Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “regression”

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.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Multiobjective Constrained Symbolic Regression for Predictive Modeling of Material Creep Behavior

When creep testing is repeated on samples of the same alloy under the same parametric conditions (i.e., stress and temperature), the resulting strain/time curves can vary from each other considerably as shown in Figure 1 [1]. The time required to creep test a material to rupture can extend to the order of years. Because of this, a numerical model that can quickly analyze the incomplete results of an ongoing experiment to predict 1) the incomplete portion of the strain/time curve leading up to the rupture point and 2) the rupture point itself would be of great utility to the materials community. Such a model has the potential to save 1) the time required to finish running the experiment to rupture 2) the associated monetary cost of finishing said experiment. Furthermore, it would be advantageous if the predictive model could give a parametric function modeling strain/time curves for material scientists to investigate the impact of the temperature and stress parameters on the resulting creep behavior. This work introduces a piecewise symbolic regression algorithm to predict the remainder of the strain/time curve. Preliminary results show good model performance.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Proxy quality control of biomass particles using thermogravimetric analysis and Gaussian process regression models

Abstract The temperature experienced by reactants during preparation in a reactor is a key component in determining the yield and homogeneity of usable chemical products such as biomass particles. Thermocouples with sensors can be used to monitor spatial temperature gradients within reactors but these sensors are often too expensive and/or invasive. The present work proposes a strategy to identify optimal machine learning models to infer the maximum effective temperature experienced by particles during oxidative biomass torrefaction using key thermochemical combustion parameters. The maximum rate of weight loss, the corresponding temperature, and fixed carbon content on a dry‐ash‐free basis are used as literature‐based predictor variables obtained from thermogravimetric analysis. The evaluation of 24 machine‐learning models using the standard tenfold cross‐validation method suggests that the exponential Gaussian process regression (GPR) model is the most effective, followed by other GPR models. These high‐performing GPR models were also utilized to predict the effective preparation temperature distribution of reactor‐produced biomass particles under eight conditions of varying residence time and air‐to‐biomass ratio. The effective preparation temperature and residence time of individual biomass particles were then encoded into the torrefaction severity factor and used to estimate the energy yield of the reactor output as a novel quality control method. © 2023 The Authors. Biofuels, Bioproducts and Biorefining published by Society of Industrial Chemistry and John Wiley & Sons Ltd.

09 BIOMASS FUELS↗
DOE OSTI2023

Probabilistic partition of unity networks for high–dimensional regression problems

We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the target function is approximated by a mixture of experts model on a low-dimensional manifold, where each cluster is associated with a fixed-degree polynomial. We present a training strategy that leverages the expectation maximization (EM) algorithm. During the training, we alternate between (i) applying gradient descent to update the DNN coefficients; and (ii) using closed-form formulae derived from the EM algorithm to update the mixture of experts model parameters. Under the probabilistic formulation, step (ii) admits the form of embarrassingly paralleliazable weighted least-squares solves. The PPOU-Nets consistently outperform the baseline fully-connected neural networks of comparable sizes in numerical experiments of various data dimensions. Here, we also explore the proposed model in applications of quantum computing, where the PPOU-Nets act as surrogate models for cost landscapes associated with variational quantum circuits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Prediction of Creep-Induced Strain Using a Symbolic Regression-Based Model

Material creep under high-temperature conditions limits the lifetime and safety of structural systems such as advanced nuclear reactors. Conventional creep testing is slow and often produces inconsistent results across nominally identical experiments, making lifetime prediction uncertain. Here, to address these challenges, this work develops a data-driven symbolic regression (SR) model that consolidates results from duplicate creep tests and predicts the remaining strain-time curve of an ongoing experiment. The method uses piece-wise multi-objective SR with physical constraints to generate analytic, interpretable functions describing transient creep strain. Applied to Inconel Alloy 617 data, the approach achieved relative mean absolute errors of 1.0–9.5%, providing closed-form predictions of strain evolution. These results demonstrate a first step toward reducing the duration and cost of long-term creep testing while retaining physically interpretable model forms.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold

This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by projecting it onto a Grassmann manifold. This point-wise linear dimensionality reduction harnesses the structural information to assess the similarity between solutions at different points in the input parameter space. The method utilizes a solution clustering approach in order to identify regions of the parameter space over which solutions are sufficiently similarly such that they can be interpolated on the Grassmannian. In this clustering, the reduced-order solutions are partitioned into disjoint clusters on the Grassmann manifold using the eigen-structure of properly defined Grassmannian kernels and, the Karcher mean of each cluster is estimated. Then, the points in each cluster are projected onto the tangent space with origin at the corresponding Karcher mean using the exponential mapping. For each cluster, a Gaussian process regression model is trained that maps the input parameters of the system to the reduced solution points of the corresponding cluster projected onto the tangent space. Using this Gaussian process model, the full-field solution can be efficiently predicted at any new point in the parameter space. In certain cases, the solution clusters will span disjoint regions of the parameter space. In such cases, for each of the solution clusters we utilize a second, density-based spatial clustering to group their corresponding input parameter points in the Euclidean space. The proposed method is applied to two numerical examples. Here, the first is a nonlinear stochastic ordinary differential equation with uncertain initial conditions where the surrogate is used to predict the time history solution. The second involves modeling of plastic deformation in a model amorphous solid using the Shear Transformation Zone theory of plasticity, where the proposed surrogate is used to predict the full strain field of a material specimen under large shear strains.

42 ENGINEERING↗
DOE OSTI2024

A crystal-plasticity-informed Gaussian Process Regression model to capture anisotropy in single crystal shape memory alloys

This work presents a machine learning (ML) framework that model the anisotropic actuation responses in a shape memory alloy. A Gaussian Process Regression (GPR) based ML model is trained on a set of different crystal orientations subjected to different actuation conditions. The training employed thermo-mechanical responses from a crystal-plasticity model that captures phase-transformation, stress-induced plasticity, and transformation-induced plasticity. Further, on training the GPR-ML model at fixed stress level for different orientations, it captured the thermo-mechanical responses accounting for the anisotropy, and predicted responses for new orientations with good accuracy. The GPR-ML model is able to capture the transformation temperature variations even when trained using multiple stress levels, and the transformation strain showed significant deviations. The developed GPR-ML model gave reasonable predictions for an unexplored sample set of orientations and loading conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Uncertain characterization of reservoir fluids due to brittleness of equation of state regression

Equations of state (EoS) play a central role in modeling the phase equilibrium of fluid mixtures. Their parameterization involves fitting a model to experimental data, i.e., solving a nonlinear, non-convex, multivariate optimization problem. The latter requires one to select design variables, domains of definition for each variable, and weights assigned to individual measurements. We demonstrate that subjective choices of an optimization algorithm and an initial guess also impact the regression process. Consequently, EoS predictions are fundamentally uncertain even after the EoS tuning to a limited set of experimental data points. We demonstrate this observation for two hydrocarbon reservoir fluids, in which five properties of the heaviest carbon fraction are treated as design variables. While all the optimization algorithms and initial guesses match experimental data for the gas and liquid properties, the resulting EoS parameterizations lead to dramatically different predictions of the fluid’s thermophysical behavior in the unsampled pressure and temperature regions. In conclusion, we propose the probabilistic treatment of design variables to quantify the predictive uncertainty of the resulting fluid models.

15 GEOTHERMAL ENERGY↗
DOE OSTI2026

Efficient data-driven regression for reduced-order modeling of spatial pattern formation

We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically accurate numerical simulations. The method can be applied to general nonlinear systems through the use of polynomial model form, while not requiring knowledge of the underlying physical model, governing equations, or numerical solvers. The process of learning ROMs is posed as a low-cost least-squares problem in a reduced-order subspace identified via Proper Orthogonal Decomposition (POD). Numerical experiments on classical pattern-forming systems–including the Schnakenberg and Mimura–Tsujikawa models–demonstrate that higher-order surrogate models significantly improve prediction accuracy while maintaining low computational cost. The proposed method provides a flexible, non-intrusive model reduction framework, well suited for the analysis of complex spatio-temporal pattern formation phenomena.

Data-driven modeling↗
DOE OSTI2023

Complementing a continuum thermodynamic approach to constitutive modeling with symbolic regression

Here, an interpretable machine learning method, physics-informed genetic programming-based symbolic regression (P-GPSR), is integrated into a continuum thermodynamic approach to developing constitutive models. The proposed strategy for combining a thermodynamic analysis with P-GPSR is demonstrated by generating a yield function for an idealized material with voids, i.e., the Gurson yield function. First, a thermodynamic-based analysis is used to derive model requirements that are exploited in a custom P-GPSR implementation as fitness criteria or are strongly enforced in the solution. The P-GPSR implementation improved accuracy, generalizability, and training time compared to the same GPSR code without physics-informed fitness criteria. The yield function generated through the P-GPSR framework is in the form of a composite function that describes a class of materials and is characteristically more interpretable than GPSR-derived equations. The physical significance of the input functions learned by P-GPSR within the composite function is acquired from the thermodynamic analysis. Fundamental explanations of why the implemented P-GPSR capabilities improve results over a conventional GPSR algorithm are provided.

42 ENGINEERING↗
DOE OSTI2024

Generation and validation of comprehensive synthetic weather histories using auto-regressive moving-average models

As energy system design moves to more complex methods of optimization including machine learning there is a significant need for more weather data than is available. One method to solve this is using synthetic data models such as the auto-regressive moving-average (ARMA) model which has been frequently utilized to create such data. This paper looks at extending the ARMA algorithm to generate solar components through the use of clearsky detrending, maintaining vector relationships and by leveraging physical relationships. The method for the creation of entirely synthetic weather data files including key weather variables for energy system analysis is presented. Furthermore, a detailed comparison of energy system simulations utilizing both real and synthetic data is made using NREL’s System Advisor Model. Whilst good agreement is made for the solar variables, and other weather variables, ARMA methods often fail to capture the standard deviation and skew of annual weather distributions. Vector-ARMA is shown to maintain correlations between variables and thus generate data sets that perform similarly in energy system design. Here, it is finally shown that the ARMA method fails to preserve day-today correlations in weather variables and thus over-predicts optimal energy storage by 21% for a residential solar application.

42 ENGINEERING↗
DOE OSTI2022

Characterization of Acoustic Emissions From Analogue Rocks Using Sparse Regression‐DMDc

Abstract Moisture loss in rock is known to generate acoustic emissions (AE). Phenomena that result in AE during drying are related to the movement of fluids through the pores and induced‐cracks that arise from differential mineral shrinkage, especially in clay‐bearing rock. AE from the movement of fluids occurs from the reconfiguration of fluid interfaces during drying, while AE from mineral shrinkage involves the debonding within or between minerals. Here, analogue rock samples were used to examine the differences in the AE signatures when one or both AE source‐types are present. An unsupervised sparse regression model, Dynamic Mode Decomposition with control, that extends Dynamic Mode Decomposition is used to characterize the AE signals recorded during the drying of porous analogue rock samples fabricated with ordinary Portland cement, with and without clay. This method can effectively and accurately reconstruct acoustic signals emitted from samples that only experience moisture loss without cracking. However, the method struggles to reconstruct signals from samples with intricate crack networks that formed during drying because AE generating mechanisms can emit contemporaneously, and the resulting waves propagate through drying‐induced cracks that can lead to multiple internal reflections. Thus, the differential reconstruction accuracy of time series generated by different underlying physical processes provides a robust filter for reducing large data catalogs. In general, both dynamics and sparse initiating events are learned directly from data and this method exposes a data hierarchy based on the complexity of the intrinsic dynamics.

58 GEOSCIENCES↗
DOE OSTI2022

Symbolic regression development of empirical equations for diffusion in Lennard-Jones fluids

Symbolic regression (SR) with a multi-gene genetic program has been used to elucidate new empirical equations describing diffusion in Lennard-Jones (LJ) fluids. Some examples include equations to predict self-diffusion in pure LJ fluids and equations describing the finite-size correction for self-diffusion in binary LJ fluids. The performance of the SR-obtained equations was compared to that of both the existing empirical equations in the literature and to the results from artificial neural net (ANN) models recently reported. It is found that the SR equations have improved predictive performance in comparison to the existing empirical equations, even though employing a smaller number of adjustable parameters, but show an overall reduced performance in comparison to more extensive ANNs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Generalizing the Gurson model using symbolic regression and transfer learning to relax inherent assumptions

Abstract To generate material models with fewer limiting assumptions while maintaining closed-form, interpretable solutions, we propose using genetic programming based symbolic regression (GPSR), a machine learning (ML) approach that describes data using free-form symbolic expressions. To maximize interpretability, we start from an analytical, derived material model, the Gurson model for porous ductile metals, and systematically relax inherent assumptions made in its derivation to understand each assumption’s contribution to the GPSR model forms. We incorporate transfer learning methods into the GPSR training process to increase GPSR efficiency and generate models that abide by known mechanics of the system. The results show that regularizing the GPSR fitness function is critical for generating physically valid models and illustrate how GPSR allows a high level of interpretability compared with other ML approaches. The method of systematic assumption relaxation allows the generation of models that address limiting assumptions found in the Gurson model, and the symbolic forms allow conjecture of decreased material strength due to void interaction and non-symmetric void shapes.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Enhancing Solar Power Forecasting with Regularized Constrained Quantile Regression Averaging and Bootstrapping Techniques

Probabilistic solar power forecasting (SPF) plays an essential role in optimizing power-grid operations by quantifying the forecast uncertainty. To improve the accuracy and robustness of probabilistic SPF, this paper introduces the regularized constrained quantile regression averaging (rCQRA) method to combine outputs from multiple PSPF models. In addition, a bootstrapping method was used to quantify model uncertainty, providing insights into the reliability and significance of each ensemble component. To evaluate its efficacy, the proposed rCQRA method is used to integrate four PSPF methods. The resulting SPF models are trained and validated using a real-world six-year dataset from a rooftop solar plant in the USA. The performance of the proposed rCQRA method is evaluated and compared with two benchmark methods under three categories of weather conditions. It is shown that the rCQRA method has superior performance in its forecast reliability, sharpness, and accuracy.

Ensemble learning, probabilistic solar power forec↗
DOE OSTI2022

Inference for Nonparanormal Partial Correlation via Regularized Rank-Based Nodewise Regression

Abstract Partial correlation is a common tool in studying conditional dependence for Gaussian distributed data. However, partial correlation being zero may not be equivalent to conditional independence under non-Gaussian distributions. In this paper, we propose a statistical inference procedure for partial correlations under the high-dimensional nonparanormal (NPN) model where the observed data are normally distributed after certain monotone transformations. The NPN partial correlation is the partial correlation of the normal transformed data under the NPN model, which is a more general measure of conditional dependence. We estimate the NPN partial correlations by regularized nodewise regression based on the empirical ranks of the original data. A multiple testing procedure is proposed to identify the nonzero NPN partial correlations. The proposed method can be carried out by a simple coordinate descent algorithm for lasso optimization. It is easy-to-implement and computationally more efficient compared to the existing methods for estimating NPN graphical models. Theoretical results are developed to show the asymptotic normality of the proposed estimator and to justify the proposed multiple testing procedure. Numerical simulations and a case study on brain imaging data demonstrate the utility of the proposed procedure and evaluate its performance compared to the existing methods. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Multi-Fidelity Gaussian Process Regression Method for Probabilistic Wind Farm Power Curve Estimation

Accurate estimation of the power curve for wind turbines or wind farms is crucial to ensure their efficient operation and management. However, conventional methods for power curve estimation rely either on expensive and infrequent measurements or on low-quality numerical simulations. Moreover, the majority of previous studies on power curve estimation for wind turbines or wind farms focused on deterministic estimation, which provides a point estimate of the relationship between wind speed and power generation. Nevertheless, the deterministic approach fails to consider the inherent uncertainty associated with wind energy production resulting from varying turbine characteristics. This can lead to inaccurate power generation estimation and suboptimal decisions regarding energy management. In this paper, a kernel density estimation (KDE) based Multi-Fidelity Gaussian Process Regression (MFGPR) model is proposed to fuse theoretical power curve data and the ground true measurements to create a mapping of wind speed and wind power. By conducting a case study on an actual wind farm in China, the efficacy of the proposed MFGPR model was demonstrated in characterizing the variability of wind power. The probabilistic MFGPR model was also able to generate confidence intervals that encompassed the measured power, thereby improving the accuracy and confidence in wind power estimation or wind resource assessment. Overall, the proposed MFGPR model offers a reliable approach to integrate high-fidelity ground measurements and theoretical power curve data, resulting in precise wind resource assessment and power estimation.

Gaussian process regression↗
DOE OSTI2021

Conditioned Simulation of Ground-Motion Time Series at Uninstrumented Sites Using Gaussian Process Regression

Ground-motion time series are essential input data in seismic analysis and performance assessment of the built environment. Because instruments to record free-field ground motions are generally sparse, methods are needed to estimate motions at locations with no available ground-motion recording instrumentation. In this study, given a set of observed motions, ground-motion time series at target sites are constructed using a Gaussian process regression (GPR) approach, which treats the real and imaginary parts of the Fourier spectrum as random Gaussian variables. Model training, verification, and applicability studies are carried out using the physics-based simulated ground motions of the 1906 Mw 7.9 San Francisco earthquake and Mw 7.0 Hayward fault scenario earthquake in northern California. Additionally, the method’s performance is further evaluated using the 2019 Mw 7.1 Ridgecrest earthquake ground motions recorded by the Community Seismic Network stations located in southern California. These evaluations indicate that the trained GPR model is able to adequately estimate the ground-motion time series for frequency ranges that are pertinent for most earthquake engineering applications. The trained GPR model exhibits proper performance in predicting the long-period content of the ground motions as well as directivity pulses.

58 GEOSCIENCES↗
DOE OSTI2024

Inverse prediction of PuO2 processing conditions using Bayesian seemingly unrelated regression with functional data

Over the past decade, a variety of innovative methodologies have been developed to better characterize the relationships between processing conditions and the physical, morphological, and chemical features of special nuclear material (SNM). Different processing conditions generate SNM products with different features, which are known as “signatures” because they are indicative of the processing conditions used to produce the material. These signatures can potentially allow a forensic analyst to determine which processes were used to produce the SNM and make inferences about where the material originated. This article investigates a statistical technique for relating processing conditions to the morphological features of PuO 2 particles. We develop a Bayesian implementation of seemingly unrelated regression (SUR) to inverse-predict unknown PuO 2 processing conditions from known PuO 2 features. Model results from simulated data demonstrate the usefulness of the technique. Applied to empirical data from a bench-scale experiment specifically designed with inverse prediction in mind, our model successfully predicts nitric acid concentration, while results for Pu concentration and precipitation temperature were equivalent to a simple mean model. Our technique compliments other recent methodologies developed for forensic analysis of nuclear material and can be generalized across the field of chemometrics for application to other materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗