Robust Data-Driven Aero-Elastic Flight Envelope Tailoring

Research Participants: R. Kania, A. Kebbie-Anthony, and X. ZhaoAFOSR DDDAS Program Review — 2017 PI Meeting

September 6-8, 2017

B. Balachandran and S. AzarmDepartment of Mechanical Engineering

University of MarylandCollege Park, MD 20742

Period of Performance: June 1, 2015 – May 31, 2018Grant No. FA9550150134

Outline

• Challenges and Needs• Objectives• System of Interest• Accomplishments • Approach

– DDDAS Framework for Decision Support– Aero-elastic Studies– Data-Driven Modeling and Prediction– Decision Support

• Concluding Remarks• Future Plans

2

Challenges and Needs Identified for Current Work

• Unanticipated physical responses and environmental conditions can influence mission effectiveness for unmanned aircraft systems (UAS). These challenges bring the need for:– addressing nonlinear aero-elasticity– handling instabilities and post-instability behavior– making optimal step-ahead decisions– handling large, dynamic sensor data and computational complexity – enhancing autonomy

3

[1] [2]

[1] “Advanced Joined-Wing Designs.” Above Top Secret . The Above Network, LLC. [Last Accessed on January 12, 2016] [2] Video courtesy of AFRL

http://www.abovetopsecret.com/forum/thread192824/pg1

Objectives• To develop a dynamically data-driven decision

support system for multi-objectively optimized system stability under uncertainty

• Specifically:i. Develop offline estimates of aero-elastic stability

envelope of flexible wing aircraft (SensorCraft) based on nonlinear aero-elastic computations

ii. Develop fast aero-elastic stability prediction environment

iii. Develop decision support system for aero-elastic stability through active robust multi-objective optimization

4

System of Interest

5

i. Provide decision support under uncertainty for avoiding static, dynamic, and aero-elastic instabilities

ii. Enhance fundamental understanding of flight conditions that influence system stability

iii. Serve to identify precursors in sensor data that are indicative of impending instability

Increase Altitude

System response

Sensor data

Decision Support System

Hold Steady

Decrease Altitude

Deterministic

Passive Robust

Active Robust

2. Quasi-Steady Vortex Lattice Method

1. Lifting Line & Ground Effect Reduced Order Models

3. Unsteady Vortex Lattice Method

OptimizationMulti-Fidelity Simulation

…

Data Fusion

Model Validation

Sensor Failure

Detection

Decision Variables

Previous Accomplishments

• DDDAS Framework: – Constructed a preliminary DDDAS framework for decision support

system: co-simulation capabilities and optimization under uncertainty could have useful roles to play

• Aero-elastic Studies [3]: – Co-simulation capabilities developed for joined-wing model (e.g.,

SensorCraft) using a GPU accelerated aero-elastic simulator: this approach has applicability to other flexible aircraft systems and allows for integration with different dynamical systems

• Decision Support [4]:– Extended existing active robust optimization research to multi-

objective optimization: framework shown to have relevance to DDDAS

– Automated discovery of worst case uncertain values and generation of online constraint cuts in flexible mission optimization

6

[3] Roccia, B., Preidikman, S., and Balachandran, B. (2017) “Computational Dynamics of Flapping Wings in Hover Flight: A Co-Simulation Strategy,” AIAA Journal, 55:6, 1806-1822.[4] Azarm, S. and Lee., Y.-T. (2016) “Multi-Objective Robust Optimization Formulations with Operational Flexibility and Discretized Uncertainty,” Proceedings of ASME: International Design Engineering Technical Conference, Charlotte, NC, August 21-24, 2016.

Recent Year’s Accomplishments

• DDDAS Framework:– Updated DDDAS framework for

decision support system• Aero-elastic Studies [5]:

– Applied fast multipole method for accelerating aero-elastic simulations

– Investigated effects of structural wing damage on critical flutter speed

• Data-Driven Modeling and Prediction [6]:– Developed data-driven prediction framework based on available

offline simulation data and local sensor data, with high computational efficiency and reasonable accuracy comparable to high-fidelity simulation

• Decision Support:– Formulated decision support for optimal maneuvers based on

current state estimates and future predictions, and actively robust to uncertainty

7

[5] Kebbie-Anthony, A., Gumerov, N., Preidikman, S., Balachandran, B., and Azarm, S., “Fast Multipole Method for Accelerated Nonlinear Aero-elastic Simulations.” SciTech AIAA, Kissimmee, FL, 2018 [accepted].[6] Zhao, X., Kania, R., Kebbie-Anthony, A., Azarm, S., and Balachandran, B. “On a Combined Sensor- and Simulation-based Data-driven Robust Flight Design Decision Support System.” SciTech AIAA, Kissimmee, FL, 2018 [accepted].

DDDAS Framework for Decision Support

8

Initial Data

Co-Simulation

Active Robust Optimal Mission

Planning

Accelerated Co-Simulation

Sensor Data

Data Fusion

Sensor Failure Detection

Design of Experiments

Optimization of Safe Maneuver Envelope Decisions to Take

Model Validation

Data-Driven Modeling

Decision Support System

Offline Online

DDDAS Framework for Decision Support

9

Initial Data

Co-Simulation

Active Robust Optimal Mission

Planning

Accelerated Co-Simulation

Sensor Data

Data Fusion

Sensor Failure Detection

Design of Experiments

Optimization of Safe Maneuver Envelope Decisions to Take

Model Validation

Data-Driven Modeling

Decision Support System

Offline Online

Aero-elastic Simulation: Flowcharts

10

Solution stabilization(Coord. Projection)

Correction of solution

𝑴𝑴 𝑩𝑩𝑞𝑞𝑇𝑇

𝑩𝑩𝑞𝑞 𝟎𝟎�𝒒𝒒(𝑡𝑡)𝝀𝝀

= 𝑭𝑭(𝑡𝑡)

solved for �̈�𝑞(𝑡𝑡) and Lagrange multipliers

Mass matrix 𝑴𝑴(𝑡𝑡), Jacobian matrix 𝑩𝑩(𝑡𝑡), and load vector 𝑭𝑭(𝑡𝑡)

Simulator 1, iteration for 𝒕𝒕𝒏𝒏+𝟏𝟏𝒌𝒌

Convect wake

Predict state of structure at t + ∆t

Calculate aerodynamic loads and control point forces

Initial conditions at t

Correct predicted state

YesNo

Aerodynamic Model (UVLM)Structural Model (FEM)

Convergence?Aerodynamic loads calculated, 𝑭𝑭𝑧𝑧𝑧𝑧𝑧𝑧𝑧𝑧(𝑡𝑡)

𝑨𝑨 𝑡𝑡 𝑮𝑮 𝑡𝑡 = 𝑹𝑹𝑹𝑹𝑹𝑹(𝑡𝑡)solved for circulations 𝑮𝑮(𝑡𝑡)

Wake Convection

�k = 0,k > 0,convectwake frozen

Simulator 2, iteration for 𝒕𝒕𝒏𝒏+𝟏𝟏𝒌𝒌

𝑹𝑹𝑹𝑹𝑹𝑹(𝑡𝑡)calculated

Aerodynamic matrix 𝑨𝑨 𝑡𝑡calculated

Aero-elastic Simulation: Models

11

Rear Wing

Fuselage

Vertical Tail

ForwardWing

Aerodynamic Model

Structural Model

Aerodynamic Model:• Number of nodes = 2342• Number of panels, M = 1985

Structural Model:• Number of nodes = 19• Number of elements = 18

Structural Damage0% 10% (Torsion)

Mode Number

Frequency[Hz]

Frequency[Hz]

1 0.370 0.370

2 0.868 0.857

3 1.547 1.547

4 2.216 2.208

5 2.530 2.506

Aero-elastic Studies: Influence of Damage on Flutter

12

: Beam‒Element (No damage): Beam‒Element (Damage)

Left Rear Wing

Left Forward Wing

Aero-elastic Simulation: Fast Multipole Method (FMM)

13

Algorithm Complexity (𝑲𝑲 time steps)

Step Standard FMM

Form aerodynamic coefficient matrix 𝑨𝑨 𝑡𝑡 𝑂𝑂(𝑁𝑁

2𝐾𝐾) 𝑂𝑂(𝑁𝑁2𝐾𝐾)

Evaluate RHS vector𝑹𝑹𝑹𝑹𝑹𝑹(𝑡𝑡) 𝑂𝑂(𝑁𝑁𝑁𝑁𝐾𝐾) 𝑂𝑂(𝑁𝑁𝐾𝐾 + 𝑁𝑁𝐾𝐾)

Solve linear system 𝑨𝑨 𝑡𝑡 𝑮𝑮 𝑡𝑡 = 𝑹𝑹𝑹𝑹𝑹𝑹(𝑡𝑡)

𝑂𝑂(𝑁𝑁3𝐾𝐾) 𝑂𝑂(𝑁𝑁3𝐾𝐾)

Evaluate velocity field 𝑂𝑂(𝑁𝑁𝑁𝑁𝐾𝐾 + 𝑁𝑁2𝐾𝐾) 𝑂𝑂(𝑁𝑁𝐾𝐾 + 𝑁𝑁𝐾𝐾)

[5] Kebbie-Anthony, A., Gumerov, N., Preidikman, S., Balachandran, B., and Azarm, S., “Fast Multipole Method for Accelerated Nonlinear Aero-elastic Simulations.” SciTech AIAA, Kissimmee, FL, 2018 [accepted].

Aerodynamic loads calculated, 𝑭𝑭𝑧𝑧𝑧𝑧𝑧𝑧𝑧𝑧(𝑡𝑡)

𝑨𝑨 𝑡𝑡 𝑮𝑮 𝑡𝑡 = 𝑹𝑹𝑹𝑹𝑹𝑹(𝑡𝑡)solved for circulations 𝑮𝑮(𝑡𝑡)

Wake Convection

�k = 0,k > 0,convectwake frozen

Simulator 2, iteration for 𝒕𝒕𝒏𝒏+𝟏𝟏𝒌𝒌

𝑹𝑹𝑹𝑹𝑹𝑹(𝑡𝑡)calculated

Aerodynamic matrix 𝑨𝑨 𝑡𝑡 calculated

𝐺𝐺9𝑡𝑡 𝐺𝐺10𝑡𝑡 𝐺𝐺12𝑡𝑡 𝐺𝐺13𝑡𝑡 𝐺𝐺14𝑡𝑡𝐺𝐺8𝑡𝑡 𝐺𝐺11𝑡𝑡

𝐺𝐺2𝑡𝑡 𝐺𝐺3𝑡𝑡 𝐺𝐺5𝑡𝑡 𝐺𝐺6𝑡𝑡 𝐺𝐺7𝑡𝑡𝐺𝐺1𝑡𝑡 𝐺𝐺4𝑡𝑡

𝐺𝐺2𝑡𝑡−1 𝐺𝐺3𝑡𝑡−1 𝐺𝐺5𝑡𝑡−1 𝐺𝐺6𝑡𝑡−1 𝐺𝐺7𝑡𝑡−1𝐺𝐺1𝑡𝑡−1 𝐺𝐺4𝑡𝑡−1

𝐺𝐺2𝑡𝑡−2 𝐺𝐺3𝑡𝑡−2 𝐺𝐺5𝑡𝑡−2 𝐺𝐺6𝑡𝑡−2 𝐺𝐺7𝑡𝑡−2𝐺𝐺1𝑡𝑡−2 𝐺𝐺4𝑡𝑡−2

𝑵𝑵 : number of elements on lifting surface 𝑴𝑴 : number of elements on wake 𝑲𝑲 : number of time steps

: Lifting Surface: Wake

14

Data-Driven Modeling and Prediction: Overview

Challenges:• Online Decision Support System (DSS) for

mitigating aero-elastic effects • Speed and accuracy necessary for DSS

effectiveness• Complement accurate aero-elastic simulation

with localized sensors

Objective:Develop a data-driven prediction framework • Offline simulation data (global response)• Sensor data (local response)

Sensors: Local Response

𝒙𝒙(𝑡𝑡) 𝒚𝒚(𝑡𝑡)Simulation: Global Response

𝑓𝑓(𝒙𝒙, 𝑡𝑡)

𝑓𝑓𝑠𝑠1(𝒙𝒙, 𝑡𝑡)𝒙𝒙(𝑡𝑡) 𝑦𝑦𝑠𝑠1(𝑡𝑡)+𝜖𝜖1

𝒙𝒙(𝑡𝑡) 𝑦𝑦𝑠𝑠2(𝑡𝑡)+𝜖𝜖2𝑓𝑓𝑠𝑠2(𝒙𝒙, 𝑡𝑡)

𝒙𝒙(𝑡𝑡) 𝑦𝑦𝑠𝑠𝑛𝑛(t)+𝜖𝜖𝑛𝑛𝑓𝑓𝑠𝑠𝑛𝑛(𝒙𝒙, 𝑡𝑡)

…

Simulation: Global Response Sensors: Local Response

15

Data-Driven Modeling and Prediction: Approach

[6] Zhao, X., Kania, R., Kebbie-Anthony, A., Azarm, S., and Balachandran, B. “On a Combined Sensor- and Simulation-based Data-driven Robust Flight Design Decision Support System.” SciTech AIAA, Kissimmee, FL, 2018 [accepted].

Meta-model

Local predictions

Sensordata

Data fusion

PDF

Response

Updated local

predictions

Resp

onse

Response

Local to global interpolation

Offline simulation

data

Local to global relationship construction

Data fusion

Finalglobal

predictions

Updated global

predictions

Global predictions

Operating conditions

𝑹𝑹𝟏𝟏

𝑹𝑹𝒏𝒏𝑹𝑹𝟐𝟐

16

Data-Driven Prediction: Aero-elastic Case Studies

• Simulation model: Vortex Lattice Method (VLM)• Sensors: Out of 14 locations that simulation predicts, three

have strain sensor measurements • Training: 21 points (generated by Latin Hyper Cube)• Verification: 9 points

MM MM+Sensor 1 MM+Sensor 1,2 MM+Sensor 1,2,3

RMSE 2.56 1.79 1.32 1.37

STD 2.44 1.66 1.29 1.14

Air density (𝝆𝝆)

Flight speed (𝑽𝑽𝒂𝒂)

Altitude (𝒉𝒉)

Strain at14 locations

MM: Meta-model

Decision Support Under Prediction Uncertainty

• Challenges– Current state estimation

and future state predictiondistributions

– Uncertainty increaseswith time

– Highly conservativeto avoid all possiblerisk

• Objective– Make actively robust

step-ahead decisions17

𝒚𝒚𝒕𝒕 = ℎ(𝒙𝒙𝑡𝑡,𝒑𝒑𝑡𝑡,𝒚𝒚𝑡𝑡−1 )𝒑𝒑𝑡𝑡

𝒙𝒙𝑡𝑡

𝒚𝒚𝑠𝑠𝑡𝑡

�𝒚𝒚t, �𝒚𝒚t+1

arg min𝒙𝒙𝑡𝑡, 𝒙𝒙𝑖𝑖,𝑡𝑡+1

𝐸𝐸 𝑓𝑓𝑛𝑛,𝑖𝑖 𝒙𝒙𝑡𝑡,𝒙𝒙𝑖𝑖,𝑡𝑡+1,𝒑𝒑𝑡𝑡,𝒑𝒑𝑖𝑖,𝑡𝑡+1

𝑠𝑠. 𝑡𝑡. 𝑔𝑔𝑗𝑗,𝑖𝑖 𝒙𝒙𝑡𝑡,𝒙𝒙𝑖𝑖,𝑡𝑡+1,𝒑𝒑𝑡𝑡,𝒑𝒑𝑖𝑖,𝑡𝑡+1 ≤ 0

∀𝑛𝑛 ∈ 𝑁𝑁∀𝑖𝑖 ∈ 𝐼𝐼∀𝑗𝑗 ∈ 𝐽𝐽

• Variables: – Current maneuver

xt = (𝑉𝑉𝑎𝑎(𝑡𝑡),ℎ(𝑡𝑡),𝜌𝜌(𝑡𝑡))– Future maneuver

xt+1 = (𝑉𝑉𝑎𝑎 𝑡𝑡 + 1 ,ℎ 𝑡𝑡 + 1 ,𝜌𝜌 𝑡𝑡 + 1 )• Constraints:

– Confidence that stress does not exceed limit Probability ( �𝜎𝜎𝑡𝑡 ≤ 𝜎𝜎𝑚𝑚𝑎𝑎𝑚𝑚) ≥ 0.99

– Confidence that stress will not exceed limit Probability ( �𝜎𝜎𝑡𝑡+1 ≤ 𝜎𝜎𝑚𝑚𝑎𝑎𝑚𝑚) ≥ 0.95

Decision Support SensorCraft Example Mission

18

Failure State

99% 95% 90%

Concluding Remarks• During the first 27 months:

– Framework for data-driven prediction developed: dynamic simulation data in combination with online sensor data through meta-modeling

– Fast multipole method algorithm applied to aerodynamic simulator to accelerate aero-elastic simulations

– Effect of structural wing damage on flight capabilities investigated

– Developed step-ahead active robust optimization incorporating current and future state estimates and their uncertainty

19

Future Plans• Over the next year, we plan to:

– 3rd Year: Combine multi-fidelity aero-elastic model with active robust optimization• Investigate trade-offs in FMM approximation

accuracy vs. computation speed• Data driven modeling and prediction

– Integrate multiple levels of simulation fidelity– Assess aircraft damage state

• Develop and apply auto discretizing active robust optimization for step-ahead decision support of aero-elastic system

20

Acknowledgements

• U.S. Air Force Office of Scientific Research under grant No. FA9550150134

• ONR Sabbatical Program at NSWC, Carderock, MD for Professor Shapour Azarm

• Dr. Sergio Preidikman from the National University of Córdoba, Córdoba, Argentina

• Dr. Nail Gumerov from the University of Maryland Institute of Advanced Computer Studies

• Dr. Robert Scott from NASA Langley Research Center, Hampton, VA

• Dr. Robert Canfield and Dr. Anthony Ricciardi from the Collaborative Center for Multidisciplinary Sciences of the Air Force Research Laboratory (AFRL) at Virginia Tech

21

Robust Data-Driven Aero-Elastic Flight Envelope TailoringOutlineChallenges and Needs �Identified for Current Work ObjectivesSystem of InterestPrevious AccomplishmentsRecent Year’s AccomplishmentsDDDAS Framework for �Decision SupportDDDAS Framework for �Decision SupportAero-elastic Simulation: FlowchartsAero-elastic Simulation: ModelsAero-elastic Studies: �Influence of Damage on FlutterAero-elastic Simulation: �Fast Multipole Method (FMM)Data-Driven Modeling and Prediction: OverviewData-Driven Modeling and Prediction: ApproachData-Driven Prediction: �Aero-elastic Case StudiesDecision Support �Under Prediction UncertaintyDecision Support �SensorCraft Example MissionConcluding RemarksFuture PlansAcknowledgements