COMPUTATIONAL INTELLIGENCE IN MULTISCALE AND BIOMEDICAL ENGINEERING - - PowerPoint PPT Presentation

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

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.

COMPUTATIONAL INTELLIGENCE INTELIGENT COMPUTING METHODS

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

Objective function value

pathogens

Objective function value

Individuals

Evolutionary algorithms (EA) Artificial immune systems (AIS)

The goal of AIS find the most dangerous pathogen i.e. the global optimum

• f objective function

The goal of EA find the fittest chromosom i.e. the global optimum

• f objective function

Objective function value

Locations

The goal of PSO find the best location i.e. the global optimum

• f objective function

Particle swarm

• ptimizers (PSO)

Evolutionary algorithm (EA)

Distributed EA Sequential EA

Artificial Immune System (AIS)

Parameters of AIS:

• the number of memory cells
• the number of the clones
• crowding factor
• Gaussian mutation

B-cell with antibodies T-cell (non self protein recognition)

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

The number of subpopulations The number

• f chrom.

Simple crossover Gaussian mutation 1 20 100% 100% 2 10 100% 100%

Comparison for he mathematical function

46

The number

• f memory

cells The number

• f the clones

Crowding factor Gaussian mutation 2 4 0.45 40%

The Rastrigin function  

 

2 1

( ) 10 10cos 2

n i i i

F x n x x 



  



 

5.12 5.12

i

x   

for n=2

   

min 0,0, ,0 0.0 F x F  

The stop condition: F(x) < 0.1

The optimal parameters of AIS The optimal parameters of EA The optimal parameters of PSO

Number of particles Interia weight w Acceleration coefficient c1 Acceleration coefficient c2 74 1 1.9 1.9

Multiscale approach in engineering problems

Nano

Multiscale Modelling

10

• 9

10

• 6

10

• 3

10 Length, m 10

• 15

10

• 12

10

• 9

10

• 6

10

• 3

10 10

3

Time, s Atomistic Dislocations Substructures Grain/Phase Macro-Interface

FEM/BEM

Celular Automata

Dislocation Dynamics Molecular

Dynamics

Tight Binding Ab-Initio Physical Chemical Biological Mechanical

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

• f the structures in micro scale having measured information in

macro scale.

CIS

Computational Intelligent System

Soft computing Hard computing

FEM (Finite Element Method) BEM (Boundary Element Method) MM (Meshless Methods) MD (Molecular Dynamics)

Bio-inspired Methods AI

Ansys Nastran Marc Mentat Lammps In-house software

Computational Intelligent System - interfaces

EA AIS PSO Evolutionary Computing Immune Computing 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
• Averaging theorem
• 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) l and L are characteristic lengths of body in macro/micro scales. average macroscopic value volume of RVE element stress nad strain tensors temperature gradient and heat fluxes

periodic boundary conditions

1 l L 

 

1

RVE

RVE RVE

d



    





RVE



ij ij ij ij

    

, , i i i i

T q T q 

ij ij

 

,i i

T q

Numerical homogenization

• Hook’s law
• Fourier’s law

' ij ijkl ij

c   

' , i ij i

q k T 

• Tensor of effective elastic constants
• Tensor of effective thermal constants

11 12 13 21 22 23 31 32 33 ' 44 55 66 ij

c c c c c c c c c c c c c                     

11 ' 22 33 ij

k k k k           

Numerical homogenization

• avg. - average

Macro-stresses Homogenization Macro-strains Localization

BVP

BVP – Boundary Value Problem

Macro

Micro

RVE

Optimal design on macro-micro scales

min

• DV J

 

1 2

, ,..., ,...

i n

Ch DV B cell x x x x P             

Constraints:

min max

0, 1,2,.. , ,1,2,.. ( , , ), 0,1,2,...

i i i

J m x x x i n J J u m

  

          

xi – design variables, play the role of geometrical, material

• r topologcal parameters in the micro scale

where DV=design vector J0 – objective function described in the macro scale

Meso scale: Grains

Micro scale: Single grain

Nano scale: Molecular/atomic level Macro scale: Structure

Illustration of optimization in multiscale approach

0( , , )

J J u     

1 2

, ,..., ,...

i n

DV x x x x 

Design variables

RVE Material parameters Shape parameters Topology parameters

Evolutionary/immune/swarm optimization in multiscale

in macro scale in micro scale

RVE

DEA parameters:

2 subpopulations 20 chromosomes in each Rank selection Gasuss mutation Simple crossover

g7, g8

The best solution in the 1st generation The best solution in the last generation

max

min ,

Ch J

where J u   

1 2 3 4 5 6 7 8

, , , , , , , Ch g g g g g g g g 

Optimization of Functionally Graded Materials in Multsicale Modelling

The function or composition changes gradually in the material

http://www.unl.edu/emhome/faculty/bobaru/project_shape_optim.htm

FGM in nature – clam shell Bamboo

Functionally Graded Materials

The function or composition changes gradually in the material Metal-ceramic FGMs

http://sbir.nasa.gov/SBIR/successes/ss/3-079text.html

Optimization of FGM parameters

macromodel Micromodel - RVE

Minimization of inclusions total volume

z 1

dA

Z

n z A

f h



  

max i

u u 

6 design parameters - diameters di Minimization of inclusions total volume Constraint on maximum displacement value

Displacements map for the best solution (umax=4)

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

FGM material for tooth implant

The simplified model of implant-bone systen with FGM material – optimization of porosity

Minimization of porosity p1 (mat1) and p2 (mat2) Constraints on max eqivalent stress value in the bone area are imposed Box constraints on prosity [0.0; 0.4]

i gl voids i ch

V V p p p ch p p f             ] , [ min

2 1 2 1

F F

Macromodel FEM MSC.Nastran Micromodel FMBEM model RVE

Optimization of functionally graded materials in multiscale modelling

Distribution of equivalent stresses in the optimal design

Multicriteria Optimal Design of porous microstructures

1

min d

u

def u x

f u



 



Optimization functionals for termomechanical problems

• minimization of displacement on selected part of the boundary

2

min d

q

def q x

f q



 



• minimization of heat flux on selected part of the boundary

3

max d

q

def q x

f q



 



• maximization of heat flux on selected part of the boundary

4

d max d

por RVE

por def x RVE

f

 

  

 

• maximization of the porosity of the microstructure

Numerical example

Boundary conditions P0(total)=100N T0=0°C T1=100°C Constraints (5 design variables) Z1 – [0.53 – 0.92] Z2 – [0.09 – 0.45] Z3 – [0.09 – 0.45] Z4 – [0.08 – 0.47] Z5 – [0.09 – 0.45]

Macromodel

• f aluminium plate 50x50x1 under

thermomechanical loadings RVE model

• f microstructure with void

modeled using NURBS

Variants of multicriteria optimal design of materials

Variant 1 Variant 2

1

min d

u

def u x

f u



 



minimization of displacement on selected part of the boundary

2

min d

q

def q x

f q



 



minimization of heat flux on selected part of the boundary

3

max d

q

def q x

f q



 



• maximization of heat flux on

selected part of the boundary

4

d max d

por RVE

por def x RVE

f

 

  

 

• maximization of the porosity
• f the microstructure

Results of multicriteria optimization (variant 1)

1

d

u

def u

f u



 



2

d

q

def q

f q



 



Results of multicriteria optimization (variant 2)

3

d

q

def q

f q



 



4

d d

por RVE

por def RVE

f

 

  

 

Identification: macro-micro

Goal – find the FEM microscale model parameters

• n the base of experimental measurements in macro

Real structure FEM model What material properties for FEM gives the same results in sensor points as in real structure ?

1 1

min ˆ ˆ

DV m m i i i i j j

J where J a u u b

 

     

 

IDENTIFICATION

 

1 2

, ,..., ,...

i n

DV x x x x 

xi – design variables, play the role of material or geometrical parameters in the micro scale

min max,

,1,2,..

i i i

x x x i n   

ˆ , ˆ

i i i i

u and u computed and measured displacements and computed and measured strains    

http://www.ucc.ie/bluehist/CorePages/Bone/Bone.htm

Identification of material parameters

• f a bone tissue

The femur bone is build from trabecular and compact bone. The identification of material properties of single trabeculae.

K.Tsubota, T. Adachi, S. Nishiumi , Y. Tomita, ATEM'03, JSME-MMD, 2003

• G. M. Kurtzman, 2006

femur trabecular bone RVE single trabeculae

Identification can be performed in two stages: I) Identification of anisotropic homogenized material properties of RVE on the basis of measurements for femur II) Identification of isotropic material properties of trabeculae

• n the basis of homogenized RVE anisotropic material

properties

Problem formulation for II stage (RVE) Design parameters:

chi=[Young modulus E, Poisson ratio ] material properties of single trabeculae chi=[g1, g2]

The objective function:

where: - RVE homogenized material properties from macromodel

• computed homogenized RVE material properites

n - number of coefficients (9) The homogenized anisotropic material properties for RVE: a[i] ={E11 E22 E33 E12 E13 E23 E44 E55 E66}

The constraints on design parameters values:

1

ˆ min ( )

n i i i

F a a



 



ch

ˆi a

i

a min max i i i

g g g  

11 12 13 22 23 33 44 55 66

.

x x x x z z xy xy yz yz zx zx

E E E E E E E sym E E                                                                        

The FEM model for RVE created on the basis of

• microCT. The bone sample was taken form the femur.

~70,000 DOF

The fitness function value for the best chromosome in subpopulations

iteration fitness

Actual Found E [MPa] 3300.0 3305.5  0.330 0.329

Cr Crea eati tion of

• n of new

new graphene phene-lik like e ma mater terials ials by means of by means of the the hybrid hybrid par parallel allel evolut

• lutionar

ionary algori y algorithm thm

Nano level optimization of graphene allotropes by means of a hybrid parallel evolutionary algorithm Journal Computational Materials Science (in press) by A.Mrozek, W. Kuś, T. Burczyński

Carbon allotropes

• diamond
• graphite/graphene
• nanotubes/nanorings

etc.

• fullerenes
• amorphous state

Graphene-like 2D materials / hybridization of carbon atoms acetylenic linkages, nanowires benzene rings, base of the graphite/ graphene honeycomb lattice

Optimal searching for the new atomic structures:

• proper interaction model
• optimization’s algorithm
• stable configurations of atoms correspond to the minima
• n the potential energy surface

Bond Order (BO) potentials for molecular dynamics simulations of carbon/hydrocarbons

• LCBOP (I + II) Long range Carbon Bond Order Potential
• REBO (Reactive Empirical Bond Order)
• AIREBO (Adaptive Intermolecular REBO) a variant of the

REBO with additional torsion and (Lennard-Jones-like) long-range terms*

• ReaxFF (Reactive Force Fields) with equilibration of atomic charge

All of them can handle various hybridization states of carbon atoms

*used in this work S.J. Stuart, A.B. Tutein, J.A. Harrison, A reactive potential for hydrocarbons with intermolecular interactions, The Journal of Chemical Physics, 112(14), 2000, pp. 6472–6486

Evolutionary optimization of atomic structure

• minimization of the potential energy
• Fitness function - the total potential energy of the considered atomic cluster (sum
• ver all atomic interactions)
• Design variables/genes: the real-valued Cartesian

Coordinates of each atom in the considered cluster

• Constrains: all atoms can move freely in the triclinic
• r rectangular unit cell with imposed periodic boundary

conditions

• Neighborhood-dependent behavior of carbon atoms (i.e. hybridization’s states,

bond’s lengths and angles) is handled by AIREBO potential and conjugated gradient-based molecular statics solver

• Periodicity of the lattice is guaranteed by the molecular static solver

, , , REBO LJ TORSION ij ij kijl i j i k i j l i j k

FF E E E

  

        

  

START - generation of initial population (creation of randomly-generated positions of atoms) minimization of potential energy using molecular statics/gradient method

fitness function evaluation

selection modification of genes using evolutionary operators Stop condition ?

Proposed hybrid evolutionary-molecular computational system

END N Y

• LAMMPS
• E.A.

Parallel hybrid gradient/evolutionary algorithm (small, 2D problems) Multiple instances of LAMMPS

• LAMMPS
• E.A.

Parallel hybrid gradient/evolutionary algorithm (large, 3D problems)

Proposed hybrid evolutionary/gradient algorithm

• modular structure (each part can be replaced with appropriate equivalent,

e.g.

• AIREBO -> ReaxFF (Reactive Force Fields)
• EA -> AIS etc.
• ready for 3D optimization (and not only carbon atoms…)

Validation & Results obtained using prototype version of the algorithm

Dimensions:12x10 Å triclinic unit cell, 25 atoms 4 threads 100 individuals 124800 FF evaluations 10% mutation & crossover

200 400 600 800 1000 1200 1400 1600

• 156
• 154
• 152
• 150
• 148
• 146
• 144
• 142
• 140
• 138

Example of the progress of optimization

Supergraphene, as presented in:

Enyashin A.N., Ivanovskii A.L., Graphene allotropes, Physica Status Solidi, 248, 8, 2011, pp. 1879-1883 bond’s lengths computed using classical MD and AIREBO potential: Mrozek A., Burczynski T., Examination of mechanical properties of graphene allotropes by means of computer simulation, CAMES, 20, 4, 2013, pp. 309-323.

Supergraphene found by g-optim algorithm:

(in 34th generation) Triclinic unit cell: 10x6Å, 8 atoms (finally relaxed to 10.65x6.08Å)

10 20 30 40 50 60 70 80 90 100

• 50.5
• 50
• 49.5
• 49
• 48.5
• 48
• 47.5
• 47
• 46.5
• 46
• 45.5

1.32Å 1.38Å

potential energy (eV) vs. generation

Graphyne, as presented in:

Enyashin A.N., Ivanovskii A.L., Graphene allotropes, Physica Status Solidi, 248, 8, 2011, pp. 1879-1883 bond’s lengths computed using classical MD and AIREBO potential: Mrozek A., Burczynski T., Examination of mechanical properties of graphene allotropes by means of computer simulation, CAMES, 20, 4, 2013, pp. 309-323

Graphyne found by g-optim algorithm:

(in 23th generation) Triclinic unit cell: c.a. 10x6Å, 12 atoms (finally relaxed to 10.2x5.9Å)

10 20 30 40 50 60

• 81
• 80
• 79
• 78
• 77
• 76
• 75
• 74
• 73
• 72

potential energy (eV) vs. generation

Structure found by g-optim algorithm: (in 223 generation) Orthogonal unit cell: 4x7Å, 8 atoms 2 threads 100 individuals 22300 FF evaluations 10% mutation & crossover

50 100 150 200 250 300 350 400 450 500

• 52.2
• 52.1
• 52
• 51.9
• 51.8
• 51.7

potential energy (eV) vs. generation

• 1. Example of the „new” graphene-like materials X

• 5.94eV
• 6.31eV
• 8.01eV
• 6.31eV
• 5.94eV
• 8.01eV
• 5.94eV

a) b) Unit cell close-up X

• 2. Example of the „new” graphene-like materials Y

Structure found by g-optim algorithm: (in 55th generation) Orthogonal unit cell: 6x4Å, 8 atoms 2 threads 100 individuals 5500 FF evaluations 10% mutation & crossover

20 40 60 80 100 120 140 160 180 200

• 54.5
• 54
• 53.5
• 53
• 52.5
• 52
• 51.5
• 51
• 50.5
• 50

potential energy (eV) vs. generation

• 6.81eV
• 6.87eV
• 6.81eV
• 6.59eV
• 6.59eV

a) b) Unit cell close-up Y

equilibrate the investigated „nanospecimen” at the desired temperature apply a certain, finite deformation the structure (dε, dγ) equilibrate the structure compute all the necessary time-averaged values

(displacements/deformations, components of microstress tensor)

Examination of the mechanical properties

(tensile / shear tests at the finite temperature)

1 1 2

N N i i i ij ij i j i

m



           

 

σ v v r f

Tensile test – strain(%) - stress(N/m) curve

Young moduli (0-5%) vertical axis: 176 N/m horizontal axis: 183,4 N/m

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 5 10 15 20 25 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 5 10 15 20 25 30

Mechanical Properties of X

Tensile test – strain(%) - stress(N/m) curve

Young moduli (0-5%) horizontal axis: 226 N/m vertical axis: 280 N/m

Mechanical Properties of Y

Concluding remarks

• Two-scale macro-micro materials design needs special analytical and

computational techniques and tools.

• Coupled soft and hard computing techniques based on Computational

Intelligent System (CIS) ensure the great probability of finding global

• solutions. CIS has the great flexibility.
• Effective CIS is based on the parallel computing and grid environment.
• Optimal material and geometrical parameters on the micro-scale ensure the

extremum for an objective function in the macro-scale.

• Using CSI it is possible to create material on the nano-scale ……

Concluding remarks cont.

• Proposed algorithm gives possibility of finding new flat carbon networks with unique properties
• Newly created structures are „physically” correct: form proper basic elements (benzene rings,

triads, acetylenic groups etc.), without alone atoms or unconnected branches etc.

• The AIREBO potential seems to be reasonable choice for modeling presented flat carbon

structures (except long-range interactions), where time-consuming ab-inito methods are not suitable

• Proposed optimization algorithm is easy to parallelize, since the most time-consuming step is

molecular statics and FF evaluation

• It is possible to create a new (even 3D) material with predefined density and

properties using this methodology.

^Institute of Computer Science, Cracow University of Technology, Poland

Thank you for your attention!