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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 16:06:27 +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.eduhttps://authors.library.caltech.edu/records/wh5xs-bft98Reliability-based control optimization for active
base isolation systems
https://resolver.caltech.edu/CaltechAUTHORS:20120810-114328397
Authors: {'items': [{'id': 'Scruggs-J-T', 'name': {'family': 'Scruggs', 'given': 'J.T.'}}, {'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
DOI: 10.1002/stc.107
A probability-based active control synthesis is proposed for seismic base isolation of a structure that is
modeled as a linear dynamical system subjected to uncertain future ground motions that are modeled as a
stochastic process. The performance objective is the minimization of the probability of failure, where
failure is defined as the first-passage of the system trajectory across a generalized set of hyperplanes in the
system response space. Versions of the approach are described for the case with no model uncertainty, as
well as for the case with uncertain model parameters with probabilistically distributed values. Numerical
issues pertaining to the optimization of the controller are discussed. The method is illustrated in a civil
engineering context through application to the eight-storey base isolation benchmark structure model,
using an array of ideal active control devices working in tandem with the passive base isolation bearings.
Controllers are presented for cases with specified and uncertain earthquake spectral parameters, and for
two different actuator configurations. Transient simulations are presented for seven earthquake records,
and the performances of the controllers are analyzed under a number of metrics. Comparisons with the
performance of a related linear-quadratic controller are presented and discussed, both for stationary as
well as transient response.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kdtn9-jrb75Nonlinear 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.eduhttps://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.eduhttps://authors.library.caltech.edu/records/2h6cg-0j444Robust Mass Damper Design using Stochastic Simulation
https://resolver.caltech.edu/CaltechAUTHORS:20120905-122344321
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'Alexandros'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'James'}}, {'id': 'Angelides-D-C', 'name': {'family': 'Angelides', 'given': 'Demos'}}]}
Year: 2006
Mass dampers (for example, TMDs or TLCDs) are widely used for
suppression of structural vibrations. Their design is based on the adjustment
of their parameters, referred to herein as design variables, to
the dynamic characteristics of the coupled damper-structure system.
Uncertainty in the parameters of the model considered for the system
significantly influences the effectiveness of this design. Prior knowledge
about the system is quantified in this study by specifying probability
distributions for the uncertain model parameters. The objective
function for optimal design is chosen to be maximization of the systems
reliability against failure, an appropriate concept for applications
that involve uncertainty. Failure is defined to be exceedance of limit
states for some of the systems response quantities that are important.
Stochastic simulation is used to evaluate the systems response to efficiently
address the high complexity that exists in many applications
of mass dampers and to overcome the limitations related to analytical
approximations when there are non-linearities (e.g associated with
TLCDs or base-isolated civil structures) or when there is a need to
consider transient response. The use of stochastic simulation for the
calculation of the objective function, however, significantly increases
the computational cost for the required optimization with respect to the
design variables. An efficient approach is proposed for this task. It
combines two algorithms suggested for simulation-based optimization:
the Stochastic Subset Optimization, for identification of a set that
icludes the design variables, and the Simultaneous Perturbation Stochastic
Averaging with common random numbers, for pinpointing the
optimal solution inside the identified set. Examples are presented that
show the efficiency of the proposed design for cases with model uncertainty.
The suggested techniques have applications to a large variety
of excitations and simple or complex systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8cc9v-hfc95Reliability-based Performance Objectives and Probabilistic Model Uncertainty in Optimal Structural Control Applications
https://resolver.caltech.edu/CaltechAUTHORS:20120905-120329310
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'Alexandros'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Scruggs-J-T', 'name': {'family': 'Scruggs', 'given': 'Jeffrey'}}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'James'}}]}
Year: 2006
A reliability-based structural control design approach is presented,
which optimizes a control system explicitly to minimize the probability of structural failure. Here, failure is interpreted as the probability that
the system state trajectory will exit a safe region, inside a given time
duration. This safe region is bounded by hyperplanes in the system
state space, each of which corresponds to an important dynamic
response variable. The failure threshold for each of these response
variables is designated as a bound on acceptable performance. Thus
defined, an accurate analytical approximation for the probability of
failure, and for its optimization through feedback control, are
discussed. Versions of the approach are described for the case with no
model uncertainty as well as for the case with uncertain model parameters.
For the case with uncertain parameters it is reasonable to
assume that, in most engineering applications, there will be a considerable
knowledge about the relative likelihood of the different possible
values of these parameters. This information is quantified through the
use of probability distributions on the uncertain parameter space. The
standard tools for design of feedback controllers which are robust to
model uncertainty, such as Hoo and miou-synthesis, do not account
for such probabilistic information.Examples are presented which
apply the above ideas to a simple active structural control system. The
influence of model uncertainty in the optimization process and the
advantages of adopting a probabilistic uncertainty approach are
discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n03mf-rqz17Analytical Approximation for Stationary Reliability of Certain and Uncertain Linear Dynamic Systems with Higher Dimensional Output
https://resolver.caltech.edu/CaltechAUTHORS:20120817-162204202
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
DOI: 10.1002/eqe.581
An analytical approximation for the calculation of the stationary reliability of linear dynamic systems with higher-dimensional output under Gaussian excitation is presented. For systems with certain parameters theoretical and computational issues are discussed for two topics: (1) the correlation of failure events at different parts of the failure boundary and (2) the approximation of the conditional out-crossing rate across the failure boundary by the unconditional one. The correlation in the first topic is approximated by a multivariate integral, which is evaluated numerically by an efficient algorithm. For the second topic some existing semi-empirical approximations are discussed and a new one is introduced. The extension to systems with uncertain parameters requires the calculation of a multi-dimensional reliability integral over the space of the uncertain parameters. An existing asymptotic approximation is used for this task and an efficient scheme for numerical calculation of the first- and second-order derivatives of the integrand is presented. Stochastic simulation using an importance sampling approach is also considered as an alternative method, especially for cases where the dimension of the uncertain parameters is moderately large. Comparisons between the proposed approximations and Monte Carlo simulation for some examples related to earthquake excitation are made. It is suggested that the proposed analytical approximations are appropriate for problems that require a large number of consistent error estimates of the probability of failure, as occurs in reliability-based design optimization. Numerical problems regarding computational efficiency may arise when the dimension of both the output and the uncertain parameters is large.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/j09y5-p1y24Probabilistically-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.eduhttps://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.eduhttps://authors.library.caltech.edu/records/07s9f-ppb23Stochastic System Design and Applications to Stochastically Robust Structural Control
https://resolver.caltech.edu/CaltechEERL:EERL-2007-05
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'Alexandros'}, 'orcid': '0000-0002-9784-7480'}]}
Year: 2007
The knowledge about a planned system in engineering design applications is never
complete. Often, a probabilistic quantification of the uncertainty arising from this missing
information is warranted in order to efficiently incorporate our partial knowledge about the
system and its environment into their respective models. In this framework, the design
objective is typically related to the expected value of a system performance measure, such
as reliability or expected life-cycle cost. This system design process is called stochastic
system design and the associated design optimization problem stochastic optimization. In
this thesis general stochastic system design problems are discussed. Application of this
design approach to the specific field of structural control is considered for developing a
robust-to-uncertainties nonlinear controller synthesis methodology.
Initially problems that involve relatively simple models are discussed. Analytical
approximations, motivated by the simplicity of the models adopted, are discussed for
evaluating the system performance and efficiently performing the stochastic optimization.
Special focus is given in this setting on the design of control laws for linear structural
systems with probabilistic model uncertainty, under stationary stochastic excitation. The
analysis then shifts to complex systems, involving nonlinear models with high-dimensional
uncertainties. To address this complexity in the model description stochastic simulation is
suggested for evaluating the performance objectives. This simulation-based approach
addresses adequately all important characteristics of the system but makes the associated
design optimization challenging. A novel algorithm, called Stochastic Subset Optimization
(SSO), is developed for efficiently exploring the sensitivity of the objective function to the
design variables and iteratively identifying a subset of the original design space that has
v i
high plausibility of containing the optimal design variables. An efficient two-stage
framework for the stochastic optimization is then discussed combining SSO with some
other stochastic search algorithm. Topics related to the combination of the two different
stages for overall enhanced efficiency of the optimization process are discussed.
Applications to general structural design problems as well as structural control problems
are finally considered. The design objectives in these problems are the reliability of the
system and the life-cycle cost. For the latter case, instead of approximating the damages
from future earthquakes in terms of the reliability of the structure, as typically performed in
past research efforts, an accurate methodology is presented for estimating this cost; this
methodology uses the nonlinear response of the structure under a given excitation to
estimate the damages in a detailed, component level.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bpa9q-wve13Robust Reliability-based Design of Liquid Column Mass Dampers under Earthquake Excitation using an Analytical Reliability Approximation
https://resolver.caltech.edu/CaltechAUTHORS:20120817-152236677
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': 'James L.'}}, {'id': 'Angelides-D-C', 'name': {'family': 'Angelides', 'given': 'Demos C.'}}]}
Year: 2007
DOI: 10.1016/j.engstruct.2007.08.004
The robust reliability-based design of Tuned Liquid Column Dampers (TLCD) and Liquid Column Vibration Absorbers (LCVA) under earthquake excitation is studied. The design objective is the minimization of the probability of failure, where failure is defined as the first-passage of the dynamical system trajectory out of a hypercubic safe region in the space of the performance variables. These variables correspond to response characteristics of the system that are considered important. Versions of the approach are described for the case of a nominal model and the case considering model uncertainty. In the latter case the concept of robust probability of failure is employed which considers a set of possible models for the dynamic system. The nonlinear characteristics of the damper response are addressed by including the excitation intensity as an uncertain parameter in the system description. An analytical approximation is used for the reliability estimation that allows for computationally efficient, gradient-based design optimization. Numerical issues are discussed. The validity of the reliability approximation is checked by comparing the results to those derived through direct Monte Carlo simulation of the nonlinear model. Applications to dynamical systems with single and multiple degrees of freedom are presented. For the latter case, other standard control synthesis methods are also considered and significant differences are illustrated between them and robust reliability-based design. Although this study focuses on optimization of TLCDs and LCVAs, it shows the efficiency of the proposed methodology for other systems that also involve model uncertainty.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vc3ee-fjy52Stochastic 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.eduhttps://authors.library.caltech.edu/records/w6txy-d2839Stochastic Subset Optimization for optimal reliability problems
https://resolver.caltech.edu/CaltechAUTHORS:20100708-132708802
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: 2008
DOI: 10.1016/j.probengmech.2007.12.011
Reliability-based design of a system often requires the minimization of the probability of system failure over the admissible space for the design variables. For complex systems 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. A new method called Stochastic Subset Optimization (SSO) 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 techniques are implemented in order to simulate samples of them that lead to system failure. In each iteration, a set with high likelihood 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. For problems that are characterized by small sensitivity around the optimal design choice, a combination of SSO with other optimization algorithms is proposed for enhanced overall efficiency.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1vj6b-jct17Reliability-Based Performance Objectives and Probabilistic Robustness in Structural Control Applications
https://resolver.caltech.edu/CaltechAUTHORS:20120817-155747138
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'Alexandros A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Scruggs-J-T', 'name': {'family': 'Scruggs', 'given': 'Jeffrey T.'}}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'James L.'}}]}
Year: 2008
DOI: 10.1061/(ASCE)0733-9399(2008)134:4(291)
A reliability-based structural control design approach is presented that optimizes a control system explicitly to minimize the
probability of structural failure. Failure is interpreted as the system's state trajectory exiting a safe region within a given time duration.
This safe region is bounded by hyperplanes in the system state space, each of them corresponding to an important response quantity. An
efficient approximation is discussed for the analytical evaluation of this probability, and for its optimization through feedback control. This
analytical approximation facilitates theoretical discussions regarding the characteristics of reliability-optimal controllers. Versions of the
controller design are described for the case using a nominal model of the system, as well as for the case with uncertain model parameters.
For the latter case, knowledge about the relative plausibility of the different possible values of the uncertain parameters is quantified
through the use of probability distributions on the uncertain parameter space. The influence of the excitation time duration on feedback
control design is discussed and a probabilistic treatment of this time duration is suggested. The relationship to H_2 i.e., minimum variance controller synthesis is also examined.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x4725-bxn89Robust-to-Modeling-Uncertainties Nonlinear Control Design for Offshore Structures
https://resolver.caltech.edu/CaltechAUTHORS:20100722-140702542
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.'}}, {'id': 'Angelides-D-C', 'name': {'family': 'Angelides', 'given': 'Demos C.'}}]}
Year: 2008
A controller design methodology for offshore structures is investigated. Because stochastic simulation is used for evaluation
of the system's performance in the design stage, nonlinear characteristics of the structural response and excitation can be
explicitly incorporated into the assumed system model. Model parameters whose values are uncertain are probabilistically
described. In this context, the controller is designed for optimal reliability, quantified as the probability that the performance
will not exceed some acceptable bounds over some time duration. The methodology is illustrated with an example involving
the control of a tension leg platform in an uncertain sea environment.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5w1r5-aef49Probabilistically robust nonlinear design of control systems for base-isolated structures
https://resolver.caltech.edu/CaltechAUTHORS:TAFschm08
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'Alexandros A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Scruggs-J-T', 'name': {'family': 'Scruggs', 'given': 'Jeffrey T.'}}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'James L.'}}]}
Year: 2008
DOI: 10.1002/stc.275
A stochastic-simulation-based nonlinear controller design for base-isolation systems is discussed in this study. The performance objective is the maximization of structural reliability, quantified as the probability, based on the available information, that the structural response trajectory will not exceed acceptable thresholds. A simulation-based approach is implemented for evaluation of the performance of the controlled system. This approach explicitly takes into account nonlinear characteristics of the structural response and the control law in the design process. A realistic probabilistic model for representation of near-fault ground motions is adopted in the design stage. The variability of future earthquake events is addressed by incorporating a probabilistic description for the ground-motion model parameters, leading to a design approach that is robust to probabilistic uncertainty. The methodology is illustrated through application to the base-isolated benchmark building with elastomeric and friction pendulum isolators and an array of regenerative force actuators. Skyhook control implementation is considered and an efficient scheme is presented for the clipping of the control forces in order to satisfy the actuator force constraints. The performance of the controlled system is evaluated under seven earthquake records using a number of metrics. Comparison with the performance of a similar network of viscous dampers is also discussed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/g4nb2-y9t90An efficient framework for optimal robust stochastic system design using stochastic simulation
https://resolver.caltech.edu/CaltechAUTHORS:TAFcmame08
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
DOI: 10.1016/j.cma.2008.03.029
The knowledge about a planned system in engineering design applications is never complete. Often, a probabilistic quantification of the uncertainty arising from this missing information is warranted in order to efficiently incorporate our partial knowledge about the system and its environment into their respective models. This leads to a robust stochastic design framework where probabilistic models of excitation uncertainties and system modeling uncertainties can be introduced; the design objective is then typically related to the expected value of a system performance measure, such as reliability or expected life-cycle cost. For complex system models, this expected value can rarely be evaluated analytically and so it is
often calculated using stochastic simulation techniques, which involve an estimation error and significant
computational cost. An efficient framework, consisting of two stages, is presented here for the optimization
in such robust stochastic design problems. The first stage implements a novel approach, called stochastic subset optimization (SSO), 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 other stochastic optimization algorithm to pinpoint the optimal design variables within that subset. The focus is primarily on the theory and implementation issues for SSO but also on topics related to the combination of the two different stages for overall enhanced efficiency. An illustrative example is presented that shows the efficiency of the proposed methodology; it considers the optimization of the reliability of a base-isolated structure considering future near-fault ground motions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3gcvs-1kd46Stochastic Subset Optimization for reliability optimization and sensitivity analysis in system design
https://resolver.caltech.edu/CaltechAUTHORS:20090914-141053110
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: 2009
DOI: 10.1016/j.compstruc.2008.12.015
Design problems that involve the system reliability as the objective function are discussed. In order to appropriately address the challenges of such applications when complex system models are involved, stochastic simulation is selected to evaluate the probability of failure. An innovative algorithm, called Stochastic Subset Optimization (SSO), is discussed for performing the reliability optimization as well as an efficient sensitivity analysis. The basic principle in SSO is the formulation of an augmented problem where the design variables are artificially considered as uncertain. Stochastic simulation techniques are implemented in order to simulate samples of these variables that lead to system failure. The information that these samples provide is then exploited in an iterative approach in SSO to identify a smaller subset of the design space that consists of near-optimal design variables and also that has high plausibility of containing the optimal design. At the same time, a sensitivity analysis for the influence of both the design variables and the uncertain model parameters is established.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cct3e-gwf77Life-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.eduhttps://authors.library.caltech.edu/records/qhs9d-12q23Life-cycle cost optimal design of passive dissipative devices
https://resolver.caltech.edu/CaltechAUTHORS:20091120-105913672
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: 2009
DOI: 10.1016/j.strusafe.2009.06.010
The cost-effective performance of structures under natural hazards such as earthquakes and hurricanes has long been recognized to be an important topic in the design of civil engineering systems. A realistic comprehensive treatment of such a design requires proper integration of (i) methodologies for treating the uncertainties related to natural hazards and to the structural behavior over the entire life-cycle of the building, (ii) tools for evaluating the performance using socioeconomic criteria, as well as (iii) algorithms appropriate for stochastic analysis and optimization. A systematic probabilistic framework is presented here for detailed estimation and optimization of the life-cycle cost of engineering systems. This framework is a general one but the application of interest here is the design of passive dissipative devices for seismic risk mitigation. A comprehensive methodology is initially presented for earthquake loss estimation; this methodology uses the nonlinear time-history response of the structure under a given excitation to estimate the damage in a detailed, component level. A realistic probabilistic model is then presented for describing the ground motion time history for future earthquake excitations. In this setting, the life-cycle cost is uncertain and can be quantified by its expected value over the space of the uncertain parameters for the structural and excitation models. Because of the complexity of these models, calculation of this expected value is performed using stochastic simulation techniques. This approach, though, involves an unavoidable estimation error and significant computational cost, features which make efficient design optimization challenging. A highly efficient framework, consisting of two stages, is discussed for this stochastic optimization. An illustrative example is presented that shows the efficiency of the proposed methodology; it considers the seismic retrofitting of a four-story non-ductile reinforced-concrete building with viscous dampers.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gcv5r-cdq67Robust Stochastic Design of Linear Controlled Systems for Performance Optimization
https://resolver.caltech.edu/CaltechAUTHORS:20100914-113201336
Authors: {'items': [{'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'Alexandros A.'}, 'orcid': '0000-0002-9784-7480'}, {'id': 'Scruggs-J-T', 'name': {'family': 'Scruggs', 'given': 'Jeffrey T.'}}, {'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'James L.'}}]}
Year: 2010
DOI: 10.1115/1.4001849
This study discusses a robust controller synthesis methodology for linear, time invariant systems, under probabilistic parameter uncertainty. Optimization of probabilistic performance robustness for [script H]_2 and multi-objective [script H]_2 measures is investigated, as well as for performance measures based on first-passage system reliability. The control optimization approaches proposed here exploit recent advances in stochastic simulation techniques. The approach is illustrated for vibration response suppression of a civil structure. The results illustrate that, for problems with probabilistic uncertainty, the explicit optimization of probabilistic performance robustness can result in markedly different optimal feedback laws, as well as enhanced performance robustness, when compared to traditional "worst-case" notions of robust optimal control.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4j01h-8bf55Robust 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.eduhttps://authors.library.caltech.edu/records/q9ve4-kgg86Reliability-Based Design Using Two-Stage Stochastic Optimization with a Treatment of Model Prediction Errors
https://resolver.caltech.edu/CaltechAUTHORS:20101213-121011348
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: 2010
DOI: 10.1061/(ASCE)EM.1943-7889.0000189
Design problems that involve optimization of the reliability of engineering systems are the focus of this paper. Methodologies are discussed applicable to problems that involve nonlinear systems and a large number of uncertain parameters specifying the system and excitation models. To address the complexity of these problems, stochastic simulation is considered for evaluation of the system reliability. An innovative approach, called stochastic subset optimization (SSO), is discussed for performing a sensitivity analysis with respect to the design variables of the problem as well as the uncertain model parameters. In a small number of iterations, SSO converges to a smaller subset of the original design space that has high plausibility of containing the optimal design variables and that consists of near-optimal designs. For higher accuracy, an appropriate stochastic optimization algorithm may then be used to pinpoint the optimal design variables within this subset. This produces an efficient two-stage framework for optimal reliability design. Topics related to the combination of the two different stages for overall enhanced efficiency are discussed. An example is presented that illustrates the effectiveness of the proposed two-stage methodology for a challenging dynamic reliability problem. Also, a study is performed of the influence on the optimal design decisions of the prediction error of the system model, which is introduced because no model makes perfect predictions of the system response.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/p1ww2-s5041Smart Base Isolation Design including Model Uncertainty in Ground Motion Characterization
https://resolver.caltech.edu/CaltechAUTHORS:20120904-164556868
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: 2012
N/Ahttps://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7pxkr-7q302Prior and Posterior Robust Stochastic Predictions for Dynamical Systems using Probability Logic
https://resolver.caltech.edu/CaltechAUTHORS:20120817-150858509
Authors: {'items': [{'id': 'Beck-J-L', 'name': {'family': 'Beck', 'given': 'James L.'}}, {'id': 'Taflanidis-Alexandros-Angelos', 'name': {'family': 'Taflanidis', 'given': 'Alexandros A.'}, 'orcid': '0000-0002-9784-7480'}]}
Year: 2013
DOI: 10.1615/Int.J.UncertaintyQuantification.2012003641
An overview is given of a powerful unifying probabilistic framework for treating modeling uncertainty, along with
input uncertainty, when using dynamic models to predict the response of a system during its design or operation. This
framework uses probability as a multivalued conditional logic for quantitative plausible reasoning in the presence of
uncertainty due to incomplete information. The fundamental probability models that represent the system's uncertain
behavior are specified by the choice of a stochastic system model class: a set of input–output probability models for
the system and a prior probability distribution over this set that quantifies the relative plausibility of each model. A
model class can be constructed from a parametrized deterministic system model by stochastic embedding which utilizes
Jaynes' principle of maximum information entropy. Robust predictive analyses use the entire model class with the
probabilistic predictions of each model being weighted by its prior probability, or if response data are available, by its
posterior probability from Bayes' theorem for the model class. Additional robustness to modeling uncertainty comes
from combining the robust predictions of each model class in a set of competing candidates weighted by the prior or
posterior probability of the model class, the latter being computed from Bayes' theorem. This higher-level application
of Bayes' theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more complex model
classes that extract more information from the data. Robust predictive analyses involve integrals over high-dimensional
spaces that usually must be evaluated numerically by Laplace's method of asymptotic approximation or by Markov
chain Monte Carlo methods. These computational tools are demonstrated in an illustrative example involving the
vertical dynamic response of a car being driven along a rough road.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vmtb7-pd741Non-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.eduhttps://authors.library.caltech.edu/records/1qvr3-e4041Non-parametric stochastic subset optimization for design problems with reliability constraints
https://resolver.caltech.edu/CaltechAUTHORS:20160108-095611832
Authors: {'items': [{'id': 'Jia-Gaofeng', 'name': {'family': 'Jia', 'given': 'Gaofeng'}}, {'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: 2015
DOI: 10.1007/s00158-015-1300-6
The Non-Parametric Stochastic Subset Optimization (NP-SSO) is a recently developed algorithm appropriate for optimization problems that use reliability criteria as objective function and involve computationally expensive numerical models for the engineering system under consideration. This paper discusses its extension to reliability-based design optimization (RBDO) applications involving reliability criteria 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 reliability of the engineering system 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 approximation of this reliability through kernel density estimation (KDE) using these samples. The RBDO problem is then solved using this approximation for evaluating the reliability constraints over the entire design domain and identifying the feasible region satisfying them. To improve computational efficiency, an iterative approach is proposed; at the end of each iteration, a new reduced search space is identified with reliability satisfying relaxed constraints, until the algorithm converges to the feasible design domain satisfying the desired constraints. A second refinement stage after initial convergence is also proposed to further improve the accuracy of the identified feasible region. A non-parametric characterization of the search space using a framework based on multivariate boundary KDE and support vector machine is established. To further improve the efficiency of the stochastic sampling stage, an adaptive selection of the number of samples required for the KDE approximation is proposed.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8pkbj-4nn31