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Bayesian Sensitivity Analysis of Flight Parameters in a Hard-Landing Analysis Process

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This is a repository copy of Bayesian Sensitivity Analysis of Flight Parameters in a Hard-Landing Analysis Process. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/121812/ Version: Accepted Version Article: Sartor, P., Becker, W., Worden, K. orcid.org/0000-0002-1035-238X et al. (2 more authors) (2016) Bayesian Sensitivity Analysis of Flight Parameters in a Hard-Landing Analysis Process. Journal of Aircraft, 53 (5). pp. 1317-1331. ISSN 0021-8669 https://doi.org/10.2514/1.C032757 Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ Sartor, P. N., Becker, W., Worden, K., Schmidt, R. K., & Bond, D. (2016). Bayesian Sensitivity Analysis of Flight Parameters in a Hard Landing Analysis Process. Journal of Aircraft, 53(5), 1317-1331. DOI: 10.2514/1.C032757 Peer reviewed version License (if available): CC BY-NC Link to published version (if available): 10.2514/1.C032757 Link to publication record in Explore Bristol Research PDF-document This is the author accepted manuscript (AAM). The final published version (version of record) is available online via AIAA at http://arc.aiaa.org/doi/abs/10.2514/1.C032757. Please refer to any applicable terms of use of the publisher. University of Bristol - Explore Bristol Research General rights This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms.html Submitted to Journal of Aircraft for Review Bayesian Sensitivity Analysis of Flight Parameters in a Hard Landing Analysis Process Journal:For Journal Peer of Aircraft Review Manuscript ID 2013-12-C032757.R2 Manuscript Type: Full aper Date Submitted by the Author: n/a Complete List of Authors: Sartor, ia; ,niversity of .ristol, Department of Aerospace En0ineerin0 .ec1er, 2illiam; European Commission, Joint Research Centre 2orden, 3eith; ,niversity of Sheffield, Department of Mechanical En0ineerin Schmidt, R.; Messier-.u0atti-Dowty, A350 ro0ramme Chief En0ineer .ond, David; Messier-.u0atti-Dowty, 5ice resident En0ineerin0 01700 Landin0 Dynamics 8 00000 AIRCRAFT TEC9NOLOGY, Sub6ect Inde7 Cate0ory: CON5ENTIONAL, STOL/5TOL, 02800 Simulation 8 00000 AIRCRAFT TEC9NOLOGY, CON5ENTIONAL, STOL/5TOL Note: The followin0 files were submitted by the author alon0 with the article. You may review these files online, if you wish. Acceptance for publication will be based solely on the content of the article. AIAA_Late7_files_ ia_Sartor18 November 2015.7z Review copy- Do not distribute Page 1 of 40 Submitted to Journal of Aircraft for Review 1 2 Bayesian Sensitivity Analysis of Flight Parameters 3 4 5 in a Hard Landing Analysis Process 6 7 8 Pia Sartor1 9 10 Department of Aerospace Engineering, University of Bristol, 11 12 Queens Building, University Walk, Bristol, 13 14 BS8 1TR, UK, Email: [email protected] 15 16 17 William Becker2 18 Econometrics and Applied Statistics, European Commission 19 20 For- Joint Research Peer Centre, TPReview 361, 21027 Ispra, Italy 21 22 23 Keith Worden3 24 Department of Mechanical Engineering, 25 26 University of Sheeld, Mappin Street, Sheeld, S1 3JD, UK 27 28 29 4 5 30 R. Kyle Schmidt and David Bond 31 Messier-Bugatti-Dowty, Cheltenham Road East, Gloucester, GL2 9QH, UK 32 33 34 35 A Flight Parameter Sensor Simulation (FPSS) model was developed to assess the 36 37 conservatism of the landing gear component loads calculated using a typical hard land- 38 39 ing analysis process. Conservatism exists due to factors of safety that are incorporated 40 41 into any hard landing analysis process to account for uncertainty in the measurement 42 43 of certain ight parameters. The FPSS model consists of: (1) an aircraft and land- 44 45 ing gear dynamic model to determine the `actual' landing gear loads during a hard 46 47 landing; (2) an aircraft sensor and data acquisition model to represent the aircraft sen- 48 49 sors and ight data recorder systems to investigate the eect of signal processing on 50 51 52 53 1 Lecturer 54 2 Postdoctorial Researcher 55 3 Professor 4 56 Programme Chief Engineer 5 Vice President Engineering 57 58 59 60 1 Review copy- Do not distribute Submitted to Journal of Aircraft for Review Page 2 of 40 1 the ight parameters; (3) an automated hard landing analysis process, representative 2 3 of that used by airframe and equipment manufacturers, to determine the `simulated' 4 5 6 landing gear loads. Using a technique of Bayesian sensitivity analysis, a number of 7 8 ight parameters are varied in the FPSS model to gain an understanding of the sen- 9 10 sitivity of the dierence between `actual' and `simulated' loads to the individual ight 11 12 parameters in symmetric and asymmetric, two-point landings. This study shows that 13 14 the error can be reduced by learning the true value of the following ight parameters: 15 16 longitudinal tire-runway friction coecient, aircraft vertical acceleration (related to 17 18 vertical descent velocity), lateral acceleration (related to lateral velocity), Euler roll 19 20 angle, mass, centreFor of gravity Peer position and Review main landing gear tire type. It was also 21 22 shown that due to the modelling techniques used, shock absorber servicing state and 23 24 tire pressure do not contribute signicantly to the error. 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 2 Review copy- Do not distribute Page 3 of 40 Submitted to Journal of Aircraft for Review 1 Nomenclature 2 3 CG = Aircraft Centre of Gravity 4 5 CS = Certication Specication 6 7 DOE = Design of Experiments 8 9 FAR = Federal Aviation Regulations 10 11 FDIU = Flight Data Interface Unit 12 13 FDR = Flight Data Recorder 14 15 FPSS = Flight Parameter Sensor Simulation 16 17 GEM-SA = Gaussian Emulation Machine for Sensitivity Analysis 18 19 GP = Gaussian Process 20 For Peer Review 21 mass = Aircraft mass 22 23 MEI = Main Eects Index 24 25 MLG = Main Landing Gear 26 27 28 MSE = Normalised Mean Square Error 29 30 Port SA = Port main landing gear servicing state 31 32 Starboard SA = Starboard main landing gear servicing state 33 34 TEI = Total Eects Index 35 36 tire = Tire type 37 38 tire press = Tire pressure 39 = Aircraft longitudinal velocity 40 VAx 41 42 = Aircraft lateral velocity VAy 43 44 = Aircraft vertical descent velocity VAz 45 46 VRTG = Aircraft vertical acceleration 47 48 LAT G = Aircraft lateral acceleration 49 50 Factual = `Actual' landing gear output data 51 52 F = `Simulated' landing gear output data 53 simulated 54 θ = Aircraft Euler pitch angle 55 56 φ = Aircraft Euler roll angle 57 58 ψ = Aircraft Euler yaw angle 59 60 3 Review copy- Do not distribute Submitted to Journal of Aircraft for Review Page 4 of 40 1 2 µlong = Longitudinal tire-runway friction coecient 3 4 µlat = Lateral tire-runway friction coecient 5 6 σ2 = Variance of the `actual' landing gear output data 7 Factual 8 σ2 = Variance of the `simulated' landing gear output data 9 Fsimulated 10 B = Roughness coecients for the GP covariance function 11 12 c(·, ·) = Covariance function of the GP 13 14 c∗ , = Posterior covariance function of the GP 15 (· ·) 16 d = Number of model input parameters 17 18 cov = Covariance 19 20 = ExpectedFor value Peer Review 21 E(·) 22 23 h(·) = Regression function of the GP 24 25 m(·) = Mean function 26 ∗ 27 m (·) = Posterior mean function 28 29 n = Number of training data points 30 31 p(·) = Multivariate probability distribution 32 33 σ2 = Scaling factor of the GP covariance function 34 35 Si = Scaled main eect index of input xi 36 37 STi = Scaled total eect index of input xi 38 39 t(x) = Covariance of x with all training data 40 41 Vi = Unscaled main eect index of input xi 42 43 VTi = Unscaled total eect index of input xi 44 45 var = Variance 46 47 w = Regression function coecients 48 49 x = Model input 50 51 X = Uncertain model input 52 53 y = Model output 54 55 Y = Uncertain model output 56 57 = Main eect 58 z(xi) 59 = First order interaction 60 z(xi,j) 4 Review copy- Do not distribute Page 5 of 40 Submitted to Journal of Aircraft for Review 1 2 3 4 5 I. Introduction 6 7 A static structural overload occurs when a landing gear exceeds its material yield point in any 8 9 location. A common aircraft operational occurrence which may result in a landing gear overload 10 11 is a hard landing. A hard landing is dened by the regulatory authorities in EASA Certication 12 13 Specication (CS) 25 and Federal Aviation Regulations (FAR) 25 as a landing with a limit vertical 14 15 descent velocity exceeding 10 ft/s at the design landing weight [1, 2].
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