Gaussian Uncertainties Research Articles

Fast Numerical Powertrain Optimization Strategy for Connected Hybrid Electric Vehicles

Connected vehicle (CV) technology allows traffic information sharing that can be utilized to improve fuel benefits of hybrid electric vehicles (HEVs). However, there are challenges from the powertrain optimization perspective. First, optimizing powertrain operations is computational heavy due to the nonlinearities, constraints, and high dimensionality of the problem, especially with long optimization time horizon. Secondly, a slow powertrain optimization means the solution may not be optimal anymore at current time if the traffic states change. In this paper, a fast, near global-optimal, and practical HEV powertrain optimization utilizing vehicle speed prediction in CV environment is systematically formulated and solved. First, the minimum fuel rate and battery state-of-charge rate are calculated for different engine and battery power-split ratios. Then, the nonlinear minimum fuel rate and battery state-of-charge rate are piecewise-linearized by introducing dimensionless variables. The engine operating range, engine dynamics, and battery charge-sustaining constraint are represented by the dimensionless variables and treated as linear constraints. This transformation exploits the problem's structure, known as Separable Programming, which is solved efficiently as a large-dimension constrained linear problem. Fast optimization allows utilization of repeated speed predictions to maintain prediction accuracy. Results show comparable fuel economy with Dynamic Programming with significantly less computation time. Average fuel savings of 4.0% and 10.4% over Pontryagin's Minimum Principle and Rule-Based optimization methods are observed. Experimental results show the feasibility of the optimized engine operating points with fuel benefits over the rule-based method. Simulations with vehicle speed prediction and limited Gaussian uncertainties to emulate CV settings also show satisfactory fuel benefits.

Statistical evaluation of worst-case robust optimization intensity-modulated proton therapy plans using an exhaustive sampling approach

PurposeTo assess the worst-case robust optimization IMPT plans with setup and range uncertainties and to test the hypothesis that the worst-case robust optimization strategies could cover most possible setup and range uncertainties in the real scenarios.MethodsWe analyzed the nominal and worst-case robust optimization IMPT plans of seven patients with head and neck cancer patients. To take uncertainties into account for the dose calculation, we performed a comprehensive simulation in which the dose was recalculated 625 times per given plan using Gaussian systematic setup and proton range uncertainties. Subsequently, based on the simulation results, we calculated the target coverage in all perturbation scenarios, as well as the ratios of target coverage located within the threshold of eight worst-case scenarios. We set the criteria for the optimized plan to be the ratios of 1) the dose delivered to 95% (D95%) of clinical target volumes 1 and 2 (CTV1 and CTV2) above 95% of the prescribed dose, and 2) the D95% of clinical target volume 3 (CTV3) above 90% of the prescribed dose in worst-case situations.ResultsThe probability that the perturbed-dose indices of the CTVs in each scenario were within the worst-case scenario limits ranged from 89.51 to 91.22% for both the nominal and worst-case robust optimization IMPT plans. A quartile analysis showed that the selective robust optimization IMPT plans all had higher D95% values for CTV1, CTV2, and CTV3 than did the nominal IMPT plans.ConclusionsThe worst-case strategy for robust optimization is adequately models and covers most of the setup and range uncertainties for the IMPT treatment of head and neck patients in our center.

Outage Constrained Secrecy Rate Maximization for MIMOME Multicast Wiretap Channels

In this letter, we investigate a robust transmit optimization design based on an artificial noise (AN)-aided precoding scheme for maximizing secrecy rate in a multiple-input multiple-output multiple-eavesdropper multicast network where a transmitter sends confidential information to multiple intended users and provides energy for multiple idle nodes while multiple passive eavesdroppers try to overhear the secret information. Supposing Gaussian CSI uncertainties, the proposed outage-constrained secrecy rate maximization (OC-SRM) problem is nonconvex and its analytical analysis is more challenging than several existing OC-SRM schemes. Technically, to circumvent this mathematically intractable secrecy problem, we resort to low SNR approximation and some conservative approximations (e.g., Bernstein-type inequality and sphere bounding) to reformulate the OC-SRM problem into two convex subproblems which can be efficiently solved by the off-the-shelf optimization solver. Simulation results are provided to validate the security performance of the robust AN-aided precoding design.

Robust SINR-Constrained Symbol-Level Multiuser Precoding With Imperfect Channel Knowledge

In this paper, we address robust design of symbol-level precoding for the downlink of multiuser multiple-input multiple-output wireless channels, in the presence of imperfect channel state information (CSI) at the transmitter. In particular, we consider two common uncertainty models for the CSI imperfection, namely, spherical (bounded) and stochastic (Gaussian). Our design objective is to minimize the total (per-symbol) transmission power subject to constructive interference (CI) constraints as well as users' quality-of-service requirements in terms of signal-to-interference-plus-noise ratio. Assuming bounded channel uncertainties, we obtain a convex CI constraint based on the worst-case robust analysis, whereas in the case of Gaussian uncertainties, we define probabilistic CI constraints in order to achieve robustness to statistically-known CSI errors. Since the probabilistic constraints of actual interest are difficult to handle, we resort to their convex approximations, yielding tractable (deterministic) robust constraints. Three convex approximations are developed based on different robust conservatism approaches, among which one is introduced as a benchmark for comparison. We show that each of our proposed approximations is tighter than the other under specific robustness conditions, while both always outperform the benchmark. Using the developed CI constraints, we formulate the robust precoding optimization as a convex conic quadratic program. Extensive simulation results are provided to validate our analytic discussions and to make comparisons with existing robust precoding schemes. We also show that the robust design increases the computational complexity by an order of the number of users in the large system limit, compared to its non-robust counterpart.

Stochastic Energy Scheduling in Microgrids Considering the Uncertainties in Both Supply and Demand

Microgrids have emerged as a promising paradigm to integrate the renewable generation units, energy storage systems, and dispersed loads. However, the inherent fluctuation of renewable generations adds significant uncertainty to the supply side of microgrid. On the other hand, due to the small scale of the microgrid, the load demand in microgrid also has higher uncertainty than that observed in utility grids. Furthermore, the supply uncertainty and demand uncertainty may have different distribution characteristics, e.g., Gaussian and non-Gaussian uncertainties may exist simultaneously. These uncertainties pose significant challenges to the microgrid energy management. To address these challenges, this paper establishes a new stochastic energy scheduling scheme for microgrids. In this scheme, the energy scheduling is formulated as a stochastic model predictive control problem, which incorporates the uncertainties in both sides of supply and demand. Using machine-learning techniques, the corresponding stochastic optimization problem is converted to a standard convex quadratic programming, and thus can be solved efficiently. A key feature of this scheme is that it handles the coexistence of Gaussian and non-Gaussian uncertainties. Simulation results validate the effectiveness of the proposed scheme.

A generalized framework for chance-constrained optimal power flow

Abstract Deregulated energy markets, demand forecasting, and the continuously increasing share of renewable energy sources call – among others – fora structured consideration of uncertainties in optimal power flow problems. The main challenge is to guarantee power balance while maintaining economic and secure operation. In the presence of Gaussian uncertainties affine feedback policies are known to be viable options for this task. The present paper advocates a general framework for chance-constrained opf problems in terms of continuous random variables. It is shown that, irrespective of the type of distribution, the random-variable minimizers lead to affine feedback policies. Introducing a three-step methodology that exploits polynomial chaos expansion, the present paper provides a constructive approach to chance-constrained optimal power flow problems that does not assume a specific distribution, e.g. Gaussian, for the uncertainties. We illustrate our findings by means of a tutorial example and a 300-bus test case.

“Super-deblended” Dust Emission in Galaxies. I. The GOODS-North Catalog and the Cosmic Star Formation Rate Density out to Redshift 6

Abstract We present a new technique to measure multi-wavelength “super-deblended” photometry from highly confused images, which we apply to Herschel and ground-based far-infrared (FIR) and (sub-)millimeter (mm) data in the northern field of the Great Observatories Origins Deep Survey. There are two key novelties. First, starting with a large database of deep Spitzer 24 μm and VLA 20 cm detections that are used to define prior positions for fitting the FIR/submm data, we perform an active selection of useful priors independently at each frequency band, moving from less to more confused bands. Exploiting knowledge of redshift and all available photometry, we identify hopelessly faint priors that we remove from the fitting pool. This approach significantly reduces blending degeneracies and allows reliable photometry to be obtained for galaxies in FIR+mm bands. Second, we obtain well-behaved, nearly Gaussian flux density uncertainties, individually tailored to all fitted priors for each band. This is done by exploiting extensive simulations that allow us to calibrate the conversion of formal fitting uncertainties to realistic uncertainties, depending on directly measurable quantities. We achieve deeper detection limits with high fidelity measurements and uncertainties at FIR+mm bands. As an illustration of the utility of these measurements, we identify 70 galaxies with and reliable FIR+mm detections. We present new constraints on the cosmic star formation rate density at , finding a significant contribution from dusty galaxies that are missed by optical-to-near-infrared color selection. Photometric measurements for 3306 priors, including more than 1000 FIR+mm detections, are released publicly with our catalog.

Stochastic dynamic analysis of marine risers considering Gaussian system uncertainties

This paper performs the stochastic dynamic response analysis of marine risers with material uncertainties, i.e. in the mass density and elastic modulus, by using Stochastic Finite Element Method (SFEM) and model reduction technique. These uncertainties are assumed having Gaussian distributions. The random mass density and elastic modulus are represented by using the Karhunen–Loève (KL) expansion. The Polynomial Chaos (PC) expansion is adopted to represent the vibration response because the covariance of the output is unknown. Model reduction based on the Iterated Improved Reduced System (IIRS) technique is applied to eliminate the PC coefficients of the slave degrees of freedom to reduce the dimension of the stochastic system. Monte Carlo Simulation (MCS) is conducted to obtain the reference response statistics. Two numerical examples are studied in this paper. The response statistics from the proposed approach are compared with those from MCS. It is noted that the computational time is significantly reduced while the accuracy is kept. The results demonstrate the efficiency of the proposed approach for stochastic dynamic response analysis of marine risers.

Symbolic and numeric scheme for solution of linear integro-differential equations with random parameter uncertainties and Gaussian stochastic process input

• A system of linear stochastic integro-differential equations is under consideration. • Gaussian nonstationary noises and random model uncertainties excite the system. • The problem is to find the mean and covariance functions of the state vector process. • Green matrix-valued functions are used to solve the problem. • As example, a response of a thermoviscoelastic system is estimated by our scheme. The paper describes a theoretical apparatus and an algorithmic part of application of the Green matrix-valued functions for time-domain analysis of systems of linear stochastic integro-differential equations. It is suggested that these systems are subjected to Gaussian nonstationary stochastic noises in the presence of model parameter uncertainties that are described in the framework of the probability theory. If the uncertain model parameter is fixed to a given value, then a time-history of the system will be fully represented by a second-order Gaussian vector stochastic process whose properties are completely defined by its conditional vector-valued mean function and matrix-valued covariance function. The scheme that is proposed is constituted of a combination of two subschemes. The first one explicitly defines closed relations for symbolic and numeric computations of the conditional mean and covariance functions, and the second one calculates unconditional characteristics by the Monte Carlo method. A full scheme realized on the base of Wolfram Mathematica and Intel Fortran software programs, is demonstrated by an example devoted to an estimation of a nonstationary stochastic response of a mechanical system with a thermoviscoelastic component. Results obtained by using the proposed scheme are compared with a reference solution constructed by using a direct Monte Carlo simulation.

Analytical probabilistic modeling of RBE-weighted dose for ion therapy

Particle therapy is especially prone to uncertainties. This issue is usually addressed with uncertainty quantification and minimization techniques based on scenario sampling. For proton therapy, however, it was recently shown that it is also possible to use closed-form computations based on analytical probabilistic modeling (APM) for this purpose. APM yields unique features compared to sampling-based approaches, motivating further research in this context.This paper demonstrates the application of APM for intensity-modulated carbon ion therapy to quantify the influence of setup and range uncertainties on the RBE-weighted dose. In particular, we derive analytical forms for the nonlinear computations of the expectation value and variance of the RBE-weighted dose by propagating linearly correlated Gaussian input uncertainties through a pencil beam dose calculation algorithm. Both exact and approximation formulas are presented for the expectation value and variance of the RBE-weighted dose and are subsequently studied in-depth for a one-dimensional carbon ion spread-out Bragg peak. With V and B being the number of voxels and pencil beams, respectively, the proposed approximations induce only a marginal loss of accuracy while lowering the computational complexity from order to for the expectation value and from to for the variance of the RBE-weighted dose. Moreover, we evaluated the approximated calculation of the expectation value and standard deviation of the RBE-weighted dose in combination with a probabilistic effect-based optimization on three patient cases considering carbon ions as radiation modality against sampled references. The resulting global γ-pass rates (2 mm,2%) are 99.15% for the expectation value and 94.95% for the standard deviation of the RBE-weighted dose, respectively. We applied the derived analytical model to carbon ion treatment planning, although the concept is in general applicable to other ion species considering a variable RBE.

Looking through the same lens: Shear calibration for LSST, Euclid, and WFIRST with stage 4 CMB lensing

The next generation weak lensing surveys (i.e., LSST, Euclid and WFIRST) will require exquisite control over systematic effects. In this paper, we address shear calibration and present the most realistic forecast to date for LSST/Euclid/WFIRST and CMB lensing from a stage 4 CMB experiment (CMB S4). We use the CosmoLike code to simulate a joint analysis of all the two-point functions of galaxy density, galaxy shear and CMB lensing convergence. We include the full Gaussian and non-Gaussian covariances and explore the resulting joint likelihood with Monte Carlo Markov Chains. We constrain shear calibration biases while simultaneously varying cosmological parameters, galaxy biases and photometric redshift uncertainties. We find that CMB lensing from CMB S4 enables the calibration of the shear biases down to 0.2% - 3% in 10 tomographic bins for LSST (below the ~0.5% requirements in most tomographic bins), down to 0.4% - 2.4% in 10 bins for Euclid and 0.6% - 3.2% in 10 bins for WFIRST. For a given lensing survey, the method works best at high redshift where shear calibration is otherwise most challenging. This self-calibration is robust to Gaussian photometric redshift uncertainties and to a reasonable level of intrinsic alignment. It is also robust to changes in the beam and the effectiveness of the component separation of the CMB experiment, and slowly dependent on its depth, making it possible with third generation CMB experiments such as AdvACT and SPT-3G, as well as the Simons Observatory.

Multi‐sensor fusion for robust target tracking in the simultaneous presence of set‐membership and stochastic Gaussian uncertainties

This study proposes a novel data fusion algorithm in sensor networks with simultaneous presence of set-membership and stochastic Gaussian measurement uncertainties. The proposed method is grounded in the marriage of ellipsoidal calculus theory and data compression algorithm. The point-valued measurement and the set-valued measurement are compressed into a uniform framework during the estimation. An optimal Kalman gain is obtained that minimises the upper bound of the mean square error of the estimation set. The proposed algorithm is applied to the target tracking problem and the estimation results show that the proposed algorithm improves the tracking performance.

Robust Tomlinson–Harashima Precoding With Gaussian Uncertainties for SWIPT in MIMO Broadcast Channels

Nonlinear transceiver based on Tomlinson–Harashima (TH) precoding outperforms the linear minimum mean-square-error (MSE) architecture in terms of minimum achievable MSE. In this paper, we investigate nonlinear TH precoding design problem for simultaneous wireless information and power transfer in multiple-input-multiple-output broadcast channels, where there are one information-decoding (ID) receiver and multiple energy harvesting (EH) receivers. We consider the scenario that the transmitter knows imperfect channel state information of all links and the channel uncertainties are modeled by Gaussian random variables. Our objective is to jointly optimize TH precoding matrices and linear equalizer to minimize average MSE subject to transmit power constraint and EH constraints on average harvested power. We transform the robust transceiver design problem into a difference of convex programming and propose a constrained concave convex procedure (CCCP) based locally optimal solution. To reduce computational complexity, we propose a noniterative upper bound based suboptimal solution that minimizes the upper bound on average MSE. We also extend the CCCP-based locally optimal solution to the single group multicast scenario where there are multiple ID receivers. Simulation results demonstrate that our proposed TH precoding transceiver design achieves lower average MSE than linear precoding transceiver design.

The effect of unresolved contaminant stars on the cross-matching of photometric catalogues

A fundamental process in astrophysics is the matching of two photometric catalogues. It is crucial that the correct objects be paired, and that their photometry does not suffer from any spurious additional flux. We compare the positions of sources in Wide-field Infrared Survey Explorer (WISE), INT Photometric H α Survey, Two Micron All Sky Survey and AAVSO Photometric All Sky Survey with Gaia Data Release 1 astrometric positions. We find that the separations are described by a combination of a Gaussian distribution, wider than naively assumed based on their quoted uncertainties, and a large wing, which some authors ascribe to proper motions. We show that this is caused by flux contamination from blended stars not treated separately. We provide linear fits between the quoted Gaussian uncertainty and the core fit to the separation distributions. We show that at least one in three of the stars in the faint half of a given catalogue will suffer from flux contamination above the 1 per cent level when the density of catalogue objects per point spread function area is above approximately 0.005. This has important implications for the creation of composite catalogues. It is important for any closest neighbour matches as there will be a given fraction of matches that are flux contaminated, while some matches will be missed due to significant astrometric perturbation by faint contaminants. In the case of probability-based matching, this contamination affects the probability density function of matches as a function of distance. This effect results in up to 50 per cent fewer counterparts being returned as matches, assuming Gaussian astrometric uncertainties for WISE–Gaia matching in crowded Galactic plane regions, compared with a closest neighbour match.

Robust beamforming and power splitting design in MISO SWIPT downlink system

In this study, the authors consider simultaneous wireless information and power transfer (SWIPT) in a multiple-input-single-output (MISO) downlink system, where power splitting scheme is considered for each user of this system. Since channel state information of each user cannot be available at the transmitter, robust beamforming for SWIPT in the MISO downlink system is presented by incorporating with different types of channel uncertainty models. The authors first formulate the robust power minimisation problem subject to the signal-to-inference-plus-noise ratio (SINR) and energy harvesting (EH) constraints by incorporating two Gaussian channel uncertainties. The original problem is not convex in terms of channel uncertainties, and cannot be solved efficiently. The authors employ the well-known Bernstein-type inequality and Gaussian error function to make probability based constraints tractable, respectively, in order to recast the original problem as the convex form. Moreover, the robust power minimisation problem with the probability based SINR and EH constraints is formulated by incorporating random distribution with known error mean and covariance matrix. By exploiting conditional value-at-risk functional and semi-definite relaxation, this optimisation problem is relaxed as the convex form. Finally, numerical results are provided to validate the performance of these proposed robust schemes.

Efficient visual object detection with spatially global Gaussian mixture models and uncertainties

In this paper, we deal with the problem of visual detection of moving objects using innovative Gaussian mixture models (GMM). The proposed method, the Spatially Global Gaussian Mixture Model (SGGMM) uses RGB and pixel uncertainty for background modelling. The SGGMM with colours only is used for scenes with moderate illumination changes. When combined with pixel uncertainty statistics, the method can deal efficiently with dynamic backgrounds and scene backgrounds with fast change in luminosity. Experimental evaluation in indoor and outdoor environments shows the performance of the foreground segmentation with the proposed SGGMM model using solely RGB colour or in combination with pixel uncertainties. These experimental scenarios take into account changes in the background within the scene. They are also used to compare the proposed technique with other state-of-the-art segmentation approaches in terms of accuracy and execution time performance. Further, our solution is implemented and tested in embedded camera sensor network nodes.

On the dual iterative stochastic perturbation-based finite element method in solid mechanics with Gaussian uncertainties

On the dual iterative stochastic perturbation-based finite element method in solid mechanics with Gaussian uncertainties

Tight Probabilistic SINR Constrained Beamforming Under Channel Uncertainties

In downlink multi-user beamforming, a single basestation is serving a number of users simultaneously. However, energy intended for one user may leak to other unintended users, causing interference. With signal-to-interference-plus-noise ratio (SINR) being one of the most crucial quality metrics to users, beamforming design with SINR guarantee has always been an important research topic. However, when the channel state information is not accurate, the SINR requirements become probabilistic constraints, which unfortunately are not tractable analytically for general uncertainty distribution. Therefore, existing probabilistic beamforming methods focus on the relatively simple Gaussian and uniform channel uncertainties, and mainly rely on probability inequality based approximated solutions, resulting in conservative SINR outage realizations. In this paper, based on the local structure of the feasible set in the probabilistic beamforming problem, a systematic method is proposed to realize tight SINR outage control for a large class of channel uncertainty distributions. With channel estimation and quantization errors as examples, simulation results show that the SINR outage can be realized tightly, which results in reduced transmit power compared to the existing inequality based probabilistic beamformers.

IMFIT: A FAST, FLEXIBLE NEW PROGRAM FOR ASTRONOMICAL IMAGE FITTING

I describe a new, open-source astronomical image-fitting program called Imfit, specialized for galaxies but potentially useful for other sources, which is fast, flexible, and highly extensible. A key characteristic of the program is an object-oriented design which allows new types of image components (2D surface-brightness functions) to be easily written and added to the program. Image functions provided with Imfit include the usual suspects for galaxy decompositions (Sersic, exponential, Gaussian), along with Core-Sersic and broken-exponential profiles, elliptical rings, and three components which perform line-of-sight integration through 3D luminosity-density models of disks and rings seen at arbitrary inclinations. Available minimization algorithms include Levenberg-Marquardt, Nelder-Mead simplex, and Differential Evolution, allowing trade-offs between speed and decreased sensitivity to local minima in the fit landscape. Minimization can be done using the standard chi^2 statistic (using either data or model values to estimate per-pixel Gaussian errors, or else user-supplied error images) or Poisson-based maximum-likelihood statistics; the latter approach is particularly appropriate for cases of Poisson data in the low-count regime. I show that fitting low-S/N galaxy images using chi^2 minimization and individual-pixel Gaussian uncertainties can lead to significant biases in fitted parameter values, which are avoided if a Poisson-based statistic is used; this is true even when Gaussian read noise is present.

Application of the generalized Polynomial Chaos expansion to the simulation of an internal combustion engine with uncertainties

The study of combustion associated phenomena in internal combustion engines is important for reasons that include pollutant formation control, and the heat transfer between the hot gases, the piston and combustion chamber walls. Although there are several models for the chemically reacting turbulent flow inside the combustion chamber, such models always suffer from some level of uncertainties in their formulations or in the physical parameters used for their simulation. The main objective of the present paper consists in modeling the combustion phenomena in a combustion chamber of an internal combustion engine, using a model based on the First Law of Thermodynamics, considering uncertainties in the mass fraction of burned fuel. As a result, the curve describing the in-cylinder pressure as a function of the crank angle can be obtained for different uncertainties levels. For this purpose, the generalized Polynomial Chaos (gPC) and Monte Carlo techniques were applied to a set of ordinary differential equations obtained from a First Law analysis, and the stochastic moments of the solution were obtained. Uniform and Gaussian uncertainties distributions were considered in order to obtain the stochastic solution. Results show that the gPC is more computationally efficient than the Monte Carlo simulation for the considered application . Besides, experimental engine results were also used in order to validate the implemented numerical procedure.