“Optimization and Applications”
Dr.-Ing. Thomas Vietor
Keywords
Vehicle Engineering, Vehicle Attributes, Robust
Design, Stochastic Optimization
1. Introduction
The development of a passenger car is a multidisciplinary task. The
vehicle has to fulfill demands out of different attributes like vehicle
dynamics, driveability, acoustics, thermal and heat management, safety, durability,
crash and economics. Very often demands out of these areas are conflicting. One
main problem is the variability of mechanical quantities responsible for the
performance and customer perception of a car. To overcome this, the extension
of the conventional deterministic oriented development process to a process
which includes stochastic quantities is necessary. In this paper the current
deterministic approach is described briefly. It is not possible to perform the
extension in a single step. In a first extended version of the process the
variability of material parameters is included. In further steps the
formulation and solution of stochastic optimization problems for sub-problems
is necessary. Finally the complete approach should fully integrate the
variability of stochastic quantities. This paper outlines the importance of the
stochastic model used for the design variables and the stochastic parameters.
2. Development Process
Vehicle system concepts (e.g. body structure, front- and rear suspension,
powertrain mounting systems, etc.), which are selected in an early program
phase, have significant influence on the attribute performance of the vehicle.
It is almost impossible to solve attribute concerns resulting from selection of
poor concepts in a later program phase.
3. Introduction of Scattering Design
Variables
In the development process a number of
parameters and design variables are scattering. In conventional approaches they
are assumed deterministic. With increasing importance of reliability the
deterministic approach has to be extended and at least the most important
parameters and variables have to be modelled stochastically. These most
important quantities have to be identified with sensitivity methods. Only with
the limitation to the most sensitive quantities the models can be calculated.
The key factors for the introduction of scattering design variables are:
·
stochastic data
like geometry, dimensions, thicknesses and statical and dynamical stiffnesses
of different materials
·
different stochastic
models like gaussian, weibull, lognormal distributions
·
objectives like
sound pressure, vibrations, safety, ride and handling, costs, manufacturing,
assembly, package
·
solution
strategies like RSM, First Order Second Moment reliability methods (FOSM) and
different methods of stochastic
optimization like mean value Taylor methods
·
use of
Monte-Carlo methods for large scale models and structural analysis methods
without semi-analytical gradient calculation
·
use of Genetic
Algorithms for stochastic optimization of large scale models
4. Solution Strategies for Stochastic
Variables
In the presentation different methods to handle
industrial applications will be presented and characterized.
5. Augmented optimization procedure and
sequential realization
An optimization loop has been augmented by an
Advanced First Order Second Moment Method (AFOSM) - procedure for calculating
the reliability indices. By integrating the procedure, one obtains two
interlocked optimization loops. The same linkage would occur with a nonlinear
structural analysis that is also performed iteratively. The outer loop
comprises the quasi-stochastic optimization described above, while in the inner
loop the reliability indices and the sensitivities are calculated.
Other authors are developing optimization
procedures with the application of evolution methods. These methods are
currently being tested at practical large scale models. The use of AFOSM and
the application of evolution methods is compared for different criteria like
convergence, number of structural analysis and costs.
Address: Thomas
Vietor, Ford Werke GmbH, D-50725 Cologne, Germany.
This paper is describing the status of a
project with substantial contribution of Dr.-Ing. Axel Hänschke and Dipl.-Ing.
Jörgen Hilmann, Ford-Motor Co.