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DOE OSTI2021

Constrained Block Nonlinear Neural Dynamical Models

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear dynamical models by embedding local model structure and constraints. The proposed method consists of neural network blocks that represent input, state, and output dynamics with constraints placed on the network weights and system variables. For handling partially observable dynamical systems, we utilize a state observer neural network to estimate the states of the system's latent dynamics. We evaluate the performance of the proposed architecture and training methods on system identification tasks for three nonlinear systems: a continuous stirred tank reactor, a two tank interacting system, and an aerodynamics body. Models optimized with a few thousand system state observations accurately represent system dynamics in open loop simulation over thousands of time steps from a single set of initial conditions. Experimental results demonstrate an order of magnitude reduction in open-loop simulation mean squared error for our constrained, block-structured neural models when compared to traditional unstructured and unconstrained neural network models.

Skomski, Elliott↗

DOE OSTI2025

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.

Shen, Yizhi↗

DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1975

New method for propagating the square root covariance matrix in triangular form

A method proposed by Potter of applying the Kalman-Bucy filter to the problem of estimating the state of a dynamic system is described, in which the square root of the state error covariance matrix is used to process the observations. A new technique which propagates the covariance square root matrix in lower triangular form is given for the discrete observation case. The technique is faster than previously proposed algorithms and is well-adapted for use with the Carlson square root measurement algorithm.

Choe, C. Y.↗

NASA NTRS2012

Accelerated Aging in Electrolytic Capacitors for Prognostics

The focus of this work is the analysis of different degradation phenomena based on thermal overstress and electrical overstress accelerated aging systems and the use of accelerated aging techniques for prognostics algorithm development. Results on thermal overstress and electrical overstress experiments are presented. In addition, preliminary results toward the development of physics-based degradation models are presented focusing on the electrolyte evaporation failure mechanism. An empirical degradation model based on percentage capacitance loss under electrical overstress is presented and used in: (i) a Bayesian-based implementation of model-based prognostics using a discrete Kalman filter for health state estimation, and (ii) a dynamic system representation of the degradation model for forecasting and remaining useful life (RUL) estimation. A leave-one-out validation methodology is used to assess the validity of the methodology under the small sample size constrain. The results observed on the RUL estimation are consistent through the validation tests comparing relative accuracy and prediction error. It has been observed that the inaccuracy of the model to represent the change in degradation behavior observed at the end of the test data is consistent throughout the validation tests, indicating the need of a more detailed degradation model or the use of an algorithm that could estimate model parameters on-line. Based on the observed degradation process under different stress intensity with rest periods, the need for more sophisticated degradation models is further supported. The current degradation model does not represent the capacitance recovery over rest periods following an accelerated aging stress period.

Celaya, Jose R.↗

NASA NTRS2016

Feasibility for Orbital Life Extension of a CubeSat in the Lower Thermosphere

Orbital flight of CubeSats at altitudes between 150 and 250 km has the potential to enable a new class of scientific, commercial, and defense-related missions. A study is presented to demonstrate the feasibility of extending the orbital lifetime of a CubeSat in a 210 km orbit. Propulsion consists of an electrospray thruster operating at a 2 W, 0.175 mN thrust, and an specific impulse (Isp) of 500 s. The mission consists of two phases. In phase 1, the CubeSat is deployed from a 414 km orbit and uses the thruster to deorbit to the target altitude of 210 km. In phase 2, the propulsion system is used to extend the mission lifetime until propellant is fully expended. A control algorithm based on maintaining a target orbital energy is presented that uses an extended Kalman filter to generate estimates of the orbital dynamic state, which are periodically updated by Global Positioning System measurements. For phase 1, the spacecraft requires 25.21 days to descend from 414 to 210 km, corresponding to a delta V = 96.25 m/s and a propellant consumption of 77.8 g. Phase 2 lasts 57.83 days, corresponding to a delta V = 119.15 m/s, during which the remaining 94.2 g of propellant are consumed.

Blandino, John J.↗

NASA NTRS2020

Search and Rescue under the Forest Canopy using Multiple UAS

We consider the problem of multi-robot search and rescue under the forest canopy. Forest is a particularly challenging environment for collaborative mapping and exploration, mainly due to the existence of severe perceptual aliasing, which hinders reliable mutual localization and map fusion. Our proposed system features unmanned aerial vehicles (UAVs) with onboard sensing and autonomy. Each UAV runs a lightweight filtering algorithm for local state estimation, and a dynamic-aware frontier selection algorithm for fast exploration. The essential and computationally intensive task of collaborative simultaneous localization and mapping (CSLAM) is performed at a central ground station. To handle perceptual aliasing, we make use of stable landmarks extracted from trees, which significantly improve precision and recall during place recognition. Furthermore, to recover from incorrect pairwise data associations during loop closure, we propose a novel procedure for global data association based on recently developed techniques on cycle consistent multiway matching. Our algorithm returns a global data association that is guaranteed to be cycle consistent, and is shown to significantly improve precision compared to the input pairwise associations. The overall multi-UAV system is extensively validated during real-world collaborative exploration missions in a forest at NASA Langley Research Center.

Multi-robot systems↗

NASA NTRS1999

Developing a Fundamental Model for an Integrated GPS/INS State Estimation System with Kalman Filtering

This work will demonstrate the integration of sensor and system dynamic data and their appropriate models using an optimal filter to create a robust, adaptable, easily reconfigurable state (motion) estimation system. This state estimation system will clearly show the application of fundamental modeling and filtering techniques. These techniques are presented at a general, first principles level, that can easily be adapted to specific applications. An example of such an application is demonstrated through the development of an integrated GPS/INS navigation system. This system acquires both global position data and inertial body data, to provide optimal estimates of current position and attitude states. The optimal states are estimated using a Kalman filter. The state estimation system will include appropriate error models for the measurement hardware. The results of this work will lead to the development of a "black-box" state estimation system that supplies current motion information (position and attitude states) that can be used to carry out guidance and control strategies. This black-box state estimation system is developed independent of the vehicle dynamics and therefore is directly applicable to a variety of vehicles. Issues in system modeling and application of Kalman filtering techniques are investigated and presented. These issues include linearized models of equations of state, models of the measurement sensors, and appropriate application and parameter setting (tuning) of the Kalman filter. The general model and subsequent algorithm is developed in Matlab for numerical testing. The results of this system are demonstrated through application to data from the X-33 Michael's 9A8 mission and are presented in plots and simple animations.

Canfield, Stephen↗

NASA NTRS1999

Real-Time Parameter Estimation in the Frequency Domain

A method for real-time estimation of parameters in a linear dynamic state space model was developed and studied. The application is aircraft dynamic model parameter estimation from measured data in flight for indirect adaptive or reconfigurable control. Equation error in the frequency domain was used with a recursive Fourier transform for the real-time data analysis. Linear and nonlinear simulation examples and flight test data from the F-18 High Alpha Research Vehicle HARV) were used to demonstrate that the technique produces accurate model parameter estimates with appropriate error bounds. Parameter estimates converged in less than 1 cycle of the dominant dynamic mode natural frequencies, using control surface inputs measured in flight during ordinary piloted maneuvers. The real-time parameter estimation method has low computational requirements, and could be implemented aboard an aircraft in real time.

Morelli, Eugene A.↗

DOE OSTI2026

Ensemble Kalman filter for data assimilation coupled with low-resolution computations techniques applied in fluid dynamics

This paper presents an innovative Reduced-order model (ROM) for merging experimental and simulation data using data assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our methodology introduces a novel approach by implementing the ensemble Kalman filter (EnKF) within a reduced-dimensional framework, grounded in a robust theoretical foundation and applied to fluid dynamics. To address the substantial computational demands of DA, the proposed ROM employs low-resolution (LR) techniques to drastically reduce computational costs. This innovative approach involves downsampling datasets for DA computations, followed by an advanced reconstruction technique based on low-cost singular value decomposition (lcSVD). The lcSVD method, a key innovation in this paper, has never been applied to DA before and offers a highly efficient way to enhance resolution with minimal computational resources. Our results demonstrate significant reductions in both computation time and RAM usage through these LR techniques without compromising the accuracy of the estimations. For instance, in a turbulent test case, for a data compression rate of 15.9, the LR approach can achieve a speed-up of 13.7 and a RAM compression of 90.9% while maintaining a low relative root mean square error (RRMSE) of 2.6%, compared to 0.8% in the high-resolution (HR) reference. Furthermore, we highlight the effectiveness of the EnKF in estimating and predicting the state of fluid flow systems based on limited observations and given low-fidelity numerical data. This paper highlights the potential of the proposed DA method in fluid dynamics applications, particularly for improving computational efficiency in CFD and related fields. Its ability to balance accuracy with low computational and memory costs makes it especially suitable for large-scale and real-time applications, such as environmental monitoring or engineering design. This method will be incorporated into ModelFLOWs-app.

Data Assimilation↗

NASA NTRS1975

Estimation of unmodeled forces on a low-thrust space vehicle

The application of a sequential estimation algorithm, which compensates for random errors in the dynamic model, to the problem of estimating the state of a continuously thrusting solar electric propulsion space vehicle is investigated. The dynamic model errors, due to random anomalies in the propulsion system, are approximated successfully by both first order and second order Gauss-Markov processes to obtain a more accurate and stable orbit determination algorithm. The importance of correct dynamic and measurement modeling in achieving accurate estimates is demonstrated.

Tapley, B. D.↗

DOE OSTI2023

Uncertainty Error Modeling for Non-Linear State Estimation With Unsynchronized SCADA and µPMU Measurements

Distribution systems of the future smart grid require enhancements to the reliability of distribution system state estimation (DSSE) in the face of low measurement redundancy, unsynchronized measurements, and dynamic load profiles. Micro phasor measurement units (µPMUs) facilitate co-synchronized measurements with high granularity, albeit at an often prohibitively expensive installation cost. Supervisory control and data acquisition (SCADA) measurements can supplement µPMU data, although they are received at a slower sampling rate. Further complicating matters is the uncertainty associated with load dynamics and unsynchronized measurements–not only are the SCADA and µPMU measurements not synchronized with each other, but the SCADA measurements themselves are received at different time intervals with respect to one another. This paper proposes a non-linear state estimation framework which models dynamic load uncertainty error by updating the variances of the unsynchronized measurements, leading to a time-varying system of weights in the weighted least squares state estimator. Case studies are performed on the 33-Bus Distribution System in MATPOWER, using Ornstein–Uhlenbeck stochastic processes to simulate dynamic load conditions.

Cooper, Austin↗

NASA NTRS1996

Application of Consider Covariance to the Extended Kalman Filter

The extended Kalman filter (EKF) is the basis for many applications of filtering theory to real-time problems where estimates of the state of a dynamical system are to be computed based upon some set of observations. The form of the EKF may vary somewhat from one application to another, but the fundamental principles are typically unchanged among these various applications. As is the case in many filtering applications, models of the dynamical system (differential equations describing the state variables) and models of the relationship between the observations and the state variables are created. These models typically employ a set of constants whose values are established my means of theory or experimental procedure. Since the estimates of the state are formed assuming that the models are perfect, any modeling errors will affect the accuracy of the computed estimates. Note that the modeling errors may be errors of commission (errors in terms included in the model) or omission (errors in terms excluded from the model). Consequently, it becomes imperative when evaluating the performance of real-time filters to evaluate the effect of modeling errors on the estimates of the state.

Lundberg, John B.↗

NASA NTRS2000

Real-Time Parameter Estimation in the Frequency Domain

A method for real-time estimation of parameters in a linear dynamic state-space model was developed and studied. The application is aircraft dynamic model parameter estimation from measured data in flight. Equation error in the frequency domain was used with a recursive Fourier transform for the real-time data analysis. Linear and nonlinear simulation examples and flight test data from the F-18 High Alpha Research Vehicle were used to demonstrate that the technique produces accurate model parameter estimates with appropriate error bounds. Parameter estimates converged in less than one cycle of the dominant dynamic mode, using no a priori information, with control surface inputs measured in flight during ordinary piloted maneuvers. The real-time parameter estimation method has low computational requirements and could be implemented

Morelli, Eugene A.↗

NASA NTRS2005

Kalman Filter Constraint Tuning for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter, which has been shown to generally improve the filter s estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy as the Kalman filter is theoretically optimal. This paper proposes a way to tune the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.

Simon, Dan↗

NASA NTRS2006

Constrained Kalman Filtering Via Density Function Truncation for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the PDF (probability density function) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. The turbofan engine model contains 3 state variables, 11 measurements, and 10 component health parameters. It is also shown that the truncated Kalman filter may be a more accurate way of incorporating inequality constraints than other constrained filters (e.g., the projection approach to constrained filtering).

Simon, Dan↗

NASA NTRS2003

Kalman Filtering with Inequality Constraints for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops two analytic methods of incorporating state variable inequality constraints in the Kalman filter. The first method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satisfied rather than exactly satisfied.) The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results. The use of the algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate health parameters. The turbofan engine model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.

Simon, Dan↗

DOE OSTI2020

Molecular Simulation of Covalent Bond Dynamics in Liquid Silicon

Many atomic liquids can form transient covalent bonds reminiscent of those in the corresponding solid states. These directional interactions dictate many important properties of the liquid state, necessitating a quantitative, atomic-scale understanding of bonding in these complex systems. A prototypical example is liquid silicon, wherein transient covalent bonds give rise to local tetrahedral order and consequent nontrivial effects on liquid-state thermodynamics and dynamics. To further understand covalent bonding in liquid silicon, and similar liquids, we present an ab initio-simulation-based approach for quantifying the structure and dynamics of covalent bonds in condensed phases. Through the examination of structural correlations among silicon nuclei and maximally localized Wannier function centers, we develop a geometric criterion for covalent bonds in liquid Si. We use this to monitor the dynamics of transient covalent bonding in the liquid state and estimate a covalent bond lifetime. We compare covalent bond dynamics to other processes in liquid Si and similar liquids and suggest experiments to measure the covalent bond lifetime.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗