Magic gap ratio for optimally robust superfluidity and high-Tc superconductivity
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High Magnetic Field Science↗
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A Robust Optimization Approach to Determine Power Line Undergrounding under Wildfire Risk
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Engineering - Power transmission and distribution,↗
A review on the integration of probabilistic solar forecasting in power systems
As one of the fastest growing renewable energy sources, the integration of solar power poses great challenges to power systems due to its variable and uncertain nature. As an effective approach to promote the integration of solar power in power systems, the value of probabilistic forecasts is being increasingly recognized in the recent decade. While the current use of probabilistic forecasts in power systems is limited, enormous amount of research has been conducted to promote the adoption of probabilistic forecasts and many methods have been proposed. This paper gives a comprehensive review on how probabilistic solar forecasts are utilized in power systems to address the challenges. Potential methods to deal with uncertainties in power systems are summarized, such as probabilistic load flow models, stochastic optimization, robust optimization, and chance constraints. Additionally, specific areas where these methods can be applied are discussed and state-of-the-art studies are summarized.
14 SOLAR ENERGY↗
TEAL
TEAL is a financial performance calculator plugin for the RAVEN code, framework, resolving around the computation of Net Present Value and associated financial metrics. TEAL can make use of inflation rates, taxation, escalation factors, capital expenditure economy of scale scaling factors. The unique feature of TEAL is the capability to be linked with RAVEN external models and build corresponding cash flows using the variables computed by those external models. In addition to be able to use the capability to generate cash flows derived from complex physical models generated by RAVEN, another distinctive feature of TEAL is the capability to provide financial risk/probabilistic metrics that can empower RAVEN to perform optimization/analysis driven by financial risk augmentations. Optimization, robust optimization, parametric studies, large parallel simulations, sensitivity analysis, data mining, etc. are just some of the capabilities that can be leveraged.
Alfonsi, Andrea↗
Options for Robust Airfoil Optimization under Uncertainty
A robust optimization method is developed to overcome point-optimization at the sampled design points. This method combines the best features from several preliminary methods proposed by the authors and their colleagues. The robust airfoil shape optimization is a direct method for drag reduction over a given range of operating conditions and has three advantages: (1) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (2) it uses a large number of spline control points as design variables yet the resulting airfoil shape does not need to be smoothed, and (3) it allows the user to make a tradeoff between the level of optimization and the amount of computing time consumed. For illustration purposes, the robust optimization method is used to solve a lift-constrained drag minimization problem for a two-dimensional (2-D) airfoil in Euler flow with 20 geometric design variables.
Padula, Sharon L.↗
SU-F-T-208: An Efficient Planning Approach to Posterior Fossa Tumor Bed Boosts Using Proton Pencil Beam Scanning in Fixed-Beam Room
Purpose: A fixed-beam room could be underutilized in a multi-room proton center. We investigated the use of proton pencil beam scanning (PBS) on a fixed-beam as an alternative for posterior fossa tumor bed (PF-TB) boost treatments which were usually treating on a gantry with uniform scanning. Methods: Five patients were treated with craniospinal irradiation (CSI, 23.4 or 36.0 Gy(RBE)) followed by a PF-TB boost to 54 Gy(RBE) with proton beams. Three PF-TB boost plans were generated for each patient: (1) a uniform scanning (US) gantry plan with 4–7 posterior fields shaped with apertures and compensators (2) a PBS plan using bi-lateral and vertex fields with a 3-mm planning organ-at-risk volume (PRV) expansion around the brainstem and (3) PBS fields using same beam arrangement but replacing the PRV with robust optimization considering a 3-mm setup uncertainty. Results: A concave 54-Gy(RBE) isodose line surrounding the brainstem could be achieved using all three techniques. The mean V95% of the PTV was 99.7% (range: 97.6% to 100%) while the V100% of the PTV ranged from 56.3% to 93.1% depending on the involvement of the brainstem with the PTV. The mean doses received by 0.05 cm{sup 3} of the brainstem were effectively identical: 54.0 Gy(RBE), 53.4 Gy(RBE) and 53.3 Gy(RBE) for US, PBS optimized with PRV, and PBS optimized with robustness plans respectively. The cochlea mean dose increased by 23% of the prescribed boost dose in average from the bi-lateral fields used in the PBS plan. Planning time for the PBS plan with PRV was 5–10 times less than the US plan and the robustly optimized PBS plan. Conclusion: We have demonstrated that a fixed-beam with PBS can deliver a dose distribution comparable to a gantry plan using uniform scanning. Planning time can be reduced substantially using a PRV around the brainstem instead of robust optimization.
60 APPLIED LIFE SCIENCES↗
Stochastic robust mathematical programming model for power system optimization
We present a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with different uncertainty sets. In addition, a case study of unit commitment shows the effectiveness of the proposed model and algorithms.
97 MATHEMATICS AND COMPUTING↗
An Ecological Robustness Oriented Optimal Power Flow for Power Systems’ Survivability
Not provided.
Engineering↗
Profile Optimization Method for Robust Airfoil Shape Optimization in Viscous Flow
Simulation results obtained by using FUN2D for robust airfoil shape optimization in transonic viscous flow are included to show the potential of the profile optimization method for generating fairly smooth optimal airfoils with no off-design performance degradation.
Li, Wu↗
Robust Airfoil Optimization in High Resolution Design Space
The robust airfoil shape optimization is a direct method for drag reduction over a given range of operating conditions and has three advantages: (1) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (2) it uses a large number of B-spline control points as design variables yet the resulting airfoil shape is fairly smooth, and (3) it allows the user to make a trade-off between the level of optimization and the amount of computing time consumed. The robust optimization method is demonstrated by solving a lift-constrained drag minimization problem for a two-dimensional airfoil in viscous flow with a large number of geometric design variables. Our experience with robust optimization indicates that our strategy produces reasonable airfoil shapes that are similar to the original airfoils, but these new shapes provide drag reduction over the specified range of Mach numbers. We have tested this strategy on a number of advanced airfoil models produced by knowledgeable aerodynamic design team members and found that our strategy produces airfoils better or equal to any designs produced by traditional design methods.
Li, Wu↗
Optimal and robust control of transition
Optimal and robust control theories are used to determine feedback control rules that effectively stabilize a linearly unstable flow in a plane channel. Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control. Control algorithms are considered that depend both on full flowfield information and on estimates of that flowfield based on wall skin-friction measurements only. The development of these control algorithms accounts for modeling errors and measurement noise in a rigorous fashion; these disturbances are considered in both a structured (Gaussian) and unstructured ('worst case') sense. The performance of these algorithms is analyzed in terms of the eigenmodes of the resulting controlled systems, and the sensitivity of individual eigenmodes to both control and observation is quantified.
Bewley, T. R.↗
Robust Operation of Soft Open Points in Active Distribution Networks with High Penetration of Photovoltaic Integration
Distributed generators (DGs) including photovoltaic panels (PVs) have been integrated dramatically in active distribution networks (ADNs). Due to the strong volatility and uncertainty, the high penetration of PV generation immensely exacerbates the conditions of voltage violation in ADNs. However, the emerging flexible interconnection technology based on soft open points (SOPs) provides increased controllability and flexibility to the system operation. For fully exploiting the regulation ability of SOPs to address the problems caused by PV, this paper proposes a robust optimization method to achieve the robust optimal operation of SOPs in ADNs. A two-stage adjustable robust optimization model is built to tackle the uncertainties of PV outputs, in which robust operation strategies of SOPs are generated to eliminate the voltage violations and reduce the power losses of ADNs. A column-and-constraint generation (C&CG) algorithm is developed to solve the proposed robust optimization model, which are formulated as second-order cone program (SOCP) to facilitate the accuracy and computation efficiency. Here, case studies on the modified IEEE 33-node system and comparisons with the deterministic optimization approach are conducted to verify the effectiveness and robustness of the proposed method.
14 SOLAR ENERGY↗
Robust Trajectory Optimization Techniques Using a Sweeping Gradient Method and Linear Covariance Analysis
We present robust trajectory optimization techniques using a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov). SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve robust optimal trajectory design problems. We describe the individual methods and some details on how they can be combined. Then we apply the combined techniques to a variety of orbital trajectory design problems to demonstrate its use, including minimum fuel transfer and mid-course correction burn scheduling.
Benjamin W L Margolis↗
Robust Trajectory Optimization for NRHO Rendezvous Using SPICE Kernel Relative Motion
In this paper, robust optimization is performed on trajectory correction maneuvers during the lunar lander return phase of an Artemis mission, treating the trajectory from one hour after low lunar orbit departure to arrival in the vicinity of the lunar Gateway as a relative motion problem. To enable rapid stochastic optimization techniques requiring many candidate trajectories, SPICE kernel relative motion as implemented by the Quadratic Interpolated State Transition (QIST) system is used as the underlying dynamics propagation. The optimization is performed with a genetic optimizer using linear covariance (LinCov) software in a simplified operational context, taking into account the availability of navigation sensors with varying measurement models, ranges, and accuracies. No numerical integration is used, since the relative motion around Gateway is fully characterized with the a priori computation of the QIST coefficients. Maneuver placements are computed to optimize the minimum 3σ delta-v of the trajectory, the position dispersion at a target point, and a convex combination of these two metrics. An order of magnitude runtime improvement is provided over legacy methods with less than 10% error introduced. All QIST results are shown to be in-family with legacy methods. The tradespace for optimal delta-v design is found to range from 77.0 to 93.9 m/s, while the range of optimal dispersion is between 1.4 and 11.7 km.
Relative Motion↗
Robust Design Optimization via Failure Domain Bounding
This paper extends and applies the strategies recently developed by the authors for handling constraints under uncertainty to robust design optimization. For the scope of this paper, robust optimization is a methodology aimed at problems for which some parameters are uncertain and are only known to belong to some uncertainty set. This set can be described by either a deterministic or a probabilistic model. In the methodology developed herein, optimization-based strategies are used to bound the constraint violation region using hyper-spheres and hyper-rectangles. By comparing the resulting bounding sets with any given uncertainty model, it can be determined whether the constraints are satisfied for all members of the uncertainty model (i.e., constraints are feasible) or not (i.e., constraints are infeasible). If constraints are infeasible and a probabilistic uncertainty model is available, upper bounds to the probability of constraint violation can be efficiently calculated. The tools developed enable approximating not only the set of designs that make the constraints feasible but also, when required, the set of designs for which the probability of constraint violation is below a prescribed admissible value. When constraint feasibility is possible, several design criteria can be used to shape the uncertainty model of performance metrics of interest. Worst-case, least-second-moment, and reliability-based design criteria are considered herein. Since the problem formulation is generic and the tools derived only require standard optimization algorithms for their implementation, these strategies are easily applicable to a broad range of engineering problems.
Crespo, Luis G.↗
Angles-Only Robust Trajectory Optimization for NRHO Rendezvous
This study demonstrates a robust trajectory optimization approach for rendezvous and proximity operations with angles-only navigation measurements. Often, sensors that directly measure relative range and velocity require communication or coordination between the chaser and target vehicle and can have limiting pointing accuracy, mass, or power requirements compared to angle measurement sensors. Thus, the capability to perform a rendezvous with only angle measurements can be advantageous for vehicle design and to improve robustness to failures. However, the well studied limitation of angles-only navigation in measuring range results in large uncertainties in the navigation system that must be reduced with chaser vehicle thrust maneuvers to induce observability in range for the navigation filter. This analysis presents a trajectory optimization problem for a lunar ascent rendezvous during a crewed lunar mission in a Near-Rectilinear Halo Orbit (NRHO) that is limited to only angle measurements. The objective of this study is to show that an angles-only rendezvous is feasible in an NRHO and to present the sensitivity to an assortment of constraints generated from a systematic optimization process using linear covariance analysis and particle swarm optimization. Linearized NRHO dynamics and linearized relative targeting are applied to use linear covariance analysis to determine the expected delta-v and trajectory dispersions due to initial state uncertainty, sensor errors, maneuver execution errors, and unmodeled dynamics. The delta-v and trajectory dispersions are passed into a particle swarm optimization algorithm to find the optimized maneuver profile that minimizes fuel use while satisfying constraints such as free drift and underburn to 3-sigma certainty. The trajectory constraints including time available, desired final uncertainty, and initial uncertainty are varied to ascertain sensitivity and desirable engineering trades.
Linear Covariance Analysis↗
Robust Trajectory Optimization and GN&C Performance Analysis for NRHO Rendezvous
This paper evaluates several candidate Near-Rectilinear Halo Orbits (NRHO) rendezvous trajectory designs using linear covariance (LinCov) analysis and determines the optimal locations for NRHO rendezvous translational maneuver locations. The performance of several candidate relative trajectory designs are determined as a function of relative navigation accuracy (angles only), inertial optical navigation (OpNav), range observability maneuvers, maneuver execution errors, relative maneuver targeting, and environment uncertainties. Further, the optimal locations of rendezvous maneuvers are determined for each of the candidate reference trajectories. The long-term goal of this research is to utilize LinCov and a genetic optimization algorithm (GA) to determine a complete end-to-end optimal NRHO trajectory design that is robust to navigation errors, maneuver execution errors, and environment uncertainties. This paper represents a first step toward this goal. Three candidate rendezvous trajectories with varying numbers of range-observability maneuvers are evaluated for their robustness to uncertainties, errors, and total trajectory correction delta-v performance. Some key elements of this analysis include relative navigation performance in an NRHO, relative trajectory dispersion performance, and total 3-sigma delta-v performance. This development provides the foundation to then determine an optimal and robust end-to-end NRHO rendezvous trajectory, including the determination of the optimal locations of range observability maneuvers, if needed.
Linear Covariance Analysis↗
An efficient and robust grid optimization algorithm
The development of an efficient and robust grid optimization is presented. This algorithm is developed by combining the best characteristics of algebraic, elliptic, and hyperbolic grid generation techniques. This development is based on the following observations and evaluations: (1) algebraic systems are fast and economical; (2) precise spacing control is always achieved; (3) grid generation by elliptic systems is always smooth; and (4) the hyperbolic system preserves the orthogonality at the solid boundary and the point distribution in the field. Computational examples representing practical internal flow configurations are presented to demonstrate the algorithm.
Soni, Bharat K.↗