ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

This article is available in the ASME Digital Collection at .

This article is available in the ASME Digital Collection at .

This paper reviews the state of the art in applying uncertainty quantification (UQ) methods to additive manufacturing (AM). Physics-based as well as data-driven models are increasingly being developed and refined in order to support process optimization and control objectives in AM, in particular to maximize the quality and minimize the variability of the AM product. However, before using these models for decision-making, a fundamental question that needs to be answered is to what degree the models can be trusted, and consider the various uncertainty sources that affect their prediction. UQ in AM is not trivial because of the complex multiphysics, multiscale phenomena in the AM process. This article reviews the literature on UQ methodologies focusing on model uncertainty, discusses the corresponding activities of calibration, verification, and validation, and examines their applications reported in the AM literature. The extension of current UQ methodologies to additive manufacturing needs to address multiphysics, multiscale interactions, increasing presence of data-driven models, high cost of manufacturing, and complexity of measurements. The activities that need to be undertaken in order to implement verification, calibration, and validation for AM are discussed. Literature on using the results of UQ activities toward AM process optimization and control (thus supporting maximization of quality and minimization of variability) is also reviewed. Future research needs both in terms of UQ and decision-making in AM are outlined. This article is available in the ASME Digital Collection at .

Keywords: additive manufacturing, uncertainty quantification, calibration, verification, validation, process optimization, process control

Regression models are widely used as data-driven methods for predicting a continuous target variable. From a set of input variables, regression models predict a deterministic point value for the target variable. But the deterministic point value prediction is not always sufficient because a target variable value often varies due to diverse sources of uncertainty. For instance, in the fused deposition modeling process, the inconsistent results of replications are associated with natural randomness, environmental condition, and noisy process parameters. The point value estimation is not sufficient to represent the variability in this kind of scenario. Instead of point estimation, the interval prediction of a target variable is more useful in this application. In this paper, linear optimization-based techniques are proposed to predict conservative confidence intervals for linear and polynomial regression models. Two linear optimization models, one for ordinary least squares (OLS) regression and the other for weighted least squares (WLS) regression, are proposed. The proposed methods are implemented on several datasets, including an experimental fused deposition modeling dataset to demonstrate the effectiveness of the proposed methods. The results show that the proposed method is useful for the fused deposition modeling process where the level of uncertainty or the lack of knowledge of uncertainty sources is high. The proposed method can also be leveraged to the Bayesian neural network (BNN), where the optimization techniques for interval prediction will be nonlinear optimization instead of linear optimization. This article is available in the ASME Digital Collection at .

A persistent problem in the selective laser sintering process is to maintain the quality of additively manufactured parts, which can be attributed to the various sources of uncertainty. In this work, a two-particle phase-field microstructure model has been analyzed using a Gaussian process-based model. The sources of uncertainty as the two input parameters were surface diffusivity and interparticle distance. The response quantity of interest (QOI) was selected as the size of the neck region that develops between the two particles. Two different cases with equal and unequal-sized particles were studied. It was observed that the neck size increased with increasing surface diffusivity and decreased with increasing interparticle distance irrespective of particle size. Sensitivity analysis found that the interparticle distance has more influence on variation in neck size than that of surface diffusivity. The machine learning algorithm Gaussian process regression was used to create the surrogate model of the QOI. Bayesian optimization method was used to find optimal values of the input parameters. For equal-sized particles, optimization using Probability of Improvement provided optimal values of surface diffusivity and interparticle distance as 23.8268 and 40.0001, respectively. The Expected Improvement as an acquisition function gave optimal values of 23.9874 and 40.7428, respectively. For unequal-sized particles, optimal design values from Probability of Improvement were 23.9700 and 33.3005, respectively, while those from Expected Improvement were 23.9893 and 33.9627, respectively. The optimization results from the two different acquisition functions seemed to be in good agreement. This article is available in the ASME Digital Collection at .

Laser powder bed fusion (LPBF) process is one of popular additive manufacturing techniques for building metal parts through the layer-by-layer melting and solidification process. To date, there are plenty of successful product prototypes manufactured by the LPBF process. However, the lack of confidence in its quality and long-term reliability could be one of the major reasons prevent the LPBF process from being widely adopted in industry. The existing LPBF process is an open loop control system with some in situ monitoring capability. Hence, manufacturing quality and long-term reliability of the part cannot be guaranteed if there is any disturbance during the process. Such limitation can be overcome if a feedback control system can be implemented. This article studies the control effectiveness of the proportional-integral-derivative (PID) control and the model predictive control (MPC) for the LPBF process based on a physics-based machine learning model. The control objective is to maintain the melt pool width and depth at required level under process uncertainties from the powder and laser. A sampling-based dynamic control window approach is further proposed for MPC as a practical approach to approximate the optimal control actions within limited time constraint. Control effectiveness, pros, and cons of the PID control and the MPC for the LPBF process are investigated and compared through various control scenarios. It is demonstrated that the MPC is more effective than the PID control under the same conditions, but the MPC demands a valid digit twin of the LPBF process. This article is available in the ASME Digital Collection at .

Melt pool modeling is critical for model-based uncertainty quantification (UQ) and quality control in metallic additive manufacturing (AM). Finite element (FE) simulation for thermal modeling in metal AM, however, is tedious and time-consuming. This paper presents a multifidelity point-cloud neural network method (MF-PointNN) for surrogate modeling of melt pool based on FE simulation data. It merges the feature representations of the low-fidelity (LF) analytical model and high-fidelity (HF) FE simulation data through the theory of transfer learning (TL). A basic PointNN is first trained using LF data to construct a correlation between the inputs and thermal field of analytical models. Then, the basic PointNN is updated and fine-tuned using the small size of HF data to build the MF-PointNN. The trained MF-PointNN allows for efficient mapping from input variables and spatial positions to thermal histories, and thereby efficiently predicts the three-dimensional melt pool. Results of melt pool modeling of electron beam additive manufacturing (EBAM) of Ti-6Al-4V under uncertainty demonstrate the efficacy of the proposed approach. This article is available in the ASME Digital Collection at .

Silicon is one of the commonly used semiconductors for various industrial applications. Traditional silicon synthesis methods are often expensive and cannot meet the continuously growing demands for high-purity Si; electrodeposition is a promising and simple alternative. However, the electrodeposited products often possess nonuniform thicknesses due to various sources of uncertainty inherited from the fabrication process; to improve the quality of the coating products, it is crucial to better understand the influences of the sources of uncertainty. In this paper, uncertainty quantification (UQ) analysis is performed on the silicon electrodeposition process to evaluate the impacts of various experimental operation parameters on the thickness variation of the coated silicon layer and to find the optimal experimental conditions. To mitigate the high experimental and computational cost issues, a Gaussian process (GP) based surrogate model is constructed to conduct the UQ study with finite element (FE) simulation results as training data. It is found that the GP surrogate model can efficiently and accurately estimate the performance of the electrodeposition given certain experimental operation parameters. The results show that the electrodeposition process is sensitive to the geometric settings of the experiments, i.e., distance and area ratio between the counter and working electrodes; whereas other conditions, such as the potential of the counter electrode, temperature, and ion concentration in the electrolyte bath are less important. Furthermore, the optimal operating condition to deposit silicon is proposed to minimize the thickness variation of the coated silicon layer and to enhance the reliability of the electrodeposition experiment. This article is available in the ASME Digital Collection at .

Accurate identification and modeling of process maps in additive manufacturing remains a pertinent challenge. To ensure high quality and reliability of the finished product researchers, rely on models that entail the physics of the process as a computer code or conduct laboratory experiments, which are expensive and oftentimes demand significant logistic and overheads. Physics-based computational modeling has shown promise in alleviating the aforementioned challenge, albeit with limitations like physical approximations, model-form uncertainty, and limited experimental data. This calls for modeling methods that can combine limited experimental and simulation data in a computationally efficient manner, in order to achieve the desired properties in the manufactured parts. In this paper, we focus on demonstrating the impact of probabilistic modeling and uncertainty quantification on powder-bed fusion (PBF) additive manufacturing by focusing on the following three milieu: (a) accelerating the parameter development processes associated with laser powder bed fusion additive manufacturing process of metals, (b) quantifying uncertainty and identifying missing physical correlations in the computational model, and (c) transferring learned process maps from a source to a target process. These tasks demonstrate the application of multifidelity modeling, global sensitivity analysis, intelligent design of experiments, and deep transfer learning for a meso-scale meltpool model of the additive manufacturing process. This article is available in the ASME Digital Collection at .

The use of three-dimensional (3D) printing for lattice structures has led to advances in diverse applications benefitting from mechanically efficient designs. Three-dimensional printed lattices are often used to carry loads, however, printing defects and inconsistencies potentially hinder performance. Here, we investigate the design, fabrication, mechanics, and reliability of lattices with repeating cubic unit cells using probabilistic analysis. Lattices were designed with 500 μm diameter beams and unit cell lengths from 0.8 mm to 1.6 mm. Designs were printed with stereolithography and had average beam diameters from 509 μm to 622 μm, thereby demonstrating a deviation from design intentions. Mechanical experiments were conducted and demonstrated an exponential increase in yield stress for lattice relative density that facilitated probabilistic failure analysis. Sensitivity analysis demonstrated lattice mechanics were most sensitive to fluctuations for beam diameter (74%) and second to lattice yield stress (8%) for lattices with 1.6 mm unit cells, while lattices with smaller 1.0 mm unit cells were most sensitive to yield stress (48%) and second to beam diameter (43%). The methodological framework is generalizable to further 3D printed lattice systems, and findings provide new insights linking design, fabrication, mechanics, and reliability for improved system design that is crucial for engineers to consider as 3D printing becomes more widely adopted. This article is available in the ASME Digital Collection at .

Additive manufacturing (AM) has been extensively investigated in recent years to explore its application in a wide range of engineering functionalities, such as mechanical, acoustic, thermal, and electrical properties. A data-driven approach is proposed to investigate the influence of major fabrication parameters in the laser-based additively manufactured Ti–6Al–4V. Two separate laser-based powder bed fusion techniques, i.e., selective laser melting (SLM) and direct metal laser sintering (DMLS), have been investigated and several data regarding the tensile properties of Ti–6Al–4V alloy with their corresponding fabrication parameters are collected from open literature. Statistical data analysis is performed for four fabrication parameters (scanning speed, laser power, hatch spacing, and powder layer thickness) and three postfabrication parameters (heating temperature, heating time, and hot isostatically pressed or not) which are major influencing factors and have been investigated by several researchers to identify their behavior on the static mechanical properties (i.e., yielding strength, ultimate tensile strength, and elongation). To identify the behavior of the relationship between the input and output parameters, both linear regression analysis and artificial neural network (ANN) models are developed using 53 and 100 datasets for SLM and DMLS processes, respectively. The linear regression model resulted in an average R squared value of 0.351 and 0.507 compared to 0.908 and 0.833 in the case of nonlinear ANN modeling for SLM and DMLS based modeling, respectively. Both local and global sensitivity analyses are carried out to identify the important factors for future optimal design. Based on the current study, local sensitivity analysis (SA) suggests that SLM is most sensitive to laser power, scanning speed, and heat treatment temperature while DMLS is most sensitive to heat treatment temperature, hatch spacing, and laser power. In the case of DMLS fabricated Ti–6Al–4V alloy, laser power, and scan speed are found to be the most impactful input parameters for tensile properties of the alloy while heating time turned out to be the least affecting parameter. The global sensitivity analysis results can be used to tailor the alloy's static properties as per the requirement while results from local sensitivity analysis could be useful to optimize the already tailored design properties. Sobol's global sensitivity analysis implicates laser power, heating temperature, and hatch spacing to be the most influential parameters for alloy strength while powder layer thickness followed by scanning speed to be the prominent parameters for elongation for SLM fabricated Ti–6Al–4V alloy. Future work would still be needed to eradicate some of the limitations of this study related to limited dataset availability. This article is available in the ASME Digital Collection at .

Additive manufacturing (AM) has been growing rapidly to transform industrial applications. However, the fundamental mechanism of AM has not been fully understood which resulted in low success rate of building. A remedy is to introduce surrogate modeling based on experimental dataset to assist additive design and increase design efficiency. As one of the first papers for predictive modeling of AM especially direct energy deposition (DED), this paper discusses a bidirectional modeling framework and its application to multiple DED benchmark designs including: (1) forward prediction with cross-validation, (2) global sensitivity analyses, (3) backward prediction and optimization, and (4) intelligent data addition. Approximately 1150 mechanical tensile test samples were extracted and tested with input variables from machine parameters, postprocess, and output variables from mechanical, microstructure, and physical properties. This article is available in the ASME Digital Collection at .

Tremendous efforts have been made to use computational and simulation models of additive manufacturing (AM) processes. The goals of these efforts are to better understand process complexities and to realize better high-quality parts. However, understanding whether any model is a correct representation for a given scenario is a difficult proposition. For example, when using metal powders, the laser powder-bed fusion (L-PBF) process involves complex physical phenomena such as powder morphology, heat transfer, phase transformation, and fluid flow. Models based on these phenomena will possess different degrees of fidelity since they often rely on assumptions that may neglect or simplify process physics, resulting in uncertainties in their prediction accuracy. Prediction accuracy and its characterization can vary greatly between models due to their uncertainties. This paper characterizes several sources of L-PBF model uncertainty for low, medium, and high-fidelity thermal models including modeling assumptions (model-form uncertainty), numerical approximations (numerical uncertainty), and input parameters (parameter uncertainty). This paper focuses on the input uncertainty sources, which we model in terms of a probability density function (PDF), and its propagation through all other L-PBF models. We represent uncertainty sources using the web ontology language, which allows us to capture the relevant knowledge used for interoperability and reusability. The topology and mapping of the uncertainty sources establish fundamental requirements for measuring model fidelity and for guiding the selection of a model suitable for its intended purpose. This article is available in the ASME Digital Collection at .

Modeling and simulation for additive manufacturing (AM) are critical enablers for understanding process physics, conducting process planning and optimization, and streamlining qualification and certification. It is often the case that a suite of hierarchically linked (or coupled) simulation models is needed to achieve the above tasks, as the entirety of the complex physical phenomena relevant to the understanding of process-structure-property-performance relationships in the context of AM precludes the use of a single simulation framework. In this study using a Bayesian network approach, we address the important problem of conducting uncertainty quantification (UQ) analysis for multiple hierarchical models to establish process-microstructure relationships in laser powder bed fusion (LPBF) AM. More significantly, we present the framework to calibrate and analyze simulation models that have experimentally unmeasurable variables, which are quantities of interest predicted by an upstream model and deemed necessary for the downstream model in the chain. We validate the framework using a case study on predicting the microstructure of a binary nickel-niobium alloy processed using LPBF as a function of processing parameters. Our framework is shown to be able to predict segregation of niobium with up to 94.3% prediction accuracy on test data. This article is available in the ASME Digital Collection at .

This work presents a data-driven methodology for multi-objective optimization under uncertainty of process parameters in the fused filament fabrication (FFF) process. The proposed approach optimizes the process parameters with the objectives of minimizing the geometric inaccuracy and maximizing the filament bond quality of the manufactured part. First, experiments are conducted to collect data pertaining to the part quality. Then, Bayesian neural network (BNN) models are constructed to predict the geometric inaccuracy and bond quality as functions of the process parameters. The BNN model captures the model uncertainty caused by the lack of knowledge about model parameters (neuron weights) and the input variability due to the intrinsic randomness in the input parameters. Using the stochastic predictions from these models, different robustness-based design optimization formulations are investigated, wherein process parameters such as nozzle temperature, nozzle speed, and layer thickness are optimized under uncertainty for different multi-objective scenarios. Epistemic uncertainty in the prediction model and the aleatory uncertainty in the input is considered in the optimization. Finally, Pareto surfaces are constructed to estimate the tradeoffs between the objectives. Both the BNN models and the effectiveness of the proposed optimization methodology are validated using the actual manufacturing of the parts. This article is available in the ASME Digital Collection at .