222 research outputs found
GRADIENT-BASED STOCHASTIC OPTIMIZATION METHODS IN BAYESIAN EXPERIMENTAL DESIGN
Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue OED for nonlinear systems from a Bayesian perspective, with the goal of choosing experiments that are optimal for parameter inference. Our objective in this context is the expected information gain in model parameters, which in general can only be estimated using Monte Carlo methods. Maximizing this objective thus becomes a stochastic optimization problem. This paper develops gradient-based stochastic optimization methods for the design of experiments on a continuous parameter space. Given a Monte Carlo estimator of expected information gain, we use infinitesimal perturbation analysis to derive gradients of this estimator.We are then able to formulate two gradient-based stochastic optimization approaches: (i) Robbins-Monro stochastic approximation, and (ii) sample average approximation combined with a deterministic quasi-Newton method. A polynomial chaos approximation of the forward model accelerates objective and gradient evaluations in both cases.We discuss the implementation of these optimization methods, then conduct an empirical comparison of their performance. To demonstrate design in a nonlinear setting with partial differential equation forward models, we use the problem of sensor placement for source inversion. Numerical results yield useful guidelines on the choice of algorithm and sample sizes, assess the impact of estimator bias, and quantify tradeoffs of computational cost versus solution quality and robustness.United States. Air Force Office of Scientific Research (Computational Mathematics Program)National Science Foundation (U.S.) (Award ECCS-1128147
Fault Prognosis of Turbofan Engines: Eventual Failure Prediction and Remaining Useful Life Estimation
In the era of industrial big data, prognostics and health management is
essential to improve the prediction of future failures to minimize inventory,
maintenance, and human costs. Used for the 2021 PHM Data Challenge, the new
Commercial Modular Aero-Propulsion System Simulation dataset from NASA is an
open-source benchmark containing simulated turbofan engine units flown under
realistic flight conditions. Deep learning approaches implemented previously
for this application attempt to predict the remaining useful life of the engine
units, but have not utilized labeled failure mode information, impeding
practical usage and explainability. To address these limitations, a new
prognostics approach is formulated with a customized loss function to
simultaneously predict the current health state, the eventual failing
component(s), and the remaining useful life. The proposed method incorporates
principal component analysis to orthogonalize statistical time-domain features,
which are inputs into supervised regressors such as random forests, extreme
random forests, XGBoost, and artificial neural networks. The highest performing
algorithm, ANN-Flux, achieves AUROC and AUPR scores exceeding 0.95 for each
classification. In addition, ANN-Flux reduces the remaining useful life RMSE by
38% for the same test split of the dataset compared to past work, with
significantly less computational cost.Comment: Preprint with 10 pages, 5 figures. Submitted to International Journal
of Prognostics and Health Management (IJPHM
Accelerated Bayesian experimental design for chemical kinetic models
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 129-136).The optimal selection of experimental conditions is essential in maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. A general Bayesian framework for optimal experimental design with nonlinear simulation-based models is proposed. The formulation accounts for uncertainty in model parameters, observables, and experimental conditions. Straightforward Monte Carlo evaluation of the objective function - which reflects expected information gain (Kullback-Leibler divergence) from prior to posterior - is intractable when the likelihood is computationally intensive. Instead, polynomial chaos expansions are introduced to capture the dependence of observables on model parameters and on design conditions. Under suitable regularity conditions, these expansions converge exponentially fast. Since both the parameter space and the design space can be high-dimensional, dimension-adaptive sparse quadrature is used to construct the polynomial expansions. Stochastic optimization methods will be used in the future to maximize the expected utility. While this approach is broadly applicable, it is demonstrated on a chemical kinetic system with strong nonlinearities. In particular, the Arrhenius rate parameters in a combustion reaction mechanism are estimated from observations of autoignition. Results show multiple order-of-magnitude speedups in both experimental design and parameter inference.by Xun Huan.S.M
Expert Elicitation and Data Noise Learning for Material Flow Analysis using Bayesian Inference
Bayesian inference allows the transparent communication of uncertainty in
material flow analyses (MFAs), and a systematic update of uncertainty as new
data become available. However, the method is undermined by the difficultly of
defining proper priors for the MFA parameters and quantifying the noise in the
collected data. We start to address these issues by first deriving and
implementing an expert elicitation procedure suitable for generating MFA
parameter priors. Second, we propose to learn the data noise concurrent with
the parametric uncertainty. These methods are demonstrated using a case study
on the 2012 U.S. steel flow. Eight experts are interviewed to elicit
distributions on steel flow uncertainty from raw materials to intermediate
goods. The experts' distributions are combined and weighted according to the
expertise demonstrated in response to seeding questions. These aggregated
distributions form our model parameters' prior. A sensible, weakly-informative
prior is also adopted for learning the data noise. Bayesian inference is then
performed to update the parametric and data noise uncertainty given MFA data
collected from the United States Geological Survey (USGS) and the World Steel
Association (WSA). The results show a reduction in MFA parametric uncertainty
when incorporating the collected data. Only a modest reduction in data noise
uncertainty was observed; however, greater reductions were achieved when using
data from multiple years in the inference. These methods generate transparent
MFA and data noise uncertainties learned from data rather than pre-assumed data
noise levels, providing a more robust basis for decision-making that affects
the system.Comment: 23 pages of main paper and 10 pages of supporting informatio
FP-IRL: Fokker-Planck-based Inverse Reinforcement Learning -- A Physics-Constrained Approach to Markov Decision Processes
Inverse Reinforcement Learning (IRL) is a compelling technique for revealing
the rationale underlying the behavior of autonomous agents. IRL seeks to
estimate the unknown reward function of a Markov decision process (MDP) from
observed agent trajectories. However, IRL needs a transition function, and most
algorithms assume it is known or can be estimated in advance from data. It
therefore becomes even more challenging when such transition dynamics is not
known a-priori, since it enters the estimation of the policy in addition to
determining the system's evolution. When the dynamics of these agents in the
state-action space is described by stochastic differential equations (SDE) in
It^{o} calculus, these transitions can be inferred from the mean-field theory
described by the Fokker-Planck (FP) equation. We conjecture there exists an
isomorphism between the time-discrete FP and MDP that extends beyond the
minimization of free energy (in FP) and maximization of the reward (in MDP). We
identify specific manifestations of this isomorphism and use them to create a
novel physics-aware IRL algorithm, FP-IRL, which can simultaneously infer the
transition and reward functions using only observed trajectories. We employ
variational system identification to infer the potential function in FP, which
consequently allows the evaluation of reward, transition, and policy by
leveraging the conjecture. We demonstrate the effectiveness of FP-IRL by
applying it to a synthetic benchmark and a biological problem of cancer cell
dynamics, where the transition function is inaccessible
Compressive sensing adaptation for polynomial chaos expansions
Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of
the underlying Gaussian germ. Several rotations have been proposed in the
literature resulting in adaptations with different convergence properties. In
this paper we present a new adaptation mechanism that builds on compressive
sensing algorithms, resulting in a reduced polynomial chaos approximation with
optimal sparsity. The developed adaptation algorithm consists of a two-step
optimization procedure that computes the optimal coefficients and the input
projection matrix of a low dimensional chaos expansion with respect to an
optimally rotated basis. We demonstrate the attractive features of our
algorithm through several numerical examples including the application on
Large-Eddy Simulation (LES) calculations of turbulent combustion in a HIFiRE
scramjet engine.Comment: Submitted to Journal of Computational Physic
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