Acceleration and Velocity Sensing from Measured Strain

Prepared For: AFDC 2016 Fall meeting November 5-6, San Diego, California

Chan-gi Pak and Roger Truax Structural Dynamics Group, Aerostructures Branch (Code RS) NASA Armstrong Flight Research Center

Overview

What the technology does (Slide 3)

Previous technologies (Slide 4)

Technical features of two-step approach: Deflection (Slides 5-7) Technical features of new technology: Acceleration & Velocity (Slides 8-9)

Computational Validation (Slides 10-22) Cantilevered Rectangular Wing Model (Slide 11) Model Tuning (Slide 12)

Mode Shapes (slide 13)

Two Sample Cases (Slide 14)

Case 1 Results (Slides 15-18)

Case 2 Results (Slides 19-22)

LJ} Summary of Computation Error (Slide 23)

_] Conclusions (Slide 24)

Structural Dynamics Group Chan-gi Pak-2/21

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Problem Statement LW Improving fuel efficiency for an aircraft “* Reducing weight or drag > Similar effect on fuel savings “«* Multidisciplinary design optimization (design phase) or active control (during flight)

Complete degrees of freedom

Deflection

Wire for FOSS Wires for Strain Gage

Slope (angle)

L) Real-time measurement of deflection, slope, and loads in flight are a valuable tool.

©

“eo Active flexible motion control

©

“* Active induced drag control

LJ) Wing deflection and slope (complete degrees of freedom) are essential quantities for load computations during flight.

“* Loads can be computed from the following governing equations of motion.

IMJiq(é)s + [G]iq(®} + [K]iq@} = tQa(Mach, q(t))}

> Internal Loads: using finite element structure model Y [Ml{q(t)}, [G]{q(t)}, |[K]{q(t)}: Inertia, damping, and elastic loads > External Load: using unsteady aerodynamic model Y {Q,(Mach, q(t))}: Aerodynamic load FOSS

LJ Traditionally, strain over the wing are measured using strain gages.

“* Cabling would create weight and space limitation issues.

“* Anew innovation is needed. Fiber optic strain sensor (FOSS) is an ideal choice for aerospace applications.

Sinctural Dyeaies Group Wing deflection & slope at time t will be computed from measured strain. Strain Gage Chan-gi Pak-3/21

Previous technologies

LI Liu, T., Barrows, D. A., Burner, A. W., and Rhew, R. D., “Determining Aerodynamic Loads Based on Optical Deformation Measurements,” AIAA Journal, Vol.40, No.6, June 2002, pp.1105-1112 “* NASA LRC; Application is limited for “beam”; static deflection & aerodynamic loads LJ Shkarayev, S., Krashantisa, R., and Tessler, A., “An Inverse Interpolation Method Utilizing In-Flight Strain Measurements for Determining Loads and Structural Response of Aerospace Vehicles,’ Proceedings of Third International Workshop on Structural Health Monitoring, 2001 “* University of Arizona and NASA LRC; “Full 3D” application; strain matching optimization; static deflection & loads LJ Kang, L.-H., Kim, D.-K., and Han, J.-H., “Estimation of Dynamic Structural Displacements using fiber Bragg grating strain sensors,” 2007 “* KAIST; displacement-strain-transformation (DST) matrix; Use strain mode shape; Application was based on beam structure; dynamic deflection LI Igawa, H. et al., “Measurement of Distributed Strain and Load Identification Using 1500 mm Gauge Length FBG and Optical Frequency Domain Reflectometry,’ 20th International Conference on Optical Fibre Sensors, 2009 “* JAXA; using inverse analysis. “Beam” application only; static deflection & loads LI Ko, W. and Richards, L., “Method for real-time structure shape-sensing,” US Patent #7520176B1, April 21, 2009 “* NASA AFRC; closed-form equations (based on beam theory); static deflection LJ Richards, L. and Ko, W., “Process for using surface strain measurements to obtain operational loads for complex structures,” US Patent #7715994, May 11,2010 “* NASA AFRC; “sectional” bending moment, torsional moment, and shear force along the “beam”. LI Moore, J.P., “Method and Apparatus for Shape and End Position Determination using an Optical Fiber,” U.S. Patent No. 7813599, issued October 12, 2010 “* NASA LRC; curve-fitting; static deflection LJ Park, Y.-L. et al., “Real-Time Estimation of Three-Dimensional Needle Shape and Deflection for MRI-Guided Interventions,” JEEE/ASME Transactions on Mechatronics, Vol. 15, No. 6, 2010, pp. 906-915 “* Harvard University, Stanford University, and Howard Hughes Medical Institute; Uses beam theory; static deflection & loads LJ Carpenter, T.J. and Albertani, R., “Aerodynamic Load Estimation from Virtual Strain Sensors for a Pliant Membrane Wing,” AIAA Journal, Vol.53, No.8, August 2015, pp.2069-2079 «* Oregon State University; Aerodynamic loads are estimated from measured strain using virtual strain sensor technique. LJ Pak, C.-g., “Wing Shape Sensing from Measured Strain,” AIAA 2015-1427, AIAA Infotech @ Aerospace, Kissimmee, Florida, January 5-9, 2015; accepted for publication on AJAA Journal (June 29, 2015); U.S. Patent Pending: Patent App No. 14/482784 StructuraféyNASACAFRG; “Full 3D" application; based on System Equivalent Reduction Expansion Process; static deflection Chan-gi Pak-4/21

Technical features of two-step approach: Deflection Computation

Proposed solutions: L) The method for obtaining the deflection over a flexible full 3D A aircraft structure was based on the following two steps. Fiber optic strain sensor

“* First Step: Compute wing deflection along fibers using measure Strain data Wing deflection will be computed along the fiber optic sensor line. module

>

> Strains at selected locations will be “fitted”.

> These fitted strain will be integrated twice to have deflection controller information. (Relative deflection w.r.t. the reference point)

> This is a finite element model independent method.

“* Second Step: Compute wing slope and deflection of entire structures lif ener: - it Acceleration > Slope computation will be based on a finite element model

dependent technique. Velocity _ > Wing deflection and slope will be computed at all the finite analysis | Deflection and | module Deflection analyzer

Strain Drag and

element grid points. Slope 5.(2) 0x(€) of z(t ret (q©} = aan {Qa(Mach,q(t))} es BI} = 9 ae) {éx(t)} * _e® . 0 (C) * e 0,(t)

Compute Measure P

{qo} ta}

First Step

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Structural Dyn

Technical features of two-step approach : Deflection Computation (continued)

LI First Step 001 - I “* Use piecewise least-squares method to minimize noise in the Piecewise least squares curve fit boundaries measured strain data (strain/offset) 000 t : t ep RAPED “* Obtain cubic spline (Akima spline) function using re-generated | ! ! 205F" rm strain data points (assume small motion): -.001 a a ee rir ry Pa rr I l 5 i : VI | 265 | oi k <€-002 | Extrapolated data “| yp ttt Popp py ez —€,(s)/c(s) = A : ht | | . = : | om > -.003 EP “* Integrate fitted spline function to get slope data: © E | I | | Se Zz I +? I I I >. ao I f Il 1 i | [| | fT ddr © ~-004 | i. | | | aa ok (s) 4 Ve | | : | td -.005 §—9— : “* Obtain cubic spline (Akima spline) function using computed slope O : raw data data -006 -—_&—— — : direct curve fit : curve fit after piecewise LS “* Integrate fitted spline function to get deflection data: 6;(s) -007 - |

0 10 20 30 40 90 Along the fiber direction, in.

Deflection

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Technical features of two-step approach : Deflection Computation (continued)

L] Second Step: Based on General Transformation

©

“* Definition of the generalized coordinates vector {q}; and the othonormalized coordinates vector {7}; at discrete time k

Cale = {4}, = (elo = |g | Oe

“* For all model reduction/expansion techniques, there is a relationship between the master (measured or tested) degrees of freedom and the Slave (deleted or omitted) degrees of freedom which can be written in general terms as

(dusk = [uli tOsSk = [Ps lim “* Changing master DOF at discrete time k {qv}; to the corresponding measured values {qy }x (dusk = [Pulinge [ul use = [ul [Puli (MK = ([®yl[@ul) [ul Gude (Bk = aul ([®y]"[@u)) [Ou] ude

_] Expansion of displacement using SEREP: kinds of least-squares surface fitting; most accurate reduction-expansion technique “* {@y;}: master DOF at discrete time k; deflection along the fiber “computed from the first step”

% {qs} = [®5]([Py]*[Pyl) [ul Gun}: deflection and slope all over the structure {Gy,} + —1 ~ % {aun} = [ul] ([®u)[®u]) [®u)" {Guz}: smoothed master DOF

{quk3

Structural Dynamics Group Chan-gi Pak-7/21

Technical features of new technology: Acceleration Computation

G1 From (a= {4} =[9"| On Ce = {GN} = [on | oi 1 Assume simple harmonic motion for normalized coordinates. i(k) = —w7ni(k) i= 1,2,..,n LI Acceleration at discrete time k can be expressed

Hy (k) wy OO .. O] (mC) ula : ; tp = Pr = | ; = : ; I" x = —|w7|{n}x {n= - hu 2 j {mx Eq-(9) {mx = ([®u]'[®u]) ‘[®uy)" Gut Eq. (6) Tin (Kk) 0 0 Nn(k)

LI Substituting Eq. (6) into (9) gives

“snitch aaa

Dy | w* 4 {de =- aia ([Py)"[®y]) [ul ude | / “tctoer"coapul roa be trataeg”

(ade = | gnt| (lem) leml) fem)" Gude

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Structural Dynamics Group

ar Technical features of New Technology: Velocity Computation

UO) From = am — —j4m{ _ : Py|o;7 = pe (Dk = lass, 7 on | om (Dx = tae \ ei (Di = | | ([®y)"[@u}) [®u)" ude STi L} Consider “+ Backward difference: {1}, = ae has “phase shift" issue tqdk = ‘| ([@yl[@yl) [®ul? Gude

“* Central difference: {nh. = Dara — UD e-1

Te needs future response at time k

LJ From linear AR model for the i-th orthonormalized coordinate 17;(kK) = a1;n;(k — 1) + a2;n;(k — 2)

o

* Future prediction 7,;(k+1) attimek nj(k +1) = a,jn;(k) + a2jni(k — 1) f 22? Dy i T —1 T(~ Br = é ([®y][®y]) [ul {Gude ayini(K) + (ag; — 1)ni(k — 1) Psljoi!

2At

o

* Central difference becomes ni(k) =

»

o

q Dx = is, - on | Ok ),(k) = anti + ef — Dni(k — 1) nD) i x = ([@mI"l@nl) len!" Gwde tp = I ni(K)

Structural Dynamics Group

Chan-gi Pak-9/21

Computational Validation

Z Cantilevered rectangular wing model

ss) Cantilevered Rectangular Wing Model

LJ Configuration of a wind tunnel test article “* Has aluminum insert (thickness = 0.065 in ) covered with 6% circular arc cross-sectional shape (plastic foam) “* Impulsive load is applied at the leading-edge of wing tip section LI MSC/NASTRAN sol 112: Modal transient response analysis

©

“* Compute strain

©

“* Compute deflection & acceleration (target) LI Two-step approach

“* Compute deflection and acceleration from computed strain “* Compare computed deflection and acceleration with respect to

Applied load

target values Rigid 22 Simulated FOSS locations element Fiber optic strain sensors: 11(upper) + 11 (lower) A Fiber X Y —

Se Se a ee ee Kt 1 TTT TT TTT TT TT TT TC MT EE ET TE ee ey 5 . MTT EE TE TT TP , i, My a : UCN Lae MT TT TT TT 7 me Fe @, > Grid 2601 Leer ME ET EE Plate os K; >< ica me Se Ky MT TTT TT TTT TTT TTT 9 7 oT , Pe “ LA TEER De Tee eee I Ie ae SE oe ee e l ements we “by > ‘ we ees My MT TT TT TT TT TTT 11 ™~ ~~ & 7 ee oe Se @, UEC TT TEE eT ye ee ee %, ~< TN ON LE 7 MT TT TT TT TTT 13 ~~ & ae om Ue ey, 6 eee eee eee eee ee ee ee ee 2 ee ee ee ee eee eee eee . a, My a, ee he ie ee %, MT TTT TT TT TT TT 15 : i a & 7 ce iL Le” &: e, 8 oe eee een eee a et . ne an. oN S te. Ng Be NUN eee eee eee ee 2 eee ee ee ee ee ee eee 17 ™ ce, ee a” sa Nee & £ 70 ee ee ee ee ee eee eee eee ~ ae, ~ ™ Sy ae Be Md 19 hy Se 79 ON NN BR: € oe)

ee eee ee ee eee eee eee eee De i _ “pes Be fe | ff 71 . 2 0CU™ ae ee al & . 7g

~ N % A - ae. ate eel a: @, 76

Se Wy f 11.5 in. ae ey Xx A-A : “bey 5 oe

6% Circular arc ‘og “22 0.065" aluminum insert 7 . Flexible plastic foam

4.56 in.

Structural Dynamics Group Chan-gi Pak-11/21

Model Tuning

LI Idealization of the plastic foam weight

©

“* Case 1: equally smeared in aluminum plate.

“* Case 2: lumped mass weight are computed based on 6% circular-arc cross sectional shape.

> Use structural dynamic model tuning technique

> Chan-gi Pak and Samson Truong, “Creating a Test-Validated Finite-Element Model of

the X-56A Aircraft Structure,” Journal of Aircraft, (2015), doi: 0.065” aluminum insert Flexible plastic foam

http: //arc.aiaa.org/doi/abs/10.2514/1.C033043

Design variables

“Properties | Caseamodel | \ case 2Model ET ere sr e*aeas67e | \aea6s70 7” eensiy [ones [oa

Structural Dynamics Group

Objective function: frequency error

Measured vs. Computed Frequencies

‘Mode [ Measured (iz) [ Case 1 (Ha ce [Nae

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“ay Mode Shapes

Mode I: 14.29 Hz Mode 2: 80.17 Hz | Mode 3: 89.04 Hz

Mode 4: 248.76 Hz Mode 5: 252.41 Hz

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Two Sample Cases

L] Case 1 computations | Mode Measured (Hz) | Case 1 (Hz) | Case2 (Hz) “* Case 1 properties are used to make the target responses. 14.29 15.09 14.29 > Use NASTRAN modal transient response analysis (sol112) : : > 1200 time steps 80.41 77.40 80.17 “* Mode shapes from Case 1 are used to calculate transformation matrices. 89.80 93.57 39.04 > Mode shapes are eigen function. 246.37 248.76 “* Frequencies are estimated from strain data computed using Case 1 model. 262.02 957.41 {Bx = ‘en ([®ul[®ul) [Sul Gute (@e=- | | ([®y][@y]) (Ou) Gade | * So LiL? 85.6

_] Case 2 computations

“* Case 2 properties are used to make the target responses.

> Use NASTRAN modal transient response analysis (sol112) fat, = du Mf \ ee : Bk =a. Mk ff}, = nak) > 1200 time steps ‘ “* Mode shapes from Case 1 are used to calculate transformation matrices. (k) = ayini(kK) + (azi — Uni(k — 1), nC) > Mode shapes are comparison function. ” DAE Y Case 1 model: Not validated model imi = ([®y]™[al) [ul Gude Y Case 2 model: Validated model *

“* Frequencies are estimated from strain data computed using Case 2 model. _ From Case 1 model (comparison function) —

Structural Dynamics Group

LJ Use Bierman’s U-D Factorization Algorithm

LJ Number of AR Coefficients = 20

0.188001 sec

T=

Strain distribution

So eS a S bp Bs =O Zi a ov on Got © DO wv = a n Oo 4 or D 8S & ams) Q Vv Y) oa: i o wo © a ag E Ere — = 00 = oe XX = SD SB Ux I fo A 3 2 @. \ > Vo Sf 3! c Bg © s © Suc @B S Dt ng 2 OO Oo DSS Be Sc eat aa) N BOORE OR noon oO VY oo, 2 = © Cy oS. oo I ; ALoovgsE a o i Oo i & O S TP gg VET SE aS > oD am © © Dp oO oOo oO 0 SS Ost & qe os Ww © 8 o S bp 2 2 op PEE So om Oo t+ © 0 Om > ow 1 i 1 we OMNnZE wow wow : ° ™ = i) oO fNoooa sais

-5.0E-4

-1.0E-3

-1.5E-3

0.02 0.04 0.06 0.08 0.10

0.00

15/21

Chan-gi Pak

Time (sec)

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Deflection Time Histories: Case 1

0.3

0.2

0.1

0.0

Z deflection (inch)

0.00 0.02 0.04 0.06

Time (sec)

Z deflection (inch) © ©

0.00 0.01

Time (sec) Structural Dynamics Group

0.02

— : Current Method

L) 22 fibers LI At grid 51

0.02 0.04 0.06 0.08 0.10 Time (sec)

0.01 0.02 0.03 Time (sec)

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Acceleration Time Histories: Case 1

6.E+5 4.E+5 S T4645 — : Current Method oO 3.E+5 oO 7 | — ® ft O 22 fib a = 2.E+5 | Hw di | ene s e Wel | | WHA a LI At grid 51 £ 1.E+5 S 0.E+0 | | | | | , 6 0.E+0 | ® wi g 1.E+5 @ -2.E+5 : oo" © © -2.E+5 © AES | N ee 90253 o ov << a -6.E+5 0.00 0.02 0.04 0.06 0.08 0.02 0.04 0.06 0.08 0.10 Time (sec) Time (sec) 6.E+5 S 4.645 oO ® “” = 2.E+5 O = 5 0.E+0 ‘ E : ® -2,.E45 :: ® + O O s -4.E+5 -6.E+5 0.00 0.01 0.02 “903 0.00 0.01 0.02 0.03 Time (sec) Time (sec)

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Velocity Time Histories: Case 1

150 100

O1 ©

on o

-100

Z velocity (inch/sec) ©

-150

-200 0.00 0.02

200

150 100

-50

velocity (inch/sec)

N -1 00 -150

-200 0.00

Structural Dynamics Group

0.01

0.04 0.06

Time (sec)

Time (sec)

0.02

0.08

— : Current Method

L) 22 fibers LI At grid 51

100

0.02 0.04 0.06 0.08 0.10 Time (sec)

0.01 0.02 0.03 Time (sec)

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Case 2

LJ Use Bierman’s U-D Factorization Algorithm

LJ Number of AR Coefficients = 20

0.19461 sec

T=

Strain distribution

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-5.0E-4

-1.0E-3

-1.5E-3

0.04 0.06 0.08 0.10 Time (sec)

0.02

0.00

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Deflection Time Histories: Case 2

inch)

0.25 0.20 0.15 0.10

= 0.05

eflection

So N

Structural Dynamics Group

0.00 -0.05 -0.10 -0.15 -0.20 -0.25

0.00

0.25 0.20 0.15 0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.20 -0.25

0.00

LI 6,10, & 22 fibers 0.03 LI At grid 2601

0.02 0.04 0.06 0.02 0.04 0.06 0.08 0.10 Time (sec) Time (sec)

0.01 0.02 0.01 0.02 0.03 Time (sec) Time (sec)

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Acceleration Time Histories: Case 2

2.5E+5 2.0E+5 1.5E+5 1.0E+5 5.0E+4 0.0E+0 : 5.0E+4 1.0E+5 | 1.5E+5 -2.0E+5 |

-2.5E+5 0.00

Z acceleration (inch/sec‘’2)

2.5E+5 2.0E+5 1.5E+5 1.0E+5 5.0E+4 0.0E+0 5.0E+4 4.0E+5 | © -1.5E+5 N' -2.0E+5

-2.5E+5 0.00

celeration (inch/sec‘’2)

Structural Dynamics Group

0.02 0.04 0.06 0.08 Time (sec)

(radian/sec’2:

itch acceleratio

0.01 0.02 Time (sec)

3.0E+5 2.0E+5 1.0E+5

0.0E+0 :

-1.0E+5 |]

-2.0E+5 | -3.0E+5 0.00 3.0E+5 2.0E+5

1.0E+5

0.02

0.04 0.06 0.08 0.10 Time (sec)

0.01 0.02 0.03 Time (sec)

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Velocity Time Histories: Case 2

Z velocity (inch/sec)

Z velocity (inch/sec)

100

100

-100 0.00

0.02 0.04 0.06 0.08 Time (sec)

0.01 0.02 Time (sec)

Structural Dynamics Group

0.03

SS 22 fibers So

Pitch rate (radian/sec)

Pitch rate (adian/sec)

0.02 0.04 0.06 0.08 0.10 Time (sec)

0.01 0.02 0.03

Time (sec) Chan-gi Pak-22/21

aa Summary of Computation Error

QO % Error = »¢=0|Current approach (k)—Target(k)| yk-o0l Target(k)|

% Error

OLS =>

wwndan =.

LJ} Zdeflection errors are the smallest ‘“* Z deflections are input for the second step. SSSSA “= > Z deflections along the leading-edge fiber (grid 51) are input for SS 22 fibers SS WE the second step. (master DOF) SSSR

> Pitch angle at grid 51 as well as Z deflection and pitch angle at erid 2601 are output from the second step. (slave DOF) Therefore, it’s less accurate than master DOFs.

LI Acceleration and velocity errors are bigger than the displacement errors. LJ Even six fibers also give good answer. “«* No big difference between 6, 10, & 22 fibers.

Structural Dynamics Group

Chan-gi Pak-23/21

Conclusions

_] Acceleration and velocity of the cantilevered rectangular wing is successively

obtained using the proposed approach. «* Simple harmonic motion was assumed for the acceleration computations. > System frequencies are estimated from the time histories of strain measured at the leading-edge of the root section through the use of the parameter estimation technique together with the ARMA model. “* The central difference equation with a linear AR model is used for the computations of velocity. > ARcoefficients are computed using the estimated system frequencies. > Phase shift issue associated with the backward difference equation are overcome with the proposed approach. “* The total of six fibers provides the good results. > Quality of results based on 6, 10, and 22 fibers are similar.

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Structural Dynamics Group

Questions ?