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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Online Output-Based Inertia Estimation of Modern Power Systems

The overall inertia of modern power systems is drastically impacted by the penetration level of converter-based resources (CBRs). The intermittent output of CBRs and their dependence on the weather conditions affirm the need for a realtime inertia estimation approach. This can help the transmission system operators(TSOs) to be continuously aware of the changes in the system inertia and to take suitable control actions. This paper is a step forward to a totally data-driven framework for power system inertia estimation using the available measurements from the phasor measurement units (PMUs). This inertia estimation is done based on the spectral analysis of the so-called Koopman linear operator. Koopman operator considers the relationship between the system's inertia and its dynamical response to slight disturbances in the load. Simulation results show that Koopman operator can approximate the system behavior in a reconstructed linear space hence inertia constant is estimated accurately.

data-driven↗
DOE OSTI2023

Sensor and Actuator Attacks on Hierarchical Control Systems with Domain-Aware Operator Theory

Cyber-Physical Systems (CPSs) provide opportunities for cyber attacks to have physical impacts. Advanced Persistent Threats (APTs) are a subclass of cyber threats that act stealthily to avoid detection and enable long-term attacks. Here, we build on our past work in APT modelling to combine deception-based sensor bias attacks and direct actuator manipulations in attacks against a hierarchical control system. That past work used the Koopman operator to develop a data-driven, domain-aware, optimization-based attacker model. Using an expansion of this model, we compute several different attacks, including multiple simultaneous attacks, against a high-fidelity commercial building emulator and compare the impacts of those attacks to each other. One next step of interest is to construct a defender system, built on the same modelling approach, designed to detect and mitigate such attacks.

koopman operator, Cyber-Physical Security, machine↗
DOE OSTI2022

Nonequilibrium statistical mechanics and optimal prediction of partially-observed complex systems

Abstract Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently outperform physics-based models for systems with few observable degrees of freedom; e.g. hydrological systems. Here, we provide an operator-theoretic explanation for this empirical success. To predict a partially-observed system’s future behavior with physics-based models, the missing degrees of freedom must be explicitly accounted for using data assimilation and model parametrization. Data-driven models, in contrast, employ delay-coordinate embeddings and their evolution under the Koopman operator to implicitly model the effects of the missing degrees of freedom. We describe in detail the statistical physics of partial observations underlying data-driven models using novel maximum entropy and maximum caliber measures. The resulting nonequilibrium Wiener projections applied to the Mori–Zwanzig formalism reveal how data-driven models may converge to the true dynamics of the observable degrees of freedom. Additionally, this framework shows how data-driven models infer the effects of unobserved degrees of freedom implicitly, in much the same way that physics models infer the effects explicitly. This provides a unified implicit-explicit modeling framework for predicting partially-observed systems, with hybrid physics-informed machine learning methods combining both implicit and explicit aspects.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Convex Data-Driven Approach for Nonlinear Control Synthesis

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is built on the density-function-based stability certificate that is the dual to the Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently using the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory can be understood through the lens of Perron–Frobenius and Koopman operators. This allows us to use data-driven methods to approximate these operators and combine them with the SOS techniques to establish a convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Predicting Critical Transitions in Multiscale Data

Predicting the dynamics of complex nonlinear systems remains a challenging problem both in dynamical systems theory as well as real world science and engineering applications. Data-driven methods utilizing the latest advances in machine learning (ML) provide a promising new paradigm for this task. Our work centered on Reservoir Computing (RC), which has shown itself to be capable of skillfully predicting chaotic dynamics in multiscale systems. In the first part of the work, the focus is on how to improve predictions of critical transitions in a class of slow-fast metastable systems in which the equations are known. An additional goal was to determine whether a relationship exists between RC and Koopman operator theory, to improve the efficiency and broaden the applicability of the approach. In the second part of this work, a variation on the RC model known as Reconstructive Reservoir Computing (RRC) is applied to real-world data to identify anomalies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Deception-Based Cyber Attacks on Hierarchical Control Systems using Domain-Aware Koopman Learning

Industrial control systems are subject to cyber attacks that produce physical consequences. These attacks can be both hard to detect and protracted. Here, we focus on deception-based sensor bias attacks made against a hierarchical control system where the attacker attempts to be stealthy. We develop a a data-driven, optimization-based attacker model and use the Koopman operator to represent the system dynamics in a domain-aware and computationally efficient manner. Using this model, we compute several different attacks against a high-fidelity commercial building emulator and compare the impacts of those attacks to each other. Finally, we discuss some computational considerations and identify avenues for future research.

koopman operator, Cyber-Physical Security, machine↗
DOE OSTI2023

Deep Koopman learning of nonlinear time-varying systems

Here this paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which results from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Data-driven Resilience Characterization of Control Dynamical Systems

In this paper, we define and quantify resiliency of a power network and propose data-driven algorithms for computing the same for the power grid. To do this, we use the Koopman operator framework to lift the controlled dynamical system to an abstract (possibly higher) dimensional space, where the evolution is linear. The linear system representation allows us to relate small time local controllability and observability of a general nonlinear control system to the controllability and observability of the lifted linear system. Finally, we define the resiliency of the underlying power grid in terms of the controllability and observability gramians of the lifted linear system. We illustrate the proposed approach to compute the resiliency metrics on time-series data obtained from a microgrid.

koopman operator, resilience, control↗
DOE OSTI2025

Multi-scale, Multi-disciplinary, and Multi-agent Explainable AI with Koopman-Undergirded Learning, Prediction, and Analysis (M3EA KULPA) (Project Closeout Report)

The goal of this project was to develop and use domain-aware machine learning formulations, based on the Koopman Operator (KO), for modelling multi-scale, multi-disciplinary (e.g., multi-physics), and/or multi-agent systems. The project developed these formulations for the following cases: • Systems with dynamics at two separate time scales, • Systems with a bi-level hierarchical control structure, • Systems with bi-level hierarchical control and dynamics at two separate time scales (the lower level controls operating at the faster time scale), and • Systems with n separate but interacting agents/disciplines (with/without control, respectively); the controls for each agent could include bi-level hierarchical control and dynamics at two separate time scales as described above. The project then defined a set of dynamical systems consisting of different nonlinear oscillators that could be used to test these different formulations and then subsequently learned the KO models for those systems. With the KO models, we were able to do the following: • Quantify system stability, including both long-term and transient behavior, • Quantify the effects of feedbacks between the different time scales and agents/disciplines in terms of those feedbacks’ effects on system stability, • Replace a standard Proportional-Integral (PI) control in the hierarchical control structure with a KO-based Linear-Quadratic Regular (LQR), a form of optimal control, • Calculate optimal supervisory control policies a) with and without time scale separated dynamics at the lower level control levels and b) with both PI and KO-based LQR lower level control policies, and • Calculate dynamic Nash equilibria for multi-agent systems where each agent makes its own control decisions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Data-Centric Approach to Capture Non-Polynomial Nonlinear Dynamics

We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating the spectral properties of the Koopman operator. The choice of observable functions is fundamental for applying EDMD to nonlinear problems arising in systems and control. Existing methods either start from a set of dictionary functions and look for the subset that best fits the underlying nonlinear dynamics or rely on machine learning algorithms to “learn” observable functions. Conversely, in this paper, we start from the dynamical system model and lift it through the Lie derivatives, rendering it into a polynomial form. This proposed transformation into a polynomial form is exact and provides an adequate set of observable functions. The strength of the proposed approach is its applicability to a broader class of nonlinear dynamical systems, particularly those with nonpolynomial functions and compositions thereof. Moreover, it retains the physical interpretability of the underlying dynamical system and can be readily integrated into existing numerical libraries. We demonstrate the proposed approach with an application to electric power systems. The modeled system consists of a single generator connected to an infinite bus, where nonlinear terms include sine and cosine functions. The results demonstrate the effectiveness of the proposed procedure in off-attractor nonlinear dynamics for estimation and prediction; the observable functions obtained from the proposed construction outperform methods that use dictionary functions comprising monomials or radial basis functions.

extended dynamic mode decomposition↗
DOE OSTI2025

Temporally-consistent koopman autoencoders for forecasting dynamical systems

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the Temporally-Consistent Koopman Autoencoder (tcKAE), designed to generate accurate long-term predictions even with limited and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE’s superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasma, and fluid flow data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2024

A Koopman-based residual modeling approach for the control of a soft robot arm

Soft robots are challenging to model and control due to their poorly defined kinematics and nonlinear dynamics. Recently, Koopman operator theory has been shown capable of constructing control-oriented soft robot models from data. However, building these models requires extensive data collection and they do not necessarily generalize well outside of the training observations. This paper presents a more data-efficient and generalizable approach to soft robot modeling that first identifies a physics-based Koopman model then supplements it with a data-driven residual Koopman model. The resulting combined model is linear and thus compatible with real-time model-based control techniques such as Model Predictive Control (MPC). The efficacy of the approach is demonstrated on several simulated systems and on a real soft robot arm, where it is shown to generate models that are more accurate than purely physics-based models and require less data to construct than purely data-driven models. Using a model-based controller, the soft arm is able to successfully track end effector trajectories, perform a pick-and-place task, and write on a dry-erase board, showcasing the applicability of this framework to increase the capabilities of soft robotic systems.

Daniel Bruder↗
DOE OSTI2022

Parametric dynamic mode decomposition for reduced order modeling

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiple parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. Here in this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigen-pair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Enabling in-time Prognostics with Surrogate Modeling through Physics-enhanced Dynamic Mode Decomposition Method

Computational models provide essential quantitative tools for assessing and predicting the health and performance of physical systems. However, high-fidelity models are rarely used in real-time operations or large optimization loops, due to their time-intensive nature. A common approach to improving computational efficiency of prognosis is to employ surrogate models. Such models can significantly decrease computation time for some accuracy loss. In this context, use of Dynamic Mode Decomposition (DMD) is proposed to generate surrogate models for lithium-ion (Li-ion) battery discharge. DMD has been suggested and used successfully in the area of fluid dynamics for over a decade, but it has not been applied to the PHM domain, where far-ahead prediction of nonlinear behavior is crucial to propagate faults or predict Remaining Useful Life (RUL). For Li-ion battery health management, the standard application of DMD using only the observable quantities of interest was unable to capture the nonlinear discharge of batteries exhibited in lab testing. The Koopman theory, however, provides a mechanism to tradeoff low dimensional nonlinear models with high-dimensional linear ones in a DMD framework, by augmenting nonlinear state variables into the system representation. In this way, DMD allows for configurable simulation accuracy dependent on the dimensionality of the Koopman operator. For battery health management, we augmented the observable variables with the hidden states of a higher-fidelity physics model to build the DMD surrogate. In comparison to a high-fidelity model, the surrogate improved computational efficiency with only a minimal loss of accuracy, and enabled long-term prognostics horizons. A generalized method for this was implemented in the prog models python package.

prognostics and health management↗
DOE OSTI2024

Data-driven models of nonautonomous systems

Nonautonomous dynamical systems are characterized by time-dependent inputs, which complicates the discovery of predictive models describing the spatiotemporal evolution of the state variables of quantities of interest from their temporal snapshots. When dynamic mode decomposition (DMD) is used to infer a linear model, this difficulty manifests itself in the need to approximate the time-dependent Koopman operators. Our approach is to approximate the original nonautonomous system with a modified system derived via a local parameterization of the time-dependent inputs. The modified system comprises a sequence of local parametric systems, which are subsequently approximated by a parametric surrogate model using the DRIPS (dimension reduction and interpolation in parameter space) framework. The offline step of DRIPS relies on DMD to build a linear surrogate model, endowed with reduced-order bases for the observables mapped from training data. The online step interpolates on suitable manifolds to construct a sequence of iterative parametric surrogate models; the target/test parameter points on these manifolds are specified by a local parameterization of the test time-dependent inputs. Here, we use numerical experimentation to demonstrate the robustness of our method and compare its performance with that of deep neural networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Online real-time learning of dynamical systems from noisy streaming data

Abstract Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by physical sensors, it is natural that the obtained data is corrupted by measurement noise. In this paper, we present a novel algorithm for online real-time learning of dynamical systems from noisy time-series data, which employs the Robust Koopman operator framework to mitigate the effect of measurement noise. The proposed algorithm has three main advantages: (a) it allows for online real-time monitoring of a dynamical system; (b) it obtains a linear representation of the underlying dynamical system, thus enabling the user to use linear systems theory for analysis and control of the system; (c) it is computationally fast and less intensive than the popular extended dynamic mode decomposition (EDMD) algorithm. We illustrate the efficiency of the proposed algorithm by applying it to identify the Van der Pol oscillator, the chaotic attractor of the Henon map, the IEEE 68 bus system, and a ring network of Van der Pol oscillators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Application of advanced causal analyses to identify processes governing secondary organic aerosols

Abstract Understanding how different physical and chemical atmospheric processes affect the formation of fine particles has been a persistent challenge. Inferring causal relations between the various measured features affecting the formation of secondary organic aerosol (SOA) particles is complicated since correlations between variables do not necessarily imply causality. Here, we apply a state-of-the-art information transfer measure coupled with the Koopman operator framework to infer causal relations between isoprene epoxydiol SOA (IEPOX-SOA) and different chemistry and meteorological variables derived from detailed regional model predictions over the Amazon rainforest. IEPOX-SOA represents one of the most complex SOA formation pathways and is formed by the interactions between natural biogenic isoprene emissions and anthropogenic emissions affecting sulfate, acidity and particle water. Since the regional model captures the known relations of IEPOX-SOA with different chemistry and meteorological features, their simulated time series implicitly include their causal relations. We show that our causal model successfully infers the known major causal relations between total particle phase 2-methyl tetrols (the dominant component of IEPOX-SOA over the Amazon) and input features. We provide the first proof of concept that the application of our causal model better identifies causal relations compared to correlation and random forest analyses performed over the same dataset. Our work has tremendous implications, as our methodology of causal discovery could be used to identify unknown processes and features affecting fine particles and atmospheric chemistry in the Earth’s atmosphere.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗