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At least 1,009 records · Page 56

Evidence Report, Risk of Inadequate Design of Human and Automation/Robotic Integration

The success of future exploration missions depends, even more than today, on effective integration of humans and technology (automation and robotics). This will not emerge by chance, but by design. Both crew and ground personnel will need to do more demanding tasks in more difficult conditions, amplifying the costs of poor design and the benefits of good design. This report has looked at the importance of good design and the risks from poor design from several perspectives: 1) If the relevant functions needed for a mission are not identified, then designs of technology and its use by humans are unlikely to be effective: critical functions will be missing and irrelevant functions will mislead or drain attention. 2) If functions are not distributed effectively among the (multiple) participating humans and automation/robotic systems, later design choices can do little to repair this: additional unnecessary coordination work may be introduced, workload may be redistributed to create problems, limited human attentional resources may be wasted, and the capabilities of both humans and technology underused. 3) If the design does not promote accurate understanding of the capabilities of the technology, the operators will not use the technology effectively: the system may be switched off in conditions where it would be effective, or used for tasks or in contexts where its effectiveness may be very limited. 4) If an ineffective interaction design is implemented and put into use, a wide range of problems can ensue. Many involve lack of transparency into the system: operators may be unable or find it very difficult to determine a) the current state and changes of state of the automation or robot, b) the current state and changes in state of the system being controlled or acted on, and c) what actions by human or by system had what effects. 5) If the human interfaces for operation and control of robotic agents are not designed to accommodate the unique points of view and operating environments of both the human and the robotic agent, then effective human-robot coordination cannot be achieved.

Zumbado, Jennifer Rochlis↗

Advanced Usage of Vehicle Sketch Pad for CFD-Based Conceptual Design

Conceptual design is the most fluid phase of aircraft design. It is important to be able to perform large scale design space exploration of candidate concepts that can achieve the design intent to avoid more costly configuration changes in later stages of design. This also means that conceptual design is highly dependent on the disciplinary analysis tools to capture the underlying physics accurately. The required level of analysis fidelity can vary greatly depending on the application. Vehicle Sketch Pad (VSP) allows the designer to easily construct aircraft concepts and make changes as the design matures. More recent development efforts have enabled VSP to bridge the gap to high-fidelity analysis disciplines such as computational fluid dynamics and structural modeling for finite element analysis. This paper focuses on the current state-of-the-art geometry modeling for the automated process of analysis and design of low-boom supersonic concepts using VSP and several capability-enhancing design tools.

Ordaz, Irian↗

Practical Application of PRA as an Integrated Design Tool for Space Systems

This paper presents the application of the first comprehensive Probabilistic Risk Assessment (PRA) during the design phase of a joint NASA/NOAA weather satellite program, Geostationary Operational Environmental Satellite Series R (GOES-R). GOES-R is the next generation weather satellite primarily to help understand the weather and help save human lives. PRA has been used at NASA for Human Space Flight for many years. PRA was initially adopted and implemented in the operational phase of manned space flight programs and more recently for the next generation human space systems. Since its first use at NASA, PRA has become recognized throughout the Agency as a method of assessing complex mission risks as part of an overall approach to assuring safety and mission success throughout project lifecycles. PRA is now included as a requirement during the design phase of both NASA next generation manned space vehicles as well as for high priority robotic missions. The influence of PRA on GOES-R design and operation concepts are discussed in detail. The GOES-R PRA is unique at NASA for its early implementation. It also represents a pioneering effort to integrate risks from both Spacecraft (SC) and Ground Segment (GS) to fully assess the probability of achieving mission objectives. PRA analysts were actively involved in system engineering and design engineering to ensure that a comprehensive set of technical risks were correctly identified and properly understood from a design and operations perspective. The analysis included an assessment of SC hardware and software, SC fault management system, GS hardware and software, common cause failures, human error, natural hazards, solar weather and infrastructure (such as network and telecommunications failures, fire). PRA findings directly resulted in design changes to reduce SC risk from micro-meteoroids. PRA results also led to design changes in several SC subsystems, e.g. propulsion, guidance, navigation and control (GNC), communications, mechanisms, and command and data handling (C&DH). The fault tree approach assisted in the development of the fault management system design. Human error analysis, which examined human response to failure, indicated areas where automation could reduce the overall probability of gaps in operation by half. In addition, the PRA brought to light many potential root causes of system disruptions, including earthquakes, inclement weather, solar storms, blackouts and other extreme conditions not considered in the typical reliability and availability analyses. Ultimately the PRA served to identify potential failures that, when mitigated, resulted in a more robust design, as well as to influence the program's concept of operations. The early and active integration of PRA with system and design engineering provided a well-managed approach for risk assessment that increased reliability and availability, optimized lifecyc1e costs, and unified the SC and GS developments.

Kalia, Prince↗

Coupled Solid Rocket Motor Ballistics and Trajectory Modeling for Higher Fidelity Launch Vehicle Design

Multi-stage launch vehicles with solid rocket motors (SRMs) face design optimization challenges, especially when the mission scope changes frequently. Significant performance benefits can be realized if the solid rocket motors are optimized to the changing requirements. While SRMs represent a fixed performance at launch, rapid design iterations enable flexibility at design time, yielding significant performance gains. The streamlining and integration of SRM design and analysis can be achieved with improved analysis tools. While powerful and versatile, the Solid Performance Program (SPP) is not conducive to rapid design iteration. Performing a design iteration with SPP and a trajectory solver is a labor intensive process. To enable a better workflow, SPP, the Program to Optimize Simulated Trajectories (POST), and the interfaces between them have been improved and automated, and a graphical user interface (GUI) has been developed. The GUI enables real-time visual feedback of grain and nozzle design inputs, enforces parameter dependencies, removes redundancies, and simplifies manipulation of SPP and POST's numerous options. Automating the analysis also simplifies batch analyses and trade studies. Finally, the GUI provides post-processing, visualization, and comparison of results. Wrapping legacy high-fidelity analysis codes with modern software provides the improved interface necessary to enable rapid coupled SRM ballistics and vehicle trajectory analysis. Low cost trade studies demonstrate the sensitivities of flight performance metrics to propulsion characteristics. Incorporating high fidelity analysis from SPP into vehicle design reduces performance margins and improves reliability. By flying an SRM designed with the same assumptions as the rest of the vehicle, accurate comparisons can be made between competing architectures. In summary, this flexible workflow is a critical component to designing a versatile launch vehicle model that can accommodate a volatile mission scope.

Ables, Brett↗

Conceptual Design Optimization of an Augmented Stability Aircraft Incorporating Dynamic Response and Actuator Constraints

Empirical sizing guidelines such as tail volume coefficients have long been used in the early aircraft design phases for sizing stabilizers, resulting in conservatively stable aircraft. While successful, this results in increased empty weight, reduced performance, and greater procurement and operational cost relative to an aircraft with optimally sized surfaces. Including flight dynamics in the conceptual design process allows the design to move away from empirical methods while implementing modern control techniques. A challenge of flight dynamics and control is the numerous design variables, which are changing fluidly throughout the conceptual design process, required to evaluate the system response to some disturbance. This research focuses on addressing that challenge not by implementing higher order tools, such as computational fluid dynamics, but instead by linking the lower order tools typically used within the conceptual design process so each discipline feeds into the other. In thisresearch, flight dynamics and control was incorporated into the conceptual design process along with the traditional disciplines of vehicle sizing, weight estimation, aerodynamics, and performance. For the controller, a linear quadratic regulator structure with constant gains has been specified to reduce the user input. Coupling all the disciplines in the conceptual design phase allows the aircraft designer to explore larger design spaces where stabilizers are sized according to dynamic response constraints rather than historical static margin and volume coefficient guidelines.

Welstead, Jason↗

A Methodology to Assess the Capability of Engine Designs to Meet Closed-loop Performance and Operability Requirements

Designing a closed-loop controller for an engine requires balancing trade-offs between performance and operability of the system. One such trade-off is the relationship between the 95% response time and minimum high-pressure compressor (HPC) surge margin (SM) attained during acceleration from idle to takeoff power. Assuming a controller has been designed to meet some specification on response time and minimum HPC SM for a mid-life (nominal) engine, there is no guarantee that these limits will not be violated as the engine ages, particularly as it reaches the end of its life. A characterization for the uncertainty in this closed-loop system due to aging is proposed that defines elliptical boundaries to estimate worst-case performance levels for a given control design point. The results of this characterization can be used to identify limiting design points that bound the possible con- troller designs yielding transient results that do not exceed specified limits in response time or minimum HPC SM. This characterization involves performing Monte Carlo simulation of the closed-loop system with controller constructed for a set of trial design points and developing curve fits to describe the size and orientation of each ellipse; a binary search procedure is then employed that uses these fits to identify the limiting design point. The method is demonstrated through application to a generic turbofan engine model in closed- loop with a simplified controller; it is found that the limit for which each controller was designed was exceeded by less than 4.76%. Extension of the characterization to another trade-off, that between the maximum high-pressure turbine (HPT) entrance temperature and minimum HPC SM, showed even better results: the maximum HPT temperature was estimated within 0.76%. Because of the accuracy in this estimation, this suggests another limit that may be taken into consideration during design and analysis. It also demonstrates the extension of the characterization to other attributes that contribute to the performance or operability of the engine. Metrics are proposed that, together, provide information on the shape of the trade-off between response time and minimum HPC SM, and how much each varies throughout the life cycle, at the limiting design points. These metrics also facilitate comparison of the expected transient behavior for multiple engine models.

engine control↗

A Methodology to Assess the Capability of Engine Designs to Meet Closed-Loop Performance and Operability Requirements

Designing a closed-loop controller for an engine requires balancing trade-offs between performance and operability of the system. One such trade-off is the relationship between the 95 percent response time and minimum high-pressure compressor (HPC) surge margin (SM) attained during acceleration from idle to takeoff power. Assuming a controller has been designed to meet some specification on response time and minimum HPC SM for a mid-life (nominal) engine, there is no guarantee that these limits will not be violated as the engine ages, particularly as it reaches the end of its life. A characterization for the uncertainty in this closed-loop system due to aging is proposed that defines elliptical boundaries to estimate worst-case performance levels for a given control design point. The results of this characterization can be used to identify limiting design points that bound the possible controller designs yielding transient results that do not exceed specified limits in response time or minimum HPC SM. This characterization involves performing Monte Carlo simulation of the closed-loop system with controller constructed for a set of trial design points and developing curve fits to describe the size and orientation of each ellipse; a binary search procedure is then employed that uses these fits to identify the limiting design point. The method is demonstrated through application to a generic turbofan engine model in closed-loop with a simplified controller; it is found that the limit for which each controller was designed was exceeded by less than 4.76 percent. Extension of the characterization to another trade-off, that between the maximum high-pressure turbine (HPT) entrance temperature and minimum HPC SM, showed even better results: the maximum HPT temperature was estimated within 0.76 percent. Because of the accuracy in this estimation, this suggests another limit that may be taken into consideration during design and analysis. It also demonstrates the extension of the characterization to other attributes that contribute to the performance or operability of the engine. Metrics are proposed that, together, provide information on the shape of the trade-off between response time and minimum HPC SM, and how much each varies throughout the life cycle, at the limiting design points. These metrics also facilitate comparison of the expected transient behavior for multiple engine models.

systems analysis↗

Building a Practical Natural Laminar Flow Design Capability

A preliminary natural laminar flow (NLF) design method that has been developed and applied to supersonic and transonic wings with moderate-to-high leading-edge sweeps at flight Reynolds numbers is further extended and evaluated in this paper. The modular design approach uses a knowledge-based design module linked with different flow solvers and boundary layer stability analysis methods to provide a multifidelity capability for NLF analysis and design. An assessment of the effects of different options for stability analysis is included using pressures and geometry from an NLF wing designed for the Common Research Model (CRM). Several extensions to the design module are described, including multiple new approaches to design for controlling attachment line contamination and transition. Finally, a modification to the NLF design algorithm that allows independent control of Tollmien-Schlichting (TS) and cross flow (CF) modes is proposed. A preliminary evaluation of the TS-only option applied to the design of an NLF nacelle for the CRM is performed that includes the use of a low-fidelity stability analysis directly in the design module.

Campbell, Richard L.↗

SLS Model Based Design: A Navigation Perspective

The SLS Program has implemented a Model-based Design (MBD) and Model-based Requirements approach for managing component design information and system requirements. This approach differs from previous large-scale design efforts at Marshall Space Flight Center where design documentation alone conveyed information required for vehicle design and analysis and where extensive requirements sets were used to scope and constrain the design. The SLS Navigation Team is responsible for the Program-controlled Design Math Models (DMMs) which describe and represent the performance of the Inertial Navigation System (INS) and the Rate Gyro Assemblies (RGAs) used by Guidance, Navigation, and Controls (GN&C). The SLS Navigation Team is also responsible for navigation algorithms. The navigation algorithms are delivered for implementation on the flight hardware as a DMM. For the SLS Block 1B design, the additional GPS Receiver hardware model is managed as a DMM at the vehicle design level. This paper describes the models, and discusses the processes and methods used to engineer, design, and coordinate engineering trades and performance assessments using SLS practices as applied to the GN&C system, with a particular focus on the navigation components.

Oliver, T. Emerson↗

Challenges of Designing a Passive Thermal Control System for the Astrobotic Peregrine Lunar Lander

The Astrobotic Peregrine is a lunar lander currently undergoing design by Astrobotic Technology with help from NASA through the Lunar Cargo Transportation and Landing by Soft Touchdown (Lunar CATALYST) program. This paper will discuss the challenges of designing a passive thermal control system for the lander, and how the design has evolved from the initial passive concept. These challenges include drastically varying worst hot and worst cold case thermal environments, narrow temperature limits of critical components, limited available locations for spacecraft component mounting, and unexpected changes causing significant thermal impacts. The initial thermal control strategy was to cold bias the spacecraft by thermally coupling all spacecraft components to one mounting deck, which also doubled as a radiator, and using heaters to maintain each component’s temperature above its lower temperature limit when in the cold environments. As the design evolved, this strategy alone became inadequate. As heat dissipations increased and became more varying with the addition of components, the thermal design was changed and additional thermal control technologies added. Thermal control strategies incorporated into the design include dictating the lander orientation in demanding environments, defining locations for critical spacecraft components, limiting component operation when possible, and using technology to create variable thermal contacts. Additional design changes will occur as the design continues to evolve to optimize the most effective thermal control system. The thermal design of Peregrine is still in progress, with Critical Design Review (CDR) scheduled for December 2019.

Mauro, Stephanie↗

SAFE50 Reference Design Study for Large-Scale High-Density Low-Altitude UAS Operations in Urban Areas

Enabling safe, routine, and high-density flight operations of small UAS at low-altitude over heavily populated urban centers presents a difficult challenge for emerging UAS Traffic Management (UTM) system concepts. Urban operations by definition involve flight over people, property, and infrastructure. Low-altitude urban environments - such as urban canyons – are one of the most difficult areas for UTM to consider. Mission concepts require routine operations in a cluttered radio-frequency (RF) environment with degraded or denied Global Positioning System (GPS) reception. Flights with any appreciable distance will be beyond visual and communications line-of-sight from ground operators. Timely detection and response to emergencies and onboard failures, which is critical for safe aircraft operation, will be difficult. This work seeks to establish a feasible reference autonomy architecture for autonomous vehicles in an urban UTM system, then verifying and validating this architecture within a complete UTM concept point-design and systems analysis study. In this paper, we present the results from the NASA SAFE50 conceptual design and systems study that investigates the trade-space of urban UTM operations. This advanced conceptual design study develops a feasible, verified, validated point-design solution. The SAFE50 point-design concept places emphasis on advanced, highly-autonomous, and highly-capable vehicles that favors intelligent onboard autonomy over direct human control with today's technologies and operating in today's urban environments. This paper focuses on an general overview of the design study, highlighting decisions made in the architectural solution. This paper will presents a summary of the study, architectures, and requirements. We present an overview of the architecture designs as derived from the top-level UTM system. The point-design has been implemented in both simulation and through flight testing of hardware design prototypes. The results from simulation and flight testing as part of the verification and validation process of the reference design study.

Ippolito, Corey A.↗

Application of a Knowledge-Based Optimization Method for Aerodynamic Design

The current research is investigating the application of an optimization technique to an existing knowledge-based design tool. The optimization method, referred to as CODISC, helps improve the results from a knowledge-based design by eliminating the required advanced design knowledge, or help fine-tune a well-performing vehicle. Three CODISC designs are presented using a generic transonic transport, the Common Research Model (CRM). One design optimizes the baseline CRM to demonstrate the ability to improve a well-performing vehicle. Another design is performed from the CRM with camber and twist removed, which highlights the ability to use CODISC in the conceptual design phase. The final design implements laminar flow on the CRM, showing how CODISC can optimize the extent of laminar flow to find the best aerodynamic performance. All three CODISC designs reduced the vehicle drag compared to the baseline CRM, and highlight the new optimization technique’s versatility in the aircraft design industry.

CODISC↗

Design of an Advanced Inlet Liner for the Quiet Technology Demonstrator 3

The utilization of advanced fan designs (including higher bypass ratios) and shorter engine nacelles has highlighted a need for increased fan noise reduction over a broad frequency range. Thus, improved broadband liner designs must account for these constraints and take advantage of novel liner configurations. With these observations in mind, the development and assessment of a broadband acoustic liner optimization process has been pursued through a series of design and experimental studies. In this work, an advanced inlet liner was designed for a Boeing 737MAX-7 to reduce drag and to improve the broadband noise reduction relative to conventional liners in use today. Specifically, a three layer liner was designed, fabricated, and flight tested as part of the Quiet Technology Demonstrator 3 flight test program. Initial tonal predictions captured the behavior of the measured data very well and both prediction and measurements show an increased acoustic benefit at larger observer angles, particularly at the takeoff condition. Ultimately, flight test results showed the three degree-of-freedom liner to provide a 3.2 EPNdB cumulative inlet component benefit and a 0.7 EPNdB cumulative airplane benefit over the production liner. This excellent result provides valuable validation of the broadband liner design process, as well as the enhancements made to the overall approach. It also illustrates the value of the design process in concurrently evaluating various liner designs (i.e., SDOF, MDOF, etc.) and their application to various locations. Thus, the design process may be applied with further confidence to investigate novel liner configurations in future design studies.

Nark, Douglas M.↗

Optimal Experimental Design With Fast Neural Network Surrogate Models

Designing optimal experiments minimizes the uncertainty of results and maximizes the efficient use of resources. Herein, machine learning surrogate models and the approximate coordinate exchange (ACE) algorithm are used to determine optimum experimental designs over large or arbitrarily restrictive design spaces. Optimal experimental design is particularly salient in materials science where experiments are expensive and material properties must often be inferred indirectly. The proposed framework is demonstrated by finding optimal experiments with which the hidden constituent properties of composite materials can be most efficiently inferred from observable experimental outcomes. The optimum experimental design is given by an information-theoretic criteria, which maximizes the conditional mutual information between the hidden properties and the expected experimental outcomes. To perform tractable optimization a neural network is trained as a surrogate model to mimic a physics based simulation, which can calculate the expected experimental outcome based on a candidate experimental design and sampled constituent properties. The ACE algorithm is used to optimize over large design spaces with many tests and controlled parameters where an exhaustive search would be intractable even with the surrogate model. Using this approach, optimal experimental designs that are consistent with those produced by heuristic knowledge and established best practices are found; then optimal designs in larger design spaces where heuristic knowledge is unavailable are examined.

machine learning↗

Designing A Coaxial Quadrotor for Urban Air Mobility

The NASA Revolutionary Vertical Lift Technology Project has created several Urban Air Mobility reference design vehicles to aid the burgeoning UAM industry. With over 700 conceptual designs already proposed, much interest has been generated across many unique configurations to bring vertical flight to the masses. The quadrotor configuration is one of the NASA reference vehicles, and does have some conceptual designs proposed in the industry. This study looks at the conceptual design of a coaxial quadrotor vehicle as an extension of the NASA RVLT quadrotor concept vehicle. The coaxial quadrotor has a similar layout to the quadrotor, but with a coaxial rotor at each of the four corners of the vehicle. Trade studies carried out using the NASA Design and Analysis of Rotorcraft (NDARC) tool analyzed the vehicle sizing, design gross weight, and performance for four design variants. The variants all use the baseline coaxial quadrotor layout, but analyze the effects of two major design choices: 1) variable pitch vs variable speed rotor control, and 2) motor to rotor power transmission via a gearbox vs direct-drive. The results indicate one design variant may have more benefits on some of the design objectives while another configuration may better satisfy the others.

UAM↗

System Analysis and Generative Design for Icenode, a Buoyant Vehicle for Measuring Melt Rate Under Ice Shelves

Antarctic ice shelves buttress the Antarctic Ice Sheet from sliding into the ocean, and their collapse could trigger a meter or more of global sea level rise by the end of the century. Current state-of-the-art predictions for ice shelf behavior in a warming climate have large uncertainty, significantly hindered by a lack of in situ melt rate observations under ice shelves, especially near grounding zones. IceNode is a novel robotic vehicle under development at the NASA Jet Propulsion Laboratory to acquire such measurements, but presents a complex design problem owing to the large design space and conflicting performance requirements. Evaluating a preliminary design requires several types of tedious analysis which prevents rapid iteration and exploration of the design space. We present the implementation of a custom system analysis framework which was used to automate analysis such as resource budgeting, mission simulation, mass and buoyancy balancing, and static landing stability analysis of a given design configuration. Using this framework, we selected parameters which had the largest effects on design success and conducted a generative design study in which we programmatically varied a handful of parameters to generate 1540 different design candidates and test them across 160 different environmental scenarios. The custom built system analysis tool enabled rapid development of critical analysis and automated exploration of a large design space to guide preliminary design of the IceNode vehicle.

Gebara, Christine↗

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Uncertainty quantification (UQ) is a rapidly growing and evolving discipline, especially within the aerospace community. Performing analysis with UQ can provide decision makers with a wealth of information about a candidate design. However, the value of UQ is fully realized when the information gained during UQ analysis is leveraged in a feedback loop of a design optimization process, often referred to as design under uncertainty. Although design under uncertainty can be a powerful risk mitigation technique, there are a number of roadblocks that prevent its implementation. Two primary factors are computational costs and added complexity of the analysis. High fidelity simulations on the order tens of uncertain variables quickly become computationally infeasible. Also, implementing UQ into an existing multidisciplinary design and optimization (MDO) process often requires extensive knowledge of the UQ methods and careful treatment of the problem formulation. The objective of this work is to address these two primary roadblocks and enable practitioners to efficiently perform design under uncertainty with limited knowledge of the UQ discipline. Methods outlined in this paper demonstrate MDO incorporating UQ into the design process, leveraging an analytic derivative tool chain through the entire optimization. The proposed approach leverages machine learning techniques to generate a differentiable confidence interval output from polynomial chaos models. This technique, coupled with the incorporation of analytical derivatives through the Polynomial Chaos Expansion (PCE) process, eliminates the need to estimate derivatives which are usually obtained from finite difference, complex step, or similar methods. Developing a differentiable confidence interval allows mixed uncertainty problems (both epistemic and aleatory) to be modeled. Without such modeling, these problems cannot accurately predict objective functions containing statistical quantities such as mean and variance. The addition of analytic derivatives to a polynomial chaos-based UQ method decreases the computational costs of performing design under uncertainty by orders of magnitude in comparison with methods such as complex step. The method and codes developed are modular in nature and are a drop-in solution for design under uncertainty within existing MDO problems. A low-fidelity analytical multidisciplinary optimization under uncertainty for a wing design in OpenMDAO is detailed in this paper. This demonstration case will include both objective functions and constraints which are influenced by uncertain parameters.

Ben D Phillips↗

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Uncertainty quantification (UQ) is a rapidly growing and evolving discipline, especially within the aerospace community. Performing analysis with UQ can provide decision makers with a wealth of information about a candidate design. However, the value of UQ is fully realized when the information gained during UQ analysis is leveraged in a feedback loop of a design optimization process, often referred to as design under uncertainty. Although design under uncertainty can be a powerful risk mitigation technique, there are a number of roadblocks that prevent its implementation. Two primary factors are computational costs and added complexity of the analysis. High fidelity simulations on the order tens of uncertain variables quickly become computationally infeasible. Also, implementing UQ into an existing multidisciplinary design and optimization (MDO) process often requires extensive knowledge of the UQ methods and careful treatment of the problem formulation. The objective of this work is to address these two primary roadblocks and enable practitioners to efficiently perform design under uncertainty with limited knowledge of the UQ discipline. Methods outlined in this paper demonstrate MDO incorporating UQ into the design process, leveraging an analytic derivative tool chain through the entire optimization. The proposed approach leverages machine learning techniques to generate a differentiable confidence interval output from polynomial chaos models. This technique, coupled with the incorporation of analytical derivatives through the Polynomial Chaos Expansion (PCE) process, eliminates the need to estimate derivatives which are usually obtained from finite difference, complex step, or similar methods. Developing a differentiable confidence interval allows mixed uncertainty problems (both epistemic and aleatory) to be modeled. Without such modeling, these problems cannot accurately predict objective functions containing statistical quantities such as mean and variance. The addition of analytic derivatives to a polynomial chaos-based UQ method decreases the computational costs of performing design under uncertainty by orders of magnitude in comparison with methods such as complex step. The method and codes developed are modular in nature and are a drop-in solution for design under uncertainty within existing MDO problems. A low-fidelity analytical multidisciplinary optimization under uncertainty for a wing design in OpenMDAO is detailed in this paper. This demonstration case will include both objective functions and constraints which are influenced by uncertain parameters.

Ben Phillips↗