on computational simulations and predictionssokocalo.engr.ucdavis.edu/~jeremic/ · 2007-11-01 ·...
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Before We Start Why Do You Trust a Simulation? Examples Summary
On Computational Simulations andPredictions
Boris Jeremic
Department of Civil and Environmental EngineeringUniversity of California, Davis
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Outline
Before We Start
Why Do You Trust a Simulation?Verification, ValidationPrediction
ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations
Summary
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Before We Start
Important SourcesI W. L. OBERKAMPF, T. G. TRUCANO, AND C. HIRSCH.
Verification, validation and predictive capability incomputational engineering and physics. In Proceedings ofthe Foundations for Verification and Validation on the 21stCentury Workshop, pages 1–74, Laurel, Maryland,October 22-23 2002. Johns Hopkins University / AppliedPhysics Laboratory.
I P. J. ROACHE. Verification and Validation in ComputationalScience and Engineering. Hermosa publishers, 1998.ISBN 0-913478-08-3.
I Material from Verification and Validation in ComputationalMechanics web site http://www.usacm.org/vnvcsm/at the USACM.
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Before We Start
Motivation
I How do we use experiments to develop and improvemodels?
I How much can (should) we trust model implementations(verification)?
I How much can (should) we trust numerical simulations(validation)?
I How good are our predictions?
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Before We Start
Verification, Validation and PredictionI Verification: the process of determining that a model
implementation accurately represents the developer’sconceptual description and specification. Mathematicsissue. Verification provides evidence that the model issolved correctly.
I Validation: The process of determining the degree to whicha model is accurate representation of the real world fromthe perspective of the intended uses of the model. Physicsissue. Validation provides evidence that the correct modelis solved.
I Prediction: use of computational model to foretell the stateof a physical system under consideration under conditionsfor which the computational model has not been validated
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Verification, Validation
Outline
Before We Start
Why Do You Trust a Simulation?Verification, ValidationPrediction
ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations
Summary
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Verification, Validation
Importance of V & V
I V & V procedures are the primary means of assessingaccuracy in modeling and computational simulations
I V & V procedures are the tools with which we buildconfidence and credibility in modeling and computationalsimulations
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Verification, Validation
Maturity of Computational SimulationsNRC committee (1986) identified stages of maturity in CFD
I Stage 1: Developing enabling technologies (scientificpapers published)
I Stage 2: Demonstration of and Confidence in technologiesand tools (capabilities and limitations of technologyunderstood)
I Stage 3: Compilation of technologies and tools(capabilities and limitations of technology understood)
I Stage 4: Spreading of the effective use (changes theengineering process, value exceeds expectations)
I Stage 5: Mature capabilities (fully dependable, costeffective design applications)
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Verification, Validation
Role of Verification and Validation
MathematicalModel
ComputerImplementationDiscrete Mathematics
Continuum Mathematics
Programming
Analysis
Code Verification
SimulationComputer
ValidationModel
Reality Model Discovery
and Building
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Verification, Validation
Fundamentals of Verification and Validation
Real World
Benchmark PDE solutionBenchmark ODE solutionAnalytical solution
Complete System
Subsystem Cases
Benchmark Cases
Unit ProblemsHighly accurate solution
Experimental Data
Conceptual Model
Computational Model
Computational Solution
ValidationVerification
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Verification, Validation
Verification: Model is solved correctly (Mathematics)Verification: The process of determining that a modelimplementation accurately represents the developer’sconceptual description and specification.
I Identify and remove errors in computer codingI Numerical algorithm
verificationI Software quality
assurance practiceI Quantification of the
numerical errors incomputed solution
Benchmark PDE solutionBenchmark ODE solutionAnalytical solution
Highly accurate solution
Conceptual Model
Computational Model
Computational Solution
Verification
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Verification, Validation
Validation: Correct model is solved (Physics)Validation: The process of determining the degree to which amodel is accurate representation of the real world from theperspective of the intended uses of the model.
I Tactical goal:Identification and minimization ofuncertainties and errors inthe computational model
I Strategic goal:Increase confidence inthe quantitative predictivecapability ofthe computational model
Real World
Complete System
Subsystem Cases
Benchmark Cases
Unit Problems
Experimental Data
Conceptual Model
Computational Model
Computational Solution
Validation
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Verification, Validation
Validation Procedure Uncertainty
I Aleatory uncertainty→ inherent variation associated withthe physical system of the environment (variation inexternal excitation, material properties...). Also knowknown as irreducible uncertainty, variability and stochasticuncertainty.
I Epistemic uncertainty→ potential deficiency in any phaseof the modeling process that is due to lack of knowledge(poor understanding of mechanics...). Also known asreducible uncertainty, model form uncertainty andsubjective uncertainty
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Verification, Validation
Types of Physical Experiments
I Traditional ExperimentsI 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 (SimTool) (conceptual model,computational model, computational solution) is thecustomer
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Verification, Validation
Validation ExperimentsI A validation experiment should be jointly designed and
executed by experimentalist and computationalistI A validation Experiment should be designed to capture the
relevant physicsI A validation experiment should use any possible synergism
between experiment and computational approachesI Maintain independence between computational and
experimental resultsI Validate experiments on unit level problems, hierarchy of
experimental measurements should be made whichpresent an increasing range of computational difficulty
I Experimental uncertainty analysis should be developedand employed
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Prediction
Outline
Before We Start
Why Do You Trust a Simulation?Verification, ValidationPrediction
ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations
Summary
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Prediction
Prediction
I Prediction: use of computational model to foretell the stateof a physical system under consideration under conditionsfor which the computational model has not been validated
I Validation does not directly make a claim about theaccuracy of a prediction
I Computational models are easily misused (unintentionallyor intentionally)
I How closely related are the conditions of the prediction andspecific cases in validation database
I How well is physics of the problem understood
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Prediction
Relation Between Validation and Prediction
Quantification of confidence in a prediction:
I How do I quantify verification and its inference value in aprediction?
I How do I quantify validation and its inference value in apredictions?
I How far are individual experiments in my validationdatabase from my physical system of interest?
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Prediction
Application Domain Complete or Partial Overlap
System Parameter
Sys
tem
com
plex
ity
DomainValidation
DomainApplication Domain
Application
System Parameter
Sys
tem
com
plex
ity
DomainValidation
I Rarely applicable to engineering systems, certainly not forbridges, buildings, port facilities, dams...
I Even if the engineering system is small, environmentalinfluences (generalized loads, conditions, wear and tare)are hard to predict
I Human factors (Mars rover example: memory overflow,operator forgot to flush the memory...)
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Prediction
Application Domain – No Overlap
System Parameter
Sys
tem
com
plex
ity
ApplicationDomain
DomainValidation
Inference
I Inference⇒ Based on physics or statistics (or both)I Validation domain is actually an aggregation of tests and
thus might not be convex (bifurcation of behavior)I Experimental facilities provide for validation domain that
are exclusively non–overlapping with the applicationdomain.
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Prediction
Importance of Models and Numerical Simulations
I Verified and Validated models can be used for assessingbehavior of
I components orI complete systems,
I with the understanding that the environmental influencescannot all be taken into the account prior to operation
I but with a good model, their influence on system behaviorcan be assessed as need be (before or after the event)
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Prediction
Prediction under Uncertainty
I Ever present uncertainty needs to be estimated forpredictions
I Identify all relevant sources of uncertainty
I Create mathematical representation of individual sources
I Propagate representation of sources through modeling andsimulation process
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Piles in Layered Soils
Outline
Before We Start
Why Do You Trust a Simulation?Verification, ValidationPrediction
ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations
Summary
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Piles in Layered Soils
Single Pile in Layered Soils: Model
����������������������������������������������������
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1.72m
1.72m
7.86m
0.429m 2.40m
Interface
Case 3&4: SandCase 1&2: Clay
Case 1 & 2: ClayCase 3 & 4: Sand
Case 2&3: SandCase 1&4: Clay
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Piles in Layered Soils
Available Data for Prototype
I Sand:I friction angle φ of 37.1o,I Shear modulus at a depth of 13.7 m of 8960 kPa (Eo =
17400 kPa),I Poisson ratio of 0.35I Unit weight of 14.50 kN/m3.I Dilation angle 0o
I Clay (made up)I Shear strength 21.7 kPaI Young’s modulus 11000 kPaI Poisson ratio 0.45I Unit weight 13.7 kN/m3
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Piles in Layered Soils
Single Pile in Sand: M, Q, p
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Piles in Layered Soils
Single Pile in Sand with Clay Layer: M, Q, p
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Piles in Layered Soils
Single Pile in Sand: p − y Response
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Piles in Layered Soils
Single Pile in Sand with Clay Layer: p − y Response
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Piles in Layered Soils
p − y Pressure Ratio Reduction for Layered Soils
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Liquefying Soils
Outline
Before We Start
Why Do You Trust a Simulation?Verification, ValidationPrediction
ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations
Summary
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Liquefying Soils
VerificationNumber ofclosed formsolutions used(elastic, coupled,static and dynamic) 0 2 4 6 8 10 12 14 16
−0.2
0
0.2
0.4
0.6
0.8
1
time (µsec)
Sol
id D
ispl
. (x1
0−3 cm
)
@ depth of 1cm
0 2 4 6 8 10 12 14 16−0.2
0
0.2
0.4
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1
time (µsec)
Flu
id D
ispl
. (x1
0−3 cm
)
Closed form, K=10−8m/s (k=10−9cm3s/gr)u elementup elementupU element
Note: All simulations withγ=0.65, K=10−8m/s,200 Elements, L=4cm(.02x.02x.02cm)
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Liquefying Soils
Material Model Validation (Dafalias-Manzari)
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Liquefying Soils
Loose Sand, Level Ground
−20
0
20
E10
τ h (kP
a)
−20
0
20
E07
τ h (kP
a)
−20
0
20
E04
τ h (kP
a)
0 50 100−20
0
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τ h (kP
a)
σ′v (kPa)
0
1E10
Ru
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Ru
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Ru
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Ru
Time (s)
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τ h (kP
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a)
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τ h (kP
a)
0 2 4 6−20
0
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τ h (kP
a)
εh (%)
−4
0
4
K
Dz
(cm
)
SoilWater
−4
0
4
H
Dz
(cm
)
−4
0
4
E
Dz
(cm
)
0 20 40 60 80−4
0
4
B
Dz
(cm
)
Time (s)
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Liquefying Soils
Loose Sand, Sloping Ground
−25
0
25
E10
τ h (kP
a)
−25
0
25
E07
τ h (kP
a)
−25
0
25
E04
τ h (kP
a)
0 50 100−25
0
25
E01
τ h (kP
a)
σ′v (kPa)
0
1E10
Ru
0
1E07
Ru
0 20 40 60 800
1E04
Ru
0 20 40 60 800
1E01
Ru
Time (s)
−25
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25
E10
τ h (kP
a)
−25
0
25
E07
τ h (kP
a)
−25
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25
E04
τ h (kP
a)
0 10 20−25
0
25
E01
τ h (kP
a)
εh (%)
0
1.5
K
Dx
(m)
0
1.5
H
Dx
(m)
0
1.5
E
Dx
(m)
0 10 200
1.5
B
Dx
(m)
Time (s)
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
ESS Simulations
Outline
Before We Start
Why Do You Trust a Simulation?Verification, ValidationPrediction
ExamplesPiles in Layered SoilsLiquefying SoilsESS Simulations
Summary
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
ESS Simulations
Detailed 3D, FEM model
I Construction processI Two types of soil: stiff soil (UT, UCD), soft soil (Bay Mud)I Deconvolution of given surface ground motionsI Use of the DRM (Bielak et al.) for seismic inputI Soil:
I Sand (single monotonic triax test from UT...)I Clay (made up, bay mud, total stress)
I Piles→ beam-column elements in soil holesI Structural model: collaboration UCD, UCB and UWI No artificial damping (only mat. dissipation, radiation)
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
ESS Simulations
Element Size Issue
Filtering of frequencies depending on element size (want atleast 10 nodes per full wave form)
model size (el) el. size fcutoff min. G/Gmax γ
12K 1.0 m 10 Hz 1.0 <0.5 %15K 0.9 m >3 Hz 0.08 1.0 %150K 0.3 m 10 Hz 0.08 1.0 %500K 0.15 m 10 Hz 0.02 5.0 %
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
ESS Simulations
FEM Mesh (one of)
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
ESS Simulations
Simulation Results
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kN*m
)
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Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
ESS Simulations
Northridge Input Motions
0 10 20 30 40 50 60
−2
0
2
Time (s)
Acc
eler
atio
n (m
/s2 ) Acceleration Time Series − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)
0 10 20 30 40 50 60−0.2
0
0.2
Time (s)
Dis
plac
emen
t (m
) Displacement Time Series − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)
1 2 3 4 5 6 7 8 9 100
1
2
Period (s)Fou
rier
Am
plitu
de (
m/s
2 )
Acceleration Frequency Content − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)
1 2 3 4 5 6 7 8 9 100
0.2
0.4
Period (s)Fou
rier
Am
plitu
de (
m)
Displacement Frequency Content − Input Motion (NORTHRIDGE EARTHQUAKE, 1994)
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
ESS Simulations
Short Period E.: Left Bent, Structure and Soil, Disp.
0 10 20 30 40 50 60
−0.2
−0.1
0
0.1
0.2
0.3
Time (s)
Dis
plac
emen
t (m
)
SSS CCC SSC CCS SCS CSC SCC CSS
0 10 20 30 40 50 60
−0.2
−0.1
0
0.1
0.2
0.3
Time (s)
Dis
plac
emen
t (m
)
SSS CCC SSC CCS SCS CSC SCC CSS Freefield Input Motion
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
ESS Simulations
Short Period E.: Left Bent, Structure and Soil, Acc.
0 10 20 30 40 50 60−3
−2
−1
0
1
2
3
Time (s)
Acc
eler
atio
n (m
/s2 )
SSS CCC SSC CCS SCS CSC SCC CSS
0 10 20 30 40 50 60−3
−2
−1
0
1
2
3
Time (s)
Acc
eler
atio
n (m
/s2 )
SSS CCC SSC CCS SCS CSC SCC CSS Freefield Input Motion
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
ESS Simulations
Short Period E.: Left Bent, Structure and Soil, Acc.Sp.
0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
2
4
6
8
10
Period (s)
Fou
rier
Am
plitu
de (
m/s
2 )
SSS CCC SSC CCS SCS CSC SCC CSS
0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
1
2
3
4
5
Period (s)
Fou
rier
Am
plitu
de (
m/s
2 )
SSS CCC SSC CCS SCS CSC SCC CSS Freefield Input Motion
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
ESS Simulations
Short Period E.: Left Bent, Free Field vs Real Disp.
0 5 10 15 20 25
−0.1
−0.05
0
0.05
0.1
0.15
Time (s)
Dis
plac
emen
t (m
)
SSS CCC Freefield Input Motion
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions
Before We Start Why Do You Trust a Simulation? Examples Summary
Summary
I Importance of verification and validation for numericalprediction (simulations)
I Detailed treatment in new courses:I Spring ’08 ECI280A, Nonlinear Finite ElementsI Spring ’09 ECI280B, Nonlinear Dynamic Finite Elements
I Would you (and others) trust simulations if you followed Vand V procedures?
Jeremic Computational Geomechanics Group
On Computational Simulations and Predictions