Results for “nonlinear regression” — Page 8

DOE OSTI2023

AI-Based EMT Dynamic Model of PV Systems

Several electromagnetic transient (EMT) dynamic modeling methods are available to model systems like photovoltaic (PV) plants, wind power plants, variable-speed drives, among others. The methods include: (a) physics-based models and (b) data-driven models. The physics-based dynamic models may include high-fidelity switched system model and average-value model that both require the control algorithms included in the models. However, manufacturers typically prefer to provide black-box models to avoid disclosing proprietary. One of the solutions to prevent disclosing control algorithms is the use of data-driven dynamic EMT models of PV systems. In this paper, data-driven dynamic EMT model based on artificial intelligence (AI) algorithms are presented. The AI algorithms evaluated include convolutional neural networks, recurrent neural networks, and nonlinear auto-regressive exogenous model. Automation in generating data and training these models is also discussed in this paper. The results generated by the best AI algorithms have been observed to be greater than 95 % accurate.

Debnath, Suman↗

NASA NTRS2000

Determining a Prony Series for a Viscoelastic Material From Time Varying Strain Data

In this study a method of determining the coefficients in a Prony series representation of a viscoelastic modulus from rate dependent data is presented. Load versus time test data for a sequence of different rate loading segments is least-squares fitted to a Prony series hereditary integral model of the material tested. A nonlinear least squares regression algorithm is employed. The measured data includes ramp loading, relaxation, and unloading stress-strain data. The resulting Prony series which captures strain rate loading and unloading effects, produces an excellent fit to the complex loading sequence.

Tzikang, Chen↗

NASA NTRS2017

Statistical Approaches for the Definition of Landslide Rainfall Thresholds and their Uncertainty Using Rain Gauge and Satellite Data

Models for forecasting rainfall-induced landslides are mostly based on the identification of empirical rainfall thresholds obtained exploiting rain gauge data. Despite their increased availability, satellite rainfall estimates are scarcely used for this purpose. Satellite data should be useful in ungauged and remote areas, or should provide a significant spatial and temporal reference in gauged areas. In this paper, the analysis of the reliability of rainfall thresholds based on rainfall remote sensed and rain gauge data for the prediction of landslide occurrence is carried out. To date, the estimation of the uncertainty associated with the empirical rainfall thresholds is mostly based on a bootstrap resampling of the rainfall duration and the cumulated event rainfall pairs (D,E) characterizing rainfall events responsible for past failures. This estimation does not consider the measurement uncertainty associated with D and E. In the paper, we propose (i) a new automated procedure to reconstruct ED conditions responsible for the landslide triggering and their uncertainties, and (ii) three new methods to identify rainfall threshold for the possible landslide occurrence, exploiting rain gauge and satellite data. In particular, the proposed methods are based on Least Square (LS), Quantile Regression (QR) and Nonlinear Least Square (NLS) statistical approaches. We applied the new procedure and methods to define empirical rainfall thresholds and their associated uncertainties in the Umbria region (central Italy) using both rain-gauge measurements and satellite estimates. We finally validated the thresholds and tested the effectiveness of the different threshold definition methods with independent landslide information. The NLS method among the others performed better in calculating thresholds in the full range of rainfall durations. We found that the thresholds obtained from satellite data are lower than those obtained from rain gauge measurements. This is in agreement with the literature, where satellite rainfall data underestimate the 'ground' rainfall registered by rain gauges.

landslide prediction↗

NASA NTRSDate not supplied

Hybrid Model Based Approaches for Systems Health Management and Prognostics

To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision making. In principle, data driven approaches can replace expensive experimental test-setups as well as reduce the number of simulations needed to explore, e.g., the parametric space of a multi-parameter model. Nonetheless, the limitations of pure data-driven methods came to light rather quickly, at least for some industries. In many industrial applications, data acquisition is costly, and the volume of data that can be collected does not satisfy the requirements for an effective model training and cross-validation. Therefore, some recent works in the area of machine learning is focusing on blending physics with data-driven algorithms, thus mitigating the drawbacks of the two approaches and emphasizing respective advantages. Partial physical knowledge of the problem can aid the learning process by “guiding” the algorithm towards efficient solutions that satisfy the physics driving the system behavior. The result is a hybrid modeling approach combining physical knowledge as well data driven methods to develop a unified hybrid approach. A hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety critical systems is presented. In this framework, physics-based performance models infer unobservable model parameters related to the system's components health solving a calibration problem in the deep learning approach.

Hybrid Modeling↗

NASA NTRSDate not supplied

Systems Health Management and Prognostics Approaches for Electric Aircrafts

As more and more electric vehicles emerge in our daily operation progressively, a very critical challenge lies in the prediction of remaining driving flying time/distance for the flying vehicles. This information is important, particularly in the case of auto vehicles, because such vehicles can become self-aware, autonomously compute its own capabilities, and identify how to best plan and successfully complete vehicular missions safely. In case of electric aircrafts, computing the remaining flying time is also safety-critical, since an aircraft that runs out of power (battery charge) while in the air will eventually lose control leading to catastrophe. To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision-making. A systematic prediction framework is implemented to identify all possible sources of uncertainty, quantify each of them individually, and mathematically estimate their combined effect on the system-level quantity of interest, in this case, the remaining flying time/distance of the unmanned aircraft. Note - This presentation contains all previously published information.

Systems Health Managent↗

NASA NTRSDate not supplied

Hybrid Approaches to Systems Health Management and Prognostics

To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision making. In principle, data driven approaches can replace expensive experimental test-setups as well as reduce the number of simulations needed to explore, e.g., the parametric space of a multi-parameter model. Nonetheless, the limitations of pure data-driven methods came to light rather quickly, at least for some industries. In many industrial applications, data acquisition is costly, and the volume of data that can be collected does not satisfy the requirements for an effective model training and cross-validation. Therefore, some recent works in the area of machine learning is focusing on blending physics with data-driven algorithms, thus mitigating the drawbacks of the two approaches and emphasizing respective advantages. Partial physical knowledge of the problem can aid the learning process by “guiding” the algorithm towards efficient solutions that satisfy the physics driving the system behavior. The result is a hybrid modeling approach combining physical knowledge as well data driven methods to develop a unified hybrid approach. A hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety critical systems is presented. In this framework, physics-based performance models infer unobservable model parameters related to the system's components health solving a calibration problem in the deep learning approach.

Systems Health Management↗

NASA NTRS2022

Hybrid Model Based Approaches for Systems Health Management and Prognostics

This is a previously approved and published presentation. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Present achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision-making. In principle, data-driven approaches can replace expensive experimental test-setups as well as reduce the number of simulations needed to explore, e.g., the parametric space of a multi-parameter model. Nonetheless, the limitations of pure data-driven methods came to light rather quickly, at least for some industries. In many industrial applications, data acquisition is costly, and the volume of data that can be collected does not satisfy the requirements for effective model training and cross-validation. Therefore, some recent works in the area of machine learning is focusing on blending physics with data-driven algorithms, thus mitigating the drawbacks of the two approaches and emphasizing respective advantages. Partial physical knowledge of the problem can aid the learning process by “guiding” the algorithm towards efficient solutions that satisfy the physics driving the system behavior. The result is a hybrid modeling approach combining physical knowledge as well data-driven methods to develop a unified hybrid approach. A hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety-critical systems is presented. In this framework, physics-based performance models infer unobservable model parameters related to the system's components health solving a calibration problem in the deep learning approach.

Prognostics↗

NASA NTRSDate not supplied

Health Monitoring and Prognostics for Electric Aircrafts

As more and more electric vehicles emerge in our daily operation progressively, a very critical challenge lies in the prediction of remaining driving flying time/distance for the flying vehicles. This information is important, particularly in the case of auto vehicles, because such vehicles can become self-aware, autonomously compute its own capabilities, and identify how to best plan and successfully complete vehicular missions safely. In case of electric aircrafts, computing the remaining flying time is also safety-critical, since an aircraft that runs out of power (battery charge) while in the air will eventually lose control leading to catastrophe. To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision-making. A systematic prediction framework is implemented to identify all possible sources of uncertainty, quantify each of them individually, and mathematically estimate their combined effect on the system-level quantity of interest, in this case, the remaining flying time/distance of the unmanned aircraft. Note - This presentation contains all previously approved and published information.

Systems Health Managent↗

NASA NTRSDate not supplied

Physics Informed Neural Nets for Systems Health Management

To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Development in data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. The research work presents application of physics-informed neural nets application to a representative electric powertrain for unmanned aerial vehicles. The model is composed of physics-derived and empirical equations, integrated with connected networks that are strategically placed within the model to substitute equations that are subject to large uncertainty. Polynomial fit driven by heuristics or empirical observations can be substituted by more flexible networks that can minimize the error between model predictions and observations without being restricted to a predefined functional form. This modeling strategy allows training of networks deep inside the model and unknown parameters in a single learning stage.

Physics Informed↗

DOE OSTI2025

End–to–End Metasurface Design for Temperature Imaging via Broadband Planck‐Radiation Regression

A theoretical framework is presented for temperature imaging from long-wavelength infrared (LWIR) thermal radiation (e.g., 8–12 µm) through the end-to-end design of a metasurface-optics frontend and a computational-reconstruction backend. A new nonlinear reconstruction algorithm, “Planck regression”, is introduced to reconstruct the temperature map from a gray scale sensor image, even in the presence of severe chromatic aberration, by exploiting black body and optical physics particular to thermal imaging. This algorithm is combined with an end-to-end approach that optimizes manufacturable, single-layer metasurfaces to yield the most accurate reconstruction. The designs demonstrate high-quality, noise-robust reconstructions of arbitrary temperature maps (including completely random images) in simulations of an ultra-compact thermal-imaging device. Here, it is also shown that Planck regression is much more generalizable to arbitrary images than a straightforward neural-network reconstruction, which requires a large training set of domain-specific images.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Efficient Data-Driven Geologic Feature Characterization from Pre-stack Seismic Measurements using Randomized Machine-Learning Algorithm

Conventional seismic techniques for detecting the subsurface geologic features are challenged by limited data coverage, computational inefficiency and subjective human factors. We developed a novel data-driven geological feature characterization approach based on pre-stack seismic measurements. Our characterization method employs an efficient and accurate machine learning method to extract useful subsurface geologic features automatically. Specifically, we use kernel ridge regression to account for the nonlinear relationship between seismic data and geological features. We moreover employ kernel tricks to avoid the explicit nonlinear mapping and infinite dimension of feature space. Yet, the conventional kernel ridge regression can be computationally prohibitive because of the large volume of seismic measurements. We employ a data reduction technique in combination with the conventional kernel ridge regression method to improve the computational efficiency and reduce memory usage. In particular, we utilize a randomized numerical linear algebra technique, named Nyström method, to effectively reduce the dimensionality of the feature space without compromising the information content required for accurate characterization. We provide thorough computational cost analysis to show the efficiency of our new geological feature characterization methods. We validate the performance of our method in characterizing geologic fault zones because faults play an important role in various subsurface applications. Our numerical examples demonstrate that our new characterization method significantly improves the computational efficiency while maintaining comparable accuracy. Interestingly, we demonstrate that our approach yields a speedup ratio on the order of ~102 to ~103 in a multicore computational environment.

58 GEOSCIENCES↗

DOE OSTI2019

Unscented Kalman Filter-based Unbiased Minimum-Variance Estimation for Nonlinear Systems with Unknown Inputs

This paper proposes an unscented Kalman filter (UKF)-based unbiased minimum-variance estimation (UMV) method for the nonlinear system with unknown inputs. By utilizing the statistical linerization, the nonlinear system and measurement functions are transformed into a “linear-like” regression form. The latter preserves the nonlinearity of the system and the measurement models. To this end, the unknown inputs can be estimated by the weighted least-squares. This “linear-like” regression form also allows us to resort to the UMV state estimation framework for the development of new nonlinear filter to handle unknown inputs. Specifically, two approaches have been developed: 1) given the estimated inputs, we derive a filter by minimizing the trace of the state error covariance matrix; 2) without input estimation, we derive the filter by minimizing the trace of the state error covariance matrix subject to a constraint imposed on the gain matrix. We prove that these two approaches provide the same results. Numerical results validate the effectiveness of the proposed method.

Unscented Kalman filter, unbiased minimumvariance ↗

DOE OSTI2021

Deterministic symbolic regression with derivative information: General methodology and application to equations of state

Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real–world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. Herein we present a novel deterministic mixed–integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics–based constraints on the first and second derivatives.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Prediction of Subsidence of Buildings as a Result of Earthquakes by Gaussian Process Regression

Subsidence of a foundation caused by liquefaction of sandy soil is a critical step in the creation of a building. Seven measured indicators of soil liquefaction in the course of an earthquake were selected as key impacting indicators that predict subsidence of a building. These indicators are the earthquake intensity EI, length–height ratio L/H, average contact pressure p, width-depth ratio, relative density D{sub R}, thickness of the non-liquefied layer, and the depth of the gravel layer. Furthermore, as a probabilistic machine learning kernel and powerful tool for solving highly nonlinear problems, Gaussian process regression (GPR model) can meet execution time requirements and assure a high level of precision of subsidence prediction due to the intrinsic defects of theoretical analysis and numerical calculation. A total of 41 groups of typical cases were first selected as a training sample and 20 groups of typical cases were defined as a test sample, where these cases possess input test value and were obtained at the yield of the prediction accuracy from the GPR model. Next, the PLS method, MLR method and LSSVM method were selected to verify the validity and reliability of the GPR model. Finally, the simulation result shows that the GPR model can improve the prediction precision for the case of the above problems and is of great value for practical applications.

58 GEOSCIENCES↗

DOE OSTI2016

Estimation of trabecular bone parameters in children from multisequence MRI using texture-based regression

Purpose: This paper presents a statistical approach for the prediction of trabecular bone parameters from low-resolution multisequence magnetic resonance imaging (MRI) in children, thus addressing the limitations of high-resolution modalities such as HR-pQCT, including the significant exposure of young patients to radiation and the limited applicability of such modalities to peripheral bones in vivo. Methods: A statistical predictive model is constructed from a database of MRI and HR-pQCT datasets, to relate the low-resolution MRI appearance in the cancellous bone to the trabecular parameters extracted from the high-resolution images. The description of the MRI appearance is achieved between subjects by using a collection of feature descriptors, which describe the texture properties inside the cancellous bone, and which are invariant to the geometry and size of the trabecular areas. The predictive model is built by fitting to the training data a nonlinear partial least square regression between the input MRI features and the output trabecular parameters. Results: Detailed validation based on a sample of 96 datasets shows correlations >0.7 between the trabecular parameters predicted from low-resolution multisequence MRI based on the proposed statistical model and the values extracted from high-resolution HRp-QCT. Conclusions: The obtained results indicate the promise of the proposed predictive technique for the estimation of trabecular parameters in children from multisequence MRI, thus reducing the need for high-resolution radiation-based scans for a fragile population that is under development and growth.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

Biomass char gasification kinetic rates compared to data, including ash effects

This investigation provides both experimental and theoretical analyses of biomass char gasification kinetics over 1150–1350 °C in the environment of CO 2 , H 2 O and combinations of these reactants. The experimental data include continuous measurements of particle mass, external and internal temperatures, shape, and size with periodic but not continuous measurements of char porosity, pore size distribution, and pore surface area. The model describes heterogeneous char gasification for poplar wood, corn stover and switchgrass in different shapes and industrially relevant sizes (12.5 mm and smaller). Nonlinear least-squares regression produces optimized power-law model parameters for global kinetics that describe biomass char gasification with respect to both CO 2 and H 2 O separately and in combination. A single set of kinetic parameters describes reaction rates for all three fuels. Model simulations agree with measured data at all stages of char conversion even though the observed mass loss rates change significantly with conversion. In conclusion, the change in rate with conversion depends strongly on ash content, and this investigation provides a simple and theoretically based reaction rate expression that includes the effect of inert ash occupying an increasing portion of the reactive surface with increased conversion.

09 BIOMASS FUELS↗

DOE OSTI2024

Integration and Optimization of a Waste Heat Driven Organic Rankine Cycle for Power Generation in Wastewater Treatment Plants

The study focuses on achieving energy self-sufficiency in Wastewater Treatment Plants by proposing a comprehensive model for integrating, sizing, and optimizing an Organic Rankine Cycle system. The Organic Rankine Cycle system is designed to utilize waste heat from the gensets at As Samra Wastewater Treatment Plant in Jordan, where it will contribute to the overall electrical energy supply of the plant. Real data from As Samra Wastewater Treatment Plant is used to model and calculate the available waste heat using TRNSYS® software. The Organic Rankine Cycle model is then developed using ASPEN PLUS® software to explore the impact of operational parameters and determine their optimal values for maximizing the plant's energy profile. An economic analysis is conducted to assess the feasibility of the proposed model, considering system components, installation, operation, and maintenance costs. To optimize the Organic Rankine Cycle system, the study employs the Multi-Output Support Vector Regression technique to capture nonlinear relationships between independent variables (fluid type, turbine inlet pressure, turbine inlet temperature, turbine outlet pressure, and mass flow rate) and dependent variables (pump power input, waste heat input, and turbine specific work). The Osprey optimization algorithm is used to address the multi-objective optimization problem, with the proposed Pareto-based Osprey Optimization Algorithm and the Multi-Objective Particle Swarm Optimization technique being employed to evaluate critical performance and economic parameters such as system thermal efficiency, net power output, and the levelized cost of electricity. The results of the optimization strategies indicate that the M-SVR model's prediction accuracy is significantly improved after parameter optimization, with the model returning high R 2 and low Mean Square Error values of 0.991 and 0.00216, respectively. The Pareto-Based Osprey Optimization Algorithm optimizer identifies the best working fluid as Isobutane/Isopentane in a ratio of 66:34, with optimal turbine inlet pressure and temperature of 15 bars and 218 °C, respectively. In conclusion, the Organic Rankine Cycle model at these optimal conditions achieves a cycle efficiency of 19.93% and an Levelized Cost of Electricity value of 0.0353 USD/kWh.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS1971

The thunderstorm forecasting system at the Kennedy Space Center.

One of the major problems concerning meteorologists at the Kennedy Space Center, Fla, involves the forecasting of thunderstorm activity and associated adverse weather phenomena. The purpose of the study is to outline some of the more successful diagnostic tools which have been developed to aid the forecaster. These involve a variety of statistical procedures including conditional probabilities, exposure-period probabilities, and systems of multiple-regression equations based on nonlinear predictors.

Charles J Neumann↗