Advances in Aircraft System Identification at NASA Langley Research Center

Advances in Aircraft System Identification

at NASA Langley Research Center

Jared Grauer

Department of Mechanical & Aerospace Engineering

Princeton University

16 April 2024

Grauer, NASA LaRC MAE Princeton University 1 / 33

Special Issue in the Journal of Aircraft

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US Army: Berger, Tobias, Tischler, Juhasz

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NASA LaRC: Morelli, Grauer

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DLR: Deiler, M¨ onnich, Sehere-Weiß,

Wartmann

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IPEV: Dias, Silva

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TUM: Hosseini, Steinert, Hofmann, Fang,

Steffensen, Holzapfel, G¨ ottlicher

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TAMU: Leshikar, Valasek, McQuinn

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Barron: Cooper, DeVore, Reed, Morelli

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TUDelft: de Visser, Pool

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VT: Simmons, Gresham, Woolsey

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STI: Lampton, Klyde, Schulze

Grauer, NASA LaRC MAE Princeton University 2 / 33

Self Introduction

Grauer, NASA LaRC MAE Princeton University 3 / 33

University of Maryland

credit: Grauer, 2011 Grauer, NASA LaRC MAE Princeton University 4 / 33

NASA Langley Research Center

credit: NASA / Sandie Gibbs Grauer, NASA LaRC MAE Princeton University 5 / 33

Research Engineer Duties

Technical Analysis

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IAWTM wind tunnel test

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X-59 low-boom flight demonstrator

Publications

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Conference papers, journal articles, and

technical reports ( www.ntrs.nasa.gov )

credit: NASA / Mark Knopp

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Internal presentations and reviews

Professional Service

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Technical committees

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Journal reviewer

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Advise industry and academia

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Teaching

credit: Lockheed Martin Skunk Works Grauer, NASA LaRC MAE Princeton University 6 / 33

Introduction to Aircraft System Identification

Grauer, NASA LaRC MAE Princeton University 7 / 33

What is System Identification?

“System identification is the determination, on the basis of observation of input and output, of a system within a specified class of systems to which the system under test is equivalent”

— Lofti Zadeh, 1962

Input, Output,

u ( t ) y ( t )

System,

G

Given u ( t ) and y ( t ) , identify G

Grauer, NASA LaRC MAE Princeton University 8 / 33

Uses of Aircraft System Identification

Aerodynamic Modeling

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Linear stability and control derivatives, e.g., C or M

m α α

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Nonlinear models, e.g., post-stall, unsteady aerodynamics, control interaction effects

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Validate prediction tools, e.g., wind tunnel tests, CFD, DatCom

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Update models for pilot simulation, mission rehearsal, control system tuning

System Modeling

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Extract gain and phase margins for robustness analysis

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Verify controller performance

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Low-order equivalent systems (LOES) for flying qualities analysis, e.g., CAP

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Reduced-order models (ROMs)

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Characterize subsystems, e.g., actuators, sensor calibration errors, fault detection

Grauer, NASA LaRC MAE Princeton University 9 / 33

Flowchart for Aircraft System Identification

credit: Morelli & Klein, 2016 Grauer, NASA LaRC MAE Princeton University 10 / 33

Traditional Inputs for Identification

Doublet 3211 4 4 2 2 0 0 Input, deg Input, deg -2 -2 -4 -4 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 1 2 3 4 5 6 7 8 9 10 Time, s Time, s Frequency Sweep Input, deg -2 -4 0 10 20 30 40 50 60 Time, s Grauer, NASA LaRC MAE Princeton University 11 / 33

Output Error Parameter Estimation

Drive a simulation model with measured inputs, and adjust parameters until the modeled

outputs “best” match the measured outputs in a maximum likelihood sense

         

˙ α Z 1 ∆ α 0 b δ

α ˙ α e Data

= +

Model

˙ q M M q M b 1

α q δ ˙ q e

      4

alpha, deg

   

1 0

α 0 b

α

∆ α δ

e

     

0 1 0 5 10 15

q = + 0 b

q

q 1

V

a Z 0 0 b

z α a z g q, deg/s -10 0 5 10 15 -0.5 -1 az, g -1.5 0 5 10 15 Time, s Grauer, NASA LaRC MAE Princeton University 12 / 33

Output Error with Fourier Transform Data

Same idea, but match Fourier transform data over a bandwidth of interest instead of time

history data with the analogous estimator

 

M

δ e Data Model

 

( jω − Z ) M

δ ( jω )

 α δ 

  e e

α ( jω ) 2

V alpha, deg

Z M

α δ

  g e

q ( jω ) =

 

0 0.5 1 1.5 2

− ω − ( Z + M ) jω + ( Z M − M )

α q α q α

a ( jω )

z q, deg/s 0 0.5 1 1.5 2 0.5 az, g 0 0.5 1 1.5 2 Frequency, Hz Grauer, NASA LaRC MAE Princeton University 13 / 33

Frequency Responses and Parameter Estimation

Can also match the complex-valued MIMO frequency

q(s) / (s)

responses in a maximum likelihood sense e

Data

 

Model

M

δ e

 

  ( jω − Z ) M

 α δ 

α ( jω ) e Mag., dB δ ( jω ) e V

  Z M

α δ e 10 g q ( jω )

 

=

δ ( jω )

 e  2

− ω − ( Z + M ) jω + ( Z M − M )

α q α q α 0 1 10 10 a ( jω ) z δ ( jω ) e Phase, deg -100 0 1 10 10 Frequency, rad/s Grauer, NASA LaRC MAE Princeton University 14 / 33

Equation Error Parameter Estimation

-0.2

The aerodynamic modeling problem can usually be

Data Model -0.3

reworked into a least squares problem

-0.4 CZ

C = C + C ∆ α -0.5

Z Z Z 0 α

q ¯ c -0.6

C = C + C ∆ α + C + C ∆ δ

m m m m m e 0 α q δe -0.7

2 V

0 5 10 15 0.1 0.05 Cm -0.05 -0.1 0 5 10 15 Time, s Grauer, NASA LaRC MAE Princeton University 15 / 33

System IDentification Programs for AirCraft (SIDPAC)

https://software.nasa.gov/software/LAR-16100-1

Grauer, NASA LaRC MAE Princeton University 16 / 33

Recent Applications at NASA LaRC

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Some Recent Applications

credit: Morelli & Grauer, 2023 Grauer, NASA LaRC MAE Princeton University 18 / 33

T-2 Generic Transport Model

credit: NASA Langley Research Center Grauer, NASA LaRC MAE Princeton University 19 / 33

AirSTAR Mobile Operations Station

credit: NASA / Sean Smith Grauer, NASA LaRC MAE Princeton University 20 / 33

Recent Advancements at NASA LaRC

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Orthogonal Phase-Optimized Multisine Inputs

 

X

2 πk

r ( t ) = a sin t + ϕ

j k k

T

k ∈ K j credit: Morelli & Grauer, 2023 Grauer, NASA LaRC MAE Princeton University 22 / 33

Locations to Inject Multisine Inputs

r

cl

r r

mb ba

Pilot

inputs

Flight

Responses

Bare

Control Mixer Actuators

Airframe

System

r

sb

Sensors

credit: Grauer, 2022 Grauer, NASA LaRC MAE Princeton University 23 / 33

Real-Time Parameter Estimation with Equation Error

Recursive Fourier transform (25 Hz), e.g., − jω t k i

y ( jω , t ) = y ( jω , t ) + y ( t ) e

k i k i − 1 i

Periodic updating of estimates ( ∼ 1 Hz)




− 1 † †

ˆ

θ = ℜ X X ℜ X z

credit: Morelli, 2012 credit: Morelli & Grauer, 2020 Grauer, NASA LaRC MAE Princeton University 24 / 33

Real-Time Estimation of MIMO Frequency Responses

Apply multisine excitations before the actuators

Recursive Fourier transform of the input and

output data at the multisine frequencies, e.g., − jω t k i

y ( jω , t ) = y ( jω , t ) + y ( t ) e

k i k i − 1 i

Periodic updating (e.g., 1 Hz) of frequency

response estimates from Fourier transforms

y ( jω , t )

k i

ˆ

G ( jω , t ) =

k i

u ( jω , t )

k i credit: Morelli & Grauer, 2020 Grauer, NASA LaRC MAE Princeton University 25 / 33

MIMO Frequency Responses from Closed-Loop Data

SP SW1B | δ | bf s

Feedback control correlates

the plant input data and

Mag., | δ | wf 1 s dB

biases frequency response

Output error

estimates

General approach | δ | wf 2 s Basic approach

Joint input-output approach

| δ | wf 3 s

to correctly estimate plant

dynamics from closed-loop

Phase, | δ | deg wf 4 s

data

y ( jω ) r ( jω )

k k gyr

ˆ

| q |

G ( jω ) =

k

r ( jω ) u ( jω )

k k Frequency Frequency credit: Grauer & Boucher, 2020 Grauer, NASA LaRC MAE Princeton University 26 / 33

Multiple-Loop MIMO Frequency Response Estimation

10 40 Mag., Mag., dB

Can add multisines to multiple points within dB

− 10

the system for simultaneous frequency response

− 20

estimation of different MIMO loops

•

Bare airframe

Phase, 0 Phase, deg deg

•

− 90

Closed loop

− 90 − 180 − 180

•

Broken loop at mixer 0.1 1 10

0.1 1 10 Frequency, rad/s Frequency, rad/s

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Broken loop at sensors 10

Mag., 10 Mag., dB dB − 10 − 10 − 20 − 20 Phase, Phase, deg 0 deg − 90 − 90 − 180 − 180 credit: Lockheed Martin Skunk Works 0.1 1 10 0.1 1 10 Frequency, rad/s Frequency, rad/s credit: NASA / Jim Ross credit: Grauer, 2022 Grauer, NASA LaRC MAE Princeton University 27 / 33

Turbulence Reconstruction as a Measured Input

2 2 10 10

Atmospheric turbulence can be thought of as

− 3 − 1 1 1 10 10

an unmeasured input acting on the system − 3 . 5

0 0 10 10 − 1 . 5 C C Z α m α − 4 − 1 − 1 10 10 G , ww − 4 . 5 − 2

One approach is to reconstruct the turbulence 2 3

− 2 − 2 10 ft /s 10 − 3 − 3 σ w = 0 . 79 ft/s

from other data and use it in the modeling 10 [ 2–7 Hz ] 10 25 0

σ = 0 . 51 ft/s 0 w − 4 [ 2–7 Hz ] − 4 10 10 − 20 − 25 σ = 0 . 35 ft/s w [ 2–7 Hz ] C C Z N/A m ˙ α ˙ α − 5 − 5 − 50 10 10 − 40 The original concept is from the 1950’s, e.g., − 1 0 1 − 1 0 1 − 75 10 10 10 10 10 10 − 100 − 60 Frequency, Hz

x y

a a 25 20

α = α − q + p + α

m g

V V

− 25 − 20 C Z C m q q − 50 − 40 − 75 − 100 − 60 1 − 1 0 . 5 − 1 . 5 C C Z m δe δe − 0 . 5 − 2 − 1 − 1 . 5 − 2 . 5 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 σ , ft/s σ , ft/s w w [2 − 7 Hz ] [2 − 7 Hz ] credit: NASA Langley Research Center credit: Grauer, 2021 Grauer, NASA LaRC MAE Princeton University 28 / 33

Filter Error Parameter Estimation

− 0 . 5

Another approach is to use maximum likelihood

a , z m − 1

estimators that explicitly account for process g

noise and disturbances − 1 . 5

–

z ( i ) q , m deg/s − 5

ˆ y

− 10 Data Model 4

u ( i )

Kalman

α , m

ˆ deg

Filter

R

ν ( i )

 

S

ˆ 4

θ

θ m , deg

ˆ

Q

− 2 0 5 10 15 20

Optimization

Time, s

ˆ

θ

credit: Grauer & Morelli, 2015 Grauer, NASA LaRC MAE Princeton University 29 / 33

X-56A Aeroelastic System Identification

Aeroservoelasticity in the X-56A

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Created a flutter instability

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Coupled with rigid-body dynamics

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Interacted with the control system

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Observed in sensor data

SW1T Linear quasi-steady models for identification:

       

˙ x A A x B

r rr re r r

= + u

˙ x A A x B

e er ee e e

 

SW1B

 

x SP

r

C C

y = + Du

r e

x

e Imag.

credit: Grauer, 2020 Grauer, NASA LaRC MAE Princeton University 30 / 33

Modal State Estimation from Multiple Sensors

Vibration states are measured in linear combination and not directly by sensors

An abundance of strain and accelerometer measurements with an accurate finite element

model facilitates estimation of modal displacements, rates, and accelerations

This can be used for aeroelastic system identification and feedback control

ϵ ( t )

ˆ ˆ

η ( t ) , cov[ ˆ η ( t )] η ( t ) , cov[ ˆ η ( t )]

Least

Ψ

Squares

˙ ˙

ˆ η ( t ) , cov[ ˆ η ( t )]

Kalman

Filter

a ( t )

¨ ¨ ¨ ¨

ˆ η ( t ) , cov[ ˆ η ( t )] ˆ η ( t ) , cov[ ˆ η ( t )]

Least

Φ

Squares

credit: Grauer & Boucher, 2018 and Grauer & Waite, 2021 Grauer, NASA LaRC MAE Princeton University 31 / 33

Unsteady Aerodynamics ROM from CFD

credit: NASA / Mark Knopp

Computed the full 14x14-element frequency

response matrix and modeled it with rational

function approximations from a single CFD run

credit: Grauer, Waite, & Stanford, 2021 Grauer, NASA LaRC MAE Princeton University 32 / 33

Summary and Future Outlook

Active research field with several open problems

Helpful to have a variety of modeling tools, e.g., SIDPAC

Expect continued emphasis on

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Real-time identification

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Efficient testing and rapid model update

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Aeroelastic systems and spatially-distributed sensors

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Large-amplitude maneuvers and unusual conditions

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High-order and nonlinear modeling

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Non-conventional vehicle configurations

Grauer, NASA LaRC MAE Princeton University 33 / 33