Metal additive manufacturing (AM) works on the principle of consolidating feedstock material in layers towards the fabrication of complex objects through localized melting and resolidification using high-power energy sources. Powder bed fusion and directed energy deposition are two widespread metal AM processes that are currently in use. During layer-by-layer fabrication, as the components continue to gain thermal energy, the melt pool geometry undergoes substantial changes if the process parameters are not appropriately adjusted on-the-fly. Although control of melt pool geometry via feedback or feedforward methods is a possibility, the time needed for changes in process parameters to translate into adjustments in melt pool geometry is of critical concern. A second option is to implement multi-physics simulation models that can provide estimates of temporal process parameter evolution. However, such models are computationally near intractable when they are coupled with an optimization framework for finding process parameters that can retain the desired melt pool geometry as a function of time. To address these challenges, a hybrid framework involving machine learning-assisted process modeling and optimization for controlling the melt pool geometry during the build process is developed and validated using experimental observations. A widely used 3D analytical model capable of predicting the thermal distribution in a moving melt pool is implemented and, thereafter, a nonparametric Bayesian, namely, Gaussian Process (GP), model is used for the prediction of time-dependent melt pool geometry (e.g., dimensions) at different values of the process parameters with excellent accuracy along with uncertainty quantification at the prediction points. Finally, a surrogate-assisted statistical learning and optimization architecture involving GP-based modeling and Bayesian Optimization (BO) is employed for predicting the optimal set of process parameters as the scan progresses to keep the melt pool dimensions at desired values. The results demonstrate that a model-based optimization can be significantly accelerated using tools of machine learning in a data-driven setting and reliable a priori estimates of process parameter evolution can be generated to obtain desired melt pool dimensions for the entire build process.

A multi-fidelity (MF) surrogate involving Gaussian processes (GPs) is used for designing temporal process maps in laser directed energy deposition (L-DED) additive manufacturing (AM). Process maps are used to establish relationships between the melt pool properties (e.g., melt pool depth) and process parameters (e.g., laser power and scan velocity). The MFGP surrogate involves a high-fidelity (HF) and a low-fidelity (LF) model. The Autodesk Netfabb${}^{\circledR }$ finite element model (FEM) is selected as the HF model, while an analytical model developed by Eagar-Tsai is chosen as the LF one. The results show that the MFGP surrogate is capable of successfully blending the information present in different fidelity models for designing the temporal forward process maps (e.g., given a set of process parameters for which the true depth is not known, what would be the melt pool depth?). To expand the newly-developed formulation for establishing the temporal inverse process maps (e.g., to achieve the desired melt pool depth for which the true process parameters are not known, what would be the optimal prediction of the process parameters as a function of time?), a case study is performed by coupling the MFGP surrogate with Bayesian Optimization (BO) under computational budget constraints. The results demonstrate that MFGP-BO can significantly improve the optimization solution quality compared to the single-fidelity (SF) GP-BO, along with incurring a lower computational budget. As opposed to the existing methods that are limited to developing steady-state forward process maps, the current work successfully demonstrates the realization of temporal forward and inverse process maps in L-DED incorporating uncertainty quantification (UQ).

Data-driven prediction of spatiotemporal fields in fluid flow problems has received significant interest lately. However, the scarcity of data often plagues the accuracy of the prevalent approaches, particularly in situations where the cost associated with the generation of high-fidelity data is prohibitively expensive. Moreover, the data sources in many spatiotemporal fluid flow problems present a hierarchy of fidelities with respect to their computational cost/accuracy, such that the higher fidelity sources are more accurate and also more expensive than the low-fidelity sources. This article presents a novel multi-fidelity spatiotemporal modeling approach whereby the lower fidelity data source for a dynamical process is gainfully utilized in increasing the accuracy of predicting the higher fidelity fields, thereby reducing the overhead of high-fidelity simulations for data-driven prediction. The methodology is based on non-intrusive reduced order modeling using deep convolutional autoencoders, combined with a latent-space evolution framework based on multi-fidelity Gaussian processes. This framework results in probabilistic spatiotemporal predictions for unknown operating conditions of the dynamical system, which provides the end user with quantified levels of uncertainties associated with the data-driven predictions. The framework is validated on a prototypical fluid flow problem of interest: two-dimensional incompressible viscous flow around a cylinder.

Serpentine channels are a common feature seen in heat ex-changer geometries. For example, they are present in midchord regions of gas turbine blades to prevent material failure at high turbine inlet temperatures. Due to their serpentine nature, these channels contain 180 deg turns or U-bends. These U-bends are responsible for nearly 20% of the pressure drop in such channels (Verstraete et al., 2013, “Optimization of a U-Bend for Minimal Pressure Loss in Internal Cooling Channels-Part I: Numerical Method,” ASME J. Turbomach., 135(5), p. 051015). A topology optimization (TO) method has been used in this study to optimize the shape of a baseline U-bend for minimum pressure drop, at a Reynolds number of 17,000. TO uses a variable permeability approach to design an optimum flow-path by manipulation of solid blockage distribution in the flow-path. The pressure drop across the channel was lowered by 50% when compared to a standard U-bend channel profile from literature. Postprocessing was performed to extract the flow-path and run a forward simulation in star-ccm+ after remeshing with wall refinement. A 3D printed model of the TO shape and benchmark U-bend was created using acrylonitrile butadiene styrene as the printing material, to confirm the results of the turbulent fluid TO, which is a relatively untouched topic in current TO literature. Experimental results showed deviation from computational fluid dynamics (CFD) by about 5%. Comparison of the TO optimum was carried out with an in-house parametric shape optimization using surrogate model-based Bayesian optimization (BO) and a similar shape optimization study from literature. A higher reduction in pressure drop was seen in the case of the TO geometry when compared to the benchmark and the BO cases.