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Multidisciplinary Design Optimization with Minamo

Multidisciplinary Design Optimization (MDO) has considerable impact on the design by increasing performance, lowering lifecycle cost and shortening design time for complex products. Minamo can not only help reaching an improvement in the design solution, but will contribute to quickly gain insight into the design space, quantitatively assess key factors and trades, and most importantly, find innovative design options. Minamo multi-objective robust design optimization is based on the most advanced genetic algorithms, powerful design of experiments techniques, efficient nonlinear surrogate models, CAD native access, etc. It can be used stand-alone or as an engine plug-in in other commercial optimization software.

Efficient Design Exploration
 
Beyond trying to achieve performance targets and minimizing performance variation, Minamo’s Design of Experiments (DoE) and Surrogates modules enable the exploration of the design space in a cost efficient manner, giving critical insight into the variations of often conflicting objectives and the associated trade-offs.
 
Design of Experiments
 
DoE techniques aim at efficient and systematic analysis of the design space, so as to extract the most relevant information from a minimum number of experiments or function calls. For computationally intensive realistic simulations, such techniques are then used to provide reference building support for fast-running surrogate models, the goal being to define an experiments set that will maximize the ratio of the model accuracy to the number of experiments.
 
In many engineering applications with large design space, optimizers face the major challenge of efficiently building sufficiently accurate models. Minamo overcomes this issue thanks to its innovative space-filling techniques. Much more efficient than competing software, Minamo is capable of providing information about all portions of the experimental region and give complete flexibility in fitting models where there is a considerable a priori uncertainty about the forms of the response surfaces.
 
Besides classical filling techniques such as quasi-random sequences methods (Halton and Hammersley) and Latin Hypercube Samplings (LHS), Minamo offers several innovative a priori sampling techniques based on Centroidal Voronoï Tessellations (CVT) and Latinized Centroidal Voronoï Tessellations (LCVT). Independent of the number of variables, the latter techniques most efficiently generate highly uniform/even distributions of the sample points over arbitrarily shaped N-dimensional parameter spaces.
 
Surrogates
 
Minamo Surrogates module offers a series of generic and powerful interpolators of nonlinear functions such as Radial Basis Functions (RBF) networks, ordinary and universal Kriging and Support Vector Machines (SVM). As unevenly sampled points typically yield interpolators that are very inaccurate in sparsely observed parts of the experimental region, the superior space-fill techniques available in Minamo’s DoE module constitute a first choice star ting base. To fur ther tailor the sampling in order to capture the responses’ underlying physics, Minamo features auto-adaptive DoE techniques in order to locally increase the sampling intensity depending on the response observed at one or several sample point(s).
 
Also known as capture/recapture sampling or response-adaptive design, such techniques automatically explore the space while simultaneously fitting the response surface, using predictive uncertainty to guide subsequent experiments. Auto-adaptive DoE and powerful surrogates models are hence exploited in a fully integrated manner in order to minimize the number of function calls.
 
Multi-Objective Robust Design Optimization
 
Several variants of real-coded genetic algorithms are available in the Minamo optimization module and efficiently coupled to the surrogates through a trust region management  framework, in an online modeling approach. All along the design, the surrogates are hence continuously enhanced to offer an increasingly accurate capture of the underlying nonlinear physics.
 
For finding or approximating the Pareto-optimal set for multiobjective optimization problems, Minamo optimization module features, the SPEA II (Strength Pareto Evolutionary Algorithm II) method, superior to other modern elitist methods such as PESA (Pareto Envelope-based Selection Algorithm) and NSGA II (Non Dominated Sorting Genetic Algorithm II) in terms of better distribution of points, especially when the number of objectives increases.
 
Minamo is easily coupled to almost any CAE software tool and comes with a comprehensive suite of monitoring and analysis tools, a.o. leave-k-out cross-validation for surrogate reliability monitoring, global sensitivity analysis and Sobol indices calculation (variance-based impor tance measures of the parameters), self organizing maps for high-dimensional data visualization and understanding, etc. Multi-physics multi-criteria designs tackling over a hundred parameters within a heavily constrained setting are successfully handled on a day-to-day basis.
 
CAD Access
 
Minamo integrates CAD systems inside the optimization loop in a vendorneutral manner, featuring:
  • Bidirectional gateway from and to the CAD system* (CATIA V5, PRO-E, UG, SolidWorks, ... ),
  • Access to the master model feature tree,
  • Access to the topological structure of the geometry,
  • Parameterization embedded in CAD models.
Applications
 
Minamo is successfully applied in projects for
  • Automotive
    • tire structural properties optimization
    • inverse analysis (e.g. material laws parameters identification)
    • automotive fuel tanks shape optimization
  • Aeronautics
    • turbine and compressors blade shape aero-mechanical optimization
    • turbomachinery platforms shape optimization
    • contra-rotating fan and compressor optimization
  • Space
    • air-intake geometry optimization
  • Manufacturing
  • Biomedical
  • Aerostructure
  • Composite
  • Marine
  • Civil engineering
  • ...