The MADELEINE project

The Final Public Event of the MADELEINE project was held virtually on 25-26 November 2021. The related dissemination material is available.

The links below let you download the public versions of the presentations that were given during the Final Public Event:

Thursday 25th of November 2021:

Friday 26th of November 2021:

The recordings of the two sessions of the Final Public Event can be seen on YouTube:

The answers to the questions that were asked during the Final Public Event are provided below:

  • Multidisciplinary Adjoint Methods Varvara Asouti on behalf of Kyriakos Giannakoglou (National Technical University of Athens)

Question: Regarding the slide with the results for frozen assumption, there were some oscillations in the sensitivities. Are they normal?

Answer: The horizontal axis of the sensitivity derivative plots indicates the design variable ID. In the C3X internally cooled turbine the blade is parametrized using a control grid and both the x and y coordinates of the control points are allowed to vary. In the presented plots, two consecutive points correspond to the sensitivity derivative with respect to thex and y coordinate of a control point; these two values are not necessarily ofthe same order.

Regarding the frozen turbulence and frozen distance curve (purple curve), we may see differences both in the sensitivity value and its sign which indicates that these sensitives are not good for a gradient-based optimization algorithm. Thus, we should develop and use the adjoint to all governing equations especially in multi-disciplinary optimization problems.

  • Adjoint-Based Aerostructural Airframe Optimisation of a Business Jet by Gilbert Rogé (Dassault Aviation)

Question 1: How is sigma CD computed ? (slides 12-13)

Answer 1: COUT =10000*(0.5*(CD_pt1+CD_pt2)+3.0*sqrt(0.5*((CD_pt1-0.5*(CD_pt1+CD_pt2))**2+(CD_pt2-0.5*(CD_pt1+CD_pt2))**2)))

Question 2: Can you explain why in slide 17 the flexible optimisation "converges" much faster than the rigid one?

Answer 2: SLSQP convergence deals with à non-linear constrained optimization problem. Path of rigid & flexible optimizations have been plotted respect to SLSQP iteration number. Mainly a flexible fixed-point cost is 3 times cost of rigid one. 1 SLSQP iteration deals with 1 gradient computation (adjoint approach, so 3 linear systems, 1 for CD, 1 for CL, 1 for CM) and 1 line-search (1 or more non-linear system). CL & CM non-linear constraints (accuracy required 10-4) could give a faster convergence for rigid or flexible optimization because we have also to take into account RANS convergence (10-5 accuracy on CD, CL & CM).

Question 3: Even if the gain is zero, what does this mean in terms of the optimised parameters? Are they the same as well?

Answer 3: Yes, they are the same (at 10-4).

Question 4: What exactly do you mean by flexible in this context? Is it the deflection of the wing in vertical direction in addition to the variable twist change?

Answer 4: Flexible deals with frozen FEM (thickness & wing planform are frozen). Yes, deflection of the wing (flexible displacement) is added to optimization parameters displacement.

Question 5: Remarkable 8% L/D improvement - rather large. Does this meant starting wing should have been a better design in first place?

Answer 5: No. It is only a toys problem. Real life optimization deals with MDO, multipoint including both take-off, landing and cruise, larger set of load cases. Moreover, Jig Shape deals with Mach=0.82, AoA=2.5 deg. Aerostructural optimization has been done for Mach=0.8, AoA=2 deg.

  • Benefits of Coupled Aero-Elastic Adjoint for Optimising the Long Range XRF-1 Aircraft Configuration by Joël Brézillon and Romain Olivanti (Airbus)

Question 1: Both Dassault/National Technical University of Athens and Airbus/DLR/ONERA compared rigid & flexible optimisations using coupled adjoint. Did you compare both approaches and aero-structural optimisations?

Answer 1: Such comparison were not considered since they are answering to different aircraft design needs: the aero-structural optimisations is rather taking place in early design phase to support aircraft architecture decision ;while the rigid&flexible optimisations is used for a later design phase,like detailed design, to get the “last” drag improvement.

Question 2: XRF-1 flexible wing shape optimisation: Is a constraint for spanwise lift distribution included?

Answer 2: All XRF-1 flexible wing optimisations presented were performed without considering a spanwise lift distribution constraint.

Question 3: Understanding that NASTRAN is an industrial-certified tool, have you considered using a different CSM source code to enable better integration with you tools?

Answer 3: The use of this CSM solver was rather motivated by 1) the availability of the baseline CSM model in NASTRAN format right at the beginnin gof the project, and 2) communal use of NASTRAN by all partners working on theXRF-1 model. It is worth mentioning that the CFD/CSM coupling strategy as implemented at Airbus (for the primal and adjoint states) is generic enough to consider alternative CSM models.

  • Open Source Environment for Multidisciplinary Optimisation (GEMSEO) by Anne Gazaix and François Gallard (IRT Saint Exupéry)

Question: (on slide 17) Are the many coupling variables handled by the optimiser or in the MDA problem?

Answer: The 4 millions coupling variables are solved by the MPI parallel MDA, which is the new feature developed in this WP. To our knowledge there exists no optimizer that runs in parallel (MPI) and that would be able to handle such large number of nonlinear equality constraints and their Jacobians. But this may be a direction for future work.

  • Linear Solvers for Adjoint Problems by Haysam Telib (Optimad)

Question 1: Do you notice strong dependencies of the adjoint solvers with respect to the accuracy of primary solutions, in particular for more complex applications?

Answer 1: We do not notice a big difference in converging the primal or the adjoint, since we use an implicit method based on the exact Jacobian even in the primal. Then, of course, if the matrix is ill-conditioned,we see an increase in number of iterations, both in the primal and adjoint.Convergence of adjoint problems seems to depend slightly on primal problem resolution, but of course the accuracy of the computed gradients will depend on that.

Question 2: How do set-up a space-time BC (chorochronic)regarding mesh generation, or can it be arbitrary modelled?

Answer 2: The method is not dependent on the type of mesh,so it can be arbitrary. The mesh has to be setup in a domain consisting of one blade passage with proper periodic boundaries, like in the steady simulation.

  • Uncertainty Quantification and Robust Design (Methods and Validation) by Tiziano Ghisu (University of Cagliari)

Question 1: What is the difference between design variables and design parameters?

Answer 1: We have called design variables the ones the designer can change during the optimisation, parameters are fixed. Both have an impact on the figures of merit, and both can be uncertain.

Question 2: Can you handle objective functions comprising statistics other than mean and standard deviation of the QoI with this approach?

Answer 2: Yes, but capturing higher moments reliably requires higher Polynomial Chaos expansions

Question 3: You only consider uncertainties in the design variables. How much of the noise is related to the model?

Answer 3: We only considered uncertainties in the design variables. However, noise in the model will be considered in the future, but requires a validation with higher fidelity models or experimental data.

Question 4: How you choose the number of terms (p) in the Polynomial Chaos Expansion (slide 9/10)?

Answer 4: By comparing expansions with increasing orders. For example, in the fan optimisation, we used a first order expansion during the optimisation, after verifying that a second order expansion would have given the same result. After the optimisation, we verified that the results obtained with the first order expansion were reliable.
  • Aero-Thermal-Manufacturing Turbine Blade Design by Shahrokh Shahpar (Rolls Royce)

Question 1: Did you find the best strategy for topology and sizing optimizations (sequential or more coupled?)

Answer 1: Good question. Through this study we discovered that gradient-based optimisation (adjoint or otherwise) not very effective, as multiple fences and fins disappear and appear, most optimisation shown in my presentation are based on evolutionary methodology, however we did make use of adjoint gradient in making better metamodels (RSMs) to aid the GA population to converge better and faster.

Question 2: How did you get a CAD model (well suited for next sizing adjoint optimisation)?

Answer 2: It depends on which test case this question is referring to, most of the PADRAM design space used in Rolls-Royce e.g. for the blades is exportable as standard CAD format like STEP, and the underlying mathematical description of these i.e. NURBS is the same, however, for the Topology optimisation (of the tip), STL format is used and the idea is we learn from topology optimisation to define a more compact parametric design for the subsequent refinement of the tip shape. Also we do have detailed parametric model of a given blade using UG NX (CAD package we use in Rolls-Royce), however, the aforementioned PADRAM designspace is still very efficient as it does not directly represent a complex shape but morph a given geometry with a small number of “orthogonal” and compact design parameters.
  • Aero-Acoustic Isolated Propeller Design by Itham Salah El Din (French Aerospace Lab, ONERA)

Question 1: Really great work! Can you mention the cost ratio for steady / unsteady MDO? What is 1-step MDO?

Answer 1: The ratio for the studied case ranges from 1 day for steady optimisation up to one week for the unsteady one.

Question 2: 33k design variables must be difficult to handle. Where is the limit in the number of variables?

Answer 2: There are no known limitations. Applications up to1M nodes have been treated. As only skin nodes are considered no limitation is foreseen.

Question 3: What are the perspectives of such workflow in other configuration (VTOL …)?

Answer 3: These workflows can be used for other configurations. The next step will be able to consider ducted and integrated configurations to be able to take into account interactional effects. For non axial conditions unsteady resolution is mandatory but costly.

Question 4: What geometrical constraints (apart from the radius) have you considered?

Answer 4:Only radius and thickness constraints have been taken into account apart from the variation ranges of the design variables used in the different optimisation setups.
  • Adjoint-Based Multidisciplinary Optimisation of a Fan Blade by Long Wu (University of Southampton)

Question: What is the noise intensity/power model you used to define the objective function?

Answer: The sound intensity formula in the case of nonuniform mean flows proposed by C.L. Morfey (1971) was used.
  • Conclusions and Perspectives by Michaël Méheut (French Aerospace Lab, ONERA)

Question 1: Which approach was used to integrate the CAD into the adjoint-based MDO process? Was the CAD differentiated or finite-differences were used?

Answer 1: For the parametrisation, CAD-based tools available in the industrial partners were used for most of the applications (PADGE for Airbus, GANIMEDE for Dassault and PADRAM for Rolls Royce). Two of these tools are differentiated and give access to the shape sensitivities with regard to design variables.               .

Airbus: PADGE is used in R&T context exclusively, CAD based rom is used on industrial cases instead.

Dassault: GANIMEDE is a Master-Slave approach (CAD-Surface Mesh) with fully differentiated (direct mode) CAD and Mesh.

Rolls Royce: PADRAM is CAD compatible but not directly CAD. Finite-difference approach is used for mesh sensitivity in the adjoint chain because:

a) PADRAM is very fast (runs in seconds),

b) You can parallelize this operation quite easily on a HPC cluster,

c) Linearization would be a huge work.

Question 2: In the slide 33, IDF/MDF behave better on the business / XFR1 testcase. Is it driven by the different aero-structural coupling (flying - jig shapes)? For the XFR1 you showed all at once vs.sequential approach, not IDF vs MDF.

Answer 2: For the GBJ test case, an explanation of the superiority of IDF over MDF could be that the coupling space has a low dimension (between 2 and 100 according to the dimension of the scalable problem). This dimension corresponds to the number of basis functions resulting from the dimension reduction of the original coupling space. For the XRF1 testcase, we did not compare the state-of-the-art MDO formulations but ad-hoc formulations already existing and mastered by the partners: an all-at-once formulation with a single optimizer controlling all the design variables and without MDA, and a sequential formulation with a sub-optimizer controlling the structural parameters.