Webinar Parameter Identification with optiSLang...default settings is the method of choice Nature...

Webinar

Parameter Identification

with optiSLang

Dynardo GmbH

2Webinar Parameter Identification with optiSLang

Technical Notes

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Outline

Theoretical background

Process Integration

Sensitivity analysis

Least squares minimization

Examples:

Theoretical Background

Inverse Identification of Model Parameters

• Identification of unknown model parameters by the calibration of the model with respect to given measurements

• Direct relation between measurements and model parameters is known only inversely as forward simulation model

The Forward Simulation

• For given set of model parameters p the model responses y can be calculated with a given simulation model

• Deviation of model responses and measurements y* can be evaluated

• For which parameter set popt model responses and measurement agree sufficiently well?

Model parameters Simulation model Model responses

Measurements

Least Squares Minimization

• The likelihood of the parameters is proportional to the conditional

probability of measurements y* from a given parameter set p

• For correct model (y* - y) is caused only by measurement errors

• Assuming normally distributed measurement errors:

• If the errors are independent we obtain

• With constant standard deviation the objective simplifies

Requirements to the Identification Procedure

• The simulation model needs to represent the main physical behavior

(systematic model errors are not considered)

• Since the least squares minimization may lead to a local optimum a

global optimization strategy is necessary

• Only sensitive parameters can be identified

• Different parameter combinations may lead to a similar objective

Uniqueness of identified parameters has to be assessed

• use scalar values or signals inside ANSYS Workbench

• identify which parameters have influence and

can be calibrated

• match experimental data with simulation

Model CalibrationModel update to increase your simulation quality!

Question?

Process Integration

Parametric model as base for

• User defined optimization (design) space

• Naturally given robustness (random) space

Design variablesEntities that define the design space

Response variablesOutputs from the system

The CAE processGenerates the results according to the inputs

Scattering variablesEntities that define the robustness space

optiSLang Integrations & Interfaces

Direct integrations ANSYS Workbench MATLAB Excel Python AMESim SimulationX

Supported connections ANSYS APDL Abaqus Adams AMESim …

Arbitary connection ofASCII file based solvers

Signals can be directly imported from MATLAB, Excel, Python, AMESim, SimulationX & ASCII

Signals in optiSLang

• Signals are vector outputs having an abscissa (e.g. time axis)

and several output channels (e.g. displacements, velocities)

• Signal functions enables the user to extract local and statistical

quantities and to analyze differences between several signals

• Match signal data (curves) with Signal Processing

Signal Processing – Definition of Signals

• The ETK node enables the

definition of several solver

and reference signals

• Reads many CAE binary output

formats and text files

• Can read signals, vectors

and matrices

• Instant visualization of

vectors and signals

Sensitivity Analysis

Automatic workflow

with a minimum of solver runs to:

• identify the important parameters for each response

• Generate best possible metamodel (MOP) for each response

• understand and reduce the optimization task

• check solver and extraction noise

Understand the most important input variables!

Sensitivity Analysis

Least Squares Minimization

Definition of objective

• Monotonous increasing of abscissa

• Hysteresis Curve

• Decomposition in load and unload

• Additional terms for max force and intersection with x-axis

• 2 load-curves for 1 material behavior

• Weighting of different experiments in one objective function by

normalizing the RMSE by the response ranges (or standard deviations)

optiSLang Optimization Algorithms

Gradient-based Methods

• Most efficient method if gradients are accurate enough

• Consider its restrictions like local optima, only continuous variablesand noise

Adaptive Response Surface Method

• Attractive method for a small set of continuous variables (<20)

• Adaptive RSM with default settings is the method of choice

Nature inspired Optimization

• GA/EA/PSO imitate mechanisms of nature to improve individuals

• Method of choice if gradient or ARSM fails

• Very robust against numerical noise, non-linearity, number of variables,…

Decision Tree for Optimizer Selection

• optiSLang automatically suggests an optimizer depending on the

parameter properties, the defined criteria and user specified settings

Question?

Examples

Identification of:

1. the geometry parameters of a press contact

2. material parameters of spring steel

3. material parameters of sandstone

4. fracture parameters of concrete

5. hyperelasticity parameters of an OGDEN law

6. the geometry parameters of a cantilever beam

1st example: Press fit contact

• Finite element model in ANSYS Workbench

• Variation of geometry parameters

• Reaction forces as Insertion Force and

Pull out Force

1st example: Problem Definition

0 0,0002 0,0004 0,0006 0,0008 0,001 0,0012 0,0014 0,0016

Insertion Force

Pull out Force

desired behavior

initial simulation

• Simulation with initial geometry parameters vs. reference (desired behavior)

• Finite element model in ANSYS Workbench

• Nonlinear material behavior

• Tensile bar is deformed by a

predefined displacement

• Reaction forces at deformed tensile bar end (1)

are monitored depending on deformation

between named selection u1 (2) and u2 (3)

and saved into the result file file.rst

1.3.2.

2nd example: Tension Test of Spring Steel

2nd example: Problem Definition

• Simulation with initial materials parameters vs. reference (measurements)

2nd example: Problem Definition

• Identification of the material parameters to optimally fit the

force-displacement curve to the measurements

• Unknown material parameters for

nonlinear isotropic hardening (nliso):

• Young´s modulus

• Yield stress σ0

• Linear hardening coefficient R0

• Exponential hardening coefficient R∞

• Exponential saturation parameter b

• Objective function is the sum of squared errors

between the reference and the calculated

force-displacement function values

σ = σ0 + R0εpl + R∞ (1-e-b εpl)

2nd example: Task Description

• Generation of a solver chain using ANSYS Workbench

and Signal Processing

• Definition of the input parameters

• Definition of output and

reference signals

• Sensitivity analysis of signal

extraction terms using

the given parameter bounds

• Single objective, unconstrained

optimization by minimizing

the sum of squared errors

• Unknown parameters defined in ASCII input file

2nd example: Tension Test of Spring Steel

• Displacements and forces

of measurements are

parameterized as signal

2nd example: Definition of the Reference Signal

2nd example: Definition of the Output Signal

• Displacements and forces

of simulation are

parameterized as signal

from a binary format

(file.rst)

• With Instant Visualization (1) it is possible to compare both signals

Both signals do not have the same discretization (2) and length (3)

To get the same length and discretization it is necessary to extract the abscissa from the Signal_Ref and than interpolate the Signal_raw to this abscissa

2nd example: Definition of the Output Signal

2nd example: Definition of Signal Functions

• The displacement is divided in 15 equally spaced steps (1-15) to get

more detailed information about the influence of the 5 material

parameters

• At these steps the forces will be extracted

15.…1.

2nd example: Definition of the Design Variables

1. Adjust lower and upper bounds for all parameters

2nd example: Results of the Sensitivity Analysis

• The reference is covered sufficiently by the simulations

• Parameter bounds seem to be adequate for the calibration

• The CoP value of the signal difference indicates a good explainability

of this function

• Linear hardening coefficient R0 are not detected as important

Check also single force_steps_sim values

force_steps[0]

force_steps[14]…

• Single values can be explained much

better as global difference

• Only Linear hardening coefficient R0 is

unimportant in all force values

• The influence of the Young´s modulus

decreases meanwhile the influence of

the exponential hardening coefficient

R∞ increases with increasing

displacement

2nd example: Optimization using the MOP

• Linear hardening coefficient R0 is not sensitive to any of the force values

It can not be identified and is not considered in the optimization

• Single force value are approximated by MOP and the criteria (sum of

squared errors) is formulated based on their approximation

2nd example: Results of the Optimization on MOP

• The optimizer converges in a few iterations

• The best design is validated

The agreement between reference and simulation is already very good

Summary

• The single force values could by approximated by the MOP

much better as the global difference value

The objective function was formulated directly with the force values

The optimization on the MOP obtained a very good agreement of

simulation and measurement curve

Excellent agreement could by finally achieved with the Simplex optimizer

Initial: difference = 3864N MOP: difference = 268N Simplex: difference = 205N

optiSLang Training Program

Need More information? Training?

Upcoming Events

Webinars (approx. 1hr.)Introduction to optiSLang Sep. 16, 2016optiSLang and ANSYS Workbench Sep. 19, 2016optiSLang and ANSYS Maxwell Sep. 20, 2016Data Analysis with optiSLang Sep. 21, 2016Parameter Identification with optiSLang Sep. 22, 2016optiSLang and Simulation X Sep. 27, 2016Customization and Automation in optiSLang Sep. 27, 2016Introduction to Statistics on Structures Sep. 28, 2016

optiSLang Basic training (3days in Weimar) Oct. 24-26, 2016

Info and registration athttp://dynardo.de/en/training/training/seminaroverview.html

Need more information?

support@dynardo.de

03643/9008-32

Trainings…

Any request or recommendation…

kontakt@dynardo.de

Need a helping hand?

Pilot projects

CAE-Consulting

Thank you

For more information please

visit our homepage:

www.dynardo.com

Webinar Parameter Identification with optiSLang...default settings is the method of choice Nature...

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