Surface quality characterization is essential for ensuring product functionality as well as for guiding the design and the manufacturing process. Although surface quality characterization has been well studied in the context of mass production, it faces a number of challenges in additive manufacturing (AM). The infinite dimensionality of free-form geometric designs combined with a limited sample size of available products hinders the statistical analysis of product quality in AM. In addition, surface quality patterns in AM are driven by multiple geometric and process covariates such as size of the shape and location on the printing bed. As a result, conventional data-intensive characterization and modeling methods designed for mass production are ill-suited for AM. To address these challenges, the idea of printing primitives is utilized to reduce infinite two-dimensional (2D) free-form shapes into a finite set of simple primitives. A Gaussian process (GP) changepoint detection algorithm is applied to partition the 2D free-form shapes into basic segments with distinct surface quality characteristics. Then, we construct a surface quality characterization procedure using a GP representation of the surface quality in each class of shape primitives. Within each primitive, surface quality patterns are modeled using tensor product bases to efficiently capture the covariate dependency. The effectiveness of the proposed method is demonstrated in two actually printed AM sample sets.

Large-scale metal additive manufacturing has become increasingly popular in aerospace and petroleum industries alike for sustainable fabrication of thin-shelled structural components. For example, wire-arc additive manufacturing (WAAM) offers high-deposition rates on large printing areas by robot-assisted welding of thick layers of material. However, WAAM technologies suffer from significant layer displacement and resultant part-scale distortion due to unstable high temperature deposition processes and lack of economically viable support structures. Therefore, geometric accuracy qualification at layer level is critical to process optimization and control. However, layer quality assessment relies on layer identification from large point clouds. Manual layer segmentation is experience-dependent and time-consuming due to high surface roughness, excessive layer remelting, and severe out-of-plane layer displacement. To enable automated layer segmentation for quality assessment, we computationally model a human operator’s intuition utilized in the process of finding layer boundaries, that is, locating nearby regions with a large number of possible boundary points, and finetuning boundaries by learning boundaries functions. In our proposed approach, geometrical features of the boundaries between printed layers are exploited to identify candidate boundary points. Cooperative multi-learning-agents efficiently process the large point clouds to locate sets of nearby regions with a high density of boundary points. Learning agents then sample promising boundary points. Gaussian process regression is employed to fine-tune layer boundaries through learning mean boundary functions and their uncertainties from the sampled points. Simulation studies demonstrate the accuracy and robustness of the procedure under severe surface roughness conditions. WAAM experimental studies illustrate the applicability of the methodology in practice.

Surface patches have been utilized to reduce shape complexity in qualification of product geometric quality. However, specifying surface patches case-by-case is impractical for qualifying 3D-printed products with complicated freeform designs. Automating patch extraction must overcome the issue of potentially infinite variety of surface patches. To achieve dimension reduction for automated qualification, this work defines and characterizes surface patches using Laplace-Beltrami (LB) operator and critical points to capture a finite number of patch deviation patterns. The deviation-pattern-driven characterization enables the automated determination of patch centroids through active landmark selection. The patch sizes are determined using the LB operator within a changepoint detection formulation. To verify the finite dimensionality of patch types, patches extracted from product designs are clustered based on geometric dissimilarity that is quantified by wave kernel and curvature signatures. To verify that extracted patches capable of capturing deviation patterns in printed products, we derive patch deviation signatures that are invariant to printing covariates to facilitate product qualification. Analysis of actual 3D-printed freeform products demonstrates the efficacy of the developed methodology by comparing with existing approaches. It also shows the potential of inferring deviation patterns of a new design using the surface patch characterization and extraction approach. Note to Practitioners—Qualification of geometric quality for products with complex geometries relies on specifying regions of interest in the form of features or surface patches. In 3D printing, the potentially infinite variety of product designs requires manual specification of context-dependent surface patches for new and unseen designs. This work establishes an automated framework to reduce the dimensionality of qualification by specifying finite types of surface patches and automating their extraction across an infinite variety of designs. This approach streamlines the qualification process and will support the inference and learning of geometric quality of previously unseen designs.

In additive manufacturing (AM), final product geometries are often deformed or distorted. The deviations of three-dimensional (3D) shapes from their intended designs can be represented as 2D surfaces in a$\mathbb {R}^{3}$space, which constitutes a complicated set of data for learning and predicting geometric quality. Patterns of deviation surfaces vary with shape geometries, sizes/volumes, materials, and AM processes. Our previous work has established an engineering-informed convolution framework to learn shape deviation from a small set of training products built with the same material and process. It incorporates the characteristics of the layer-wise shape forming process through a convolution formulation and the size factor for a category of smooth 3D shapes such as domes or cylinders. This study extends this fabrication-aware learning framework to a larger class of products including both smooth and non-smooth surfaces (polyhedral shapes). The key idea of learning heterogeneous deviation surface data under a unified model is to establish the association between the deviation profiles of smooth base shapes and those of non-smooth polyhedral shapes. The association, which is characterized by a novel 3D cookie-cutter function, views polyhedral shapes as being carved out from smooth base shapes. In essence, the AM process of building non-smooth shapes is mathematically decomposed into two steps: additively fabricate smooth base shapes using a convolution learning framework, and then subtract extra materials using a cookie-cutter function. The proposed joint learning framework of shape deviation data reflects this decomposition by adopting a sequential model estimation procedure. The model learning procedure first establishes the convolution model to capture the effects of layer-wise fabrication and sizes, and then estimates the 3D cookie-cutter function to realize geometric differences between smooth and non-smooth shapes. A new Gaussian process model is proposed to consider the spatial correlation among neighboring regions within a 3D shape and across different shapes. The case study demonstrates the feasibility and prospects of prescriptive learning of complex 3D shape deviations in AM and extension to broader engineering surface data.Note to Practitioners—Engineering processes such as 3D printing generate complex shape data in the form of 3D point clouds. Qualification and verification of 3D shapes involves modeling and learning of heterogeneous shape deviation data that are affected by both product geometries and process physics. This study develops an engineering-informed, small-sample machine learning methodology to learn and predict deviations of smooth and non-smooth 3D shapes in a unified modeling framework. The fabrication of a non-smooth 3D shape is mathematically decomposed into the smooth base shape formation and shape difference realization. Both process knowledge and shape geometries are captured in the learning framework. It provides a new data analytical tool for shape engineering in additive manufacturing and beyond.

A significant challenge in comprehensive geometric accuracy control of an additive manufacturing (AM) system is the specification of shape deviation models for different computer-aided design products manufactured on its constituent AM processes. Current deviation modeling techniques do not satisfactorily address this challenge because they can require substantial user inputs and efforts to implement. We present a new model building methodology based on a class of Bayesian neural networks (NNs) that directly addresses this challenge with much less effort. Our method enables automated deviation modeling of different shapes and AM processes and yields models with higher predictive accuracies compared to the existing modeling methods on the same samples of manufactured products. A fundamental innovation in our methodology is the design of new and connectable NN structures that facilitate the leveraging of previously specified deviation models for adaptive model building of new shapes and AM processes. The power and broad scope of our method are demonstrated with several case studies on both in-plane and out-of-plane deviations for a wide variety of shapes manufactured under different stereolithography processes. Our Bayesian methodology for automated and comprehensive deviation modeling can ultimately help to advance flexible, efficient, and high-quality manufacturing in an AM system. Note to Practitioners-Additive manufacturing (AM) systems possess an intrinsic capability for one-of-a-kind manufacturing of a vast variety of shapes across a wide spectrum of constituent processes. Learning how to control geometric shape accuracy in a comprehensive manner for an AM system is vital to its operation. This task is challenging due to constraints on the number of test shapes that can be manufactured and user efforts that can be devoted for learning and predicting geometric errors of different sets of shapes and AM processes. This article presents an automated machine learning methodology for comprehensive learning and prediction of geometric errors in an AM system based on a limited number of test shapes manufactured under different processes. Several case studies serve to validate the potential of our methodology to learn effective geometric accuracy control policies for general AM systems in practice.

The 3-D shape accuracy is a critical performance measure for products built via additive manufacturing (AM). With advances in computing and increased accessibility of AM product data, machine learning for AM (ML4AM) has become a viable strategy for enhancing 3-D printing performance. A proper description of the 3-D shape formation through the layer-by-layer fabrication process is critical to ML4AM, such as feature selection and AM process modeling. The physics-based modeling and simulation approaches present voxel-level description of an object formation from points to lines, lines to surfaces, and surfaces to 3-D shapes. However, this computationally intensive modeling framework does not provide a clear structure for machine learning of AM data. Significant progress has been made to model and predict the shape accuracy of planar objects under data analytical frameworks. In order to predict, learn, and compensate for 3-D shape deviations using shape measurement data, we propose a shape deviation generator (SDG) under a novel convolution formulation to facilitate the learning and prediction of 3-D printing accuracy. The shape deviation representation, individual layer input function, and layer-to-layer transfer function for the convolution modeling framework are proposed and derived. A deconvolution problem for identifying the transfer function is formulated to capture the interlayer interaction and error accumulation effects in the layer-by-layer fabrication processes. Physics-informed sequential model estimation is developed to fully establish the SDG models. The Gaussian process regression is adopted to capture spatial correlations. The printed 2-D and 3-D shapes via a stereolithography (SLA) process are used to demonstrate the proposed modeling framework and derive new process insights for AM processes. Note to Practitioners-With advances in computing and increased availability of product data, machine learning for additive manufacturing (ML4AM) has become a viable strategy for enhancing 3-D printing accuracy. This work establishes the shape deviation generator (SDG) as a novel data analytical framework through a convolution formulation to model the 3-D shape formation in the AM process. This new engineering-informed machine-learning framework will facilitate the learning of AM data to establish models for geometric shape accuracy prediction and control.

Research on nanowire growth with patterned arrays of catalyst has shown that wire-to-wire spacing is an important factor affecting nanowire quality. To improve the process yield and the length uniformity of fabricated nanowires, it is important to reduce the resource competition between nanowires during the growth process. In this paper, we propose a physical-statistical nanowire-interaction model considering the shadowing effect and shared substrate diffusion area to determine the optimal pitch that would ensure the minimum competition between nanowires. A sigmoid function is used in the model, and the method of least squares is used to estimate the model parameters. The estimated model is then used to determine the optimal spatial arrangement of catalyst arrays. This work is an early attempt at the physical-statistical modeling of selective nanowire growth for the improvement of process yield.

Although 3-D printing or additive manufacturing (AM) holds great promise as a direct manufacturing technology, the geometric accuracy of AM built products remains a critical issue, especially for freeform products with complex geometric shapes. Efforts have long been attempted to improve the accuracy of AM built freeform products. But there is a lack of generic and prescriptive methodology transparent to specific designs and AM processes. This paper fills the gap by establishing the methodology to predict and compensate the in-plane (x - y plane) geometric deformation of AM built freeform products based on a limited number of simple trial shapes. Built upon our previous predictive model and optimal compensation study for the cylinder and polyhedron shapes, this paper makes a breakthrough by directly controlling arbitrary freeform shape deformation from computer-aided design. Experimental investigation using stereolithography process successfully validates the proposed prescriptive modeling and compensation methodology. This paper provides the prospect of proactively improving printing accuracy of arbitrary products built by a variety of AM processes.

Additive manufacturing (AM) or 3-D printing refers to a new class of technologies that actively construct products directly from any 3-D digital model. In the future, the broader applications of AM will require a cost reduction of AM machines. Currently, the products fabricated by low-end machines, such as those fabricated using fused deposition modeling (FDM) processes, suffer from the issue of low dimensional accuracy due to multiple error sources. To properly manage error sources for improved prevision, this paper proposes a novel strategy for error compensation in the FDM processes. First, we consecutively attribute the dimensional inaccuracy to two major error sources that affect the geometric shape of the product: 1) positioning error of the extruder and 2) shape deformation induced by processing error, including material phase change and other variations that occur. The extruder positioning error is characterized by a Kriging model, while the modeling of shape deformation due to processing error follows the method developed by Huang et al. Second, using error equivalence concept, we transform the positioning error into the equivalent amount of design input error. Finally, we adjust the design to compensate for the overall shape deviation. To validate this strategy, we conduct a designed experiment for the shape deviation prediction and the compensation. The experimental results successfully demonstrate the effectiveness of the proposed three-step strategy to manage multiple error sources in the FDM processes.

In the above paper (ibid., vol. 10, no. 3, pp. 571-578, Jul. 2013), in Section III-C, equations (16) and (17) were incorrect by missing a minus sign. The corrected equations are presented here.

Understanding nanostructure growth faces issues of limited data, lack of physical knowledge, and large process uncertainties. These issues result in modeling difficulty because a large pool of candidate models almost fit the data equally well. Through the Integrated Nanomanufacturing and Nanoinformatics (INN) strategy, we derive the process models from physical and statistical domains, respectively, and reinforce the understanding of growth processes by identifying the common model structure across two domains. This cross-domain model building strategy essentially validates models by domain knowledge rather than by (unavailable) data. It not only increases modeling confidence under large uncertainties, but also enables insightful physical understanding of the growth kinetics. We present this method by studying the weight growth kinetics of silica nanowire under two temperature conditions. The derived nanowire growth model is able to provide physical insights for prediction and control under uncertainties.

Automatic assessment of nanostructure quality is essential for scale-up nanomanufacturing. In our previous work, we have developed a method to quantify nanostructure growth quality and detect structural defects through interaction analysis. However, because the method builds on complete feature measurement, its direct application to nanomanufacturing systems is severely constrained by nanostructure metrology. For current inspection techniques such as scanning electron microscope (SEM), the major difficulties of measuring nanostructures lie in two aspects: (i) taking and calibrating images for seamless coverage and (ii) extracting and matching feature information from the images. In this paper, we develop a tailored sampling strategy to relax the metrology constraint. It not only explores the growth region with greatly reduced metrology efforts but maintains desired sampling resolution. In addition, we customize Expectation-Maximization algorithm to optimize interaction estimation with corresponding “incomplete” measurement. Our developed approach enables nanostructure characterization within manufacturing relevant time spans and thus provides a supporting tool for nanomanufacturing. Note to Practitioners-Automatic assessment of nanostructure quality is essential for scale-up nanomanufacturing, but current characterization of nanostructures based on SEM or transmission electron microscopy (TEM) is labor and computation intensive. This paper develops methods to quantify nanostructure local variability and detect defects with minimum metrology efforts.

Since properties of nanomaterials are determined by their structures, characterizing nanostructure feature variability and diagnosing structure defects are of great importance for quality control in scale-up nanomanufacturing. It is known that nanostructure interactions such as competing for source materials during growth contribute strongly to nanostructure uniformity and defect formation. However, there is a lack of rigorous formulation to describe nanostructure interactions and their effects on nanostructure variability. In this work, we develop a method to relate local nanostructure variability (quality measure) to nanostructure interactions under the framework of Gaussian Markov random field. With the developed modeling and estimation approaches, we are able to extract nanostructure interactions for any local region with or without defects based on its feature measurement. The established connection between nanostructure variability and interactions not only provides a metric for assessing nanostructure quality, but also enables a method to automatically detect defects and identify their patterns based on the underlying interaction patterns. Both simulation and real case studies are conducted to demonstrate the developed methods. The insights obtained from real case study agree with physical understanding.

This work intends to understand and model the kinetic aspect or the change of substrate weight over time in the selective growth of silica nanowires (NWs) catalyzed through Pd thin film. Various adsorption-induced, diffusion-induced, or unified vapor-liquid-solid (VLS) growth models have been developed to describe the NW length varying with time. Since NW length has been difficult to be measured, substrate weight change is therefore used as an alternative in this study to investigate growth kinetics of NWs. We investigate six different weight kinetics models in predicting weight changes during growth. Model estimation and comparison are conducted using both maximum-likelihood estimation (MLE) and Bayesian approaches. Owing to the embedded kinetics information in the nonlinear growth models, the Bayesian hierarchical model is shown to be more desirable when process data is limited.

In this paper, a state space model is developed to describe the dimensional variation propagation of multistage machining processes. A complicated machining system usually contains multiple stages. When the workpiece passes through multiple stages, machining errors at each stage will be accumulated and transformed onto the workpiece. Differential motion vector, a concept from the robotics field, is used in this model as the state vector to represent the geometric deviation of the workpiece. The deviation accumulation and transformation are quantitatively described by the state transition in the state space model. A systematic procedure that builds the model is presented and an experimental validation is also conducted. The validation result is satisfactory. This model has great potential to be applied to fault diagnosis and process design evaluation for complicated machining processes.