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At least 865 records · Page 48

Investigation and appreciation of optimal output feedback. Volume 1: A convergent algorithm for the stochastic infinite-time discrete optimal output feedback problem

The stochastic, infinite time, discrete output feedback problem for time invariant linear systems is examined. Two sets of sufficient conditions for the existence of a stable, globally optimal solution are presented. An expression for the total change in the cost function due to a change in the feedback gain is obtained. This expression is used to show that a sequence of gains can be obtained by an algorithm, so that the corresponding cost sequence is monotonically decreasing and the corresponding sequence of the cost gradient converges to zero. The algorithm is guaranteed to obtain a critical point of the cost function. The computational steps necessary to implement the algorithm on a computer are presented. The results are applied to a digital outer loop flight control problem. The numerical results for this 13th order problem indicate a rate of convergence considerably faster than two other algorithms used for comparison.

Halyo, N.↗

Application of the Maximum Entropy/optimal Projection Control Design Approach for Large Space Structures

The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modelling and reduced order control design method for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed and the application of the methodology to several large space structure (LSS) problems of representative complexity is illustrated.

Hyland, D. C.↗

Tradeoff methods in multiobjective insensitive design of airplane control systems

The latest results of an ongoing study of computer-aided design of airplane control systems are given. Constrained minimization algorithms are used, with the design objectives in the constraint vector. The concept of Pareto optimiality is briefly reviewed. It is shown how an experienced designer can use it to find designs which are well-balanced in all objectives. Then the problem of finding designs which are insensitive to uncertainty in system parameters are discussed, introducing a probabilistic vector definition of sensitivity which is consistent with the deterministic Pareto optimal problem. Insensitivity is important in any practical design, but it is particularly important in the design of feedback control systems, since it is considered to be the most important distinctive property of feedback control. Methods of tradeoff between deterministic and stochastic-insensitive (SI) design are described, and tradeoff design results are presented for the example of the a Shuttle lateral stability augmentation system. This example is used because careful studies have been made of the uncertainty in Shuttle aerodynamics. Finally, since accurate statistics of uncertain parameters are usually not available, the effects of crude statistical models on SI designs are examined.

Schy, A. A.↗

Health Monitoring for Airframe Structural Characterization

This study established requirements for structural health monitoring systems, identified and characterized a prototype structural sensor system, developed sensor interpretation algorithms, and demonstrated the sensor systems on operationally realistic test articles. Fiber-optic corrosion sensors (i.e., moisture and metal ion sensors) and low-cycle fatigue sensors (i.e., strain and acoustic emission sensors) were evaluated to validate their suitability for monitoring aging degradation; characterize the sensor performance in aircraft environments; and demonstrate placement processes and multiplexing schemes. In addition, a unique micromachined multimeasure and sensor concept was developed and demonstrated. The results show that structural degradation of aircraft materials could be effectively detected and characterized using available and emerging sensors. A key component of the structural health monitoring capability is the ability to interpret the information provided by sensor system in order to characterize the structural condition. Novel deterministic and stochastic fatigue damage development and growth models were developed for this program. These models enable real time characterization and assessment of structural fatigue damage.

Munns, Thomas E.↗

Robust Design Under Uncertainty of Hypersonic Inlets

The objective of this work is to optimize scramjet inlet designs under uncertainty at multiple fidelity levels. Optimizations are performed for both deterministic and stochastic conditions. For stochastic conditions, robust design is used to minimize the variance in system performance in addition to optimizing mean system performance. Uncertainty quantification is performed using non-intrusive polynomial chaos. Comparisons are made between low-fidelity analysis and high-fidelity analysis, as well as deterministic optimization and robust optimization. Results indicate that the general design trend of previous inlet optimization techniques is recovered for the external compression portion of an inlet. For the internal compression portion of an inlet, when viscous effects become more significant and boundary layer separation becomes more likely, the optimal trend departs from previous results. Multifidelity uncertainty quantification methods are found to substantially reduce the computation time of robust design while obtaining results that nearly match those of high-fidelity analysis. Robust optimization is found to decrease the standard deviation of throat Mach number by up to 40% compared to deterministic optimization. Changes in the design variables and total turning that lead to robust scramjet inlets are identified and linked back to fundamental physical principles through the theta-beta-Mach function.

Hypersonic↗

Global stochastic optimization of stellarator coil configurations

In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case of the National Compact Stellarator Experiment (NCSX) project. Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the sample average approximation; and Adam, equipped with a control variate for variance reduction. Numerical simulations performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than 0.1% of the cost of previous work, which considered solely local stochastic optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Stochastic Vector Techniques in Ground-State Electronic Structure

Herein we review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order many-body perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss effective techniques to reduce statistical errors. Finally, we review the use of stochastic vectors for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Does nucleation theory apply to the formation of refractory circumstellar grains?

It is pointed out that kinetic factors inherent in cosmic systems will prevent the attainment of an approximate equilibrium precondensation cluster distribution, and that therefore such systems will violate one of the most fundamental assumptions of nucleation theory. More importantly, it is shown that of the 11 refractory metal/metal oxide systems which have been studied experimentally none are consistent with the predictions of either classical nucleation theory or the Lothe-Pound modification. Since no valid method is known by which these deficiencies can be circumvented, it is concluded that nucleation theory cannot be made to work in expanding circumstellar shells. However, a stochastic, kinetic treatment which makes use of experimental and theoretical data for specific refractory systems does appear to be feasible.

Donn, B.↗

A Methodology to Evaluate the Grid Reliability Impact of Oscillations Induced by Large Loads

The rapid growth of hyperscale AI data centers is bringing renewed attention to the reliability risk that sustained forced oscillations pose to bulk power systems, with cyclic computational workloads emerging as a new forcing source. Unlike the broadband, stochastic disturbances from traditional industrial loads such as arc furnaces, AI training and inference facilities can inject large active power swings concentrated at specific frequencies over extended durations - characteristics that existing grid planning practices do not account for. While the North American Electric Reliability Corporation (NERC) has recognized this gap and called for system-level studies of large load interconnections, no standardized methodology exists to screen, simulate, and quantify these risks at the planning stage. This report presents the Risk Assessment Tool for Large Load-induced Events (RATLLE), a Python-based, publicly available script suite developed at the Pacific Northwest National Laboratory to evaluate bulk power system reliability risks from data center-induced oscillations. RATLLE implements a three-module workflow: a screening module that identifies vulnerable interconnection locations and excitable system modes; a simulation module that models cyclic data center load behavior using a commercial positive sequence simulation platform; and an analysis module that computes risk metrics and generates interactive visualization dashboards. The risk metrics, formulated around simulation observables, map oscillation impacts to a three-stage severity scale spanning latent equipment fatigue through imminent cascading failure. The methodology is demonstrated on two Western Electricity Coordinating Council (WECC) system models: a publicly available 240-bus reduced representation and a detailed 2031 Heavy Winter planning case. Case studies illustrate that even modest 50 MW forced oscillations at resonant frequencies can produce wide-area power swings, N-1 security constraint violations, and cascading generator trips through protection actions - outcomes that would not occur under normal operating conditions without oscillations present. The results underscore the need for standardized oscillation impact assessment in large load interconnection studies and provide a reproducible, extensible framework for utilities to adopt or customize within their existing planning workflows.

Biswas, Shuchismita↗

Stochastic parametric skeletal dosimetry model for humans: Anatomical-morphological basis and parameter evaluation

Radiation exposure of the hematopoietic system that results in a radiation dose to bone marrow of more than 100 mGy leads to an increase in the risk of leukemia in humans. Excess relative risk of leukemia was observed in cohorts whose members lived in the territories of the Southern Urals that were radioactively contaminated in the 1950s. As part of the dosimetric support of epidemiological studies of these cohorts, an original methodology for stochastic bone dosimetric modeling was developed, termed the Stochastic Parametric Skeletal Dosimetry (SPSD) model. The purpose of this work was to present the anatomical and morphological bases of the SPSD model, which includes an assessment of the parameters of the microstructure of the trabecular bone in the hematopoietic areas of the human skeleton, as well as a description of the macrostructural division (segmentation) of hematopoietic areas into simple bone segments. As a result, an anatomical-morphological basis of the SPSD model was created based on published data. Data collection work included the analysis of original articles, atlases, manuals, monographs and the formation of primary data files. Data on the duration of hematopoiesis in various parts of the skeleton; and data on age-related changes in the microstructure and linear dimensions of human bones and their segments were analyzed. The paper describes the full set of parameters to be used for the dosimetric model for newborns, children aged 1, 5 and 10 years, as well as for adolescents aged 15 years and adults; for the latter, sex differences in bone size were considered. In total, the SPSD model includes 289 unique basic (bone) phantom segments, each of which is described by 7 or more parameters describing the microstructure, thickness of the cortical layer and linear dimensions. Population variability was estimated for each parameter. The approach to SPSD modeling, i.e., the use of simple geometric shapes, was successfully verified using independent datasets on bone masses and volumes.

Science & Technology - Other Topics↗

Linear stochastic optimal control and estimation problem

Problem involves design of controls for linear time-invariant system disturbed by white noise. Solution is Kalman filter coupled through set of optimal regulator gains to produce desired control signal. Key to solution is solving matrix Riccati differential equation. LSOCE effectively solves problem for wide range of practical applications. Program is written in FORTRAN IV for batch execution and has been implemented on IBM 360.

Geyser, L. C.↗

A data based random number generator for a multivariate distribution (using stochastic interpolation)

Let X be a K-dimensional random variable serving as input for a system with output Y (not necessarily of dimension k). given X, an outcome Y or a distribution of outcomes G(Y/X) may be obtained either explicitly or implicity. The situation is considered in which there is a real world data set X sub j sub = 1 (n) and a means of simulating an outcome Y. A method for empirical random number generation based on the sample of observations of the random variable X without estimating the underlying density is discussed.

Thompson, J. R.↗

Stochastic histories of dust grains in the interstellar medium

The purpose is to study an evolving system of refractory dust grains within the Interstellar Medium (ISM). This is done via a combination of Monte Carlo processes and a system of partial differential equations, where refractory dust grains formed within supernova remnants and ejecta from high mass loss stars are subjected to the processes of sputtering and collisional fragmentation in the diffuse media and accretion within the cold molecular clouds. In order to record chemical detail, the authors take each new particle to consist of a superrefractory core plus a more massive refractory mantle. The particles are allowed to transfer to and fro between the different phases of the interstellar medium (ISM) - on a time scale of 10(exp 8) years - until either the particles are destroyed or the program finishes at a Galaxy time of 6x10(exp 9) years. The resulting chemical and size spectrum(s) are then applied to various astrophysical problems with the following results. For an ISM which has no collisional fragmentation of the dust grains, roughly 10 percent by mass of the most refractory material survives the rigors of the ISM intact, which leaves open the possibility that fossilized isotopically anomalous material may have been present within the primordial solar nebula. Stuctured or layered refractory dust grains within the model cannot explain the observed interstellar depletions of refractory material. Fragmentation due to grain-grain collisions in the diffuse phase plus the accretion of material in the molecular cloud phase can under certain circumstances cause a bimodal distribution in grain size.

Liffman, Kurt↗

Adaptive resource allocation for surrogate modeling of systems comprised of multiple disciplines with varying fidelity

We present an adaptive algorithm for constructing surrogate models for integrated systems composed of a set of coupled components. With this goal we introduce ‘coupling’ variables with a priori unknown distributions that allow approximations of each component to be built independently. Once built, the surrogates of the components are combined and used to predict system-level quantities of interest (QoI) at a fraction of the cost of interrogating the full system model. We use a greedy experimental design procedure, based upon a modification of Multi-Index Stochastic Collocation (MISC), to minimize the error of the combined surrogate. This is achieved by refining each component surrogate in accordance with its relative contribution to error in the approximation of the system-level QoI. Our adaptation of MISC is a multi-fidelity procedure that can leverage ensembles of models of varying cost and accuracy, for one or more components, to produce estimates of system-level QoI. Several numerical examples demonstrate the efficacy of the proposed approach on systems involving feed-forward and feedback coupling. For a fixed computational budget, the proposed algorithm is able to produce approximations that are orders of magnitude more accurate than approximations that treat the integrated system as a black-box.

97 MATHEMATICS AND COMPUTING↗

Coarsening dynamics of Ising-nematic order in a frustrated Heisenberg antiferromagnet

We study the phase ordering dynamics of the classical antiferromagnetic 𝐽 1 −𝐽 2 (nearest-neighbor and next-nearest-neighbor couplings) Heisenberg model on the square lattice in the strong frustration regime (𝐽 2 /𝐽 1 > 1/2). While thermal fluctuations preclude any long-range magnetic order at finite temperatures, the system exhibits a long-range spin-driven nematic phase at low temperatures. The transition into the nematic phase is further shown to belong to the two-dimensional Ising universality class based on the critical exponents near the phase transition. Our large-scale stochastic Landau-Lifshitz-Gilbert simulations find a two-stage phase ordering when the system is quenched from a high-temperature paramagnetic state into the nematic phase. In the early stage, collinear alignments of spins lead to a locally saturated Ising-nematic order. Once domains of well-defined Ising order are developed, the late-stage relaxation is dominated by curvature-driven domain coarsening, as described by the Allen-Cahn equation. The characteristic size of Ising-nematic domains scales as the square root of time, similar to the kinetic Ising model described by the time-dependent Ginzburg-Landau theory. Our results confirm that the late-stage ordering kinetics of the spin-driven nematic, which is a vestigial order of the frustrated Heisenberg model, belongs to the dynamical universality class of a nonconserved Ising order. Interestingly, the system shows no violation of the superuniversality hypothesis under weak bond disorder. The dynamic scaling invariance is preserved in the presence of weak bond disorder. Here, we also discuss possible applications of our results to materials for which vestigial Ising-nematic order is realized.

Antiferromagnets↗

Role of Forcing Uncertainty and Background Model Error Characterization in Snow Data Assimilation

Accurate specification of the model error covariances in data assimilation systems is a challenging issue. Ensemble land data assimilation methods rely on stochastic perturbations of input forcing and model prognostic fields for developing representations of input model error covariances. This article examines the limitations of using a single forcing dataset for specifying forcing uncertainty inputs for assimilating snow depth retrievals. Using an idealized data assimilation experiment, the article demonstrates that the use of hybrid forcing input strategies (either through the use of an ensemble of forcing products or through the added use of the forcing climatology) provide a better characterization of the background model error, which leads to improved data assimilation results, especially during the snow accumulation and melt-time periods. The use of hybrid forcing ensembles is then employed for assimilating snow depth retrievals from the AMSR2 (Advanced Microwave Scanning Radiometer 2) instrument over two domains in the continental USA with different snow evolution characteristics. Over a region near the Great Lakes, where the snow evolution tends to be ephemeral, the use of hybrid forcing ensembles provides significant improvements relative to the use of a single forcing dataset. Over the Colorado headwaters characterized by large snow accumulation, the impact of using the forcing ensemble is less prominent and is largely limited to the snow transition time periods. The results of the article demonstrate that improving the background model error through the use of a forcing ensemble enables the assimilation system to better incorporate the observational information.

assimilation↗

Uncertainty-Informed Operation Coordination in a Water-Energy Nexus

The widespread deployment of smart heterogeneous technologies and the growing complexity in our modern society calls for effective coordination of the interdependent lifeline networks. In particular, operation coordination of electric power and water infrastructures is urgently needed as the water system is one of the most energy-intensive networks, an interruption in which may quickly evolve into a dramatic societal concern. This paper develops a novel analytic for uncertainty-aware day-ahead operation optimization of the interconnected power and water systems (PaWS). Joint probabilistic constraint (JPC) programming is employed to capture the uncertainties in wind resources and water demand forecasts. The proposed integrated stochastic model is presented as a non-linear non-convex optimization problem, where the non-linear hydraulic constraints in the water network are linearized using piece-wise linearization technique, and the non-convexity is efficiently tackled with a solution methodology to convert the proposed model with JPCs to a tractable mixed-integer linear programming (MILP) formulation that can be quickly solved to optimality. Here, the suggested framework is applied to a 15-node commercial-scale water network jointly operated with a power transmission system using a modified IEEE 57-bus test system. The numerical results demonstrate the of the proposed stochastic framework, resulting in cost reduction (13% on average when compared to the traditional setting) and energy saving of the integrated model under different realizations of uncertain renewable energy sources (RESs) and water demand scenarios. Additionally, the scalability of the proposed model is tested on a modified IEEE 118-bus test system connected to five water networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Stochastic Continuous-time Flexibility Scheduling and Pricing in Wholesale Electricity Markets

Large-scale integration of intermittent renewable energy sources (RES) is calling for additional flexibility resources as well as more advanced modeling and optimization techniques to account for the increasing uncertainty and variability in power systems operation. As the RES integration gains momentum, the magnitude and frequency of their variations increase, which may trigger ramping scarcity events in real-time power systems operation. This necessitates revisiting the present definition of power systems flexibility and reserve services to reflect their robustness and adequacy towards sub-interval variations of the load and RES, as well as adjusting the operation models to accommodate the new reserve services. This project took a fundamental approach and aimed at developing continuous-time scheduling and pricing model that accurately models the continuous-time variations of load and RES and efficiently deploys the ramping capability of flexible resources to compensate the sources of variability and uncertainty in the market. In this regard, this project pursued the following goals: Developing stochastic multi-fidelity continuous-time optimization models for scheduling of energy storage (ES) systems and flexible loads in wholesale energy markets; Developing the theory and practices of continuous-time locational marginal pricing for valuating energy storage systems and flexible loads in wholesale energy markets; Developing function space solution approach to convert the proposed stochastic multi-fidelity continuous-time optimization models into tractable mixed-integer linear optimization models; and Defining flexibility reserve as a new type of reserve in markets that would enable ultimate participation of energy storage devices in provision of services to compensate the variability and uncertainty of RES in electricity markets. This project successfully completed all five major tasks defined in the SOPO, and produced 8 high-impact journal papers, 6 conference papers, 3 published U.S. patents, and one web-based software for continuous-time operation optimization of power systems. The application of the proposed flexibility reserve and the stochastic multi-fidelity continuous-time operation scheduling models would modify the forward commitment and schedule of generating units, ES devices and flexible loads, and would line up the resources in such a way that the composition of available resources is better prepared to respond to the sub-hourly variations of the load and renewable resources in real-time operation. Therefore, this project paves the way to sustainable, reliable, and economic integration of renewable energy resources in power system, supporting the progress towards reaching the national targets on energy independence. Even if the proposed models offers a radically different point of view as compared to existing models, it does not alter fundamentally the architecture of power systems operations, nor the complexity of the scheduling problem, so the integration of this project in power systems is extremely practical.

24 POWER TRANSMISSION AND DISTRIBUTION↗