# Truncated Newton Kernel Ridge Regression for Prediction of Porosity in Additive Manufactured SS316L
###### Abstract  
Despite the many benefits of additive manufacturing, the final quality of the fabricated parts remains a barrier to the wide adoption of this technique in industry. Predicting the quality of parts using advanced machine learning techniques may improve the repeatability of results and make additive manufacturing accessible to different fields. This study aims to integrate data extracted from various sources and use them to obtain accurate predictions of relative density with respect to the governing process parameters. Process parameters such as laser power, scan speed, hatch distance, and layer thickness are used to predict the relative density of 316L stainless steel specimens fabricated by selective laser melting. An extensive dataset is created by systematically combining experimental results from prior studies with the results of the current work. Analysis of the collected dataset shows that the laser power and scan speed significantly impact the relative density. This study compares ridge regression, kernel ridge regression, and support vector regression using the data collected for SS316L. Computational results indicate that kernel ridge regression performs better than both ridge regression and support vector regression based on the coefficient of determination and mean square error. a 2022 12 20  
Selective laser melting (SLM) is a laser powder bed fusion (L-PBF) process in which layers of powdered metal are melted at specific locations by a high-power laser beam, and dense sections of parts are fabricated at each layer after solidification according to ASTMS2900-15 [1]. Many parameters affect the performance characteristics of parts fabricated by SLM, including material qualities; powder properties; machine specifications; and process parameters such as laser power, scan speed, hatch distance, and layer thickness. Surface roughness, strength, and relative density are the typically measured performance characteristics of SLM-manufactured parts [5]. Modeling AM processes is critical to understanding and optimizing process parameters and predicting performance characteristics in three-dimensional printed parts. Many studies have attempted to model various AM processes using data-driven methodologies that directly assess the effects of process parameters on part quality. A traditional design of the experiment is commonly applied in data-driven methods for laser-based AM processes. For instance, a two-level factorial design has been applied to determine the effects of build parameters on the deposition of titanium alloys [6]. [PERSON] et al. [7] have used a full-factorial design to identify the optimal set of process parameters and analyze the microstructure of the final parts and the mechanical properties resulting from different steel powders. The response surface method has also been used to evaluate the fused deposition modeling process and capture the relationships between multiple performance characteristics and process parameters [8]. However, the design of the experimental approach usually involved trial and error, which is time-consuming and expensive, especially in the case of metal AM [9]. Empirical modeling techniques, such as regression models of linear and quadratic functions, have been used to model AM and predict the performance characteristics of fabricated parts [2; 10]. Regression analysis and the analysis of variance rely strongly on statistical assumptions and require a strong assumption of the model structure (e.g., linear or nonlinear). As a result, the structure of a model and its dependence on statistical assumptions cause uncertainty in the prediction ability of the model [4]. Because of the nonlinearity and complexity of AM processes, the possibility of using machine learning (ML) techniques and kernel methods has been considered to overcome these modeling issues. ML algorithms include but are not limited to artificial neural networks, genetic algorithms, and support vector machines (_SVM_s).