Skip to main content
Skip to article control options
No AccessRegular Articles

Sparse Pressure-Based Machine Learning Approach for Aerodynamic Loads Estimation During Gust Encounters

Published Online:https://doi.org/10.2514/1.J063263

Estimation of aerodynamic loads is a significant challenge in complex gusty environments due to the associated complexities of flow separation and strong nonlinearities. In this study, we explore the practical feasibility of multilayer perceptron (MLP) for estimating aerodynamic loads in gusts, when confounded by noisy and spatially distributed sparse surface pressure measurements. As a demonstration, a nonslender delta wing experiencing various gusts with different initial and final conditions is considered. Time-resolved lift and drag, and spatially distributed sparse surface pressure measurements are collected in a towing-tank facility. The nonlinear MLP model is used to estimate gust scenarios that are unseen in training progress. A filtering process allows us to examine the fluctuation of the dynamic response from the pressure measurements on the MLP. Estimation results show that the MLP model is able to capture the relationship between surface pressure and aerodynamic loads with a minimum quantity of learning samples, delivering accurate estimations, despite the slightly large errors for the cases at the boundary of the datasets. The results also indicate that the dynamic response of the pressure measurements has an influence on the learning of MLP. We further utilize gradient maps to perform a sensitivity analysis, so as to evaluate the contribution of the pressure data to the estimation of gust loads. This study reveals the significant contribution of the sensors located near the leading edge and at the nose of the delta wing. Our findings suggest the potential for an efficient sensor deployment strategy in data-driven aerodynamic load estimation.

References

  • [1] Lamar J. E., “Recent Studies of Subsonic Vortex Lift Including Parameters Affecting Stable Leading-Edge Vortex Flow,” Journal of Aircraft, Vol. 14, No. 12, 1977, pp. 1205–1211. https://doi.org/10.2514/3.58916 LinkGoogle Scholar

  • [2] Wu J., Vakili A. and Wu J., “Review of the Physics of Enhancing Vortex Lift by Unsteady Excitation,” Progress in Aerospace Sciences, Vol. 28, No. 2, 1991, pp. 73–131. https://doi.org/10.1016/0376-0421(91)90001-K CrossrefGoogle Scholar

  • [3] Zhao Z., Huang W., Yan L., Zhang T., Li S. and Wei F., “Low Speed Aerodynamic Performance Analysis of Vortex Lift Waveriders with a Wide-Speed Range,” Acta Astronautica, Vol. 161, Aug. 2019, pp. 209–221. https://doi.org/10.1016/j.actaastro.2019.05.029 CrossrefGoogle Scholar

  • [4] Djojodihardjo R. H. and Widnall S. E., “A Numerical Method for the Calculation of Nonlinear, Unsteady Lifting Potential Flow Problems,” AIAA Journal, Vol. 7, No. 10, 1969, pp. 2001–2009. https://doi.org/10.2514/3.5494 LinkGoogle Scholar

  • [5] Frampton K. D., Clark R. L. and Dowell E. H., “State-Space Modeling for Aeroelastic Panels with Linearized Potential Flow Aerodynamic Loading,” Journal of Aircraft, Vol. 33, No. 4, 1996, pp. 816–822. https://doi.org/10.2514/3.47019 LinkGoogle Scholar

  • [6] Kier T. M., “Comparing Different Potential Flow Methods for Unsteady Aerodynamic Modelling of a Flutter Demonstrator Aircraft,” AIAA SciTech 2023 Forum, AIAA Paper 2023-0177, 2023. https://doi.org/10.2514/6.2023-0177 LinkGoogle Scholar

  • [7] Polhamus E. C., “A Concept of the Vortex Lift of Sharp-Edge Delta Wings Based on a Leading-Edge-Suction Analogy,” NASA TN d-3767, 1966. Google Scholar

  • [8] Hemati M. S., Dawson S. T. and Rowley C. W., “Parameter-Varying Aerodynamics Models for Aggressive Pitching-Response Prediction,” AIAA Journal, Vol. 55, No. 3, 2017, pp. 693–701. https://doi.org/10.2514/1.J055193 LinkGoogle Scholar

  • [9] Engelmann J., Hanke W., Mogdans J. and Bleckmann H., “Hydrodynamic Stimuli and the Fish Lateral Line,” Nature, Vol. 408, No. 6808, 2000, pp. 51–52. https://doi.org/10.1038/35040706 Google Scholar

  • [10] Mogdans J., “Sensory Ecology of the Fish Lateral-Line System: Morphological and Physiological Adaptations for the Perception of Hydrodynamic Stimuli,” Journal of Fish Biology, Vol. 95, No. 1, 2019, pp. 53–72. https://doi.org/10.1111/jfb.13966 Google Scholar

  • [11] Cheney J. A., Stevenson J. P., Durston N. E., Song J., Usherwood J. R., Bomphrey R. J. and Windsor S. P., “Bird Wings Act as a Suspension System that Rejects Gusts,” Proceedings of the Royal Society B, Vol. 287, No. 1937, 2020, Paper 2020-1748. https://doi.org/10.1098/rspb.2020.1748 Google Scholar

  • [12] Feo T. J. and Prum R. O., “Theoretical Morphology and Development of Flight Feather Vane Asymmetry with Experimental Tests in Parrots,” Journal of Experimental Zoology Part B: Molecular and Developmental Evolution, Vol. 322, No. 4, 2014, pp. 240–255. https://doi.org/10.1002/jez.b.22573 Google Scholar

  • [13] Duriez T., Brunton S. L. and Noack B. R., Machine Learning Control-Taming Nonlinear Dynamics and Turbulence, Vol. 116, Springer, Berlin, 2017, pp. 1–10. Google Scholar

  • [14] Brunton S. and Kutz J., Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control, Cambridge Univ. Press, Cambridge, MA, 2019, pp. 264–274. Google Scholar

  • [15] Fukami K., Fukagata K. and Taira K., “Assessment of Supervised Machine Learning Methods for Fluid Flows,” Theoretical and Computational Fluid Dynamics, Vol. 34, No. 4, 2020, pp. 497–519. https://doi.org/10.1007/s00162-020-00518-y CrossrefGoogle Scholar

  • [16] Brunton S. L., Noack B. R. and Koumoutsakos P., “Machine Learning for Fluid Mechanics,” Annual Review of Fluid Mechanics, Vol. 52, No. 1, 2020, pp. 477–508. https://doi.org/10.1146/annurev-fluid-010719-060214 CrossrefGoogle Scholar

  • [17] Fukami K., Fukagata K. and Taira K., “Machine-Learning-Based Spatio-Temporal Super Resolution Reconstruction of Turbulent Flows,” Journal of Fluid Mechanics, Vol. 909, Feb. 2021, p. A9. https://doi.org/10.1017/jfm.2020.948 CrossrefGoogle Scholar

  • [18] Kim H., Kim J., Won S. and Lee C., “Unsupervised Deep Learning for Super-Resolution Reconstruction of Turbulence,” Journal of Fluid Mechanics, Vol. 910, March 2021, p. A29. https://doi.org/10.1017/jfm.2020.1028 CrossrefGoogle Scholar

  • [19] Brunton S. L., Hemati M. S. and Taira K., “Special Issue on Machine Learning and Data-Driven Methods in Fluid Dynamics,” Theoretical and Computational Fluid Dynamics, Vol. 34, No. 4, 2020, pp. 333–337. https://doi.org/10.1007/s00162-020-00542-y CrossrefGoogle Scholar

  • [20] Brenner M., Eldredge J. and Freund J., “Perspective on Machine Learning for Advancing Fluid Mechanics,” Physical Review Fluids, Vol. 4, No. 10, 2019, Paper 100501. https://doi.org/10.1103/PhysRevFluids.4.100501 Google Scholar

  • [21] Yu J. and Hesthaven J. S., “Flowfield Reconstruction Method Using Artificial Neural Network,” AIAA Journal, Vol. 57, No. 2, 2019, pp. 482–498. https://doi.org/10.2514/1.J057108 LinkGoogle Scholar

  • [22] Erichson N. B., Mathelin L., Yao Z., Brunton S. L., Mahoney M. W. and Kutz J. N., “Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors,” Proceedings of the Royal Society A, Vol. 476, No. 2238, 2020, Paper 2020-0097. https://doi.org/10.1098/rspa.2020.0097 Google Scholar

  • [23] Li B., Yang Z., Zhang X., He G., Deng B.-Q. and Shen L., “Using Machine Learning to Detect the Turbulent Region in Flow Past a Circular Cylinder,” Journal of Fluid Mechanics, Vol. 905, Dec. 2020, p. A10. https://doi.org/10.1017/jfm.2020.725 CrossrefGoogle Scholar

  • [24] Ribeiro B. L. R. and Franck J. A., “Machine Learning to Classify Vortex Wakes of Energy Harvesting Oscillating Foils,” AIAA Journal, Vol. 61, No. 3, 2023, pp. 1281–1291. https://doi.org/10.2514/1.J062091 LinkGoogle Scholar

  • [25] Lee H., Simone N., Su Y., Zhu Y., Ribeiro B. L. R., Franck J. A. and Breuer K., “Leading Edge Vortex Formation and Wake Trajectory: Synthesizing Measurements, Analysis, and Machine Learning,” Physical Review Fluids, Vol. 7, No. 7, 2022, Paper 074704. https://doi.org/10.1103/PhysRevFluids.7.074704 Google Scholar

  • [26] Rumelhart D. E., Hinton G. E. and Williams R. J., “Learning Representations by Back-Propagating Errors,” Nature, Vol. 323, No. 6088, 1986, pp. 533–536. https://doi.org/10.1038/323533a0 CrossrefGoogle Scholar

  • [27] Linse D. J. and Stengel R. F., “Identification of Aerodynamic Coefficients Using Computational Neural Networks,” Journal of Guidance, Control, and Dynamics, Vol. 16, No. 6, 1993, pp. 1018–1025. https://doi.org/10.2514/3.21122 LinkGoogle Scholar

  • [28] Schreck S. J., Faller W. E. and Luttges M. W., “Neural Network Prediction of Three-Dimensional Unsteady Separated Flowfields,” Journal of Aircraft, Vol. 32, No. 1, 1995, pp. 178–185. https://doi.org/10.2514/3.46698 LinkGoogle Scholar

  • [29] Faller W. E. and Schreck S. J., “Neural Networks: Applications and Opportunities in Aeronautics,” Progress in Aerospace Sciences, Vol. 32, No. 5, 1996, pp. 433–456. https://doi.org/10.1016/0376-0421(95)00011-9 CrossrefGoogle Scholar

  • [30] Ling J., Kurzawski A. and Templeton J., “Reynolds Averaged Turbulence Modelling Using Deep Neural Networks with Embedded Invariance,” Journal of Fluid Mechanics, Vol. 807, Nov. 2016, pp. 155–166. https://doi.org/10.1017/jfm.2016.615 CrossrefGoogle Scholar

  • [31] Lui H. F. and Wolf W. R., “Construction of Reduced-Order Models for Fluid Flows Using Deep Feedforward Neural Networks,” Journal of Fluid Mechanics, Vol. 872, Aug. 2019, pp. 963–994. https://doi.org/10.1017/jfm.2019.358 CrossrefGoogle Scholar

  • [32] Burelle L. A., Yang W., Kaiser F. and Rival D. E., “Exploring the Signature of Distributed Pressure Measurements on Non-Slender Delta Wings During Axial and Vertical Gusts,” Physics of Fluids, Vol. 32, No. 11, 2020, Paper 115110. https://doi.org/10.1063/5.0025860 CrossrefGoogle Scholar

  • [33] Iacobello G., Kaiser F. and Rival D. E., “Load Estimation in Unsteady Flows from Sparse Pressure Measurements: Application of Transition Networks to Experimental Data,” Physics of Fluids, Vol. 34, No. 2, 2022, Paper 025105. https://doi.org/10.1063/5.0076731 Google Scholar

  • [34] He X. and Williams D. R., “Pressure Feedback Control of Aerodynamic Loads on a Delta Wing in Transverse Gusts,” AIAA Journal, Vol. 61, No. 4, 2023, pp. 1659–1674. https://doi.org/10.2514/1.J062442 LinkGoogle Scholar

  • [35] Breiman L., “Random Forests,” Machine Learning, Vol. 45, No. 1, 2001, pp. 5–32. https://doi.org/10.1023/A:1010933404324 CrossrefGoogle Scholar

  • [36] Smola A. J. and Schölkopf B., “A Tutorial on Support Vector Regression,” Statistics and Computing, Vol. 14, No. 3, 2004, pp. 199–222. https://doi.org/10.1023/B:STCO.0000035301.49549.88 CrossrefGoogle Scholar

  • [37] Williams R. J. and Zipser D., “A Learning Algorithm for Continually Running Fully Recurrent Neural Networks,” Neural Computation, Vol. 1, No. 2, 1989, pp. 270–280. https://doi.org/10.1162/neco.1989.1.2.270 CrossrefGoogle Scholar

  • [38] LeCun Y., Bottou L., Bengio Y. and Haffner P., “Gradient-Based Learning Applied to Document Recognition,” Proceedings of the IEEE, Vol. 86, No. 11, 1998, pp. 2278–2324. https://doi.org/10.1109/5.726791 CrossrefGoogle Scholar

  • [39] Jain P., Choudhury A., Dutta P., Kalita K. and Barsocchi P., “Random Forest Regression-Based Machine Learning Model for Accurate Estimation of Fluid Flow in Curved Pipes,” Processes, Vol. 9, No. 11, 2021, p. 2095. https://doi.org/10.3390/pr9112095 Google Scholar

  • [40] Wang Q., Qian W. and He K., “Unsteady Aerodynamic Modeling at High Angles of Attack Using Support Vector Machines,” Chinese Journal of Aeronautics, Vol. 28, No. 3, 2015, pp. 659–668. https://doi.org/10.1016/j.cja.2015.03.010 CrossrefGoogle Scholar

  • [41] Deng Z., Chen Y., Liu Y. and Kim K. C., “Time-Resolved Turbulent Velocity Field Reconstruction Using a Long Short-Term Memory (LSTM)-Based Artificial Intelligence Framework,” Physics of Fluids, Vol. 31, No. 7, 2019, Paper 075108. https://doi.org/10.1063/1.5111558 CrossrefGoogle Scholar

  • [42] Chen X., Wang H., Zhan J., Chen K. and Cao Y., “Unsteady Aerodynamic Modeling Based on Recurrent Neural Network,” Aerodynamic Research & Experiment, Vol. 32, No. 1, 2020, p. 101. https://doi.org/10.12050/are20200107 Google Scholar

  • [43] Jones A. R., Cetiner O. and Smith M. J., “Physics and Modeling of Large Flow Disturbances: Discrete Gust Encounters for Modern Air Vehicles,” Annual Review of Fluid Mechanics, Vol. 54, No. 1, 2022, pp. 469–493. https://doi.org/10.1146/annurev-fluid-031621-085520 CrossrefGoogle Scholar

  • [44] Mangalam S. M., “Phenomena-Based Real-Time Aerodynamic Measurement System (PRAMS),” 2003 IEEE Aerospace Conference Proceedings (Cat. No. 03TH8652), Vol. 7, IEEE, New York, 2003, pp. 3347–3356. https://doi.org/10.1109/AERO.2003.1234177 Google Scholar

  • [45] Mangalam A., Mangalam S. and Flick P., “Unsteady Aerodynamic Observables for Gust Load Alleviation,” 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 16th AIAA/ASME/AHS Adaptive Structures Conference, 10th AIAA Non-Deterministic Approaches Conference, 9th AIAA Gossamer Spacecraft Forum, 4th AIAA Multidisciplinary Design Optimization Specialists Conference, AIAA Paper 2008-1725, 2008. https://doi.org/10.2514/6.2008-1725 AbstractGoogle Scholar

  • [46] Hoblit F. M., Gust Loads on Aircraft: Concepts and Applications, AIAA Education Series, AIAA, Reston, VA, 1988, pp. 7–20. Google Scholar

  • [47] Magar K. T., Reich G. W., Kondash C., Slinker K., Pankonien A. M., Baur J. W. and Smyers B., “Aerodynamic Parameters from Distributed Heterogeneous CNT Hair Sensors with a Feedforward Neural Network,” Bioinspiration & Biomimetics, Vol. 11, No. 6, 2016, Paper 066006. https://doi.org/10.1088/1748-3190/11/6/066006 CrossrefGoogle Scholar

  • [48] Samy I., Postlethwaite I., Gu D.-W. and Green J., “Neural-Network-Based Flush Air Data Sensing System Demonstrated on a Mini Air Vehicle,” Journal of Aircraft, Vol. 47, No. 1, 2010, pp. 18–31. https://doi.org/10.2514/1.44157 LinkGoogle Scholar

  • [49] Shen H., Xu Y. and Remeikas C., “Pitch Control of a Micro Air Vehicle with Micropressure Sensors,” Journal of Aircraft, Vol. 50, No. 1, 2013, pp. 239–248. https://doi.org/10.2514/1.C031894 LinkGoogle Scholar

  • [50] Thompson K., Xu Y. and Dickinson B. T., “Aerodynamic Moment Model Calibration from Distributed Pressure Arrays,” Journal of Aircraft, Vol. 54, No. 2, 2017, pp. 716–723. https://doi.org/10.2514/1.C033898 LinkGoogle Scholar

  • [51] Hou W., Darakananda D. and Eldredge J. D., “Machine-Learning-Based Detection of Aerodynamic Disturbances Using Surface Pressure Measurements,” AIAA Journal, Vol. 57, No. 12, 2019, pp. 5079–5093. https://doi.org/10.2514/1.J058486 LinkGoogle Scholar

  • [52] Wood K. T., Araujo-Estrada S., Richardson T. and Windsor S., “Distributed Pressure Sensing–Based Flight Control for Small Fixed-Wing Unmanned Aerial Systems,” Journal of Aircraft, Vol. 56, No. 5, 2019, pp. 1951–1960. https://doi.org/10.2514/1.C035416 LinkGoogle Scholar

  • [53] Zhong Y., Fukami K., An B. and Taira K., “Sparse Sensor Reconstruction of Vortex-Impinged Airfoil Wake with Machine Learning,” Theoretical and Computational Fluid Dynamics, Vol. 37, April 2023, pp. 269–287. https://doi.org/10.1007/s00162-023-00657-y CrossrefGoogle Scholar

  • [54] Winroth P. M., “Characterization of and Correction for Pressure-Measurement Installation,” Trita-Mek Technical Report, Centres, Competence Center for Gas Exchange (CCGEx), KTH Mechanics, Royal Institute of Technology, Stockholm, Sweden, 2017, p. 11. Google Scholar

  • [55] Hougen J., Martin O. and Walsh R., “Dynamics of Pneumatic Transmission Lines,” Control Engineering, Vol. 10, No. 9, 1963, pp. 114–117. Google Scholar

  • [56] Bergh H. and Tijdeman H., Theoretical and Experimental Results for the Dynamic Response of Pressure Measuring Systems, Rept. NLR-TR F.238, National Lucht- en Ruimtevaartlaboratorium, Amsterdam, Netherlands, 1965. Google Scholar

  • [57] Irwin H., Cooper K. and Girard R., “Correction of Distortion Effects Caused by Tubing Systems in Measurements of Fluctuating Pressures,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 5, Nos. 1–2, 1979, pp. 93–107. https://doi.org/10.1016/0167-6105(79)90026-6 CrossrefGoogle Scholar

  • [58] Kobayashi H., Leger T. and Wolff J. M., “Experimental and Theoretical Frequency Response of Pressure Transducers for High Speed Turbomachinery,” International Journal of Turbo and Jet Engines, Vol. 17, No. 2, 2000, pp. 153–160. https://doi.org/10.1515/TJJ.2000.17.2.153 CrossrefGoogle Scholar

  • [59] Whitmore S. A. and Wilson M. D., “Wiener Deconvolution for Reconstruction of Pneumatically Attenuated Pressure Signals,” AIAA Journal, Vol. 49, No. 5, 2011, pp. 890–897. https://doi.org/10.2514/1.J050102 LinkGoogle Scholar

  • [60] Semaan R. and Scholz P., “Pressure Correction Schemes and the Use of the Wiener Deconvolution Method in Pneumatic Systems with Short Tubes,” Experiments in Fluids, Vol. 53, June 2012, pp. 829–837. https://doi.org/10.1007/s00348-012-1332-2 CrossrefGoogle Scholar

  • [61] Naughton J., Strike J., Hind M., Babbitt A., Magstadt A., Nikoueeyan P., Davidson P. and Shareman J., “Characterization and Control of Unsteady Aerodynamics on Wind Turbine Aerofoils,” Journal of Physics: Conference Series, Vol. 524, No. 1, June 2014, Paper 012025. https://doi.org/10.1088/1742-6596/524/1/012025 Google Scholar

  • [62] Hind M. D., Nikoueeyan P. and Naughton J. W., “Quantification of Uncertainty in the Correction of Remotely Measured Unsteady Pressure Signals on Pitching Airfoils,” 33rd AIAA Aerodynamic Measurement Technology and Ground Testing Conference, AIAA Paper 2017-3733, 2017. https://doi.org/10.2514/6.2017-3733 LinkGoogle Scholar

  • [63] Nikoueeyan P. and Naughton J. W., “Analysis of the Unsteady Surface Pressure Distribution of a Pitching Airfoil Using Modal Decomposition,” Experiments in Fluids, Vol. 64, No. 5, 2023, pp. 1–19. https://doi.org/10.1007/s00348-023-03644-5 Google Scholar

  • [64] Geddes L., Athens W. and Aronson S., “Measurement of the Volume Displacement of Blood-Pressure Transducers,” Medical and Biological Engineering and Computing, Vol. 22, No. 6, 1984, pp. 613–614. https://doi.org/10.1007/BF02443881 Google Scholar

  • [65] Kawata T., Maeda H. and Obi S., “An Attempt to Measure Fluctuating Local Pressure in Free Turbulent Flow in Water,” Journal of Fluid Science and Technology, Vol. 9, No. 2, 2014, Paper JFST0014.https://doi.org/10.1299/jfst.2014jfst0014 Google Scholar

  • [66] Selvaraju R. R., Das A., Vedantam R., Cogswell M., Parikh D. and Batra D., “Grad-CAM: Why Did you Say That?arXiv preprint, arXiv:1611.07450, 2016. https://doi.org/10.48550/arXiv.1611.07450 Google Scholar

  • [67] Selvaraju R. R., Cogswell M., Das A., Vedantam R., Parikh D. and Batra D., “Grad-CAM: Visual Explanations from Deep Networks via Gradient-Based Localization,” Proceedings of the IEEE International Conference on Computer Vision, 2017, pp. 618–626. Google Scholar

  • [68] Jagodinski E., Zhu X. and Verma S., “Inverse Identification of Dynamically Important Regions in Turbulent Flows Using Three-Dimensional Convolutional Neural Networks,” Physical Review Fluids, Vol. 8, No. 9, Sept. 2023, Paper 094605. https://doi.org/10.1103/PhysRevFluids.8.094605 Google Scholar

  • [69] Kim H., Kim J. and Lee C., “Interpretable Deep Learning for Prediction of Prandtl Number Effect in Turbulent Heat Transfer,” Journal of Fluid Mechanics, Vol. 955, Jan. 2023, p. A14. https://doi.org/10.1017/jfm.2022.1069 Google Scholar

  • [70] Morimoto M., Fukami K., Zhang K. and Fukagata K., “Generalization Techniques of Neural Networks for Fluid Flow Estimation,” Neural Computing and Applications, Vol. 34, No. 5, 2022, pp. 3647–3669. https://doi.org/10.1007/s00521-021-06633-z CrossrefGoogle Scholar

  • [71] Manohar K., Brunton B. W., Kutz J. N. and Brunton S. L., “Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns,” IEEE Control Systems Magazine, Vol. 38, No. 3, 2018, pp. 63–86. https://doi.org/10.1109/MCS.2018.2810460 CrossrefGoogle Scholar

  • [72] Clark E., Askham T., Brunton S. L. and Kutz J. N., “Greedy Sensor Placement with Cost Constraints,” IEEE Sensors Journal, Vol. 19, No. 7, 2018, pp. 2642–2656. https://doi.org/10.1109/JSEN.2018.2887044 Google Scholar

  • [73] Saito Y., Nonomura T., Yamada K., Nakai K., Nagata T., Asai K., Sasaki Y. and Tsubakino D., “Determinant-Based Fast Greedy Sensor Selection Algorithm,” IEEE Access, Vol. 9, April 2021, pp. 68,535–68,551. https://doi.org/10.1109/ACCESS.2021.3076186 Google Scholar

  • [74] Yamada K., Saito Y., Nankai K., Nonomura T., Asai K. and Tsubakino D., “Fast Greedy Optimization of Sensor Selection in Measurement with Correlated Noise,” Mechanical Systems and Signal Processing, Vol. 158, Sept. 2021, Paper 107619. https://doi.org/10.1016/j.ymssp.2021.107619 Google Scholar

  • [75] Marzanek M. F. and Rival D. E., “Separation Mechanics of Non-Slender Delta Wings During Streamwise Gusts,” Journal of Fluids and Structures, Vol. 90, Oct. 2019, pp. 286–296. https://doi.org/10.1016/j.jfluidstructs.2019.07.001 CrossrefGoogle Scholar

  • [76] He K., Zhang X., Ren S. and Sun J., “Delving Deep into Rectifiers: Surpassing Human-Level Performance on Imagenet Classification,” Proceedings of the IEEE International Conference on Computer Vision, 2015, pp. 1026–1034. Google Scholar

  • [77] Kingma D. P. and Ba J., “Adam: A Method for Stochastic Optimization,” arXiv preprint, arXiv:1412.6980, 2014. https://doi.org/10.48550/arXiv.1412.6980 Google Scholar

  • [78] Abadi M., Agarwal A., Barham P., Brevdo E., Chen Z., Citro C., Corrado G. S., Davis A., Dean J., Devin M. and et al., “Tensorflow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” arXiv preprint, arXiv:1603.04467, 2016. https://doi.org/10.48550/arXiv.1603.04467 Google Scholar

  • [79] Chollet F., “Keras: The Python Deep Learning Library,” Astrophysics Source Code Library, 2018, pp. ascl.1806. Google Scholar

  • [80] Talos [Computer Software],” Autonomio, 2020, http://github.com/autonomio/talos. Google Scholar

  • [81] Bergstra J. and Bengio Y., “Random Search for Hyper-Parameter Optimization,” Journal of Machine Learning Research, Vol. 13, No. 2, 2012, pp. 281–305. Google Scholar

  • [82] Snoek J., Larochelle H. and Adams R. P., “Practical Bayesian Optimization of Machine Learning Algorithms,” 26th Annual Conference on Neural Information Processing Systems, Vol. 4, NIPS, Lake Tahoe, NV, 2012, pp. 2951–2959. Google Scholar