失败中英文文献翻译-机械结构的可靠性优化设计

2021年1月21日发(作者：肃穆)

英文原文

Optimize the reliability of mechanical structure design
It
is
now
generally
recognized
that
structural
and
mechanical
problems
are
nondeterministic
and,
consequently,
engineering
optimum
design
must
cope
with
un- certainties
，
Reliability
technology
provides
tools
for
formal
assessment
and
analysis
of
such
uncertainties
，
Thus,
the
combination
of
reliability-based
design
procedure sand optimization promises to provide a practical optimum design solution,
i
，
e
，
,
a
de- sign
having
an
optimum
balance
between
cost
and
risk
，

However,
reliabilty-based
structural
optimization
programs
have
not
enjoyed
the
name
popularity as their deterministic counterparts
，

Some reasons for this are suggested
，

First,
reliability
analysis
can
be
complicated
even
for
simple
systems
，

There
are
various methods for handling the uncertainty in similar situations (e
，
g
，
, first order
second
moment
methods,
full
distribution
methods)
，

Lacking
a
single
method,
individuals are likely to adopt separate strategies for handling the uncertainty in their
particular problems
，

This suggests the possibility of different reliability predictions
in similar structural design situations
，

Then, there are diverging opinions on many
basic issues, from the very definition of reliability-based optimization, including the
definition of the
optimum
solution, the objective function and the constraints, to
its
application in structural design practice
，

There is a need to formally consider these
itess
in
the
merger
of
present
structural
optimization
research
with
reliability-based
design philosophy
。

In general, an optimization problem can be stated as follows,Minimize

subject to the constraints

where X is an-dimensional vector called the design vector
，

f(X) is called the
objective function and,
constraints
，

The number of variables n and the number of constraints
，

L need not be
related in any way
，

Thus, L could be less than, equal to or greater than n in a given
mathematical
programming
problem
，

In
some
problems,
the
value
of
L
might
be
zero which means there are no constraints on the problem
，

Such type of problems are


called
，

Those problems for which L is not
equal to zero are known as
。







Traditionally the designer assumes the loading on an element and the strength of
that element to be a single valued characteristic or design value
，

Perhaps it is equal
to some maximum (or minimum) anticipated or nominal value
，

Safety is assured by
introducing a factor of safety, greater than one, usually applied as a reduction factor to
strength
。

Probabilistic
design
is
propose:
as
an
alternative
to
the
conventional
approach
with the promise of producing
，

each factor in the design
process can be defined and treated as a random variable
，

Using method-ology from
probabilistic theory, the designer defines the appropriate limit state and computes the
probability of failure P} of the element
，

The basic design requirement is that
，
where
p f

is the maximum allowable probability of failure
。

Advantages of adopting the probabilistic design approach are well documented
(Wu, 1984)
，

Basically the arguments for probabilistic design center around the fact
that,
relative
to
the
conventional
approach,
a)
risk
is
a
more
meaningful
index
of
structural performance, and b) a reliability approach to design of a sys-tom can tend to
produce an
。


Optimization, which may be considered a component of operations research, is
the
process
of
obtaining
the
best
result
by
finding
conditions
that
produce
the
maximum or minimum value of a function
，

Table 1
，
1 illustrates area of operations
research
。


Mathematical programming techniques, also known as optimization methods, are
useful in finding the minimum (or maximum) of a function of several variables under
a prescribed set of constraints
，

Rao (1979) presented a definition and description of
some
of
the
various
methods
of
mathematical
programming
，

Stochas-tic
process
techniques can be used to analyze problems which are described by a set of random
variables
，

Statistical methods enable one to analyze the experimental data and build
empirical models to obtain the most accurate representations of physical behavior
。









Origins of optimization theory can be traced to the days of Newton, La-grange and
Cauchy in the 1800'x
，

The application of differential calculus to optimization was
possible because of the contributions of Newton and Leibnitz
，

The foundations of
calculus of variations were laid by Bernoulli, Euler, Lagrange and Weirstrass
，

The
method
of
optimization
for
constrained
problems,
which
involves
the
addition
of
unknown multipliers became known by the name its inventor, La-grange
，

Cauchy
presented the
first
application of the steepest
descent
method to solve minimization
problems
。

In spite of these early contributions, very little progress was made until the middle


of the twentieth Gentry, when high-speed digital computers made the implementation
of
optimization
procedures
possible
and
stimulate,
d
further
research
on
new
methods
，

Spectacular
advances
followed,
producing
a
m;}sssive
literature
on
optimization techniques
，

This advancement also resulted in the emergence of several
well- defined new areas in optimization theory
。

It is interesting to note that major developments in the area of numerical methods
of unconstrained optimization have been made in
the TTnited Kingdom
only
in
the
1960'x
，

The
development
of
the
simplex
method
by
Dantzig
(1947)
for
linear
programming and the annunciation of the principle of optimality by Bellman (195?)
for dynamic programming problems paved the wa
，
; f}= development of the methods
of constrained optimization
，

The work by Kuhn and Tucker (1951) on necessary and
xuflicient
conditions
for
the
optimal
xolution
of
programming
problems
laid
foundations for later research in nonlinear programming, the optimization area of this
thesis
。

Although
no
single
technique
has
been
found
to
be
universally
applicable
for
nonlinear programming, the works by Cacrol (1961)and Fiacco and McCormic (1968)
suggested practical solutions by employing well-known techniques of uncon xtrained
optimization
，

Geometric programming was developed by Dufhn, Zener and Peterson
(1960)
，

Gomory
(1963)
pioneered
work
in
integer
programming,
which
is
at
this
time
an
exciting
and
rapidly
developing
area
of
optimization
research
，

Many

，

Dantzig (1955) and
Charnel and Cooper (1959) developed stochastic programming techniques and solved
problems by assuming design parameters to be independent and normally distributed
。

Techniques of nonlinear programming, employed in this study, can be categorized

1
，

one- dimensional minimization method
2
，

unconstrained multivariable minimization








A
，

gradient based method








B
，

nongradient based method
3
，

constrained multivariable minimization








A
，

gradient based method








B
，
gradient based method

The gradient based methods require function and derivative evaluations while the
non gradient based methods require function evaluations only
，

In general, one would
expect
the
gradient
methods
to
be
more
effecti;re,
due
to
the
added
information
provided
，

However, if analytical derivatives are available, the question of whether a
search
technique
should
be
used
at
all
is
presented
，


If
numerical
derivative
approximations are utilized, the efficiency of the
gradient
based methods should be
approximately
the
same
as
that
of
nongradient
based
methods
，

Gradient
based


methods
incorporating
numerical
derivatives
would
be
expected
to
present
some
numerical problems in the vicinity of the optimum, i
，
e
，
, approximations to slopes
would become small
，

Fig
，

1
，
1 shows the $$ow chart of general iterative scheme of
optimization (Rao, 1979)
，








No
claim
is
made
that
some
methods
are
better
than
any
others
，

A
method
works well on one problem may perform very poorly on another problem of the same
general type
，

Only after much experience using all the methods can one judge which
method would be better for a particular problem (Kuester snd Mize, 1973).

First attempts to apply probabilistic and statistical concepts in structural analysis
date
back
to
the
beginning
of
this
century
，

However,
the
subject
aid
not
receive
much attention until after the World War II
，

In October 1945, a historic paper written
by
A
，

M
，

Freudenthal
entitled

Safety
of
Structures
appeared
in
the
proceedings of the American Society of Civil Engineers
，


The publication
of this paper marked the genesis of structural reliability in the U
，
S
，
A
，
，

Professor
F:eudenthal
continued
for
many
years
to
be
in
the
forefront
of
structural
reliability
and risk analysis
，



During
the
1960's
there
was
rapid
growth
of
academic
interest
in
struc-total
reliability
theory
，

Classical
theory
became
well
developed
and
widely
known
through
a
few
influential
publications
such
as
that
of
Freudenthal,
Garrelts,
and
Shi-nouzuka (1966), Pugsley
(1966), Kececioglu and Cormier (1964),
Ferry-Borges
and Castenheta (1971, and Haugen (1968)
，

However, professional acceptance was
low
for
several
reasons
，

Probabilistic
design
seemed
cumbersome,
the
theory,
particularly
system
analysis,
seemed
mathematically
intractible
，

Little
data
were
available, and modeling error was an issue which needed to be addressed
，

But
there
were
early
efforts
to
circumvent
these
limitations
，

Turkstra(l070)
Yr}}nted
structural
design
as
a
problem
of
decision
making
under
uncertainty
and
risk
，

Lind, Turkstra, and Wright (1965) defined the problem of rational design of a
code as finding a set of best values of the load and resistance factors
，

Cornell (1967)
suggested the use of a second moment format, and subsequently it was demonstrated
that Cornell's safety index requirement could be used to derive a set of safety factors
on
loads
and
resistances
，

This
approach
related
reliability
analysis
to
practically
accepted methods of design The Cornell approach has been refined and employed in
many structural standards
，

Difficulties
with
the
second
moment
format
were
uncovered
1969
when
Ditlevsen and Lind independently discovered the problem of invariance
，

Cornell's
index
was
not
constant
when
certain
simple
problems
were
reformulated
in
a
mechanically
equivalent
way
，

But
the
lack
of
invariance
dilemma
was
overcome
when Hasofer and Lind (1974) defined a generalized safety index which was invariant


to
mechanical
formulation
，

This
landmark
paper
represented
a
turning
point
in
structural
reliability
theory
，

More
sophisticated
extensions
of
the
Hasofer-Lind
approach proposed in recent
years by Rackwitz and Fiessler (1978), Chen and Lind
(1982),
and
Wu
(1984)
provide
accurate
probability
of
failure
estimates
for
complicated limit state functions
，

There
are
many
modes
of
failure
in
structural
systems,
depending
on
the
configuration
of
the
system,
shapes
and
materials
of
the
members,
the
loading
conditions, etc
，

Lz order to perform a system reliability assessment the failure modes
must be defined
，

However, for a large system with a high degree of redundancy it is
difficult
in
practice
to
determine
a
priori
which
failure
modes
are
probabilistically
significant
，


The
following
methods
have
been
proposed
to
produce
approximate
solutions: (a) automatic generation of safety margins, (b) the p-unzipping method, and
(c) branch-and-bound method (Thoft-Christensen and Murotsu, 1986)
，


The state of
the
art
in
sysiems
structural
reliability
analysis
is
comprehended
in
the
works
vi
Bennett
(1983),
Ang
and
Tang
(1984),
Guenard
('1984),
Ditlevsen
(1986),
Madsen,
Krenk, and Lind (1986), and Thoft-Christensen and Murotsu (1986)
，

Butat this time
there
no
general
me
hon
for
obtaining
practical
solutions
to
the
system
reliability
problem
。