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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

Barghouty, A. F.↗
DOE OSTI2018

Advanced trust region optimization strategies for glass box / black box models

We present an improved trust region filter (TRF) method for optimization of combined glass box/black box systems. Glass box systems refer to models that are easily expressed in an algebraic modeling language, providing cheap and accurate derivative information. By contrast, black box systems may be computationally expensive and derivatives are unavailable. The TRF method, as first introduced in our previous work (Eason and Biegler, AIChE J . 2016; 62:3124–3136), is able to handle hybrid systems containing both glass and black box components, which can frequently arise in chemical engineering, for example, when a multiphase reactor model is included in a flow sheet optimization problem. We discuss several recent modifications in the algorithm such as the sampling region, which maintains the algorithm's global convergence properties without requiring the trust region to shrink to zero in the limit. To benchmark the development of this optimization method, a test set of problems is generated based on modified problems from the CUTEr and COPS sets. The modified algorithm demonstrates improved performance using the test problem set. Finally, the algorithm is implemented within the Pyomo environment and demonstrated on a rigorous process optimization case study for carbon capture. © 2018 American Institute of Chemical Engineers AIChE J , 64: 3934–3943, 2018

Eason, John P.↗
DOE OSTI2020

Cloud-based implementation of white-box model predictive control for a GEOTABS office building: A field test demonstration

Model predictive control (MPC) has been proven in simulations and pilot case studies to be a superior control strategy for large buildings. MPC can utilize the weather and occupancy schedule forecasts, together with the system model, to predict the future thermal behavior of the building and minimize the overall energy use and maximize thermal comfort. However, these advantages come with the cost of increased modeling effort, computational demands, communication infrastructure, and commissioning efforts. Thus a typical approach is to, often rapidly, simplify the building modeling and MPC optimization problem while paying a price of not reaching the full performance potential. It has been shown that by employing accurate physics-based models, MPC performance can be notably increased closer to its theoretical performance bound. However, implementation of such high-fidelity MPC in real buildings remains a challenge, resulting in a lack of successful field test studies. This work presents the methodology and field test demonstration of a computationally efficient implementation of the white-box MPC in an office building in Belgium. The detailed model of the building is based on first-principle physical equations. The deployment and supervision of MPC operation in a practical setting are supported by an automated cloud-based communication infrastructure. The motivating factor behind the cloud-based architecture is its compatibility with a commercially appealing control as a service concept. The building is equipped with a ground source heat pump (GSHP) and thermally activated building structures (TABS), where the combination of both is also known as GEOTABS. From a control perspective, GEOTABS buildings are particularly challenging systems due to large scale, complex heating, ventilation and air conditioning (HVAC) system, and slow dynamics with time delays. On the other hand, there is an increased potential for energy savings due to the high thermal mass, which acts as thermal storage. The MPC operation is demonstrated during the challenging transient seasons (switching between heating and cooling), and its performance is compared to a traditional rule-based controller (RBC). We provide a proof of concept of real MPC operation for the most difficult seasons with notable GSHP energy use savings equal to 53.5% and thermal comfort improvement by 36.9%. Other MPC applications found in the literature describe tests for only cooling or only heating, and up to now only for a black-box or a grey-box approach.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1985

Why do leaky-box models work so fine?

By introducing the concept of the age distribution of cosmic rays it is possible to decouple spatial from momentum transport, and simple leaky-box type equations result. The influence of spatial inhomogeneities, geometries, and source distributions enters the spatially homogeneous, infinite (i.e., leaky box) problem through appropriate mean lifetimes. A precise prescription of how to obtain these mean lifetimes, i.c., for comparison with data measured in the vicinity of the solar system they have to be calculated from the age distribution at the spatial position of the observer.

Schlickeiser, R.↗
DOE OSTI2022

A Stability Analysis Tool for Bulk Power Systems Using Black-Box Models of Inverter-based Resources

This paper presents a small-signal stability analysis tool for large-scale power systems with high penetration of inverter-based resources (IBRs). Firstly, a network transfer function matrix (NTFM), which represents the information of the system topology, transmission lines, loads, IBRs locations, etc., is derived to model the entire power system network. Secondly, small-signal perturbation method is applied to obtain the sequence impedance/admittance responses of IBRs considering the frequency cross-coupling effects. With the obtained NTFM as well as IBRs' models, a multi-input, multi-output (MIMO) feedback system is constructed, and the generalized Nyquist criterion (GNC)-based stability method is employed to analyze the stability of the entire power system. Different testing cases based on a modified IEEE-14 bus system are leveraged to verify the proposed stability analysis tool.

Sun, Dongsen↗
DOE OSTI2026

Empirical Comparison of Machine Learning Approaches for Black-Box Modeling of Power Conversion System Dynamics

Inverter-based resources are key components in modern power systems, but accurately modeling their complex behavior can be challenging. Standard, generic converter models often oversimplify inverter dynamics, leading to significant errors in predicting performance. In this work, we compare several data-driven machine learning (ML) approaches for inverter modeling, performing experiments on power conversion systems, systematically varying input conditions, and recording the resulting voltages and currents. The ML models were then trained on this measured data to capture the inverter's dynamic response and to predict the inverter's output current. A performance comparison between the four ML models under study is conducted, laying the foundation for future work on hardware implementation for real-time inference.

30 DIRECT ENERGY CONVERSION↗
NASA NTRS1989

Stochastic acceleration of cometary pickup ions - The classic leaky box model

The acceleration of cometary pickup ions by magnetohydrodynamic waves at P/Giacobini-Zinner is examined in a model where acceleration predominantly occurs downstream of the bow shock throughout the cometosheath where intense magnetic turbulence exists. The mean free path for scattering by the magnetic fluctuations in this region is less than the characteristic dimension of the cometosheath so that pickup ions are rendered isotropic and energized by a modest amount in the process. This principal loss mechanism for the ions is spatial diffusion out of the acceleration region moderated by the self-same accelerating waves. This particular feature constrains the model in a way that the predicted ion spectrum is uniquely determined by the power spectrum of the magnetic turbulence. At both P/Giacobini-Zinner and P/Halley, the turbulence is non-Kolmogoroff with a spectral index of 2 resulting in an ion spectral behavior that is approximately an exponential in ion speed, consistent with a recent analysis of the Giacobini-Zinner data (see Richardson et al.).

Barbosa, D. D.↗
DOE OSTI2022

Reduced-Order Modeling Method for Phase-Change Thermal Energy Storage Heat Exchangers

Thermal energy storage can facilitate the effective utilization of renewable energy. To speed up the design process of thermal energy storage devices, it is critical to develop fast and accurate modeling methods for phase change material embedded heat exchangers (PCM HXs). This study developed and compared two approximation-assisted reduced-order PCM HX models for the simulation of thermal storage components and systems, which were verified against a validated finite-volume model. They are a pure black-box model, and a grey-box model based on the Number of Transfer Units (or effectiveness-NTU) approach. We used the reduced-order models to predict the performance of standalone PCM HX for 1000 cases with different fluid inlet conditions and HX designs. We also integrated the models with a vapor compression system to predict the compressor energy consumption and total charging time under various conditions. The results show that overall, the black-box model gave more accurate results than the grey-box model. On average, the mean absolute deviation in the PCM HX fluid outlet temperature was 0.05 K and 0.1 K for the black-box model and grey-box model, respectively. The grey-box model gave larger temperature deviation toward the end of the phase change process, due to the simplified two-node PCM representation. On the system level, the mean absolute deviation in compressor energy consumption was 0.2% and 0.3% for the black-box model and grey-box model, respectively. Their mean absolute deviation in total charging time was 1.1% and 2.6%, respectively. In terms of computation efficiency, the system simulation speedup ratio gained by using the reduced-order models was 11 to 57. System simulation time was decreased from an average of 1465 s to an average of 59 s. This shows that the proposed reduced-order modeling methods can be used to predict system performance of PCM HXs with less than 3% accuracy penalty, and 25 times less computational time than finite-volume models, enabling faster design and evaluation of PCM thermal storage devices.

25 ENERGY STORAGE↗
DOE OSTI2023

Development, calibration, and validation of a novel gray-box energy model for residential split air conditioners

Energy models for vapor compression refrigeration in residential air conditioners have been developed through white-box, gray-box, and black-box methods in decades. However, existing white-box and gray-box models require complicated equations with detailed geometries while black-box models require substantial experimental data. Further, this paper aims to develop and validate a simple gray-box steady-state energy model without the need for detailed geometries, which can accurately predict the cooling capacity and electrical power input based on outdoor and indoor air conditions, and supply airflow rates. First three state variables, including the evaporation and condensation temperatures, and refrigerant mass flowrate, are applied to develop the energy model and are solved by three physical equations, including the energy conservations at the evaporator and condenser, and the refrigerant volume-mass flow correlation of the compressor. Secondly, seven performance property functions related to three state variables and three physical equations are identified and calibrated by simple temperature and power measurements. Finally, field experiments are conducted on a residential air conditioner to calibrate these performance property functions and validate the developed model. The validated results reveal the model can accurately predict the cooling capacity and electrical power input, with the normalized root mean square errors of 2.3% and 0.87% respectively.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Expanding-box Quasilinear Model of the Solar Wind

The expanding-box model of the solar wind has been adopted in the literature within the context of magnetohydrodynamics, hybrid, and full particle-in-cell simulations to investigate the dynamic evolution of the solar wind. The present paper extends such a method to the framework of self-consistent quasilinear kinetic theory. It is shown that the expanding-box quasilinear methodology is largely equivalent to the inhomogeneous steady-state quasilinear model discussed earlier in the literature, but a distinction regarding the description of wave dynamics between the two approaches is also found. The expanding-box quasilinear formalism is further extended to include the effects of a spiraling solar-wind magnetic field as well as collisional age effects. The present finding shows that the expanding-box quasilinear approach and the steady-state global-kinetic models may be employed interchangeably in order to address other more complex problems associated with the solar-wind dynamics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Grey-box Fault Models and Applications for Low Carbon Emission CO2 Refrigeration System

CO2 refrigeration systems have attracted more attentions in recent years because of their zero-carbon emission advantages compared with traditional refrigerants. These systems are widely used in certain commercial buildings such as supermarkets. However, very limited energy studies have been done for such refrigeration systems under faults. Furthermore, this study investigated five common faults for supermarket transcritical CO2 refrigeration systems with display cases. The following major tasks were implemented for this study. (1) Five fault models (gray-box format) regarding the power consumption and supply air temperature were proposed for low- and high-temperature display cases, respectively. The models cover: ice accumulation on evaporator coil, evaporator fan partial failure, expansion valve failure, display door open, and condenser blockage. (2) These fault models were calibrated with field tests, and the modeling accuracies were in good agreement with measurement datasets. (3) The proposed fault models demonstrated more than 90% of fault detection for Fault Detection and Diagnostics (FDD) purposes for both field measurement and simulated data.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Gray-Box Fault Models and Applications for Low-Carbon Emission CO 2 Refrigeration Systems

CO 2 refrigeration systems have attracted more attentions in recent years because of their zero-carbon emission advantages compared with traditional refrigerants. These systems are widely used in certain commercial buildings such as supermarkets. However, very limited energy studies have been done for such refrigeration systems under faults. This study investigated five common faults for supermarket transcritical CO 2 refrigeration systems with display cases. The following major tasks were implemented for this study. (1) Five fault models (gray-box format) regarding the power consumption and supply air temperature were proposed for low- and high-temperature display cases, respectively. The models cover: ice accumulation on evaporator coil, evaporator fan partial failure, expansion valve failure, display door open, and condenser blockage. (2) These fault models were calibrated with field tests, and the modeling accuracies were in good agreement with measurement datasets. (3) The proposed fault models demonstrated more than 90% of fault detection for Fault Detection and Diagnostics (FDD) purposes for both field measurement and simulated data.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.

creep-fatigue↗
DOE OSTI2026

Machine learning-enhanced hybrid modeling approach for better identification of a building thermal network model and improved prediction

The gray-box modeling approach, which uses a semi-physical thermal network model, has been widely used in building prediction applications, such as model predictive control (MPC). However, unmeasured disturbances, such as occupants, lighting, and in/exfiltration loads, make it challenging to apply this approach to practical buildings. In this word, we propose a hybrid modeling approach that integrates the gray-box model with a model for unmeasured disturbance. After reviewing several system identification approaches, we systematically designed the unmeasured disturbance model with a model selection process based on statistical tests to make it robust. We generated data based on the building model calibrated by real operational data and then trained the hybrid model for two different weather conditions. The hybrid model approach demonstrates an RMSE reduction of approximately 0.2–0.9 °C and 0.3–2 °C on 1-day ahead temperature prediction compared to the Conventional approach for mild (Berkeley, CA) and cold (Chicago, IL) climates, respectively. In addition, this approach was applied to experimental data obtained from the laboratory building to be used for the MPC application, showing superior prediction performances.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1988

Analytic solution of the box diffusion model for a global ocean

The paper presents an analytic solution for the temperature of the mixed layer for a box diffusion model of a global ocean. It is shown that the exact solution approaches the appropriate limits of a mixed layer ocean model and of a diffusive ocean without a mixed layer on top. It is also shown that, over a large range of parameters of the box diffusion model, the difference between the temperature calculated using a box diffusion model and the temperature calculated using a purely diffusive ocean is buried in the noise.

Lebedeff, Sergej A.↗
DOE OSTI2019

Enhancing the Implementation of a First-order Equivalent Thermal Parameter Model to Enable Accurate and Robust Building Thermal Response Prediction

Predicting indoor temperature conditions are often necessary for advanced building controls. Gray-box models are preferable to do so because they can over- come limitations of white-box and black-box models; however, their current implementation methods can be problematic due to their difficulties in capturing non-linear behaviors and time-varying disturbances. This paper proposes a novel method to implement a popular gray-box model, the 1st-order equivalent thermal parameter (ETP) model. To evaluate performance, we applied the proposed method to predict in- door temperatures for a medium-office building, over the course of one day. Predictions are compared against two existing methods: the ETP model implemented through a common approach and a black-box model. Results suggest that the proposed method can yield more accurate results compared to the other methods; additionally, the proposed method demonstrated similar capabilities in capturing non-linear behaviors as the black-box model.

Hinkelman, Kathryn↗
DOE OSTI2018

A simplified regression building thermal modelling method for detached two-floor house in U.S.

The residential building sector accounts for approximately 37% of total U.S. electricity consumption. Within the residential building sector, heating and cooling is the main target for peak load shifting/reduction since it is the largest contributor to peak demand. In fact, the flexibility of residential HVAC loads can provide continuous variation of demand to provide grid services by varying their demand over a baseline. The performance of HVAC load control to provide grid services relies heavily on the accuracy of indoor air temperature or cooling/heating demand predictions and therefore the quality of building model. Besides forward models, popular building models are data-driven models which can be broken down into two categories: gray-box model, e.g. Resistance-Capacitance (RC) model and black-box model. RC model, also called lumped capacitance or network model, which is constituted with electrical analogue pattern with resistance (R) and capacitance (C). In general, RC models require considerable computation burden and long periods of data to train limited number of model coefficients. Black-box models have gained increasing interest due to their capability in analyzing large-scale data and flexibility in practical applications. But, the data-mining based (machine learning algorithms/techniques based) models tend to have invisible model structures which poses a problem when trying to use the model for optimal control or model predictive control of the HVAC system. Hence, there is a continuing need for efficient online system identification techniques, which can provide explicit parameters for the model. Traditional regression models fit well for this specific purpose. This paper presents an innovative way to predict average indoor temperature in separate floors of typical detached residential house. A rolling horizon linear regression model, which includes online adaptive correction component, is proposed to predict the temperature difference between downstairs and upstairs. A RC model is used to predict the overall mean indoor air temperature. Since the adaptive algorithm needs to be implemented online, a less computation-demanding polynomial fitting algorithm is adopted. This kind of fitting problem can be cast as linear regression problem with multiple variables, parameters of which can be efficiently obtained by well-known gradient descent method.The validation is conducted by comparing the predicted results with the results from data-mining based models as well as measured data from a real typical detached two-floor house. The results show that the developed method has satisfactory performance in predicting the building indoor temperature in 1st and 2nd floors.

Cui, Borui↗