modelling and simulation uncertainty - boris jeremicsokocalo.engr.ucdavis.edu/~jeremic/ modeling and...

Introduction Modeling and Parametric Uncertainty Summary [

Modelling and Simulation Uncertainty

Boris Jeremic

University of California, DavisLawrence Berkeley National Laboratory, Berkeley

Computational Mechanics Working GroupUC Davis, February 2016

Jeremic

Modeling and Simulation Uncertainty


Outline

IntroductionMotivationUncertaintiesReal ESSI Simulator

Modeling and Parametric UncertaintyModeling Uncertainty: 3D Dam/Slope Model, Expert OpinionModeling Uncertainty: Seismic Behavior of Nuclear Power PlantsParametric Uncertainty: Wave Propagation

Summary

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Motivation

Outline



Summary

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Motivation

Motivation

I Improve seismic design of soil structure systems

I Earthquake Soil Structure Interaction (ESSI) in time andspace, plays a major role in successes and failures

I Accurate following and directing (!) the flow of seismicenergy in ESSI system to optimize for

I Safety andI Economy

I Development of high fidelity numerical modeling andsimulation tools to analyze realistic ESSI behavior:Real ESSI simulator

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Motivation

Predictive CapabilitiesI Verification provides evidence that the model is solved

correctly. Mathematics issue.

I Validation provides evidence that the correct model issolved. Physics issue.

I Prediction under Uncertainty (!): use of computationalmodel to predict the state of SSI system under conditionsfor which the computational model has not been validated.

I Modeling and Parametric Uncertainties

I Predictive capabilities with low Kolmogorov Complexity

I Modeling and simulation goal:predict and inform, rather than (force) fit

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Uncertainties

Outline



Summary

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Uncertainties

Modeling Uncertainty

I Simplified modeling: Features (important ?) are neglected(6D ground motions, inelasticity)

I Modeling Uncertainty: unrealistic and unnecessarymodeling simplifications

I Modeling simplifications are justifiable if one or two levelhigher sophistication model shows that features beingsimplified out are not important

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Uncertainties

Parametric Uncertainty: Material Stiffness

5 10 15 20 25 30 35

5000

10000

15000

20000

25000

30000

SPT N Value

You

ng’s

Mod

ulus

, E (

kPa)

E = (101.125*19.3) N 0.63

−10000 0 10000

0.00002

0.00004

0.00006

0.00008

Residual (w.r.t Mean) Young’s Modulus (kPa)

Nor

mal

ized

Fre

quen

cy

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Uncertainties

Parametric Uncertainty: Material Properties

20 25 30 35 40 45 50 55 60Friction Angle [ ]

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Prob

abili

ty D

ensi

ty fu

nctio

n

Min COVMax COV

10 20 30 40 50 60 70 80Friction Angle [ ]

0.0

0.2

0.4

0.6

0.8

1.0

Cum

ulat

ive

Prob

abili

ty D

ensi

ty fu

nctio

n

Min COVMax COV

0 200 400 600 800 1000 1200 1400Undrained Shear Strength [kPa]

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

Prob

abili

ty D

ensi

ty fu

nctio

n

Min COVMax COV

0 200 400 600 800 1000 1200 1400Undrained Shear Strength [kPa]

0.0

0.2

0.4

0.6

0.8

1.0

Cum

ulat

ive

Prob

abili

ty D

ensi

ty fu

nctio

n

Min COVMax COV

Field φ Field cu

20 25 30 35 40 45 50 55 60Friction Angle [ ]

0.00

0.05

0.10

0.15

0.20

0.25

Prob

abili

ty D

ensi

ty fu

nctio

n

Min COVMax COV

10 20 30 40 50 60 70 80Friction Angle [ ]

0.0

0.2

0.4

0.6

0.8

1.0

Cum

ulat

ive

Prob

abili

ty D

ensi

ty fu

nctio

n

Min COVMax COV

0 50 100 150 200 250 300Undrained Shear Strength [kPa]

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

Prob

abili

ty D

ensi

ty fu

nctio

n

Min COVMax COV

0 50 100 150 200 250 300 350 400Undrained Shear Strength [kPa]

0.0

0.2

0.4

0.6

0.8

1.0

Cum

ulat

ive

Prob

abili

ty D

ensi

ty fu

nctio

n

Min COVMax COV

Lab φ Lab cu

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Real ESSI Simulator

Outline



Summary

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Real ESSI Simulator

Real ESSI Simulator SystemI The Real ESSI-Program is a 3D, nonlinear, time domain,

parallel finite element program specifically developed forHi-Fi modeling and simulation of Earthquake Soil/RockStructure Interaction problems for NPPs (infrastructureobjects) on ESSI-Computers.

I The Real ESSI-Computer is a distributed memory parallelcomputer, a cluster of clusters with multiple performanceprocessors and multiple performance networks.

I The Real ESSI-Notes represent a hypertextdocumentation system (Theory and Formulation, Softwareand Hardware, Verification and Validation, and CaseStudies and Practical Examples) detailing modeling andsimulation of ESSI problems.

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Real ESSI Simulator

Real ESSI Simulator System

I Developed with funding from US-NRC, US-NSF,CNSC-CCSN, and US-DOE

I The Real ESSI simulator system is designed based onpremise of high fidelity modeling and simulation

I Reduction of modeling uncertainty and propagation ofparametric uncertainty

I Real ESSI simulator, also known as Vrlo Prosto, ,, Muy Fácil, Molto Facile, , Πραγματικά

Εύκολο, , , Très Facile, VistinskiLesno, Wirklich Einfach, .

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Real ESSI Simulator

Real ESSI Modelling

input

loading stage

increment

iteration

output

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Real ESSI Simulator

Verification and Validation for High Fidelity PredictiveCapabilities

I Verification provides evidence that the model is solvedcorrectly. Mathematics issue.

I Validation provides evidence that the correct model issolved. Physics issue.

I Goal: predictive capabilities with low information(Kolmogorov) Complexity

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Modeling Uncertainty: 3D Dam/Slope Model, Expert Opinion

Outline



Summary

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3D Dam – Slope Stability

I 3D earth slope part of a concrete, earth damI Movements recorded during lowering of reservoirI 3D slope unstable (?), no one could tell, all commercial

software does 2D slope stabilityI 2D vs 3D slope stabilityI Shear strength (?) as the only material parameterI (")Expert(") increased value of measured shear strengthI Load cases: lowering and raising reservoir, slow and fastI Dam build using untreated alluvium

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Dam, Satellite Photo

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Dam, 3D Slope, Satellite Photo

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3D Slope

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3D Slope, Ground Photo

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Dam, Construction Photo

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Dam, Section

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Dam, Model

//

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Dam Slope, Failure Modes

I 3D failure patternI 3D has lower FS than 2DI Original Su FS barely enough,I With "increased" Su a bit higher

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Modeling Uncertainty: Seismic Behavior of Nuclear Power Plants

Outline



Summary

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Modeling and Simulation of Nuclear Power Plants

I Nuclear Power Plants (NPPs) design based on a numberof simplified assumptions!

I Linear elastic material behavior

I Seismic Motions: 1D or 3 × 1D, or real 3D (6D)

I Savings in construction cost possible with more accuratemodeling of NPPs

I Improvements in safety of NPPs also possible, even withhigher seismic motions, as inelastic effects "eat up"(dissipate) seismic energy

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Nuclear Power Plants: 6D or 1D Seismic MotionsI Assume that a full 6D (3D) motions at the surface are only

recorded in one horizontal directionI From such recorded motions one can develop a vertically

propagating shear wave in 1DI Apply such vertically propagating shear wave to the same

soil-structure system

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Synthetic Test MotionsI Develop free field models with sources withinI Sources are simple, point (mostly), line and surfaceI Sources will send both P and S wavesI Variation in strike and dipI Simulation programs, Real ESSI Simulator and SW4

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Synthetic Test Motions, 6D vs 1DI Danger of picking one component of motions for 1D or

3×1D (it is done all the time!)I Excellent (forced) fit, but not a prediction and information is

lost (goal is to predict and inform and not (force) fit)

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6D vs 1D NPP ESSI Response Comparison

(MP4)

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http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4



6D vs 1D: Containment Acceleration Response

0.0 0.5 1.0 1.5 2.00.30.20.10.00.10.20.3

Acce

l-X [g

]

Containment building bottom

0.0 0.5 1.0 1.5 2.00.30.20.10.00.10.20.3

Acce

l-Y [g

]

3-D1-D

0.0 0.5 1.0 1.5 2.0Time [s]

0.30.20.10.00.10.20.3

Acce

l-Z [g

]

0.0 0.5 1.0 1.5 2.00.30.20.10.00.10.20.3

Acce

l-X [g

]

Containment building top

0.0 0.5 1.0 1.5 2.00.30.20.10.00.10.20.3

Acce

l-Y [g

]

3-D1-D

0.0 0.5 1.0 1.5 2.0Time [s]

0.30.20.10.00.10.20.3

Acce

l-Z [g

]

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Parametric Uncertainty: Wave Propagation

Outline



Summary

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Uncertain Material Parameters and Loads

I Decide on modeling complexity

I Determine model/material parameters

I Model/material parameters are uncertain!I MeasurementsI TransformationI Spatial variability

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Uncertainty Propagation through Inelastic System

I Incremental el–pl constitutive equation

∆σij = EEPijkl ∆εkl =

[Eel

ijkl −Eel

ijmnmmnnpqEelpqkl

nrsEelrstumtu − ξ∗h∗

]∆εkl

I Dynamic Finite Elements

Mu + Cu + Kepu = F

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Probabilistic Elasto-Plasticity: von Mises Surface

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Gradient Theory of Probabilistic Elasto-Plasticity:Verification, Elastic-Perfectly Plastic

0.03 0.02 0.01 0.00 0.01 0.02 0.03εx

1.0

0.5

0.0

0.5

1.0

σx [M

pa]

RBFMCS

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Wave Propagation Through Uncertain Soil

0 100 200 300 400 500Shear modulus G [MPa]

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

PDF

min COVmax COV

30 20 10 0 10 20 30 40 50 60Shear strength τ [kPa]

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

PDF

min COVmax COV

0.0 0.1 0.2 0.3 0.4 0.5Time [s]

0.03

0.02

0.01

0.00

0.01

0.02

0.03

Disp

lace

men

t [m

]

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Uncertain Elastic Response at the Surface (COV = 120%)

0.0 0.1 0.2 0.3 0.4 0.5Time [s]

0.08

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.08

0.10

Disp

lace

men

t [m

]

MM - SD

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Displacement PDFs at the Surface (COV = 120%)

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Displacement CDFs (Fragilities) at the Surface (COV = 120%)

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Probability of Exceedance, disp = 0.1m (COV = 120%)

0.0 0.1 0.2 0.3 0.4 0.5Time [s]

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Prob

. of e

xcee

danc

e (d

= 0

.1m

)

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Summary

Concluding Remarks

I Modeling and simulation of infrastructure object requireshigh sophistication

I Uncertainties (modeling and parametric) influences results

I Those uncertainties need to be addressed and propagatedto results and used in decision making

I Goal is to predict and inform, and not force fit

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Summary

Acknowledgement

I Funding from and collaboration with the US-NRC,US-DOE, US-NSF, CNSC, AREVA NP GmbH, and ShimizuCorp. is greatly appreciated,

I Collaborators: Prof. Yang, Dr Cheng, Dr. Jie, Dr. Tafazzoli,Prof. Pisanò, Mr. Watanabe, Mr. Vlaski, Mr. Orbovic, andUCD students: Mr. Abell, Mr. Karapiperis, Mr. Feng, Mr.Sinha, Mr. Luo, Mr. Lacour, Mr. Yang, Ms. Behbehani

I Real ESSI Simulator: http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/

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http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/

http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/


]Real ESSI Simulator

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Real ESSI: Finite ElementsI Dry/single phase solids (8, 20, 27, 8-27 node bricks),

elastic and/or inelasticI Saturated/two phase solids (8 and 27 node bricks,

liquefaction modeling), elastic and/or inelasticI Truss, elasticI Beams (six and variable DOFs per node), elastic, inelasticI Shell (ANDES) with 6DOF per node, linear elastic, inelastic

shell soonI Contacts (dry and/or saturated soil/rock - concrete, gap

opening-closing, frictional slip), inelasticI Base isolators (elastomeric, frictional pendulum), inelastic

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Real ESSI: Material Models

I Linear and nonlinear, isotropic and anisotropic elastic

I Elastic-Plastic (von Mises, Drucker Prager, RoundedMohr-Coulomb, Leon Parabolic, Cam-Clay, SaniSand,SaniClay, Pisanò...). All elastic-plastic models can be usedas perfectly plastic, isotropic hardening/softening andkinematic hardening models.

I Viscous damping solids, Rayleigh and Caughey damping

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Real ESSI: Solution Advancement AlgorithmsI Constitutive

I Explicit, Implicit, Sub-incrementation, Line SearchI Nonlinear Static FEM

I No equilibrium iterationI Equilibrium Iterations (full Newton, modified N, Initial Stiff.)I Hyperspherical constraint (arch length, displacement

control, load control)I Line SearchI Convergence criteria: displacement, load, energy

I Nonlinear Dynamic FEMI No equilibrium iterationI Equilibrium Iterations (full Newton, modified N, Initial Stiff.)I Constant or variable time steppingI Convergence criteria: displacement, load, energy

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Real ESSI: Seismic Input

I Analytic input of seismic motions (both body (P, S) andsurface (Rayleigh, Love, etc., waves), including analyticradiation damping using Domain Reduction Method (Bielaket al.)

Pe(t)

ui

ub

ue

Γ

Large scale domain

Local feature

+Ω

Ω

Seismic source

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Real ESSI Simulator Program: Parallel, HPC

I High Performance Parallel Computing: both parallel andsequential version available, however, for high fidelitymodeling, parallel is really the only option. Parallel RealESSI Simulator runs on clusters of PCs and on largesupercomputers (Distributed Memory Parallel machines,all top national supercomputers). Plastic DomainDecomposition Method (PDD, dynamic computational loadbalancing) for elastic-plastic computations with multipletypes of finite elements and on variable speed CPUs (andnetworks)

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Real ESSI Simulator Program: Probabilistic/StochasticI Constitutive: Euler-Lagrange form of Fokker-Planck

(forward Kolmogorov) equation for probabilisticelasto-plasticity (PEP)

I Spatial: stochastic elastic plastic finite element method(SEPFEM)

Uncertainties in material and load are analytically taken intoaccount. Resulting displacements, stress and strain areobtained as very accurate (second order accurate for stress)Probability Density Functions. PEP and SEPFEM are notbased on a Monte Carlo method, rather they expand uncertaininput variables and uncertain degrees of freedom (unknowns)into spectral probabilistic spaces and solve for PDFs ofresulting displacement, stress and strain in a single run.

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VerificationI Code Verification (code coverage, memory leaks and

pointer assignment testing, static argument list testing, &c.)

I Solution verification (finite elements, constitutiveintegration, material models, algorithms, seismic input, &c.)based on analytic, closed form solutions

I Method of manufactured solutions for elasto-plasticverification

I Parameter bounds (finite elements, material models,algorithms, &c.)

I Develop error plots for elements, models, algorithms over arange of parameter

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ValidationI Traditional Experiments

I Improve the fundamental understanding of physics involvedI Improve the mathematical models for physical phenomenaI Assess component performance

I Validation ExperimentsI Model validation experimentsI Designed and executed to quantitatively estimate

mathematical model’s ability to simulate well definedphysical behavior

I The simulation tool (Real ESSI Simulator) (conceptualmodel, computational model, computational solution) is thecustomer

I New US-DOE project to validate inelastic seismic wavepropagation and soil-structure interaction

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