Problems of controllability, observability, and stabilizability of dynamic systems
Solving problems of controllability, observability, and motion stability of dynamic control systems pertaining to theory of optimal processes
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Solving problems of controllability, observability, and motion stability of dynamic control systems pertaining to theory of optimal processes
There are considerable ongoing research and testing campaigns to qualify new fuel designs such as metallic fuels for advanced reactor designs and the Accident Tolerant Fuel (ATF) campaign for light water reactors (LWR). The typical research and development lifecycle needed to qualify a nuclear fuel design, under ideal conditions, can take up to 20-25 years which limits the ability for new fuels to make fast deployments into commercial, test, and research reactors. While there are several efforts to accelerate nuclear fuel qualification through advanced modeling coupled with state-of-the-art experiments, there is not yet a framework to methodically quantify and rank distortions occurring in experimental test specimens needed to validate nuclear fuel performance codes. This study uses the Dynamical System Scaling (DSS) methodology to quantify transient scaling distortions that occur over experiment and simulated transients. DSS analysis metrics provide a researcher with several tools and information embedded within test data to identify dominant phenomena, associated timescales, and quantify a transient?s overall dynamic distortion. This is demonstrated with separate analyses of the SETH-C and CHF-SERTTA thermal-hydraulic experiments in the TREAT facility at Idaho National Laboratory. The outcome of this work is a scaling and data analysis approach to account for the influence a scaled fuel test specimen?s geometric and temporal distortions have on its ability to be representative of the full-scale design.
NASA's WIND mission has been operating in a large amplitude Lissajous orbit in the vicinity of the interior libration point of the Sun-Earth/Moon system since 2004. Regular stationkeeping maneuvers are required to maintain the orbit due to the instability around the collinear libration points. Historically these stationkeeping maneuvers have been performed by applying an incremental change in velocity, or (delta)v along the spacecraft-Sun vector as projected into the ecliptic plane. Previous studies have shown that the magnitude of libration point stationkeeping maneuvers can be minimized by applying the (delta)v in the direction of the local stable manifold found using dynamical systems theory. This paper presents the analysis of this new maneuver strategy which shows that the magnitude of stationkeeping maneuvers can be decreased by 5 to 25 percent, depending on the location in the orbit where the maneuver is performed. The implementation of the optimized maneuver method into operations is discussed and results are presented for the first two optimized stationkeeping maneuvers executed by WIND.
Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, {PIML} models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, {PIML} models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of {PIML} is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in {PIML} for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of {PIML} models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.
Optimal deterministic inputs derived for estimating dynamic control system parameters from white observation noise
Generalized matrix inverses application to estimation of state vector in dynamic control system, determining covariance matrix of estimator
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A unique attribute of the nuclear industry is the extent by which designers, developers, operators, and regulators pay attention to demonstrating the safety case. The safety case for nuclear systems is a written, traceable expression of safety, demonstrating the system’s protective measures against uncontrolled radiological releases. The nuclear installation resiliency or safety takes overriding priority over function and performance. The preparation of the safety case heavily relies on extensive experimental campaigns that challenge the target design under a spectrum of postulated accident scenarios. For safety reasons, these experiments are typically conducted in sub-scale test apparatuses intended to reproduce the postulated accident scenarios and event sequences realistically but subject to proven similarity criteria, often referred to as scaling analyses. Since the dawn of the nuclear industry, significant resources have been committed to the construction and operation of such test facilities and a massive amount of data has been generated. Such test data have been and are still used to validate the fundamental assumptions of nuclear power plant phenomena. As we move into the digital world, capturing this multi-decades worth of information in a transparent, easily accessible, and usable manner for the public and industry stakeholders is of paramount importance. Over the last few years FPoliSolutions has been actively developing an enterprise digital data ontology platform (FPoliDON) intended to do just that. The concept was introduced in a paper at the previous NURETH edition and has been significantly enhanced since. With the vision of helping designers use the data to assess their safety case evaluation models, the platform was designed not only to ontologically organize the experimental data, but also to guide the user in the complex analytics associated with the interpretation and use of such test results. A new feature which has been recently added is the ability for the user to access a library of sophisticated mathematical procedures for performing scaling analyses. For this purpose, the Dynamical System Scaling (DSS) procedure invented by Dr. Jose’ Reyes was formulated as one of the services in the digital platform. These methods have been demonstrated to provide an excelled mathematical apparatus to identify similarity criteria or quantify distortions between measured data and the target prototypical conditions. Moreover, DSS can provide a level of synthesis across SETs and IETs which has the promise to yield efficiency in the evaluation code assessment activities. This is often a daunting and expensive task to set up evaluation models that support the safety case of current and future nuclear power plants.
The integration of new energy technologies into electric power systems requires methods which recognize the full range of dynamic events in both the new generating unit and the power system. Since new energy technologies are initially perceived as small contributors to large systems, little attention is generally paid to system integration, i.e. dynamic events in the power system are ignored. As a result, most new energy sources are only capable of base-load operation, i.e. they have no load following or cycling capability. Wind turbines are no exception. Greater awareness of this implicit (and often unnecessary) limitation is needed. Analysis methods are recommended which include very low penetration (infinite bus) as well as very high penetration (stand-alone) scenarios.
In these 18 years, the research has touched every major dynamical problem in the solar system, including: the effect of chaotic zones on the distribution of asteroids, the delivery of meteorites along chaotic pathways, the chaotic motion of Pluto, the chaotic motion of the outer planets and that of the whole solar system, the delivery of short period comets from the Kuiper belt, the tidal evolution of the Uranian arid Galilean satellites, the chaotic tumbling of Hyperion and other irregular satellites, the large chaotic variations of the obliquity of Mars, the evolution of the Earth-Moon system, and the resonant core- mantle dynamics of Earth and Venus. It has introduced new analytical and numerical tools that are in widespread use. Today, nearly every long-term integration of our solar system, its subsystems, and other solar systems uses algorithms that was invented. This research has all been primarily Supported by this sequence of PGG NASA grants. During this period published major investigations of tidal evolution of the Earth-Moon system and of the passage of the Earth and Venus through non-linear core-mantle resonances were completed. It has published a major innovation in symplectic algorithms: the symplectic corrector. A paper was completed on non-perturbative hydrostatic equilibrium.
Liapunov theory of stochastic stability, discussing use to obtain information about random trajectories
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The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.
The United States urgently needs to tackle the climate crisis while enhancing energy security and resiliency. The complexity of the U.S. energy system, with its interconnected elements, makes predicting future states challenging, especially with the introduction of novel energy systems like wind, solar, clean hydrogen, and advanced nuclear technologies. Modern systems engineering methods and tools can provide deeper insights into these dynamics and future behaviors. This research aims to develop a comprehensive model that captures the main elements and behaviors of new energy technologies within the existing energy system. We hypothesized that the market uptake of novel energy systems is influenced by multiple diverse factors, such as technological learning, availability of resources, and economic incentives; examined the history of electricity generation using land-based wind technologies; and developed a system dynamics model to investigate the relationships between capacity growth and influencing factors, both internal and external. The developed model yielded outcomes that confirmed the hypothesized dynamics of wind energy system diffusion through a quantitative comparison of installed capacity and highlighted the significant influence of resource availability, federal incentives (production tax credits), and technological learning on capacity growth and cost reduction. This research aims to support informed decision-making for investments in novel energy systems and aid in developing effective policies for technology deployment.
A rational criterion for structural dynamic analysis-test correlation has been established by using a matrix perturbation technique. This criterion can be used for the verification of an analytical model by the test results. Also, the same technique can be applied to update the analytical results by using the test results without repeating the entire analytical procedure. A sample problem has been used to demonstrate this technique. Very satisfactory results are obtained with only the first-order perturbation solution included for transient loading. For periodic loading, higher-order perturbation solutions are needed to achieve the same accuracy.
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing much accuracy, which results in a considerably more speed-up than the spatial reduction only. Recently, a novel space–time reduced order model for dynamical problems has been developed [17], where the space–time reduced order model shows an order of a hundred speed-up with a relative error of 10 –4 for small academic problems. However, in order for the method to be applicable to a large-scale problem, an efficient space–time reduced basis construction algorithm needs to be developed. Here we present the incremental space–time reduced basis construction algorithm. The incremental algorithm is fully parallel and scalable. Additionally, the block structure in the space–time reduced basis is exploited, which enables the avoidance of constructing the reduced space–time basis. These novel techniques are applied to a large-scale particle transport simulation with million and billion degrees of freedom. The numerical example shows that the algorithm is scalable and practical. Also, it achieves a tremendous speed-up, maintaining a good accuracy. Finally, error bounds for space-only and space–time reduced order models are derived.
Absolute stability of dynamic control systems with single nonlinear element function of two feedback state variables, giving sufficient conditions
Linear Algebra is essential for numerous aerospace problems of interest. Formal reasoning about hybrid systems that contain variables modeled by differential equations rely on concepts from Linear Algebra such as eigenvalues, matrix decompositions, and matrix valued functions. For example, the long-term dynamics of a system of differential equations depend on the stability/instability of its equilibrium points, which often reduces to an eigenvalue problem. This talk will embark on a quest to formalize theorems and results about eigenvalues and eigenvectors using PVS. We shall start our journey with 2 x 2 complex matrices, where we will apply our PVS code to a simple example of a dynamical system. Since it can be difficult or impossible to give simple expressions of eigenvalues for larger matrices (i.e. 5 x 5 or higher), we then move towards specifying the power method for verified computation of eigenvalue approximations in PVS. This effort requires development of multivariate complex arithmetic. At the end of the day, having such additions to the PVS NASA libraries will help move towards the use of formal methods to verify concepts of control theory and system level verification.