Six-Sigma Quality Management of Additive Manufacturing

A. Quality Management for High-Volume–Low-Mix Production

It is well known that “quality is inversely proportional to variability” [23], [24]. Fig. 3 shows the mass manufacturing that focuses on the production of a large volume of parts with a low-level mix. Traditionally, the measure of “variability” often refers to the scenario of high-volume–low-mix production in the context of mass manufacturing. In other words, if there is a large number of parts produced from the manufacturing systems, then it will be a logical step to characterize and measure the process variability and repeatability. The variability can be due to random or assignable causes in the manufacturing process. If the quality variations are solely because of random factors (i.e., nonassignable causes, not identifiable), then the distribution should be normal. However, if there are assignable causes, then statistical control charts are often used to monitor the process and detect when and how the process performance is affected. As such, the process can be stopped to look for assignable causes and eliminate them to resume normal production. Quality improvement involves a series of managerial, operational, and engineering activities to reduce the variability in the process. Especially, statistical DOE is utilized to realize a robust process by studying the effects of controllable settings under the uncertainty of uncontrollable factors, also called “robust parameter design” [25].

As a result, the 6S program emerged to meet the needs of mass manufacturing in the automotive and semiconductor industries and has achieved enormous successes in the past century. As shown in Fig. 4, the 6S program utilizes the DMAIC methodology for the reduction of process variability to the level that failures and defects are extremely unlikely. If the 3σ limits overlap with product specification limits, then the probability for a part falling outside the μ ± 3σ limit is 0.27%, which means that the number of defective parts per million (PPM) is about 2700. For the μ ± 6σ limit, the probability will be 0.0000002%, which means that the PPM is 0.002 (i.e., extremely unlikely). In the 6S scenario, if a finished product has 100 components and each component must be nondefective for the product to be nondefective, then the probability of the product to be nondefective is (0.999999998)¹⁰⁰ ≈ 1.0. The 6S concepts (e.g., design for 6S, lean production, and variation reduction) have been widely used to improve the capability of many business processes nowadays. The development of the 6S program has gone through three phases as follows.

1. Phase I: Address process monitoring, defect elimination, and variability reduction.

2. Phase II: Reduce total production cost and increase system performance.

3. Phase III: Emphasize the value creation to business organizations.

However, AM moves toward a high level of customization by enabling low-volume–high-mix production (even one-of-a-kind production) directly from the digital designs from the customers, resulting in “economies of one” [26]. The large quantity of parts produced from the same design is not available anymore, as in the traditional paradigm of mass manufacturing, to establish and measure process variability. Therefore, the 6S practice from mass manufacturing tends to be limited in the ability to be generally applicable to AM. There is an urgent need to push forward the next phase of the 6S program for AM. Fig. 5 shows the low-volume–high-mix production scheme for a customized design, which may only be fabricated once or in low volume. Note that there are significant layer-to-layer variations in part geometry. AM presents new QA/QC challenges: mass customization, low-volume production, and layer-to-layer variations in part geometry. In particular, because of the customized design and layer-by-layer fabrication in AM, it is not uncommon that each layer is different in terms of part geometry. Hence, it is difficult to characterize and measure the process variability and repeatability from one layer to another or from one build to the next.

B. Multilayer and Sequential Manufacturing Process

The layer-by-layer approach to AM brings significant challenges for QA/QC. Many AM processes use the raw materials of metal powders, where particle sizes and shapes vary between batches. Also, a laser or electron beam is utilized as the heating source in LPBF and DED. Slight variations in the intensity and diameter of the beam contribute to the issue of repeatability both between different machines and between the same machines at different locations on the build plate. Thus, every parameter that affects the end result of the process must be tailored to the materials used [27]. Furthermore, an AM system can utilize different layer thicknesses when manufacturing parts. A 2-cm-high object that uses a layer thickness of 100 μm will require 200 layers. IF the layer thickness is 50 μm, then the number of layers would be 400. Each of these layers has the opportunity for failure. Even if a single layer has a small probability of having a defect, the overall build will have a high probability of having at least one defect. To illustrate the effects and challenges of multilayer fabrication, consider the following example.

1. If the probability to contain defects is 0.0114 in a layer, then what is the probability for this layer to be nondefective?

   $$1-0.0114=98.86\%.$$

2. For an AM build with 100 layers, what is the probability to have no defects?

   $${(1-0.0114)}^{100}=31.77\%.$$

3. For an AM build with 100 layers, what is the probability of having at least a defect?

   $$1-{(1-0.0114)}^{100}=68.23\%.$$

4. If the probability of a build to contain defects is specified to be less than 10%, then what should be the probability for a layer to have defects?

   $$1-{(1-x)}^{100}=10\%\Rightarrow x=0.0011.$$

It is worth noting that this example assumes that each layer is independent of each other. However, AM is highly correlated from one layer to another layer. In other words, the defects in one layer can be corrected during the processing of the subsequent layer or can negatively impact the next layer and all the subsequent layers. This is analogous to the multistage assembly line in the traditional manufacturing paradigm. In the automotive industry, a car body assembly often involves a sequence of assembly operations. The variations in one assembly step can potentially introduce a stream of variations in the following steps [28]. However, the physics of multistage assembly operations are different from multilayer AM with LPBF in each layer. A 6S program for multistage manufacturing systems typically analyzes the current state of a process and then incrementally improves system performance with statistical methods and tools.

Establishing a 6S paradigm for AM calls upon new innovations to tackle these emerging quality challenges, including mass customization, low-volume production, lay-to-layer variations, and multilayer manufacturing process, which are unique when moving from traditional mass production to the new paradigm of AM. “Measure” requires the design and development of new sensor technologies for materials, processes, and postbuild inspections at different stages of AM. “Analyze” should be able to handle and connect the big data that are generated during the AM product lifecycle. “Improve” calls upon a better understanding of the process physics and an ontological knowledge of the underlying phenomena through statistical DOE on physical machines, AM processes, and/or computer experiments on simulation models. “Control” should consider the sequential decision-making problem for the multilayer fabrication process in AM and further address the multiobjective optimization of AM, for example, minimizing total cost (e.g., energy or time) consumed in the LPBF process and maximizing the quality of final parts. The new scientific basis of 6S quality management will impact the production-scale viability of AM and enable wider exploitation of AM capabilities beyond the current rapid prototyping status quo.

A. Prebuild Measurement and Characterization

Fig. 6 shows a broad representation of AM qualification flow about the material, process, and product. Metal powders are used as the input to the LPBF (and many DED) AM machines. Material qualification is indispensable to avoid the scenario of “garbage in, garbage out.” Standard powder characterization techniques include X-ray photoelectron spectroscopy, sieve analysis, inert gas fusion, scanning electron microscopy, laser light diffraction, and differential thermal analysis. These techniques allow the characterization of powders in three main aspects: particle morphology and distribution (e.g., the shape, surface roughness, or size), powder chemistry (i.e., elemental composition), and powder microstructure (e.g., porosity and rheology) (see [29] for a review of AM powder characterization). The standard practices for sampling metal powders are provided by standards organizations, such as ASTM International B215 and Metal Powder Industries Federation (MPIF). These sampling standards provide practical guidelines to obtain a representative sample from the whole lot and then apply the powder characterization techniques to measure the powder properties. Furthermore, manufacturers will be able to leverage the characterization results to pose requirements for suppliers, select the best supplier, and improve the powder reuse practices.

After prebuild material qualification, there are also system qualifications in the AM process and performance qualification of the part after the build is completed (see Fig. 6). In this article, we mainly focus on the in situ sensing of AM process performance to improve the understanding of machine–process physics, in-process monitoring, diagnostics, and prognostics (see details in Section III-B), Then, we briefly discuss postbuild measurement and inspection in Section III-C.

B. In Situ Sensing and Measurement

The in situ sensing of AM is a rapidly developing area encompassing new hardware systems, approaches for system integration, and data analytics. The need for in situ sensing in AM is motivated by the fact that a defect in any layer, if not detected and promptly corrected, will remain permanently sealed in on the deposition of subsequent layers. Recent review articles in this area include Grasso and Colosimo [30], Mani et al. [31], [32], Moylan et al. [33], Everton et al. [34], Spears and Gold [35], and Tapia and Elwany [36]. The challenges for in situ sensing of AM are steep and discussed as follows.

1. Each type of AM process (there are currently seven) imposes a unique layer bonding mechanism ranging from photochemical-initiated bonding to thermal-induced bonding; therefore, it is not possible to devise a generalized sensing scenario that is decoupled from the process physics.

2. The defects in AM are multifarious and are linked to specific process phenomena that range across length scales [37]. For example, delamination and cracking in LPBF processes occur at the part level (100 μm and above, and extending to the millimeter scale and beyond) due to thermal-induced residual stresses. In contrast, balling and keyhole melting are related to the instability at the meltpool level (less than 100 μm). A single sensor is not likely capable of capturing these diverse phenomena.

3. Integrating sensors into AM machines is difficult due to the tight form factor and mechanics of the process [38]. In the fused filament fabrication process, for instance, material in the form of a polymer filament is heated past its glass transition temperature and deposited by a nozzle. The gap between the nozzle and the top of the part is of the order of tens of millimeters. Therefore, sensors, such as an infrared (IR) thermal camera, are intractable to be mounted near the nozzle to obtain the surface distribution. This is because a large surface of the part will be blocked by the nozzle as it translates over the part [39]. A similar argument is made for the material jetting process.

4. In the LPBF process, layers of the powder material are spread across a bed and melted with a laser. The temperature gradient in the part is responsible for a host of defects, such as microstructural heterogeneity and delamination [40]–[42]. However, it is tractable only to obtain an estimate of the surface temperature distribution with the use of IR cameras and pyrometers. The temperature at the bottom layer is not easy to obtain in LPBF because the part is surrounded by powder, which acts as an insulating medium and progressively attenuates the thermal signatures generated as the laser melts the material on the layers near the top.

   Moreover, it is not possible to obtain the temperature distribution in the interior of the part without altering the process flow, for example, a thermocouple can be introduced inside the part by stopping the process [43], [44]. However, this will lead to loss of the chamber atmosphere and invariably alter the thermal profile. Researchers in Penn State’s CIMP-3D have pioneered wireless sensing attachments that fit into the power bed and collect temperature information from thermocouples and strain gages [43], [44]. Moreover, the thermal phenomena in LPBF occur at multiple spatial and temporal scales. For example, the meltpool-related thermal phenomena are at the order of a few micrometers and last for tenths of seconds, with cooling rates exceeding 10⁵ °/s. In the same vein, the surface-level thermal signatures last for a few seconds. Hence, different thermal imaging modalities are required for measuring meltpool-level and part-level phenomena. For the meltpool thermal imaging, a high frame-rate thermal camera with imaging range in the shortwave IR region is typically used, while, at the part level, a long-wave IR camera with a large field-of-view and smaller frame rate and integration time is used [33], [45], [46].

5. Even though the process dynamics might be notionally similar, such as DED and LPBF, the sensors from one process cannot be readily transferred between them. For example, in the DED AM process, the meltpool is several orders of magnitude larger than in LPBF, and in the former, the meltpool can approach the millimeter level, while, in LPBF, it is close to 100 μm [47]. Likewise, the deposition rates in DED can be more than ten times that of LPBF. Moreover, in DED, the part is exposed on all sides of the chamber and therefore convection forces (due to carrier gases from the nozzle) and radiation are all active at the same time. Consequently, it is exceedingly difficult to demarcate and measure all of these heat transfer mechanisms.

6. The sensor measurements must be synchronized with the state of the process if the data is to be used for process control. Furthermore, the data from multiple sensors must be synchronized with each other. From an LPBF perspective, recording the process state would involve capturing the position of the laser (i.e., the angular displacement of the galvanometer) and merging the laser position with the sensor data being acquired. In other words, the data acquisition system must communicate with the AM machine and sensor hardware with temporal error in the microsecond range (the laser in LPBF can translate at a velocity exceeding 0.5–1.0 m/s). The challenge is further complicated given that the sensor array may include both temporal sensors, such as photodetectors, and image-based sensors, such as thermal and optical cameras.

To overcome these barriers, researchers use heterogeneous sensing modalities [47]. A notable example of such a multiphenomena sensing array in LPBF is the so-called open architecture LPBF platform at the Edison Welding Institute (EWI), which is currently instrumented with the following sensors [48], [49]:

1. local sensors for monitoring the meltpool-level phenomena (10–200 μm scale):

   1. a coaxial shortwave IR thermal camera for meltpool temperature measurement (85 frames per second (fps), 13.4 × 7.12 mm field of view, and 5-μm spatial resolution);
   2. a coaxial high-speed camera to track the meltpool shape (1000 fps and 10-μm resolution);
   3. a photodetector to record the meltpool intensity (350–1100 nm and 10-kHz sampling rate);
   4. an spectrometer to measure the optical emission in the meltpool region (200–1100 nm and 1 kHz).
2. global sensors for monitoring phenomena at the bulk part level (500 μm–100 mm):

   1. a coaxial short-wave IR thermal camera focused on the powder bed to detect part temperature gradients (4 fps, 127 × 95 mm field of view, and 400-μm resolution);
   2. a laser interferometer (405 nm) for measuring surface finish and distortion in a layer;
   3. an structured light optical imaging of the powder bed with two digital cameras to detect distortion of the part (21 fps, 25.4 × 14.7 mm field of view, 6.6-μm pixel resolution, and 165-pixel/mm fidelity);
   4. an acoustic microphone and a surface acoustic wave transducer to detect when the part cracks due to distortion or makes contact with the powder recoater (sampling rate of 10–40 kHz).
3. sensor data acquisition, data synchronization with the laser position, and noise isolation:

   1. close to two terabytes of sensor data are acquired in a 12-h build cycle on EWI’s LPBF platform. Researchers at EWI have built the hardware and software mechanisms to ensure the seamless acquisition of sensor data of such high volume, variety, and sampling speed (a big data problem).

EWI’s open-architecture LPBF platform provides the capability to measure the temperature distribution in the part and track changes of thermal gradients that are not available on other commercial LPBF systems. Another recently operational and comparable apparatus is the Additive Manufacturing Metrology Testbed at the National Institute of Standards and Technology (NIST). In addition, CIMP-3D at Penn State developed a multisensor suite for monitoring and control of a commercial 3D System ProX 320 PBFAM system, as shown in Fig. 7. The multisensor suite has also been demonstrated on 3D Systems ProX 200, EOS M280, and GE Concept Laser M2 machines. The system consists of a variety of sensors as follows:

1. a high-resolution/high-magnification imaging system (six differing lighting schemes);

2. two high-speed/high-magnification cameras, including a coaxial camera with 405-nm filter and a front-facing camera with 520-nm filter;

3. high-speed video (>33 000 fps);

4. optical process emissions (100 kHz), including a spectrometer and multispectral sensors;

5. acoustic sensors (100 kHz);

6. a thermal imaging and DMP meltpool sensor.

This multisensor suite includes an optical layerwise imaging system to monitor the LPBF AM process, which consists of a 36.3 Mpixel digital single-lens-reflex (DSLR) camera that is placed inside the chamber of the EOS M280 machine [15]. In-process optical images have also been collected and used to identify and characterize defects caused by lack-of-fusion in the LPBF process [50]. Stutzman et al. [13], Nassar et al. [51], and Dunbar and Nassar [52] describe the use of an in situ optical emission spectroscopy system consisting of two filtered photodetectors in a series of papers.

Montazeri et al. [53] demonstrated the use of this relatively inexpensive system to monitor lack-of-fusion porosity in Inconel 718 test parts an use features derived from the line-to-continuum ratio as inputs to detect lack-of-fusion porosity. Inconel has chromium as an alloying element. When Inconel is fused (melted) by the laser, atomically excited chromium is vaporized and emits photons corresponding to electronic transition. One set of transitions occurs in the wavelength around 520 nm [54]. If melting is stable, so will be line emission from the vapor. A key innovation is the use of two photodetectors, one of which is filtered to have a frequency spectrum in a region where line emissions are not likely and measures emissions pertaining to the background radiation (a wavelength different from the line emission wavelength, called the continuum emission spectrum). Furthermore, Nassar et al. [51], [52] divide this difference (line emission intensity minus continuum emission intensity) by the continuum emission intensity; this ratio is called the line-to-continuum ratio. In summary, multisensor systems generate high-dimensional and heterogeneous data (e.g., time series, video, and image profiles) that provide rich information about AM processes. However, realizing the full potential of these data for AM system qualification depends, to a great extent, on the development of analytical methods to characterize, represent, and extract useful information about the defective state in each layer of AM builds, as detailed in Section IV.

C. Postbuild Measurement and Inspection

As shown in Fig. 8, postbuild quality inspection and function integrity assessment for AM are often performed with radiographic-based computed tomography (CT). Here, CT scans of AM builds are collected with a GE vTomex M300 microfocus X-ray CT (XCT) scanner and are processed using the Volume Graphic myVGL3.0 software to extract the 2-D image profiles of every layer in an AM build. CT reconstructs hundreds to thousands of 2-D radiographs in a 3-D volume of voxels. The resolution of image profiles is determined by the CT voxel size, typically with a pixel size of 10–50 μm or less. These data will enable the investigation of the effect of design parameters or LPBF process settings, for example, hatch spacing (H), scan velocity (V ), and laser power (P), on the defect patterns in AM image profiles. The sensor data and offline CT scans can be used to create a library of (sensor) patterns that correlate to specific defects using sensor fusion and predictive analytics. These sensor signal patterns, which exemplify specific process defects, can be integrated with prescriptive models (i.e., for decision-making) to optimize the selection of corrective action in case an anomaly is detected in the process. The focus is to minimize defects, delamination, and warpage of the final workpiece and maximize final strength and fatigue resistance. In addition, other equipment, such as coordinate measuring machines (CMMs) and surface probing machines, provide important information about part dimensional metrology and surface roughness [55], [56].

D. AM Data Management

Large amounts of data are generated, exchanged, and used dynamically during AM test coupon and part development processes. As the volume of data grows with increased in situ sensing and nondestructive examination (NDE), the types of data generated by AM activities also become richer. The information necessary for AM process qualification includes not only measurement data but also material/machine specifications, design models, control, and management data. Characterizing the entire AM process demands a comprehensive analysis of all the information collected through the build history of thousands of parts and coupons, in the context of the complete AM value chain. As a result, it requires an effective and efficient AM data management system to ensure that data are captured, stored, and used appropriately.

In the area of data management, several AM information management systems are available as commercial products. For example, the Senvol Database (http://senvol.com/database/) provides researchers and manufacturers with open access to information about industrial AM machines and materials. Granta, a material information management technology provider, offers the product GRANTA MI: Additive Manufacturing, specifically customized for AM data capturing and use. At the same time, multiple database and data management systems are built to organize and manage the data generated from research and industry projects. The Data Management System for Additive Manufacturing (DMSAM) was developed by researchers at Penn State’s CIMP-3D (http://www.cimp3d.org/datamanagement). DMSAM is a schema-based software tool that stores and tracks all of the data and information related to an AM part, including the state of associated AM resources (e.g., powder, software, and machine), part requirements for sponsors, 3-D solid models, part workflow, build plan, postprocessing plan, and all data associated with part properties, in situ monitoring, postprocessing, testing, and inspection. DMSAM stores data locally, communicating with global (i.e., shared) databases and generating build reports for QA/QC as needed through XML, as well as Excel. NIST’s Additive Manufacturing Materials Database (AMMD) [57] is a data management system built with Not Only Structured Query Language (NoSQL) database technology and provides a Representational State Transfer (REST) interface for application integration. The database captures rich research data sets generated by the NIST AM program (https://ammd.nist.gov/) based on an open XML schema. In addition, as an open data management platform, the AMMD system is set to evolve through codevelopment of the AM schema and contributions of data from the AM community.

However, due to the multifarious factors that could affect AM part quality, existing data-driven AM process qualification requires extensive testing of material, which is beyond the capability of any individual organization. None of the existing databases provide comprehensive data sets with a multitude of geometries and processes settings by itself to qualify an AM process for parts with various features and specifications. In order to significantly reduce the cost and time associated with the data management for AM process qualification, a collaborative data space is required, and a collaborative data management system is necessary. Fig. 9 shows a multitier AM collaborative data management system with the characteristics: 1) distributed data storage facilitated by using common data terms and definitions; 2) collaborative linked data through federation based on neutral data formats; 3) continuous knowledge management by extracting AM material process–structure–property relationship automatically from AM data; 4) lifecycle and value chain-based decision support; and 5) an adaptive data generation system that helps AM community to efficiently design experiments. The collaborative data management system is set to identify, generate, curate, and analyze AM data through AM product lifecycle and can significantly reduce the cost and time associated with AM product deployment.

A. Engineering Design Versus Build Quality

Engineering design and relevant parameters are some of the key process input variables during the AM process. Traditional subtractive manufacturing tends to be limited in the ability to handle complex designs. “Design for manufacturing” refers to the conventional scheme that adapts a design to enable manufacturing within the capability of available machines and tools. AM offers a higher level of design freedom and enables the new scheme of “manufacturing for design.” Complex designs can now be manufactured in a layer-upon-layer fashion with the new generation of AM technology. Nonetheless, complex designs still pose quality challenges on AM-fabricated products, despite the fact that AM can handle certain aspects of fabrication better than traditional manufacturing technologies.

The new research question is whether and how design parameters influence the quality of AM builds? Our prior work has designed and performed experiments on an LPBF machine to investigate how design parameters (i.e., height, width, recoating orientation, and hatching pattern) impact the quality in the final build of thin-wall structures [59], [60] that are widely used in the fabrication of heat exchangers. As shown in Fig. 10, our experiments built the thin-wall structures with a variety of design parameters, that is, heights, widths, recoating orientations, and hatching patterns. The metal powder is Spherical ASTM B348 Grade 23 Ti-6Al-4V, with the distribution of powder size in the range of 14–45 μm. Each build includes 25 thin walls that are fabricated on a 15 mm × 15 mm × 55 mm platform. Experimental factors such as height, width, recoating orientation, and hatching pattern are detailed as follows.

1. Height: The height of thin walls varies from 0.6 to 3.0 mm with a step size of 0.1 mm. The height-to-width ratio is 0.1 in each thin wall.

2. Width: The width of thin walls ranges from 0.06 to 0.3 mm with a step size of 0.01 mm.

3. Orientation: Thin-wall structures are fabricated vertically upward with the layer thickness of 60 μm in three orientations with respect to the travel direction of the recoater blade (i.e., 0°, 60°, and 90°). Fig. 10 shows three orientations with the reference of recoating direction.

4. Hatching: The hatching patterns of thin walls follow the standard processing path of EOS machines, but various categories of scan paths are utilized when the width increases (see Fig. 10). Fins 1 and 2 have two inner rectangle paths, two outer layer paths (or contours), and rotating diagonal hatching from rectangles. In Fins 3–14, there are three outer layer paths and rotating diagonal hatching inside the innermost rectangle. In Fins 15–18, there is one rectangular hatching. In Fins 19–25, there is one thin area path.

As shown in Fig. 10, we fabricate three thin-wall parts in this experimental study, each of which includes 25 thin walls. The orientations are different for three thin-wall parts on the build plate. In other words, the orientation of each thin-wall part is adjusted to the degree of 0°, 60°, or 90° with respect to the travel direction of the recoater blade in the EOS machine. After fabrication, we scan each build with XCT. These XCT images are then registered with the original CAD models to extract the quality characteristics (e.g., edge roughness and defect levels) in each layer of the thin wall. Here, the edge roughness refers to the geometric deviation of build boundary between CT scans and CAD designs. The defect level refers to the number and degree of defects in each layer of the thin wall. These quality characteristics are tracked from one layer to another for the detection of the impending collapse of thin-wall failures (see [59] and [60] for the analysis of variance with respect to design parameters).

Through the analysis of XCT data and in-process imaging data, experimental results show that the build quality of thin-wall parts is impacted by design parameters (height, width, and height-to-length ratio) and machine settings (hatching and recoating orientation). This study helps provide a set of design guidelines on the use of LPBF machines for the fabrication of thin-wall structures as follows.

1. The 0° orientation gives a superior quality in the thin-wall builds to other orientations. Fewer defects are generated when the travel direction of the recoater blade is parallel to the long edge of a thin wall. The 90° orientation should be avoided to build thin-wall structures, which tends to generate more flaws by making the recoater motion perpendicular to the long edge of a thin wall.

2. The height of a thin wall should not be more than nine times its width. Otherwise, this thin-wall build tends to collapse. The LPBF machine in this experiment is limited to build the thin-wall structures with a width that is smaller than 0.15 mm. If the length-to-width ratio exceeds 73 (11 mm/0.15 mm), thin walls also tend to collapse.

This study made an attempt to answer the research question about whether and how design complexity influences quality characteristics of AM thin-wall builds. There is more research to be done to optimize the engineering design for AM. For example, it is imperative to generalize design guidelines for different LPBF machines, process conditions, or thin walls with overhang structures.

B. Machine Setting Versus Build Quality

Machine settings (e.g., hatching space, laser power, and scan velocity) often influence the final outcomes of the AM manufacturing process, including the cosmetic appearance and build quality. To increase the information visibility and cope with the complexity in the machine–process interactions, advanced sensing is increasingly employed in AM (see the multisensor suite and CT scanner in Figs. 7 and 8), thereby generating large amounts of data (e.g., optical images and postbuild CT scans). Realizing the full potential of sensor data hinges on the development of new statistical QC (SQC) methods. Existing SQC methods for conventional manufacturing processes are more concerned about key features of finished products (e.g., dimensional accuracy) and linear and nonlinear profiles, as opposed to high-dimensional sensor data. The research on AM sensing, machine–process interaction, and QA/QC poses several new challenges:

1. Sensor-based metrology for in situ quality inspection: Traditional QA/QC techniques, such as surface metrology geometric and dimensioning and tolerancing (GD&T), are more concerned about the Euclidean features of the finished AM products. They are offline and not amenable to the inspection of internal defects in AM parts with complex geometries [61]–[64]. In the absence of sensor-based approaches for in situ quality monitoring, benchmarking of AM builds remains relegated to postbuild inspection and qualitative attributes [65]–[67].

2. Statistical quality management for AM: Current quality monitoring approaches are offline, based on purely data-driven techniques (neural networks, mixture Gaussian modeling, and statistical analysis), or lumped-mass formulations [68]–[71]. Very little has been done to investigate AM quality management using sensor-based analytical models and layerwise AM QA/QC strategies. In situ monitoring provides an opportunity to in-process AM defect mitigation that is indispensable for manufacturing industries mandating stringent quality standards and product esthetics.

Hence, the first step is to extract useful information from AM sensing data and then estimate the defect levels in AM builds. Fig. 11 shows an illustration of AM images in different scales, where multiscale self-similarity can be observed to some extent. In other words, fine-grained images of AM builds can often show multifractal characteristics over a range of scales. Traditional linear methods are limited in the ability to handle nonlinear fractals and irregular patterns in the images. Fractal analysis extracts a single fractal dimension that describes the self-similarity (scale-invariant) behavior of fractal objects but cannot fully characterize multifractal patterns that are often shown in real-world objects [72], [73]. However, image profiles of AM builds are often comprised of complex self-similar patterns that are not due to a single fractal but rather the existence of a spectrum of fractal dimensions. These fractals interact with each other and then generate highly nonlinear and complex self-similar behaviors (see Fig. 11).

Little has been done to characterize multifractal patterns in large amounts of image profiles to investigate how machine settings influence the AM build quality. Our prior work has developed new multifractal methods for the analysis of large amounts of AM imaging data and extracts features that are sensitive to the defects, instead of extraneous factors and random noises [72]–[76]. As shown in Fig. 12, multifractal analysis characterizes the nonlinear and self-similar behaviors of AM images in multiscale lenses, ranging from large-scale approximations to small-scale details. AM images are then decomposed as an interwoven set of fractals with different dimensions, which is shown as the multifractal spectrum. In addition, lacunarity measures the degree or extent to which this set of fractals fill the space, which cannot be provided by multifractal analysis alone. Therefore, we developed the method of joint multifractal and lacunarity analysis to characterize and quantify the nonlinear and multifractal patterns in AM images that cannot be otherwise achieved by either traditional statistical methods or fractal analysis.

After the multifractal characterization results of AM images, we investigated how AM machine settings [e.g., laser power (P), hatch spacing (H), and velocity (V)] influence the build quality. In the experimental study, we printed cylinder parts in the EOS M280 machine with varying levels of machine settings (see Fig. 20). Especially, laser scanning velocity is increased from 1250, 1562.5, to 1875 mm/s. The hatching space is varied from 0.12, 0.15, to 0.18, and laser power is decreased from 340 250, to 170 W. Furthermore, a regression model is constructed to predict the relationship between machine settings with the Hotelling T² indices of build quality, which are computed with multifractal and lacunarity features of XCT image profiles [72]–[76]. The model achieves the adjusted R² value of 94.76%, showing a strong correlation between process conditions and build quality.

C. In Situ Sensing Variables Versus Build Quality

CT scans help characterize the quality of a finished build but cannot detect the flaws during the AM process. In situ sensing provides a means for on-the-fly defect characterization. As shown in Fig. 13, a drag link part with complex geometry was printed in CIMP-3D with intentional defects at four layers (i.e., 1.5, 6.7, 12.0, and 16.0 mm), each of which includes eight defects as follows:

1. 0.050-, 0.250-, 0.500-, and 0.750-mm cubed defects are on each plane.

2. 0.050-, 0.250-, 0.500-, and 0.750-mm diameter cylinder defects are also on each plane surrounding the cubes. All cylinders have a 1:1 diameter to depth ratio except for 0.050, which has a depth of 0.250 mm.

3. The top of the defect is the flat plane in the build direction.

In situ optical images are recorded after each layer is printed. This experimental study is aimed at predicting incipient defects from in situ imaging data for QC in the AM processes. The state-of-the-art deep neural network (DNN) models show superior performance in the handling of imaging data. However, layerwise imaging data from AM processes pose significant challenges to DNN defect analysis.

1. Region of Interests (ROIs): Each image contains not only metal powders but also many AM parts in the build plate. As such, there is a need to delineate the image for a specific part. Often, a squared region is cropped around the part, and then, the images of layers are fed to the DNN model. This guarantees the same dimensionality of input images to the DNN model. However, due to the broad geometrical diversity from one layer to another, images of some layers will have small part geometries and large powder areas, while others have large part geometries and small powder areas. DNN learning will be biased by the layerwise geometrical diversity, as well as the varying areas of unfused powders. Therefore, it is more desirable to leverage CAD files to delineate and register the ROI for the part geometry in each layer (see Fig. 14).

2. Layer-to-Layer Geometry Variation: AM provides a higher level of flexibility for the low-volume and high-mix production, even for a one-of-a-kind design. As shown in Fig. 5, AM fabricates the build directly from a complex CAD design through layer-upon-layer deposition of materials. Although we may register the ROI for the part geometry in each layer, there will be ROI variations among layers. Hence, both the shape and dimensionality of ROIs will be varying from one layer to another. The inconsistent ROIs consist of different numbers of pixels and cannot be used as inputs to the DNN models for learning the incipient defects in the layers.

3. ROI Segmentation and Spatial Characterization: To tackle the challenge of inconsistent ROIs, one approach is to extract features from layerwise ROIs (e.g., mean, median, and variance). However, statistical features tend to aggregate useful information within the ROIs, thereby leading to the deficiency in defect characterization and predictive modeling. The other approach is to segment ROIs into smaller ROIs with the same number of pixels. Although the dimensionality of ROIs is changing from one layer to another, the greatest common divisor (GCD) for ROIs of all layers can be leveraged to segment ROIs with the same number of pixels. However, these ROIs may still have variations in shapes. Furthermore, spatial characterization can be used to measure spatial correlations among pixels and describe pertinent patterns about defects in the ROIs. As the number of pixels is constant in the ROIs, characterization images share the same dimensionality that can be fed into DNN models for the learning and prediction of defects in each ROI in the AM processes.

As shown in Fig. 14, our prior work has designed a new DNN model to learn incipient defects from sROIs of in situ image profiles [77], [78]. The experimental study provides large amounts of images taken for each layer with different lighting schemes. To tackle the aforementioned challenges, DNN learning of in situ AM defects consists of the following critical steps.

1. Image Registration and Segmentation: We first used the CAD design to perform shape-to-image registration and extract the ROIs of 362 layers in the drag link part. Then, these ROIs are segmented into 1708 sROIs, each of which has the same number of pixels. Furthermore, the dyadic partitioning of sROIs can be used to split each region into smaller subregions and provides a large amount of data for multiresolution DNN learning of layerwise AM defects.

2. Spatial Characterization: Although these sROIs are in different shapes, we utilized the spatial characterization to extract pertinent patterns about defects from sROIs and then fed images of spatial correlations for deep learning.

3. Deep Learning: The DNN model includes a series of convolutional layers to learn sROI characterization images with multiple levels of abstraction. Each hidden layer is followed by nonlinear modules, which transforms the representation at one level into a representation at a higher, slightly more abstract level [77]. The DNN builds up effective learning and representations of various intentional defects [i.e., embedded in the drag link part (see Fig. 13)] that help significantly reduce the size of state space and state-action pairs for predictive modeling and optimization in the following.

The DNN model described earlier is shown to effectively predict the layerwise defects with the specificity of 93.85±0.83%, the sensitivity 90.01±1.56%, the negative predictive value of 93.83±0.67%, the positive predictive value of 90.03±2.34%, and the accuracy of 92.50±1.03%. This experimental study avoids the use of DNN as a blackbox by just feeding cropped images of layers (i.e., with the broad geometrical diversity) into the neural networks and then letting AI classify ROIs and identify the defects. Indeed, engineering domain knowledge is indispensable to preprocessing AM training data and developing effective AI methods for in situ AM defect learning and analysis.

A. Ontology Modeling

As shown in Fig. 15, the growing body of AM research exists in many forms (e.g., papers, models, simulations, graphs, and data) and is both specific to a given AM process and generalizable to AM more broadly. Several complementary efforts are underway to develop data management systems by NIST,¹ CIMP-3D,² Granta,³ and many others. Also, numerous sensing capabilities (e.g., photodiodes, cameras, pyrometers, thermocouples, and spectrometers) are available for metal AM processes (e.g., PBF and DED). Different sensors have been installed on different AM systems to generate empirical data to help validate simulation models, for instance, or develop process maps for different AM systems and materials. The challenge now lies in the integration of all the information into useful AM knowledge, which includes the selection of the right sensors to generate the right data for the right analytics for QA/QC.

Our previous work developed an ontology to support AM process model development and reuse [81], [82]. The AM ontologies sought to overcome pertinent challenges about disparate AM process models and simulations (e.g., with variations in the input–output specification), not to mention the levels of detail, fidelity, and composability. This limitation restricts their reuse and makes it difficult to integrate different models from different groups into the most accurate AM simulation model or for different use cases. The AM ontologies developed by Penn State and NIST allowed users to navigate complex relationships and understand the connections between different process parameters, microstructural characteristics, and mechanical properties for AM parts. A sample of the ontology is shown in Fig. 16 where the details on the class hierarchy for AM thermal models can be seen along with the definition of the Absorbed_laser_power class.

The AM process ontology generates a network of parameters that can be visualized as a graph to look for similarities and differences across different models from different researchers. We will refer to these as knowledge graphs as they can be navigated forward (or backward) to identify important relationships between parameters and phenomena that were previously disconnected. Two examples of navigating such a knowledge graph to identify important relationships during AM are shown in Fig. 17. In Fig. 17(a), the knowledge graph is used to trace a process parameter that we can measure (i.e., meltpool area) to understand how it influences different mechanical properties that may be of interest (e.g., tensile strength, yield strength, elongation, and the Vickers hardness). The graph does not tell us exactly how they are related, but we know from the AM ontology that these parameters influence each other based on data and models in the literature.

These same ontologies developed to manage process models can be easily extended to support data management and configuration. As noted in Section III, a vast amount of AM process data is being measured, often used for the development and validation of AM process models. Fig. 17(b) shows an example of how the AM ontology can be leveraged to navigate the knowledge graph in reverse to identify what sensor data should be captured to help ensure that a requirement is met. In this example, we assume that a requirement is specified on the Vickers hardness of the part, and then, we navigate the knowledge graph backward until we find process parameters that we might be able to sense, namely, scanning speed and absorbed laser power in this case. While we may not be able to measure absorbed laser power directly, this, nonetheless, provides an indication of what we might want to sense during the process to gather data to help ensure that our requirement is met.

The AM ontology and corresponding knowledge graphs can also be used to support the analysis of process parameters and sensor data. For instance, Table 1 shows data from an experiment where several input process parameters (e.g., laser power, velocity, and spot size) were varied, and sensors were used to capture meltpool depth and width; deposition height and width were also measured for each test specimen [83]. Linear regression was then used to analyze the data in Table 1, and $R_{\text{adjusted}}^2$ values for deposition height and deposition depth are 91.75 and 89.97, respectively, as a function of the process parameters that were varied. The $R_{\text{adjusted}}^2$ value for meltpool width is also good (94.85); however, the $R_{\text{adjusted}}^2$ value for meltpool depth is not (68.00). When we trace these relationships in our AM ontology, we find that the Marangoni effect, the velocity of the fluid, and the Buoyancy effect have a relationship with meltpool depth, yet none of these are in the data because they were not measured or sensed during the experiment. Had the researchers had the ontology, the corresponding knowledge graph could have been used to plan the experiment more carefully, that is, what data to sense and capture based on what they wanted to analyze after the experiment. This simple example demonstrates what might be achieved (and potentially avoided) by using a knowledge graph, such as the AM ontology to guide sensing and inform the analysis.

B. Design of Experiments

The distinctive aspects of AM compared to traditional subtractive and formative manufacturing processes are the relative tight coupling of the part geometry (shape), microstructure evolved, and process conditions [84]–[86]. In other words, the shape, microstructure, and process conditions interact to influence the functional integrity aspects of the part, such as its strength, fatigue life, adherence to geometric, and dimensional specifications, among others. This coupling of part shape, process parameters, microstructure, and part properties is rather weak in conventional manufacturing; for instance, in subtractive machining, although the near-subsurface microstructure is influenced by the cutting conditions and geometry, the bulk microstructure is largely unaltered. Some of these process–structure–property relationships in AM are exemplified in Fig. 18.

This intricate interaction in AM lies at the crux of the large uncertainty in part quality aspects, and accordingly, the use of traditional DOE-based methods to achieve the optimal processing conditions is constrained for the following reasons.

C. Simulation Modeling and Analysis

Computationally efficient and accurate physical models are critically needed for AM to: 1) narrow the process parameter space for a property of interest; 2) identify red-flag problems in the part design; 3) aid support placement, build orientation, and build plans; 4) predict the distortion and microstructure evolved; and 5) augment process control by providing a model-based baseline for adjusting the process (feedforward control) [94]–[97]. From a broader vista, simulation in AM can be categorized into three classes contingent on the dominant phenomena: thermal, fluid, and photopolymerization based. To explain further, in the metal AM processes, such as LPBF and DED, the energy applied in joining the layers is supplied by a laser; accordingly, researchers have focused on modeling the thermal phenomena in metal AM. Melting- and extrusion-based polymer AM approaches, such as fused filament fabrication, may also be considered to fall under the category of thermal initiated AM. Processes such as binder jetting and aerosol jet printing are governed by the mechanics of droplet formation, fluid flow, and wetting. Finally, material jetting stereolithography is governed by photochemical reactions.

In this article, we have chosen to focus on metal AM processes given their popularity in high-value industries, such as aerospace and biomedical. The industrial interests in LPBF and DED have propelled active research in simulation modeling of these processes, with several commercial ventures being initiated in the last decade. The three key problems faced by researchers in this area are as follows:

1. simulation time;

2. coupling of phenomena across multiple scales;

3. difficulty in experimental validation.

These difficulties originate because thermal modeling in LPBF and DED involves multiscale physics, which starts at the meltpool level, progressing to the layer level, and, finally, the part level [42], [96], [98]. The various process-part thermal interactions in the LPBF and DED processes are depicted in Fig. 22. The meltpool or particle-level dynamics are tied to material solidification rates and the interaction of the laser beam with the powder, and hence, it is the key to predict the microstructure evolved and, as a consequence, mechanical properties, such as hardness, strength, and fatigue life [99]. Next, in ascending order, is the so-called mesoscale or track level, which ranges from a few hundreds of micrometers to under a millimeter. The aim of track-level simulations is to predict consolidation of the powder and dynamic evolution of the meltpool as the laser is scanned, which is consequential to the density of the part formed. Finally, at the macroscopic or part level, which ranges from millimeters and beyond, the thrust is to predict the thermal-related residual stresses and geometric deformation.

At the meltpool or particle level, the interaction of the laser beam with particles is the focus. Particularly, in LPBF, the energy absorbed by the material is a function of its reflectivity (in electron beam PBF, the electronegativity is of importance). Highly reflective material will tend to absorb a smaller magnitude of the incident laser energy. Furthermore, the laser is reflected repeatedly by the powder particles when it is incident on the powder bed. This is advantageous to material melting as the energy absorbed by the material increases on account of multiple reflections. The laser–particle interaction is also important to understand the formation of the pinhole (due to vaporization) and keyhole-type porosity. The former occurs due to one of three reasons: first, the vaporization of remnants of moisture on the surface of powder particles; second, the escaping gases trapped within the meltpool; and third, due to the vaporization of impurities within the powder that has a lower melting point than the desired alloy. Keyhole melting porosity occurs at inordinately high laser energy conditions, which causes the powder to vaporize and create a cavity. This cavity serves to further focus the laser into a narrow beam, exacerbating the vaporization of more material. Eventually, the surrounding material falls into the cavity and fills it incompletely, causing a void (keyhole collapse). In the case of the DED process, the simulation at this scale includes modeling the interaction of the falling powder with the carrier gas, as well as the laser.

At the track levels, the simulations must take into account surface tension-related phenomena, such as the Plateau–Rayleigh effect, which is the root cause of meltpool instability and, consequently, inferior consolidation of the material. Furthermore, at the meltpool level, the material changes from solid to liquid and back to solid again; as a result, latent heat effects cannot be neglected. The simulations at this scale have been used to model the segregation or breakup of the meltpool into discrete chunks, called balling. This phenomenon is typically observed underneath unsupported features in the part and is related to the accumulation of heat in a region. The temperature increase causes the surface tension of the meltpool to decrease, which, in turn, leads to an increase in its length. The inordinate increase in the meltpool causes the onset of the Plateau–Rayleigh instability causing the meltpool to break up into discrete chunks. Each of these chunks eventually coalesces into spheroid shapes. The occurrence of balling phenomena is tied closely to the laser power and hatch spacing. This example serves to emphasize that the dynamics of the meltpool and track levels involve both fluid and heat transfer phenomena.

Finally, at the part level, the prediction of the temperature distribution has garnered commercial interest, with the emphasis on four aspects: 1) predicting distortion during and after the build; 2) possibility of a recoater crash due to part distortion during the build; 3) optimizing part orientation and placement of supports; and 4) build layout planning. To explain further, the three main factors that influence the thermal distribution at the part level in LPBF are as follows:

1. the geometry of the part, including features such as steep overhangs, and the presence of anchoring supports [90], [101]–[103];

2. type and characteristics of the feedstock material and process parameters, such as the laser power, hatch spacing, layer thickness, laser scan velocity, and scanning strategy, which influences the average heat input (global energy density) [104];

3. the time required for scanning a layer and the interval between the melting of successive layers (interlayer cooling time), which are functions of the build layout determined by the number, geometry, orientation, placement, and scanning sequence of other parts on the build plate.

At the part level, the effect of meltpool-level phenomena (e.g., latent heat aspects) is neglected to aid computation. Mathematically, the aim is to solve the heat diffusion equation, in which conduction is the model heat transfer, and radiative and convective effects are considered postfacto, that is, after the heat diffusion equation is solved. The heat diffusion equation takes the following form:

Solving the heat equation results in the instantaneous temperature T(x, y, z, t) at a time t for a Cartesian spatial coordinate (x, y, z). The temporal map of T(x, y, z, t), that is, the trace of the temperature T at the location (x, y, z) over time, gives the temperature history in the part for that location. The right-hand side term is the energy supplied by the laser per unit volume of the material per second (Q). Although the units are identical to the global energy density (E_v), Q is a more encompassing term because of the flexibility to include the effect of the beam shape.

The benchmark computational approach for solving the heat equation originates in the welding literature, as exemplified in the work of Goldak et al. [105]. This model called Goldak’s double-ellipsoid model considers, as the name suggests, the laser source to be ellipsoidal in shape. The beam energy is assumed to be concentrated in the center and dissipates near the boundary of the ellipse. In the AM context, researchers tend to model the beam to be ellipsoidal and the energy distribution within its Gaussian. A key difference between welding and AM is that, in the latter, the heat source has a smaller profile, and the translation speed (scan velocity) is a magnitude higher. Consequently, the cooling rates in LPBF approach the order of nearly 10⁵ °/s. In DED, the spot sizes are much larger than LPBF.

The main problem faced at the part-level thermal modeling is the evolving nature of the part geometry in AM. To explain further, the model must take into account the change in the computational domain and boundary conditions as the material is deposited layer-upon-layer. The key challenge is to keep track of the elements from a finite-element modeling perspective [106]. Typically, this is done through the element birth-and-death approach, where the elements are slowly activated. The second is the quiet element method, wherein the part was meshed beforehand, but the thermal properties of an element are activated at the appropriate interval. Commercial software, such as Netfabb, makes use of a hybrid strategy involving both the quite element and birth-and-death approach. It may be noted that researchers at the Lawrence Livermore National Laboratories have developed comprehensive multiscale modeling tools based on their extensive code base, at the mesoscale (ALE3D) to the part level (Diablo). Techniques such as finite difference and discrete element methods have been employed to solve the heat diffusion equation [107]. Newer approaches based on circuit theory and graph analysis have been introduced for mapping the thermal distribution in AM [100], [108].

Fig. 23 shows a schematic of the mesh-free graph theory to solve the heat diffusion equation. The key idea is that the discrete heat diffusion equation is solved as a function of the eigenvalues and eigenvectors of the Laplacian matrix of a graph projected onto the geometry of the part. The main advantage of the graph theory approach is that the temperature distribution part can be potentially computed many times faster compared to FE because: 1) graph theory eliminates time-consuming meshing steps and 2) it avoids cumbersome matrix inversion operations needed to solve the heat equation and, instead, uses the matrix eigendecomposition.

Furthermore, the graph theory approach is verified with a finite-element implementation of the so-called gold standard Goldak’s double-ellipsoid model, which has its genesis in welding [105]. The graph theory solution was also quantitatively compared with the commercial Netfabb solution. The results for three-part geometries are shown in Fig. 24. The graph theory simulation accurately predicts the accumulation of heat in the overhang region of a C-shaped part. Moreover, the approach also predicts that heat trapped in an overhang region can be dissipated by build extra supports. More pertinently, at the graph theory, the approach converged to within 90% of Goldak’s solution within 10% of the computation time. The fast convergence of the graph theory approach opens the possibility of recognizing and correcting red flag problems in part design even before the part is printed. In other words, thermal simulations can be used as a viable path for design optimization in AM.

A. Sequential Decision-Making Under Uncertainty

Modern industries pose more stringent standards in product esthetics, QA, and functional integrity. Thus, it is critical that AM machines can mitigate incipient defects. Hybrid machines with both additive and subtractive manufacturing abilities provide an opportunity to take corrective actions and perform layerwise repairs, thereby realizing a new paradigm of zero-defect AM [109]. For instance, sensor-based analytical methods (see Section IV) help characterize and estimate the state of defects in each layer of the AM build. If a layer is estimated to have a small likelihood s_l to contain defects, the AM process will continue and take no corrective action, denoted as a_W. On the other hand, if a layer has a high likelihood s_h to have embedded defects, the AM process will pause and take an action to machine off this defective layer, denoted as a_M. The number of available actions depends, to a great extent, on the technological advancement of hybrid machines. For example, for the defects due to lack of fusion, a potential action is to refuse with the laser and mitigate such defects, denoted as a_L. If there are more actions available after each layer is built, then dynamic transitions among state-action pairs will become more complex. This is mainly due to the fact that AM layers are not independent but rather highly interrelated with each other. As shown in Fig. 25(a), the action chosen for one layer will impact the evolving dynamics of defect states in the next layer and, through that, all subsequent layers. In addition, there are uncertainties in the sensor measurements, machine settings, environments, defect estimation, and layer-to-layer transitions. The new sequential optimization framework needs to account for the uncertainty in AM processes and realize the zero-defect AM by minimizing the expected cumulative cost at the end when all layers are completed.

As shown in Fig. 25(b), each layer of AM builds will be captured by the sensors (i.e., high-resolution cameras) as imaging profiles. The probability for a layer to contain defects (e.g., s_h, s_m, and s_l) will be estimated with sensor-based analytical methods, such as layerwise deep learning of incipient defects [77], [78]. The sequential decision-making framework for smart AM is formulated as a Markov decision process (MDP) model. Although the MDP has been widely used and proved to be effective in the management of engineering systems [110]–[113], very little has been done to realize smart AM using MDPs. Our prior work formulated this problem as an MDP corresponding to a five-tuple (Ω, S, A, T, and R), where Ω is the set of sensor observations, S is the set of defective states, A is the set of actions, T : S × A × S represents the state transition, and R is the reward function. The main objective is to search for an optimal policy π*(s) specifying the optimal action a* in state s, which will maximize the sum of rewards after taking the action a* and, thereafter, keeping being optimal.

1. States, Actions, and Observations: The complexity of AM poses challenges in measuring and characterizing the exact defective state of a layerwise build. As shown in Fig. 14, we have developed a DNN learning method that tackles the challenge of layerwise geometrical variations and then estimate the risk probability of defects in a layer. As such, we can take full advantage of in-process image profiles and integrate them with MDP models. Each action affects the state transitions between layerwise builds in the AM process. Here, actions that are generally available in hybrid AM may include doing nothing, cutting off a layer, refusion, or process adjustments.

2. State Transitions: p(s, a, s′) provides the probability that an intervention a in state s at layer i will lead to the state s′ at layer i + 1. The transition can be estimated from rich data collected in the AM processes, but it is influenced by the uncertainty in sensor measurements and process conditions. Few works in the AM literature studied sequential decision-making under uncertainty.

3. Reward Function: R(s, a, s′) is a reward that the decision agent receives for a specific state transition. For example, if an action drives the defect likelihood from high to low, it will be rewarded. Otherwise, this action will be penalized. The utility V* (s) represents the sum of rewards received when starting in the state s and acting optimally, and Q*(s, a) is the utility when taking the action a from the state s and, thereafter, acting optimally.

Furthermore, we performed preliminary studies to develop a novel “sensing-modeling-optimization” framework that is tailored for AM processes. First, we leveraged the advanced sensing capabilities readily available in Penn State CIMP-3D to collect large amounts of layerwise image data. Second, we developed new sensor-based models to estimate the risk probability for a layer to contain defects and then predict the evolving dynamics of defect conditions from one layer to the next. Third, new MDP models are developed to model state-action transition dynamics among layers as a stochastic Markov process and further derive the optimal control policy [114], [115]. The new “sensing–modeling–optimization” framework enables the implementation of in-process corrective actions to repair and counteract incipient defects in each layer of AM builds prior to the completion. The propagation of defects will be detected by sensor-based modeling and analysis of in situ data and will be mitigated long before they reach the nonrecoverable stage.

B. Constrained Optimization of AM Processes

MDP helps optimize the policy to choose layerwise actions by maximizing expected rewards (or minimizing the expected cumulative cost incurred by the AM defects) for a sequential decision-making problem in the real-world AM environment. Traditional MDP frameworks commonly focus on a single objective (e.g., minimizing the defects in each layer of AM build) [114] and are less concerned about multiple simultaneous objectives that may be added to the AM processes (i.e., minimizing total cost—wasted materials, consumed energy, or lead time, as well as improving the quality). As a vertical step to advance smart and sustainable AM, there is an urgent need to investigate the multiobjective optimization of sequential decision-making problems for 6S quality management of AM.

If there are multiple objectives, for example, minimizing total cost (e.g., lead time or consumed energy) in the AM process while improving the quality of layerwise builds, then sequential optimization becomes a challenging task because some objectives may be conflicting with others. For instance, if we increase the frequency to take corrective actions and make sure that each layer has a small likelihood to contain defects, then the lead time to complete the build will be longer, and more energy will be consumed. In other words, the number of defects will be minimized in each layer of the build, but the total cost will be high. On the other hand, if we do not take as many corrective actions as needed, the build can be completed in a shorter period of lead time, and less energy will be consumed. The total cost is low, but the likelihood to contain defects in the AM build will be higher. In the state of the art, few, if any, previous works have considered multiobjective optimization of the sequential decision-making strategy for AM processes. In particular, there is a need to balance multiple conflicting objectives for the quality management of AM builds.

To address these challenges, our prior work proposed a new constrained MDP (CMDP) framework to derive the optimal control policy in each layer of the AM processes that minimize the total cost (e.g., lead time or consumed energy) and makes sure that the quality standards are met for the AM builds [115]. The CMDP formulation is detailed as follows:

1. State Space: The state space is defined as S = (T, S), where T = {1,2,..., T} denotes the set of layer index, and S is the set of defect states, i.e., s₁, s₂, . . ., s_l, which is structured in the increasing order of defect levels (i.e., s₁ is the lowest defect level, and s_l denotes the highest defect level).

2. Action Space: In this study, the action space is simplified to include three actions, A = {a_M, a_L, a_W}, where a_M denotes the action of removing a layer with the cost of c_M, a_L is the action of laser repair and refusion with the cost of c_L, and a_W represents the action to do nothing with the cost of c_W. With rapid advances of hybrid AM technology, it is anticipated that more actions will be available with different costs to be considered in future work.

3. Decision Policy: Let Q_t(s_t, a) denote the decision rule at layer t, which is defined as the probability to choose an action $a\in A$ given the presence of defect state s_t at the layer t.

4. State Transition: Let $P_t^a\left(s_{t+1}\mid s_t\right)$ be the transition probability from state s_t of layer t to state s_t+1 of layer t + 1 under the action $a\in A$. Given the decision policy Q_t(s_t, a), the state transition is then defined as

   $$M_t(i,j)=\sum _{a\in A}{Q}_t\left(s_t,a\right)P_t^a\left(s_{t+1}=s_j\mid s_t=s_i\right).$$

Let the vector ${\mathit{x}}_t={\left[x_{t1},\dots ,x_{tl}\right]}^T$ (${\mathbf{1}}^{\mathit{T}}{\mathit{x}}_{\mathit{t}}=1$, where 1 is a vector of 1’s) represent the probability distribution of defect states $s_t\in \left\{s_1,\dots ,s_l\right\}$ at layer t, which means that the probability of defect state s_t staying in the defect level s_i is x_ti. Then, x_t evolves according to

The CMDP model will then be formulated as follows:

where Q_t is the decision matrix for layer t, ${\nu }_T$ is the expected total cost in energy or time, $c_t\left(x_t,Q_t\right)={\sum }_{aϵA}{c}_a{Q}_t\left(s_t,a\right)$ is the immediate cost at layer t, and c_T is the terminal cost at the final layer T. The first constraint makes sure that the quality standards are met by bounding the probability of each defect state with an upper limit h and 0 ≤ h ≤ 1. The second constraint guarantees each row of Q_t to be a valid probability distribution. If we delete the quality constraint (i.e., x_t ≤ h) in the CMDP model, then the rows of Q_t will be independent and not correlated. As such, the CMDP model can be solved with dynamic programming and simple backward induction algorithms. However, due to the quality constraint on the density distribution x_t of defect state s_t, the rows of Q_t are correlated in the formulation through state-action transition dynamics x_t+1 = M_tx_t. As a result, it is difficult to solve the CMDP model here with traditional dynamic programming algorithms. Therefore, our prior work developed new dynamic programming algorithms to solve the CMDP model and demonstrated the optimal control policy for the worst case scenario of the probability distribution of defect states [115].

In the proposed “sensing–modeling–optimization” framework, in situ sensor signals, which exemplify specific process defects, are integrated with AI, machine learning, and CMDP models to optimize the selection of corrective actions for smart and sustainable AM. In addition, the objectives can also be extended to include the minimization of delamination and warpage of the final workpiece and the maximization of reliability measures, such as build strength and fatigue resistance. As opposed to purely data-driven approaches, which cannot suggest process adjustments, this sensor-based modeling and optimization approach not only detects process anomalies but also guides the optimal corrective action, thereby enabling closed-loop control of AM to build quality and functional integrity.