Wing Load and Angle of Attack Identification by Integrating Optical

applied sciences

Article Wing Load and Angle of Attack Identiﬁcation by Integrating Optical Fiber Sensing and Neural Network Approach in Wind Tunnel Test

Daichi Wada * and Masato Tamayama

Aeronautical Technology Directorate, Japan Aerospace Exploration Agency, 6-13-1 Osawa, Mitaka-shi, Tokyo 181-0015, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-50-3362-5566

Received: 18 March 2019; Accepted: 2 April 2019; Published: 8 April 2019

Abstract: The load and angle of attack (AoA) for wing structures are critical parameters to be monitored for efficient operation of an aircraft. This study presents wing load and AoA identification techniques by integrating an optical fiber sensing technique and a neural network approach. We developed a 3.6-m semi-spanned wing model with eight flaps and bonded two optical fibers with 30 fiber Bragg gratings (FBGs) each along the main and aft spars. Using this model in a wind tunnel test, we demonstrate load and AoA identification through a neural network approach. We input the FBG data and the eight flap angles to a neural network and output estimated load distributions on the eight wing segments. Thereafter, we identify the AoA by using the estimated load distributions and the flap angles through another neural network. This multi-neural-network process requires only the FBG and flap angle data to be measured. We successfully identified the load distributions with an error range of −1.5–1.4 N and a standard deviation of 0.57 N. The AoA was also successfully identified with error ranges of −1.03–0.46◦ and a standard deviation of 0.38◦.

Keywords: fiber Bragg grating (FBG); load identification; machine learning; neural network; optical fiber sensor; structural monitoring

1. Introduction Load monitoring techniques for wing structures are a promising technology for enhancing the flight performance of future aircrafts. Load monitoring is beneficial in terms of structural safety and reliability. There has been significant demand for high-aspect-ratio wings for efficient long-endurance flight, and the loading for such structurally challenging designs is critical [1]. Monitoring results of loading history can be utilized for structural fatigue analysis. By controlling applied loads to wings based on real-time load monitoring, it could be feasible to alleviate undesirable large moments at the wing root. When wings are flexible, aerodynamic loads cause large deflections, which affect the aeroelastic stability and response [2–4]. Load monitoring is beneficial to estimate structural deformation and conduct reliable structural analysis based on practical assumptions of deflected wing shape. Another potential benefit of load monitoring is stable and efficient control of an aircraft, including unmanned air vehicles (UAVs). Considering the gust perturbation process for example, the load variations from oncoming gusts result in attitude and flight path variations, and there is a theoretical phase-lag between the cause (load) and effect (attitude and flight path) [5–7]. The load is a “phase-advanced” phenomena in this sense, and, therefore, its observation in addition to the conventional inertia observations could potentially enhance vehicle controllability. Aerodynamic loads are not always directly measurable. The wing structure is complex and space in wings is limited. It is difficult to install sufficient pressure sensors and tubes. To overcome

Appl. Sci. 2019, 9, 1461; doi:10.3390/app9071461 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 1461 2 of 15 these engineering obstacles, studies have been conducted to estimate, as opposed to directly measure, the loads using a measurable parameter, which is a strain. In a mechanical sense, load causes strain. When strain is used to identify loads, it creates an inverse problem [8–10]. Inverse analyses tend to be ill-conditioned, specifically when distributed aerodynamic loads are to be calculated. The solution becomes highly unstable for the strain measurement errors. There have been a number of studies to obtain stable solutions. For example, using the inverse interpolation method, Shkarayev et al. assumed polynomial functions, whereas Coates et al. used Fourier cosine series terms for spatial load distribution functions [11,12]. Nakamura et al. reported a finite-element-based inverse analysis in which aerodynamic restriction was coupled with elastic equations [13]. These techniques to assume functions for aerodynamic load distributions are effective in improving the identification accuracy. There have been other studies to identify loads by using neural networks. Using strain as an input and load as an output of the neural network, the strain-to-load transfer is represented by the neural network that is optimized through a learning algorithm. The optimization through a learning algorithm contributes to stable solutions. Cao et al. conducted numerical simulations of a cantilever beam to validate the neural network applicability [14]. Trivailo et al. used strain gauge data to estimate loads in fatigue tests that simulated maneuver and buffet loads [15]. They reported successful results, although they focused primarily on the load identification in the form of a limited number of concentrated forces. Wada et al. reported that the approach was applicable for the identification of distributed loads by using a number of strain gauges bonded on a flat panel [16]. These techniques remain limited to a level of conceptual demonstration, and validation of the applicability in the aerodynamic environment needs to be conducted. Currently, one of the primary challenges is the collection of sufficient amounts of strain data from the wing structure under flight conditions. It is not practical to install a myriad strain gauges on the surface of the wings considering the amount of wiring required. The digital image correlation technique would be a candidate to efficiently observe strain distribution profiles and there is a successful example of measuring strains for load estimation of membrane wings in wind tunnel tests [17]; however, some difficulties arise for in-flight uses. Stable setup of observation devices is not always available specifically when small UAVs are assumed and the observed images are under strong influence of flight environments such as the weather. On the other hand, recent studies indicate that optical fiber sensors are potentially promising techniques for obtaining strain information. By measuring multiple strains in a distributed manner along a single fiber, optical fiber-sensing exhibits significant effectiveness for collecting great volumes of data for wing and blade structures [18,19]. The sensing fibers are lightweight, thin, and can be attached to the surface of wings with only a marginal effect on the flight performance. A number of studies have demonstrated the feasibility of monitoring wings in wind tunnel tests [20] and UAV wings in flight using fiber Bragg gratings (FBGs) [21–23]. Multiple FBGs inscribed along fibers successfully measured strain distributions and enabled discussions about usage conditions, such as wing deformation. In this study, by using optical fiber sensors, we conduct practical and efficient strain monitoring of a wing structure under actual aerodynamic loading conditions. Furthermore, we propose an integration of the strain monitoring technique and the neural network approach for load identification and investigate its applicability through an experimental demonstration in a wind tunnel test. A 3.6-m semi-spanned high-aspect-ratio wing model, with eight flaps on the trailing edge that enable arbitrary variations of load distributions, was developed. Two optical fibers with 30 FBGs each were bonded along the main and aft spars and measured strain distributions in a wavelength-division-multiplexing manner [24]. Aerodynamic loads were applied in a wind tunnel, and load distributions were identified by using the FBG and data from the eight flap angles through a neural network. We discussed both structural and aerodynamic problems to which neural networks could be applied, based on which we proposed and examined another parameter identification, the angle of attack (AoA). The AoA is also one of the essential parameters that has a significant effect on the static and dynamic response of high-aspect-ratio wings [2–4]. We introduce an identification process for loads and AoAs that require only the FBG and flap angle data to be measured. We illustrate Appl. Sci. 2019, 9, 1461 3 of 15 the applicability of the optical fiber sensing and neural network through experimental results and discussions and demonstrate the effect of their integration for wing structures.

2. Materials and Methods

2.1. Wing Model with Multiple Flaps and Optical Fiber Sensors We developed a 3.6-m semi-spanned wing model with eight flaps on the trailing edge. The wing structure had balsa wood main and aft spars and skin. Woven carbon fiber-reinforced plastic fabrics covered the balsa wood. A 400-mm stainless-steel shaft was inserted from the wing root in the main spar in order to attach the wing model to the wind tunnel base. Figure1 shows a photograph and a schematic of the wing model. We set the Z axis along the span. We labelled the flaps Flap 1, 2, ... , 8 from the wing root. For each wing segment with Flap 1, 2, ... , 8, we listed in Table1 the position Z of the center of the flap, the span-wise length of the flaps, the chord length of the wing measured at the center of the flaps, and the flap width measured in chord-wise. Servomotors (BLS177SV, Futaba) controlled the flap angles. The movable range of the flap angles was from −15–15◦. The positive angle indicates flap down so that the lift force increases, with zero degrees being the neutral setting. We set eight static pressure-port arrays at the center of each wing segment. For each pressure sensor array, there were 15 pressure ports on the upper side and 8 on the lower side. A total of 184 silicon tubes for pressure sensors were installed and connected to an interrogator (Electronic Pressure Scanners, Pressure System) that was placed out of the wind tunnel. Figure2 shows the cross-section of the wing model with the locations of the pressure ports and spars. We set the X and Y axes. We labelled the pressure ports on the upper side as u1, u2, ... , u15 and on the lower side as l1, l2, ... , l8, counting from the leading edge. The normal direction at each pressure port was expressed by θ. Table2 listed the geometry of the pressure ports at the wing segment of Flap 1. The geometry was not identical but similar for other wing segments. The distributions of the pressure coefficient, Cp, of the wing segment with Flap 1 are shown in Figure3. The flap position was neutral. We calculated the applied lift loads on each wing segment by integrating the measured static pressures around the airfoil. By dividing the airfoil into segments as labelled U1, U2, ... , U15, L1, L2, ... , L8 corresponding to each pressure port as seen in Figure2, we multiplied the measured pressures with corresponding areas of the segments based on the approximation that the pressures were uniform in the segments. By considering the normal direction, we calculated the out-of-plane forces on the wing and defined them as the lift loads. Figure4 shows the lift coefficient, CL, of the wing model with respect to AoA. The positions of the flaps were neutral. We bonded two optical fibers with inscribed FBGs on the upper side of the wing along the main and aft spars. We used an epoxy adhesive and fully covered the fibers with the minimum possible thickness. We applied a small pre-strain to set the fibers straight before bonding. We inscribed 30 FBGs at 120 mm intervals in individual fibers in order to cover the whole semi-span of the wing. The gauge length of the FBGs was 5 mm and the reflectivity was 70%. We designed the Bragg wavelengths of the 30 FBGs ranging from 1530–1595 nm (in the C- and L-bands) so that we could monitor the individual Bragg spectra in the wavelength-division-multiplexing manner. Figure5 shows the reflected Bragg spectra from the optical fibers bonded to the main and aft spars. We used FBG interrogation monitors (I-MON 512 USB, Ibsen) to observe the reflected spectra and observed 30 FBGs in the wavelength domain. The Bragg wavelength intervals were set wider at shorter wavelengths. We aligned the FBGs with shorter Bragg wavelengths closer to the wing root as the wing root was expected to have greater strain variation amplitudes in general, and it was aimed at avoiding spectral overlap. A wind shield was placed at the wing root. The lead wires of the servomotors, the pressure sensor tubes, and the optical fibers were routed to the basement of the wind tunnel and connected to the controller and the interrogators. Appl. Sci. 2019,, 9,, 1461x FOR PEER REVIEW 44 of of 15 Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 15

Figure 1. Wing model. Left: Photograph in wind tunnel taken from upstream and lower side of wing. FigureRight: Schematic 1. Wing model. of flaps Left and:: Photograph Photograph sensors viewed in in wind wind from tunnel tunnel upper taken taken side from from of wing. upstream upstream and and lower lower side side of of wing. wing. Right: Schematic of ﬂapsflaps and sensors viewed fromfrom upper sideside ofof wing.wing. Table 1. Wing geometry. Table 1. Wing geometry. Position Z of TableFlap 1. WingSpan geometry.‐Wise Flap Chord Flap Width Segment No. Position Z of Flap Span-Wise Flap Chord Length Flap Width Segment No. PositionCenter Z (m)of Flap SpanLength‐Wise (m) Flap LengthChord (mm) Flap(mm) Width Segment No. Center (m) Length (m) (mm) (mm) 1 Center0.277 (m) Length0.472 (m) Length297 (mm) (mm)54 121 0.2770.2770.749 0.4720.472 297297283 54 5451 32 0.7491.221 0.4720.472 283271 51 48 23 1.2210.749 0.4720.472 271283 48 51 344 1.6861.2211.686 0.4580.4720.458 258271258 45 4845 455 2.1441.6862.144 0.4580.458 243258243 43 4543 566 2.6022.1442.602 0.4580.458 226243226 40 4340 7 3.025 0.388 208 39 67 2.6023.025 0.4580.388 226208 4039 8 3.413 0.388 186 37 78 3.0253.413 0.388 208186 3937 8 3.413 0.388 186 37

Figure 2. CrossCross-section‐section of wing model with locations of pressure ports and spars. Figure 2. Cross‐section of wing model with locations of pressure ports and spars.

Appl. Sci. 2019, 9, x FOR PEER REVIEW 5 of 15

Table 2. Pressure port geometry. C represents chord length.

Position Position Normal Direction Port X/C Y/C (deg) Appl. Sci. 2019, 9,(leading 1461 edge) 0 0 180 5 of 15 u1 0.02 0.024 125 u2 Table 2. Pressure0.03 port geometry. C represents0.037 chord length. 117 u3 0.06 0.047 110 Position Position Normal Direction u4 Port 0.08 0.057 107 X/C Y/C (deg) u5 0.13 0.067 102 (leadingu6 edge)0.19 0 00.077 180 98 u1 0.02 0.024 125 u7 u20.24 0.03 0.0370.084 117 96 u8 u30.29 0.06 0.0470.088 110 94 u9 u40.42 0.08 0.0570.088 107 90 u10 u50.52 0.13 0.0670.084 102 87 u6 0.19 0.077 98 u11 u70.61 0.24 0.0840.077 96 84 u12 u80.70 0.29 0.0880.064 94 82 u13 u90.79 0.42 0.0880.047 90 80 u10 0.52 0.084 87 u14 0.87 0.034 79 u11 0.61 0.077 84 u15 u120.93 0.70 0.0640.020 82 77 b1 u130.07 0.79 − 0.0470.030 80 260 b2 u140.17 0.87 − 0.0340.040 79 267 u15 0.93 0.020 77 b3 0.29 −0.044 270 b1 0.07 −0.030 260 b4 b20.42 0.17 −−0.0400.040 267 273 b5 b30.56 0.29 −−0.0440.034 270 275 b6 b40.70 0.42 −−0.0400.020 273 276 b5 0.56 −0.034 275 b7 b60.79 0.70 −−0.0200.013 276 276 b8 b70.87 0.79 −−0.0130.0067 276 274 (trailing edge)b8 1 0.87 −0.00670 274 0 (main(trailing spar) edge)0.30–0.40 1 −0.043–0.091 0 ‐ 0 (main spar) 0.30–0.40 −0.043–0.091 - (aft spar)(aft spar) 0.74–0.76 0.74–0.76 −−0.017–0.0570.017–0.057 ‐ -

FigureFigure 3. 3.Pressure Pressure coefﬁcient coefficient distribution. distribution. Appl. Sci. 2019, 9, 1461 6 of 15 Appl.Appl. Sci. Sci. 2019 2019, 9, ,9 x, xFOR FOR PEER PEER REVIEW REVIEW 6 6of of 15 15

FigureFigureFigure 4. 4. 4.Lift Lift Lift coefﬁcientcoefficient coefficient versus versus versus AoA. AoA. AoA.

FigureFigureFigure5. 5. 5.Reﬂected Reflected Reflected spectraspectra spectra fromfrom from opticaloptical optical ﬁber fiber fiber sensors sensors sensors bonded bonded bonded along along along the the the main main main ( a( a)(a) and )and and aft aft aft ( b( b)(b) spars. )spars. spars.

2.2.2.2.2.2.Wind Wind Wind Tunnel Tunnel Tunnel Test Test Test WeWeWe applied applied applied aerodynamic aerodynamic aerodynamic loads loads loads to to to the the the wing wing wing model model model by by by wind wind wind tunnel tunnel tunnel tests. tests. tests. FigureFigure Figure1 1 (left)1 (left) (left) is is ais a a photographphotographphotograph of of of the the the wing wing wing in in thein the the closed-circuit closed closed-circuit-circuit wind wind wind tunnel. tunnel. tunnel. The The windThe wind wind tunnel tunnel tunnel test sectiontest test section section was 6.5was was m 6.5 high6.5 m m andhighhigh 5.5 and and m wide.5.5 5.5 m m In wide. wide. this study,In In this this we study, study, defined we we the defined defined wind anglethe the wind wind at the angle angle wing at rootat the the as wing wing the AoA,root root andas as the the changed AoA, AoA, theandand AoAchangedchanged by rotating the the AoA AoA the by by turntable. rotating rotating the Athe constantturn turntabletable wind. .A A constant constant speed of wind wind 14 m/s speed speed and of of a 14 dynamic14 m/s m/s and and pressure a a dynamic dynamic of 118.7pressure pressure Pa × 5 5 wereofof 118.7 118.7 used Pa Pa in were were the followingused used in in the the experiments. following following experiments. experiments. Reynolds number Reynolds Reynolds was number 2number10 .was was 2 2 × × 10 105. . AAA totaltotal total ofof of 586586 586 testtest test casescases cases werewere were conducted.conducted. conducted. TheThe The detailsdetails details ofof of thethe the testtest test casescases cases areare are presentedpresented presented inin in TableTab Tablele3 3.. 3. CombinationsCombinationsCombinations of of of flap flap flap angles a anglesngles were were were used used used for for for each each each AoA AoA AoA case case case for for for the the the individual individual individual test test test types. types. types. The The The flap flap flap angles angles angles werewerewere maintained maintained maintained for for for approximately approximately approximately 10 s 10 10for s s each for for each testeach case, test test case,and case, visual and and visual checks visual checks were checks conducted were were conducted conducted to ensure to to thatensureensure there that that was there there no vibration was was no no vibration on vibration the wing on on model. the the wing wing In this model model manner,. . In In this this the manner manner measurements, ,the the measur measur wereementsements performed were were ◦ withoutperformedperformed any without dynamicwithout any any effects. dynamic dynamic In the effects. effects. “aligned” In In the the test “aligned” “aligned” cases, all test eighttest cases, cases, flap all angles all eight eight were flap flap setangles angles to 0 were, were and set testsset to to ◦ ◦ were0°,0°, and and conducted tests tests were were for conducted conducted 15 AoAs rangingfor for 15 15 AoAs AoAs from ranging −ranging4.0–10.0 from fromwith − −4.04.0 1––10.0°10.0°intervals. with with 1° 1° In intervals. intervals. the “random” In In the the test“random” “random” cases, wetesttest aimed cases, cases, towe we apply aimed aimed 10 to to pseudo-random apply apply 10 10 pseudo pseudo- combinationsra-randomndom combinations combinations of flap angles of of flap flap for angles angles 29 AoA for for 29 29 cases AoA AoA ranging cases cases ranging ranging from ◦ ◦ −fromfrom4.0–10.0 − −4.04.0––10.0°with10.0° with 0.5with intervals.0.5° 0.5° intervals. intervals. In order In In order order to avoidto to avoid avoid large large large changes changes changes in in flapin flap flap angles angles angles in in in a a singlea single single test test test step step step thatthatthat could could could result result result in in in large large large amplitudes amplitudes amplitudes of of of vibrations vibrations vibrations during during during testing, testi testing,ng, constant constant constant intervals intervals intervals of of of the th the flape flap flap angle angle angle variationsvariationsvariations betweenbetween between eacheach each testtest test casecase case werewere were set,set, set, asas as presentedpresented presented inin in TableTable Table4 .4. 4. We We We aimed aimed aimed to to to minimize minimize minimize the the the flap flap flap angleangleangle variation variation variation rate, rate, rate, specifically specifically specifically at at at the the the wingwing wing tiptip tip (i.e.,(i.e., (i.e., FlapFlap Flap 8)8) 8) wherewhere where thethe the greatestgreatest greatest momentsmoments moments werewere were caused.caused. caused. FigureFigure 6 6 s howsshows examples examples of of the the Flaps Flaps 1 1, ,4, 4, and and 7 7 angles angles for for a a number number of of the the sequential sequential “random” “random” test test Appl. Sci. 2019, 9, 1461 7 of 15

Figure6 shows examples of the Flaps 1, 4, and 7 angles for a number of the sequential “random” test cases. The flap angles “rebounded” within the range −15–15◦. The bias remained in individual AoA cases (29 cases), although it was felt that the angle combinations were fully investigated across the 290 “random” case measurements. The primary aim of the “random” test cases was to obtain sufficient amounts of training data for the subsequent machine learning. In the “single” cases, a single flap was moved for eight AoAs ranging from −4.0–10.0◦ with 2.0◦ intervals. In the individual AoA cases, we moved a single flap through −15.0◦, −5.0◦, 5.0◦, and 15.0◦ while the other flaps remained at 0◦ degrees. This sequence was repeated for all eight flaps. It was anticipated that the “single” test cases would highlight the effect of individual flaps on the aerodynamic load distributions. In “controlled” cases, a flap angle combination was applied as presented in Table5. The flap angle combination was designed to reduce the moment while maintaining the lift force. The wing root tended to increase the lift force while the wing tip tended to decrease the moment. Measurements were conducted for 14 AoA cases ranging from −4.0–10.0◦ with 1.0◦ intervals. We did not conduct measurements at AoA = 4.0◦ as undamped wing vibration occurred. It was surmised that the vortex around the wing caused the resonance. The “controlled” cases were aimed at identifying the optimum load distribution control; therefore, it was regarded as the target data to be identified. The efficiency of the acquisition of the training data is important from the practical point of view. The “aligned”, “random” and “single” test cases were designed to enable us to acquire data with simple maneuvers. It was only needed to pre-set the angle increments for single or all flaps between each test case, and the data was obtained automatically in individual test cases. There was no overlapping of the cases. For each test case, the Bragg wavelengths, which correspond to the strains and pressures from which lift load distributions were calculated, were measured. We also recorded the AoA and eight flap angles.

Table 3. Test cases.

Measurements at Each AoA Type AoA (deg) (Total Measurements) 1 time Aligned −4.0, −3.0, −2.0, –10.0 (15 cases) (15 times) 10 times Random −4.0, −3.5, −3.0, –10.0 (29 cases) (290 times) 32 times Single −4.0, −2.0, 0.0, –10.0 (8 cases) (256 times) 1 time Controlled −4.0, −3.0, −2.0, –10.0 (14 cases *) (14 times) * We did not conduct measurements at AoA = 4.0◦.

Table 4. Flap angle variation rate for “random” test cases.

Flap No. Flap Angle Variation Rate (deg/test case) 1 9.8 2 7.2 3 5.7 4 4.8 5 3.6 6 2.6 7 1.9 8 1.2 Appl.Appl. Sci. Sci.2019 2019, 9,, 9 1461, x FOR PEER REVIEW 88 of of 15 15

FigureFigure 6. 6.Examples Examples of of ﬂap flap angles angles for for “random” “random” test test cases. cases.

Table 5. Flap angle combination for “controlled” test cases. Table 5. Flap angle combination for “controlled” test cases.

FlapFlap No. No. Flap Flap AngleAngle (deg) (deg) 11 15.015.0 22 15.015.0 3 13.0 43 13.0 0.8 5 4 −12.10.8 6 5 −−15.012.1 7 6 −−15.0 8 −15.0 7 −15.0 8 −15.0 2.3. Load Identification Method 2.3.For Load conceptual Identification introduction, Method we first assume a simple linear elastic problem. Non-uniform distributedFor conceptual lift loads acting introduction, on the eight we first wing assume segments a simple of the winglinear model, elastic a problem. load vector NonL,‐ induceuniform strainsdistributed at individual lift loads FBGs, acting strain on the vector eightε, whichwing segments is expressed of the as wing model, a load vector L, induce strains at individual FBGs, strain vector ε, which is expressed as ε = SL, (1) 𝛆𝐒𝐋, (1) where S is a transfer matrix. This is a direct problem where loads are input and strains are output. where S is a transfer matrix. This is a direct problem where loads are input and strains are output. When applied loads are to be identified from measured strains, it is inversely solved as When applied loads are to be identified from measured strains, it is inversely solved as + 𝐋𝐒L =S𝛆, ε,(2) (2)

+ wherewhereS +Sis is a a generalized generalized inverse inverse matrix matrix of ofS S. This. This solution solution tends tends to to be be unstable. unstable. In In the the neural neural network network + approach,approach, a a neural neural network network is is used used to to replace replaceS +Sas as 𝐋𝑁𝑁𝛆, (3) L = NN(ε), (3) where NN(x) expresses the output of a neural network when x was the input. In detail, an output of whereith neuronNN(x) in expresses lth layer, the ai(l), output is expressed of a neural by a weighted network whensum from x was the the previous input. In layer detail, and an a outputbias as of (l) ith neuron in lth layer, ai , is expressed by a weighted sum from the previous layer and a bias as 𝑎 𝜎 ∑ 𝑤 𝑎 𝑏 , (4) ! where bi(l) is the bias of the ith (neuronl) (l )in the (lthl−1 )layer(l−1 )and (wl)ji(l−1) is the weighted coefficient. The ai = σ ∑ wji aj + bi , (4) weight’s subscript ji represents the link fromj the jth neuron in the (l−1)th layer to the ith neuron in lth layer. The weighted sum with the bias is activated through the activation function σ. When a (l) (l−1) wheresimpleb ithreeis‐ thelayer bias neural of the networkith neuron is used, in the the ithlth element layer andof L, wLjii, is calculatedis the weighted from the coefﬁcient.strain input Theas weight’s subscript ji represents the link from the jth neuron in the (l−1)th layer to the ith neuron Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 15

𝐿 𝜎 𝑤 𝜎 𝑤 𝜀 𝑏 𝑏 . (5) Appl. Sci. 2019, 9, 1461 9 of 15 In this manner, the strain‐to‐load transfer can be represented by the neural network whose parameters are optimized through regression. This contributes to the stability of solutions [16]. In inaddition,lth layer. the The activation weighted functions sum with enable the biasnon‐ islinear activated transformation, through the which activation enhances function the applicabilityσ. When a simpleto a non three-layer‐linear problem. neural network is used, the ith element of L, Li, is calculated from the strain input as We created a neural network to calculate the lift load distribution. The architecture of the neural " " !# !# network, which was a feed‐forward neural( ) network (with) one( )hidden layer,( ) is depicted in Figure 7. L = σ(3) w 2 σ(2) w 1 ε + b 2 + b 3 . (5) The input layer had 68 neurons,i the∑ hiddenji layer∑ 12 neurons,kj k andj the outputi layer eight neurons, and j k i i they were fully‐connected. The number of neurons and layers were determined experimentally. For the inputIn this layer, manner, we used the data strain-to-load from 60 FBGs transfer bonded can along be represented the main and by aft the spars, neural as network well as the whose data parametersof the eight areflap optimized angles. It was through evident regression. that the strain This contributeshad a mechanical to the cause stability‐and of‐effect solutions (or rather [16]. Ineffect addition,‐and‐cause) the activation relationship functions and, enabletherefore, non-linear the FBG transformation, signals should which be used enhances for load the identification. applicability toTheoretically, a non-linear the problem. input of the strain information should be sufficient for the load identification as seen Wein createdEquations a neural (3) and network (5); however, to calculate it is the anticipated lift load distribution. that the strain The variations architecture would of the be neural less network,responsive which with wasrespect a feed-forward to local load neuralvariations network specifically with one at the hidden wing layer,root due is depicted to the high in Figurestiffness.7. TheIn order input to layer enhance had 68the neurons, responsiveness the hidden between layer the 12 neurons, input and and output the output of the layerneural eight network, neurons, the andflap theyangle were information fully-connected. was added The as number an input of in neurons this study. and layersTherefore, were the determined load identification experimentally. process For is theredefined input layer, as we used data from 60 FBGs bonded along the main and aft spars, as well as the data of the eight flap angles. It was evident that the strain had a mechanical cause-and-effect (or rather 𝐋𝑁𝑁𝛆, 𝛅 , (6) effect-and-cause) relationship and, therefore, the FBG signals should be used for load identification. Theoretically,where δ is the theeight input flap ofangles. the strain The FBG information signal, which should is the be Bragg sufficient wavelength for the load shift identificationfrom a reference as seencondition, in Equations is typically (3) converted and (5); however, to strain itvalues is anticipated by using a that wavelength the strain‐strain variations coefficient; would however, be less responsivethe physical with unit respect was irrelevant to local load in this variations instance specifically of machine at thelearning. wing rootTherefore, due to thewe highused stiffness.the raw InBragg order wavelength to enhance shifts the responsiveness in wavelength betweenunits. The the reference input and Bragg output wavelengths of the neural were network, the resting the state flap angleof the informationwing without was wind. added We as used an input sigmoid in this transfer study. functions Therefore, (hyperbolic the load identification tangent) in the process hidden is redefinedlayer and asa linear function in the output layer. The eight outputs corresponded to the lift load on the eight span‐wise wing segments. The Levenberg–MarquardtL = NNload(ε, δ), backpropagation algorithm [25] was (6) used as an optimizer, and the Nguyen–Widrow initialization method [26] was used to initialize δ whereweights isand the biases. eight flapThe angles.learning The parameters FBG signal, used which are identical is the Bragg to those wavelength used in a shift previous from astudy reference [25]. condition,Test cases is typically of “aligned”, converted “random”, to strain and values “single” by using were a used wavelength-strain as training data coefficient; to train the however, neural thenetwork. physical The unit “controlled” was irrelevant cases in were this instance excluded of so machine that they learning. could Therefore,be treated we as usednew conditions the raw Bragg for wavelengththe neural network shifts in after wavelength training. units. For the The training reference data, Bragg we used wavelengths “aligned”, were “single”, the resting and 80% state (232 of thecases) wing of the without “random” wind. test We cases used sigmoidfor optimization transfer functionsiterations. (hyperbolic The balance tangent) of the “random” in the hidden test layercases andwas aused linear for function validation in the purposes output in layer. order The to eight avoid outputs overfitting. corresponded The loss toof thethe liftvalidation load on data the eight was span-wisemonitored wingduring segments. the optimization The Levenberg–Marquardt iterations. When the backpropagation loss of the validation algorithm data [increased25] was used across as anfive optimizer, sequential and iterations, the Nguyen–Widrow the optimization initialization process was method stopped [26] and was usedthe weights to initialize and biases weights at and the biases.minimum The loss learning were parametersselected. used are identical to those used in a previous study [25].

Figure 7. Architecture of neural network for load identiﬁcation.identification.

Test cases of “aligned”, “random”, and “single” were used as training data to train the neural network. The “controlled” cases were excluded so that they could be treated as new conditions for the neural network after training. For the training data, we used “aligned”, “single”, and 80% (232 cases) of the “random” test cases for optimization iterations. The balance of the “random” test cases was used for validation purposes in order to avoid overﬁtting. The loss of the validation data was monitored Appl. Sci. 2019, 9, 1461 10 of 15 during the optimization iterations. When the loss of the validation data increased across ﬁve sequential iterations, the optimization process was stopped and the weights and biases at the minimum loss were selected.

3. Results: Load Identification Measurements were conducted for the planned test cases. As an example of the wing deformation, the measured strain distributions for AoA = −4◦ and 10◦ in the “controlled” cases are shown in Figure8. In order to better understand the mechanical implication of the data, we converted the measured Bragg wavelength shifts to strain values by using the Bragg wavelength-strain coefficient of 827 µε/nm. The coefficient was experimentally calibrated in advance. In general, the amplitudes of strain variations were greater for the main spar than the aft spar due to the thickness difference under wing deflection. The strain amplitude was smaller at the wing tip, and this was in good agreement with typical strain distributions of a cantilever beam. However, the strain amplitude decreased at the wing root because of the greater cross-sectional area as well as the 400-mm stainless-steel shaft inserted at the wing root that increased the stiffness. The maximum strain amplitude was observed at approximately 400 mm. In the case of AoA = −4◦, it exhibited tensile strains, which indicated that the wing model deflected downward. In the case of AoA = 10◦, it exhibited compressive strains as the wing model deflected upward. The neural network was trained using the measured data. Thereafter, we used the trained neural network to identify load distributions. Figure9 shows examples of the load identification results for the test cases used to train the neural network. We plotted an “aligned” test case where AoA = 0◦ and “single” test cases with AoA = −4◦ and Flap 2 at 15◦, and AoA = 4◦ and Flap 7 at −15◦. In the “aligned” test case, the load distribution was relatively uniform, however, in the “single” test cases, load variations were observed at the repositioned flaps. The positive flap angle of Flap 2 at AoA = −4◦ produced a lift increase, and the negative flap angle of Flap 7 at AoA = 4◦ produced a decrease in lift. The lift variations were observed locally at the wing segments with the repositioned flaps. The three plots also indicated that greater AoA values produced greater lift loads. The solid lines represent the estimated loads and the dashed lines the applied loads that were calculated from the pressure values, and there is good agreement between them. This indicated that the neural network training was satisfactorily completed and the neural network could be applied to the load identification problem. In order to examine the neural network performance for new conditions, we input the FBG and flap angle data of the “controlled” test cases, which were not used for the training. Figure 10 shows the load identification results for AoA = −4◦ and 10◦. It could be seen that for the “controlled” flap angles, the wing root was subjected to greater lift loads and the wing tip to smaller or negative lift loads. The total lift loads increased with increasing AoA. The solid lines represent the estimated loads and the dashed lines the applied loads. The results were in good agreement, which indicated that the neural network successfully learned to generalize unexperienced conditions. The errors appeared greater for the data not used for training, and thus for a quantitative comparison, we plotted the estimated loads with regard to the applied loads in Figure 11. The load values correspond to the lift loads on the individual wing segments. The black circles represent the results for the training data that includes the “aligned,” “random,” and “single” test cases. The red squares represent the results for other data, the “controlled” test cases. The error ranges were from −0.89–0.84 N and from −1.5–1.4 N for the training and other data, respectively. The standard deviations of the errors were 0.14 N and 0.57 N for the training and other data, respectively. The slight difference of the accuracy between the training and other data reflected that the neural network output better results for the data used for training. This also indicated that the load identification performance would be improved by adding load cases of interest to training data set. In the experiment, the out-of-plane forces of the wing model were identified as the lift loads. On the other hand, the in-plane forces were applied to the wing model, which were out of focus in this study. The applied in-plane forces were unavailable because the in-plane force consisted of the in-plane Appl. Sci. 2019, 9, 1461 11 of 15 component (X-component in Figure2) of the pressure values and the friction drag, which were difficult to directly and accurately measure simply by the equipped pressure ports. If the applied in-plane forcesAppl. Sci. were 2019 measured, 9, x FOR PEER and REVIEW the training data were prepared, the in-plane forces would potentially11 of be 15 identifiedAppl. Sci. 2019 through, 9, x FOR the PEER same REVIEW identification process. By identifying both the out-of-plane and in-plan11 of 15 Appl. Sci. 2019, 9, x FOR PEER REVIEW 11 of 15 forces of the wing, the lift and drag forces for aircraft would be estimated.

Figure 8. Measured strain distributions at AoA = −4° and 10° in “controlled” test cases. Figure 8. Measured strain distributions at AoA = −4° and 10° in “controlled” test cases. FigureFigure 8. Measured8. Measured strain strain distributions distributions at AoAat AoA = −= 4−◦4°and and 10 10°◦ in in “controlled” “controlled” test test cases. cases.

Figure 9. Load identification results in “aligned” test case (AoA = 0°) and “single” test case (AoA = ◦ Figure−Figure4° and 9. 9. 4°).Load Load Flap identiﬁcation identification 2 angle 15° resultswhen results AoA in in “aligned” “aligned”= −4°, and test testFlap case case 7 angle (AoA (AoA − =15° = 0 0°) )when and and “single”A “single”oA = 4°. test test case case (AoA (AoA = = −−Figure44°◦ andand 49.4°).◦ ).Load Flap identification 2 angleangle 1515°◦ when results AoA in =“aligned” −4°,4◦ ,and and Flaptest Flap case 7 7angle angle (AoA −−15° =15 0°)when◦ when and A “single”oA AoA = 4°. = 4 ◦test. case (AoA = −4° and 4°). Flap 2 angle 15° when AoA = −4°, and Flap 7 angle −15° when AoA = 4°.

◦ ◦ FigureFigure 10. 10.Load Load identiﬁcation identification results results in in “controlled” “controlled” test test cases cases with with AoA AoA = −= 4−4°and and 10 10°.. Figure 10. Load identification results in “controlled” test cases with AoA = −4° and 10°. Figure 10. Load identification results in “controlled” test cases with AoA = −4° and 10°. Appl. Sci. 2019, 9, 1461 12 of 15 Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 15

FigureFigure 11. 11.Comparison Comparison between between applied applied and and estimated estimated loads. loads.

4.4. Discussion: Discussion: AoA AoA Identiﬁcation Identification LoadsLoads were were identiﬁed identified by by solving solving the the mechanical mechanical problems problems as as in in Equations Equations (1)–(6). (1)–(6). At At the the same same time,time, the the lift lift load load distribution, distribution,L ,L is, is in in an an aerodynamic aerodynami problemc problem as as 퐋 = 푞퐂 (훅, 훼)퐀, (7) L = q퐋CL(δ, α) A, (7)

where q is the dynamic pressure, α is the AoA, CL is the lift coefficients, and A is the areas of the wing where q is the dynamic pressure, α is the AoA, C is the lift coefficients, and A is the areas of the wing segments. In the experiment, we could assumeL that the dynamic pressure q and the wing areas A segments. In the experiment, we could assume that the dynamic pressure q and the wing areas A were constant, and the CL was a function of the flap angles δ and the AoA α. The variables in the were constant, and the C was a function of the flap angles δ and the AoA α. The variables in the aerodynamic problem wereL the lift loads L, the flap angles δ, and the AoA α. Considering that the aerodynamic problem were the lift loads L, the flap angles δ, and the AoA α. Considering that the flap flap angles are observable and the lift loads are now identified, it was anticipated that the AoA could angles are observable and the lift loads are now identified, it was anticipated that the AoA could be be theoretically and practically solved by setting L and δ as inputs as theoretically and practically solved by setting L and δ as inputs as 훼 = 푁푁(퐋, 훅). (8) α = NN(L, δ). (8) In this case again, the regression nature of the neural network approach would enhance the stability of solutions. Furthermore, the non-linear transformation is beneficial specifically because the In this case again, the regression nature of the neural network approach would enhance the aerodynamic problems show non-linearity. stability of solutions. Furthermore, the non-linear transformation is beneficial specifically because the We designed a neural-network-based identification process for the AoA as shown in Figure 12. aerodynamic problems show non-linearity. In this design, we identify load distributions by using the 60 FBGs (strain) and flap angle data through We designed a neural-network-based identification process for the AoA as shown in Figure 12. the neural network for the load identification as discussed above, and thereafter we identify the AoA In this design, we identify load distributions by using the 60 FBGs (strain) and flap angle data through by using the identified load distribution and the flap angles through another neural network for the the neural network for the load identification as discussed above, and thereafter we identify the AoA AoA identification. This process requires only the FBG and flap angle data to be observed, which is by using the identified load distribution and the flap angles through another neural network for the a feasible assumption. AoA identification. This process requires only the FBG and flap angle data to be observed, which is a The neural network for the AoA identification had one hidden layer with 10 neurons, which was feasible assumption. determined experimentally. We set other properties and training parameters in the same way as the The neural network for the AoA identification had one hidden layer with 10 neurons, which was load identification. In order to train the neural network for the AoA identification, we prepared a determined experimentally. We set other properties and training parameters in the same way as the dataset of flap angles and estimated loads, which were the output from the neural network for the load identification. In order to train the neural network for the AoA identification, we prepared a load identification for the training test cases (“aligned,” “random,” and “single”). The other cases dataset of flap angles and estimated loads, which were the output from the neural network for the (“controlled”) were used to check the performance from the new conditions. load identification for the training test cases (“aligned,” “random,” and “single”). The other cases Figure 13 shows the results of the neural network AoA predictions. The good agreement (“controlled”) were used to check the performance from the new conditions. between the applied and estimated AoAs indicated the theoretical validation of the AoA Figure 13 shows the results of the neural network AoA predictions. The good agreement identification approach. The error ranges were from −0.78–0.46° and from −1.03–0.16° for the training between the applied and estimated AoAs indicated the theoretical validation of the AoA identification and other data, respectively. The standard deviations of the errors were 0.15° and 0.38° for the approach. The error ranges were from −0.78–0.46◦ and from −1.03–0.16◦ for the training and other training and other data, respectively. data, respectively. The standard deviations of the errors were 0.15◦ and 0.38◦ for the training and other Because of limitations of the experimental setup, we defined and observed the AoA as the data, respectively. turntable angle. If we could measure the profile of the AoA along the wing span, the neural network Appl. Sci. 2019, 9, 1461 13 of 15

Because of limitations of the experimental setup, we deﬁned and observed the AoA as the Appl. Sci. 2019, 9, x FOR PEER REVIEW 13 of 15 turntableAppl. Sci. 2019 angle., 9, x IfFOR we PEER could REVIEW measure the proﬁle of the AoA along the wing span, the neural network13 of 15 approach might be capable of identifying local AoAs, which would contribute to the development of approachapproach might might be be capable capable of of identifying identifying local local AoAs, AoAs, which which would would contribute contribute to to the the development development of of effective wing twist techniques. effectiveeffective wing wing twist twist techniques. techniques.

FigureFigure 12. 12. Design Design of of NN NN-based NN‐based-based identification identiﬁcation identification process process for for load load and and AoA. AoA.

Figure 13. Comparison between applied and estimated AoA. FigureFigure 13. 13.Comparison Comparison between between applied applied and and estimated estimated AoA. AoA.

5.5. Conclusions Conclusions WeWe integratedintegrated integrated thethe the opticaloptical optical fiberfiber fiber sensingsensing sensing techniquetechnique technique andand and thethe the neuralneural neura l networknetwork network approaches,approaches, approaches, and and investigatedinvestigated the the applicability applicability forfor for loadsloads loads and and AoAs AoAs identificationidentification identification ofof of wingwing wing structures.structures. structures. WeWe developeddeveloped developed aa a 3.6-m3.6 3.6‐m-m semi-spannedsemi semi‐spanned-spanned wing wing modelmodel model withwith with eighteight eight trailingtrailing trailing edgeedge edge flaps.flaps. flaps. Two Two optical optical fibersfibersfibers with with 30 30 FBGs FBGs were were bonded bonded on on the the upper upper side side of of the the wing wing model model along along the the main main main and and and aft aft aft spars. spars. spars. AerodynamicAerodynamic loadsloads loads werewere were appliedapplied applied toto to the the wing wing model model by by wind wind tunnel tunnel tests, tests, and and load load identification identification identification was was performedperformed by by using using the the neural neural network network approach. approach. The The FBG FBG data data and and eight eight flap flap flap angles angles were were input input to to thethe neural neural network, network ,and and the the estimated estimated load load distributions distributions on on the the the eight eight wing wing segments segments were were were output. output. TheThe loadload load distributionsdistributions distributions were were were successfully successfully successfully identified, identified, identified, even even even for for for data data data that that that were were were not not usednot used used for for training for training training of the of of neuralthethe neural neural network. network. network. The The errorThe error er rangeror range range was was fromwas from from−1.5–1.4 − 1.5–1.4−1.5– N1.4 with N N with with a standard a astandard standard deviation deviation deviation of 0.57 of of 0.57 N.0.57 N. N. WeWe solvedsolved solved thethe the mechanicalmechanical mechanical inverse inverse problem problem by by usingusing using the the neuralneural neural network.network. network. We We alsoalso also investigatedinvestigated investigated thethe application application of of the the neural neural network network to to solve solve the the aerodynamic aerodynamic problem problem to to identify identify the the AoA. AoA. In In this thi s process,process, load load distributions distributions were were firstfirst first identified,identified, identified, and and thereafter thereafter the the AoA AoA was was determined determined by by using using the the loadload distributions distributions and and the the flapflap flap angles angles throughthrough through another another neural neural network. network. This This process process required required only only thethe FBG FBG and and flapflap flap angle angle data data to to be be observed. observed. The The neural neural network network successfully successfully identified identified identified the the AoA AoA with with ◦ ◦ errorerror ranges ranges from from −− 1.03–0.46°−1.03–0.461.03–0.46° withwith with a a astandard standardstandard deviation deviationdeviation of ofof 0.38°. 0.380.38°. .

AuthorAuthor Contributions:Contributions: Contributions: D.W.D.W. D.W proposed proposed. proposed the the the idea, idea, idea, and and and conducted conducted conducted the the simulationthe simulation simulation and and analysis.and analysis. analysis. The The experiment The experiment experiment was conducted by D.W. and M.T. The article was written and completed by D.W., and checked by M.T. waswas conducted conducted by by D.W. D.W and. and M.T. M.T. The The article article was was written written and and completed completed by by D.W., D.W .and, and checked checked by by M.T. M.T. Funding: This research was funded by JSPS KAKENHI, grant number JP17K14878. Funding:Funding: This This research research was was funded funded by by JSPS JSPS KAKENHI, KAKENHI, grant grant number number JP17K14878. JP17K14878.

ConflictsConflicts of of Interest: Interest: The The authors authors declare declare no no conflict conflict of of interest. interest.

ReferencesReferences Appl. Sci. 2019, 9, 1461 14 of 15

Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Nguyen, N.; Ting, E.; Chaparro, D.; Drew, M.; Swei, S. Multi-objective flight control for drag minimization and load alleviation of high-aspect ratio flexible wing aircraft. In Proceedings of the 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Grapevine, TX, USA, 9–13 January 2017. [CrossRef] 2. Tang, D.; Dowell, E.H. Experimental and theoretical study on aeroelastic response of high-aspect-ratio wings. AIAA J. 2001, 39, 1430–1441. [CrossRef] 3. Tang, D.; Dowell, E.H. Experimental and theoretical study of gust response for high-aspect-ratio wing. AIAA J. 2002, 40, 419–429. [CrossRef] 4. Tang, D.; Grasch, A.; Dowell, E.H. Gust response for flexibly suspended high-aspect ratio wings. AIAA J. 2010, 48, 2430–2444. [CrossRef] 5. Mohamed, A.; Massey, K.; Watkins, S.; Clothier, R. The attitude control of fixed-wing MAVs in turbulent environments. Prog. Aerosp. Sci. 2014, 66, 37–48. [CrossRef] 6. Mohamed, A.; Clothier, R.; Watkins, S.; Sabatini, R.; Abdulrahim, M. Fixed-wing MAV attitude stability in atmospheric turbulence, part 1: Suitability of conventional sensors. Prog. Aerosp. Sci. 2014, 70, 69–82. [CrossRef] 7. Mohamed, A.; Watkins, S.; Clothier, R.; Abdulrahim, M.; Massey, K.; Sabatini, R. Fixed-wing MAV attitude stability in atmospheric turbulence, part 2: Investigating biologically-inspired sensors. Prog. Aerosp. Sci. 2014, 71, 1–13. [CrossRef] 8. Tarantola, A. Inverse Problem Theory and Methods for Model Parameter Estimation; SIAM: Philadelphia, PA, USA, 2005; ISBN 978-0898715729. 9. Hansen, P.C. Discrete Inverse Problems: Insight and Algorithms; SIAM: Philadelphia, PA, USA, 2010; ISBN 978-0898716962. 10. Aster, R.C.; Borchers, B.; Thurber, C.H. Parameter Estimation and Inverse Problems, 2nd ed.; Academic Press: Cambridge, MA, USA, 2012; ISBN 978-0123850485. 11. Shkarayev, S.; Krashantisa, R.; Tessler, A. An inverse interpolation method utilizing in-flight strain measurements for determining loads and structural response of aerospace vehicles. In Proceedings of the 3rd International Workshop on Structural Health Monitoring, Stanford, CA, USA, 12–14 September 2001. 12. Coates, C.W.; Thamburaj, P. Inverse method using finite strain measurement to determine flight load distribution functions. J. Aircr. 2008, 45, 366–370. [CrossRef] 13. Nakamura, T.; Igawa, H.; Kanda, A. Inverse identification of continuously distributed loads using strain data. Aerosp. Sci. Technol. 2012, 23, 75–84. [CrossRef] 14. Cao, X.; Sugiyama, Y.; Mitsui, Y. Application of artificial neural networks to load identification. Comput. Struct. 1998, 69, 63–78. [CrossRef] 15. Trivailo, P.M.; Carn, C.L. The inverse determination of aerodynamic loading from structural response data using neural networks. Inverse Prob. Sci. Eng. 2006, 14, 379–395. [CrossRef] 16. Wada, D.; Sugimoto, Y.; Murayama, H.; Igawa, H.; Nakamura, T. Investigation of inverse analysis approach and neural network approach for distributed load identification using distributed strains. Trans. Jpn. Soc. Aeronaut. Space Soc. 2019, 62. 17. Carpenter, T.J.; Albertani, R. Aerodynamic load estimation from virtual strain sensors for a pliant membrane wing. AIAA J. 2015, 53, 2069–2079. [CrossRef] 18. Wada, D.; Igawa, H.; Kasai, T. Vibration monitoring of a helicopter blade model using the optical fiber distributed strain sensing technique. Appl. Opt. 2016, 55, 6953–6959. [CrossRef][PubMed] 19. Wada, D.; Igawa, H.; Tamayama, M.; Kasai, T.; Arizono, H.; Murayama, H. Flight demonstration of aircraft wing monitoring using optical fiber distributed sensing system. Smart Mater. Struct. 2019, 28, 055007. [CrossRef] 20. Pak, C. Wing shape sensing from measured strain. AIAA J. 2016, 54, 1064–1073. [CrossRef] 21. Kim, J.; Park, Y.; Kum, Y.; Shrestha, P.; Kim, C. Aircraft health and usage monitoring system for in-flight strain measurement of a wing structure. Smart Mater. Struct. 2015, 24, 105003. [CrossRef] Appl. Sci. 2019, 9, 1461 15 of 15

22. Kressel, I.; Balter, J.; Mashiach, N.; Sovran, I.; Shapira, O.; Shemesh, N.Y.; Glamm, B.; Dvorjetski, A.; Yehoshua, T.; Tur, M. High speed, in-ﬂight structural health monitoring system for medium altitude long endurance unmanned air vehicle. In Proceedings of the 7th European Workshop on Structural Health Monitoring, Nantes, France, 8–11 July 2014. 23. Lance, R.; Allen, R.P., Jr.; Anthony, P.; Patrick, C.; Harmory, P.; Pena, F. NASA Armstrong Flight Research Center (AFRC). Fiber Optic Sensing System (FOSS) Technology; NASA Technical Reports Server: Edwards, CA, USA, 2014. 24. Kersey, A.D.; Davis, M.A.; Patrick, H.J.; LeBlanc, M.; Koo, K.P.; Askins, C.G.; Putnam, M.A.; Friebele, E.J. Fiber grating sensors. J. Lightwave Technol. 1997, 15, 1442–1463. [CrossRef] 25. Hagan, M.T.; Menhaj, M.B. Training feedforward networks with the Marquardt algorithm. IEEE Trans. Neural Netw. 1994, 5, 989–993. [CrossRef][PubMed] 26. Nguyen, D.; Widrow, B. Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights. In Proceedings of the 1990 IJCNN International Joint Conference on Neural Networks, San Diego, CA, USA, 17–21 June 1990.

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