Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Data Driven Analysis”

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 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Deep Koopman learning of nonlinear time-varying systems

Here this paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which results from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Data-driven design of molecular nanomagnets

Three decades of research in molecular nanomagnets have raised their magnetic memories from liquid helium to liquid nitrogen temperature thanks to a wise choice of the magnetic ion and coordination environment. Still, serendipity and chemical intuition played a main role. In order to establish a powerful framework for statistically driven chemical design, here we collected chemical and physical data for lanthanide-based nanomagnets, catalogued over 1400 published experiments, developed an interactive dashboard (SIMDAVIS) to visualise the dataset, and applied inferential statistical analysis. Our analysis shows that the Arrhenius energy barrier correlates unexpectedly well with the magnetic memory. Furthermore, as both Orbach and Raman processes can be affected by vibronic coupling, chemical design of the coordination scheme may be used to reduce the relaxation rates. Indeed, only bis-phthalocyaninato sandwiches and metallocenes, with rigid ligands, consistently present magnetic memory up to high temperature. Analysing magnetostructural correlations, we offer promising strategies for improvement, in particular for the preparation of pentagonal bipyramids, where even softer complexes are protected against molecular vibrations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Entropy and Boundary Based Adversarial Learning for Large Scale Unsupervised Domain Adaptation

Supervised semantic segmentation methods provide state-of-the-art performance, but their performance is limited by the amount of quality labeled data they need for training. Scarcity of labeled data and non-transferablity of models, due to cross-domain discrepancy makes it a bigger challenge for remote sensing imagery analysis. In this work, we approach this problem through adversarial learning, driven by entropy and boundary of region-of-interest for unsupervised domain adaptation. This concept helps with better boundary prediction and encourages target domain entropy maps (probability/uncertainty maps) to be similar to source domains. In particular, we showed that deriving informative entropy through the adversarial learning is essential to enable the adaptation. We used a large scale cross country building extraction dataset to validate the framework. The experimental results show the usefulness of considering boundary and entropy driven adversarial learning for adaptation.

Makkar, Nikhil↗
DOE OSTI2021

Soft X-ray measurements of transport and MHD activity in the core and edge NSTX plasma (Final Technical Report)

A comprehensive suite of innovative diagnostic instrumentation and techniques has been developed by the Johns Hopkins collaboration for measurements of transport and MHD activity in the core and edge of the National Spherical Torus Experiment (NSTX) at the Princeton Plasma Physics Laboratory (PPPL). These include ultrafast multi-energy poloidal soft X-ray arrays, high spatial resolution multi-energy tangential soft X-ray arrays, high spectral resolution transmission grating imaging VUV spectrometers and ultrafast bolometric arrays, which measure over a broad range of spatial, spectral, and temporal scales the emission from ohmic, RF, and beam driven NSTX plasmas. The instrumentation was designed to fulfill the specific measurement needs of the Spherical Torus (ST) magnetic fusion concept and is accompanied by a comprehensive set of numerical tools for data analysis and modeling, aimed at determining as many as possible plasma parameters and at extracting as much as possible physics information from NSTX experiments. The Johns Hopkins diagnostics have been and continue to be instrumental for essentially all the NSTX experiments. In addition, our own research and experiments using these diagnostics has led over the years to fundamental conclusions for the ST fusion physics, such as the establishment of near neoclassical impurity transport in the NSTX core and edge plasma, and the critical role of the Global Alfven Eigenmode (GAE) MHD activity for the ST core electron thermal transport. The Johns Hopkins Diagnostics continue to be operational on the upgraded NSTX-U and will provide key plasma information in its upcoming high field, current and power experimental campaigns. The present report summarizes the main technical characteristics and measurement capabilities of the diagnostic instrumentation and methods developed within our research and describes a key physics result achieved during this research. Success in our research was made possible also by the excellent support and cooperation of the NSTX research team and of PPPL researchers, who are warmly acknowledged here.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Machine Learning-Based Anomaly Detection for PMT Data Quality Monitoring in the SBN and DUNE

Maintaining high-quality detector data is essential for achieving the scientific objectives of the Short-Baseline Neutrino (SBN) Program at Fermilab. Current data quality monitoring (DQM) procedures rely primarily on threshold-based metrics and manual inspection of detector monitoring plots, making the detection of subtle or gradually developing anomalies both time-consuming and dependent on expert interpretation. This project developed and evaluated a machine-learning workflow for automatically identifying anomalous photomultiplier tube (PMT) channels in the Short-Baseline Near Detector (SBND) using optical-hit amplitude data. A Python-based analysis program was developed to process ROOT files, extract statistical features describing individual PMT amplitude distributions, and generate feature vectors for anomaly detection. These features were used to train an Isolation Forest model using data representing normal detector operation. The trained model was subsequently applied to independent detector runs to identify channels exhibiting statistically unusual behavior relative to the learned reference response. To support expert interpretation, the workflow generated complementary diagnostic products, including anomaly score distributions, normalized amplitude comparisons, decision-tree visualizations, and principal component analysis (PCA) projections. This project demonstrated the feasibility of integrating unsupervised machine learning into detector data-quality monitoring and developed a complete workflow for automated PMT performance assessment to aid expert-driven review. Beyond its technical contributions, the VFP appointment fostered a research collaboration between Aurora University and Fermilab and provided direct workforce development benefits by training the visiting faculty member in detector-scale machine-learning methods that are now being incorporated into undergraduate coursework and research. The methodology developed here provides a foundation for future applications to ProtoDUNE and other liquid argon time projection chamber (LArTPC) detectors, contributing to ongoing efforts to improve detector reliability, reduce manual monitoring requirements, and enable scalable data quality monitoring for future large-scale neutrino experiments, including the Deep Underground Neutrino Experiment (DUNE).

Colón Santana, Juan A. [Unlisted, US, IL]↗
NASA NTRS1985

Beam-driven ion cyclotron harmonic resonances in the terrestrial foreshock

A terrestrial upstream wave event which demonstrates multiple, ion cyclotron harmonic resonances between the interplanetary wave population and an observed proton beam is analyzed. The techniques and parameters employed in the data analysis are discussed, including the use of differential and band-pass filters. An upstream wave event demonstrating multiple harmonic waves is examined, and the instability analysis relevant to the ion beam observations thought to be responsible for that event is discussed. It is shown that an observed bi-Maxwellian ion beam is capable of generating right and left-hand polarized waves through ion cyclotron harmonic resonance.

Smith, C. W.↗
NASA NTRSDate not supplied

Towards a program of record of inland water quality: Exploiting present and heritage multispectral sensors for maximum information extraction

Degradation of Earth’s inland water resources due to anthropogenic perturbations and climate anomalies at both local and global scales continues to place human health at substantial risk. There is now a growing necessity to develop pragmatic approaches that allow timely and effective extrapolation of local processes, to spatially resolved global products, and to promote operational and sustainable resource policy management. This research exploits recent advancements in bio-optical modeling, cloud computing, and machine learning to enhance our capacity to leverage present and heritage satellite data. Recent research suggests that sensors with low spectral resolution, such as Sentinel 2 and Landsat missions, contain enough hidden spectral variation which can be exploited using data-driven approaches. The availability of three decades of archival imagery will open doors to discover global trends of eutrophication and increased cyanobacteria dominance and provide valuable insight to the development of predictive methodologies. Preliminary efforts in synthetic emulation of global natural inland waters will be discussed and contextualized against satellite radiometric measurement uncertainty, satellite data product uncertainties and causal signal ambiguity over the visible wavelength range, supported by high quality field and image data for selected inland aquatic sites. Insights on water quality estimation via data-driven machine learning models versus matrix inversions will be discussed, and how we can exploit spectral-spatial relationships in high spatial resolution data. A cross-sensor synergistic approach with detailed uncertainty analysis based on optical water types, will allow for unprecedented global snapshots of fine scale ecological dynamics of inland waters.

Inland↗
DOE OSTI2024

$Z$-Pinch Interferometry Analysis With the Fourier-Based TNT Code

Here, we present the analysis of interferometry diagnostics with the user-friendly Talbot Numerical Tool (TNT), a Fourier-based postprocessing code that enables real-time assessment of plasma systems. TNT performance was explored with visible and infrared interferometry in pulsed-power-driven Z -pinch configurations to expand its capabilities beyond Talbot X-ray interferometry in the high-intensity laser environment. TNT enabled accurate electron density characterization of magnetically driven plasma flows and shocks through phase-retrieval methods that did not require data modification or masking. TNT demonstrated enhanced resolution, detecting below 4 % fringe shift, which corresponds to 8.7 × 10 15 cm –2 within 28 μ m, approaching the laser probing system limit. TNT was tested against a well-known interferometry analysis software, delivering an average resolving power nearly ten times better (~28 μ m versus ~ 210 μ m) when resolving plasma ablation features. TNT demonstrated higher sensitivity when probing sharp electron density gradients in supersonic shocks. A maximum electron areal density of 4.1 × 10 17 cm –2 was measured in the shocked plasma region, and a minimum electron density detection of ~ 1.0 × 10 15 cm –2 was achieved. When probing colliding plasma flows, the calculations of the effective adiabatic index and the associated errors were improved from γ* = 2.6 ± 1.6 – 1.4 ± 0.2 with TNT postprocessing, contributing valuable data for the interpretation of radiative transport. Additional applications of TNT in the characterization of pulsed-power plasmas and beyond are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Toward Drilling the Perfect Geothermal Well: An International Research Coordination Network for Geothermal Drilling Optimization Supported by Deep Machine Learning and Cloud Based Data Aggregation

The EDGE project, supported by the U.S. Department of Energy Geothermal Technologies Office under award DE-EE0008793, established a data-driven framework for improving the efficiency, cost-effectiveness, and reliability of geothermal well drilling. The project focused on developing scalable data infrastructure, advanced machine learning and probabilistic models, and integrated analytics tools to support continuous drilling optimization. A central objective was to reduce geothermal drilling costs by up to seventy percent while minimizing the risk of well failure through predictive diagnostics and adaptive planning. Over the project period, a comprehensive data repository was designed and deployed, incorporating records from over one hundred geothermal wells across varied geological settings. This repository supported both structured and unstructured data and adhered to FAIR data principles, enabling provenance tracking, quality control, and standardized metadata. The project introduced automated ingestion pipelines and a cloud-hosted platform that facilitated access to raw, processed, and derived datasets. This infrastructure served as the foundation for model development and analysis. Machine learning workflows were developed to predict key drilling metrics including rate of penetration, non-productive time, and total drilling costs. Self-organizing maps and dimensionality reduction methods were used to uncover operational patterns and outliers, while supervised learning algorithms such as random forests and deep neural networks were applied to forecast performance outcomes. The models were validated on heterogeneous datasets from both U.S. and Icelandic fields, demonstrating variable but significant predictive accuracy. The results indicated that finer temporal resolution, inclusion of lithological data, and consistency in operational annotations could substantially improve model performance. The project also implemented process mining techniques to reconstruct state-transition models from drilling event logs. These models enabled the identification of deviations from optimal workflows and provided insights into recurring failure modes. Analysis of non-productive time highlighted the impact of equipment failures, geological challenges, and human factors, offering opportunities for targeted mitigation strategies. The EDGE Dashboard was developed as a web-based expert system integrating data visualization, model outputs, and user-driven queries. It provided an accessible interface for operators to explore historical data, evaluate predicted outcomes, and compare drilling scenarios. Initial feedback from project partners suggested that the dashboard could serve as a foundation for more advanced advisory and optimization tools. Overall, the EDGE project demonstrated the feasibility and value of applying modern data science techniques to geothermal drilling. It delivered a set of interoperable tools and models that can support more efficient, lower-risk well development. The findings point toward a viable path for transitioning from advisory analytics to semi-autonomous drilling systems, contingent on continued collaboration, expanded datasets, and field validation. The project results have immediate relevance for drilling operations, data management practices, and future geothermal R&D efforts aimed at achieving reliable, cost-competitive geothermal energy at scale.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Unsupervised Learning for Improved Gamma-Ray Spectrometry in Pixelated Cadmium Zinc Telluride (CZT) Detectors

Machine learning has been found to be ubiquitously useful across many industries, presenting an opportunity to improve radiation detection performance using data-driven algorithms. Improved detector resolution can aid in the detection, identification, and quantification of radionuclides. Here, in this work, a novel, data-driven, unsupervised learning approach is developed to improve detector spectral characteristics by learning, and subsequently rejecting, poorly performing regions of the pixelated detector. Feature engineering is used to fit individual characteristic photo peaks to a Doniach lineshape with a linear background model. Then, principal component analysis is used to learn a lower-dimension latent space representation of each photo peak where the pixels are clustered, and subsequently ranked, based on the cluster mean distance to an optimal point. Pixels within the worst cluster(s) are rejected to improve the full-width at half-maximum (FWHM) by 10% to 15% (relative to the bulk detector) at 50% net efficiency when applied to training data obtained from measurements of a 100 μCi 154 Eu source using a H3D M400i pixelated cadmium zinc telluride detector. These results compare well with, but do not outperform, a greedy algorithm that accumulates pixels in order of FWHM from lowest to highest used as a benchmark. In the future, this approach can be extended to include the detector energy and angular response. Finally, the model is applied to newly seen natural and enriched uranium spectra relevant for nuclear safeguards applications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Adaptive Data-Driven Deep-Learning Surrogate Model for Frontal Polymerization in Dicyclopentadiene

Frontal polymerization (FP) is a self-sustaining curing process that enables rapid and energy-efficient manufacturing of thermoset polymers and composites. Computational methods conventionally used to simulate the FP process are time-consuming, and repeating simulations are required for sensitivity analysis, uncertainty quantification, or optimization of the manufacturing process. Here, in this work, we develop an adaptive surrogate deep-learning model for FP of dicyclopentadiene (DCPD), which predicts the evolution of temperature and degree of cure orders of magnitude faster than the finite-element method (FEM). The adaptive algorithm provides a strategy to select training samples efficiently and save computational costs by reducing the redundancy of FEM-based training samples. The adaptive algorithm calculates the residual error of the FP governing equations using automatic differentiation of the deep neural network. A probability density function expressed in terms of the residual error is used to select training samples from the Sobol sequence space. The temperature and degree of cure evolution of each training sample are obtained by a 2D FEM simulation. The adaptive method is more efficient and has a better prediction accuracy than the random sampling method. With the well-trained surrogate neural network, the FP characteristics (front speed, shape, and temperature) can be extracted quickly from the predicted temperature and degree-of-cure fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Securing Grid-interactive Efficient Buildings (GEB) through Cyber Defense and Resilient System (CYDRES)

The DOE CYDRES project is driven by the urgent need to address critical research gaps in the domain of cyber-physical security of smart buildings, including Grid-interactive Efficient Buildings (GEBs). CYDRES, a real-time advanced building resilient platform, aims to enhance the cyber-attack-immune capabilities of buildings through multi-layered prevention, detection, and adaptation mechanisms. CYDRES consists of five key modules: a multi-layer network analyzer, an Automatic Fault Detection, Diagnosis, and Prognosis (AFDDP) framework, an intelligent mode selector, a cyber-resilient control framework, and a situation awareness platform. The Network Analyzer employs a data-driven framework that includes a protocol state learning tool and a CRF (Conditional Random Field) command validator. In Hardware-In-the-Loop (HIL) testbeds, it achieved 100% detection accuracy with a false alarm rate of 3%, validating its efficacy in identifying selected cyber-attacks. The AFDDP framework leverages pattern matching, PCA (Principal Component Analysis)-based strategies, and a DBN (Dynamic Bayesian Network)-based fault diagnosis approach to pinpoint the causes of physical system abnormalities using Building Automation System (BAS) data. In HIL experiments, the AFDDP module attained a detection accuracy of over 95% with a false alarm rate below 7%. Additionally, the fault detector utilized machine learning (Random Forest) and deep learning (Multi-Layer Perceptron) methods with acoustic sensor data to achieve a 100% fault detection accuracy in Heating, Ventilation, and Air-Conditioning (HVAC) equipment. The Mode Selector offered real-time impact analysis, allowing immediate actions to protect BASs in the face of emerging threats. The cyber-resilient control framework included an adaptive Model Predictive Control (MPC) and a measurement compensator, reducing temperature violations by up to 94% and improving the total demand flexibility by up to 70% in HIL experiments. Such HIL experiments covered a cyber-attack case and a physical fault case, showcasing CYDRES’ efficiency in maintaining operational continuity during threats. The situation awareness platform in Grafana enhanced real-time threat detection and response visualization, augmenting the operational awareness for building operators. CYDRES demonstrated high technical effectiveness in various test scenarios, particularly in HIL environments. The project's phased development approach ensured efficient use of resources, highlighting its practical feasibility and readiness for commercialization. By enhancing the security and resilience of building operations, CYDRES represents a significant advance in mitigating risks associated with cyber-physical systems, thereby enhancing public confidence in the safety of modern building infrastructure. Future directions for the project include expanding testing protocols, refining AFDDP methodologies, exploring more comprehensive resilient control strategies, and testing in real commercial buildings.

42 ENGINEERING↗
DOE OSTI2021

Predicting orientation-dependent plastic susceptibility from static structure in amorphous solids via deep learning

It has been a long-standing materials science challenge to establish structure-property relations in amorphous solids. Here we introduce a rotationally non-invariant local structure representation that enables different predictions for different loading orientations, which is found essential for high-fidelity prediction of the propensity for stress-driven shear transformations. This novel structure representation, when combined with convolutional neural network (CNN), a powerful deep learning algorithm, leads to unprecedented accuracy for identifying atoms with high propensity for shear transformations (i.e., plastic susceptibility), solely from the static structure in both two- and three-dimensional model glasses. The data-driven models trained on samples at one composition and a given processing history are found transferrable to glass samples with different processing histories or at different compositions in the same alloy system. Our analysis of the new structure representation also provides valuable insight into key atomic packing features that influence the local mechanical response and its anisotropy in glasses.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Focused Interest Groups Propel Innovation in the Emerging Data-Driven Hardware Ecosystem

Over the past several decades, the science of electron microscopy (EM) has risen to become one of the cornerstone approaches to understanding material structure, chemistry, and defects at exceptional spatial resolution. This rise can be attributed to the hard work of researchers and companies who have pushed the bounds of instrumentation and analysis, but it is also the result of advocacy by members of professional societies. Furthermore, such advocacy is exemplified by the Aberration Corrected EM (ACEM) focused interest group (FIG) of the Microscopy Society of America (MSA), which has played an important role in facilitating new hardware developments, promoting the exchange of ideas to catalyze discovery, and building the next generation of leaders in electron microscopy. From the early 2000s to the present, aberration correction has moved from proof-of-concept instrumentation to an established technique, providing unprecedented improvements in spatial and chemical resolution for breakthroughs in chemistry, physics, and materials science.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Search for Electron Neutrino Anomalies with the MicroBooNE Detector

The Micro Booster Neutrino Experiment (MicroBooNE) is a Liquid Argon Time Projection Chamber (LArTPC) located in the Booster Neutrino Beam at Fermi National Accelerator Laboratory. The experiment was devised to investigate a series of observed anomalies concerning short-baseline neutrino oscillation physics. The LArTPC technology enables the experiment to study neutrino-argon scattering with unprecedented detail.This thesis presents a cosmic-ray characterisation and rate measurement. The understanding of cosmic activity in the detector - MicroBooNE's dominant background - is then used to develop cosmic rejection tools. A flavour-agnostic neutrino selection is constructed, which forms the cornerstone of this and further analyses. Inclusive muon and electron charged-current neutrino interaction selections with unprecedented purity and efficiency are presented.The first fully-automated characterisation of electron neutrinos in a muon neutrino beam with the LArTPC detector technology is performed. The Booster Neutrino Beam has an energy peaking around 1GeV and an intrinsic electron content of approximately 0.5%. The analysis investigates electrons produced in charged-current electron neutrino interactions. The kinematics of the electrons are measured along with comparisons to simulation. Most of the systematic uncertainties are constrained using a data-driven sample of charged-current muon neutrino events. The measurement of electron neutrinos originating from the Booster Neutrino Beam is a crucial component towards understanding the nature of the observed excess of low-energy electromagnetic-like events at its predecessor, MiniBooNE.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Charged-Current Electron Neutrino Measurement with the MicroBooNE Detector

MicroBooNE is the first phase of Fermilab’s Short Baseline Neutrino (SBN) Liquid Argon Time Projection Chamber (LArTPC) programme.This proceeding outlays the first characterisation of electron neutrinos in a muon neutrino beam with the LArTPC detector technology. The Booster Neutrino Beam has an energy peaking around 1GeV and an electron content of approximately 0.5%. The analysis investigates electrons produced in charged-current electron neutrino interactions. The kinematics of the electrons are measured along with comparisons to simulation. Most of the systematic uncertainties are constrained using a data-driven sample of charged-current muon neutrino events. The measurement of electron neutrinos originating from the Booster Neutrino Beam is a crucial component to understand the nature of the observed excess of low energy electromagnetic-like events at MiniBooNE.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Enabling Renewable Energy While Protecting Wildlife: An Ecological Risk-Based Approach to Wind Energy Development Using Ecosystem-Based Management Values

Acceptance of wind energy development is challenged by stakeholders’ concerns about potential effects on the environment, specifically on wildlife, such as birds, bats, and (for offshore wind) marine animals, and the habitats that support them. Communities near wind energy developments are also concerned with social and economic impacts, as well as impacts on aesthetics, historical sites, and recreation and tourism. Lack of a systematic, widely accepted, and balanced approach for measuring the potential damage to wildlife, habitats, and communities continues to leave wind developers, regulators, and other stakeholders in an uncertain position. This paper explores ecological risk-based management (RBM) in wind energy development for land-based and offshore wind installations. This paper provides a framework for the adaptation of ecosystem-based management to wind energy development and examines that framework through a series of case studies and best management practices for applying risk-based principles to wind energy. Ten case studies indicate that wind farm monitoring is often driven by regulatory requirements that may not be underpinned by scientific questions. While each case applies principles of adaptive management, there is room for improvement in applying scientific principles to the data collection and analysis. Challenges and constraints for wind farm development to meet RBM framework criteria include collecting sufficient baseline and monitoring data year-round, engaging stakeholder facilitators, and bringing together large and diverse scientific teams. The RBM framework approach may provide insights for improved siting and consenting/permitting processes for regulators and their advisors, particularly in those nations where wind energy is still in the early development stages on land or at sea.

17 WIND ENERGY↗
NASA NTRS1989

Experimental verification of dynamic simulation

The dynamics model here is a backhoe, which is a four degree of freedom manipulator from the dynamics standpoint. Two types of experiment are chosen that can also be simulated by a multibody dynamics simulation program. In the experiment, recorded were the configuration and force histories; that is, velocity and position, and force output and differential pressure change from the hydraulic cylinder, in the time domain. When the experimental force history is used as driving force in the simulation model, the forward dynamics simulation produces a corresponding configuration history. Then, the experimental configuration history is used in the inverse dynamics analysis to generate a corresponding force history. Therefore, two sets of configuration and force histories--one set from experiment, and the other from the simulation that is driven forward and backward with the experimental data--are compared in the time domain. More comparisons are made in regard to the effects of initial conditions, friction, and viscous damping.

Yae, K. Harold↗