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NASA NTRS2023

Advances in Aero-Propulsive Modeling for Fixed-Wing and eVTOL Aircraft Using Experimental Data

Small unmanned aircraft and electric vertical takeoff and landing (eVTOL) aircraft have recently emerged as vehicles able to perform new missions and stimulate future air transportation methods. This dissertation presents several system identification research advancements for these modern aircraft configurations enabling accurate mathematical model development for flight dynamics simulations based on wind-tunnel and flight-test data. The first part of the dissertation focuses on advances in flight-test system identification methods using small, fixed-wing, remotely-piloted, electric, propeller-driven aircraft. A generalized approach for flight dynamics model development for small fixed-wing aircraft from flight data is described and is followed by presentation of novel flight-test system identification applications, including: aero-propulsive model development for propeller aircraft and nonlinear dynamic model identification without mass properties. The second part of the dissertation builds on established fixed-wing and rotary-wing aircraft system identification methods to develop modeling strategies for transitioning, distributed propulsion, eVTOL aircraft. Novel wind-tunnel experiment designs and aero-propulsive modeling approaches are developed using a subscale, tandem tilt-wing, eVTOL aircraft, leveraging design of experiments and response surface methodology techniques. Additionally, a method applying orthogonal phase-optimized multisine input excitations to aircraft control effectors in wind-tunnel testing is developed to improve test efficiency and identified model utility. Finally, the culmination of this dissertation is synthesis of the techniques described throughout the document to form a flight-test system identification approach for eVTOL aircraft that is demonstrated using a high-fidelity flight dynamics simulation. The research findings highlighted throughout the dissertation constitute substantial progress in efficient empirical aircraft modeling strategies that are applicable to many current and future aeronautical vehicles enabling accurate flight simulation development, which can subsequently be used to foster advancement in many other pertinent technology areas.

system identification↗

DOE OSTI2013

A Case Study on Maximizing Aqua Feed Pellet Properties Using Response Surface Methodology and Genetic Algorithm

Aims: The present case study is on maximizing the aqua feed properties using response surface methodology and genetic algorithm. Study Design: Effect of extrusion process variables like screw speed, L/D ratio, barrel temperature, and feed moisture content were analyzed to maximize the aqua feed properties like water stability, true density, and expansion ratio. Place and Duration of Study: This study was carried out in the Department of Agricultural and Food Engineering, Indian Institute of Technology, Kharagpur, India. Methodology: A variable length single screw extruder was used in the study. The process variables selected were screw speed (rpm), length-to-diameter (L/D) ratio, barrel temperature (degrees C), and feed moisture content (%). The pelletized aqua feed was analyzed for physical properties like water stability (WS), true density (TD), and expansion ratio (ER). Extrusion experimental data was collected by based on central composite design. The experimental data was further analyzed using response surface methodology (RSM) and genetic algorithm (GA) for maximizing feed properties. Results: Regression equations developed for the experimental data has adequately described the effect of process variables on the physical properties with coefficient of determination values (R2) of > 0.95. RSM analysis indicated WS, ER, and TD were maximized at L/D ratio of 12-13, screw speed of 60-80 rpm, feed moisture content of 30-40%, and barrel temperature of = 80 degrees C for ER and TD and > 90 degrees C for WS. Based on GA analysis, a maxium WS of 98.10% was predicted at a screw speed of 96.71 rpm, L/D radio of 13.67, barrel temperature of 96.26 degrees C, and feed moisture content of 33.55%. Maximum ER and TD of 0.99 and 1346.9 kg/m3 was also predicted at screw speed of 60.37 and 90.24 rpm, L/D ratio of 12.18 and 13.52, barrel temperature of 68.50 and 64.88 degrees C, and medium feed moisture content of 33.61 and 38.36%. Conclusion: The present data analysis indicated that WS is mainly governed by barrel temperature and feed moisture content, which might have resulted in formation of starch-protein complexes due to denaturation of protein and gelatinization of starch. Screw speed coupled with temperature and feed moisture content controlled the ER and TD values. Higher screw speeds might have reduced the viscosity of the feed dough resulting in higher TD and lower ER values. Based on RSM and GA analysis screw speed, barrel temperature and feed moisture content were the interacting process variables influencing maximum WS followed by ER and TD.

09 BIOMASS FUELS↗

NASA NTRS2015

Experiment Design for Complex VTOL Aircraft with Distributed Propulsion and Tilt Wing

Selected experimental results from a wind tunnel study of a subscale VTOL concept with distributed propulsion and tilt lifting surfaces are presented. The vehicle complexity and automated test facility were ideal for use with a randomized designed experiment. Design of Experiments and Response Surface Methods were invoked to produce run efficient, statistically rigorous regression models with minimized prediction error. Static tests were conducted at the NASA Langley 12-Foot Low-Speed Tunnel to model all six aerodynamic coefficients over a large flight envelope. This work supports investigations at NASA Langley in developing advanced configurations, simulations, and advanced control systems.

Murphy, Patrick C.↗

NASA NTRS2002

Probabilistic Design of a Plate-Like Wing to Meet Flutter and Strength Requirements

An approach is presented for carrying out reliability-based design of a metallic, plate-like wing to meet strength and flutter requirements that are given in terms of risk/reliability. The design problem is to determine the thickness distribution such that wing weight is a minimum and the probability of failure is less than a specified value. Failure is assumed to occur if either the flutter speed is less than a specified allowable or the stress caused by a pressure loading is greater than a specified allowable. Four uncertain quantities are considered: wing thickness, calculated flutter speed, allowable stress, and magnitude of a uniform pressure load. The reliability-based design optimization approach described herein starts with a design obtained using conventional deterministic design optimization with margins on the allowables. Reliability is calculated using Monte Carlo simulation with response surfaces that provide values of stresses and flutter speed. During the reliability-based design optimization, the response surfaces and move limits are coordinated to ensure accuracy of the response surfaces. Studies carried out in the paper show the relationship between reliability and weight and indicate that, for the design problem considered, increases in reliability can be obtained with modest increases in weight.

Stroud, W. Jefferson↗

NASA NTRS1995

Application of response surface techniques to helicopter rotor blade optimization procedure

In multidisciplinary optimization problems, response surface techniques can be used to replace the complex analyses that define the objective function and/or constraints with simple functions, typically polynomials. In this work a response surface is applied to the design optimization of a helicopter rotor blade. In previous work, this problem has been formulated with a multilevel approach. Here, the response surface takes advantage of this decomposition and is used to replace the lower level, a structural optimization of the blade. Problems that were encountered and important considerations in applying the response surface are discussed. Preliminary results are also presented that illustrate the benefits of using the response surface.

Henderson, Joseph Lynn↗

DOE OSTI2022

DBD plasma-assisted ethanol steam reforming for green H 2 production: Process optimization through response surface methodology (RSM)

Herein this work investigates ethanol steam reforming (ESR) to produce hydrogen (H 2 ) in a dielectric barrier discharge (DBD) plasma reactor. A five-level, three-factor experiment design was performed using a response surface methodology (RSM) to evaluate the combined effects of the three process parameters, including discharge power, total flow rate, and ethanol-to-water (EtOH/H 2 O) molar ratio on the plasma-assisted ESR reaction. Quadratic regression models were employed in RSM to fit the experimental results and present the correlation between process parameters and targeted responses (EtOH conversion, H 2 yield, H 2 selectivity, and specific energy requirement (SER) for H 2 production). The results suggested that the EtOH/H 2 O molar ratio is considered to have the most significant effect on the EtOH conversion and H 2 , H 2 selectivity, while the total flow rate is the most significant parameter determining SER for H 2 production. Process optimization demonstrated the optimal process conditions, including a discharge power of 55.9 W, a total flow rate of 26.7 ml/min, and an EtOH/H 2 O molar ratio equal to 0.34. A validation test was performed and confirmed the feasibility of the optimization process.

08 HYDROGEN↗

DOE OSTI2018

Final Report: Optimal Model Complexity in Geological Carbon Sequestration: A Response Surface Uncertainty Analysis

The critical component of a risk assessment study in evaluating GCS is an analysis of uncertainty in CO2 modeling. In such analyses, direct numerical simulation of CO2 flow and leakage requires many time-consuming model runs. Alternatively, analytical methods have been developed which allow fast and efficient estimation of CO2 storage and leakage, although restrictive assumptions on formation rock and fluid properties are employed. In this study, an intermediate approach is proposed based on the Design of Experiment and Response Surface methodology, which consists of using a limited number of numerical simulations to estimate a prediction outcome as a combination of the most influential uncertain site properties. The methodology can be implemented within a Monte Carlo framework to efficiently assess parameter and prediction uncertainty while honoring the accuracy of numerical simulations. The choice of the uncertain properties is flexible and can include geologic parameters that influence reservoir heterogeneity, engineering parameters that influence gas trapping and migration, and reactive parameters that influence the extent of fluid/rock reactions. The method was tested and verified on modeling long-term CO2 flow, non-isothermal heat transport, and CO2 dissolution storage by coupling two-phase flow with explicit miscibility calculation using an accurate equation of state that gives rise to convective mixing of formation brine variably saturated with CO2. All simulations were performed using three-dimensional high-resolution models including a target deep saline aquifer, overlying caprock, and a shallow aquifer. To evaluate the uncertainty in representing reservoir permeability, sediment hierarchy of a heterogeneous digital stratigraphy was mapped to create multiple irregularly shape stratigraphic models of decreasing geologic resolutions: heterogeneous (reference), lithofacies, depositional environment, and a (homogeneous) geologic formation. To ensure model equivalency, all the stratigraphic models were successfully upscaled from the reference heterogeneous model for bulk flow and transport predictions (Zhang & Zhang, 2015). GCS simulation was then simulated with all models, yielding insights into the level of parameterization complexity that is needed for the accurate simulation of reservoir pore pressure, CO2 storage, leakage, footprint, and dissolution over both short (i.e., injection) and longer (monitoring) time scales. Important uncertainty parameters that impact these key performance metrics were identified for the stratigraphic models as well as for the heterogeneous model, leading to the development of reduced/simplified models at lower characterization cost that can be used for the reservoir uncertainty analysis. All the CO2 modeling was conducted using PFLOTRAN – a massively parallel, multiphase, multi-component, and reactive transport simulator developed by a multi-laboratory DOE/SciDAC (Scientific Discovery through Advanced Computing) project (Zhang et al., 2017, in review). Within the uncertainty analysis framework, increasing reservoir depth were investigated to explore its effect on the uncertainty outcomes and the potential for developing gravity-stable injection with increased storage security (Dai et al., 20126; Dai et al., 2017, in review). Finally, to accurately model CO2 fluid-rock reactions and resulting long-term storage as secondary carbonate minerals, a modified kinetic rate law for general mineral dissolution and precipitation was proposed and verified that is invariant to a scale transformation of the mineral formula weight. This new formulation will lead to more accurate assessment of mineral storage over geologic time scales (Lichtner, 2016).

58 GEOSCIENCES↗

NASA NTRS2003

CFD-Based Design Optimization for Single Element Rocket Injector

To develop future Reusable Launch Vehicle concepts, we have conducted design optimization for a single element rocket injector, with overall goals of improving reliability and performance while reducing cost. Computational solutions based on the Navier-Stokes equations, finite rate chemistry, and the k-E turbulence closure are generated with design of experiment techniques, and the response surface method is employed as the optimization tool. The design considerations are guided by four design objectives motivated by the consideration in both performance and life, namely, the maximum temperature on the oxidizer post tip, the maximum temperature on the injector face, the adiabatic wall temperature, and the length of the combustion zone. Four design variables are selected, namely, H2 flow angle, H2 and O2 flow areas with fixed flow rates, and O2 post tip thickness. In addition to establishing optimum designs by varying emphasis on the individual objectives, better insight into the interplay between design variables and their impact on the design objectives is gained. The investigation indicates that improvement in performance or life comes at the cost of the other. Best compromise is obtained when improvements in both performance and life are given equal importance.

Vaidyanathan, Rajkumar↗

DOE OSTI2017

Ultrasound-assisted facile synthesis of a new tantalum(V) metal-organic framework nanostructure: Design, characterization, systematic study, and CO{sub 2} adsorption performance

This work presents a fast route for the preparation of a new Ta(V) metal-organic framework nanostructure with high surface area, significant porosity, and small size distribution. X-ray diffraction (XRD), scanning electron microscopy (SEM), Transition electron microscopy (TEM), energy dispersive spectrometer (EDS), thermo-gravimetric analysis (TGA), differential scanning calorimetry (DSC), fourier transform infrared spectroscopy (FTIR), CHNS/O elemental analyser, and Brunauer-Emmett-Teller (BET) surface area analysis were applied to characterize the synthesized product. Moreover, the influences of ultrasonic irradiation including temperature, time, and power on different features of the final products were systematically studied using 2{sup k-1} factorial design experiments, and the response surface optimization was used for determining the best welding parameter combination. The results obtained from analyses of variances showed that ultrasonic parameters affected the size distribution, thermal behaviour, and surface area of Ta-MOF samples. Based on response surface methodology, Ta-MOF could be obtained with mean diameter of 55 nm, thermal stability of 228 °C, and high surface area of 2100 m{sup 2}/g. The results revealed that the synthesized products could be utilized in various applications such as a novel candidate for CO{sub 2} adsorption. - Graphical abstract: A facile route was used for fabrication of a new metal -organic framework based on tantalum nanostructures that have high surface area, considerable porosity, homogenous morphology, and small size distribution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2000

Experimental Analysis of Steady-State Maneuvering Effects on Transmission Vibration Patterns Recorded in an AH-1 Cobra Helicopter

Flight experiment was designed primarily to determine the extent to which steady-state maneuvers influence characteristic vibration patterns measured at the input pinion and output annulus gear locations of the main transmission. If results were to indicate that maneuvers systematically influence vibration patterns, more extensive studies would be planned to explore the response surface. It was also designed to collect baseline data for comparison with experimental data to be recorded at a later date from test stands at Glenn Research Center. Finally, because this was the first vibration flight study on the Cobra aircraft, considerable energy was invested in developing an in-flight recording apparatus, as well as exploring acceleration mounting methods, and generally learning about the overall vibratory characteristics of the aircraft itself.

Huff, Edward M.↗

DOE OSTI2011

Optimizing separation of iodine from halogen interferences in preparation for TIMS analysis

Low-level analysis of radioiodine performed by TIMS requires an initial chemical separation from interfering higher electron-affinity halogens. Experiments using 125I and 36Cl tracers have shown that iodide can be selectively oxidized and purged from solution while the chloride remains in the solution. A systematic investigation of the experimental factors that affect the oxidation and transfer of iodine along with the separation of iodide from chloride has been completed. Experimental design was used to determine the optimum experimental conditions by obtaining a better understanding of factor affects and interactions. Factors such as gas purge rate, experiment run time, and oxidant concentration were simultaneously studied in a central composite design of experiments and response surfaces were generated from results. Optimizing experimental factors resulted in improved iodide oxidation and transfer efficiencies, halogen separation, and shorter analysis times.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗

DOE OSTI2014

SIMPLIFIED PREDICTIVE MODELS FOR CO₂ SEQUESTRATION PERFORMANCE ASSESSMENT RESEARCH TOPICAL REPORT ON TASK #3 STATISTICAL LEARNING BASED MODELS

We compare two approaches for building a statistical proxy model (metamodel) for CO₂ geologic sequestration from the results of full-physics compositional simulations. The first approach involves a classical Box-Behnken or Augmented Pairs experimental design with a quadratic polynomial response surface. The second approach used a space-filling maxmin Latin Hypercube sampling or maximum entropy design with the choice of five different meta-modeling techniques: quadratic polynomial, kriging with constant and quadratic trend terms, multivariate adaptive regression spline (MARS) and additivity and variance stabilization (AVAS). Simulations results for CO₂ injection into a reservoir-caprock system with 9 design variables (and 97 samples) were used to generate the data for developing the proxy models. The fitted models were validated with using an independent data set and a cross-validation approach for three different performance metrics: total storage efficiency, CO₂ plume radius and average reservoir pressure. The Box-Behnken–quadratic polynomial metamodel performed the best, followed closely by the maximin LHS–kriging metamodel.

Mishra, Srikanta↗

NASA NTRS2003

Aerodynamic Design Using Neural Networks

The design of aerodynamic components of aircraft, such as wings or engines, involves a process of obtaining the most optimal component shape that can deliver the desired level of component performance, subject to various constraints, e.g., total weight or cost, that the component must satisfy. Aerodynamic design can thus be formulated as an optimization problem that involves the minimization of an objective function subject to constraints. A new aerodynamic design optimization procedure based on neural networks and response surface methodology (RSM) incorporates the advantages of both traditional RSM and neural networks. The procedure uses a strategy, denoted parameter-based partitioning of the design space, to construct a sequence of response surfaces based on both neural networks and polynomial fits to traverse the design space in search of the optimal solution. Some desirable characteristics of the new design optimization procedure include the ability to handle a variety of design objectives, easily impose constraints, and incorporate design guidelines and rules of thumb. It provides an infrastructure for variable fidelity analysis and reduces the cost of computation by using less-expensive, lower fidelity simulations in the early stages of the design evolution. The initial or starting design can be far from optimal. The procedure is easy and economical to use in large-dimensional design space and can be used to perform design tradeoff studies rapidly. Designs involving multiple disciplines can also be optimized. Some practical applications of the design procedure that have demonstrated some of its capabilities include the inverse design of an optimal turbine airfoil starting from a generic shape and the redesign of transonic turbines to improve their unsteady aerodynamic characteristics.

Rai, Man Mohan↗

DOE OSTI2021

Machine learning enables national assessment of wind plant controls with implications for land use

Summary As deployment of wind energy continues to expand, computationally efficient tools for predicting wind plant performance over a wide range of layout designs, technology innovations, and spatial locations are increasingly important for policy and investment decisions. We demonstrate two approaches to training a surrogate model to predict annual energy production (AEP) of parameterized wind plant layouts: one using a Gaussian process (GP) and the other using a fully convolutional neural network (FCNN). We leverage the powerful FCNN architecture by encoding wind plant design parameters and output response surface as an image. The FCNN produces more accurate results than the GP with mean absolute errors equivalent to 1% and 1.9% of plant rated power, respectively, although the GP performs well under limited training data and provides useful uncertainty information. We also evaluate a surrogate model for wake steering, enabling a nationwide assessment of the impact of plant control strategies and plant layout decisions. Across two million locations, we find that wake steering strategies boost AEP with relative gains upwards of 3%. Gains are most pronounced at sites without a dominant wind direction and where layout optimization is less fruitful. Additionally, we perform a nationwide sensitivity analysis showing that wake steering can mitigate wake losses from higher density plant layouts. Our results suggest that regions which have not been previously viable for wind deployment due to moderate wind resources are especially well enhanced by wake steering strategies that could help overcome land constraints and inflexible layout options, potentially identifying new deployment opportunities.

17 WIND ENERGY↗

DOE OSTI2026

Deep Gaussian process-based cost-aware batch Bayesian optimization for complex materials design campaigns

The accelerating pace and expanding scope of materials discovery demand optimization frameworks that efficiently navigate vast design spaces with complex response surfaces while judiciously allocating limited evaluation resources. We present a cost-aware, batch Bayesian optimization scheme powered by deep Gaussian process (DGP) surrogates and a heterotopic querying strategy. Our DGP surrogate, formed by stacking GP layers, models complex hierarchical relationships among high-dimensional compositional features and captures correlations across multiple target properties, propagating uncertainty through successive layers. We integrate evaluation cost into an upper-confidence-bound acquisition extension, which, together with heterotopic querying, proposes small batches of candidates in parallel, balancing exploration of under-characterized regions with exploitation of high-mean, low-variance predictions across correlated properties. Applied to refractory high-entropy alloys for high-temperature applications, our framework converges to optimal formulations in fewer iterations with cost-aware queries than conventional GP-based BO, highlighting the value of deep, uncertainty-aware, cost-sensitive strategies in materials campaigns.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Statistical Design of Experiments Enables Rapid Exploration of Perfluorobutane Sulfonate Degradation

The phase-out of long-chain PFAS has led to the proliferation of highly recalcitrant short-chain analogs, and mineralization technologies for these short-chain PFAS are needed to mitigate their deleterious effects on environmental and human health. In this study, we utilize a statistical design of experiments, specifically, response surface methodology, to rapidly evaluate the electrochemical degradation of the short-chain PFAS, perfluorobutane sulfonate (PFBS). We evaluate the impacts of the three primary electrochemical parameters (concentration of PFBS, concentration of supporting electrolyte, and applied current) over multiple orders of magnitude on the three primary reaction outcomes of electrochemical PFBS degradation (incomplete PFBS decomposition, complete PFBS mineralization as fluorine, and anodic energy consumption). Our results correspond with literature and clearly identify the well-known tradeoff between energy consumption and complete mineralization. Intriguingly, partial PFBS decomposition and energy consumption demonstrate nonlinear dependencies in the current/supporting electrolyte concentration space and the current/PFBS concentration space, respectively. These findings highlight the utility of the response surface methodology model to efficiently interrogate a large parameter space, identifying both common results and less-obvious interactions between electrochemical parameters and their influences on reaction outcomes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

Uncertainty Quantification of Inducer Natural Frequency using Conditional Assessment of Modeling and Modal Testing of Simpler Systems

The low pressure fuel pump inducer of the new Space Launch System RS25 core stage engine operates in a highly complex environment that substantially affects its modal characteristics. Some of the more important effects are fluid-added mass resulting from operation within a light liquid (Hydrogen), and the magnification of this effect due to tight tip clearance. Since higher order cavitation has been identified as a significant harmonic driver, knowledge of the natural frequency of potentially excitable modes is critical for safe operation, but this frequency cannot be measured during the severe operational environment. A comprehensive testing and analysis program has therefore been performed over the last four years to identify the nominal value and uncertainty of the frequency by modeling and testing four simpler structures which share some of the characteristics of the operational inducer. This testing was used to assess and adjust modeling techniques and excellent correlation was achieved. Identification of the uncertainty in the inducer frequency itself was still problematic, however. This difficulty led to an investigation of Bayesian uncertainty quantification techniques, and to the application of the relatively simple technique of Multi-Variate Normal conditional distributions to calculate the inducer natural frequency uncertainty. Assumptions on prior distributions of uncertainty of the fluid-added mass and tip clearance effect are initially applied to models of each of the simple structures and the inducer itself, and these uncertainties are propagated to generate natural frequencies using design of experiments. Simple response surfaces are then created from this data in order to calculate a Covariance Matrix relating all of these natural frequencies. Finally, the results from modal test of the simple structures are considered to be observations and used to calculate the conditional variance of the desired inducer frequencies. As this method is less rigorous than more complicated Bayesian methods reported in the literature, a conservative factor is applied to the result, but the resulting uncertainty is still significantly less than originally estimated and will greatly assist certification of the inducer for use in the engine.

Uncertainty Quantification↗