The confidence level of the RL-based classification in this case (Wasmer et al. 2018) was between 74% and 82%, which shows a slightly lower performance compared to their SCNN approach. Despite the encouraging results from the SCNN and RL, researchers at Empa empowered their acoustic-based ML approach by verifying the results using high-speed X-ray imaging techniques. Four categories of conduction welding, stable keyhole, unstable keyhole, and spatter were defined in a laser welding experiment and gradient boost with both independent component analysis and with CART were used to classify the different process conditions. 74% to 95% of accuracy was achieved in their assessments (Wasmer et al. 2018). SUPPORT VECTOR MACHINE Support vector machines (SVMs) can be used for both classi- fication and regression problems, although typically used for classification. The idea behind the SVM is to find the optimal hyperplane (the hyperplane with the highest margin) that separates the two classes. SVM is fundamentally a binary classifier, and a hyperplane is a decision boundary that sep- arates the two classes. If the dimension of the input data or the number of features is two, then the hyperplane is a line. For a three-dimensional feature space, the hyperplane is a two-dimensional plane. AE, in combination with accelerometers and thermo- couples data, was used by Nam et al. (2020) to train an SVM algorithm for diagnosing health states of the FDM process. The researchers first obtained the RMS values from the AE, accelerometers, and thermocouples data. They applied both linear and nonlinear SVM algorithms to identify the state of the FDM process as healthy or faulty. This research is a good case study of how to use SVMs for studying an AM process with the help of AE. However, it is to be noted that the SVM algo- rithm is ineffective when the dataset has more noise, which is a downside of using AET. Unsupervised Classification of AM Process States Unsupervised learning is a learning paradigm that does not require prior knowledge of the solution to the problem at hand, which implies that specifying the output is not required, or in some cases where such data may not be available. The implications of this approach are that we can learn inherent patterns in the data that we were not privy to there may be several solutions to the problem and different results can be obtained each time we run the model. In the following sections, we discuss the application of specific unsupervised learning algorithms to the study of AM using AET. CLUSTERING BY FAST SEARCH AND FIND OF DENSITY PEAKS The clustering by fast search and find of density peaks (CFSFDP) approach was used by Liu et al. (2018) to identify the FDM process state. Liu et al. used reduced feature space dimension by combining both time and frequency domain features and then reducing them with the linear discriminant analysis for their work. Consequently, CFSFDP, as an unsuper- vised density-based clustering method, is applied to classify and recognize different machine states of the extruder (Liu et al. 2018). Density-based clustering methods such as CFSFDP used by Liu et al. update the clusters iteratively without grouping the data. This approach is contrary to distance-based clustering methods such as hierarchical and partitioning algo- rithms like k-means. As a result of using CFSFDP, the FDM machine states were identified within a much smaller feature space, which helps to reduce the computational cost of classi- fication and state identification. Liu et al.’s work declared that reducing dimension in feature space remarkably improves the efficiency of state identification. For dimensionality reduction, the operator part of the algorithm can be customized by linear discriminant analysis. K-MEANS CLUSTERING The k-means clustering algorithm is one of the most widely used algorithms due to its flexibility and ease of implementa- tion. It is an unsupervised learning algorithm, a class of ML algorithms that can find patterns within a dataset without being explicitly told what the underlying mechanism is or might be. The only user-defined parameter required to train a k-means clustering algorithm is the number of clusters, k. Figure 5 shows an example of two clusters, with optimal loca- tions of centroids represented by triangles. The algorithm works as follows: 1. The user defines the number of clusters, k, and a corre- sponding number of cluster centroids (or means) are randomly chosen. 2. Each observation (or point) in the dataset is assigned to one of the clusters, based on its distance from a given centroid. There are several metrics used in ML to compute distances, but a commonly utilized measure is known as the Euclidean distance. Figure 5. Setup for a k-means clustering algorithm. J U L Y 2 0 2 3 • M A T E R I A L S E V A L U A T I O N 57 2307 ME July dup.indd 57 6/19/23 3:41 PM

3. The centroid locations are recomputed based on the assign- ment of data points in the previous step. 4. The process repeats, until one of the following conditions is met: (a) the centroid locations are stable (b) the data points do not change clusters or (c) the maximum number of itera- tions has been reached. An application of the k-means clustering algorithm to the in situ monitoring of an AM process using AET is found in Taheri et al. (2019). In this study, acoustic signatures were used for in situ monitoring of the DED AM process where the depo- sition was performed with the machine operating in five differ- ent states. These states included “control,” under which there was just powder spray, and “baseline,” under which there were no active deposition activities, as well as optimum (normal) process, low laser power, and low powder feed. Dominant features of acoustic signatures in both the time and frequency domains were identified and extracted from the acoustic signatures for all process conditions. The k-means clustering algorithm was applied to classify different process conditions, as shown in Figure 6. Correlations were demon- strated between metrics and various process conditions, which showcase the capability of AE for in situ monitoring of the AM process. Clear isolation of the baseline condition, at which no active deposition or laser-powder interaction occurs, shows that basic acoustic response of the AM system is distinct from when active manufacturing is happening. The next observa- tion is related to the optimum settings (C1) versus powder feed only (CO) conditions. However, a separation of C1 and CO clusters was observed for C1 and CO, but the smaller iso- lation of clusters and larger overlap of cluster data could be an indication of significant influence of laser-material interac- tion compared to system and material characteristics. Last but not least, comparison of the conditions where manufacturing processes are happening (C1, C2, and C3) is interpreted as the indication of AET for separation of manufacturing processes and significant influence of laser-material interaction in AM processes. Summary and Conclusions Acoustic techniques are proven methods for many traditional inspection and quality monitoring applications. Due to the promising capabilities of acoustic methods for nondestructive inspection and monitoring of many kinds of processes, they have been identified as an auspicious candidate for in situ measurement and monitoring for AM processes. Two major reasons impede the application of acoustic techniques for in situ monitoring in AM processes. First is the quite low SNR due to the high sensitivity of acoustic sensors to environmen- tal noise, which is the case in AM processes. The second is interpreting the signals to identify a correlation between the acoustic signals and the actual events. Various sensors and sensing approaches have been used to enhance the low SNR, such as using noncontact acoustic measurement via micro- phone or laser. Researchers have also utilized fiber-optic sensors to improve acoustic signal detection, which provides a new way of improving signal recording for in situ monitoring. Advanced signal processing techniques were used to perform data preparation, such as noise reduction and band filtering, to address the data processing and interpretation challenge. Consequently, ML algorithms have been adapted in different formats to extract and analyze the features of acoustic signals effectively. These algorithms showed an effective way and significant improvement in analyzing acoustic signals under different conditions for in situ process monitoring of AM and provide a promising pathway for the manufacturers to imple- ment acoustic techniques for monitoring and maintaining the quality of products. Sensor integration into the AM system, detection scheme, and SNR are the existing major gaps and barriers in acoustic-based in situ monitoring of AM processes ME |AI/ML 20 15 10 5 0 Centroid amplitude of Fourier transform (CA) Centroid frequencyufreq of Fourier transform (Cf) (kHz) 2.5 2 1.55 1 0.5 0 1150 12000 13000 13500 1400 BL: Baseline C1: Optimum settings C2: Low powerp C3: Low powder feed C0: Powder feed only f F f m 5 1 0 5 1 112500 B C O in s p Figure 6. A three- dimensional graphical representation of the additive manufacturing process condition using three spectral features (Taheri et al. 2019). 58 M A T E R I A L S E V A L U A T I O N • J U L Y 2 0 2 3 2307 ME July dup.indd 58 6/19/23 3:41 PM Peak amplitude of Fourier transform (PA)