32,727 research outputs found
Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework
This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.Peer ReviewedPostprint (published version
Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport
In this work, we propose a novel method for quantifying distances between
Toeplitz structured covariance matrices. By exploiting the spectral
representation of Toeplitz matrices, the proposed distance measure is defined
based on an optimal mass transport problem in the spectral domain. This may
then be interpreted in the covariance domain, suggesting a natural way of
interpolating and extrapolating Toeplitz matrices, such that the positive
semi-definiteness and the Toeplitz structure of these matrices are preserved.
The proposed distance measure is also shown to be contractive with respect to
both additive and multiplicative noise, and thereby allows for a quantification
of the decreased distance between signals when these are corrupted by noise.
Finally, we illustrate how this approach can be used for several applications
in signal processing. In particular, we consider interpolation and
extrapolation of Toeplitz matrices, as well as clustering problems and tracking
of slowly varying stochastic processes
Intersection SPaT Estimation by means of Single-Source Connected Vehicle Data
The file attached to this record is the author's final peer reviewed version.Current traffic management systems in urban networks require real-time estimation of the traffic states. With the development of in-vehicle and communication technologies, connected vehicle data has emerged as a new data source for traffic measurement and estimation. In this work, a machine learning-based methodology for signal phase and timing information (SPaT) which is highly valuable for many applications such as green light optimal advisory systems and real-time vehicle navigation is proposed. The proposed methodology utilizes data from connected vehicles travelling within urban signalized links to estimate the queue tail location, vehicle accumulation, and subsequently, link outflow. Based on the produced high-resolution outflow estimates and data from crossing connected vehicles, SPaT information is estimated via correlation analysis and a machine learning approach. The main contribution is that the single-source proposed approach relies merely on connected vehicle data and requires neither prior information such as intersection cycle time nor data from other sources such as conventional traffic measuring tools. A sample four-leg intersection where each link comprises different number of lanes and experiences different traffic condition is considered as a testbed. The validation of the developed approach has been undertaken by comparing the produced estimates with realistic micro-simulation results as ground truth, and the achieved simulation results are promising even at low penetration rates of connected vehicles
Sliced Wasserstein Distance for Learning Gaussian Mixture Models
Gaussian mixture models (GMM) are powerful parametric tools with many
applications in machine learning and computer vision. Expectation maximization
(EM) is the most popular algorithm for estimating the GMM parameters. However,
EM guarantees only convergence to a stationary point of the log-likelihood
function, which could be arbitrarily worse than the optimal solution. Inspired
by the relationship between the negative log-likelihood function and the
Kullback-Leibler (KL) divergence, we propose an alternative formulation for
estimating the GMM parameters using the sliced Wasserstein distance, which
gives rise to a new algorithm. Specifically, we propose minimizing the
sliced-Wasserstein distance between the mixture model and the data distribution
with respect to the GMM parameters. In contrast to the KL-divergence, the
energy landscape for the sliced-Wasserstein distance is more well-behaved and
therefore more suitable for a stochastic gradient descent scheme to obtain the
optimal GMM parameters. We show that our formulation results in parameter
estimates that are more robust to random initializations and demonstrate that
it can estimate high-dimensional data distributions more faithfully than the EM
algorithm
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