WO2023111542A1

WO2023111542A1 - Defect identification in additive manufacturing based on time series in-process parameter data

Info

Publication number: WO2023111542A1
Application number: PCT/GB2022/053201
Authority: WO
Inventors: Peter Green; Paolo Paoletti; Jayasinghe Arachchige Sarini JAYASINGHE
Original assignee: The University Of Liverpool
Priority date: 2021-12-13
Filing date: 2022-12-13
Publication date: 2023-06-22
Also published as: GB202118009D0

Abstract

A method of additive manufacturing, AM, preferably powder bed fusion, PBF, of an article or a part thereof is described. The method is implemented, at least in part, by a computer comprising a processor and a memory. The method comprises: additive manufacturing a first layer of a set of layers of the article, comprising: obtaining a time series of an in-process parameter of the additive manufacturing of the first layer, wherein respective obtained values pd _t of the in-process parameter have positions (X,Y)_t associated therewith; estimating a value pd _t, _est of the in- process parameter, based, at least in part, on an obtained preceding value pd _t- _n of the in- process parameter, wherein n is a natural number greater than or equal to 1; comparing the estimated value pd _t, _est of the in-process parameter and the obtained value pd _t of the in-process parameter; and identifying a defect in the article based, at least in part, on a result of the comparing.

Description

METHOD AND APPARATUS Field The present invention relates to additive manufacturing (AM). Background to the invention Additive manufacturing (AM), popularly known as three-dimensional (3D) printing, generally refers to processes used to create articles (also known as components, parts or objects) from layers including one or more different materials sequentially formed under computer control. AM provides creation of articles having complex geometries (i.e. shapes or structures), including internal voids, that may not readily be formed according to conventional subtractive manufacturing processes, such as machining, or conventional casting or moulding processes. Materials suitable for AM include metals, ceramics, glasses and polymers. The ability of AM techniques to fabricate geometrically complex and light-weight parts, unmatched by conventional manufacturing techniques, is encouraging adoption of AM across different industries (e.g. aerospace and biomedical). Metal AM is one of many categories of AM techniques and laser powder bed fusion (L-PBF) is one of the process categories suitable for metal AM. Recent developments in AM monitoring methods have been introduced to satisfy the quality standards expected in risk-averse industries (e.g. aerospace and biomedical implants). However, due to limitations such as slow response rates of the sensors equipped in AM systems and significant image processing requirements, it is difficult to apply these developmental monitoring methods on production systems in real-time. According to Mani et al. and Yadroitsev et al., there are over 50 process parameters that contribute to the overall quality of a part built via L-PBF. Therefore, the L-PBF process requires tuning and control of many parameters to produce high-quality parts, since numerous combinations of process parameters could lead to the generation of defects during the build. Moreover, part quality needs to be monitored during the L-PBF build process and, ideally, process conditions should be altered in real-time to rectify build faults. This would enhance the robustness and repeatability of the process. Global post-process inspection techniques (for example, Archimedes density measurements) are often used to analyse the quality of a build, but they are not sensitive to small localised defects. On the other hand, the locations of those defects significantly affect the part’s performance and, as such, local post-processing inspection techniques (e.g. CT scans) are preferable for critical parts. However, even though CT scans can provide a detailed assessment of the L-PBF build quality, they are expensive and limited in the range of part sizes that can be inspected; for example, large parts cannot be analysed with sufficient resolution to detect relevant defects. Several techniques are being developed for in-situ monitoring of additively manufactured parts but are yet to become prevalent in the industry. Many developmental in-situ monitoring systems employ images collected via cameras to detect defects in L-PBF builds. Since these camera sensing systems have slow response rates (typically 0.5kHz - 1kHz) and provide high- dimensional datasets, most of these systems cannot operate in an environment where real-time analysis is required. Spatially integrated single-channel detectors (photodiodes), on the other hand, have fast data collection rates (50kHz - 100kHz) that satisfy the requirements for real-time monitoring systems. Any in-situ monitoring system needs to be calibrated to provide acceptable performance. However, it is difficult to design experiments to rigorously study build defect formation in realistic settings. Indeed, the vast majority of available studies are limited to adjusting build parameters (e.g. laser power, scanning speed or hatch distance) to artificially induce defects and analyse the response of a monitoring system to their occurrence. This may, however, provide a poor representation of real defect phenomena occurring under well-tuned build conditions and process parameters. Hence, there is a need to additive manufacturing, for example in-situ monitoring thereof. Summary of the Invention It is one aim of the present invention, amongst others, to provide a method of additive manufacturing which at least partially obviates or mitigates at least some of the disadvantages of the prior art, whether identified herein or elsewhere. A first aspect provides a method of additive manufacturing, AM, preferably powder bed fusion, PBF, of an article or a part thereof, the method implemented, at least in part, by a computer comprising a processor and a memory, the method comprising: additive manufacturing a first layer of a set of layers of the article, comprising: obtaining a time series of an in-process parameter of the additive manufacturing of the first layer, wherein respective obtained values pd_t of the in-process parameter have positions (X, Y)_t associated therewith; estimating a value pd_t,est of the in-process parameter, based, at least in part, on an obtained preceding value pd_t-n of the in-process parameter, wherein n is a natural number greater than or equal to 1; comparing the estimated value pd_t,est of the in-process parameter and the obtained value pd_t of the in-process parameter; and identifying a defect in the article based, at least in part, on a result of the comparing. A second aspect provides an additive manufacturing, AM, apparatus, preferably a powder bed fusion, PBF, apparatus, including a computer comprising a processor and a memory, wherein the apparatus comprises: a sensor configured to obtain a time series of an in-process parameter of additive manufacturing of a first layer of a set of layers of an article, wherein respective obtained values pd_t of the in- process parameter have positions (X, Y)_t associated therewith; wherein the computer is configured to: estimate a value pd_t,es of the in-process parameter, based, at least in part, on an obtained preceding value pd_t-n of the in-process parameter, wherein ^ is a natural number greater than or equal to 1; compare the estimated value pd_t,es of the in-process parameter and the obtained value pd_t of the in-process parameter; and identify a defect in the article based, at least in part, on a result of the comparing. A third aspect provides a computer comprising a processor and a memory configured to implement a method according to the first aspect, a computer program comprising instructions which, when executed by a computer comprising a processor and a memory, cause the computer to perform a method according to the first aspect, or a non-transient computer- readable storage medium comprising instructions which, when executed by a computer comprising a processor and a memory, cause the computer to perform a method according to the first aspect. Detailed Description of the Invention According to the present invention there is provided a method, as set forth in the appended claims. Also provided is an apparatus, a computer, a computer program and a non-transient computer-readable storage medium. Other features of the invention will be apparent from the dependent claims, and the description that follows. Method The first aspect provides a method of additive manufacturing, AM, preferably powder bed fusion, PBF, of an article or a part thereof, the method implemented, at least in part, by a computer comprising a processor and a memory, the method comprising: additive manufacturing a first layer of a set of layers of the article, comprising: obtaining a time series of an in-process parameter of the additive manufacturing of the first layer, wherein respective obtained values pd_t of the in-process parameter have positions ^^, ^^_^ associated therewith; estimating a value pd_t,est of the in-process parameter, based, at least in part, on an obtained preceding value pd_t-n of the in-process parameter, wherein ^ is a natural number greater than or equal to 1; comparing the estimated value pd_t,est of the in-process parameter and the obtained value pd_t of the in-process parameter; and identifying a defect in the article based, at least in part, on a result of the comparing. That is, the value pd_t,est of the in-process parameter, such as a photodiode signal, is estimated (i.e. predicted) based on one or more obtained (for example, measured) values pd_t-n of the in- process parameter (i.e. the same in-process parameter as for the estimated value) for the same layer (i.e. the first layer of the set of layers) during the AM of this layer. It should be understood that the steps of obtaining, estimating, comparing and identifying are intra-layer (c.f. inter-layer) and thus the value pd_t,est of the in-process parameter is estimated based on one or more obtained preceding (i.e. with respect to the time series) values pd_t-n of the in-process parameter for the layer being currently AM. The estimated value pd_t,est is compared with the obtained (for example, measured) value pd_t of the in-process parameter and based on the result of the comparing, the defect is identified. In this way, defects may be identified during the AM (i.e. in situ, in real-time, online), allowing responsive remediation of the defects during the AM. In this way, in situ monitoring of the AM is improved, thereby improving the method of AM and a quality of the article. The inventors have developed a real-time predictive model that can be used to indicate defective areas in layers of, for example, laser powder bed fusion (L-PBF) builds. By way of example, a second-order auto-regressive (AR) model was trained on a photodiode signal. By comparing predicted photodiode signal values from the trained AR model and corresponding measured photodiode signal values, porous regions of the builds may be determined. Existing defective areas of the build were first identified using a database of computer tomography (CT) images. Induced defects (i.e. synthesized) could provide a poor representation (i.e. may not be representative) of real defect phenomena encountered in AM. Hence an L-PBF build with naturally formed defects was examined by the inventors. By comparing the machine-learning predictions with the CT images, the inventors demonstrated that the predictive model, in this example, is capable of predicting (i.e. identifying) pores (i.e. defects), having a minimum diameter of approximately 100 μm, in L-PBF builds, with an average true positive rate (TPR) of 88.47%. Such a high accuracy of defect prediction, of almost 90% TPR, during the in situ monitoring of L-PBF allows responsive remediation of the defects during the AM (c.f. remediation after completion of the AM) or rejection of the article as non-compliant with respect to quality criteria without further non-destructive testing, for example Additive manufacturing The method is of additive manufacturing, AM, preferably powder bed fusion, PBF, of the article or a part thereof. ISO/ASTM 52900-15 defines seven categories of AM processes, including binder jetting, directed energy deposition (DED), material extrusion, material jetting, powder bed fusion (PBF), sheet lamination, and vat photopolymerization. These AM processes are known. Particularly, DED and PBF techniques, such as direct metal laser sintering (DLMS), selective heat sintering (SHS), selective laser sintering (SLS), selective laser melting (SLM) also known as laser PBF or L-PBF, laser metal deposition (LMD) and electron beam melting (EBM), are suitable for creating (i.e. manufacturing, forming) for example, metal articles, from feed materials such as metal powders and/or wires (also known as filaments). Similarly, polymeric articles may be manufactured from feed materials such as powders and/or filaments comprising polymeric compositions, for example including thermoplastics. The feed materials are heated to elevated temperatures, including melting thereof. In one example, the AM comprises and/or is DED, for example wire or powder DED or LMD, and/or PBF, for example DMLS, SHS, SLS, SLM (aka L-PBF) or EBM. Computer The method is implemented, at least in part, by a computer comprising a processor and a memory, or equivalent such as a Field Programmable Gate Array (FPGA) or Application Specific Integrated Circuit (ASIC). Suitable computers, FPGAs and ASICs are known. At least some of the examples described herein may be constructed, partially or wholly, using general purpose and/or dedicated special-purpose hardware. Terms such as ‘component’, ‘module’ or ‘unit’ used herein may include, but are not limited to, a hardware device, such as circuitry in the form of discrete or integrated components, a Field Programmable Gate Array (FPGA) or Application Specific Integrated Circuit (ASIC), which performs certain tasks or provides the associated functionality. In some examples, the described elements may be configured to reside on a tangible, persistent, addressable storage medium and may be configured to execute on one or more processor circuits. These functional elements may in some embodiments include, by way of example, components, such as software components, object- oriented software components, class components and task components, processes, functions, attributes, procedures, subroutines, segments of program code, drivers, firmware, microcode, circuitry, data, databases, data structures, tables, arrays, and variables. Although the examples are described with reference to the components, modules and units discussed herein, such functional elements may be combined into fewer elements or separated into additional elements. Various combinations of optional features have been described herein, and it will be appreciated that described features may be combined in any suitable combination. In particular, the features of any one example may be combined with features of any other example, as appropriate, except where such combinations are mutually exclusive. Throughout this specification, the term “comprising” or “comprises” may mean including the component(s) specified but is not intended to exclude the presence of other components. Layers The method comprises additive manufacturing of the first layer of the set of layers of the article. Typically, AM of articles comprises AM of 10s, 100s, or 1000s of layers, as understood by the skilled person. In one example, the method comprises additive manufacturing of ^ layers of the set of layers of the article, wherein ^ is a natural number greater than or equal to 1, for example, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000 or more layers, wherein each of the ^ layers of the set of layers of the article is AM as described with respect to the first layer mutatis mutandis. Article The method comprises additive manufacturing of the article. In one example, the article comprises and/or is an aerospace component, such as an airframe component, a vehicle component, such as an engine component, or a medical component, such as an implantable medical device. Obtaining, estimating, comparing and identifying It should be understood that the steps of obtaining, estimating, comparing and identifying are intra-layer (c.f. inter-layer) i.e. for the first layer and hence the same layer. In one example, the method comprises the steps of obtaining, estimating, comparing and identifying during (i.e. while, simultaneously with) manufacturing the article by AM. That is, the method is implemented in situ (i.e. in real-time, online). In this way, quality control and optionally remediation of defects may be performed during the AM. Additionally and/or alternatively, the method comprises the step of obtaining during (i.e. while, simultaneously with) manufacturing the article by AM and one or more of the steps of estimating, comparing and/or identifying are performed after manufacturing the article by AM (i.e. post-manufacturing, offline). In this way, quality control and optionally remediation of defects may be performed after the AM. Obtaining Additive manufacturing of the first layer of the set of layers of the article comprises obtaining the time series of the in-process parameter. It should be understood that the in-process parameter may include an output and/or an input parameter. In one example, obtaining the time series of the in-process parameter comprises monitoring output parameters, for example, emissions such as optical, thermal, and/or acoustic emissions, during the AM of the article. Generally, output parameters may also be referred to as process signatures, which may include observable signatures and derived signatures. Observable signatures may be measured or sensed during the AM, for example using in situ sensors. Derived signatures may be determined, for example calculated, using analytical models or simulations. In situ sensors suitable for AM include non-contact temperature measurement, for example using pyrometers and IR sensors, including 1D, 2D and 3D sensors, for example for NIR to LWIR sensing, optical sensing in the visible range, low-coherence interferometric imaging, 2D laser displacement sensors, optical coherence tomography devices, accelerometers, ultrasound detectors, strain gauges, thermocouples and X-ray detectors. Sensors may be configured coaxially, for example for IR imaging, or off axially. In this way, output parameters may be obtained at rates compatible with the AM, for example at the spatial resolution of the AM. For PBF and DED, for example, observable signatures may relate to the melt pool, the plasma, the track along the scan path, the slice and for PBF, the powder bed (i.e. the layer of powder before fusion thereof). In-process parameters related to the melt pool include size (for example area or diameter), shape, temperature intensity (average or cumulative) and/or temperature profile (1D profiles along the transversal and longitudinal direction or 2D profile over the entire area). The melt pool properties may determine the geometrical accuracy of the track, surface and/or geometrical properties of the article, porosity of the component, incomplete melting and/or development of residual stresses, cracking and/or delamination. The melt pool may be monitored in situ using pyrometery, imaging (visible to NIR) and/or thermal imaging (NIR to LWIR), and acoustic sensors, as described below in more detail. In-process parameters related to the plasma (for example ionised plasma resulting from laser or electron beam melting) include temperature and composition. Generally, optical, thermal and/or acoustic emissions originate from the melt pool and the ionised plasma. These are coupled phenomena but are separate sources of signals. The melt pool will emit as determined by its temperature, usually at longer peak wavelength to the plasma. Some material will be ionised on interaction with the incident laser and may emit in spectral bands as well as black body radiation. The plasma may be monitored in situ using pyrometery, imaging (visible to NIR) and/or thermal imaging (NIR to LWIR), acoustic sensors and/or spectroscopy, as described below in more detail. In-process parameters related to the track include geometry, temperature profile and/or material ejected from the melt pool and surrounding area. The geometry and the temperature profile of the track enable determination of defects such as balling, lack of fusion, local overheating, surface and geometric errors and/or porosity formation. Material ejection may be relevant for characterisation of by-products and/or local composition. The track may be monitored in situ using pyrometery, imaging (visible to NIR), thermal imaging (NIR to LWIR) and/or interferometric imaging, as described below in more detail. In-process parameters related to the slice include surface pattern, geometry (including deviation from nominal geometry), local thickness profile and/or temperature profile over the entire slice (usually a 2D profile). These parameters enable reconstruction of the actual shape of a printed slice made layer by layer basis, for example. The slice may be monitored in situ using imaging (visible to NIR), thermal imaging (NIR to LWIR) and/or interferometric imaging, as described below in more detail. In-process parameters related to the powder bed include bed uniformity, temperature and/or temperature profile. For example, the temperature stability from one layer to the next layer and the 2D temperature profile in each layer may be used to characterise temporal and/or spatial evolution of the AM. The powder bed may be monitored in situ using pyrometery, imaging (visible to NIR), thermal imaging (NIR to LWIR) and/or interferometric imaging, as described below in more detail. Analogously, in-process parameters may relate to powder or wire feed for DED. Additionally and/or alternatively, observable signatures may be obtained from vibration, ultrasonic emission and/or baseplate distortion. Monitoring Everton et al., Spears et al. and Grasso and Colosimo have conducted detailed reviews of the state-of-the-art sensing and monitoring techniques, specifically focusing on metal AM processes. Among the many in-situ monitoring methods for L-PBF that have been explored in recent times, thermal and visual monitoring methods are the most prevalent techniques. Considering the type of sensors equipped for monitoring the process, these monitoring systems can be divided into three main categories: image-based systems, photodiode sensor-based systems and hybrid monitoring systems where both photodiode sensors and cameras are simultaneously used. The following subsections provide an overview of techniques belonging to these families. Image-based monitoring CCD or CMOS detectors are commonly used in melt-pool monitoring and can provide a detailed picture of the melt-pool (as opposed to a picture of the entire layer). These camera-based systems typically have a slower response time (0.5-1kHz) compared to single-channel detectors such as photodiodes (50-100kHz). Data management can also be a great challenge as, with camera sensing systems, the amount of data that can be collected increases with the number of pixels in each captured image. Layer-wise imaging of the powder bed can also be used to obtain insight into the health of the manufacturing process and quality of the part. There are several ways to obtain images of the powder bed, however, significant image post-processing is often required due to the lack of image contrast between the part and the powder. Monitoring systems which employ these different imaging approaches are discussed in detail below. Melt-pool imaging A data-driven methodology has been proposed by Kleszczynski et al. to predict the size and location of pores from thermal images of melt-pools. Melt-pool images of size 752 × 480 were captured and cropped to a smaller size to focus more on the melt-pool area. A data reduction scheme called multi-linear principal component analysis (MPCA) was initially used to extract low dimensional features from the melt-pool images. Support Vector Machines (SVM) and Random Forests (RF) were then trained using images characterised by X-ray CT scans. For training purposes, images were manually categorised as healthy, or as having small pores or large pores. Subsequently, a fatigue model was trained to predict the fatigue life based on the predicted size and location of the pores. The average error percentage in fatigue life prediction of training and testing datasets was found to be 9.7% and 12.1%, respectively. The study conducted by Repossini et al. used in-situ image acquisition equipment consisting of a high-speed camera (Olympus I-speed 3 with CMOS sensor, 1000 frames/second) to capture the material ejections produced by the beam-material interaction (spattering). The captured images, coupled with image segmentation and feature extraction, were used to estimate different statistical descriptors that explain the spattering behaviour in terms of number, size and spatial spread. A logistic regression model was then employed to determine the ability of these descriptors to classify the different energy density conditions that can lead to different quality states such as under-melting and over-melting. A porosity prediction method was developed by Khanzadeh et al., using morphological characteristics of the melt-pool boundary. The nominal image collection rate of the IR camera used to capture melt-pool images was approximately 12.58 Hz and each melt-pool image consisted of 1.7 MB of data. The proposed method employed a polar transformation to convert the Cartesian co-ordinates of the melt-pool boundaries into polar co-ordinates. A curve was fitted to the polar-transformed co-ordinates of the melt-pool boundaries using cubic spline smoothing. Functional principal component analysis (FPCA) was then used on the fitted curve to extract key features that describe the morphological model of melt-pools. These features were then used to classify melt-pools as being defective or non-defective. During the fabrication of a thin-wall structure, the approach correctly classified 98.44% of the melt-pools. In one example, the in-process parameter relates to a melt pool, for example a plume thereof, formed during the additive manufacturing of the first layer. For example, each successive value may relate to a successive melt pool. In one example, obtaining the time series of an in-process parameter comprises measuring plasma emissions during the additive manufacturing of the first layer, for example using a photodiode. Layer-wise camera imaging The method suggested by Aminzadeh et al. used a database of camera images, with manually identified defective and non-defective zones, to train a Bayesian classifier. Features were selected by taking texture characteristics into consideration and by converting the images into the frequency domain. The developed Bayesian classifier was able to achieve a 89.5% true positive rate and 82% true negative rate. Gobert et al. proposed a method to identify discontinuities, such as porosity and cracks, by matching the coordinates of anomalies and nominal voxels in CT scans with layer-wise images captured by a 36.3-megapixel DSLR camera. Features extracted from this matching layer-wise image stack were used to train a binary classifier. As a result, discontinuities were detected with an 80% success rate. A combination of thermographic off-axis imaging (50 images per second) and a deep learning- based neural network architecture was used by Baumgartl et al. to detect defects. According to the authors, the proposed neural network architecture enables real-time operation and light computational costs compared to well-known architectures such as VGG or ResNet. With the proposed technique, defects such as delamination and splatter were recognised with an accuracy of 96.80%. However, the computing-platform used to obtain these results was not reported. Hybrid monitoring via camera and photodiode sensors Spatially integrated, single-channel detectors such as photodiodes, pyrometers, and photomultiplier tubes have fast data collection rates (50-100kHz) and require little data processing relative to systems based only on cameras. On the other hand, camera-based systems provide a more detailed overview of the melt-pool characteristics. Consequently, the choice of the sensor system used to perform melt-pool monitoring is often a trade-off between the response rate, cost and usefulness of the data that can be collected. Thus, some studies, such as Clijsters et al., Craeghs et al. and Berumen et al., have explored the combined usage of photodiodes and CCD or CMOS cameras to capture the process dynamics of the melt-pool. Clijsters et al. suggested an approach for in-situ monitoring, where measurements of light intensity emitted by the melt-pool and the area of each melt-pool were gathered via, respectively, a photodiode and a high-speed NIR CMOS camera. By using an illumination laser beam and a field-programmable gate array, images were captured and processed at a high sample rate (10kHz). Sensor data, mapped into a position-domain representation, were examined for anomalies using pre-defined thresholds of intensity and area of melt-pool. This system requires a position-dependent reference database unique to each part, generated by traditional validation techniques, before the appropriate thresholds can be identified. It was found that different thresholds were required for different scanning patterns (i.e. bulk and contour). While the study stated that there is excellent compatibility between the detected errors and actual defects, the obtained accuracy was not reported numerically. The experimental setup introduced by Montazeri and Rao integrated three sensors, namely, a photodetector (spectral response 300–1200 nm), a highspeed visible spectrum video camera (4000 frames per second, spectral response 300–950 nm), and a short wave infrared (SWIR) thermal camera (1800 frames per second, spectral response 1350 nm to 1600 nm). Different process states (i.e. over-hang, bulk) were identified after the sensor data had been projected onto an orthogonal basis. The study compares results from the three sensors in terms of their statistical fidelity in distinguishing between process states. An F-score of 95% was obtained with the thermal camera signatures, 83% with the high-speed visible camera and 79% with the photodetector. Photodiode sensor-based monitoring Photodiodes have seen widespread use in melt-pool monitoring, see for example Yadroitsev et al., Craeghs et al. and Berumen et al. The major difference between a photodiode- and camera- based in-process monitoring is that a photodiode compresses the light emitted from a large zone around the melt-pool into a single voltage reading. Craeghs et al. have shown that the voltage reading collected via a photodiode sensor correlates to the pixel area of the melt-pool captured by a CMOS camera. Different arrangements can be used for photodiode-based systems, which will be briefly discussed below. Co-axial photodiode sensors Sensors may be employed in a manner that allows the sensor to follow the melt pool, i.e., with a moving, Lagrangian reference frame. Using the same galvos and optics as the scanning laser ensures that the area probed by the sensor is coincident with the focal point of the laser and presumably the heat affected-zone. Co-axial photodiode sensing allows the melt-pool instabilities and variation to be observed in real-time. In the study conducted by Pavlov et al., temperature was measured in the laser impact zone by a bi-colour pyrometer with optical filters, 100 nm bandwidth and 50 ms sampling time. It was found that the pyrometer signal was sensitive to variations in the main operational parameters (powder layer thickness, hatch distance between consecutive laser beam passes, scanning velocity, etc.), and has the potential to be used for on-line monitoring. Alberts et al. identified a correlation between part density and the outputs of photodiode sensors. Independent and combined analyses of two photodiodes, which captured radiation at different wavelengths, were carried out to observe the signal behaviour as the energy transferred to the material was changed. According to Alberts et al. the quotient of the two photodiode readings provides a new quality assurance measure since both part density and photodiode signal ratio were found to gradually increase as the energy per unit volume (transferred to the material) increased up until 100% of part density. Off-axial photodiode sensors An alternative process monitoring approach is to utilise an Eulerian reference frame monitoring a fixed point or area on the build surface or the entire build platform. The abrupt fluctuations in an off-axial photodiode sensor signal (collected at 50 kHz) observed by Bisht et al. were identified as being correlated to instabilities in the melt-pool that may create material discontinuities. Those data points with abrupt fluctuations were mapped to a 2D bitmap according to their corresponding position co-ordinates (‘DMP melt-pool events’). After exploring correlations between the static tensile properties of L-PBF builds (ultimate tensile strength and plastic elongation) and DMP melt-pool events, an inverse relation between plastic elongation and the DMP melt-pool event density was identified in Ti-6Al-4V ELI bars. DMP melt-pool events observed for adjacent scan vectors in a localised region were recognised as a signature of abnormalities in Coeck et al. According to Coeck et al., if those events were observed in more than two consecutive layers, it is probable that a material discontinuity (pore/defect) has been formed in the final part. Therefore, by observing DMP Melt-pool events for adjacent scan vectors that grow into at least 3 layers, pores were predicted with a prediction sensitivity of 90% for pores with a volume greater than 0.001mm³, which are roughly equivalent to 160 μm in diameter. However, the threshold for determining abnormalities was left as a tunable parameter and the details of defining this threshold were not provided. In one example, obtaining the time series of the in-process parameter comprises obtaining co- axial photodiode sensor measurements. Input parameters In one example, obtaining the set of in-process parameters of the AM of the article comprises sourcing input parameters of the AM of the article and/or readback parameters during the AM of the article. Generally, input parameters include desired control settings, such as desired laser power, desired scan speed and desired hatch distance, while readback parameters include actual control settings, such as actual laser power, actual scan speed and actual hatch distance. For example, while the desired laser power may be constant, the actual laser power may vary during the AM. Time series Additive manufacturing of the first layer of the set of layers of the article comprises obtaining the time series of the in-process parameter of the additive manufacturing of the first layer, wherein respective obtained values pd_t of the in-process parameter have positions (X, Y)_t associated therewith. It should be understood that the time series is a series of data indexed in time order, typically periodically (i.e. equally spaced in time), and thus is a one dimensional (1D) sequence of discrete-time data. Hence, it should be understood that the time series of the in-process parameter is a time series of values of the in-process parameter. It should be understood that each respective obtained value pd_t of the in-process parameter has associated temporal information, for example a time stamp, for example an absolute time or with respect to a reference time, such as start time of AM, since the obtained values pd_t of the in-process parameter are included in the time series. It should be understood that the respective obtained values ^^_^ of the in-process parameter have positions ^^, ^^_^ (i.e. two-dimensional coordinates within the first layer) associated therewith, such that each obtained value ^^_^ of the in-process parameter is spatially resolved, having associated positional information, for example with respect to a datum. Hence, each respective obtained value ^^_^ of the in-process parameter has associated therewith a time and two-dimensional coordinates within the first layer. It should be understood that the time may be inferred from the coordinates (for example, control coordinates of the AM apparatus) or vice versa (for example, a clock of the AM apparatus) or the time and the coordinates may be independently recorded. In one example, respective obtained values p of the in-process parameter have positions (X, Y, Z)_t (i.e. three-dimensional coordinates within the first layer). In one example, obtained values pd_t of the in-process parameter correspond with respective voxels (i.e. volumetric pixels) of the article, wherein the respective positions (X, Y)_t associated therewith is of the respective voxels. In one example, obtaining the time series of an in-process parameter comprises acquiring values pd_t of the in-process parameter at a rate in a range from 1 kHz to 1 MHz, preferably in a range from 10 kHz to 500 kHz, more preferably in a range from 50 kHz to 200 kHz, for example 100 kHz. Estimating Additive manufacturing of the first layer of the set of layers of the article comprises estimating the value pd_t,est of the in-process parameter, based, at least in part, on the obtained preceding value pd_t-n of the in-process parameter, wherein n is a natural number greater than or equal to 1. It should be understood that the estimated value pd_t,est of the in-process parameter is thus estimated based on a moving series of ^ preceding obtained values pd_t-n in the time series, immediately preceding the subsequently obtained value ^^_^. In one example, n is a natural number greater than or equal to 2, for example 2, 3, 4, 5, 6, 7, 8, 9, 10, 20 or 50. In one example, n is a natural number less than or equal to 3, for example less than or equal to 2, 3, 4, 5, 6, 7, 8, 9, 10, 20 or 50. That is, the value pd_t,est of the in-process parameter may be estimated using relatively few obtained preceding values pd_t-n of the in-process parameter, enabling identification of defects with relatively high spatial resolution and/or sensitive to local changes. In one example, estimating the value pd_t,est of the in-process parameter comprises estimating the value pd_t,est of the in-process parameter using an autoregressive model having an order ^, wherein ^ is a natural number greater than or equal to 1. In one example, N = 2. Autoregressive models are typically used to represent random processes. The autoregressive models used here are linear in the parameters to be estimated and are computationally inexpensive, thus the method may be implemented in real-time using a conventional computer. More generally, in one example, estimating the value pd_t,est of the in-process parameter comprises using an autoregressive–moving-average (ARMA) model, an autoregressive integrated moving average (ARIMA) model and/or a vector autoregressive model (VAR). Other models are known. In one example, the method comprises training the autoregressive model. In one example, training the autoregressive model comprises: AM a set of articles, including A articles wherein A is a natural number greater than or equal to 1, for example 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 500, 1000 or more, comprising AM a set of L layers, including a first layer, of the respective articles of the set thereof, comprising obtaining respective time series of the in-process parameter of the AM of the respective set of layers, wherein respective obtained values pd_t of the in-process parameter have positions (X, Y)_t associated therewith; determining positions of respective defects in the set of articles, for example by destructive testing and/or or non-destructive testing; and correlating the determined positions of the respective defects in the set of articles and the respective obtained values pd_t of the in-process parameter of the respective time series of the respective articles of the set thereof. Suitable methods of destructive testing include sectioning and imaging. Suitable methods of non-destructive testing include radiographic testing, ultrasonic testing and 3D computed tomography (CT). In one example, the method comprises training the autoregressive model as described in Detailed Description of the Drawings. Comparing Additive manufacturing of the first layer of the set of layers of the article comprises comparing the estimated value pd_t,est of the in-process parameter and the obtained value ^^_^ of the in- process parameter. That is, the obtained (for example measured) value ^^_^ is compared with the corresponding estimated value pd_t,est. In one example, comparing the estimated value pd_t,est of the in-process parameter and the obtained value ^^_^ of the in-process parameter comprises calculating a magnitude of a difference therebetween. That is, the result of the comparing is the magnitude of the difference between the obtained (for example measured) value pd _t and the corresponding estimated value pd_t,est i.e. Ipd_t − pd_t,estI. The inventors have determined that defects may be identified accurately based on the difference between the obtained (for example measured) value pd_t and the corresponding estimated value pd_t,est. Identifying Additive manufacturing of the first layer of the set of layers of the article comprises identifying the defect in the article based, at least in part, on a result of the comparing. Generally, defects in AM include porosity, residual stresses, cracking, delamination, balling, geometric defects and dimensional accuracy (such as shrinkage, warping and super elevated edges), surface defects, microstructural homogeneities and impurities (such as inclusions, contaminants and surface oxides). These defects adversely affect properties (i.e. a quality) of the article. For example, porosity impacts fatigue performance and crack growth while shrinkage and warping vary article geometry. Generally, these defects in AM may be induced by the AM equipment, the AM process, the AM model and/or the AM feed material. Defects induced by the AM equipment may result from, for example, beam scanning, build chamber including protective atmosphere, feed material handling and deposition and the baseplate. Defects induced by the AM process may result from, for example, control settings (such as laser power, scan speed and hatch distance which determine energy density) and scan strategies (which may determine temperature distribution and residual stresses, for example). Defects induced by the AM model may result from design errors, supports and sacrificial components and orientation of the article the respect to the base plate, for example. Defects induced by the AM feed material may result from purity and contaminants and for powders, from powder morphology, particle size distribution, flowability and apparent density. Porosity has received significant attention in the L-PBF literature, as it can strongly impact the fatigue performances and the crack growth characteristics of AM metal parts. The most common voids are situated in the bulk of the fused material, either in between adjacent layers (elongated pores) or within the layer (gas pores). Tammas-Williams et al. showed that gas pores are mainly located between the internal hatching area. Attar et al. reported that gas pores form either as a result of partially un-melted powder or due to over-melting of the powder (as over-melting increases turbulence within the melt-pool and give rise to excessive evaporation). In one example, identifying the defect in the article comprises identifying the defect using a predetermined threshold. That is, the result of the comparing is contrasted with the predetermined threshold. In one example, identifying the defect in the article comprises identifying the defect in the article if the magnitude of the difference between the obtained (for example measured) value pd _t ad the corresponding estimated value pd_t,est is at most the predetermined threshold τ i.e. Ipd_t − pd_t,est ≤I τ, for example wherein τ is determined according to the in-process parameter. Surprisingly, the inventors have determined that defects, for example pores during L-PBF, may be identified if the magnitude of the difference between the obtained value pd_t and the corresponding estimated value pd_t,est is relatively small, as described below in more detail. That is, the estimated value pd_t,est is estimated relatively more accurately if there is a defect. While this appears prima facie counterintuitive and without wishing to be bound by any theory, the time-series of the in-process parameter appears to be relatively more stochastic for defect-free AM while defects appear to be associated with abnormally predictable values of the in-process parameter. For example, for photodiode signals measured during L- PBF, porosity may cause a plume of excessive evaporation (generated as a result of over- melting) to form between the laser and the powder bed. This plume may act as a filter, removing noise from the resulting photodiode measurement and thereby increasing predictability of estimating the estimated value pd_t,est. Conversely, in one example, identifying the defect in the article comprises identifying the defect in the article if the magnitude of the difference between the obtained (for example measured) value pd_t and the corresponding estimated value pd_t,est is at least the predetermined threshold τ i.e. Ipd_t − pd_t,est ≥I τ, wherein ^ is determined according to the in-process parameter. That is, the estimated value pd_t,est is estimated relatively less accurately if there is a defect i.e. the time-series of the in-process parameter is relatively less stochastic for defect-free AM while defects appear to be associated with abnormally unpredictable values of the in-process parameter. Locating In one example, identifying the defect in the article comprises locating the defect in the article. In this way, the defect is identified and located. In one example, locating the defect in the article comprises locating the defect in the first layer, for example at a position (X, Y)_t associated with the obtained value pd_t of the in-process parameter. By knowing the position (X, Y)_t of the defect, the defect may be remediated, for example during the AM. Controlling and remediating In one example, the method comprises controlling the additive manufacturing based, at least in part, on identifying the defect in the article, for example wherein controlling the additive manufacturing comprises remediating (i.e. repairing) the defect. In this way, the AM is controlled to remediate the defect, thereby attenuating or eliminating an effect due thereto and hence improving a quality of the article. In one example, controlling the additive manufacturing comprises controlling the additive manufacturing of a second layer of the set of layers, for example proximal a position (X, Y)_t associated with the obtained value pd_t of the in-process parameter in the first layer. It should be understood that the second layer superposes the first layer i.e. the second layer is provided directly upon the first layer. For example, laser power may be increased locally during AM of the second layer, thereby causing melting of the underlying first layer proximal a position (X, Y)_t associated with the obtained value pd_t of the in-process parameter in the first layer, thereby reducing porosity (i.e. the defect) in the first layer. In one example, the defect comprises and/or is a pore. In this way, porosity may be identified during the AM and optionally, remediated during the AM. Feed material In one example, AM of the article comprises AM of the article from a feed material, for example comprising a powder and/or a wire. It should be understood that the powder comprises particles that are solid and may include discrete and/or agglomerated particles. In one example, the particles have an irregular shape, such as a spheroidal, a flake or a granular shape. Generally, the feed material may comprise any material amenable to fusion by melting, such as metals or polymeric compositions. The feed material may comprise a polymeric composition comprising a polymer, for example, a thermoplastic polymer. The thermoplastic polymer may be a homopolymer or a copolymer. The thermoplastic polymer may be selected from a group consisting of polymethyl methacrylate (PMMA), acrylonitrile butadiene styrene (ABS), aliphatic or semi-aromatic polyamides, polylactic acid (polylactide) (PLA), polybenzimidazole (PBI), polycarbonate (PC), polyether sulfone (PES), polyetherimide, polyethylene (PE), polypropylene (PP), polymethylpentene (PMP) and polybutene-1 (PB-1), polystyrene (PS) and polyvinyl chloride (PVC). The powder may comprise a ceramic, for example a refractory material, sand, SiO2, SiC, Al2O3, Si2N3, ZrO2. Ceramic particles may have regular, such as spherical, cuboidal or rod, shapes and/or irregular, such as spheroidal, flake or granular, shapes (also known as morphologies). In one example, the feed material comprises a metal or an alloy thereof. In one example, the metal is a transition metal, for example a first row, a second row or a third row transition metal. In one example, the metal is Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu or Zn. In one example, the metal is Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag or Cd. In one example, the metal is Hf, Ta, W, Re, Os, Ir, Pt, Au or Hg. In one example, the metal is a group 1 metal such as Li, Na or K; group 2 metal such as Be, Mg, Ca or Sr; group 3 metal such as Sc, Y or La; or group 13 metal such as Al, Ga or In. In one example, the feed material comprises one or more of these metals, for example an alloy. In one example, the alloy comprises one or more non-metallic alloying additions. Generally, the powder may comprise any metal from which particles may be produced by atomisation. These particles may be produced by atomisation, such as gas atomisation, close- coupled gas atomisation, plasma atomisation or water atomisation, or other processes known in the art. These particles may have regular, such as spherical, shapes and/or irregular, such as spheroidal, flake or granular, shapes. For L-PBF of Ti alloys for example, the powder preferably comprises particles having a size in a range from 15 μm to 45 μm and/or in a range from 20 μm to 63 μm, while for EBM of Ti alloys, the powder preferably comprises particles having a size in a range from 45 μm to 105 μm. For L-PBF of Ni, Al alloys and stainless steels for example, the powder preferably comprises particles having a size in a range from 15 μm to 53 μm, while for EBM of Ni, Al alloys and stainless steels, the powder preferably comprises particles having a size in a range from 50 μm to 150 μm. In one example, the feed material comprises an additive, an alloying addition, a flux, a binder and/or a coating. In one example, the powder comprises particles having different compositions, for example a mixture of particles having different compositions. In one example, the metal comprises a ferrous alloy or a nonferrous alloy, for example a stainless steel, an Al alloy, a copper alloy, a Ti alloy, a Ni alloy or mixtures of respective alloys thereof, preferably corresponding and/or compatible alloys (for example having similar or the same nominal compositions) thereof. In one example, the feed material comprises and/or consists of a Ti alloy, for example a Ti-6Al- 4V alloy. In one example, the feed material comprises and/or is a Ti alloy selected from: Carpenter CT PowderRange Ti64 S (RTM) available to ASTM Grade 5 and Grade 23, available from Carpenter Technology Corporation (USA); Osprey Ti-6Al-4V Grade 5 (RTM) and/or Osprey Ti-6Al-4V Grade 23 (RTM), available from Sandvik AB (Sweden); CPTi - Gr.1, Gr.2, Ti64 - Gr.5, Gr.23, Ti6242, Ti5553 and/or Beta 21S, available from GKN Sinter Metals Engineering GmbH (Germany). Similar Ti alloys include: LPW Ti6-4 High Performance Titanium; UNS R56400/R56407; 3D Systems Ti Gr.23; Concept Laser CL 41 TI ELI; EOS Ti64ELI; Renishaw Ti6Al4V ELI-0406; SLM Solutions TiAl6V4; and TRUMPF TitaniumT:64 ELI-A LMF. Apparatus The second aspect provides an additive manufacturing, AM, apparatus, preferably a powder bed fusion, PBF, apparatus, including a computer comprising a processor and a memory, wherein the apparatus comprises: a sensor configured to obtain a time series of an in-process parameter of additive manufacturing of a first layer of a set of layers of an article, wherein respective obtained values pd_t of the in- process parameter have positions (X, Y)_t associated therewith; wherein the computer is configured to: estimate a value pd_t,est of the in-process parameter, based, at least in part, on an obtained preceding value pd_t-n of the in-process parameter, wherein ^ is a natural number greater than or equal to 1; compare the estimated value pd_t,est of the in-process parameter and the obtained value pd_t of the in-process parameter; and identify a defect in the article based, at least in part, on a result of the comparing. The AM, the computer, the sensor, the obtaining, the time series, the in-process parameter, the first layer of the set of layers, the article, the estimating, the comparing, the identifying and/or the defect may be as described with respect to the first aspect. Computer, computer program, non-transient computer-readable storage medium The third aspect provides a computer comprising a processor and a memory configured to implement a method according to the first aspect, a computer program comprising instructions which, when executed by a computer comprising a processor and a memory, cause the computer to perform a method according to the first aspect, or a non-transient computer- readable storage medium comprising instructions which, when executed by a computer comprising a processor and a memory, cause the computer to perform a method according to the first aspect. Definitions Throughout this specification, the term “comprising” or “comprises” means including the component(s) specified but not to the exclusion of the presence of other components. The term “consisting essentially of” or “consists essentially of” means including the components specified but excluding other components except for materials present as impurities, unavoidable materials present as a result of processes used to provide the components, and components added for a purpose other than achieving the technical effect of the invention, such as colourants, and the like. The term “consisting of” or “consists of” means including the components specified but excluding other components. Whenever appropriate, depending upon the context, the use of the term “comprises” or “comprising” may also be taken to include the meaning “consists essentially of” or “consisting essentially of”, and also may also be taken to include the meaning “consists of” or “consisting of”. The optional features set out herein may be used either individually or in combination with each other where appropriate and particularly in the combinations as set out in the accompanying claims. The optional features for each aspect or exemplary embodiment of the invention, as set out herein are also applicable to all other aspects or exemplary embodiments of the invention, where appropriate. In other words, the skilled person reading this specification should consider the optional features for each aspect or exemplary embodiment of the invention as interchangeable and combinable between different aspects and exemplary embodiments. Brief description of the drawings For a better understanding of the invention, and to show how exemplary embodiments of the same may be brought into effect, reference will be made, by way of example only, to the accompanying diagrammatic Figures, in which: Figure 1 schematically depicts a Renishaw (RTM) AM 500Q machine schematic assembly of the optical sensing system (image reproduced with permission from the Renishaw Brochure ‘InfiniAM Spectral’, available at http://www.renishaw.com/en/infiniam-spectral–42310; Figure 2 schematically depicts articles manufactured using a method according to an exemplary embodiment, wherein the articles are truncated cones fabricated using Renishaw AM 500Q machine; Figure 3 schematically depicts a procedure followed to align CT images with build layers; Figure 4 schematically depicts (a) edge on the CT scan identified using the Matlab contour feature; and (b) edge identified on the build layer with an embedded notch; Figure 5 schematically depicts (a) position co-ordinates of CT scans; and (b) the clusters identified using DBSCAN and the orientation of pores; Figure 6 schematically depicts (a) hatch angle and identified hatch lines; and (b) re-sliced CT image for layer 42; Figure 7 schematically depicts (a) a hatch line which passes through defective regions with dark pixel values (grayscale < 80); and (b) corresponding photodiode signal behaviour where blue line indicates, 1-defective and 0-non defective; Figure 8 shows photodiode measurements corresponding to a hatch line (blue), the predicted photodiode values (orange) and the resulting predictive error (green): subplot (a) shows the photodiode measurements collected along a non-defective hatch line; and subplot (b) shows the photodiode measurements collected along a defective hatch line; Figure 9 shows (a) averaged predictive error calculated along the hatch lines of layer 42. The defective regions of the corresponding CT image, with a gray scale value less than 80, are shown in black; and (b) averaged predictive error ^‾_^^^^ less than 20 are indicated in red while

averaged predictive error ^‾_^^^^ higher than 20 are indicated in green;

Figure 10 shows (a) the average e_p calculated along the hatch lines (using a moving window of 10 values prior and post the current point) on layer 38. The defective regions on matched CT images with a gray scale value less than 80 are shown in black; and (b) the average e_p where values less than 20 are indicated in red and values higher than 20 shown in green; Figure 11 shows (a) the average e_p calculated along the hatch lines (using a moving window of 10 values prior and post the current point) on layer 81. The defective regions on matched CT images with a gray scale value less than 80 are shown in black; and (b) the average e_p where values less than 20 are indicated in red and values higher than 20 shown in green; Figure 12 shows the posterior probability distribution over σ² inferred from data relating to a defective hatch line (red) and a non-defective hatch line (green); Figure 13 shows (a) the change of area under the curve when the radius of the circular area used to match CT image pixels (corresponding to layer 42) was changed; and (b) the ROC curve plotted when radius of the circular area used to match CT image pixels (corresponding to layer 42) is 130 µm; Figure 14 shows (a) the matching CT image for layer 73 with thinly spread out defective region circled in colour red; and (b) photodiode readings with averaged predictive error ^‾_^^^^ less than

20 indicated in red and photodiode readings with averaged predictive error ^‾_^^^^ higher than 20

indicated in green; and Figure 15 schematically depicts a method according to an exemplary embodiment. Detailed Description of the Drawings Experimental setup and data In this study, data collected during the fabrication of a L-PBF build, in which defects are naturally formed as a result of parallel fabrication of parts placed in a row with multiple laser beams, are examined. The current study uses co-axial photodiode sensor measurements to identify defects, that have not been deliberately induced, in L-PBF build layers, using a real-time model that identifies defective melt-pools that cause pore formation. Thus, the approach described herein exploits photodiode data collected during L-PBF builds and trains a second-order auto- regressive (AR) model to predict porous regions on L-PBF build layers. A Renishaw AM 500Q machine (i.e. an apparatus), operated according to the manufacturer’s instructions, was utilised to AM the test samples used in this study and to record the associated data. Such machine is a quad laser system, and each channel has the sensing system sketched in Figure 1. The sensing system consists of two high precision co-axial single-channel detectors that are designed to capture melt-pool plume characteristics: Photodiode-1 (PD1 - no.4 in Figure 1) is sensitive to signals in the wavelength range of 300 to 1000 nm, whereas photodiode-2 (PD2 - no.5 in Figure 1) is sensitive to signals in the wavelength range of 1100 to 2000 nm. A third photodiode, photodiode-3 (PD3 - no.10 in Figure 1) measures the intensity of the laser beam. The optical window (no.16 in Figure 1), which helps focusing the laser beam, exhibits > 95% spectral transmission across the wavelength of interest. The machine has a galvo-scanner system (no.19 in Figure 1) which can control the movement of the laser focal point by following a set of demand (X, Y)_t coordinates. In this experiment, sensor data collected via photodiode-1 and the (X, Y)_t coordinates of the laser focal point collected alongside the photodiode measurements (at a sample rate of 100 kHz) were used to identify porous regions. Thirty-two pillars, each composed of 12 vertically stacked truncated cones, were fabricated from Renishaw Ti6Al4V ELI-0406 (Figure 2). Each cone had a top diameter of 15 mm, a bottom diameter of 11 mm and a height of 6 mm. Each cone was embedded with a triangular cut so that the computed tomography (CT) image could be aligned to the built part, allowing the layer and corresponding CT scan image to be identified. The AM conditions were: point distance: 30 μm; layer thickness: 60 μm; laser power: 320 W. To visualise the post-build quality of the build, CT scans were done on a set of truncated cones that were detached from the vertical stack. To allow enough material penetration by the CT scanner (and therefore enough resolution in the resulting images) only 2 cones from the vertical stack were scanned.2D images were created by slicing the 3D image, where the resolution was 1106 × 835 × 1106 voxels and the voxel size was 14.002 × 14.003 × 14.002 µm.1278 slices (2D images) were obtained after slicing the 3D image parallel to the x-y plane. CT alignment In this work, CT scans are used to obtain the ground truth about part quality. Therefore, accurate alignment of the CT images with the sensor data from each build layer is critical. Indeed, those images are used to identify defective hatch lines used for training and to validate the results produced by the proposed predictive model. To this end, both sensor readings and the corresponding position co-ordinates of the melt pools were saved in.dat files. However, the coordinate systems used for the sensor data and the CT scan are not perfectly aligned, therefore the data alignment procedure shown in Figure 3 was applied. This consists of the following main steps: 1. Calculate the geometric scaling factors to scale the X and Y coordinates so that they match; 2. Rotate CT images around the ^-axis so that the planar orientation of the CT images and of the sensor data is the same; 3. Estimate the orientation of the pores in CT images; 4. Find the CT slices corresponding to a layer in the sensor data; 5. Tilt the image stack to complete 3D alignment between CT and sensor data. Each step in this process is discussed in more detail below. Calculating the scaling factors Geometric scaling factors were determined to map CT scan images onto the co-ordinates contained in the.dat files. As a first step to calculating the scaling factors, it was assumed that the shape of each layer of the specimen was approximately elliptical with the major and minor axes aligned with the X and Y axes. The center of the ellipse (C_x , C_y) was obtained by calculating the mean value of the collected X − Y co-ordinates on the layer of interest (X_dat, Y_dat). -_dat and ._dat represent vectors of collected X and Y co-ordinates respectively. The radius of the ellipse in the / and 0 directions (denoted X_dat,+ and Y_dat, respectively) were then derived by reading the average distance between the center and points on the far-end in the ^ and ^ directions identified on the edge of the ellipse: 1₌ ^{^*} ₊ ^{− min^-} _dat ^{^^ + ^ma} d_{at,+ 2} ₁ ^{^*} d_{at, =} ^{, − min^.dat^^ + ^ma} 2

The edges of the specimen in the CT scans were identified using the Matlab function contour as demonstrated in Figure 4(a). Once the center position was identified, the radius of curvature of the ellipse in the CT image was also recorded in both X and Y directions in terms of the number of pixels occupied in each direction (R_ct,x and R_cty ). Two scaling factors, s_x for the / direction and s_y, for the 0 direction, were then calculated according to: 5_{+ =} ^1dat,+ _, 5 ¹ Equation 3 ,₌ ^dat, 1_{CT,+ 1CT,}

Rotating CT images around 7-axis With the scaling factors identified, the CT images were mapped onto the co-ordinates contained in the.dat file. Using the specimen edge identified on a layer with an embedded notch (a small triangular cut) shown in Figure 4(a), the ^ co-ordinates of the bottom half of the edge were collected excluding the points on the small notch. The maximum point-wise distance between consecutive points was then measured and the corner co-ordinates of the small notch were identified as being the coordinate with the maximum point-wise distance. The co-ordinates (N_x, N_y) of the left corner of the notch were then recorded and used to estimate the slope of the line (8₃₄) connecting the center of the ellipse and the left corner of the notch as: 8 ^{* − ^} Equation 4 C_{T =} ^{, ,} *_{+ − ^+}

The slope ψ_dat of the line connecting the center of the ellipse and the left corner of the notch in a build layer was also calculated using the same method. In this case, the edge of the circle (as shown in Figure 4(b)) was identified by comparing the distance between the center of the ellipse and the recorded points on the layer against a mean radius of R_dat. The rotation angle around the Z-axis was then calculated as 9_{rotation = tan} ^{^:} _^8dat^

and all the CT images were rotated by 9_rotation degrees so that the position of the notch in the CT images matched the position of the notch in the.dat file. Thanks to this process, the spatial coordinates of the CT images are aligned with the spatial coordinates of the photodiode measurements. Estimation of the orientation of the pores Pores are represented by dark pixels in the CT images. Therefore, by setting a threshold on the grey scale value of the CT pixels (Figure 5(a)), pixels corresponding to pores were identified. Subsequently, the density-based spatial clustering of applications with noise (DBSCAN) algorithm was used to cluster those pixels depending on their proximity on the layer. DBSCAN groups data points that are close to each other based on the pair-wise distance measurements (Euclidean distance) and on the minimum number of points that are required to be positioned together to form a dense region (these parameters are defined by the user). Once the pixels were clustered together (Figure 5(b)), the cluster composed of the largest number of pixels was selected and used to calculate the principal angle along which the defects were oriented. To do so, principal component analysis (PCA) was used to identify the unit vectors (v₁ and v₂). In PCA, v₁ and v₂ represent orthogonal directions along which the greatest variance in the data occurs. Thus, by taking the inverse tangent of the components of the first unit vector (;_:), the principal direction with respect to the /-axis is: ^^{: >:,+} Equation 6 <_{defect = tan = ?} _>:,

Finding the correspondence between CT slices and build layers In order to identify the CT slices that are positioned at a similar height to the build layer of interest, the number of CT slices (1300 images) was divided by the respective number of build layers (200 layers) and multiplied by the index of the build layer of interest. We note that, for a particular build layer, there may exist several closely matching CT slices, as the 3D CT image has a relatively high resolution along the ^-axis. We also note that the 3D CT images were captured from a slightly tilted truncated cone, as the bottom of the detached truncated cone was not perfectly flat, and so CT slices identified at the estimated height of a layer of interest will not be a perfect match for said layer. As a result, the set of CT slices that may correspond to a particular build layer were defined as those whose vertical position lies within the interval: I ^Num C_{T = A} Numb Number Number o

where the term ±8 (provided by Renishaw) was included to take into account the uncertainty introduced by the tilt. The hatch angle (shown in Figure 6(a)) used in fabrication, rotated by approximately 67° for each layer to reduce residual stresses, was recorded in an.mtt file. The accurate corresponding CT slices for each build layer were finally identified from those within I_CT by comparing the recorded hatch angle with the principal defect angle β_defect (that indicates orientation of the defects) calculated for CT images recognised in Equation 7. This is based on the assumption that defects tend to form along hatch lines, as commonly observed by Renishaw. Tilting the image stack Finally, to correct for the tilted CT scan, the matching CT slices, identified as described above, were stacked together using the nibable library (Python) creating a NifTi (Neuroimaging Informatics Technology Initiative) image which enables data to be stored as a 3D image in a single.nii file. This NifTi image was then tilted using the ITK snap software (developed by Yushkevich et al.). The tilted image stack was finally re-sliced to obtain the CT image (shown in Figure 6(b)) that corresponds to the L-PBF build layer of interest (Re-slice: an option provided by ITK snap software under the registration tool that can be used to obtain a 2D image at a chosen height of an adjusted 3D image). Predictive model development A second-order auto-regressive (AR) model was used to generate predictions of photodiode measurements. The underlying hypothesis is that the difference between predicted and observed photodiode measurements could be used to infer regions of porosity. Interestingly, it was found that the model predictions were more accurate in regions of build porosity; the rationale behind this perhaps counter-intuitive observation is explored in subsequent sections. Model description Let us define at first pd_t as the photodiode measurement obtained at time index t. Predictions of said photodiode measurement, denoted by ^^_^,^^^ were then obtained using the Auto- Regressive (AR) model pd_t,est = W_.pd_t-1 + W₂pd_t-2 + ∈ Equation 8 where W₁ and W₂ are weighting coefficients of the AR model and E is modelled as Gaussian noise with zero mean and variance ^^{^}. A second-order AR model was selected, as it provided the best compromise in terms of complexity and predictive accuracy. To train the model, the weighting coefficients were estimated using a photodiode signal collected on a defective hatch line, which contained approximately 400 data points. The first 20 readings were discarded, as on every layer we could observe a ramp at the start of all photodiode signals collected on different hatch lines. This ramping occurs as thermal reactions near the edge of the build layer are different to what is observed in the bulk. By defining F_G = ^^^_^^:, ^^_^^^^⁴ and w

^^_^,^^^ = w⁴F_G + E Equation 9

The probability distribution of observing pd_t,est is therefore: ^^^^_^,^^^|F_G,w, ^^{^}^ = K^^^_^,^^^|w⁴F_G,

For the sake of notational simplicity, we use ɸ = {φ₁, ... , φ_n}⁴ and pd_est = pd_t,est, ... , pd_N,est)^T to represent, respectively, the data set of ^ inputs and the ^ corresponding targets. By assuming that these data points are drawn independently from the distribution defined by equation 10, the likelihood of _w and σ² is: S ^^QR_^^^|ɸ ,w, ^^{^}^ = T K ^^^_U,^^^|w^TF_W, ^^{^}^ UV:

Model training In this study, prior probability distributions over the model parameters are combined with the likelihood function such that a posterior distribution over the parameters _w and ^^{^} can be realised using Bayes’ theorem. We note that, in this study, we consider a so-called conjugate prior which allow closed-form expressions for the posterior distribution to be derived. From Bayes’ theorem, the joint posterior distribution over w and σ² is: ^^{^w, ^^|QR}^^^^{, ɸ ^ ∝ ^^QR}^^^^{|ɸ ,w, ^^^^^w,} = ^^QR_^^^|ɸ ,w, ^^{^}^^^w|^^{^}^^^^^{^}^ where we choose: ^^w|^^{^}^ = K^w|m_Z, ^^{^}S_Z^ ^^^^{^}^ = Inverse-Gamma^^^{^}|\_], ^_]^

and m₀, S₀, α₀ and b₀ are defined by the user. The resulting posterior distribution can be shown to be: ^^w, ^^{^}|QR_^^^ , ɸ ^ ∝ ^^w|^^{^}, QR_^^^, ɸ ^^^^^{^}

where: ^^w|^^{^}, QR_^^^, ɸ ^ = K^w|m_^, ^^{^}S_^^ Eq

^^^^{^}|QR_^^^, _ɸ ^ = Inverse-Gam

where m_n and S_n denote the mean and covariance matrix of the posterior over w, respectively. Similarly, a_n and b_n represent the shape and scale of posterior over σ², respectively. Once the posterior over w and σ has been obtained, we can also write the probability of witnessing a new photodiode measurement, pd_new, for a new input, φ_new by evaluating the predictive distribution: ^^pd_new|F_a^b, QR_^^^ , ɸ ^ =_{c ^^ynew|Fa^b,w, ^} ^{^} _{^^^w, ^} ^{^} _{|QR^^^ , ɸ ^^w}

This predictive distribution can be shown to be a multivariate Student’s t-distribution with center e_^^, squared scale matrix s_^ ^{^} _^ and g_^^ degrees of freedom:

^^pd_new|F_a^b, QR_^^^, ɸ ^ = st^pd_a^b|e_^^, s^{^} _^^ , g_^

Model validation After training, the model was validated on signals collected from several different defective and non-defective hatch lines. The predictive error was then calculated by taking the absolute value between predicted and measured photodiode readings: e_p ^{(t) = |pd} _t,est ^{− pd} _t ^| _{Equation 21} An averaged predictive error, ^‾_^^^^, was then calculated using a sliding window of 21 re

g belonging to the same hatch line and centered on the photodiode reading under consideration: :] :] ^‾_^^^^ = i ^_^ ^^ − j^ + ^_^^^^ + i ^_{^ ^^ + j^} UV: UV:

Such predictive error ^‾_^^^^ was calculated to provide a measure

error that is smoothed over a time-window. Results and discussion Model predictions obtained for a defective and non-defective hatch line are plotted alongside measured photodiode readings in Figures 8(a) and 8(b) for a non-defective and a defective hatch, respectively. The error between the predicted and measured photodiode measurements, e_p(t) (calculated as explained previously), is also illustrated. The average predictive errors, ^‾_^^^^, collected on Layer 42, are plotted on the correspon

position co-ordinates in Figure 9(a). It can be seen that ^‾_^^^^ values below 20 often appear to

be in regions that have been identified as defective via the CT scan. We note that this is perhaps an unexpected outcome, as it indicates that the proposed model predictions are more accurate in regions of porosity. To clarify this observation, Figure 9(b) has been colour-coded such that regions where ^‾_^^^^ < 20 are plotted as red poi

g ≥ 20 are plotted as

green points. Moreover, this behaviour was observed over multiple layers; Figure 10 shows the results obtained for Layer 38, Figure 11 shows the results obtained for Layer 81 and Figure 12 shows the results obtained for Layer 73. To understand these perhaps counter-intuitive results we first note that, to the best of the inventors’ understanding, the photodiode signals relating to the porosity present in the builds described herein were collected when a plume of evaporation (generated as a result of over- melting) came between the laser and the powder bed. We hypothesise that this plume has, in essence, acted as a filter, removing noise from the resulting photodiode measurements (and increasing their predictability as a result). To test this hypothesis, the inventors trained the model on data from both a defective and non-defective hatch line. The inventors then studied the results of the Bayesian parameter estimation, described previously, specifically focusing on the posterior probability of the noise variance,. An inverse-gamma distribution with shape parameter a_n = 175.5 and scale parameter b _n = 806609.88 was obtained for a signal collected on defective hatch line while the shape and scale parameters identified on a non-defective hatch line was \_^ = 187.5 and b_n = 2854844.63 respectively. The resulting posterior parameter distributions are illustrated in Figure 12, where it is clear that the estimated noise variance for the defective hatch line is less than that of the non-defective hatch line. While this lends weight to the hypothesis, the inventors accept this is not a definitive explanation as to why the proposed model is more accurate in regions of porosity. The approach, however, does appear to work well, as will be discussed in the following sections. Calculating TPR and TNR The ability of the model to predict regions of porosity was quantified by calculating true positive rates (TPR) and true negative rates (TNR). In this context, a true positive indicates a correctly predicted region of porosity while a true negative is a correctly predicted non-porous region. To compare predictions to the CT scan, the coordinates of the CT images were mapped to the coordinates of the corresponding photodiode measurements, as described previously. With these mapped co-ordinates, a circular area around each pixel position was examined on the corresponding .dat layer to identify correlating photodiode readings. Initially, the radius of the circle was set equal to 40 µm (this value was chosen referring to the point distance used in fabricating each layer of the specimen) so that only one photodiode reading could be found within the circular range. However, although we tried to match the CT images with the.dat layers as accurately as possible, distortions in the part that occur during and after the build (e.g. due to thermal deformations) change the corresponding position co-ordinates. Therefore, the radius of the circular area was increased to minimise the effect that such deformations could have on calculating success rates. A true positive is considered to have occurred if the pixel of interest has gray-scale less than 80 and if the majority of the model predictions in the area surrounding said pixel indicate porosity.

Table 1: Area under the ROC curve for different radius values. A Receiver Operating Characteristic (ROC) curve is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied. In this study, to create a ROC curve, the classifier’s False Positive Rate (FPR) and True Positive Rate (TPR) are recorded for the specified range of classification thresholds (the threshold applied to ^‾_^^^^ was

varied from 0 to 60) before being plotted against one another. For the current example, the TPR is defined as the ratio of correctly identified regions of porosity, relative to the total number of regions of porosity. Likewise, the FPR is defined as the ratio of falsely identified regions of porosity, relative to the total number of non-porous regions. The Area Under the Curve (AUC) represents a measure of separability. The higher the AUC is, or the closer the curve is to the top-left of the plot, the better the model is at distinguishing between porous and non-porous regions. AUC=0.5 indicates that the model has no class separation capacity, while AUC=1.0 indicates that the model can separate the classes with 100% accuracy. The area under the ROC curve was calculated for different radius values, as shown in Table 1, to observe the effect of radius on success rate. The maximum AUC was obtained when the radius was set to 130 µm, as illustrated in Figure 13(a). The AUC for the predictive model with a radius value of 130 µm was found to be 0.9292. Defec

Table 2: TPR and TNR calculated for different layers. Setting τ = 130 µm and the applied threshold to ^‾_^^^^=20, TPR and TNR values calculated for several layers are summarised in Table 2. The predictive model was able to predict regions of porosity with an average accuracy of 88.47%. The capability of predicting non-porous regions was found to be lower (76.89%). However, on layer 81 (Figure 11) where pores are not visible, a TNR of 99.84% is achieved. For layer 73 the TNR value 67.43% is relatively low compared to TNR values of other layers. In this particular layer, as shown in Figure 14(a), defects were thinly spread out over a larger area. As a result, some of those defects, circled in red in Figure 14(a), are hardly visible in Figure 14(b) with the grayscale value threshold in place. Pixels on this layer could get easily mis- classified as non-defective (resulting in a low TNR value), as a consequence. Conclusions The absence of a robust quality control system in Additive Manufacturing introduces uncertainties regarding quality of end-products’ quality, thus hindering the adoption of AM technology in safety-critical sectors. Most of the monitoring systems proposed in the literature so far have focused on image-based approaches. However, the response rates and image processing requirements of such systems make it difficult to apply these monitoring methods in real-time. Therefore, the combination of photodiode sensors with relatively high sample rates and computationally inexpensive algorithms is used in this study to identify regions of porosity. The proposed approach is centered around a second-order auto-regressive model, where the future photodiode readings are predicted based on their immediate past readings. Conclusions of this study are as follows: 1. The predictive model can predict regions of porosity with an average true positive rate (TPR) of 88.47%. The capability of predicting non-porous regions is slightly lower (76.89%). However, on a layer where pores are not visible, the True Negative Rate (TNR) is 99.84%. 2. The optimal radius for the circular area defined around each CT pixel (used to find corresponding photodiode readings) is 130 µm. 3. The noise observed on a defective hatch line is of lower variance than the noise observed in a non-defective hatch line. Success rate can be improved by considering potential re-melt events. In fact, in this study each layer is analysed individually, therefore the effect of the laser scanning a successive layer and re-melting the identified defective regions has not been taken into consideration. Such re-melt events reduce the number of porous regions in the final part (as measured via CT scans), although some of them were defective when the corresponding layer was processed. We believe that by integrating the probability of re-melt events the accuracy of the proposed method can be improved. Figure 15 schematically depicts a method according to an exemplary embodiment. The method is of additive manufacturing, AM, preferably powder bed fusion, PBF, of an article or a part thereof. The method is implemented, at least in part, by a computer comprising a processor and a memory. At S1501, the method comprises additive manufacturing a first layer of a set of layers of the article. At S1502, additive manufacturing the first layer comprises obtaining a time series of an in- process parameter of the additive manufacturing of the first layer, wherein respective obtained values pd_t of the in-process parameter have positions (X, Y)_t associated therewith. At S1503, additive manufacturing the first layer comprises estimating a value pd_t,est of the in- process parameter, based, at least in part, on an obtained preceding value pd_t-n of the in- process parameter, wherein n is a natural number greater than or equal to 1. At S1504, additive manufacturing the first layer comprises comparing the estimated value pd_t,est of the in-process parameter and the obtained value pd_t of the in-process parameter. At S1505, additive manufacturing the first layer comprises identifying a defect in the article based, at least in part, on a result of the comparing. Although a preferred embodiment has been shown and described, it will be appreciated by those skilled in the art that various changes and modifications might be made without departing from the scope of the invention, as defined in the appended claims and as described above. Attention is directed to all papers and documents which are filed concurrently with or previous to this specification in connection with this application and which are open to public inspection with this specification, and the contents of all such papers and documents are incorporated herein by reference. All of the features disclosed in this specification (including any accompanying claims and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at most some of such features and/or steps are mutually exclusive. Each feature disclosed in this specification (including any accompanying claims, and drawings) may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise. Thus, unless expressly stated otherwise, each feature disclosed is one example only of a generic series of equivalent or similar features. The invention is not restricted to the details of the foregoing embodiment(s). The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed. References B. K. Foster, E. W. Reutzel, A. R. Nassar, C. J. Dickman, and B. T. Hall, A brief survey of sensing for metal-based powder bed fusion additive manufacturing, in Dimensional Optical Metrology and Inspection for Practical Applications IV, vol.9489, p.94890B, International Society for Optics and Photonics, 2015. M. Mani, S. Feng, B. Lane, A. Donmez, S. Moylan, and R. Fesperman, Measurement science needs for real-time control of additive manufacturing powder bed fusion processes. US Department of Commerce, National Institute of Standards and Technology, 2015. I. Yadroitsev, P. Bertrand, and I. 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Claims

CLAIMS 1. A method of additive manufacturing, AM, preferably powder bed fusion, PBF, of an article or a part thereof, the method implemented, at least in part, by a computer comprising a processor and a memory, the method comprising: additive manufacturing a first layer of a set of layers of the article, comprising: obtaining a time series of an in-process parameter of the additive manufacturing of the first layer, wherein respective obtained values pd_t of the in-process parameter have positions (X, Y)_t associated therewith; estimating a value pd_t,est of the in-process parameter, based, at least in part, on an obtained preceding value pd_t-n of the in-process parameter, wherein ^ is a natural number greater than or equal to 1; comparing the estimated value pd_t,est of the in-process parameter and the obtained value pd_t of the in-process parameter; and identifying a defect in the article based, at least in part, on a result of the comparing.

2. The method according to claim 1, wherein the in-process parameter relates to a melt pool, for example a plume thereof, formed during the additive manufacturing of the first layer.

3. The method according to any previous claim, wherein obtaining the time series of an in- process parameter comprises measuring plasma emissions during the additive manufacturing of the first layer, for example using a photodiode.

4. The method according to any previous claim, wherein obtaining the time series of an in- process parameter comprises acquiring values ^^_^ of the in-process parameter at a rate in a range from 1 kHz to 1 MHz, preferably in a range from 10 kHz to 500 kHz, more preferably in a range from 50 kHz to 200 kHz, for example 100 kHz.

5. The method according to any previous claim, wherein estimating the value pd_t,est of the in- process parameter comprises estimating the value pd_t,est of the in-process parameter using an autoregressive model having an order ^, wherein ^ is a natural number greater than or equal to 1.

6. The method according claim 5, comprising training the autoregressive model.

7. The method according to any of claims 5 to 6, wherein ^ = 2.

8. The method according to any previous claim, wherein comparing the estimated value pd_t,est of the in-process parameter and the obtained value pd_t of the in-process parameter comprises calculating a magnitude of a difference therebetween.

9. The method according to any previous claim, wherein identifying the defect in the article based comprises identifying the defect using a predetermined threshold.

10. The method according to any previous claim, wherein identifying the defect in the article comprises locating the defect in the article.

11. The method according to claim 10, wherein locating the defect in the article comprises locating the defect in the first layer, for example at a position (X, Y)_t associated with the obtained value pd_t of the in-process parameter.

12. The method according to any previous claim, comprising controlling the additive manufacturing based, at least in part, on identifying the defect in the article, for example wherein controlling the additive manufacturing comprises remediating the defect.

13. The method according to claim 12, wherein controlling the additive manufacturing comprises controlling the additive manufacturing of a second layer of the set of layers, for example proximal a position (X, Y)_t associated with the obtained value pd_t of the in-process parameter in the first layer.

14. The method according to any previous claim, wherein the defect comprises and/or is a pore.

15. An additive manufacturing, AM, apparatus, preferably a powder bed fusion, PBF, apparatus, including a computer comprising a processor and a memory, wherein the apparatus comprises: a sensor configured to obtain a time series of an in-process parameter of additive manufacturing of a first layer of a set of layers of an article, wherein respective obtained values pd_t of the in- process parameter have positions (X, Y)_t associated therewith; wherein the computer is configured to: estimate a value pd_t,est of the in-process parameter, based, at least in part, on an obtained preceding value pd_t-n of the in-process parameter, wherein n is a natural number greater than or equal to 1; compare the estimated value pd_t,est of the in-process parameter and the obtained value pd_t of the in-process parameter; and identify a defect in the article based, at least in part, on a result of the comparing.

16. A computer comprising a processor and a memory configured to implement a method according to any of claims 1 to 14, a computer program comprising instructions which, when executed by a computer comprising a processor and a memory, cause the computer to perform a method according to any of claims 1 to 14, or a non-transient computer-readable storage medium comprising instructions which, when executed by a computer comprising a processor and a memory, cause the computer to perform a method according to any of claims 1 to 14.