COMPUTATIONAL INTELLIGENCE IN MULTISCALE AND BIOMEDICAL ENGINEERING TADEUSZ BURCZYŃSKI Institute of Fundamental Technological Research Polish Academy of Sciences (IPPT PAN) and Cracow University of Technology JUBILEE SCIENTIFIC CONFERENCE „PRACTICAL APPLICATIONS OF INNOVATIVE SOLUTIONS RESULTING FROM SCIENTIFIC RESEARCH”
Intelligence and Interdependence between macro and micro http://hunch.net/~yan/solid.mechanics.html
Contents • Intelligent computing • Multiscale inverse problems • Computational Intelligence Systems (CIS) • Optimal Design on the micro-macro levels • Identification problems on the micro-macro levels • Smart design materials in nano-scale • Concluding remarks
COMPUTATIONAL INTELLIGENCE INTELIGENT COMPUTING METHODS Three important areas of intelligent computing methods, namely: • Evolutionary Computing based on Evolutionary Algorithms (EA) • Immune Computing based on Artificial Immune Systems (AIS) • Swarm Computing based on Particle Swarm Optimizers (PSO) are presented as intelligent computing (Artificial Intelligence - AI) methods. Criteria of AI: • Turing test, • Intelligent actions: - heuristics, - learning, • Rational perpetration.
Common features of intelligent bio-inspired methods • Formulation based on population (set of problems in each iteration). • Operators simulate some biological or natural processes. • Stochastic approach. • The great probability of finding global solutions (possibility of closing to the global optimum also when the starting population is in local optimas basins). • Impact of the best solutions on next iterations, even the worst solution can have impact. • Time consuming but there is possibility to speed up by parallel computing and grid environment.
Intelligent optimization methods inspired by biological/natural mechanisms – soft computing Evolutionary Artificial immune Particle swarm algorithms (EA) systems (AIS) optimizers (PSO) pathogens Objective function value Locations Individuals Objective function value Objective function value The goal of AIS The goal of PSO The goal of EA find the most dangerous pathogen find the best location find the fittest chromosom i.e. the global optimum i.e. the global optimum i.e. the global optimum of objective function of objective function of objective function
Evolutionary algorithm (EA) Sequential EA Distributed EA
Artificial Immune System (AIS) B-cell with antibodies T-cell (non self protein recognition) Parameters of AIS: • the number of memory cells • the number of the clones • crowding factor • Gaussian mutation
Particle Swarm Optimization (PSO) Parameters of PSO: • number of the particles, • number of design variables, • inertia weight, • two acceleration coefficients, • two random numbers with uniform distribution,
Parallel Bioinspired Algorithm
Hybrid Bioinspired Algorithm
Comparison for he mathematical function The optimal parameters of AIS The Rastrigin function The number The number Crowding Gaussian of memory of the clones factor mutation cells n 2 4 0.45 40% 2 F x ( ) 10 n x 10cos 2 x The optimal parameters of EA i i The number of The number Simple Gaussian i 1 subpopulations of chrom. crossover mutation 1 20 100% 100% 5.12 x 5.12 i 2 10 100% 100% The optimal parameters of PSO for n=2 Acceleration Acceleration Number of Interia coefficient c1 coefficient c2 particles weight w 74 1 1.9 1.9 F x F min 0,0, ,0 0.0 The stop condition: F(x) < 0.1 46
Multiscale approach in engineering problems Nano
Multiscale Modelling 3 10 FEM/BEM Macro-Interface 0 10 Celular Automata - 3 Time, s 10 Grain/Phase Dislocation - 6 Dynamics 10 Substructures Molecular - 9 10 Dynamics Tight Dislocations - 12 10 Binding Atomistic - 15 10 Ab-Initio - 9 - 6 - 3 0 Physical 10 10 10 10 Chemical Length, m Mechanical Biological
Inverse Problems in Multiscale Modelling B. Inverse problems: Optimization Identification Optimization : minimization of a given objective function in macro scale with respect to design variables in micro scale of the structure Identification : evaluation of some geometrical or material parameters of the structures in micro scale having measured information in macro scale.
CIS Computational Intelligent System Soft computing Hard computing FEM (Finite Element Method) Bio-inspired BEM (Boundary Element Method) MM (Meshless Methods) Methods MD (Molecular Dynamics) AI Ansys Nastran In-house software Marc Mentat Lammps
Computational Intelligent System - interfaces EA Evolutionary Computing Immune Computing AIS PSO Swarm Computing Multiobjective Computing Computational Intelligent System
Optimization Problems of Multiscale Modelling Macro-Micro Nano
Numerical homogenization Numerical homogenization by using RVE ( Representative Volume Element)
Numerical homogenization - requirements • Separation of scales periodic boundary conditions l and L are characteristic lengths of body in l L 1 macro/micro scales. • Averaging theorem 1 average macroscopic value d RVE volume of RVE element RVE RVE RVE • Hill ’ s condition (the equality of the averaged micro-scale energy density and the macro- scale energy density at the selected point of macro-structure corresponding to the RVE) stress nad strain tensors ij ij ij ij ij ij T q temperature gradient and heat fluxes T q T q , i i , i i , i i
Numerical homogenization • Hook ’ s law ' c ij ijkl ij • Fourier ’ s law ' q k T c c c 0 0 0 i ij , i 11 12 13 c c c 0 0 0 21 22 23 c c c 0 0 0 31 32 33 ' c • Tensor of effective elastic constants ij 0 0 0 c 0 0 44 0 0 0 0 c 0 55 0 0 0 0 0 c 66 k 0 0 11 • Tensor of effective thermal constants ' 0 0 k k ij 22 0 0 k 33
Numerical homogenization Macro avg. - average Macro-stresses Macro-strains Homogenization Localization Micro BVP RVE BVP – Boundary Value Problem
Optimal design on macro-micro scales where min DV J J 0 – objective function described o in the macro scale Ch DV B cell x x , ,..., x ,... x DV=design vector 1 2 i n P x i – design variables, play the role of geometrical, material or topologcal parameters in the micro scale J 0, 1,2,.. m Constraints: min max x x x , i ,1,2,.. n i i i J J ( , , u ), 0,1,2,... m
Meso scale: Nano scale: Micro scale: Grains Molecular/atomic Single grain level Macro scale: Structure J u J 0 ( , , ) DV x x , ,..., x ,... x 0 1 2 i n Illustration of optimization in multiscale approach
Design variables RVE Material parameters Shape parameters Topology parameters
Evolutionary/immune/swarm optimization in multiscale in macro scale in micro scale RVE
min Ch J , where J u Ch g g , , g g , , g g , , g , g 0 0 max 1 2 3 4 5 6 7 8 g 7 , g 8 The best solution The best solution in the 1st generation in the last generation DEA parameters: 2 subpopulations 20 chromosomes in each Rank selection Gasuss mutation Simple crossover
Optimization of Functionally Graded Materials in Multsicale Modelling Bamboo The function or composition changes gradually in the material FGM in nature – clam shell http://www.unl.edu/emhome/faculty/bobaru/project_shape_optim.htm
Metal-ceramic FGMs Functionally Graded Materials The function or composition changes gradually in the material http://sbir.nasa.gov/SBIR/successes/ss/3-079text.html
Optimization of FGM parameters macromodel Micromodel - RVE Minimization of inclusions total volume
6 design parameters - diameters d i Minimization of inclusions total volume n f h dA z z 1 A Z Constraint on maximum displacement value u u i max
Minimization of inclusions total volume the resuts 1 - 0.187501 2 - 0.137236 3 - 0.123124 4 - 0.104760 5 - 0.143142 6 - 0.101725 Displacements map for the best solution (u max =4)
FGM material for tooth implant
The simplified model of implant-bone systen with FGM material – optimization of porosity F min f p p F 1 2 ch ch [ p , p ] 1 2 V voids p i V gl i Minimization of porosity p 1 (mat 1 ) and p 2 (mat 2 ) Constraints on max eqivalent stress value in the bone area are imposed Box constraints on prosity [0.0; 0.4]
Optimization of functionally graded materials in multiscale modelling Macromodel FEM MSC.Nastran Micromodel FMBEM model RVE
Distribution of equivalent stresses in the optimal design
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