Search NASA⌕ Search

SEARCH · Search NASA

Results for “Autoregressive model”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Sequence modeling of higher-order wave modes of quasi-circular, spinning, non-precessing binary black hole mergers

Higher-order gravitational wave modes from quasi-circular, spinning, non-precessing binary-black-hole (BBH) mergers encode rich information about the nonlinear dynamics of strong-field gravity. We present a transformer-based sequence-completion surrogate that, given an early-inspiral segment, forecasts the subsequent late inspiral, merger, and ringdown. The intended applications are (i) patching or completing expensive or interrupted numerical-relativity (NR) simulations and (ii) providing late-time cross-checks and rapid hybridization studies. The training set is built from the NRHybSur3dq8 surrogate, which provides spherical-harmonic modes up to $\ell$ ≤ 4 (excluding (4, 0) and (4,±1), and including (5, 5)) for mass ratios q ≤ 8, dimensionless spin components s$^{z}_{1,2}$ ϵ[–0.8, 0.8], and inclination angles θ ϵ [0, π]. Waveforms are supplied on the interval t ϵ [–5000M, –100 M) and the model autoregressively generates the plus and cross polarizations (h + , h x ) on t ϵ [–100 M, 130M]. Training on the Delta supercomputer with 16 NVIDIA A100 GPUs required ~15 h on more than 14 million hybrid waveforms. Evaluation on a held-out test set of 840,000 samples yields mean and median overlaps of 0.996 and 0.997, respectively, with respect to the surrogate ground truth.

black-hole merger↗
DOE OSTI2024

Monitoring covariance in multivariate time series: Comparing machine learning and statistical approaches

Abstract In complex systems with multiple variables monitored at high‐frequency, variables are not only temporally autocorrelated, but they may also be nonlinearly related or exhibit nonstationarity as the inputs or operation changes. One approach to handling such variables is to detrend them prior to monitoring and then apply control charts that assume independence and stationarity to the residuals. Monitoring controlled systems is even more challenging because the control strategy seeks to maintain variables at prespecified mean levels, and to compensate, correlations among variables may change, making monitoring the covariance essential. In this paper, a vector autoregressive model (VAR) is compared with a multivariate random forest (MRF) and a neural network (NN) for detrending multivariate time series prior to monitoring the covariance of the residuals using a multivariate exponentially weighted moving average (MEWMA) control chart. Machine learning models have an advantage when the data's structure is unknown or may change. We design a novel simulation study with nonlinear, nonstationary, and autocorrelated data to compare the different detrending models and subsequent covariance monitoring. The machine learning models have superior performance for nonlinear and strongly autocorrelated data and similar performance for linear data. An illustration with data from a reverse osmosis process is given.

Weix, Derek↗
DOE OSTI2020

Deep anomaly detection for industrial systems: a case study

We explore the use of deep neural networks for anomaly detection of industrial systems where the data are multivariate time series measurements. We formulate the problem as a self-supervised learning where data under normal operation are used to train a deep neural network autoregressive model, i.e., use a window of time series data to predict future data values. The aim of such a model is to learn to represent the system dynamic behavior under normal conditions, while expect higher model vs. measurement discrepancies under faulty conditions. In real world applications, many control settings are discrete in nature. In this paper, vector embedding and joint losses are employed to deal with such situations. Both LSTM and CNN based deep neural network backbones are studied on the Secure Water Treatment (SWaT) testbed datasets. Also, Support Vector Data Description (SVDD) method is adapted to such anomaly detection settings with deep neural networks. Evaluation methods and results are discussed based on the SWaT dataset along with potential pitfalls.

anomaly detection, deep neural network↗
NASA NTRS1990

Rocket engine failure detection using system identification techiques

The theoretical foundation and application of two univariate failure detection algorithms to Space Shuttle Main Engine (SSME) test firing data is presented. Both algorithms were applied to data collected during steady state operation of the engine. One algorithm, the time series algorithm, is based on time series techniques and involves the computation of autoregressive models. Times series techniques have been previously applied to SSME data. The second algorithm is based on standard signal processing techniques. It consists of tracking the variations in the average signal power with time. The average signal power algorithm is a newly proposed SSME failure detection algorithm. Seven nominal test firings were used to develop failure indication thresholds for each algorithm. These thresholds were tested using four anomalous firings and one additional nominal firing. Both algorithms provided significantly earlier failure indication times than did the current redline limit system. Neither algorithm gave false failure indications for the nominal firing. The strengths and weaknesses of the two algorithms are discussed and compared. The average signal algorithm was found to have several advantages over the time series algorithm.

Meyer, Claudia M.↗
NASA NTRS1990

Rocket engine failure detection using system identification techniques

The theoretical foundation and application of two univariate failure detection algorithms to Space Shuttle Main Engine (SSME) test firing data is presented. Both algorithms were applied to data collected during steady state operation of the engine. One algorithm, the time series algorithm, is based on time series techniques and involves the computation of autoregressive models. Time series techniques have been previously applied to SSME data. The second algorithm is based on standard signal processing techniques. It consists of tracking the variations in the average signal power with time. The average signal power algorithm is a newly proposed SSME failure detection algorithm. Seven nominal test firings were used to develop failure indication thresholds for each algorithm. These thresholds were tested using four anomalous firings and one additional nominal firing. Both algorithms provided significantly earlier failure indication times than did the current redline limit system. Neither algorithm gave false failure indications for the nominal firing. The strengths and weaknesses of the two algorithms are discussed and compared. The average signal algorithm was found to have several advantages over the time series algorithm.

Meyer, Claudia M.↗
NASA NTRS1992

Signal processing for airborne doppler radar detection of hazardous wind shear as applied to NASA 1991 radar flight experiment data

Radar data collected during the 1991 NASA flight tests have been selectively analyzed to support research directed at developing both improved as well as new algorithms for detecting hazardous low-altitude windshear. Analysis of aircraft attitude data from several flights indicated that platform stability bandwidths were small compared to the data rate bandwidths which should support an assumption that radar returns can be treated as short time stationary. Various approaches at detection of weather returns in the presence of ground clutter are being investigated. Non-coventional clutter rejection through spectrum mode tracking and classification algorithms is a subject of continuing research. Based upon autoregressive modeling of the radar return time sequence, this approach may offer an alternative to overcome errors in conventional pulse-pair estimates. Adaptive filtering is being evaluated as a means of rejecting clutter with emphasis on low signal-to-clutter ratio situations, particularly in the presence of discrete clutter interference. An analysis of out-of-range clutter returns is included to illustrate effects of ground clutter interference due to range aliasing for aircraft on final approach. Data are presented to indicate how aircraft groundspeed might be corrected from the radar data as well as point to an observed problem of groundspeed estimate bias variation with radar antenna scan angle. A description of how recorded clutter return data are mixed with simulated weather returns is included. This enables the researcher to run controlled experiments to test signal processing algorithms. In the summary research efforts involving improved modelling of radar ground clutter returns and a Bayesian approach at hazard factor estimation are mentioned.

Baxa, Ernest G., Jr.↗
NASA NTRS1997

Detection of chaotic determinism in time series from randomly forced maps

Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center↗
NASA NTRS1997

Detection of "noisy" chaos in a time series

Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center↗
NASA NTRS2004

Analysis of SSEM Sensor Data Using BEAM

A report describes analysis of space shuttle main engine (SSME) sensor data using Beacon-based Exception Analysis for Multimissions (BEAM) [NASA Tech Briefs articles, the two most relevant being Beacon-Based Exception Analysis for Multimissions (NPO- 20827), Vol. 26, No.9 (September 2002), page 32 and Integrated Formulation of Beacon-Based Exception Analysis for Multimissions (NPO- 21126), Vol. 27, No. 3 (March 2003), page 74] for automated detection of anomalies. A specific implementation of BEAM, using the Dynamical Invariant Anomaly Detector (DIAD), is used to find anomalies commonly encountered during SSME ground test firings. The DIAD detects anomalies by computing coefficients of an autoregressive model and comparing them to expected values extracted from previous training data. The DIAD was trained using nominal SSME test-firing data. DIAD detected all the major anomalies including blade failures, frozen sense lines, and deactivated sensors. The DIAD was particularly sensitive to anomalies caused by faulty sensors and unexpected transients. The system offers a way to reduce SSME analysis time and cost by automatically indicating specific time periods, signals, and features contributing to each anomaly. The software described here executes on a standard workstation and delivers analyses in seconds, a computing time comparable to or faster than the test duration itself, offering potential for real-time analysis.

Zak, Michail↗
NASA NTRS2021

Argentina Food Security & Agriculture: Crop Monitoring and Forecasting for Argentina using NASA Satellite Observations

Early harvest information helps guide agricultural commodity assessments in Argentina, providing valuable planning information to identify potentially food-insecure regions, anticipate transportation and storage demands, predict price fluctuations, and project commodity trends. However, crop yield estimates are currently subjective, based on interviews with qualified informants (i.e., farmers, agribusiness actors). In partnership with the Buenos Aires Grain Exchange, we leveraged Terra Moderate Resolution Imaging Spectroradiometer (MODIS), Soil Moisture Active Passive (SMAP), and Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (GPM IMERG) NASA Earth observations to develop a Google Earth Engine (GEE) toolset to monitor vegetation growth. The first component of the toolset produces spatial and temporal maps of temperature, precipitation, soil moisture, and the Normalized Difference Vegetation Index (NDVI), allowing users to visualize the influence of the region’s climate and weather. Next, we developed an autoregressive model to predict NDVI several months in advance. Lastly, we created a linear regression model of crop yield and NDVI for soybeans, corn, and wheat, and input the forecasted NDVI to generate a predicted crop yield output. The NDVI forecasting model produced accurate predictions at two, four, and six months when examining the most recent growing season. In the crop yield model, soybeans exhibited moderately strong correlation, wheat had consistent weak correlation, and corn varied from weak to strong correlation depending on zone. This information is vital for vegetation growth monitoring by identifying areas of high growth and allocating resources to areas of lower growth to efficiently maximize crop yields.

DEVELOP Tech Paper↗
DOE OSTI2021

An Introduction to Word Embeddings and Language Models

Language models have advanced at a phenomenal pace over the past decade. This document provides a short introduction to terminology, word embeddings (aka low-dimensional representations), and popular large-scale language models (LMs). Word embeddings are used to represent words as numerical vectors and are context-independent, meaning a word can only have a single representation (e.g., club can only be club sandwich, not golf club ). Language models can determine the probability of a given sequence of words occurring in a sentence and can provide context to distinguish between words and phrases that sound similar. LMs are context-dependent (e.g., club can be club sandwich or golf club ) and largely fall in two main classes – autoregressive and autoencoding models. Autoregressive models are pretrained on the classic language modeling task: guess the next token having read all the previous ones. Those models can be fine-tuned and achieve great results on many tasks, the most natural application is text generation. A typical example of such models is GPT, but others include GPT-2, GPT-3, CTLR, TRANSFORMER-XL, REFORMER, XLNET. Autoencoding models are pretrained by corrupting the input tokens in some way and trying to reconstruct the original sentence. They can be fine-tuned and achieve great results on many tasks such as text generation, but their most natural application is sentence classification or token classification. A typical example of such models is BERT, but others include ROBERTA, ALBERT, XML, XML-ROBERTA, FLAUBERT AND LONGFORMER.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

On the maximum-entropy/autoregressive modeling of time series

The autoregressive (AR) model of a random process is interpreted in the light of the Prony's relation which relates a complex conjugate pair of poles of the AR process in the z-plane (or the z domain) on the one hand, to the complex frequency of one complex harmonic function in the time domain on the other. Thus the AR model of a time series is one that models the time series as a linear combination of complex harmonic functions, which include pure sinusoids and real exponentials as special cases. An AR model is completely determined by its z-domain pole configuration. The maximum-entropy/autogressive (ME/AR) spectrum, defined on the unit circle of the z-plane (or the frequency domain), is nothing but a convenient, but ambiguous visual representation. It is asserted that the position and shape of a spectral peak is determined by the corresponding complex frequency, and the height of the spectral peak contains little information about the complex amplitude of the complex harmonic functions.

Chao, B. F.↗
NASA NTRS2020

Forecasting Global Fire Emissions on Subseasonal to Seasonal (S2S) Time Scales

Fire emissions of gases and aerosols alter atmospheric composition and have substantial impacts on climate, ecosystem function, and human health. Warming climate and human expansion in fire‐prone landscapes exacerbate fire impacts and call for more effective management tools. Here we developed a global fire forecasting system that predicts monthly emissions using past fire data and climate variables for lead times of 1 to 6 months. Using monthly fire emissions from the Global Fire Emissions Database (GFED) as the prediction target, we fit a statistical time series model, the Autoregressive Integrated Moving Average model with eXogenous variables (ARIMAX), in over 1,300 different fire regions. Optimized parameters were then used to forecast future emissions. The forecast system took into account information about region‐specific seasonality, long‐term trends, recent fire observations, and climate drivers representing both large‐scale climate variability and local fire weather. We cross‐validated the forecast skill of the system with different combinations of predictors and forecast lead times. The reference model, which combined endogenous and exogenous predictors with a 1 month forecast lead time, explained 52% of the variability in the global fire emissions anomaly, considerably exceeding the performance of a reference model that assumed persistent emissions during the forecast period. The system also successfully resolved detailed spatial patterns of fire emissions anomalies in regions with significant fire activity. This study bridges the gap between the efforts of near‐real‐time fire forecasts and seasonal fire outlooks and represents a step toward establishing an operational global fire, smoke, and carbon cycle forecasting system.

vapor pressure↗
NASA NTRS1981

Computational problems in autoregressive moving average (ARMA) models

The choice of the sampling interval and the selection of the order of the model in time series analysis are considered. Band limited (up to 15 Hz) random torque perturbations are applied to the human ankle joint. The applied torque input, the angular rotation output, and the electromyographic activity using surface electrodes from the extensor and flexor muscles of the ankle joint are recorded. Autoregressive moving average models are developed. A parameter constraining technique is applied to develop more reliable models. The asymptotic behavior of the system must be taken into account during parameter optimization to develop predictive models.

Agarwal, G. C.↗
NASA NTRS2015

Acceleration and Velocity Sensing from Measured Strain

A simple approach for computing acceleration and velocity of a structure from the strain is proposed in this study. First, deflection and slope of the structure are computed from the strain using a two-step theory. Frequencies of the structure are computed from the time histories of strain using a parameter estimation technique together with an autoregressive moving average model. From deflection, slope, and frequencies of the structure, acceleration and velocity of the structure can be obtained using the proposed approach. Simple harmonic motion is assumed for the acceleration computations, and the central difference equation with a linear autoregressive model is used for the computations of velocity. A cantilevered rectangular wing model is used to validate the simple approach. Quality of the computed deflection, acceleration, and velocity values are independent of the number of fibers. The central difference equation with a linear autoregressive model proposed in this study follows the target response with reasonable accuracy. Therefore, the handicap of the backward difference equation, phase shift, is successfully overcome.

shape sensing↗
DOE OSTI2026

Enhanced accuracy through ensembling of randomly initialized auto-regressive models for dynamical systems

Computational mechanics simulations using traditional finite element methods (FEM) require prohibitively expensive computational resources for real-time engineering applications, design optimization, and digital twin implementations. While machine learning (ML) surrogate models offer significant computational speedups, autoregressive ML models for time-dependent mechanical systems suffer from error accumulation that compromises long-term prediction reliability - a critical concern for engineering applications where accuracy over extended time horizons is essential for safety and performance assessments. Here, we propose a deep ensemble framework specifically designed to address this challenge in computational mechanics applications, where multiple ML surrogate models with random weight initializations are trained in parallel and their predictions aggregated during inference. This approach leverages statistical diversity to maximize information gain from a fixed set of training data and to mitigate error propagation, while maintaining the computational efficiency that makes ML surrogates attractive for engineering practice. We validate the framework on three representative problems spanning critical areas of computational mechanics: stress field evolution in heterogeneous microstructures under complex loading (relevant to advanced materials design and composite analysis), planetary-scale shallow water dynamics (applicable to environmental and geotechnical engineering), and Gray-Scott reaction-diffusion systems (relevant to mass transport and chemical process engineering). Across all test cases, the ensemble approach demonstrates consistent error reduction of 15-33% compared to individual models. The codes for this work are available on GitHub (https://github.com/Graham-Brady-Research-Group/AutoregressiveEnsemble_SpatioTemporal_Evolution).

autoregressive prediction↗
NASA NTRS1988

Random Process Simulation for stochastic fatigue analysis

A simulation technique is described which directly synthesizes the extrema of a random process and is more efficient than the Gaussian simulation method. Such a technique is particularly useful in stochastic fatigue analysis because the required stress range moment E(R sup m), is a function only of the extrema of the random stress process. The family of autoregressive moving average (ARMA) models is reviewed and an autoregressive model is presented for modeling the extrema of any random process which has a unimodal power spectral density (psd). The proposed autoregressive technique is found to produce rainflow stress range moments which compare favorably with those computed by the Gaussian technique and to average 11.7 times faster than the Gaussian technique. The autoregressive technique is also adapted for processes having bimodal psd's. The adaptation involves using two autoregressive processes to simulate the extrema due to each mode and the superposition of these two extrema sequences. The proposed autoregressive superposition technique is 9 to 13 times faster than the Gaussian technique and produces comparable values for E(R sup m) for bimodal psd's having the frequency of one mode at least 2.5 times that of the other mode.

Larsen, Curtis E.↗