1
Dr.-Ing. Johannes WillCEO DYNARDO GmbH
Time to MarketCost efficient ways for optimal and robust products
DYNARDO • © Dynardo GmbH 2015
2
Dynardo
• Founded: 2001 (Will, Bucher,
CADFEM International)
• More than 50 employees,
offices at Weimar and Vienna
• Leading technology companies
Daimler, Bosch, E.ON, Nokia,
Siemens, BMW are supported
Software Development
Dynardo is your engineering specialist
for CAE-based sensitivity analysis,
optimization, robustness evaluation
and robust design optimization
• Mechanical engineering
• Civil engineering &
Geomechanics
• Automotive industry
• Consumer goods industry
• Power generation
CAE-Consulting
DYNARDO • © Dynardo GmbH 2015
3
DYNARDO • © Dynardo GmbH 2015
• Simulation is necessary for time to market and cost efficiency
• Hardware trial and error needs to be reduced, test needs to be placed late in the product development
• CAE-based optimization and CAE-based robustness evaluation becomes more and more important in virtual product development
– Optimization is introduced into virtual prototyping since 20 years
– Robustness evaluation is the key methodology for safe, reliable and robust products
– The combination of optimizations and robustness evaluation will lead to robust design optimization strategies
Challenges in Virtual Prototyping
4
Robust DesignRobust Design Optimization (RDO) optimize the design performance
with consideration of scatter of design (optimization) variables as well as other tolerances or uncertainties.
As a consequence of uncertainties the location of the optima as well as the contour lines of constraints scatters.
To proof Robust Designs safety distances are quantified with variance or probability measurements using stochastic analysis.
DYNARDO • © Dynardo GmbH 2015
5
Robust Design Optimization
Pareto Optimization
Adaptive Response Surface
Evolutionary Algorithm
DYNARDO • © Dynardo GmbH 2015
6
CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)
Robust Design Optimization
Optimization
Sensitivity Analysis
Single & multi objective (Pareto) optimization
Robust DesignVariance based
Robustness evaluation
Probability based Robustness valuation(Reliability Analysis)
Start
DYNARDO • © Dynardo GmbH 2015
7
DYNARDO • © Dynardo GmbH 2015
Sensitivity Analysis Workflow
8
Deterministic DoE
• Complex scheme required to detect multivariate dependencies
• Exponential growth with dimension
• Full factorial:
• Koshal linear:
Advanced Latin Hypercube Sampling
• Reduced sample size for statistical estimates
compared to plain Monte Carlo
• Reduces unwanted input correlation
How to Generate a Design of Experiments
DYNARDO • © Dynardo GmbH 2015
9
• Deterministic designs use maximum 3 levels for each variable
• No. of solver calls grows exponentially with dimension
• LHS with N samples produces N levels for each variable: better scan
• Reducing the variable space does not loose the information of removed
variables in LHS
Example: 4 minor and 1 major important input variables:
LHS, 100 samples Full factorial, 243 designs
Why do we prefer Stochastic Sampling?
DYNARDO • © Dynardo GmbH 2015
10
Identifying important parameters
From tornado chart of linear correlations to the Coefficient of Prognosis (CoP)
Will, J.; Most, T.: Metamodel of optimized Prognosis (MoP) – an automatic approach for user friendly design optimization; Proceedings ANSYS Conference 2009, Leipzig, Germany,www.dynardo.de
DYNARDO • © Dynardo GmbH 2015
11
Correlation Measurements
• Coefficients of pairwise linear/quadratic correlation is the simplest correlation measurement
• Multi-dimensional non-linear correlation can be detected using advanced meta models (Neural networks, Moving least squares,..)
Goodness of fit Measurements (CoD)
• Goodness of Fit (Coefficient of Determination CoD) summarize correlations on the meta models
Statistical measurements
DYNARDO • © Dynardo GmbH 2015
12
Metamodel of Optimal Prognosis (MOP)
• Approximation of solver output by fast surrogate model
• Reduction of input space to get best compromise between available
information (samples) and model representation (number of inputs)
• Advanced filter technology to obtain candidates of optimal subspace
• Determination of optimal approximation model (polynomials, MLS, …)
• Assessment of approximation quality (Coefficient of Prognosis, CoP)
MOP algorithm solves 3 important tasks:
• Best variable subspace
• Best meta-model
• Estimation of prediction quality
DYNARDO • © Dynardo GmbH 2015
13
Which optimization algorithm?
Gradient-Based
Algorithms
Evolutionary Algorithm
Pareto Optimization
Adaptive Response Surface
global Response Surface
Optimization Algorithms:
Sensitivity Analysis allows best choice!
Which one is the best?
DYNARDO • © Dynardo GmbH 2015
14
Optimization of see hammer
Dynamic performance optimization under weight and stress constraints using 30 CAD-parameter. With the help of sensitivity study and optimization (ARSM), the performance of a deep sea hammer for different pile diameters was optimized.
Design Evaluations: 200 times 4 loadcaseCAE: ANSYS workbenchCAD: ProEngineer
Initial Design valid for two pile diameter
Optimized design valid for four pile diameter
weight=4365 kg weight=5155 kg
DYNARDO • © Dynardo GmbH 2013
15
• Optimization of the total weight of two load cases with constrains (stresses)
• 30.000 discrete Variables
• Self regulating evolutionary strategy
• Population of 4, uniform crossover for reproduction
• Active search for dominant genes with different mutation rates
Solver: ANSYS
Design Evaluations: 3000
Design Improvement: > 10 % 0
Optimization of a Large Ship VesselEVOLUTIONARY ALGORITHM
Riedel, J.: Gewichtsoptimierung eines Passagierschiffes, Bauhaus Universität Weimar, Institutskolloquium, 2000, Germany, www.dynardo.de]
DYNARDO • © Dynardo GmbH 2013
16
CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)
Robust Design Optimization
Optimization
Sensitivity Analysis
Single & multi objective (Pareto) optimization
Robust DesignVariance based
Robustness evaluation
Probability based Robustness valuation(Reliability Analysis)
Start
DYNARDO • © Dynardo GmbH 2015
17
Robustness Evaluation Workflow
DYNARDO • © Dynardo GmbH 2015
18
1. Reliable Input Definition Distribution function Correlations Random fields
2. Reliable stochastic analysis variance-based robustness evaluation using optimized LHS suitable portfolio of Reliability Analysis
3. Reliable Post Processing Coefficient of Prognosis Reliable variation and correlation measurements easy and safe to use
Successful Robustness Evaluation need the balance between
Acceptance of method/result documentation/communication!
DYNARDO • © Dynardo GmbH 2015
19
Definition of Uncertainties
Correlation is an important characteristic of stochastic variables.
Distribution functions define variable scatter
Correlation of single uncertain values
Spatially correlated field values:Statistics on Structures
Translate know how about uncertainties into proper scatter definition
Tensile strength
Yie
ld s
tress
DYNARDO • © Dynardo GmbH 2015
20
Implementation of Random Field Parametric
4. Running Robustness Evaluation including Random Field effects
3. Generation of multiple imperfect structures using Random Field parametric
Introduction of spatial correlated scatter to CAE-Parameter (geometry, thickness, plastic values)
1. Input: multiple process simulation or measurements
2. Generation of scatter shapes using Random Field parametric, quantify scatter shape importance
DYNARDO • © Dynardo GmbH 2015
21
Robustness Post-processing
Traffic light plot
Overview of scatter range
Histogram & Statistical Data
Estimate sigma level
MOP/CoP Sensitivities
Monitor local forecast quality / non-linearities
Cause analysis
DYNARDO • © Dynardo GmbH 2015
22
Robustness check of optimized designs • With the availability of parametric modeling environments like
ANSYS workbench an robustness check becomes very easy!
• Menck see hammer for oil and gas exploration (up to 400m deep)
• Robustness evaluation against tolerances, material scatter and working and environmental conditions
• 60 scattering parameter
Design Evaluations: 100Process chain: ProE-ANSYS workbench- optiSLang
DYNARDO • © Dynardo GmbH 2013
23
Reliability Analysis
• Robustness evaluation reliable estimate relatively high probabilities (2, like 1% of failure)
• Reliability analysis verify rare event probabilities
(≥3, smaller then 1 out of 1000)
Monte Carlo Sampling is the safest and most robust way to calculate small event probabilities, but at the same time prohibitive expensive
There is no one magic algorithm to estimate probabilities with “minimal” sample size.
All “effective” algorithms will try to learn about the failure domain and have the risk to learn unreliable information
Therefore it is recommended to use two different algorithms to verify rare event probabilities
DYNARDO • © Dynardo GmbH 2015
24
Gradient-based algorithms = First Order Reliability algorithm (FORM)
Adaptive Response Surface Method
Latin Hypercube Sampling
Reliability Analysis AlgorithmsISPUD Importance Sampling using Design Point
Monte Carlo Sampling Directional Sampling
X1
X2
DYNARDO • © Dynardo GmbH 2015
25
Robustness & Reliability Algorithms
How choosing the right algorithm?
Robustness Analysis provide the knowledge to choose the
appropriate algorithm
DYNARDO • © Dynardo GmbH 2015
26
Reliability Analysis of turbo machines
Basic Design Objectives:
• Life of the disc
• Mass of the discThermal AnalysisStress Analysis
Analysis Disciplines:
Basic Costumer Requirements
• Lifecycles High
• Mass Low
3D Model of HPT-Disc
Performance needs to be proven which a given Probability of Failures (POF)
DYNARDO • © Dynardo GmbH 2013
27
Limit state (Lifecycles)
Probability of Failure (POF)
Design 1 Design 2
3.0*10-5
30000 cycles
1.3*10-8
28000 cycles
Requirement not fulfilled
Requirement fulfilled
For example: requirement ofPOF for predicted life < 1.0*10-6
Check reliability of predicted life
Solver: ANSYS WorkbenchMethod: ARSM30..50 Solver evaluations
DYNARDO • © Dynardo GmbH 2013
28
CAE process (FEM, CFD, MBD, Excel, Matlab, etc.)
Robust Design Optimization
Optimization
Sensitivity Analysis
Single & multi objective (Pareto) optimization
Robust DesignVariance based
Robustness evaluation
Probability based Robustness valuation(Reliability Analysis)
Start
DYNARDO • © Dynardo GmbH 2015
29
Robust Design Optimization
Pareto Optimization
Adaptive Response Surface
Evolutionary Algorithm
DYNARDO • © Dynardo GmbH 2015
30
3) From optiSLang Robustness Evaluation safety margins are derived.
4) Three steps of optimization using optiSLang ARSM and EAoptimizer improve the design to an optiSLang Six sigma design.
2) The design was checked in the space of 36 scattering variables using optiSLang Robustness evaluation. Some Criteria show high failure probabilities!
5) Reliability proof using ARSMto account the failure probability did proof six sigma quality.
Start: Optimization using 5 Parameter, then customer asked: How save is the design?
by courtesy of
Iterative RDO of a Connector
DYNARDO • © Dynardo GmbH 2015
Source: Roos, D. and R. Hoffmann (2008). Successive robust design optimization of an electronic
connector, Proceedings Weimarer Optimization and Stochastic Days 5.0, Weimar, Germany
1) From the 31 optimization parameter the most effective one are selected with optiSLang Sensitivity analysis.
31
RDO - best practise
• Substantial robustness evaluation and robustness measures are a necessary first step
• Best available translation of all available information about uncertainties is crucial
• the careful planning of a suitable algorithmic RDO workflow and careful checking of suitable measures for design robustness is recommended
• Consequently, it is recommended to start with an iterative RDO approach using decoupled optimization and robustness steps.
• This iterative approach helps to better understand scattering variable importance in order to adjust the necessary safety margins.
DYNARDO • © Dynardo GmbH 2015
32
• For serial use RDO software tools needs to support process automation and integration together with “easy and safe to use” modules, algorithmic wizards and post processing for
– large number of parameter
–non linear, noisy, imperfect (loss of designs) variation spaces
– including process integration and automation functionality
–minimization of necessary solver runs
• The CAX Tools need to support parametric modelling
• Thanks to the modern job control programs, cloud and CPU improvements job load, hardware and software recourses are significant, but no general bottle neck
Challenges of CAE based RDO
DYNARDO • © Dynardo GmbH 2015
33
optiSLang– general purpose tool for variation analysis
• optiSLang is an algorithmic toolbox for
sensitivity analysis,
model calibration
optimization,
robustness evaluation,
reliability analysis and
robust design optimization (RDO)
• optiSLang offers high end process
automations and integration functionality for
workflow design
Easy and safe to use:
• optiSLang offers the beginner and
expert users an easy and reliable
application by means of predefined
workflows, algorithmic wizards and
robust default settings
DYNARDO • © Dynardo GmbH 2015
34
optiSLang process automation and systemintegration
Adams
DYNARDO • © Dynardo GmbH 2015
35
Seamless integration intopowerful Parametric Modeling EnvironmentoptiSLang inside ANSYS
minimize
• Including process automation, third party CAE integration, bidirectional CAD interfaces, parallel computing
• Easy parametrization via parameter manager
• With this technology ANSYS Workbench is ready to address RDO task‘s
DYNARDO • © Dynardo GmbH 2015
36
Modules Sensitivity, Optimization and Robustness provide „best practice“ optiSLang workflows
optiSLang inside ANSYS Workbench
DYNARDO • © Dynardo GmbH 2015
37
RDO Booklet
The RDO Booklet aims
- to explain the CAE-based Robust Design Optimization approach to managers, engineers & designers
- try as simple as possible to introduce all relevant pieces of technology from a practical point of view
- to illustrate the RDO approach with and engineering example.
Introduction Weimar Optimization and Stochastic days 2015
DYNARDO • © Dynardo GmbH 2015
38
Dr.-Ing. Johannes WillCEO DYNARDO GmbH
DYNARDO • © Dynardo GmbH 2015
Time to MarketCost efficient ways for optimal products
39
offers to the market:
• Software
• Parametric CAX modelling environment like ANSYS Workbench together with general purpose variation analysis tool optiSLang to support virtual prototyping & product optimization
• Consulting service to establish virtual product optimization at your company at different levels
• establish parametrized CAX models & CAX process automation and integration
• establish parametrized CAE workflows (vertical applications) and calibrated CAX models to be used in variation studies
• establish functional relationships (MOP’s) to approximate variation windows of optimization parameters or uncertainties based on simulation or/and tests
Simulation is the key for time to market
DYNARDO • © Dynardo GmbH 2015
40The Dynardo Hydraulic Fracturing workflow
DYNARDO • © Dynardo GmbH 2015
41Dynardo‘s Hydraulic fracturing Simulation Toolbox
DYNARDO • © Dynardo GmbH 2015
42
42
By using cost function and Dynardo meta models (MOP) we can produce Pareto Frontier between conflicting goals Cost reduction and EUR optimization.
Stay with cost, optimize EUR
Reduce cost, stay with EUR
optimal EUR, highest costs
Workflow over all relevant disciplines
We needed to include all relevant disciplines being able to convince the asset teams.
Current frac design
DYNARDO • © Dynardo GmbH 2015
43
• Software
• Classic approach: Deliver the software (ANSYS, Dynardo HF Extension, optiSLang) environment to the customer
– But to establish the complex CAX workflow requires implementation time and team of experts
• Consulting service to establish the workflow
• Prepare a vertical application: Deliver calibrated, parametrized reservoir models including software environment to the customer to continue with variation studies
• Upfront simulation: Deliver MOP’s to approximate variations windows of operational parameters and reservoir uncertainties and combine with cost functions in EXCEL
Example hydraulic fracturing in Oil and Gas
DYNARDO • © Dynardo GmbH 2015
44
Use of MOP
DYNARDO • © Dynardo GmbH 2015
• Integrate advanced cost model via EXCEL node and couple to production model using MOP’s in optiSLang
• MOP models are updated per reservoir in regard of possible variation window of operational parameter
45
MOP- key to generate best possible functional models
• During a sensitivity analysis, MOPs (Metamodel of Optimal Prognosis) functional models are determined by optiSLang to approximate and understand as best as possible the correlation between input parameter variation and response variation.
Sensitivity Analysis
Latin Hypercube Sampling (LHS)uniform scanning of extensive design spaces
DoE
Solver
MOP
Approximation models to understand the correlation between input parameter and response variation
DYNARDO • © Dynardo GmbH 2015
The Power of using MOP
46
Include MOP‘s in your web services toprovide customer best possibleproduct selection
The Power of using MOP
DYNARDO • © Dynardo GmbH 2015
47
1. Generate parametric CAE models to calculate product performance
2. Validate the CAE models with available measurements
3. Scan possible product assemblies in advance using LHS sampling
4. Generation and Verification of Meta models to have functional representation of possible variants
5. Use MOP‘s in Customer‘s sales tool to support product selection and assembly
MOP Service
The Power of using MOP
DYNARDO • © Dynardo GmbH 2015
48
Optimization Goal: Module requirements like m² panel, solar surface, module arrangement
System Loading:Dead weight, wind load, snow load, structure/foundation interaction)
The Power of using MOP
System Optimization using MOP
BeamRafter
GS 13/58 GS 19/63 GS 25/65 GS 31/69
Module library
Search for cost-efficient configuration of System (minimized material consumption) from existing profile libraryMOP
Solar module
DYNARDO • © Dynardo GmbH 2015
49
Robust Design Optimization (RDO)
in virtual product development
optiSLang enables you to:
• Quantify risks
• Identify optimization potentials
• Adjust safety margins without limitation of input parameters
• Secure resource efficiency
• Improve product performance
• Save time to market
DYNARDO • © Dynardo GmbH 2014
Read more about theory, applications and customer stories at our
internet library: www.dynardo.com