Book Section records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:22:50 +0000Analytical reliability calculation of linear dynamical systems in higher dimensions
https://resolver.caltech.edu/CaltechAUTHORS:20110815-134109019
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'A. A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'J. L.'}}]}
Year: 2005
The recent application of reliability analysis to controller synthesis has created the need for a
computationally efficient method for the estimation of the first excursion probabilities for linear dynamical
systems in higher dimensions. Simulation methods cannot provide an adequate solution to this specific application,
which involves numerical optimization of the system reliability with respect to the controller parameters,
because the total computational time needed is still prohibitive. Instead, an analytical approach is presented
in this paper. The problem reduces to the calculation of the conditional upcrossing rate at each surface
of the failure boundary. The correlation between upcrossings of the failure surface for the different failure
events may be addressed by the introduction of a multi-dimensional integral. An efficient algorithm is
adopted for the numerical calculation of this integral. Also, the problem of approximation of the conditional
upcrossing rate is discussed. For the latter there is no known theoretical solution. Three of the semi-empirical
corrections that have been proposed previously for scalar processes are compared and it is shown that the correction
should be based on the bandwidth characteristics of the system. Finally, examples that verify the validity
of the analytical approximations for systems in higher dimensions are discussed.https://authors.library.caltech.edu/records/wh5xs-bft98Nonlinear stochastic controllers for semiactive and regenerative structural systems, with guaranteed quadratic performance margins
https://resolver.caltech.edu/CaltechAUTHORS:20110809-115233169
Authors: {'items': [{'id': 'Scruggs-J-T', 'name': {'family': 'Scruggs', 'given': 'Jeffrey T.'}}, {'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'Alexandros A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Iwan-W-D', 'name': {'family': 'Iwan', 'given': 'Wilfred D.'}}]}
Year: 2006
DOI: 10.1115/ESDA2006-95625
In many applications of vibration control, the circumstances of the application impose constraints on the energy available for the actuation of control forces. Semiactive dampers (i.e., viscous dampers with controllable coefficients) constitute the simplest example of such actuation in structural control applications. Regenerative Force Actuation (RFA) networks are an extension of semiactive devices, in which mechanical energy is first converted to electrical energy, which is then dissipated in a controllable resistive network. A fairly general class of semiactive and regenerative systems can be characterized by a differential equation which is bilinear (i.e., linear in state, linear in control input, but nonlinear in both). This paper presents a general approach to bilinear feedback control system design for semiactive and regenerative systems, which is analytically guaranteed to out-perform optimal linear viscous damping in stationary stochastic response, under the familiar Quadratic Gaussian performance measure. The design for full-state feedback and for the more practical case of noise-corrupted and incomplete measurements (i.e., output feedback) are separately discussed. Variants of the theory are shown to exist for other quadratic performance measures, including risk-sensitive and multi-objective frameworks. An illustrative application to civil engineering is presented.https://authors.library.caltech.edu/records/y5c32-9qp91Reliability-based Optimal Design by Efficient Stochastic Simulation
https://resolver.caltech.edu/CaltechAUTHORS:20120905-154516114
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'A. A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'J. L.'}}]}
Year: 2006
Reliability-based design requires the optimization of the probability of failure, over the admissible
space for the design variables. This probability can rarely be evaluated analytically and so it is often calculated
using stochastic simulation techniques, which involve an unavoidable estimation error and significant
computational cost. These features make efficient reliability-based optimal design a challenging task, especially
for dynamic problems with stochastic excitation, where the models used are typically complex. A new method
called Stochastic Subset Optimization is proposed here for iteratively identifying sub-regions for the optimal
design variables within the original design space. An augmented reliability problem is formulated where the
design variables are artificially considered as uncertain and Markov Chain Monte Carlo simulation is implemented
in order to draw samples of them that lead to failure. In each iteration, a set with high probability of
containing the optimal design parameters is identified using a single reliability analysis. Statistical properties
for the identification and stopping criteria for the iterative approach are discussed. The set optimization can be
combined with any stochastic search optimization algorithm for enhanced overall efficiency. Simultaneous-perturbation
stochastic approximation with common random numbers is used in this study for this purpose
and a complete framework for efficient reliability-based optimization is discussed. An illustrative example is
presented that shows the efficiency of the proposed methodology.https://authors.library.caltech.edu/records/2h6cg-0j444Probabilistically-robust nonlinear control of offshore structures
https://resolver.caltech.edu/CaltechAUTHORS:20110107-140554471
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'Alexandros A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Angelides-D-C', 'name': {'family': 'Angelides', 'given': 'Demos C.'}}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'James L.'}}]}
Year: 2007
A controller design for offshore structures is discussed in this study.
Stochastic simulation is considered for evaluation of the system's
performance in the design stage. This way, nonlinear characteristics of
the structural response and excitation are explicitly incorporated into
the model assumed for the system. Model parameters that have some
level of uncertainty are probabilistically described. In this context, the
controller is designed for optimal reliability, quantified as the
probability, based on the available information, that the performance
will not exceed some acceptable bounds. This treatment leads to a
robust-to-uncertainty design. The methodology is illustrated in an
example involving the control of a Tension Leg Platform in a random
sea environment. Multifold nonlinearities are taken into account for the
evaluation of the platform's dynamic response and a probabilistic
description is adopted for characterizing the random sea environment.https://authors.library.caltech.edu/records/kj5gv-3eq87Efficient simulation-based optimization for optimal reliability problems
https://resolver.caltech.edu/CaltechAUTHORS:20101105-110545967
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'A. A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'J. L.'}}]}
Year: 2007
No abstract.https://authors.library.caltech.edu/records/07s9f-ppb23Stochastic System Design Optimization using Stochastic Simulation
https://resolver.caltech.edu/CaltechAUTHORS:20120831-143713237
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'Alexandros A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'James L.'}}]}
Year: 2008
Engineering design in the presence of uncertainties often involves optimization
problems that include as objective function the expected value of a system performance measure,
such as expected life-cycle cost or failure probability. For complex systems, this expected
value can rarely be evaluated analytically. In this study, it is calculated using stochastic simulation
techniques which allow explicit consideration of nonlinear characteristics of the system
and excitation models, as well as complex failure modes. At the same time, though, these techniques
involve an unavoidable estimation error and significant computational cost which make
the associated optimization challenging. An efficient framework, consisting of two stages, is
presented here for such optimal system design problems. The first stage implements a novel
approach, called Stochastic Subset Optimization, for iteratively identifying a subset of the original
design space that has high plausibility of containing the optimal design variables. The second
stage adopts some stochastic optimization algorithm to pinpoint, if needed, the optimal design
variables within that subset. Topics related to the combination of the two different stages for
overall enhanced efficiency are discussed. An illustrative example is presented that shows the
efficiency of the proposed methodology; it considers the retrofitting of a four-story structure
with viscous dampers. The minimization of the expected lifetime cost is adopted as the design
objective. The expected cost associated with damage caused by future earthquakes is calculated
by stochastic simulation using a realistic probabilistic model for the structure and the ground
motion.https://authors.library.caltech.edu/records/w6txy-d2839Life-cycle Cost Optimal Design of Passive Dissipative Devices for Seismic Risk Mitigation
https://resolver.caltech.edu/CaltechAUTHORS:20120831-113712119
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'A. A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'J. L.'}}]}
Year: 2009
The cost effective performance of structures has long
been recognized to be an important topic in the design
of civil engineering systems. This design approach
requires proper integration of (i) methodologies for
treating the uncertainties related to natural hazards
and to the structural behavior over the entire lifecycle
of the building, (ii) tools for evaluating the
performance using socioeconomic criteria, as well as
(iii) algorithms appropriate for stochastic analysis and
optimization.
A complete probabilistic framework is presented in
this paper for detailed estimation and optimization of
the life-cycle cost of earthquake engineering systems.
The focus is placed on the design of passive dissipative
devices. The framework is based on a knowledge-based
interpretation of probability (Jaynes, 2003),
which leads to a realistic framework for formulating
the design problem, and on an efficient novel approach
to stochastic optimization problems (Taflanidis and
Beck, 2008). The latter facilitates an efficient solution
of this design problem and thus allows for consideration
of complex models for describing structural
performance.
A comprehensive methodology is initially discussed
for earthquake loss estimation; this methodology uses
the nonlinear time-history response of the structure
under a given excitation to estimate the damages in
a detailed, component level. A realistic probabilistic
model is then presented for describing the ground
motion time history for future earthquake excitations.
This model establishes a direct link between the probabilistic
seismic hazard description of the structural
site and the acceleration time history of future ground
motions. In this setting, the life-cycle cost is given
by an expected value over the space of the uncertain
parameters for the structural system, performance
evaluation and excitation models. Because of the complexity
of these models, calculation of this expected
value by means of stochastic simulation techniques is
adopted. This approach, though, involves an unavoidable
estimation error and significant computational
cost, features which make the associated optimization
challenging. An efficient framework, consisting
of two stages, is presented for the optimization in such
stochastic design problems. The first stage implements
a novel approach, called-Stochastic Subset Optimization
(SSO), for efficiently exploring the sensitivity of
the objective function to both the design variables as
well as the model parameters. Using a small number
of stochastic analyses SSO iteratively identifies a
subset of the original design space that has high plausibility
of containing the optimal design variables and
additionally consists of near-optimal solutions. The
second stage, if needed, adopts some other stochastic
optimization algorithm to pinpoint the optimal design
variables within that subset. All information available
from the first stage is exploited in order to improve the
efficiency of the second optimization stage.
An example is presented that considers the
retrofitting of a four-story reinforced concrete office
building with viscous dampers. Complex system,
excitation and performance evaluation models are
considered, that incorporate all important characteristics
of the true system and its environment into
the design process. The results illustrate the capabilities
of the proposed framework for improving the
structural behavior in a manner that is meaningful to
its stakeholders (socio-economic criteria), as well as
its capabilities for computational efficiency and the
treatment of complex analysis models.https://authors.library.caltech.edu/records/qhs9d-12q23Robust Performance Optimization of Linear Controlled Stochastic Systems
https://resolver.caltech.edu/CaltechAUTHORS:20120831-113038529
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'A. A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Scruggs-J-T', 'name': {'family': 'Scruggs', 'given': 'J. T.'}}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'J. L.'}}]}
Year: 2010
The existence of model uncertainty is important for modern control applications, as one of the main objectives
is to establish optimum robustness over all possible operational conditions. Standard tools for robust control
design, such as H_(infinity) μ-synthesis and the many offshoots of these, consider only compact sets of possible
models for the system. Information implying that some model parameters are more probable than others is not
explicitly treated. However in most real engineering applications, there is considerable knowledge about the
relative plausibility of the different model parameter values. A probability logic approach provides a rational and
consistent framework for quantifying this knowledge. This is established by characterizing the relative plausibility
of different properties of the system by probability models. A robust design may be then established by optimizing
statistics of the objective function (probabilistic performance) under the statistically described plant uncertainty,
rather than the objective function resulting from the nominal model (nominal performance).
The present paper discusses the robust-performance optimization of linear time invariant dynamical systems
with probabilistically-described parametric model uncertainties and focuses on cases including a stochastic disturbance
input. We consider H_2 and multi-objective H_2 control synthesis for quantification of the system nominal
performance. The probabilistic measure of optimality is then defined either as the average (i.e. expectation) of the
performance over the uncertain parameter space, or the probability that the performance will exceed acceptable
bounds. We also examine robust stochastic design for minimal first-passage failure probability [1], i.e. maximal
reliability of the dynamic response. In this case the definition of robust performance in presence of probabilistic
model uncertainties follows directly from the axioms of probability logic. Analysis and synthesis methodologies
are discussed, based on recently developed stochastic simulation techniques [2]. The influence of different
probability models for describing plant uncertainty is also discussed.
The design approach is illustrated in a structural control application. Probabilistically-robust controllers are
demonstrated to yield considerable different designs compared to controllers optimized using only a nominal
model, or using the "worst-case" interpretation of system robustness. Also, differences are shown in the design
characteristics between different probabilistic characterizations for the system uncertainty or for the performance
objective.https://authors.library.caltech.edu/records/q9ve4-kgg86Non-parametric stochastic subset optimization for design problems with reliability constraints
https://resolver.caltech.edu/CaltechAUTHORS:20150619-140729922
Authors: {'items': [{'id': 'Jia-Gaofeng', 'name': {'family': 'Jia', 'given': 'G.'}}, {'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'A. A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'J. L.'}}]}
Year: 2014
The Non-Parametric Stochastic Subset Optimization (NP-SSO) is a recently developed algorithm appropriate for
optimization problems that use the system reliability as objective function and involve computationally expensive numerical
models. This paper discusses its extension to reliability-based design optimization (RBDO) applications involving the system
reliability as a design constraint. The foundation of NP-SSO is the formulation of an augmented problem where the design
variables are artificially considered as uncertain. In this context, the system reliability is proportional to an auxiliary probability
density function related to the design variables. NP-SSO is based on simulation of samples from this density and approximates
the system reliability through kernel density estimation (KDE) using these samples. The RBDO problem is then solved using
this approximation for evaluating the reliability constraints. Thus, through a single analysis NP-SSO provides information for
the system reliability over the entire design domain. To improve computational efficiency, an iterative approach is proposed; at
the end of each iteration, a new reduced search domain is identified, until the algorithm converges to the feasible design domain
satisfying the reliability constraints. Through this approach the samples for the design variables gradually move from regions
with higher values of the system failure probability to regions with lower values (satisfying the required constraints). A nonparametric
characterization of the search domain using a framework based on multivariate boundary KDE and support vector
machine is established whereas to further improve the efficiency of the stochastic sampling stage, an adaptive kernel sampling
density approach is proposed.https://authors.library.caltech.edu/records/1qvr3-e4041