547 research outputs found
Reliability analysis for data-driven noisy models using active learning
Reliability analysis aims at estimating the failure probability of an
engineering system. It often requires multiple runs of a limit-state function,
which usually relies on computationally intensive simulations. Traditionally,
these simulations have been considered deterministic, i.e., running them
multiple times for a given set of input parameters always produces the same
output. However, this assumption does not always hold, as many studies in the
literature report non-deterministic computational simulations (also known as
noisy models). In such cases, running the simulations multiple times with the
same input will result in different outputs. Similarly, data-driven models that
rely on real-world data may also be affected by noise. This characteristic
poses a challenge when performing reliability analysis, as many classical
methods, such as FORM and SORM, are tailored to deterministic models. To bridge
this gap, this paper provides a novel methodology to perform reliability
analysis on models contaminated by noise. In such cases, noise introduces
latent uncertainty into the reliability estimator, leading to an incorrect
estimation of the real underlying reliability index, even when using Monte
Carlo simulation. To overcome this challenge, we propose the use of denoising
regression-based surrogate models within an active learning reliability
analysis framework. Specifically, we combine Gaussian process regression with a
noise-aware learning function to efficiently estimate the probability of
failure of the underlying noise-free model. We showcase the effectiveness of
this methodology on standard benchmark functions and a finite element model of
a realistic structural frame
Meta-models for structural reliability and uncertainty quantification
A meta-model (or a surrogate model) is the modern name for what was
traditionally called a response surface. It is intended to mimic the behaviour
of a computational model M (e.g. a finite element model in mechanics) while
being inexpensive to evaluate, in contrast to the original model which may take
hours or even days of computer processing time. In this paper various types of
meta-models that have been used in the last decade in the context of structural
reliability are reviewed. More specifically classical polynomial response
surfaces, polynomial chaos expansions and kriging are addressed. It is shown
how the need for error estimates and adaptivity in their construction has
brought this type of approaches to a high level of efficiency. A new technique
that solves the problem of the potential biasedness in the estimation of a
probability of failure through the use of meta-models is finally presented.Comment: Keynote lecture Fifth Asian-Pacific Symposium on Structural
Reliability and its Applications (5th APSSRA) May 2012, Singapor
Polynomial-Chaos-based Kriging
Computer simulation has become the standard tool in many engineering fields
for designing and optimizing systems, as well as for assessing their
reliability. To cope with demanding analysis such as optimization and
reliability, surrogate models (a.k.a meta-models) have been increasingly
investigated in the last decade. Polynomial Chaos Expansions (PCE) and Kriging
are two popular non-intrusive meta-modelling techniques. PCE surrogates the
computational model with a series of orthonormal polynomials in the input
variables where polynomials are chosen in coherency with the probability
distributions of those input variables. On the other hand, Kriging assumes that
the computer model behaves as a realization of a Gaussian random process whose
parameters are estimated from the available computer runs, i.e. input vectors
and response values. These two techniques have been developed more or less in
parallel so far with little interaction between the researchers in the two
fields. In this paper, PC-Kriging is derived as a new non-intrusive
meta-modeling approach combining PCE and Kriging. A sparse set of orthonormal
polynomials (PCE) approximates the global behavior of the computational model
whereas Kriging manages the local variability of the model output. An adaptive
algorithm similar to the least angle regression algorithm determines the
optimal sparse set of polynomials. PC-Kriging is validated on various benchmark
analytical functions which are easy to sample for reference results. From the
numerical investigations it is concluded that PC-Kriging performs better than
or at least as good as the two distinct meta-modeling techniques. A larger gain
in accuracy is obtained when the experimental design has a limited size, which
is an asset when dealing with demanding computational models
On Bayesian Search for the Feasible Space Under Computationally Expensive Constraints
We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of exploration would be prohibitive. Bayesian search is data-efficient for such problems: starting from a small dataset, the central concept is to use Bayesian models of constraints with an acquisition function to locate promising solutions that may improve predictions of feasibility when the dataset is augmented. At the end of this sequential active learning approach with a limited number of expensive evaluations, the models can accurately predict the feasibility of any solution obviating the need for full simulations. In this paper, we propose a novel acquisition function that combines the probability that a solution lies at the boundary between feasible and infeasible spaces (representing exploitation) and the entropy in predictions (representing exploration). Experiments confirmed the efficacy of the proposed function
Efficient time-dependent system reliability analysis
Engineering systems are usually subjected to time-variant loads and operate under time-dependent uncertainty; system performances are therefore time-dependent. Accurate and efficient estimate of system reliability is crucial for decision makings on system design, lifetime cost estimate, maintenance strategy, etc. Although significant progresses have been made in time-independent reliability analysis for components and systems, time-dependent system reliability methodologies are still limited. This dissertation is motivated by the need of accurate and effective reliability prediction for engineering systems under time-dependent uncertainty. Based on the classic First and Second Order Reliability Method (FORM and SORM), a system reliability method is developed for multidisciplinary systems involving stationary stochastic processes. A dependent Kriging method is also developed for general components. This method accounts for dependent responses from surrogate models and is therefore more accurate than existing Kriging Monte Carlo simulation methods that neglect the dependence between responses. The extension of the dependent Kriging method to systems is also a contribution of this dissertation. To overcome the difficulty of obtaining extreme value distributions and get rid of global optimization with a double-loop procedure, a Kriging surrogate modeling method is also proposed. This method provides a new perspective of surrogate modeling for time-dependent systems and is applicable to general systems having random variables, time, and stochastic processes. The proposed methods are evaluated through a wide range of engineering systems, including a compound cylinders system, a liquid hydrogen fuel tank, function generator mechanisms, slider-crank mechanisms, and a Daniels system --Abstract, page iv
Bayesian subset simulation
We consider the problem of estimating a probability of failure ,
defined as the volume of the excursion set of a function above a given threshold, under a given
probability measure on . In this article, we combine the popular
subset simulation algorithm (Au and Beck, Probab. Eng. Mech. 2001) and our
sequential Bayesian approach for the estimation of a probability of failure
(Bect, Ginsbourger, Li, Picheny and Vazquez, Stat. Comput. 2012). This makes it
possible to estimate when the number of evaluations of is very
limited and is very small. The resulting algorithm is called Bayesian
subset simulation (BSS). A key idea, as in the subset simulation algorithm, is
to estimate the probabilities of a sequence of excursion sets of above
intermediate thresholds, using a sequential Monte Carlo (SMC) approach. A
Gaussian process prior on is used to define the sequence of densities
targeted by the SMC algorithm, and drive the selection of evaluation points of
to estimate the intermediate probabilities. Adaptive procedures are
proposed to determine the intermediate thresholds and the number of evaluations
to be carried out at each stage of the algorithm. Numerical experiments
illustrate that BSS achieves significant savings in the number of function
evaluations with respect to other Monte Carlo approaches
Time- and space-dependent uncertainty analysis and its application in lunar plasma environment modeling
”During an engineering system design, engineers usually encounter uncertainties that ubiquitously exist, such as material properties, dimensions of components, and random loads. Some of these parameters do not change with time or space and hence are time- and space-independent. However, in many engineering applications, the more general time- and space-dependent uncertainty is frequently encountered. Consequently, the system exhibits random time- and space-dependent behaviors, which may result in a higher probability of failure, lower average lifetime, and/or worse robustness. Therefore, it is critical to quantify uncertainty and predict how the system behaves under time- and space- dependent uncertainty. The objective of this study is to develop accurate and efficient methods for uncertainty analysis. This study contains five works. In the first work, an accurate method based on the series expansion, Gauss-Hermite quadrature, and saddle point approximation is developed to calculate high-dimensional normal probabilities. Then the method is applied to estimate time-dependent reliability. In the second work, we develop an adaptive Kriging method to estimate product average lifetime. In the third work, a time- and space-dependent reliability analysis method based on the first-order and second-order methods is proposed. In the fourth work, we extend the existing robustness analysis to time- and space-dependent problems and develop an adaptive Kriging method to evaluate the time- and space-dependent robustness. In the fifth work, we develop an adaptive Kriging method to efficiently estimate the lower and upper bounds of the electric potentials of the photoelectron sheaths near the lunar surface”--Abstract, page iv
- …