SEARCH · Engineering Papers
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
It is shown that Jacobi elliptic function solutions of the nonlinear Duffing equation model the radiation field in a high-gain free electron laser through early saturation. After initial start-up, the field can be expressed equivalently with a hyperbolic secant. The model is derived for arbitrary detuning from resonance, which enables study of the spectral properties in the early nonlinear regime.
Wintertime Ural blocking (UB) has been shown to play an important role in cold extremes over Eurasia, and thus it is useful to investigate the impact of warming over the Barents–Kara Seas (BKS) on the behavior of Ural blocking. In our study the response of UB to stepwise tropospheric warming over the BKS is examined using a dry dynamic core model. Nonlinear responses are found in the frequency and local persistence of UB. The frequency and local persistence of the UB increase with the strength of BKS warming in a less strong range and decrease with the further increase of BKS warming, which is linked to the UB propagation influenced by upstream background atmospheric circulation. For a weak BKS warming, the UB becomes more persistent due to its less westward movement associated with intensified upstream zonal wind and meridional potential vorticity gradient (PVy) in the North Atlantic mid-high latitudes, which corresponds to a negative height response over the North Atlantic high latitudes. When BKS warming is strong, a positive height response appears in the early winter stratosphere, and its subsequent downward propagation leads to a negative NAO response or increased Greenland blocking events, which reduces zonal wind and PVy in the high latitudes from North Atlantic to Europe, thus enhancing the westward propagation of UB and reducing its local persistence. The transition to the negative NAO phase and the retrogression of UB are not found when numerically suppressing the downward influence of weakened stratospheric polar vortex, suggesting a crucial role of the stratospheric pathway in nonlinear responses of UB to the early winter BKS warming.
Management of the electrical grid is becoming more complex due to the increased penetration of alternative energy generation technologies and a broadening diversity of electric loads. This complexity creates challenges in balancing demand and generation that can increase the potential for grid instabilities. One effective way to address this issue is to leverage previously unexploited demand flexibility through advanced control strategies. In this work, we propose an advanced control method, called adaptive neural parameter-varying model predictive control (ANPV-MPC), to control the temperature and energy consumption of a building via its Heating, Ventilation, and Air Conditioning system. ANPV-MPC combines key ideas in parameter-varying control, adaptive control, and online learning strategies to bridge the gap between computationally efficient linear model predictive control and more accurate nonlinear model predictive control. The novelty in ANPV-MPC is the use of a physics-inspired Bayesian neural network to estimate the coefficients of the parameter-varying linear control model. The Bayesian neural network additionally provides uncertainty estimates, triggering online training to capture evolving building system conditions. We show that ANPV-MPC can approximate the building system dynamics with a 28.39% higher accuracy than traditional linear model predictive control, resulting in 36.23% better control performance without increasing complexity of the optimal control problem. ANPV-MPC also adapts in real time to previously unseen conditions using online learning, further improving its performance.
Reconstructing the initial conditions of the Universe from late-time observations has the potential to optimally extract cosmological information. Due to the high dimensionality of the parameter space, a differentiable forward model is needed for convergence, and recent advances have made it possible to perform reconstruction with nonlinear models based on galaxy (or halo) positions. In addition to positions, future surveys will provide measurements of galaxies' peculiar velocities through the kinematic Sunyaev-Zel'dovich effect (kSZ), type Ia supernovae, the fundamental plane relation, and the Tully-Fisher relation. Here we develop the formalism for including halo velocities, in addition to halo positions, to enhance the reconstruction of the initial conditions. We show that using velocity information can significantly improve the reconstruction accuracy compared to using only the halo density field. Here we study this improvement as a function of shot noise, velocity measurement noise, and angle to the line of sight. We also show how halo velocity data can be used to improve the reconstruction of the final nonlinear matter overdensity and velocity fields. We have built our pipeline into the differentiable Particle-Mesh FlowPM package, paving the way to perform field-level cosmological inference with joint velocity and density reconstruction. This is especially useful given the increased ability to measure peculiar velocities in the near future.
Aerosol jet printing (AJP) has emerged as a promising noncontact additive manufacturing method for high-resolution printing for a wide range of material systems. A key challenge limiting the broader adoption of AJP in the material science community is the lack of methods to precisely control thickness. Herein, we develop a model-based design of experiment (MBDoE) framework that integrates physics-informed models, nonlinear regression, and information criteria to postulate, select and calibrate the best model to describe and optimize the AJP manufacturing process. Starting with already available data from system commissioning (e.g., prior single variable sensitivity analysis), four candidate physics-informed models are postulated and trained. MBDoE identifies a single additional optimal experiment to validate these predictive models with quantified uncertainties, which are then used to determine the best experimental conditions to control printed film thickness. As a comparative benchmark, the analysis is repeated using the same dataset with nonparametric Gaussian process regression (GPR) model that does not incorporate physical information. Using MBDoE principles, we find that only five experiments are necessary to calibrate the nonlinear physics-informed parametric model, and with said limited data, this model outperforms the black-box machine learning GPR model. This key result underscores an emerging trend in the data science community: incorporating physical information into predictive models often drastically reduces the data requirements. Leveraging MBDoE further increased the data efficiency. By design, the proposed data science framework is general in nature and can be easily extended to other experimental and additive manufacturing systems beyond AJP.
Conventional Bayesian optimization methods implicitly assume that the data and model being optimized are “perfect.” This assumption leads to inaccurate posterior probability distribution functions (PDFs) when applied to “imperfect” data or models. The new Bayesian optimization framework presented in this report provides a way to parameterize the effect of imperfections usually encountered in a prior PDF of generalized data or a model on the posterior PDF. The effects of imperfections are parameterized by a set of constraints imposed on the posterior expectation values of deviations between the data and the model and on their covariance matrix elements. A particular set of values for these constraints conveys an evaluator’s best estimate of the effect of imperfections on the corresponding posterior expectation values. When a prior PDF of generalized data is assumed to be normal, an expression for a posterior PDF satisfying an arbitrary set of constraints is derived analytically for linear models. An analogous iterative algorithm is given for nonlinear models. The corresponding posterior PDF should be used to estimate any posterior expectation values in the presence of imperfections parameterized by that set of constraints. A posterior PDF of a conventional Bayesian optimization method is recovered analytically when all evaluator-specified constraints are set to zero (i.e., in the absence of any imperfections). The analytical expressions derived in this report for normal PDFs and linear models were verified numerically by a Metropolis–Hastings Monte Carlo method. The methods presented herein could be applied to any kind of data or models, including differential cross-section data or integral benchmark experiments.
Nonlinear modeling and optimization is a valuable tool for aiding decisions by engineering practitioners, but programming an optimization problem based on a complex electrical, mechanical, or chemical process is a time-consuming and error-prone activity. Therefore, there is a need for model analysis and debugging tools that can detect and diagnose modeling errors. One such tool is the Dulmage–Mendelsohn decomposition, which identifies structurally under- and over-determined subsets in systems of equations and variables by partitioning the bipartite graph of the system. This work provides the necessary background to understand the Dulmage–Mendelsohn decomposition and its application to the analysis of nonlinear optimization problems, demonstrates its use in diagnosing a variety of modeling errors, and introduces software implementations for analyzing nonlinear optimization problems in the Pyomo and JuMP algebraic modeling languages.
Abstract Machine learning (ML) offers promising tools to develop surrogate models for polymers' structure–property relations. Surrogate models can be built upon existing polymer data and are useful for rapidly predicting the properties of unknown polymers. The accuracy of such ML models appears to depend on the feature space representation of polymers, the range of training data, and learning algorithms. Here, we establish connections between these factors for predicting the glass transition temperature (T g ) of polymers. Our analysis suggests linear models with fewer fitting parameters are as accurate as nonlinear models with many hidden and unexplainable parameters. Also, the performance of a monomer topology‐based ML model is found to be qualitatively identical to that of a physicochemical descriptor‐based ML model. We find that the ML models's performance in the extrapolative region is enhanced as the property range of the training data increases. Moreover, we establish newT g – polymer chemistry correlations via ML. Our work illustrates how ML can advance the fundamental understanding of polymer structure–property correlations and its efficacy for extrapolation problems.
With the increasing penetration level of renewable sources and power electronics loads in modern power systems, accurate and computationally efficient models are needed. Black-box model (BBM) could be a useful method in such systems. However, not very extensive research efforts have been made for power electronics BBM so far, and existing works mostly focus on steady-state operation, neglecting the important transient behaviors such as load transients, voltage transients, and faults. This paper presents a comparative study of three commonly used nonlinear BBM approaches for transient behaviors of power electronics converters. Comparison methods are proposed, and the evaluations are conducted under different transients using a grid-connected single-phase photovoltaic inverter. The findings of this study provide valuable references for further feasibility investigations on implementing BBMs in large-scale power electronics-rich power systems.
The minimum value of the safety factor profile is related to the magnetohydrodynamic (MHD) stability of the plasma confined in a tokamak. Therefore, active control of the minimum safety factor may mitigate MHD instabilities that can degrade or even terminate plasma confinement. Typically, in most tokamak scenarios, the minimum safety factor evolves spatially with time, i.e., the location at which the safety factor achieves the minimum value changes with time. In addition to the inherent nonlinearities in the minimum safety factor evolution, its spatial variation makes the control design challenging. In particular, complexity in control design may arise from the need for time-dependent nonlinear models that account for spatial variation of the minimum safety factor. Furthermore, the minimum safety factor may drift to locations where the actuator authority is low. The problem of minimum safety factor control with target location tracking and moving electron cyclotron current drive (ECCD) is addressed in this work. A nonlinear time-dependent model that incorporates the spatial variation of the minimum safety factor is presented. A nonlinear controller based on optimal feedback linearization is developed to track a target minimum safety factor. The proposed controller treats the ECCD position as a controllable variable. In other words, the controller prescribes the ECCD position (in addition to the non-inductive powers) in real time based on an optimal criterion that is defined a priori. This work also presents the steps necessary to integrate the minimum safety factor controller with a total energy controller to achieve multiple control objectives simultaneously. In conclusion, the proposed integrated control algorithm is tested using nonlinear simulations in the Control Oriented Transport SIMulator (COTSIM) for a DIII-D tokamak scenario.
This report is a comprehensive guide to the nonlinear viscoelastic Spectacular model, which is an isotropic, thermo-rheologically simple constitutive model for glass-forming materials, such as amorphous polymers. Spectacular is intermediate in complexity to the previous PEC and SPEC models (Potential Energy Clock and Simplified Potential Energy Clock models, respectively). The model form consists of two parts: a Helmholtz free energy functional and a nonlinear material clock that controls the rate of viscoelastic relaxation. The Helmholtz free energy is derived from a series expansion about a reference state. Expressions for the stress and entropy functionals are derived from the Helmholtz free energy following the Rational Mechanics approach. The material clock depends on a simplified expression for the potential energy, which itself is a functional of the temperature and strain histories. This report describes the thermo-mechanical theory of Spectacular, the numerical methods for time-integrating the model, model verification for its implementation in LAMÉ, a user guide for its implementation in LAMÉ, and ideas for future work. A number of appendices provide supplementary mathematical details and a description of the procedure used to derive the simplified potential energy from the full expression for the potential energy. The goal of this report is create a convenient point-of-entry for engineers who wish to learn more about Spectacular, but also to serve as a reference manual for advanced users of the model.
As part of the work Terrafuse developed 1) a model for wildfire risk in California, and 2) a model for downscaled wind fields from Numerical Weather Prediction (NWP) numerical models. The wildfire model is based on 20 years of historical data and captures the dependence of wildfire incidence and spread on climatic, weather and land-use variables by training a machine learning model. Nonlinear relationships between input features are learned and expressed by the model and model transparency allows features to be ranked and interpreted. The fire model is of use for accurately predicting real-time daily and long-term wildfire risk for use cases in energy and insurance. The downscaled wind model is a spatio-temporal deep learning model that emulates the influence of high-resolution variables on wind speed, allowing coarse-resolution operational NWP models to be accurately expressed on fine grids at high resolution, with application to wind energy and weather forecasting.
Demand-side management/demand response (DSM/DR) are key strategies for mitigating the inherent variability in electricity generation rates by renewable sources. This article represents—to our knowledge—the first foray into assessing the DR potential of ammonia plants. Ammonia plants are interesting candidates for DR initiatives because of their significant electricity use (for operating compressors driving the synthesis loop) and the ability to store the ammonia product relatively easily and safely. Our approach is based on formulating and solving an optimal DR scheduling problem for an ammonia plant while accounting for the process dynamics. To this end, we introduce a new Hammerstein–Wiener-inspired modeling framework based on injecting linear dynamics in a first-principles static nonlinear model of the process. The results are encouraging; for the cases considered, peak-time power consumption decreases between 3.57% and 7.40%, coupled with 1.39% to 3.70% reductions in operating cost.
Current wind turbine design methods require tens of thousands of time-domain simulations and use different random seeds to account for the stochasticity of the environmental conditions. The account of stochasticity is nonintrusive because the sampling method calls a deterministic model multiple times without changing its underlying equations. In this work, we investigate and demonstrate using simple proof of concepts how intrusive approaches can be used to directly account for stochasticity in the equations representing a mechanical system. Our long term goal is to apply such methodology to the design of wind turbines without requiring an excessive number of simulations. Intrusive methods manipulate stochastic variables directly to provide the probability density functions (PDFs) of the states and outputs at any time as functions of the PDFs of the inputs. We illustrate how different methods can be used with a reduced-order model of a wind turbine with one degree of freedom and for linear and nonlinear models. We discuss how the methods can be extended and what it will take to apply them to a level of fidelity similar to current state-of-the-art wind turbine design tools.
Subcutaneous injection of biotherapeutics has attracted considerable attention in the pharmaceutical industry. However, there is limited understanding of the mechanisms underlying the absorption of drugs with different molecular weights and the delivery of drugs from the injection site to the targeted tissue. Here, we propose the MPET 2 -mPBPK model to address this issue. This multiscale model couples the MPET 2 model, which describes subcutaneous injection at the local tissue scale from a biomechanical view, with a post-injection absorption model at injection site and a minimal physiologically-based pharmacokinetic (mPBPK) model at whole-body scale. Utilizing the principles of tissue biomechanics and fluid dynamics, the local MPET 2 model provides solutions that account for tissue deformation and drug absorption in local blood vessels and initial lymphatic vessels during injection. Additionally, we introduce a model accounting for the molecular weight effect on the absorption by blood vessels, and a nonlinear model accounting for the absorption in lymphatic vessels. The post-injection model predicts drug absorption in local blood vessels and initial lymphatic vessels, which are integrated into the whole-body mPBPK model to describe the pharmacokinetic behaviors of the absorbed drug in the circulatory and lymphatic system. We establish a numerical model which links the biomechanical process of subcutaneous injection at local tissue scale and the pharmacokinetic behaviors of injected biotherapeutics at whole-body scale. With the help of the model, we propose an explicit relationship between the reflection coefficient and the molecular weight and predict the bioavalibility of biotherapeutics with varying molecular weights via subcutaneous injection. The considered drug absorption mechanisms enable us to study the differences in local drug absorption and whole-body drug distribution with varying molecular weights. This model enhances the understanding of drug absorption mechanisms and transport routes in the circulatory system for drugs of different molecular weights, and holds the potential to facilitate the application of computational modeling to drug formulation.
Unmanned aerial vehicles (UAVs) provide an intermediate scale of spatial and spectral data collection that yields increased accuracy and consistency in data collection for morphological and physiological traits than satellites and expanded flexibility and high-throughput compared to ground-based data collection. In this study, we used UAV-based remote sensing for automated phenotyping of field-grown switchgrass (Panicum virgatum), a leading bioenergy feedstock. Using vegetation indices calculated from a UAV-based multispectral camera, statistical models were developed for rust disease caused by Puccinia novopanici, leaf chlorophyll, nitrogen, and lignin contents. For the first time, UAV remote sensing technology was used to explore the potentials for multiple traits associated with sustainable production of switchgrass, and one statistical model was developed for each individual trait based on the statistical correlation between vegetation indices and the corresponding trait. Also, for the first time, lignin content was estimated in switchgrass shoots via UAV-based multispectral image analysis and statistical analysis. The UAV-based models were verified by ground-truthing via correlation analysis between the traits measured manually on the ground-based with UAV-based data. The normalized difference red edge (NDRE) vegetation index outperformed the normalized difference vegetation index (NDVI) for rust disease and nitrogen content, while NDVI performed better than NDRE for chlorophyll and lignin content. Overall, linear models were sufficient for rust disease and chlorophyll analysis, but for nitrogen and lignin contents, nonlinear models achieved better results. As the first comprehensive study to model switchgrass sustainability traits from UAV-based remote sensing, these results suggest that this methodology can be utilized for switchgrass high-throughput phenotyping in the field.
We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear model predictive control (MPC). Contrary to approximate MPC, DPC does not require supervision by an expert controller. Instead, a system dynamics model is learned from a small dataset of recorded observations of the perturbed system's dynamics and the control law is optimized offline by interaction with the learned system model. The DPC method is based on two sequential steps, i) system identification using a constrained neural state-space model, and ii) optimization of an explicit control law parametrized by another neural network in closed-loop simulation with the identified neural state-space model. The combination of a differentiable closed-loop system and penalty methods for constraint handling of system outputs and inputs allows us to optimize the control law's parameters directly by backpropagating economic MPC loss through the learned system model. By incorporating domain knowledge and leveraging established techniques from optimal control, our method leverages deep neural networks as nonlinear function approximators for system identification and control while avoiding concomitant costs of intractably large datasets, and computationally expensive over-parametrized models. The scalability, data efficiency, and constrained optimal control capability of the proposed DPC method are demonstrated in simulation using a multi-zone building emulator.
Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.