115,817 research outputs found
Uncertainty Analysis of the Adequacy Assessment Model of a Distributed Generation System
Due to the inherent aleatory uncertainties in renewable generators, the
reliability/adequacy assessments of distributed generation (DG) systems have
been particularly focused on the probabilistic modeling of random behaviors,
given sufficient informative data. However, another type of uncertainty
(epistemic uncertainty) must be accounted for in the modeling, due to
incomplete knowledge of the phenomena and imprecise evaluation of the related
characteristic parameters. In circumstances of few informative data, this type
of uncertainty calls for alternative methods of representation, propagation,
analysis and interpretation. In this study, we make a first attempt to
identify, model, and jointly propagate aleatory and epistemic uncertainties in
the context of DG systems modeling for adequacy assessment. Probability and
possibility distributions are used to model the aleatory and epistemic
uncertainties, respectively. Evidence theory is used to incorporate the two
uncertainties under a single framework. Based on the plausibility and belief
functions of evidence theory, the hybrid propagation approach is introduced. A
demonstration is given on a DG system adapted from the IEEE 34 nodes
distribution test feeder. Compared to the pure probabilistic approach, it is
shown that the hybrid propagation is capable of explicitly expressing the
imprecision in the knowledge on the DG parameters into the final adequacy
values assessed. It also effectively captures the growth of uncertainties with
higher DG penetration levels
Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints
This paper presents a stochastic model predictive control approach for
nonlinear systems subject to time-invariant probabilistic uncertainties in
model parameters and initial conditions. The stochastic optimal control problem
entails a cost function in terms of expected values and higher moments of the
states, and chance constraints that ensure probabilistic constraint
satisfaction. The generalized polynomial chaos framework is used to propagate
the time-invariant stochastic uncertainties through the nonlinear system
dynamics, and to efficiently sample from the probability densities of the
states to approximate the satisfaction probability of the chance constraints.
To increase computational efficiency by avoiding excessive sampling, a
statistical analysis is proposed to systematically determine a-priori the least
conservative constraint tightening required at a given sample size to guarantee
a desired feasibility probability of the sample-approximated chance constraint
optimization problem. In addition, a method is presented for sample-based
approximation of the analytic gradients of the chance constraints, which
increases the optimization efficiency significantly. The proposed stochastic
nonlinear model predictive control approach is applicable to a broad class of
nonlinear systems with the sufficient condition that each term is analytic with
respect to the states, and separable with respect to the inputs, states and
parameters. The closed-loop performance of the proposed approach is evaluated
using the Williams-Otto reactor with seven states, and ten uncertain parameters
and initial conditions. The results demonstrate the efficiency of the approach
for real-time stochastic model predictive control and its capability to
systematically account for probabilistic uncertainties in contrast to a
nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro
Scenic: A Language for Scenario Specification and Scene Generation
We propose a new probabilistic programming language for the design and
analysis of perception systems, especially those based on machine learning.
Specifically, we consider the problems of training a perception system to
handle rare events, testing its performance under different conditions, and
debugging failures. We show how a probabilistic programming language can help
address these problems by specifying distributions encoding interesting types
of inputs and sampling these to generate specialized training and test sets.
More generally, such languages can be used for cyber-physical systems and
robotics to write environment models, an essential prerequisite to any formal
analysis. In this paper, we focus on systems like autonomous cars and robots,
whose environment is a "scene", a configuration of physical objects and agents.
We design a domain-specific language, Scenic, for describing "scenarios" that
are distributions over scenes. As a probabilistic programming language, Scenic
allows assigning distributions to features of the scene, as well as
declaratively imposing hard and soft constraints over the scene. We develop
specialized techniques for sampling from the resulting distribution, taking
advantage of the structure provided by Scenic's domain-specific syntax.
Finally, we apply Scenic in a case study on a convolutional neural network
designed to detect cars in road images, improving its performance beyond that
achieved by state-of-the-art synthetic data generation methods.Comment: 41 pages, 36 figures. Full version of a PLDI 2019 paper (extending UC
Berkeley EECS Department Tech Report No. UCB/EECS-2018-8
A Factor Graph Approach to Automated Design of Bayesian Signal Processing Algorithms
The benefits of automating design cycles for Bayesian inference-based
algorithms are becoming increasingly recognized by the machine learning
community. As a result, interest in probabilistic programming frameworks has
much increased over the past few years. This paper explores a specific
probabilistic programming paradigm, namely message passing in Forney-style
factor graphs (FFGs), in the context of automated design of efficient Bayesian
signal processing algorithms. To this end, we developed "ForneyLab"
(https://github.com/biaslab/ForneyLab.jl) as a Julia toolbox for message
passing-based inference in FFGs. We show by example how ForneyLab enables
automatic derivation of Bayesian signal processing algorithms, including
algorithms for parameter estimation and model comparison. Crucially, due to the
modular makeup of the FFG framework, both the model specification and inference
methods are readily extensible in ForneyLab. In order to test this framework,
we compared variational message passing as implemented by ForneyLab with
automatic differentiation variational inference (ADVI) and Monte Carlo methods
as implemented by state-of-the-art tools "Edward" and "Stan". In terms of
performance, extensibility and stability issues, ForneyLab appears to enjoy an
edge relative to its competitors for automated inference in state-space models.Comment: Accepted for publication in the International Journal of Approximate
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