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In
the "conventional design" approach, a design is improved
by evaluating its "response" and making design changes
based on experience or intuition. This approach does not always lead
to the desired result, that of a 'best' design, since the design
objectives are often in conflict. It is therefore not always clear
how to change the design to achieve the best compromise of these
objectives. A systematic approach can be obtained by using an
inverse process of first specifying the criteria and then computing
the 'best' design according to a formulation. The improvement
procedure that incorporates design criteria into a mathematical
framework is referred to as Design
Optimization This procedure is often iterative in nature and
therefore requires multiple simulations.
No two products of the same design will be identical in performance,
nor will a product perform exactly as designed or analyzed. A design
is typically subjected to Structural
variation and Environmental variation
input variations that cause a variation in its response that may
lead to undesirable behavior or failure. In this case a Probabilistic
Analysis, using multiple simulations, is required to assess the
effect of the input variation on the response variation and to
determine the probability of failure.
To
run and control multiple analyses simultaneously, LS-OPT® provides a
simulation environment that allows distribution of simulation jobs
across multiple processors or networked computers. Each job running
in parallel consists of the simulation, data extraction and disk
cleanup. Measurements of time remaining or performance criteria such
as velocity or energy are used to measure job progress for LS-DYNA®'s explicit dynamic analysis calculations.
The graphical preprocessor LS-OPT®ui facilitates definition of the design
input and the creation of a command file while the postprocessor
provides output such as approximation accuracy, optimization
convergence, tradeoff curves, anthill plots and the relative
importance of design variables. The postprocessor also links to LS-PrePost® to allow the viewing of the model representing a chosen simulation
point.
Typical applications of LS-OPT® are
Future
versions of LS-OPT® will combine optimization and probabilistic
analysis features in Reliability-Based Design Optimization.
Capabilities
Optimization
The
Optimization capability in LS-OPT® is based on Response
Surface Methodology and Design of
Experiments. The D-Optimality Criterion
is used for the effective distribution of sampling points for
effective generalization of the design response. A Successive
Response Surface Method allows convergence of the design
response. Neural Networks provide an updateable global approximation
that is gradually built up and refined locally during the iterative
process. A Space Filling sampling scheme is used to update the
sampling set by maximizing the minimum distances amongst new and
existing sampling points.
LS-OPT®
allows the combination of multiple disciplines and/or cases for the
improvement of a unique design. Multiple criteria can be specified
and analysis results can be combined arbitrarily using C or FORTRAN
type mathematical expressions.
Response
surface methodology (RSM) is a collection of statistical and
mathematical techniques useful for developing, improving and
optimizing the design process. RSM encompasses a point selection
method (also referred to as Design of
Experiments, Approximation methods
and Design Optimization to determine
optimal settings of the design dimensions. RSM has important
applications in the design, development, and formulation of new
products, as well as in the improvement of existing product designs.
In
LS-OPT®, Response Surface Methodology is used both in Optimization
and Probabilistic Analysis as a means to reduce the number of
simulations. In the latter procedure, RSM is also used to
distinguish deterministic effects from random effects.
LS-OPT®
enables the investigation of stochastic effects using Monte Carlo
simulation involving either direct FE Analysis or analysis of Surrogate
models such as Response Surface
Methodology or neural networks. As an input distribution, any of
a series of statistical distributions such as Normal, Uniform, Beta,
Weibull or User-defined can be specified. Latin Hypercube sampling
provides an efficient way of implementing the input distribution.
Histograms and influence plots are available through the
postprocessor (Version 2.2).
Instability/Noise/Outlier Investigations (Version 2.2)
Some
structural problems may not be well-behaved i.e. a small change in
an input parameter may cause a large change in results.
LS-OPT®
computes various statistics of the displacement and history data for
viewing in the LS-DYNA® FE model postprocessor (LS-PrePost®). The
methodology differentiates between changes in results due to design
variable changes and those due to structural instabilities
(buckling) and numerical instabilities (lack of convergence or
round-off). Viewing these results in LS-PrePost® allows the engineer
to pinpoint the source of instability for any chosen response and
therefore to address instabilities which adversely affect
predictability of the results.
Tradeoff
A
tradeoff study enables the designer to interactively study the
effect of changes in the design constraints on the optimum design.
E.g. the safety factor for maximum stress in a beam is changed and
the designer wants to know how this change affects the optimal
thickness and displacement of the beam.
Variable Screening
For
each response, the relative importance of all variables can be
viewed on a bar chart together with their confidence intervals. This
feature enables the user to identify variables of lesser importance
that can be removed from the optimization, thereby contributing to
time saving while having little effect on the final result.
Glossary:
A
point selection method for determining the number and locations of
sampling points in the Design Space. A
simulation is done at each sampling point.
A
simple mathematical function acting as a substitute (or surrogate
model) to generalize the (often highly complex) Response
variation across the Design Space.
The
result obtained from an analysis (e.g. Finite Element Analysis) of a
product or process. The response is used as a criterion in Design
Optimization or Probabilistic Analysis.
The
process of setting the design variables, typically the dimensions,
of a product to minimize or maximize the value of its Response.
A more general form of optimization includes specified limits on
other responses (constrained optimization).
The
analysis of a set of different designs with a specified distribution
in order to determine the characteristics (such as the mean and
standard deviation) of the Response
distribution.
The
region between the lower and upper limit for each of the design
variables. These are specified to prevent the occurrence of designs
with extreme of nonsensical dimensions (such as negative
thicknesses).
A
part of the Design Space considered
being of interest for design exploration or Design
Optimization.
Design Variable
An
independent variable or dimension which forms part of the
description of a design. Typical design variables are thickness
dimensions, geometrical dimensions or values of material constants.
A
criterion that determines how well the coefficients of the design Approximation
are estimated. The changes in the locations of the sampling points
to maximize this criterion maximizes the confidence in the
coefficients of the Approximation
model.
Robust
A
robust product performs consistently on target and is relatively
insensitive to parameters that are difficult to control. A robust
design minimizes the noise transmitted by the noise variables.
A
parameter of a product that has some degree of uncontrollability
while the product is being manufactured or used in the field up to
the end of its lifetime.
Response Noise
The
random component of a response variation that can be caused by
instability of the structure (such as buckling), numerical roundoff
during analysis or modeling effects such as Finite Element meshing
or lack of convergence during analysis
The
successive response surface method is an iterative method which
consists of a scheme to assure the convergence of an optimization
process. The scheme determines the location and size of each
successive Region of interest in the Design
Space, builds a response surface in this region, conducts an Design
Optimization and will check the tolerances on the Responses
and design variables for termination. When using neural networks
instead of polynomials as a Surrogate model,
the Approximation is updated instead of
newly constructed in each iteration. Consequently, the final
approximation has a global representation that can be used for
optimization, tradeoff studies or probabilistic analysis.
Variation
in the dimensions or material properties of a product.
Variation
in the loads such as force (perhaps due to impact) and temperature
considered in the design of a product.
The
determination of system parameters such as material constants to
minimize the difference between computational responses and
experimental results. The purpose is to identify the system
parameters of a model by using experimental results of a physical
experiment.
Approximation
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