Presentation: Constrained Surrogate-based Optimisation for Finite Element Model Updating

Constrained Surrogate-based Optimisation for Finite Element Model Updating Eduardo Larrea Herranz & Gabriele Dessena Department of Aerospace Engineering, Universidad Carlos III de Madrid, Leganés, Madrid, Spain 4th December 2025 Turin, Italy Joint 28th AIDAA International Congress and 10th CEAS Aerospace Europe Conference [email protected] Constrained Surrogate-based Optimisation for FEMU Outline 1. Contributions 2. Background 3. Motivation 4. Surrogate-based Optimisation 5. Methodology 6. Constrained refined Efficient Global Optimisation 7. Initial Sampling 8. Robust Infill Procedure 9. Finite Element Model Updating 10. Case Study 11. Optimisation Problem 12. Results 13. Conclusions and Future Work 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 2 Constrained Surrogate-based Optimisation for FEMU Contributions •Introduce an efficient constrained optimisation framework •Apply it to an aeronautically relevant example 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 3 Constrained Surrogate-based Optimisation for FEMU Background •Aeronautical problems are complex •Often requiring high-dimensional analsyis •The design process is getting more and more computational •Optimisation is at its foundation 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 4 Complex optimisation problems Impose Computationally costly functions Retrieved from 1. 1. G. K. W. Kenway and J. R. R. A. Martins, ‘Multipoint High-Fidelity Aerostructural Optimization of a Transport Aircraft Configuration’, Journal of Aircraft, vol. 51, no. 1, pp. 144–160, Jan. 2014, doi: 10.2514/1.c032150. Constrained Surrogate-based Optimisation for FEMU Motivation •Genetic Algorithms •Gradient Searches •Surrogate-based Optimisation High number of function evaluations Expensive gradient calculations and poor behaviour with noisy data Kriging modelling: 𝑌𝑌 𝒙𝒙 = 𝜇𝜇 𝒙𝒙 +𝜖𝜖(𝒙𝒙) 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 5 𝑓𝑓(𝑥𝑥)𝜇𝜇(𝑥𝑥)𝜖𝜖(𝑥𝑥) x Constrained Surrogate-based Optimisation for FEMU Surrogate-based Optimisation •Efficient Global Optimisation (EGO): •Balance exploration and exploitation, Expected Improvement •Success in expensive black-box problems with limited evaluations •Establish foundation for modern approaches •refined Efficient Global Optimisation (rEGO): •Builds upon EGO to propose global-local approach •Adaptive reduction of the search domain •Sample point de-clustering 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 6 Focus on unconstrained problems Adequate constraint handling scheme EGO constraint implementations exist Constrained Surrogate-based Optimisation for FEMU Multiple active constraints Innovative strategy against surrogate inaccuracies Proven efficacy on G-problems Penalty Augmented Lagrangian Penalised Expected Improvement Modified Expected Improvement “Unconstrained” Methods EGO-Specific Methods Straight-forward implementation Many variants Very effective on simple problems Parametersensitive Unstable near Boundaries Combination Lagrange multipliers + Penalty term Non-linear problems in high dimensional spaces Complex implementation Bad behaviour against noisy or discontinuous constraints Adapted formulation to surrogate modelling Constraint handling with probability of feasibility Compromised behaviour multiple active constraints Near boundary solution instability De-graded performance in highdimensional spaces Cluster of data points generate instability Methodology + Plugin Control 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 7 Constrained Surrogate-based Optimisation for FEMU Methodology (Cont’d) •Modified Expected Improvement: 𝐸𝐸𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 𝒙𝒙=𝐸𝐸𝐸𝐸 𝒙𝒙·� 𝑖𝑖=1 𝑚𝑚 min 2 · 𝑃𝑃𝑃𝑃𝑃𝑃 𝑔𝑔𝑖𝑖𝒙𝒙< 0 , 1 where 𝐸𝐸𝐸𝐸 𝒙𝒙=𝑓𝑓𝑚𝑚𝑖𝑖𝑚𝑚 −𝜇𝜇 𝒙𝒙 ·Φ𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚−𝜇𝜇 𝒙𝒙 𝜎𝜎𝒙𝒙+𝜎𝜎 𝒙𝒙 ·𝜙𝜙𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚−𝜇𝜇 𝒙𝒙 𝜎𝜎𝒙𝒙 𝑃𝑃𝑃𝑃𝑃𝑃 𝑔𝑔𝑖𝑖𝒙𝒙< 0 = Φ𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚−𝜇𝜇𝑚𝑚𝒙𝒙 𝜎𝜎𝑚𝑚𝒙𝒙 •Plugin control (PC): •Dynamically adjusts the EI to prevent a shift towards the unfeasible •Was considered, but discarded •Complex and computational costly •No empirical increase in the accuracy of the solution 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 8 Constrained Surrogate-based Optimisation for FEMU Constrained refined Efficient Global Optimisation CrEGO 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 9 Constrained Surrogate-based Optimisation for FEMU Density scaling - 𝜌𝜌Young Modulus scaling - 𝑬𝑬 FEM model 𝒙𝒙𝟏𝟏𝒙𝒙𝟐𝟐𝒙𝒙𝟑𝟑𝒙𝒙𝟒𝟒𝒙𝒙𝟓𝟓𝒙𝒙𝟔𝟔𝒙𝒙𝟕𝟕𝒙𝒙𝟖𝟖 CrEGO20% 0.9163 0.8863 0.8000 1.0162 1.2000 1.2000 1.1845 1.2000 CrEGO30% 0.9602 0.9449 0.7003 0.9768 1.2999 1.1026 1.1856 1.2946 Results (Cont’d) •Variables results 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 16 General mass reduction particularly focused on 3rd element General stiffness increase reduction particularly focused on 1st element After GVT on physical model, plastic deformation spotted near the root Hardening effect increases the spar stiffness over deformed area FEMU procedure simulates this increment through 𝒙𝒙𝟓𝟓−𝟖𝟖 parameters Constrained Surrogate-based Optimisation for FEMU Results (Cont’d) •Modal frequencies and mode shapes after FEMU 3rd mode shapes 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 17 1st Bending 2nd Bending 3rd Bending Experimental 4.855 26.966 76.851 Baseline 5.563 (14.58%) 31.193 (15.68%) 92.012 (19.73%) CrEGO20% 4.853 (0.05%) 26.967 (0.00%) 78.61 (2.29%) CrEGO30% 4.855 (0.00%) 26.965 (0.00%) 76.861 (0.01%) Constrained Surrogate-based Optimisation for FEMU Conclusions and Future Work •Developed a constrained optimisation global-local surrogate method •Proposed for finite element model updating (FEMU) •Application to an aeronautically relevant problem •Future work: •Explore the problem search space further •Further validation on test functions •Application to an MDO/DSO problem 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 18 Constrained Surrogate-based Optimisation for FEMU Acknowledgements Grants for research activity of young PhD holders, part of the Universidad Carlos III de Madrid Own Research Program (TOMA -Tangential interpolation for Operational Modal Analysis project) 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 19 CEAS EuroGNC conference 2026 hosted at Universidad Carlos III de Madrid May 5th – 7th 2026 Organizing committee Local Organizing Committee Andrés Marcos, UC3M, Conference Chair Rafael Vázquez, Universidad de Sevilla, Conf. Deputy Chair Diego Navarro-Tapia, UC3M, Local Arrangements Chair Gabriele Dessena, UC3M, International Arrangements Chair CEAS GNC Technical Committee Nicolas Fezans, DLR, Chair of the Committee Raziye Tekin, Roketsan, Co-chair of the Committee TC member roster, see conference webpage Conference Venue The EuroGNC 2026 conference will be hosted at the Universidad Carlos III de Madrid (UC3M). The conference venue is located in the city center, at the Campus Puerta de Toledo. Numerous famous monuments, museums, and parks can be reached in less than 20-30 min on foot, with metro/bus stations also available just outside the conference venue. Madrid is a vibrant city known for its rich cultural heritage, lively atmosphere and warm hospitality. Madrid generally enjoys pleasant weather in May. Attendees can also look forward to experiencing the city’s renowned tapas scene. Topics: •Control Theory, Analysis and Design •Applications of GNC •Intelligent Control/AI in Aeronautics/Astronautics •Aerospace Robotics •Novel Navigation, Estimation and Tracking methods •Sensor Systems for GNC •Flight Mechanics, Dynamics, and Simulation •Modelling for Aerospace Systems •Flight Testing and Experimental Results Key dates September 30th, 2025 Full Paper Submission Deadline Nov/Dec, 2025 Author notification February 20th, 2026 Final Paper Submission Deadline Jan/Feb, 2026 End of Early-Bird Registration May 5th-7th, 2026 EuroGNC Conference in Madrid Opportunity for students to present their theses in a dedicated poster session Deadline: Feb 2026 Keep an eye on the website! Organising committee Organising Committee Erasmo Carrera, Politecnico di Torino, General Chair Yongming Liu, Arizona State University, Technical Chair Ibrahim Guven, Virginia Commonwealth University, Technical Vice-Chair Tracks: •Structures •Structural dynamics •Materials Key dates February 17th, 2026 Presentation-only Abstract deadline still open Structural dynamics track Marco Petrolo, Politecnico di Torino, Track Chair 1. Aero-, Servo-, Thermo-Elasticity of Aircraft, Rotorcraft and Spacecraft 2. Rotordynamics 3. Aeroacoustics and Vibroacoustics 4. Nonlinear Dynamics and Flexible Multibody Dynamics 5. Dynamic Loads, Wave Propagations, Response, Vibration, Control, and Alleviation of Aerospace Structures and Vehicles 6. Computational Methods and Modelling 7. Experimental Studies in Structural Dynamics 8. Machine Learning in Structural Dynamics and Aeroelasticity 9. Model Uncertainties and Uncertainty Quantification in Structural Dynamics 10. General Topics of Structural Dynamics of Aircraft, Rotorcraft, and Spacecraft Structures Invitation to submit to •Nonlinear Dynamics and Flexible Multibody Dynamics •Experimental Studies in Structural Dynamics Topic co-organiser: Gabriele Dessena, UC3M Constrained Surrogate-based Optimisation for FEMU Thank you for your attention! 4th December 2025 Dessena & Pontillo – CEAS/AIDAA 2025 22 Presentation download ResearchGate profile