SEARCH · Search NASA

Results for “Dynamic State Estimation”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 883 records · Page 49

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Granger Causality for prediction in Dynamic Mode Decomposition: Application to power systems

Here, the dynamic mode decomposition (DMD) technique extracts the dominant modes characterizing the innate dynamical behavior of the system within the measurement data. For appropriate identification of dominant modes from the measurement data, the DMD algorithm necessitates ensuring the quality of the input measurement data sequences. On that account, for validating the usability of the dataset for the DMD algorithm, the paper proposed two conditions: Persistence of excitation (PE) and the Granger Causality Test (GCT). The virtual data sequences are designed with the hankel matrix representation such that the dimensions of the subspace spanning the essential system modes are increased with the addition of new state variables. The PE condition provides the lower bound for the trajectory length, and the GCT provides the order of the model. Satisfying the PE condition enables estimating an approximate linear model, but the predictability with the identified model is only assured with the temporal causation among data searched with GCT. The proposed methodology is validated with the application for coherency identification (CI) in a multi-machine power system (MMPS), an essential phenomenon in transient stability analysis. The significance of PE condition and GCT is demonstrated through various case studies implemented on 22 bus six generator system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Particle Swarm Optimization of Dynamic Load Model Parameters in Large Systems

This paper considers two dynamic load models that are widely used in industry to account for induction motor behavior: CMLD and CLOD. These models must be parametrized for the specific utility system in a general way so that they can be used in planning studies and provide a conservative but realistic representation of load behavior. This study considers a measurement-based approach to tuning both models. The load modeling study compares the response of the tuned models to generic candidate models using historical events. This study considers one area-based subsystem to simplify the modeling approach and reduce the number of models required for simulations. Additionally, because dynamic load models often produce similar results for different sets of parameters, a sensitivity study was conducted to assess the parameter impacts on the voltage response. The sensitivity study covers the parameters that are tuned using event measurements. The process to estimate the parameters uses the particle-swarm optimization algorithm. Overall, the performance of the tuned model more accurately captures recovery voltage, delayed recovery, and settling voltage than its predecessor models while not being overly tuned so that it remains general for peak summer conditions.

dynamic load modeling↗

DOE OSTI2024

Theoretical modeling of hepatitis C acute infection in liver-humanized mice support pre-clinical assessment of candidate viruses for controlled-human-infection studies

Designing and carrying out a controlled human infection (CHI) model for hepatitis C virus (HCV) is critical for vaccine development. However, key considerations for a CHI model protocol include understanding of the earliest viral-host kinetic events during the acute phase and susceptibility of the viral isolate under consideration for use in the CHI model to antiviral treatment before any infections in human volunteers can take place. Humanized mouse models lack adaptive immune responses but provide a unique opportunity to obtain quantitative understanding of early HCV kinetics and develop mathematical models to further understand viral and innate immune response dynamics during acute HCV infection. We show that the models reproduce the measured HCV kinetics in humanized mice, which are consistent with early acute HCV-host dynamics in immunocompetent chimpanzees. Our findings suggest that humanized mice are well-suited to support development of a CHI model. In-silico and in-vivo modeling estimates provide a starting point to characterize candidate viruses for testing in CHI model studies.

Agent-based modeling↗

DOE OSTI2021

Using an Atom Interferometer to Infer Gravitational Entanglement Generation

If gravitational perturbations are quantized into gravitons in analogy with the electromagnetic field and photons, the resulting graviton interactions should lead to an entangling interaction between massive objects. We suggest a test of this prediction. To do this, we introduce the concept of interactive quantum information sensing. This novel sensing protocol is tailored to provable verification of weak dynamical entanglement generation between a pair of systems. We show that this protocol is highly robust to typical thermal noise sources. The sensitivity can moreover be increased both using an initial thermal state and/or an initial phase of entangling via a non-gravitational interaction. We outline a concrete implementation testing the ability of the gravitational field to generate entanglement between an atomic interferometer and mechanical oscillator. Preliminary numerical estimates suggest that near-term devices could feasibly be used to perform the experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Acidity Constants of the Hematite-Liquid Water Interface from Ab Initio Molecular Dynamics

The interface between transition metal oxides (TMO) and liquid water plays a crucial role in environmental chemistry, catalysis, and energy science. Yet, the mechanism and energetics of chemical transformations at solvated TMO surfaces is often unclear, largely because of the difficulty to characterize the active surface species experimentally. The hematite (alpha-Fe2O3)-liquid water interface is a case in point. Here we demonstrate that ab initio molecular dynamics is a viable tool for determining the protonation states of complex interfaces. The pK a values of the oxygen-terminated (001) surface group of hematite, OH,and half-layer terminated (012) surface groups, (OH)-O-2 and (OH2)-O-1, are predicted to be (18.5 +/- 0.3), (18.9 +/- 0.6), and (10.3 +/- 0.5) pK(a) units, respectively. These are in good agreement with recent bond-valence theory based estimates, and suggest that the deprotonation of these surfaces require significantly more free energy input than previously thought.

Gittus, Oliver↗

NASA NTRS2008

25th Space Simulation Conference. Environmental Testing: The Earth-Space Connection

Topics covered include: Methods of Helium Injection and Removal for Heat Transfer Augmentation; The ESA Large Space Simulator Mechanical Ground Support Equipment for Spacecraft Testing; Temperature Stability and Control Requirements for Thermal Vacuum/Thermal Balance Testing of the Aquarius Radiometer; The Liquid Nitrogen System for Chamber A: A Change from Original Forced Flow Design to a Natural Flow (Thermo Siphon) System; Return to Mercury: A Comparison of Solar Simulation and Flight Data for the MESSENGER Spacecraft; Floating Pressure Conversion and Equipment Upgrades of Two 3.5kw, 20k, Helium Refrigerators; Affect of Air Leakage into a Thermal-Vacuum Chamber on Helium Refrigeration Heat Load; Special ISO Class 6 Cleanroom for the Lunar Reconnaissance Orbiter (LRO) Project; A State-of-the-Art Contamination Effects Research and Test Facility Martian Dust Simulator; Cleanroom Design Practices and Their Influence on Particle Counts; Extra Terrestrial Environmental Chamber Design; Contamination Sources Effects Analysis (CSEA) - A Tool to Balance Cost/Schedule While Managing Facility Availability; SES and Acoustics at GSFC; HST Super Lightweight Interchangeable Carrier (SLIC) Static Test; Virtual Shaker Testing: Simulation Technology Improves Vibration Test Performance; Estimating Shock Spectra: Extensions beyond GEVS; Structural Dynamic Analysis of a Spacecraft Multi-DOF Shaker Table; Direct Field Acoustic Testing; Manufacture of Cryoshroud Surfaces for Space Simulation Chambers; The New LOTIS Test Facility; Thermal Vacuum Control Systems Options for Test Facilities; Extremely High Vacuum Chamber for Low Outgassing Processing at NASA Goddard; Precision Cleaning - Path to Premier; The New Anechoic Shielded Chambers Designed for Space and Commercial Applications at LIT; Extraction of Thermal Performance Values from Samples in the Lunar Dust Adhesion Bell Jar; Thermal (Silicon Diode) Data Acquisition System; Aquarius's Instrument Science Data System (ISDS) Automated to Acquire, Process, Trend Data and Produce Radiometric System Assessment Reports; Exhaustive Thresholds and Resistance Checkpoints; Reconfigurable HIL Testing of Earth Satellites; FPGA Control System for the Automated Test of MicroShutters; Ongoing Capabilities and Developments of Re-Entry Plasma Ground Tests at EADS-ASTRIUM; Operationally Responsive Space Standard Bus Battery Thermal Balance Testing and Heat Dissipation Analysis; Galileo - The Serial-Production AIT Challenge; The Space Systems Environmental Test Facility Database (SSETFD), Website Development Status; Simulated Reentry Heating by Torching; Micro-Vibration Measurements on Thermally Loaded Multi-Layer Insulation Samples in Vacuum; High Temperature Life Testing of 80Ni-20Cr Wire in a Simulated Mars Atmosphere for the Sample Analysis at Mars (SAM) Instrument Suit Gas Processing System (GPS) Carbon Dioxide Scrubber; The Planning and Implementation of Test Facility Improvements; and Development of a Silicon Carbide Molecular Beam Nozzle for Simulation Planetary Flybys and Low-Earth Orbit.

Packard, Edward↗

DOE OSTI2026

Reliability Assessment of Cooling Fans for PV Inverters: Testing, Modeling, and Case Studies

The reliability of photovoltaic (PV) inverters is critical for long-term solar system performance, with cooling fan failures frequently leading to costly downtime. While much research exists on general cooling fan reliability, little attention has been given to fans operating within PV inverters and their unique environmental challenges. Here, this article proposes a comprehensive methodology to address this gap. First, a failure mode and effects analysis is performed on fans to identify the key failure mechanisms in PV applications, their corresponding stressors, and the models necessary for lifetime prediction. Second, an accelerated life test is designed and conducted to collect valuable experimental data for PV inverter fans in a reasonable amount of time. Third, a mathematical conversion of dynamic mission profiles into effective constant stress levels is derived. Fourth, case studies are given, showcasing lifetime estimates that account for geographic variations in mission profile data. The results demonstrate that this integrated approach leads to an accurate reliability assessment for PV inverter cooling fans.

accelerated life testing (ALT)↗

DOE OSTI2020

Leveraging Fine-Grained Occupancy Estimation Patterns for Effective HVAC Control

As occupancy sensing technologies become mature, various occupancy sensors are increasingly deployed in commercial buildings for pervasive occupancy monitoring. These sensors provide occupant-count data, which contains rich spatiotemporal information about occupancy patterns. With long-term occupant-count data collected from a commercial building, we design three different predictive models that capture the occupancy dynamics and examine how a model predictive control of the HVAC system benefits from actual occupancy count prediction. Our analysis reveals that mispredictions of occupancy states, especially false positives and false negatives, may introduce inefficient control that leads to energy waste or user discomfort. To address this issue, we take a step further to design an adaptive model predictive controller that minimizes inefficient control actions according to misprediction types and distributions. A comprehensive evaluation is performed in OpenBuild and EnergyPlus simulators to study the effectiveness of the proposed end-to-end control strategy. The evaluation shows that the proposed solution reduces energy consumption by 29.5% while improving the average weighted occupants comfort by 86.7% in Predicted Mean Vote (PMV) over the fixed schedule strategy.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2004

National Airspace System Delay Estimation Using Weather Weighted Traffic Counts

Assessment of National Airspace System performance, which is usually measured in terms of delays resulting from the application of traffic flow management initiatives in response to weather conditions, volume, equipment outages and runway conditions, is needed both for guiding flow control decisions during the day of operations and for post operations analysis. Comparison of the actual delay, resulting from the traffic flow management initiatives, with the expected delay, based on traffic demand and other conditions, provides the assessment of the National Airspace System performance. This paper provides a method for estimating delay using the expected traffic demand and weather. In order to identify the cause of delays, 517 days of National Airspace System delay data reported by the Federal Aviation Administration s Operations Network were analyzed. This analysis shows that weather is the most important causal factor for delays followed by equipment and runway delays. Guided by these results, the concept of weather weighted traffic counts as a measure of system delay is described. Examples are given to show the variation of these counts as a function of time of the day. The various datasets, consisting of aircraft position data, enroute severe weather data, surface wind speed and visibility data, reported delay data and number of aircraft handled by the Centers data, and their sources are described. The procedure for selecting reference days on which traffic was minimally impacted by weather is described. Different traffic demand on each reference day of the week, determined by analysis of 42 days of traffic and delay data, was used as the expected traffic demand for each day of the week. Next, the method for computing the weather weighted traffic counts using the expected traffic demand, derived from reference days, and the expanded regions around severe weather cells is discussed. It is shown via a numerical example that this approach improves the dynamic range of the weather weighted traffic counts considerably. Time histories of these new weather weighted traffic counts are used for synthesizing two statistical features, six histogram features and six time domain features. In addition to these enroute weather features, two surface weather features of number of major airports in the United States with high mean winds and low mean visibility are also described. A least squares procedure for establishing a functional relation between the features, using combinations of these features, and system delays is explored using 36 days of data. Best correlations between the estimated delays using the functional relation and the actual delays provided by the Operations Network are obtained with two different combinations of features: 1) six time domain features of weather weighted traffic counts plus two surface weather features, and 2) six histogram features and mean of weather weighted traffic counts along with the two surface weather features. Correlation coefficient values of 0.73 and 0.83 were found in these two instances.

Chatterji, Gano B.↗

DOE OSTI2020

Development of neural network force fields for corrosion studies

To fully understand the chemistry and physics of corrosion, novel methods of simulation must be developed. One approach is designing machine learning (ML) algorithms integrated with density functional theory to develop adaptive force fields to gain insight into corrosion behavior namely at the surface of metal oxides. Current methods of modeling corrosion are slow due to the computational cost of resolving both reaction mechanics and mass transport processes. Machine learning methods can be implemented to obtain structure-activity relationships at both the molecular and bulk scale while still retaining the accuracy of density functional theory (DFT) and significantly decreasing the time needed for simulations of complex chemical processes in the various environments of corrosion. Multiscale models are needed for corrosion studies to fully understand its processes not only at the atomic length scale (chemical bonding, energies, and forces), but also at the nano and meso length scales (solid-state physics and material science processes). Current methods of study include DFT, molecular dynamics, and Monte Carlo. The limitation of DFT is that only a small number of atoms or molecules can be simulated at that level of theory. Density functional theory is used to study the electronic structure of atoms and molecules, and calculate the force component of each atom. However, these calculations are limited to about 1000 atoms. Custom periodic boundary conditions (PBC) can be used to describe the various environments and defects that affect the atomic forces to produce a large data set from which a training set can be derived. Machine learning can be utilized to overcome the barrier of modeling macroscopic and multi-scale processes from ab initio calculations through the development of adaptive force fields. Local environments determine the atomic forces of a given system, therefore adaptive force fields must be created to produce reliable quantum mechanical calculations. This can be achieved by developing a learning algorithm that uses the mapped atomic forces or fingerprint as an input to produce energies and magnetic moments as output. A systematic approach was used to begin to build a data set in order to accurately describe the atomic forces in various environments. In Figure 4 below, a simple PBC cell of Fe{sub 2}O{sub 3} was first optimized. A surface optimization was performed next, followed by a hydroxylated surface optimization. Once this calculation has converged, the adsorption of halide species to the hydroxylated surface will be investigated. TensorFlow is an open source platform for machine learning developed by Google. Using a high level application program interface (API) such as Keras allows for building and training ML models easily in a number of different environments and languages. For this project, a neural network was developed within Anaconda in Python. Future Work: Further development of reference data set; Refining neural network and learning algorithm; Fingerprinting atomic environment to enable mapping of atomic force components; Choosing appropriate training set from reference data; Learning from training set and enabling non-linear mapping of training set fingerprints and the atomic forces; Estimation of uncertainty to identify ranges of outside applicability; Testing and analysis of molecular dynamic simulations.

36 MATERIALS SCIENCE↗

DOE OSTI2024

A deep decarbonization framework for the United States economy – a sector, sub-sector, and end-use based approach

Achieving the United States' target of net-zero greenhouse gas emissions by 2050 will require technological transformations and energy sector mitigation. To understand the role of dynamically evolving technologies, identify synergies and dissonance and the effect of allocating limited low-carbon biomass resources in decarbonizing the U.S. economy, we developed the Decarbonization Scenario Analysis Model. A Life Cycle Assessment based approach is implemented considering the U.S. economy as the functional unit, to estimate greenhouse gas mitigation potential for projected energy demand based on several sector-level and cross-sectoral decarbonization pathways. Direct and supply-chain emissions are accounted, resulting from changes in patterns of energy generation and consumption, technology breakthroughs, and reductions in fugitive emissions over time at the granularity of economic sectors, sub-sectors, and end-use. Decarbonization strategies are implemented over a reference case developed using Energy Information Administration (EIA AEO) projection of economic activities for 2020–2050. Based on the considered scenarios, 80–90% economy-wide decarbonization relative to the 2020 reference case is projected. Electrification, low-carbon fuels, and reduction of fugitive emissions play the most significant role to decarbonization. The majority of the remaining emissions are accounted to the supply-chain and end-use emissions from natural gas and diesel fossil-based fuels in heavy duty transportation and heavy industries, highlighting the need for developing low-carbon and carbon-negative alternatives to mitigate those fossil-based carbon emissions.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Estimation of Electromechanical Modes of Oscillation in the Eastern Interconnection from Ambient PMU Data

A power system's inter-area electromechanical modes of oscillation determine if the system is small-signal stable. Mode meters are tools that estimate the modes based on ambient synchrophasor measurements, allowing continuous monitoring of the system's stability margin. This paper reports on the application of mode meter algorithms to 21 months of synchrophasor measurements from the United States Eastern Interconnection (EI). Estimates for three modes were updated every minute, providing a much more comprehensive set of results than previous studies based on disturbance recordings. The detailed signal designs and mode meter configurations provided in this paper can be used to accelerate mode meter deployments in the EI. Analysis of the mode estimates reveal for the first time how seasonal load changes and system reconfiguration impact the EI system's dynamics.

Follum, James D.↗

DOE OSTI2025

Impact of chemical ordering on thermodynamic properties of point defects and Xe substitutional in U-10Mo

The accurate knowledge of defect energetics is critical to understanding the aging and irradiation behavior of U-10Mo nuclear fuel, which is selected as the fuel type for conversion of the United States High-Performance Research Reactors (HPRRs). Furthermore, using hybrid molecular dynamics and Monte Carlo (MDMC) simulation, we studied the impact of chemical ordering on the formation energies of vacancies, interstitials, and the solution energy of the Xe substitutionals. Instead of forming a random solid solution (RSS), substantial short-range-order (SRO) develops in U-10Mo, particularly at low temperatures. Mo atoms are found to repel each other and prefer U-rich local atomic environments within the 1st nearest neighbor (1NN) cutoff. Compared to the case of a RSS, the state with equilibrated Mo ordering shifts the distributions of vacancy and interstitial formation energies due to the dependence of defect energies on the local atomic environment, without a clear effect on Xe solution energy. In the operation temperature range (100–250 °C) of U-Mo fuels, neglecting SRO can lead to an inaccurate estimate of thermal equilibrium point defect concentrations by over an order of magnitude and incorrectly predict the preference among different types of dumbbells, highlighting the critical importance of accounting for the impact of chemical ordering for accurate atomistic calculations of defect properties.

Molecular dynamics and Monte Carlo (MDMC)↗

DOE OSTI2019

Saddle point approaches in strong field physics and generation of attosecond pulses

Attoscience is the emerging field that accesses the fastest electronic processes occurring at the atomic and molecular length scales with attosecond (1 as = 10 –18 s) time resolution having wide ranging physical, chemical, material science and biological applications. The quintessential and one of the most fundamental processes in this domain is the generation of phase locked XUV attosecond pulses. The theoretical approach to understand the process incorporates a fully quantum or semi classical or relativistic description of coherent charge dynamics in intense ultrashort electromagnetic fields driving a quantum system (an atom, a molecule, solid band gap materials or surface plasmas). Modelling of such physical and dynamical systems in science and also in many other branches often leads to equations represented in terms of complex multi-dimensional integrals. These integrals can often be solved using the stationary phase approximation, which leads to a series of equations identifying the points in the multi-dimensional space, having most significant contributions in their evaluation. These points are usually indicated as saddle points. The description of the dynamics of quantum mechanical or relativistic systems that results from such an approach enables near to classical physics intuitive perceptions of the processes under investigation. Thus, the saddle point methods are very powerful and valuable general theoretical tools to obtain asymptotic expressions of such solutions and help also to gain physical insights on the underlying phenomena. Such techniques developed in the past have been adapted to study the emission of as pulses by different physical systems and have been widely employed in calculating and estimating the response of matter to intense electromagnetic pulses on ultrafast time scales. Here we provide an extensive disposition of the saddle point approaches unifying their ubiquitous applications within the domain of attoscience valid for simple atomic to more complex condensed matter systems undergoing ultrafast dynamics and present current trends and advancements in the field. In this review we would delineate the methodology, present a synthesis of seminal works and describe the state of the art applications. Finally we also address ultrashort time dynamics of novel materials that have gained much attention recently, namely lower dimensional material systems and micro-plasma systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Investigating controls on sea ice algal production using E3SMv1.1-BGC

We present the analysis of global sympagic primary production (PP) from 300 years of pre-industrial and historical simulations of the E3SMv1.1-BGC model. The model includes a novel, eight-element sea ice biogeochemical component, MPAS-Seaice zbgc, which is resolved in three spatial dimensions and uses a vertical transport scheme based on internal brine dynamics. Modeled ice algal chlorophyll-a concentrations and column-integrated values are broadly consistent with observations, though chl-a profile fractions indicate that upper ice communities of the Southern Ocean are underestimated. Simulations of polar integrated sea ice PP support the lower bound in published estimates for both polar regions with mean Arctic values of 7.5 and 15.5 TgC/a in the Southern Ocean. However, comparisons of the polar climate state with observations, using a maximal bound for ice algal growth rates, suggest that the Arctic lower bound is a significant underestimation driven by biases in ocean surface nitrate, and that correction of these biases supports as much as 60.7 TgC/a of net Arctic PP. Simulated Southern Ocean sympagic PP is predominantly light-limited, and regional patterns, particularly in the coastal high production band, are found to be negatively correlated with snow thickness.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Enabling robust offline active learning for machine learning potentials using simple physics-based priors

Abstract Machine learning surrogate models for quantum mechanical simulations have enabled the field to efficiently and accurately study material and molecular systems. Developed models typically rely on a substantial amount of data to make reliable predictions of the potential energy landscape or careful active learning (AL) and uncertainty estimates. When starting with small datasets, convergence of AL approaches is a major outstanding challenge which has limited most demonstrations to online AL. In this work we demonstrate a Δ-machine learning (ML) approach that enables stable convergence in offline AL strategies by avoiding unphysical configurations with initial datasets as little as a single data point. We demonstrate our framework’s capabilities on a structural relaxation, transition state calculation, and molecular dynamics simulation, with the number of first principle calculations being cut down anywhere from 70%–90%. The approach is incorporated and developed alongside AMP torch , an open-source ML potential package, along with interactive Google Colab notebook examples.

Shuaibi, Muhammed↗

NASA NTRS1975

Users manual for flight control design programs

Computer programs for the design of analog and digital flight control systems are documented. The program DIGADAPT uses linear-quadratic-gaussian synthesis algorithms in the design of command response controllers and state estimators, and it applies covariance propagation analysis to the selection of sampling intervals for digital systems. Program SCHED executes correlation and regression analyses for the development of gain and trim schedules to be used in open-loop explicit-adaptive control laws. A linear-time-varying simulation of aircraft motions is provided by the program TVHIS, which includes guidance and control logic, as well as models for control actuator dynamics. The programs are coded in FORTRAN and are compiled and executed on both IBM and CDC computers.

Nalbandian, J. Y.↗

NASA NTRS2003

Vector-Ordering Filter Procedure for Data Reduction

The vector-ordering filter (VOF) technique involves a procedure for sampling a large population of data vectors to select a subset of data vectors that fully characterize the state space of the large population. The VOF technique enables a large reduction of the volume of data that must be handled in the automated monitoring system and method discussed in the two immediately preceding articles. In so doing, the VOF technique enables the development of data-driven mathematical models of a monitored asset from sets of data that would otherwise exceed the memory capacities of conventional engineering computers. Data-driven mathematical models have been shown to offer high fidelity for purposes of control and monitoring of assets. In practice, a collection of asset-operating observations is acquired with the intention that the collection contain observations characteristic of the full dynamic range of operation of the asset. Often, such a collection contains an extremely large number of observations, many of which are redundant. The VOF technique fills the need for a means to extract, from the original collection of observational data, a reduced data matrix that excludes redundant data while maintaining the full statistical character and dynamic range of the original data. The reduced data matrix can then be used as the input data for development of a mathematical model of the monitored asset, or as training data for a neural-network substitute for an explicit mathematical model of the asset. Alternatively, the reduced data matrix can, itself, be used directly as a mathematical model of the monitored asset, as is commonly done in multivariate state-estimation techniques. The original data are collected from the asset over a range of operating states and are put in matrix form. Each column vector in the original data matrix represents the signal values acquired at a particular operational state of the asset. Thus, the number of columns of the original data matrix equals the number of observed states and the number of rows in this matrix equals the number of signals acquired at each observation. In the VOF technique, one extracts the reduced data matrix from the original data matrix through the selection of a representative subset of the column (state) vectors.

Bickford, Randall L.↗