate was obtained with the three selected features.