NASA Technical Reports Server (NTRS) 20150000844: Wing Shape Sensing from Measured Strain

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by  NASA Technical Reports Server (NTRS)

Wing Shape Sensing from Measured Strain
Prepared For:
AIAA SciTech 2015 (AIAA Infotech @ Aerospace)
January 5-9, Kissimmee, Florida
Prepared By:
Chan-gi Pak, Ph.D.
Structural Dynamics Group, Aerostructures Branch (Code RS)
NASA Armstrong Flight Research Center
Patent Pending: Patent App No. 14/482784
Overview
(cid:137) What the technology does
(cid:137) Previous technologies
(cid:137) Technical features of new technology
(cid:137) Computational Validation
(cid:153) Uniform 1g load
(cid:153) Wing tip torsion load
(cid:153) Aerodynamic load under 1° angle of attack at Mach 0.715
(cid:137) Experimental Testing
(cid:153) Leading-edge load
(cid:153) Uniform load
(cid:137) Conclusions
Structural Dynamics Group Chan-gi Pak-2
What the technology does
Problem Statement
(cid:2012) Complete degrees of freedom
(cid:137) Improving fuel efficiency for an aircraft (cid:3051)
(cid:153) Reducing weightor drag (cid:2012)(cid:3052) Deflection
(cid:2012)
(cid:190) Similar effect on fuel savings (cid:2199) (cid:2202) (cid:3404) (cid:3053)
(cid:2016)
(cid:153) Multidisciplinary design optimization (design phase) or active control (during (cid:3051)
(cid:2016)
flight) (cid:3052) Slope (angle)
(cid:2016)
(cid:3053)
(cid:137) Real-time measurement of deflection, slope, and loads in flight are a valuable tool. Wires for Strain Gage Wire for FOSS
(cid:137) Wing deflection and slope (complete degrees of freedom) are essential quantities
for load computations during flight.
(cid:153) Loads can be computed from the following governing equations of motion.
(cid:1787)(cid:2199)(cid:4663) (cid:2202) (cid:3397)(cid:1781)(cid:2199)(cid:4662) (cid:2202) (cid:3397)(cid:1785)(cid:2199) (cid:2202) (cid:3404) (cid:2162) (cid:2169)(cid:2183)(cid:2185)(cid:2190)(cid:481)(cid:2199)(cid:4666)(cid:2202)(cid:4667)
(cid:2183)
(cid:190) (cid:12)(cid:144)(cid:150)(cid:135)(cid:148)(cid:144)(cid:131)(cid:142)(cid:15)(cid:145)(cid:131)(cid:134)(cid:149)(cid:483)(cid:3)(cid:151)(cid:149)(cid:139)(cid:144)(cid:137)(cid:3)(cid:136)(cid:139)(cid:144)(cid:139)(cid:150)(cid:135)(cid:3)(cid:135)(cid:142)(cid:135)(cid:143)(cid:135)(cid:144)(cid:150)(cid:3)(cid:149)(cid:150)(cid:148)(cid:151)(cid:133)(cid:150)(cid:151)(cid:148)(cid:135)(cid:3)(cid:143)(cid:145)(cid:134)(cid:135)(cid:142)
(cid:57) (cid:1787)(cid:2199)(cid:4663) (cid:2202) (cid:481) (cid:1781)(cid:2199)(cid:4662) (cid:2202) (cid:481) (cid:1785)(cid:2199) (cid:2202) : Inertia, damping, and elastic loads
(cid:190) External Load: using unsteady aerodynamic model
(cid:57) (cid:2162) : Aerodynamic load
(cid:2183)
(cid:137) Traditionally, strain over the wing are measured using strain gages.
(cid:153) Cabling would create weight and space limitation problems.
(cid:153) A new innovation is needed.Fiber optic strain sensor(FOSS) is an ideal
choice for aerospaceapplications.
FOSS
Strain Gage
Wingdeflection & slope will be computed from measured strain.
Structural Dynamics Group Chan-gi Pak-3
Previous technologies
Beam theory; Sectional bending moment and shear loads
(cid:137) Liu, T., Barrows, D. A., Burner, A. W., and Rhew, R. D., “Determining Aerodynamic Loads Based on Optical Deformation Measurements,” AIAA 2001-0560
(cid:153) NASA LRC; Application is limited for “beam”.
(cid:137) 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
(cid:153) University of Arizona and NASA LRC; using an inverse interpolation formulation.
(cid:137) Kang, L.-H., Kim, D.-K., and Han, J.-H., “Estimation of Dynamic Structural Displacements using fiber Bragg grating strain sensors,” 2007
(cid:153) KAIST; displacement-strain-transformation (DST) matrix. Use strain mode shape. Application was based on beam structure.
(cid:137) Igawa, H. et al., “Measurement of Distributed Strain and Load Identification Using 1500 mm Gauge Length FBGand Optical Frequency Domain
Reflectometry,”20th International Conference on Optical FibreSensors, 2009
(cid:153) JAXA; using inverse analysis. “Beam” application only.
(cid:137) Ko, W. and Richards, L., “Method for real-time structure shape-sensing,” US Patent #7520176B1, April 21, 2009
(cid:153) NASA AFRC; closed-form equations(based on beam theory)
(cid:137) Richards, L. and Ko, W. , “Process for using surface strain measurements to obtain operational loads for complex structures,” US Patent #7715994, May
11, 2010
(cid:153) NASA AFRC; “sectional” bending moment and shear force along the “beam”.
(cid:137) 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
(cid:153) NASA LRC; curve-fitting
(cid:137) Park, Y.-L. et al., “Real-Time Estimation of Three-Dimensional Needle Shape and Deflection for MRI-Guided Interventions,” IEEE/ASMETransactions on
Mechatronics, Vol. 15, No. 6, 2010, pp. 906-915
(cid:153) Harvard University, Stanford University, and Howard Hughes Medical Institute; Uses beam theory.
(cid:137) Carpenter, T.J. and Albertani, R., “Aerodynamic Load Estimation: Pressure Distribution from Virtual Strain Sensors for a Pliant MembraneWing,” AIAA
2013-1917
(cid:153) Oregon State University; Aerodynamic loads are estimated from measured strain using virtual strain sensor technique.
Previous technologies are applied to a beam structure.
Structural Dynamics Group Chan-gi Pak-4
Technical features of new technology
Proposed solutions:
(cid:137) The new method for obtaining the deflection over a flexible full
3D aircraft structure is based on the following two steps. Fiber optic strain sensor
(cid:153) First Step: Compute wing deflection along fibers using measure
Assembler
strain data
module
(cid:190) Wing deflection will be computed along the fiber optic sensor line.
(cid:190) Strains at selected locations will be “fitted”. Flight
(cid:190) These fitted strain will be integrated twice to have deflection controller
information. (Relative deflection w.r.t. the reference point)
Strain
(cid:190) This is a finite element model independent method. Drag and
(cid:153) Second Step: Compute wing slope and deflection of entire structures lift
(cid:190) Slope computation will be based on a finite element model
dependenttechnique. Loading Expansion Deflection
(cid:190) Wing deflection and slope will be computed at all the finite element analysis Deflection and module Deflection analyzer
grid points. Slope
(cid:2012) (cid:2012)
(cid:3051) (cid:3051)
(cid:2012) (cid:2012)
(cid:2013) (cid:3052) (cid:3052)
(cid:3051)
(cid:2012) (cid:2012)
(cid:2199) (cid:2202) (cid:3404) (cid:3053) (cid:2199) (cid:2202) (cid:3404) (cid:3053)
(cid:2016) (cid:2016)
(cid:3051) (cid:3051)
(cid:2016) (cid:2016)
(cid:3052) (cid:3052)
(cid:2016) (cid:2016)
(cid:3053) (cid:3053)
Compute
Compute
Measure Wing Compute
Wing
Strain Deflection Loads
Deflection
& Slope
First Step Second Step
A new two-step theory is investigated for predicting the deflection and slope of an entire structure using strain measurements at discrete locations.
Structural Dynamics Group Chan-gi Pak-5
Technical features of new technology (continued)
(cid:137) First Step .001
(cid:153) Use piecewise least-squares method to minimize noise in the Piecewise least squares curve fit boundaries
measured strain data (strain/offset) .000
(cid:153) Obtain cubic spline (Akimaspline) function using re-generated strain
data points:
-.001
(cid:1856)(cid:2870)(cid:2012)
(cid:3404) (cid:3398)(cid:2035)(cid:4666)(cid:1871)(cid:4667)(cid:512)(cid:1855)(cid:4666)(cid:1871)(cid:4667)
(cid:1856)(cid:1871)(cid:2870) n.-.002 Extrapolated data
i
/

,
e
(cid:153) Integrate fitted spline function to get slope data: r
u-.003
(cid:3031)(cid:3083) t
(cid:3404) (cid:2016)(cid:4666)(cid:1871)(cid:4667) a
v
(cid:3031)(cid:3046)
r
u-.004
C
(cid:153) Obtain cubic spline (Akimaspline) function using computed slope data
-.005
(cid:153) Integrate fitted spline function to get deflection data: : raw data
(cid:2012)(cid:4666)(cid:1871)(cid:4667) : direct curve fit
-.006
: curve fit after piecewise LS
-.007
0 10 20 30 40 50
Along the fiber direction, in.
Strain Deflection
A measured strain is fitted using a piecewise least-squares curve fitting method together with the cubic spline technique.
Structural Dynamics Group Chan-gi Pak-6
Technical features of new technology (continued)
(cid:137) Second Step: Based on General Transformation
(cid:153) 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
(cid:2199)
(cid:2169)
(cid:190) (cid:2199) (cid:3404) (cid:3404) (cid:2176) (cid:2199)(cid:3557) : (cid:2199) = general displacement vector
(cid:2199) (cid:2169)
(cid:2175)
(cid:2199) (cid:2230)
(cid:57) Where, an eigen-matrix is defined as (cid:2169) (cid:3404) (cid:2169) (cid:2241) ; (cid:2241) = orthogonal displacement vector
(cid:2199) (cid:2230)
(cid:2175) (cid:2175)
(cid:190) Transformation matrix [T] can be one of the followings:
(cid:57) Guyan(or static) condensation, dynamic condensation, improved reduced system (IRS), or system equivalent reduction expansion
process (SEREP)
(cid:137) Expansion of displacement using SEREP: kinds of least-squares method; most accurate reduction-expansion technique
(cid:153) (cid:2199)(cid:3557) : master DOF; deflectionalong the fiber “computed from the first step”
(cid:2169)
(cid:2879)(cid:2778)
(cid:153) (cid:2199) (cid:3404) (cid:2740) (cid:2740) (cid:2176) (cid:2740) (cid:2740) (cid:2176) (cid:2199)(cid:3557) :deflection and slope all over the structure
(cid:2175) (cid:2175) (cid:2169) (cid:2169) (cid:2169) (cid:2169) (cid:2199)
(cid:2169)
(cid:2879)(cid:2778)
(cid:153) (cid:2199)(cid:2169) (cid:3404) (cid:2740)(cid:2169) (cid:2740)(cid:2169) (cid:2176) (cid:2740)(cid:2169) (cid:2740)(cid:2169) (cid:2176) (cid:2199)(cid:3557)(cid:2169) : smoothed master DOF (cid:2199)(cid:3557)(cid:2169)
(cid:2879)(cid:2778)
(cid:2230) (cid:2230) (cid:2176) (cid:2230) (cid:2230) (cid:2176)
(cid:2169) (cid:2169) (cid:2169) (cid:2169)
(cid:190) (cid:2176) (cid:3404)
(cid:2879)(cid:2778)
(cid:2230) (cid:2230) (cid:2176) (cid:2230) (cid:2230) (cid:2176)
(cid:2175) (cid:2169) (cid:2169) (cid:2169)
(cid:2199)
(cid:2199)(cid:3557) (cid:2169)
(cid:2169)
(cid:2199)
(cid:2175)
Computed deflection along the fibers are combined with a finite element model of the structure in order to interpolate and extrapolate
the deflection and slope of the entire structure through the use of the System Equivalent Reduction and Expansion Process.
Structural Dynamics Group Chan-gi Pak-7
Computational Validation
Cantilevered rectangular wing model
Cantilevered Rectangular Wing Model
Uniform 1gloading
(cid:137) Wind tunnel test wing (thickness = 0.065 in.)
(cid:153) Uniform 1gload
(cid:153) Wing tip torsion (1 lbfat leading-edge and -1 lbfat trailing-edge of wing tip section)
(cid:153) Aerodynamic load under 1°angle of attack at Mach 0.715
(cid:137) MSC/NASTRAN
Positive
(cid:153) Compute strain
(cid:153) Compute deflection (target)
Strain (y component)
(cid:137) ZAERO
(cid:153) Compute aerodynamic load
Wing tip torsion
(cid:137) Two-step approach
(1 lbfat leading-edge and -1 lbfat trailing-edge of wing tip section)
(cid:153) Compute deflection from computed strain
(cid:153) Compare computed deflection with respect to target value
Negative
Wing with 22 FOSS
Fiber optic strain sensors: 11(upper) + 11(lower) Fiber
Y Strain plot Positive
1 Z element
Rigid
3
5 element
Aerodynamic load under 1°angle of attack at Mach 0.715
7
n. 9
i X
6 11
5
4. 13
15
17
Negative
19 Plate
Fibers
21 elements
11.5 in.
X
Structural Dynamics Group Chan-gi Pak-9
Cantilevered Rectangular Wing Model: Uniform 1g
.00
(cid:137) Uniform 1gload
-.01
-.02
n.
Positive n, i-.03
o
cti
e-.04
efl
D
-.05 : NASTRAN results along fiber 1
Wing deflection over FE model
: NASTRAN results along fiber 11
(step 2 results with 10 modes)
-.06 : Two-step approach along fiber 1
: Two-step approach along fiber 11
-.07
Undeformed 0 1 2 3 4 5 6 7 8 9 10 11
shape Along the fiber direction, in.
b) Wing deflection (step 2 results with 10 modes)
.0005 .000
: NASTRAN results along fiber 1
-.001
.0000 : NASTRAN results along fiber 11
n-.002 : Two-step approach along fiber 1
o
ature, /in.--..00001005 (cid:3400)(cid:2782) oll directi--..000043 : Two-step approach along fiber 11
Curv-.0015 : NASTRAN results along fiber 1 Deformed ope, r-.005
: NASTRAN results along fiber 11 shape Sl-.006
-.0020 : Two-step approach along fiber 1 -.007
: Two-step approach along fiber 11
-.0025 -.008
0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11
Along the fiber direction, in. Along the fiber direction, in.
a) Curvature distribution (step 1 results) d) Wing span-wise slope (step 2 results with 10 modes)
Structural Dynamics Group Chan-gi Pak-10