REDUCED ORDER MODELS: how generalized solutions expedite simulation-based industrial computations to modify the geometry, materials, boundary conditions…

Laboratori de Càlcul Numèric (LaCàN) Universitat Politècnica de Catalunya - BarcelonaTech (Spain) http://www.lacan.upc.edu/ Laboratori de Càlcul Numèric (LaCàN) Universitat Politècnica de Catalunya - BarcelonaTech (Spain) http://www.lacan.upc.edu/ REDUCED ORDER MODELS: how generalized solutions expedite simulation-based industrial computations to modify the geometry, materials, boundary conditions… REDUCED ORDER MODELS: how generalized solutions expedite simulation-based industrial computations to modify the geometry, materials, boundary conditions… Antonio HUERTAAntonio HUERTA Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Collaborators:Collaborators: David Modesto Giorgio Giorgiani Aleksandar Angeloski Sonia Fernandez-Mendez Francisco Chinesta, A. Leygue, F. Bordeu, et al. Amine Ammar Elías Cueto et al. Xevi Roca Jaime Peraire Sergio Zlotnik Pedro Díez Marco Discacciati 2 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · PARAMETRIC SOLUTIONSPARAMETRIC SOLUTIONS Given a Initial/Boundary Value Problem: Typically: solution computed at any coordinate We now that: cost ∝dimension data: 1. material parameters , 2. external loads , 3. geometry 3 [Chinesta et al., “PGD-Based Computational Vademecum for Efficient Design, Optimization and Control”, Arch. Comput. Mech. Eng. 2013] Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · THE COMPUTATIONAL VADEMECUM !THE COMPUTATIONAL VADEMECUM ! Use “pre-cooked” solution (database), a “handbook": vademecum 4 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · THE COMPUTATIONAL VADEMECUM !THE COMPUTATIONAL VADEMECUM ! Use “pre-cooked” solution (database), a “handbook": vademecum 5 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · PARAMETRIC SOLUTIONS: 2 simple ideasPARAMETRIC SOLUTIONS: 2 simple ideas Given a Initial/Boundary Value Problem: 1. New set of coordinates: 2.Assume separation of variables: 6 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Off-line and On-line phases Off-line and On-line phases In order to approximate There are two phases: 1. Expensive (aka: OFFLINE) Compute for every function How many terms (modes)? (how big is n? stop?) How can we do it? (expensive? linear/nonlinear?) do we converge? how fast?… 2. Very very fast and cheap (aka: ONLINE) 7 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Two key observations: 1.No modification of mathematical/physical model ! 2.Online phase does not require to solve another problem 8 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · The problem: harbor agitationThe problem: harbor agitation Experimental measure of , large M. Computational domain Selection of the test cases , small m. GOAL: compute the wave height in an area of interest for all test cases. Simple wave propagation model (no reflections, simple geometry, deep water). More complex model (Reflections, varying bathymetry, geometric features,…). 9 DATA: 1. amplitude 2. wavelength 3. wave direction Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Example: Mataro harborExample: Mataro harbor 16 RED=0.7 x Incident wave-height 10º Incident wave with period from 6 to 12 s. Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Real period range (low-mid freq) Ndof (x,y): 40737 (P8) Ndof k: 100 Ndof θ: 100 Ndof (x,y,k,θ): 407 106 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Use an a priori model reduction technique: 1. offline stage: a general/static/expensive solution is computed, and 2. online phase: a real-time response is obtained on deployed platforms such as smartphones or tablets 18 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · PGD reduced basis: evaluation ONLINEPGD reduced basis: evaluation ONLINE Real-time simulation for any incident wave period in the Mataró harbor. Running on a Motorola Xoom tablet. (wave height) OUTPUT OF THE MODEL 19 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Two recent examples:Two recent examples: Geometry can be parameterized for fast (viz. real-time) or multiple-queries (viz. optimization)! [Ammar et al. “Parametric solutions involving geometry: a step towards efficient shape optimization”, CMAME 268 2014] Real-time evaluation of temperature in manufacturing! [Aguado et al. “Real-time monitoring of thermal processes by reduced order modeling”, submitted] 20 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Laplace equation with parameterized boundary 21 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · 22 GOAL: For each set of parameters determine the solution (fast, precise and robust) Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · OptimizationOptimization A shape optimization scheme minimizes a “cost” function which depends on the solution and parameters Iterative procedure that requires for each set of trial parameters to solve the BVP To iterate need good sensitivities 23 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · 24 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Multi-objective Optimization Multi-objective Optimization Minimize volume (easy) and maximize heat flux (solve BVP) Find Pareto Front use 10 values for each parameter 25 Volume Inverse of heat flux on top surface solve the problem 104 times! Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Two recent examples:Two recent examples: Geometry can be parameterized for fast (viz. real-time) or multiple-queries (viz. optimization)! [Ammar et al. “Parametric solutions involving geometry: a step towards efficient shape optimization”, CMAME 268 2014] Real-time evaluation of temperature in manufacturing! [Aguado et al. “Real-time monitoring of thermal processes by reduced order modeling”, submitted] 32 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · R ea l - ti me mon it or i ng Thermal process R ea l - ti me mon it or i ng Thermal process 33 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · 34 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Composite manufacturing for planesComposite manufacturing for planes 35 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · 36 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Expression for temperature where: Must solve for with 37 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · 38 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Signature exampleSignature example 39 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · 40 Congrès NAFEMS · Simulation numérique : moteur de performance · 4 Juin 2014 · Summary and conlusionsSummary and conlusions Reduced order models can be incorporated in today’s simulation-based engineering activities for Engineering design Optimization, control or reverse engineering Real-time monitoring and decision making No need for oversimplified models mathematical or physical. Online phase can be real-time in “mobile” devices Each generalized solution requires offline high-fidelity (robust and precise) and high-performance (efficient and fast) computations see references in www.lacan.upc.edu