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DOE OSTI2025

Dynamic Modeling, Trajectory Optimization, and Linear Control of Cable-Driven Parallel Robots for Automated Panelized Building Retrofits

The construction industry faces a growing need for automation to reduce costs, improve accuracy and productivity, and address labor shortages. One area that stands to benefit significantly from automation is panelized prefabricated building envelope retrofits, which can improve a building’s energy efficiency in heating and cooling interior spaces. In this paper, we propose using cable-driven parallel robots (CDPRs), which can effectively lift and handle large objects, to install these panels. However, implementing CDPRs presents significant challenges because of their nonlinear dynamics, complex trajectory planning, and precise control requirements. To tackle these challenges, this work focuses on a new application of established control and trajectory optimization theories in a CDPR simulation of a building envelope retrofit under real-world conditions. We first model the dynamics of CDPRs, highlighting the critical role of damping in system behavior. Building on this dynamic model, we formulate a trajectory optimization problem to generate feasible and efficient motion plans for the robot under operational and environmental constraints. Given the high precision required in the construction industry, accurately tracking the optimized trajectory is essential. However, challenges such as partial observability and external vibrations complicate this task. To address these issues, a Linear Quadratic Gaussian control framework is applied, enabling the robot to track the optimized trajectories with precision. Simulation results show that the proposed controller enables precise end effector positioning with errors under 4 mm, even in the presence of external wind disturbances. Through comprehensive simulations, our approach allows for an in-depth exploration of the system’s nonlinear dynamics, trajectory optimization, and control strategies under controlled yet highly realistic conditions. The results demonstrate the feasibility of CDPRs for automating panel installation and provide insights into their practical deployment.

CDPR↗

DOE OSTI2024

Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations

Here, we demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We conduct experiments on 38 cases from the PGLib-OPF library, showing that the LNC strengthen the SOC and CDF relaxations in 100% of the test cases, with average and maximum differences in the optimality gaps of 6.2% and 17.5% respectively. The NF relaxation is strengthened in 46.2% of test cases, with average and maximum differences in the optimality gaps of 1.3% and 17.3% respectively. We also study the trade-off between relaxation quality and solve time, demonstrating that the strengthened CDF relaxation outperforms the strengthened SOC formulation in terms of runtime and number of iterations needed, while the strengthened NF formulation is the most scalable with the lowest relaxation quality improvement due to these LNC.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Hybrid Heat Pump Controls: Conventional Dual Fuel versus Seamlessly Fuel Flexible Heat Pump

This paper compares the performance of a novel seamlessly fuel flexible heat pump (SFFHP) and conventional dual fuel heat pump (DFHP) for space heating. The conventional dual fuel systems either run on the gas furnace or electric heat pump at any given moment, as a comparison, the proposed seamlessly fuel flexible heat pump simultaneously consumes gas and electricity by continuously optimizing the proportion of each. The process air flows across the heat pump condenser first and then flows across the furnace coil, therefore, the heat pump temperature lift is reduced. SFFHP delivers energy savings by allowing each subsystem, i.e., gas furnace and electric heat pump, to operate where it performs best.For DFHP, two operation control strategies, i.e., non-restricted control and restricted control, are available on market. For the non-restricted mode, the thermostat has a switching temperature-programmed according to the balancing point of heating load and capacity curve. Heat pump operates above the switching temperature, while the furnace takes over under the switching temperature. For the restricted control, the compressor of a heat pump is disabled below a predefined lockout outdoor temperature to let the furnace take over. For SFFHP, a model predictive control strategy is developed to continuously adjust the capacities of the electric heat pump and gas furnace based on the foreseen weather data, utility price signals, and marginal grid emission signals with the goal of minimizing the utility cost and CO2 emission while guaranteeing comfort requirements.In this paper, DFHP and SFFHP are simulated using high-fidelity heat pump performance curves generated from DOE/ORNL heat pump design model. Performance comparison of DFHP and SFFHP during 2019-2020 heating season in Los Angeles shows that SFFHP with model predictive control achieves 23% utility cost reduction and 17 % CO2 emission reduction. Case studies demonstrate that SFFHP can deliver significant reductions in peak demand, utility cost, and CO2 emission. As a result, SFFHP can deliver superior benefits for utility cost reduction and CO2 emission reduction over conventional dual fuel heat pump.

Li, Zhenning↗

DOE OSTI2022

Maximizing Strength: The Stimuli and Mediators of Strength Gains and Their Application to Training and Rehabilitation

Abstract Spiering, BA, Clark, BC, Schoenfeld, BJ, Foulis, SA, and Pasiakos, SM. Maximizing strength: the stimuli and mediators of strength gains and their application to training and rehabilitation. J Strength Cond Res 37(4): 919–929, 2023—Traditional heavy resistance exercise (RE) training increases maximal strength, a valuable adaptation in many situations. That stated, some populations seek new opportunities for pushing the upper limits of strength gains (e.g., athletes and military personnel). Alternatively, other populations strive to increase or maintain strength but cannot perform heavy RE (e.g., during at-home exercise, during deployment, or after injury or illness). Therefore, the purpose of this narrative review is to (a) identify the known stimuli that trigger gains in strength; (b) identify the known factors that mediate the long-term effectiveness of these stimuli; (c) discuss (and in some cases, speculate on) potential opportunities for maximizing strength gains beyond current limits; and (d) discuss practical applications for increasing or maintaining strength when traditional heavy RE cannot be performed. First, by conceptually deconstructing traditional heavy RE, we identify that strength gains are stimulated through a sequence of events, namely: giving maximal mental effort, leading to maximal neural activation of muscle to produce forceful contractions, involving lifting and lowering movements, training through a full range of motion, and (potentially) inducing muscular metabolic stress. Second, we identify factors that mediate the long-term effectiveness of these RE stimuli, namely: optimizing the dose of RE within a session, beginning each set of RE in a minimally fatigued state, optimizing recovery between training sessions, and (potentially) periodizing the training stimulus over time. Equipped with these insights, we identify potential opportunities for further maximizing strength gains. Finally, we identify opportunities for increasing or maintaining strength when traditional heavy RE cannot be performed.

Sport Sciences↗

DOE OSTI2023

Framework for Characterizing the Performance of High-Early Strength, High-Volume Fly Ash (HVFA) Concrete Structures

This presentation will highlight the development of a comprehensive framework to characterize the performance of high-volume fly ash (HVFA) concretes at early ages and discuss the resulting implications for concrete structures built using such materials. Achieving high-early compressive and/or flexural strength is often of particular importance for precast and/or prestressed concrete components – due to early age loading demands resulting from lifting, handling, or application of initial prestress – or other types of concrete structures that can significantly benefit from rapid strength development - such as for bridge deck repairs. The framework first includes a methodology for optimizing the strength of HVFA cementitious binders before subsequently scaling up the technology to evaluation of fresh and hardened HVFA concrete performance. A series of trial mix designs will be presented to demonstrate the effectiveness of the framework to achieve not only the desired high-early strength targets but also satisfactory workability, often in the form of self-consolidating concrete. Mechanical performance was evaluated at several age-dependent milestones and, in conjunction with estimating concrete strength using the maturity method, was ultimately used to facilitate the development of novel strength development history curves. By way of these datasets, concrete mechanical properties were utilized in the design of prototype structural components, such as beams and wall panels, for subjection to larger-scale experimental testing. Implications for other pertinent HVFA concrete performance attributes, such as shrinkage or creep, will also be discussed. The framework also includes a comprehensive methodology for evaluating the environmental life-cycle performance of HVFA concrete structures focused on mitigating any unwarranted environmental consequences resulting from beneficial HVFA reuse in concrete. Strategies for more widespread implementation of HVFA concrete materials into construction practice will also be presented. Lastly, the role of the HVFA concrete framework towards the development of new provisions for building codes and/or design standards, and recommendations for future research needs will also be discussed.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2024

Electrospinner Upgrades for Nanofiber Production

Electrospinning is an inexpensive and flexible method for producing nanofibers. Nanofibers are highly adaptable with potential applications in accelerator target systems, air and water filtration, and biomedicine. This project aims to upgrade and test an existing roll-to-roll electrospinner that is more economical for industrial nanofiber production. Varying the diameter of nanofiber can change its functional properties. The current unit cannot adjust spinneret-collector separation, which determines nanofiber diameter. The electro-spinneret channel also does not have lateral adjustment capabilities for precise alignment. Lastly, the viscosities of our polymer solutions have not been quantified. Solution injection into the channel is presently inconsistent because of imperfect nozzle sizing, resulting in waste and decreased efficiency. Modeling was done with Siemens NX CAD software, and viscosity was measured using a Brookfield DVE-LV viscometer. A dual scissor lift design for channel displacement, powered by a dual-shaft DC motor coupled to precision lead screws, was approved and construction was started. Preliminary channel modifications also were initiated. Going forward, the scissor lift system will be integrated and evaluated with our electrospinner, along with further channel modifications. Viscosity measurements of polyvinyldimethylformamide (PVDF) were recorded with inconsistent results due to inadequate testing conditions. Future viscosity trials must be completed in accordance with testing requirements. The optimization and commercialization of roll-to-roll electrospinner units can make nanofiber production more feasible for many new industries and consumer products.

Black, Niko↗

DOE OSTI2023

Multi-level optimization with the koopman operator for data-driven, domain-aware, and dynamic system security

Cyber-Physical Systems (CPSs) like the power grid are critically important but also increasingly vulnerable; ensuring reliable system operation in the face of disruptions is becoming more and more challenging. Multi-Level Optimization (MLO) is a powerful way to model adversarial interactions, which naturally makes it applicable to studying CPS security. However, MLO typically does not address underlying system dynamics, and incorporating nonlinear dynamics is generally infeasible. In this paper, we show how to combine MLO with the Koopman Operator (KO) to remedy this. The KO maps nonlinear dynamics to a lifted space in which those dynamics are linear, thus making it ideal for use with MLO. Moreover, the structure of the KO also provides convenient ways to incorporate domain knowledge into the data-driven process of learning the KO representation of a given system. Here we then demonstrate the use of MLO-KO on a small example problem taken from the power grid domain, discuss the scalability and computational cost of MLO-KO, and identify future research directions for this work.

42 ENGINEERING↗

DOE OSTI2023

Reactivity Coefficient Measurements to Aid in Reducing Compensating Errors in Plutonium Nuclear Data

Compensating errors between several nuclear data observables in a nuclear data library can adversely impact application simulations. The primary goal of the EUCLID project (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) is to reduce compensating errors between fast (0.1–5 MeV) 239Pu nuclear data for prompt fission neutron spectra (PFNS), average prompt fission neutron multiplicities, and neutron induced fission, capture, elastic, and inelastic cross sections. This work will focus on the design and execution of void reactivity coefficient measurements in the EUCLID experiment, performed on the Planet vertical lift critical assembly machine at the National Criticality Experiments Research Center (NCERC). Two different base configurations were designed and measured, one with high neutron leakage, and one with low neutron leakage. Both were primarily made up of plutonium metal (Zero Power Physics Reactor plates) without interstitial moderators and reflected by half-inch aluminum. Design optimization showed that void reactivity coefficient measurements in three locations per configuration was most impactful to reduce nuclear data uncertainties due to the varying impacts from elastic and inelastic scattering, as well as fission and capture. The locations for measurements were chosen based on preliminary studies which balanced measurement uncertainty and measurement practicality. The measurements were also selected to have sensitivities maximally complementary to previous arrangements. Comparisons across nuclear data libraries highlight the potential impact.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Generalized Quantum Signal Processing

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that | P | ≤ 1 , a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where P and Q are known. In cases where only P is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding Q for polynomials of degree on the order of 10 7 . We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the ϵ -approximate fractional query problem that requires O ( ( 1 / δ ) + log ( 1 / ϵ ) ) queries to perform where O ( 1 / δ ) is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a novel framework for the implementation of normal matrices, demonstrating its applicability through synthesis of diagonal matrices, as well as the development of a new algorithm for convolution through synthesis of circulant matrices using only O ( d log N + log 2 N ) 1 and 2-qubit gates for a filter of lengths d . Published by the American Physical Society 2024

Motlagh, Danial↗

DOE OSTI2025

The Fluid Dynamics Uncertainty Quantification Challenge Problem: XFOIL vs. MFOIL

Uncertainty quantification (UQ) has become more critical in aerospace engineering due to the growing dependence on computational tools for design optimization and performance analyses of aerospace vehicles. Even though the significance of UQ in assessing the credibility of computational analyses is well recognized, its costs and complexity impede its integration into standard practices, particularly in computational fluid dynamics (CFD) and other fluid analyses. This paper presents a UQ study for low-fidelity computational aerodynamics analyses with XFOIL and mfoil (i.e., the MATLAB version of XFOIL with several implementation modifications); these tools are utilized widely in both research and education. The main contributions of this paper are as follows: 1) improved precision in quantifying the uncertainty of the baseline Monte Carlo results used to benchmark surrogate modeling techniques for UQ, 2) quantification of the effect of the implementation differences between XFOIL and mfoil on solution quantities of interest (QoIs), such as lift and pitching moment coefficients, and 3) development of an open-source UQ library for use with XFOIL and mfoil, which has educational values and helps promote UQ for fluid analyses with aerospace applications. Results and discussions revolve around cases 1-4 of the challenge problem posed by the AIAA Fluid Dynamics Technical Committee’s Uncertainty Quantification Discussion Group (UQDG). In case 3, this work employs CFDverify, an open-source solution verification software, to quantify the discretization error and evaluate the extrapolated QoIs based on the grid convergence index (GCI). This UQ study differentiates itself from previous studies in the rigor of handling baseline Monte Carlo uncertainty and in including mfoil, which is a more accessible alternative to XFOIL. Finally, despite the growing computing power, low-fidelity computational tools remain valuable, such as for aerodynamic shape optimization at Mach numbers below 0.65 and low-to-mid Reynolds numbers.

Lay, Aidan S [University of Tennessee, Knoxville (↗

DOE OSTI2025

Unsteady aerodynamic loads on pitching aerofoils represented by Gaussian body force distributions

The actuator line model (ALM) is an approach commonly used to represent lifting and dragging devices like wings and blades in large-eddy simulations (LES). The crux of the ALM is the projection of the actuator point forces onto the LES grid by means of a Gaussian regularisation kernel. The minimum width of the kernel is constrained by the grid size; however, for most practical applications like LES of wind turbines, this value is an order of magnitude larger than the optimal value that maximises accuracy. This discrepancy motivated the development of corrections for the actuator line, which, however, neglect the effect of unsteady spanwise shed vorticity. In this work we develop a model for the impact of spanwise shed vorticity on the unsteady loading of an aerofoil modelled as a Gaussian body force distribution, where the model is applicable within the regime of unsteady attached flow. The model solution is derived both in the time and frequency domain and features an explicit dependence on the Gaussian kernel width. We verify the model with ALM-LES for both pitch steps and periodic pitching. The model solution is compared with Theodorsen theory and validated with both computational fluid dynamics using body fitted grids and experiment. It is concluded that the optimal kernel width for unsteady aerodynamics is approximately 40 % of the chord. The ALM is able to predict the magnitude of the unsteady loading up to a reduced frequency of 𝑘 ≈ 0.2.

17 WIND ENERGY↗

DOE OSTI2025

Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators

The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box timesteppers. However, repeated simulations for steady-state computation, linearization, and control design are often computationally prohibitive, or the microscopic timestepper may not even be available, leaving us with data as the only resource. We propose a data-driven alternative that uses local neural operators, trained on spatiotemporal microscopic/mesoscopic data, to obtain efficient short-time solution operators. These surrogates are employed within Krylov subspace methods to compute coarse steady and unsteady-states, while also providing Jacobian information in a matrix-free manner. Krylov-Arnoldi iterations then approximate the dominant eigenspectrum, yielding reduced models that capture the open-loop slow dynamics without explicit Jacobian assembly. Both discrete-time Linear Quadratic Regulator (dLQR) and pole-placement (PP) controllers are based on this reduced system and lifted back to the full nonlinear dynamics, thereby closing the feedback loop.

93B52, 93C20, 47N70, 65J15, 65M32, 68T07, 68T20, 6↗

DOE OSTI2023

Automated tracking of prefabricated components for areal-time evaluator to optimize and automateinstallation

Trade associations for prefabricated construction estimate that about 50% of prefabricated wall projects have alignment problems that lead to defects and rework. Additionally, component installation times average between 30 and 60 minutes per component. To address these issues, a real-time evaluator (RTE) system was introduced to decrease cost and automate prefabricated component installation by reducing the installation time, decreasing rework, and enhancing energy performance through higher installation quality. The RTE uses commonly available hardware and software to perform autonomous tracking to measure the real-time location and orientation of components as they are crane-lifted and installed. The hardware, software, and algorithms that allow the autonomous tracking of components are detailed. An algorithm to automate the initial search for a component with three attached retroreflectors is proposed. Algorithms to automate the measurement of component position and orientation are also proposed. Simple lab-scale proof-of-concept experiments were conducted to assess the algorithms for automation of component searching, measurement of real-time movement, and measurement of component orientation. With additional development, the system can be used as a tool to generate the commands for autonomous crane operation or single-task construction robots.

Hayes, Nolan↗

DOE OSTI2023

Development of an Unmanned Mobile Current Turbine Platform: Preprint

The design and development of a prototype unmanned mobile floating platform, equipped with a custom low-flow marine current turbine for autonomously seeking and harnessing tidal/coastal currents is described. The platform is an unmanned surface vehicle in the form of a catamaran with two electric outboard motors and capabilities for autonomous navigation. An undershot water wheel, aided by a custom flow concentrator, has been selected as the basic design for the marine current turbine, which is mounted on the stern of the unmanned surface vehicle platform. The concept of operation is that the platform would navigate to a designated marine current resource, autonomously anchor at the location, align itself in the current and deploy the current turbine using a custom cable-lift deployment mechanism. As the turbine harnesses the local current, an onboard power-take-off device converts the harnessed mechanical energy to electricity which is stored in onboard batteries. Considerations of deployment in tidal and coastal waters required obtaining the necessary environmental permits for conducting in-water testing; developing required mitigation measures in protecting local wildlife and their habitats; and identifying potential in-water test sites and surveying them for their suitability in terms of the current resource, bottom type, water depth, and local boat traffic. The design and development of the turbine and the results of initial in-water testing are discussed. The potential for scaling up the system for extended capacity is presented.

ENGINEERING,TIDAL AND WAVE POWER↗

DOE OSTI2026

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗

DOE OSTI2023

Optimal white-noise stochastic forcing for linear models of turbulent channel flow

In the present study an optimisation problem is formulated to determine the forcing of an eddy-viscosity-based linearised Navier–Stokes model in channel flow at $Re_\tau \approx 5200$ ( $Re_\tau$ is the friction Reynolds number), where the forcing is white-in-time and spatially decorrelated. The objective functional is prescribed such that the forcing drives a response to best match a set of velocity spectra from direct numerical simulation (DNS), as well as remaining sufficiently smooth. Strong quantitative agreement is obtained between the velocity spectra from the linear model with optimal forcing and from DNS, but only qualitative agreement between the Reynolds shear stress co-spectra from the model and DNS. The forcing spectra exhibit a level of self-similarity, associated with the primary peak in the velocity spectra, but they also reveal a non-negligible amount of energy spent in phenomenologically mimicking the non-self-similar part of the velocity spectra associated with energy cascade. By exploiting linearity, the effect of the individual forcing components is assessed and the contributions from the Orr mechanism and the lift-up effect are also identified. Finally, the effect of the strength of the eddy viscosity on the optimisation performance is investigated. The inclusion of the eddy viscosity diffusion operator is shown to be essential in modelling of the near-wall features, while still allowing the forcing of the self-similar primary peak. In particular, reducing the strength of the eddy viscosity results in a considerable increase in the near-wall forcing of wall-parallel components.

Mechanics↗

DOE OSTI2023

Criticality Experiments to Reduce Compensating Errors in Plutonium Nuclear Data

Compensating errors between nuclear data observables in a library can adversely impact application simulations. The primary goal of the EUCLID project (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) is to reduce compensating errors in nuclear data. A new criticality experiment, described in this work, was designed with the specific target nuclear data of 239 Pu fission, inelastic scattering, elastic scattering, capture, nu-bar, and prompt fission neutron spectrum (PFNS). This work will focus on the design and execution of the EUCLID experiment, performed on the Planet vertical lift critical assembly machine at the National Criticality Experiments Research Center (NCERC). The criticality experiment includes two different configurations with very different geometries: one is cube-like to minimize neutron leakage while the other is slab-like to maximize leakage. Having these two widely varying configurations allows the scattering sensitivities of 239 Pu to the neutron multiplication factor to be greatly changed while minimally impacting the other cross section sensitivities. Both configurations utilize the Pu ZPPR (Zero Power Physics Reactor) plates as fuel. The experiments were designed using a D-Optimality criteria, which is an optimization method minimizing the log-determinant of the adjusted nuclear data covariance for the target reactions. These experiments include not only inference of k eff , as done in all critical benchmark experiments, but several other responses as well, such as neutron multiplication measurements and reaction rate ratios. After analysis of the measured data is complete, adjustment of nuclear data will be performed to assess whether the new experimental data successfully reduced compensating errors.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Aerodynamic Sensitivity of a Novel Data-Driven Airfoil Shape Representation Framework

We explore the aerodynamic implications of a novel data-driven separable shape tensor framework used to represent discrete airfoil shapes. In this study, we construct a data-driven parameter space defined by separable shape tensors and informed by tens of thousands of distinct airfoils. We use this design space to generate new airfoil designs to study parametric sensitivities with respect to various aerodynamic responses. We use a HAM2D RANS solver to approximate the lift, drag, and moment coefficients for the generated airfoils at two different angles-of-attack. We analyze the robustness and sensitivities of using the separable shape tensor design space by examining the coverage of the aerodynamic response space, uncovering low-dimensional polynomial ridge approximations, and computing various sensitivity metrics. The results show that the data-driven design space produce significant variation in target aerodynamic quantities and facilitate highly accurate approximations (R^2 > 0.96) of one- and two-dimensional structures in each aerodynamic response. This further reduces the effective dimension to enable simplified design and optimization tasks.

aerodynamics↗