Reliability and Optimization of Structural Systems ’90: Proceedings of the 3rd IFIP WG 7.5 Conference Berkeley, California, USA, March 26–28, 1990

398 Pages·1991·12.405 MB·English

by  T. Abdo, R. Rackwitz (auth.), A. Der Kiureghian, P. Thoft-Christensen (eds.)

Lecture Notes in
Engineering
Edited by C. A. Brebbia and S. A. Orszag
i'g~
~.
IFIP 61
.--------------------------------
....
A. Der Kiureghian,
P. Thoft-Christensen (Eds.)
Reliability and Optimization
of Structural Systems '90
Proceedings of the 3rd IFIP WG 7.5 Conference
Berkeley, California, USA, March 26-28,1990
"
I
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A. Der Kiureghian
University of California
Dept. of Civil Engineering
721B Davis Hall
Berkeley, California 94720
USA
P. Thoft-Christensen
The University of Aalborg
Institute of Building Technology
and Structural Engineering
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9000 Aalborg
Denmark
ISBN-13:978-3-540-53450-1 e-ISBN-13:978-3-642-84362-4
001: 10.1007/978-3-642-84362-4
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PREFACE
This proceedings volume contains 33 papers presented at the 3rd Working Conference on "Rel
iability and Optimization of Structural Systems", held at the University of California, Berkeley,
California, USA, March 26 - 28, 1990. The Working Conference was organised by the IFIP (Inter
national Federation for Information Processing) Working Group 7.5 of Technical Committee 7 and
was the third in a series, following similar conferences held at the University of Aalborg, Denmark,
May 1987 and at the Imperial College, London, UK, September 1988. The Working Conference
was attended by 48 participants from 12 countries.
The objectives of Working Group 7.5 are:
• to promote modern structural systems optimization and reliability theory,
• to advance international cooperation in the field of structural system optimization and reliability
theory,
• to stimulate research, development and application of structural system optimization and reli
ability theory,
• to further the dissemination and exchange of information on reliability and optimization of
structural systems
• to encourage education in structural system optimization and reliability theory.
At present the members of the Working Group are:
A. H.-S. Ang, U.S.A. G. A ugusti, Italy
M. J. Baker, United Kingdom P. Bjerager, Norway
C. A. Cornell, U.S.A. R. B. Corotis, U.S.A.
M. Grigoriu, U.S.A. A. Der Kiureghian, U.S.A.
O. Ditlevsen, Denmark D. M. Frangopol, U.S.A.
H. Furuta, Japan S. Garribba, Italy
M. R. Gorman, U.S.A. M. Grimmelt, Germany, F. R.
N. C. Lind, Canada H. O. Madsen, Denmark
R. E. Melchers, Australia F. Moses, U.S.A.
Y. Murotsu, Japan A. S. Nowak, U.S.A.
R. Rackwitz, Germany, F. R. C. G. Soares, Portugal
J. D. Slirensen, Denmark P. Thoft-Christensen (chairman), Denmark
Y. - K. Wen, U.S.A.
Members of the Organizing Committee were:
M. J. Baker, UK
P. Bjerager, Norway
D. M. Frangopol, U.S.A.
A. Der Kiureghian (co-chairman), U.S.A.
P. Thoft-Christensen (co-chairman), Denmark
IV
The Working Conference received financial supported from IFIP, University of California at Ber
keley, and University of Aalborg.
On behalf of WG 7.5 and TC-7 the co-chairmen of the Conference would like to express their
sincere thanks to the sponsors, to the members of the Organizing Committee for their valuable
assistance, and to the authors for their contributions to these proceedings. Special thanks are due
to Mrs. Kirsten Aakj~r, University of Aalborg, for her efficient work as conference secretary, and
to Ms. Gloria Partee, University of California at Berkeley, for her valuable assistance in carrying
out local organizational matters.
June 1990
A. Der Kiureghian P. Thoft-Christensen
CONTENTS
Short Presentations
A New Beta-Point Algorithm for Large Time-Invariant and Time-Variant Reliability
ProbleIllS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
T. Abdo, R. Rackwitz
Rigid-Ideal Plastic System Reliability . . . . . . . . . . . . . . . . . . . . . .. 13
Torben Arnbjerg-Nielsen, Ove Ditlevsen
Optimal Allocation of Available Resources to Improve the Reliability of Building Systems 23
Giuliano Augusti, Antonio Borri, Emanuela Speranzini
Life Expectancy Assessment of Structural Systems . . . . 33
Bilal M. Ayyub, Gregory J. White, Thomas F. Bell-Wright
Parameter Sensitivity of Failure Probabilities. 43
Karl Breitung
Expectation Ratio Versus Probability .... 53
F. Vasco Costa
Application of Probabilistic Structural Modelling to Elastoplastic and Transient Analysis 63
T. A. Cruse, H. R. Millwater, S. V. Harren, J. B. Dias
Reliability-Based Shape Optimization Using Stochastic Finite Element Methods 75
Ib Enevoldsen, J. D. S{lJrensen, G. Sigurdsson
Calibration of Seismic Reliability Models. . . . . . . . . . . . . . . . . . 89
Luis Esteva
Computational Experience with Vector Optimization Techniques for Structural Systems 99
Dan M. Frangopol, Marek Klisinski
Management of Structural System Reliability. . . . . . . . . 113
Gongkang FU, Liu Yingwei, Fred Moses
Reliability Analysis of Existing Structures for Earthquake Loads 129
Hitoshi Furuta, Masata Sugito, Shin-ya Yamamoto, Naruhito Shiraishi
Sensitivity Analysis of Structures by Virtual Distortion Method. . . . 139
J. T. Gierlinski, J. Holnicki-Szulc, J. D. S{lJrensen
Reliability of Daniels Systems with Local Load Sharing Subject to Random Time
Dependent Inputs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Mircea Grigoriu
Reliability Analysis of Elasto-Plastic Dynamic Problems. . . . . . . . . . 161
Toshiaki Hisada, Hirohisa Noguchi, Osamu Murayama, Armen Der Kiureghian
Identification of Autoregressive Process Model by the Extended Kalman Filter 173
Masaru Hoshiya, Osamu Maruyama
VI
The Effect of a Non-Linear Wave Force Model on the Reliability of a Jack-Up Platform 185
J. Juncher Jensen, Henrik O. Madsen, P. Terndrup Pedersen
Optimum Cable Tension Adjustment Using Fuzzy Regression Analysis . 197
Masakatsu Kaneyoshi, Hiroshi Tanaka, Masahiro Kamei, Hitoshi Furuta
Bayesian Analysis of Model Uncertainty in Structural Reliability . . . 211
Armen Der Kiureghian
Size Effect of Random Field Elements on Finite-Element Reliability Methods. 223
Pei-Ling Liu
Reliability-Based Optimization Using SFEM . . . . . . ... 241
Sankaran Mahadevan, Achintya Haldar
Classification and Analysis of Uncertainty in Structural Systems 251
William Manners
Directional Simulation for Time-Dependent Reliability Problems 261
Robert E. Melchers
Some Studies on Automatic Generation of Structural Failure Modes. 273
Yoshisada Murotsu, Shaowen Shao, Ser Tong Quek
Sensitivity Analysis for Composite Steel Girder Bridges 287
Andrzej S. Nowak, Sami W. Tabsh
Long-Term Reliability of a Jackup-Platform Foundation 303
Knut O. Ronold
Constant Versus Time Dependent Seismic Design Coefficients. 315
Emilio Rosenblueth, Jose Manuel Jara
Reliability of Structural Systems with Regard to Permanent Displacements. 329
J. D. S~rensen, P. Thoft-Christensen
Reliability of Current Steel Building Designs for Seismic Loads 339
Y. K. Wen, D. A. Foutch, D. Eliopoulos, C.-Y. Yu
Jackup Structures: Nonlinear Forces and Dynamic Response . 349
Steven R. Winterstein, Robert L~seth
Stochastic Programs for Identifying Significant Collapse Modes in Structural Systems 359
James J. Zimmermann, Ross B. Corotis, J. Hugh Ellis
Lectures
Critical Configurations of Systems Subjected to Wide-Band Excitation 369
Takeru Igusa
On Reliability-Based Optimal Design of Structures 387
P. Thoft-Christensen
Index of authors 403
Subject index 405
A NEW BETA-POINT ALGORITHM FOR LARGE TIME-INVARIANT
AND TIME-VARIANT RELIABILITY PROBLEMS
T. Abdo & R. Rackwitz
Technical University of Munich, F.R.G.
Introduction
Several methods exist to compute the probability integrals occurring in structural reliability. These
integrals have the general form
f
I(V) = h(x) f(x) dx (1)
v
where V is the integration domain. X the vector of uncertain basic variables. h(x) a certain smooth
function and f(x) the (continuous) probability density of X. In the general case V is given by
V = n~ Vi with Vi = {gi(X) ~ O} as individual failure domains. The state functions gi(X) are
assumed to be (locally) twice differentiable. This integral includes as special cases simple probability
integrals. integrals for the mean number of excursions in random process or random field theory and
= =
certain expectations. In many cases there is h(x) 1 and m 1. Because numerical integration fails
to be practicable except in very low dimensions of X approximate methods have been developed the
most important ones are based on the theory of asymptotic Laplace integrals (Breitung. 1984;
Hohenbichler et al.. 1987). According to that theory a critical point x' in V needs to be located where
the integrand function f(x) becomes maximal and where the boundary of the failure domain can be
expanded into first or second order Taylor series so that integration is analytic. So far computations
are mostly performed in the so-called standard space i.e. the original vector X is transformed by an
appropriate probability distribution transformation into a standard normal vector with independent
components. Proposals have also been put forward which do not need this probability distribution
transformation (Breitung. 1989). It appears. however. that this advantage does only rarely compensate
for certain difficulties which. apparently. must mainly be regarded as problems of scaling in the
numerical analysis. In the following we discuss primarily formulations in the standard space. A similar
discussion for original space formulations will be presented in a separate paper. In any case integration
is reduced to a search for the critical point and some simple algebra. Here. we will be concerned only
with the search for the critical point.
The first important step towards an accurate and efficient failure probability calculation was made by
Hasofer/Lind (1974). Their search algorithm was a simple gradient algorithm. Later it was modified
2
and made globally convergent by Rackwitz/FieBler (1978). The most important modification consisted
in truncating the step length as the number of iterations increased according to Psenicnyi (1970).
Another improvement consisted in adding certain line searches which made the algorithm quite reliable
but also expensive in complicated cases. In the following this algorithm will be denoted by RF-algo
rithm for brevity of notation. Later investigations by a number of authors have studied almost the full
spectrum of available algorithms in mathematical programing (see especially Liu/Der Kiureghian, 1986,
for a thorough discussion) for their applicability in structural reliability calculations such as gradient
free algorithms, penalty methods, stochastic programing methods but also the so-called sequential
quadratic programming method (SQP-method) which theoretically is now considered as the most
efficient method (see, for example, Gill, et aI., 1981: Hock/Schittkowski, 1983; Arora, 1989). Based on
their studies Liu/Der Kiureghian (1986) proposed a certain merit function for the line searches in the
RF-algorithm and could demonstrate both efficiency and reliability of the impoved algorithm in a
number of examples. This modification will be denoted by LDK-algorithm. The RF-algorithm and the
LDK-algorithm have originally been designed only for single constraint problems but generalizations to
multi-constraint problems have recently been proposed independently by Abdo (1989) and
S¢rensen/Thoft-Christensen (1989). A first general conclusion from a variety of related and in part
unpublished studies is that it is worthwhile to adjust general purpose algorithms to the specific
settings in reliability computations. A second conclusion is that relatively small changes in the
algorithms can improve substantially their behavior. The third conclusion from these studies is that the
gradient-based algorithms in their present form are only slightly less efficient than the SQP-algo
rithms in not too large dimensions and for well-behaved problems. The RF-algorithm and, to a lesser
degree, the LDK-algorithm are clearly inferior to the latter for highly curved constraint functions under
otherwise similar conditions due to the better convergence behavior (fewer iterations) of the
SQP-algorithms. This is especially true when very expensive structural state functions are involved
such as finite element structural analyses; All other types of search algorithms appear to be serious
competitors to the RF- LDK- or the SQP-algorithms only in very special cases. However, for larger
dimensions of the uncertainty vector, larger than 50, say, all implementations of the SQP-algorithm
available to us became less efficient and less reliable than gradient-based algorithms. This is easily
explained by the fact that those algorithms use numerical updates of certain Hessian matrices which in
part are just the reason for their efficiency. For larger dimensions the update must remain crude when
the number of iterations is significantly smaller than the dimension of the Hessian. Hence, the
theoretical superiority of the SQP-algorithm above gradient-based algorithms turns out to be not
significant in practical applications. But more important, SQP-algorithms failed to converge reliably in
higher dimensions for reasons to be explained later in detail. Also, storage and CPU time requirements
became rather high. It may therefore be asked whether it is possible to overcome the shortcomings of
the SQP-algorithms in higher dimensions while retaining its otherwise favorable properties.
In this paper the SQP-algorithm will briefly be reviewed with special reference to possible problems.
The SQP-algorithm is then specialized for reliability calculations in the standard space. Certain
simplifications and modifications are introduced resulting in a new multi-constraint algorithm. It can
also be used in time-variant problems with little modification. Results of numerical tests are reported.
3
Sequential Quadratic Programming in Nonlinear Constrained Optimization
The general optimization problem can be written in the classical form:
min f( u) (2)
subject to inequality constraints
=
for j 1,2 ...... m
The Lagrangian function of the general problem is defined by
Lm
L(u) = f(u) + /\j gj(u) (3)
j = 1
where Aj are the so---called Lagrange multipliers. The Kuhn-Tucker optimality conditions for an
optimal point u· are
Lt
VL(u') = Vf(u') + Aj Vgj(u') = 0 (4a)
j = 1
j = 1,2 .... t (4b)
k = t+1, ... m (5)
t is the number of active inequality constraints and V is the gradient operator. The inclusion of equality
constraints is easily done by considering them always as active constraints. If n is the number of
variables and the active constraints are known an optimal point u· can be found by solving the system
of nonlinear equations (4) for n + t unknowns, namely for n components of the solution point u· and t
Lagrange multipliers A'.
An algorithm based on the solution of this system of equations by a direct method such as the Newton
method is extremely inefficient. It also must be noticed that the set of active constraints in the
solution point is not known in advance. The Sequential Quadratic Programing Method is generally
considered as most efficient for a solution. This method replaces the original problem by a sequence of
quadratic programing problems which are exactly solvable and which approximate the original one.
This is done by approximating the Lagrangian function by its second order Taylor expansion in an
initial point uo.
L(u) = L(uo) + VLoT (u - uo) + ~ (u - uo)T V2Lo (u - uo) (6)
where
4
Lm
l(uo) = f(uo) + Aj gj(uo) (7)
j ; !
Lm
Vlo = Vfo + Aj Vgy (8)
j ; 1
Lm
V2lo = V2fo + Aj V2gy (9)
j;J
and V2fo represents the Hessian of the function f in the point uo. For the formulation of the optimality
conditions the constraint functions are approximated by their first order Taylor expansion. The
Kuhn-Tucker conditions are then written for the set of active constraints in the solution point of the
quadratic programing problem. With a so-called active set strategy (see Gill et al. (1981)) it is
possible to determine which constraints are to be included in the formulation in each quadratic
problem of the sequence. The optimality conditions for any iteration point k of the sequence of
quadratic expansions are
Lt Lt
Vl(u) = Vlk + V2lk (u - uk) = Vfk + A~ Vg~ + [V2fk + ,\~ V2gr] (u - uk) = 0
j;! j;J
(10)
j = 1.2 ... t (11)
In matrix form these equations can be written as
Vlk Gk] [LlUk] = [-Vfk]
[
GkT 0 Ak -fk (12)
with
Lluk = (uk+! - uk) (13)
Gk = [Vgf .... Vgr ....... Vgt]nxt (14)
fkT = [g!(uk) .... gj(uk) ....... gt(uk)hxt (15)
The exa~t calculation of the second order derivatives for the Hessian matrix in Eq. (12) is generally to
expensive and can not be efficiently implemented for a general case. Therefore. the gradient
information obtained in each point during iteration is used to build up an approximation of this matrix
using one of the known update formulas (see Gill et al. (1981)). In the first iteration a unit matrix is
used instead of the true Hessian to solve the system of equations Eq. (12). The solution of this
quadratic problem with linear constraints defines a direction (Lluk) in which a line search is performed.
This one dimensional search is performed to obtain an optimal decrease of the objective and the
constraint functions in that direction. The new iteration point is defined by