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DOE OSTI2024

Nonparametric Multiparticle Set Methods for Interpreting Environmental Samples

Collection and analysis of environmental samples is commonly used by a range of stakeholders in nuclear safeguards and security contexts. While the ubiquity of samples and their transport in the environment allow regular collection, developing and demonstrating methods for analyzing these samples is difficult. In this work, an environmental sample consists of a set of one or more individual particles. Recent advances in reactor simulation have allowed us to generate data that are more representative of real-world environmental samples, enabling statistically defensible method development and testing. The most notable of these advances is a drastic increase in the number of material depletion regions, which allows our simulations to capture the variation in isotopic composition seen at length scales consistent with environmental samples. Traditional approaches for handling multiparticle samples treat each particle in the sample individually, estimating the quantity of interest (e.g., core-average burnup) resulting from measurement and analysis of signatures (e.g., nuclide assays) from each individual particle. Individual estimates are then averaged to generate a single estimate of the quantity of interest over the entire sample. In this presentation, we introduce two novel approaches for interpreting environmental samples that comprise of multiple particles: (1) the Quantile-Quantile Comparator, which uses a multivariate generalization of quantile-quantile plots for comparing unknown statistical distributions, and (2) the Set Transformer, an attention-based neural network module designed to model interactions among elements (particles) in the input set (sample). Statistically representative sampling cannot be guaranteed as samples are passively collected and are beholden to what particles are available in the environment. These new analysis methods for set-input problems are expected to be more robust than traditional approaches to issues of sampling bias where particles are not uniformly distributed throughout regions of interest, as well as generally outperform traditional approaches by jointly considering all elements in the set. We will present results comparing the performance of traditional single particle approaches and the novel Quantile-Quantile Comparator and Set Transformer for interpretation of simulated environmental samples.

Phathanapirom, Birdy↗

DOE OSTI2018

Synchrophasor Data Correction under GPS Spoofing Attack: A State Estimation-Based Approach

GPS spoofing attack (GSA) has been shown to be one of the most imminent threats to almost all cyber-physical systems incorporated with the civilian GPS signal. Specifically, for our current agenda of the modernization of the power grid, this may greatly jeopardize the benefits provided by the pervasively installed phasor measurement units (PMU). In this paper, we consider the case where synchrophasor data from PMUs are compromised due to the presence of a single GSA, and show that it can be corrected by signal processing techniques. In particular, we introduce a statistical model for synchrophasorbased power system state estimation (SE), and then derive the spoofing-matched algorithms for synchrophasor data correction against GPS spoofing attack. Different testing scenarios in IEEE 14-, 30-, 57-, 118-bus systems are simulated to show the proposed algorithms’ performance on GSA detection and state estimation. Numerical results demonstrate that our proposed algorithms can consistently locate and correct the spoofed synchrophasor data with good accuracy as long as the system observability is satisfied. The accuracy of state estimation is significantly improved compared with the traditional weighted least square method and approaches the performance under the Genie-aided method.

Phasor measurement units, Global Positioning Syste↗

DOE OSTI2020

Deterministic and Statistical Modeling of a New Thermal Breakout Technology for Measuring the Maximum Horizontal In-Situ Stress

The current state-of-the-art technology for in-situ stress measurements involves an integrated approach that combines borehole breakout observations, drilling-induced tensile fractures, and hydraulic fracturing tests (i.e., “mini-fracs”). This methodology has achieved wide application in the oil and gas industry but has several limitations that often prevent successful in-situ stress measurements. One major limitation is that breakouts do not appear in all boreholes and are generally only a natural occurrence that cannot easily be controlled. Because borehole breakouts are used to directly measure the maximum horizontal in-situ stress magnitude, the absence of borehole breakouts presents a major data gap for in-situ stress measurements. In response to this data gap, a new US Department of Energy (US DOE)-sponsored thermal breakout technology that will provide a method for thermally inducing borehole breakouts and allow the consistent measurement of the maximum horizontal stress magnitude is currently in development. This thermal breakout technology involves heating the borehole and increasing the thermoelastic compressive stress in the rock until a breakout develops, which can be directly correlated to the maximum horizontal stress magnitude. The first step in this project was an analytical modeling study of the thermal breakout process. Based on the Kirsch solution (Kirsch 1898), a deterministic and statistical analysis was performed on the pertinent parameters that influence the maximum horizontal stress calculation. As a result of the analysis, the findings indicate that the thermal breakout technology is feasible and provides improved accuracy and/or an enhanced ability to measure the maximum horizontal stress. Future work as part of this US DOE-sponsored project includes additional validation through more detailed numerical modeling, laboratory testing, and field testing of the thermal breakout technology.

58 GEOSCIENCES↗

DOE OSTI2017

Ensemble Kalman Filter for Dynamic State Estimation of Power Grids Stochastically Driven by Time-correlated Mechanical Input Power

State and parameter estimation of power transmission networks is important for monitoring power grid operating conditions and analyzing transient stability. Wind power generation depends on fluctuating input power levels, which are correlated in time and contribute to uncertainty in turbine dynamical models. The ensemble Kalman filter (EnKF), a standard state estimation technique, uses a deterministic forecast and does not explicitly model time-correlated noise in parameters such as mechanical input power. However, this uncertainty affects the probability of fault-induced transient instability and increased prediction bias. Here a novel approach is to model input power noise with time-correlated stochastic fluctuations, and integrate them with the network dynamics during the forecast. While the EnKF has been used to calibrate constant parameters in turbine dynamical models, the calibration of a statistical model for a time-correlated parameter has not been investigated. In this study, twin experiments on a standard transmission network test case are used to validate our time-correlated noise model framework for state estimation of unsteady operating conditions and transient stability analysis, and a methodology is proposed for the inference of the mechanical input power time-correlation length parameter using time-series data from PMUs monitoring power dynamics at generator buses.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2019

Multi-‘omic’ analyses of the dynamics, mechanisms, and pathways for carbon turnover in grassland soil under two climate regimes

Soil microbial activity drives the carbon and nitrogen cycles and is an important determinant of atmospheric trace gas turnover, yet most soils are dominated by microorganisms with unknown metabolic capacities. This knowledge gap precludes meaningful predictions of relationships between microorganism types and their biogeochemical functions. Specifically, as climate change physically alters terrestrial ecosystems, the impact on microbial consortia and potential consequences for release of carbon and other nutrients from soils are difficult to predict. In this project, we investigated the identities, activity, and functional potential of microorganisms residing in a well characterized grassland ecosystem (the Angelo Coast Range Reserve) undergoing a controlled 14-year rainfall extension climate change experiment. The research was achieved using a combination of “omics”-based technologies, including genome-resolved metagenomics, transcriptomics, and proteomics. The approach allowed us to capture multiple facets of community ecology and activity in situ. Supported by this award, significant progress was made in addressing the grand challenge of achieving genome-resolution for very complex soil microbial communities. In addition to improvements in the methodology, the research required new approaches to define the 3-dimentional distributions of microorganisms and their metabolic traits in soils and to decipher the impact of climate. Underpinning such analyses was the need for sufficient statistical power to test for geographic, soil depth and rainfall controls on community composition and metabolic properties. This required that we scale up throughput substantially. We overcame significant technical barriers to achieve complex microbial community resolution.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

A Hybrid Deep Learning Approach to Cosmological Constraints from Galaxy Redshift Surveys

We present a deep machine learning (ML)–based technique for accurately determining σ g and Ω m from mock 3D galaxy surveys. The mock surveys are built from the AbacusCosmos suite of N -body simulations, which comprises 40 cosmological volume simulations spanning a range of cosmological parameter values, and we account for uncertainties in galaxy formation scenarios through the use of generalized halo occupation distributions (HODs). We explore a trio of ML models: a 3D convolutional neural network (CNN), a power spectrum–based fully connected network, and a hybrid approach that merges the two to combine physically motivated summary statistics with flexible CNNs. We describe best practices for training a deep model on a suite of matched-phase simulations, and we test our model on a completely independent sample that uses previously unseen initial conditions, cosmological parameters, and HOD parameters. Despite the fact that the mock observations are quite small (~0.07 h -3 Gpc 3 ) and the training data span a large parameter space (six cosmological and six HOD parameters), the CNN and hybrid CNN can constrain estimates of σ g and Ω m to ~3% and ~4%, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1994

Low-Earth-Orbiter resource allocation and capacity planning for the DSN using LEO4CAST

The Deep Space Network provides tracking and communication services for a number of U.S. and international low-Earth-orbiting (LEO) and near-Earth missions. This service is supplied by the 26-m subnet (located at each of the DSN complexes), the 9-m and the 34-m Antenna Research System antennas at Goldstone, and the 11-m antennas (following the orbital VLBI mission). An increasing number of LEO missions are planned for DSN support, which will result in increasingly complex ground resource allocation and mission support trades. To support TDA decision making on mission support and cost-effective ground system evolution for this 26-m subnet, LEO4CAST has been developed. LEO4CAST is a tool that uses statistical approaches to provide useful information for long-term ground system capacity planning and near-term resource allocation (prior to detailed time-of-day scheduling). LEO4CAST is currently beta-test software and is being exercised by both the Office of Telecommunications and Data Acquisition (TDA) and the JPL Systems Division.

Fox, G.↗

NASA NTRS1999

Comets after Hyakutake and Hale-Bopp

Being icy, cometary nuclei are the most easily modified bodies in the solar system - even modest heating is sufficient to induce significant weight loss. This sublimative loss and longterm storage far from the sun protect the nucleus against internal warming and ensure that cometary nuclei today contain the least processed material remaining from the early nebula - or perhaps from the natal cloud. The chemical compositions of ices, low temperature-refractory organics, and refractory minerals (and their physical states) provide sensitive probes of the origin and history of this material. The fortunate appearance of Hyakutake and Hale-Bopp has provided a wealth of information on these Oort cloud comets, obtained with a wide range of astronomical approaches. I will review certain key results for these comets, such as chemical abundances, isotopic abundance ratios, nuclear spin statistics, and nuclear vs extended production of "parent volatiles", and will illustrate how these test the origins of cometary material. A comparison with 1P/Halley--a third comet from the giant planet nebular region--will be discussed in the context of heterogeneity among these bodies.

Mumma, Michael J.↗

DOE OSTI2017

Statistical Characterization of Fracture in CFRP-Concrete Interfaces Due to Wet-Dry Cycling

The experimental fracture mechanics Single Contoured-Cantilever Beam (SCCB) specimen was implemented to evaluate environmentally conditioned concrete-CFRP interfaces. Fracture studies were conducted on specimens having undergone 10, 20 and 30 cycles of alternate wetting and drying. Half of the 24 conditioned specimens studied were placed in a 10% sodium sulfate solution (pH = 6.2–6.5) and half were soaked in sodium hydroxide (pH = 12) to simulate naturally occurring acidic and alkaline field exposure-conditions, respectively. At the end of each target age, SCCB fracture testing was conducted. Two approaches were used in determining the fracture toughness of the CFRP-concrete interface bond that depend on the proper identification of loads reaching a critical state, P{sub c}. In the first, the topmost, or “head”, −initiation and -arrestment loads were averaged, and in the second, the mean of the entire “set” of -initiation and -arrestment loads was taken. This raw-data was then reduced by a statistical-based method from which a range of permissible critical loads was designated. The final G{sub Ic} values cited are based on an averaging of this refined data. Considerable degradation of the CFRP-concrete interface bond resulted especially for cases of latter-stage cycling in the aggressive sodium-sulfate and -hydroxide solutions.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Estimating the CO 2 Fertilization Effect on Extratropical Forest Productivity From Flux‐Tower Observations

Abstract The land sink of anthropogenic carbon emissions, a crucial component of mitigating climate change, is primarily attributed to the CO 2 fertilization effect on global gross primary productivity (GPP). However, direct observational evidence of this effect remains scarce, hampered by challenges in disentangling the CO 2 fertilization effect from other long‐term confounding drivers, particularly climatic changes. Here, we introduce a novel statistical approach to separate the CO 2 fertilization effect on photosynthetic carbon uptake using eddy covariance (EC) records across 38 extratropical forest sites. We find the median stimulation rate of GPP to be 3.2 ± 0.9 gC m −2 yr −1 ppm −1 (or 16.4 ± 4.2% per 100 ppm) under increasing atmospheric CO 2 across these sites, respectively. To validate the robustness of our findings, we test our statistical method using factorial simulations of an ensemble of process‐based land surface models. We address additional factors, including nitrogen deposition and land management, that may impact plant productivity, potentially confounding the attribution to the CO 2 fertilization effect. Assuming these site‐specific effects offset to some extent across sites as random factors, the estimated median value still reflects the strength of the CO 2 fertilization effect. However, disentanglement of these long‐term effects, often inseparable by timescale, requires further causal research. Our study provides direct evidence that the photosynthetic stimulation is maintained under long‐term CO 2 fertilization across multiple EC sites. Such observation‐based quantification is key to constraining the long‐standing uncertainties in the land carbon cycle under rising CO 2 concentrations.

Environmental Sciences & Ecology↗

NASA NTRS2013

Monte Carlo Bayesian Inference on a Statistical Model of Sub-gridcolumn Moisture Variability Using High-resolution Cloud Observations : Sensitivity Tests and Results - Part II

Part I presented a Monte Carlo Bayesian method for constraining a complex statistical model of GCM sub-gridcolumn moisture variability using high-resolution MODIS cloud data, thereby permitting large-scale model parameter estimation and cloud data assimilation. This part performs some basic testing of this new approach, verifying that it does indeed significantly reduce mean and standard deviation biases with respect to the assimilated MODIS cloud optical depth, brightness temperature and cloud top pressure, and that it also improves the simulated rotational-Ramman scattering cloud optical centroid pressure (OCP) against independent (non-assimilated) retrievals from the OMI instrument. Of particular interest, the Monte Carlo method does show skill in the especially difficult case where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach allows finite jumps into regions of non-zero cloud probability. In the example provided, the method is able to restore marine stratocumulus near the Californian coast where the background state has a clear swath. This paper also examines a number of algorithmic and physical sensitivities of the new method and provides guidance for its cost-effective implementation. One obvious difficulty for the method, and other cloud data assimilation methods as well, is the lack of information content in the cloud observables on cloud vertical structure, beyond cloud top pressure and optical thickness, thus necessitating strong dependence on the background vertical moisture structure. It is found that a simple flow-dependent correlation modification due to Riishojgaard (1998) provides some help in this respect, by better honoring inversion structures in the background state.

Monte Carlo Bayesian inference↗

DOE OSTI2021

Data-Driven Learning for the Mori--Zwanzig Formalism: A Generalization of the Koopman Learning Framework

A theoretical framework which unifies the conventional Mori--Zwanzig formalism and the approximate Koopman learning of deterministic dynamical systems from noiseless observation is presented. In this framework, the Mori--Zwanzig formalism, developed in statistical mechanics to tackle the hard problem of construction of reduced-order dynamics for high-dimensional dynamical systems, can be considered as a natural generalization of the Koopman description of the dynamical system. We next show that, similar to the approximate Koopman learning methods, data-driven methods can be developed for the Mori--Zwanzig formalism with Mori's linear projection operator. We have developed two algorithms to extract the key operators, the Markov and the memory kernel, using time series of a reduced set of observables in a dynamical system. We have adopted the Lorenz `96 system as a test problem and solved for the above operators. These operators exhibit complex behaviors, which are unlikely to be captured by traditional modeling approaches in Mori--Zwanzig analysis. The nontrivial generalized fluctuation-dissipation relationship, which relates the memory kernel with the two-time correlation statistics of the orthogonal dynamics, was numerically verified as a validation of the solved operators. Here we present numerical evidence that the generalized Langevin equation, a key construct in the Mori--Zwanzig formalism, is more advantageous in predicting the evolution of the reduced set of observables than the conventional approximate Koopman operators.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗

DOE OSTI2018

An Efficient Pipeline for Abdomen Segmentation in CT Images

Computed tomography (CT) scans usually include some disadvantages due to the nature of the imaging procedure, and these handicaps prevent accurate abdomen segmentation. Discontinuous abdomen edges, bed section of CT, patient information, closeness between the edges of the abdomen and CT, poor contrast, and a narrow histogram can be regarded as the most important handicaps that occur in abdominal CT scans. Currently, one or more handicaps can arise and prevent technicians obtaining abdomen images through simple segmentation techniques. In other words, CT scans can include the bed section of CT, a patient’s diagnostic information, low-quality abdomen edges, low-level contrast, and narrow histogram, all in one scan. These phenomena constitute a challenge, and an efficient pipeline that is unaffected by handicaps is required. In addition, analysis such as segmentation, feature selection, and classification has meaning for a real-time diagnosis system in cases where the abdomen section is directly used with a specific size. A statistical pipeline is designed in this study that is unaffected by the handicaps mentioned above. Intensity-based approaches, morphological processes, and histogram-based procedures are utilized to design an efficient structure. Performance evaluation is realized in experiments on 58 CT images (16 training, 16 test, and 26 validation) that include the abdomen and one or more disadvantage(s). The first part of the data (16 training images) is used to detect the pipeline’s optimum parameters, while the second and third parts are utilized to evaluate and to confirm the segmentation performance. The segmentation results are presented as the means of six performance metrics. Thus, the proposed method achieves remarkable average rates for training/test/validation of 98.95/99.36/99.57% (jaccard), 99.47/99.67/99.79% (dice), 100/99.91/99.91% (sensitivity), 98.47/99.23/99.85% (specificity), 99.38/99.63/99.87% (classification accuracy), and 98.98/99.45/99.66% (precision). In summary, a statistical pipeline performing the task of abdomen segmentation is achieved that is not affected by the disadvantages, and the most detailed abdomen segmentation study is performed for the use before organ and tumor segmentation, feature extraction, and classification.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2025

Detecting Masquerade Attacks in Controller Area Networks Using Graph Machine Learning

Modern vehicles rely on a myriad of electronic control units (ECUs) interconnected via controller area networks (CANs) for critical operations. Despite their ubiquitous use and reliability, CANs are susceptible to sophisticated cyberattacks, particularly masquerade attacks, which inject false data that mimic legitimate messages at the expected frequency. These attacks pose severe risks such as unintended acceleration, brake deactivation, and rogue steering. Traditional intrusion detection systems (IDS) often struggle to detect these subtle intrusions due to their seamless integration into normal traffic. This paper introduces a novel framework for detecting masquerade attacks in the CAN bus using graph machine learning (ML). We hypothesize that the integration of shallow graph embeddings with time series features derived from CAN frames enhances the detection of masquerade attacks. We show that by representing CAN bus frames as message sequence graphs (MSGs) and enriching each node with contextual statistical attributes from time series, we can enhance detection capabilities across various attack patterns compared to using graph-based features only. Our method ensures a comprehensive and dynamic analysis of CAN frame interactions, improving robustness and efficiency. Extensive experiments on the ROAD dataset validate the effectiveness of our approach, demonstrating statistically significant improvements in the detection rates of masquerade attacks compared to a baseline that uses graph-based features only as confirmed by Mann-Whitney U and Kolmogorov-Smirnov tests (p < 0.05) .

Marfo, William [Univ. of Texas, El Paso, TX (Unite↗

DOE OSTI2018

Correlated prompt fission data in transport simulations

Detailed information on the fission process can be inferred from the observation, modeling and theoretical understanding of prompt fission neutron and γ-ray observables. Beyond simple average quantities, the study of distributions and correlations in prompt data, e.g., multiplicity-dependent neutron and γ-ray spectra, angular distributions of the emitted particles, n -n, n - γ, and γ - γ correlations, can place stringent constraints on fission models and parameters that would otherwise be free to be tuned separately to represent individual fission observables. The FREYA and CGMF codes have been developed to follow the sequential emissions of prompt neutrons and γ rays from the initial excited fission fragments produced right after scission. Both codes implement Monte Carlo techniques to sample initial fission fragment configurations in mass, charge and kinetic energy and sample probabilities of neutron and γ emission at each stage of the decay. This approach naturally leads to using simple but powerful statistical techniques to infer distributions and correlations among many observables and model parameters. The comparison of model calculations with experimental data provides a rich arena for testing various nuclear physics models such as those related to the nuclear structure and level densities of neutron-rich nuclei, the γ-ray strength functions of dipole and quadrupole transitions, the mechanism for dividing the excitation energy between the two nascent fragments near scission, and the mechanisms behind the production of angular momentum in the fragments, etc. Beyond the obvious interest from a fundamental physics point of view, such studies are also important for addressing data needs in various nuclear applications. The inclusion of the FREYA and CGMF codes into the MCNP6.2 and MCNPX - PoliMi transport codes, for instance, provides a new and powerful tool to simulate correlated fission events in neutron transport calculations important in nonproliferation, safeguards, nuclear energy, and defense programs. Here, this review provides an overview of the topic, starting from theoretical considerations of the fission process, with a focus on correlated signatures. It then explores the status of experimental correlated fission data and current efforts to address some of the known shortcomings. Numerical simulations employing the FREYA and CGMF codes are compared to experimental data for a wide range of correlated fission quantities. The inclusion of those codes into the MCNP6.2 and MCNPX - PoliMi transport codes is described and discussed in the context of relevant applications. The accuracy of the model predictions and their sensitivity to model assumptions and input parameters are discussed. Lastly, a series of important experimental and theoretical questions that remain unanswered are presented, suggesting a renewed effort to address these shortcomings.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

On the use of Graphs for Test Sequence Selection

This report demonstrates that applying graph theory techniques provides a way to obtain sufficient statistics in finding errors when testing complex state machines. It discusses how to define the tests, then demonstrates how to automatically generate test suites that diversify test cases, subject to constraints. If included within a continuous integration approach, these constructs provide an unbiased means to systematically check for errors within the latest controller software release.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Computational tools for multi-linked flexible structures

A software module which designs and tests controllers and filters in Kalman Estimator form, based on a polynomial state-space model is discussed. The user-friendly program employs an interactive graphics approach to simplify the design process. A variety of input methods are provided to test the effectiveness of the estimator. Utilities are provided which address important issues in filter design such as graphical analysis, statistical analysis, and calculation time. The program also provides the user with the ability to save filter parameters, inputs, and outputs for future use.

Lee, Gordon K. F.↗