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DOE OSTI2021

International collaboration framework for the calculation of performance loss rates: Data quality, benchmarks, and trends (towards a uniform methodology)

Abstract The IEA PVPS Task 13 group, experts who focus on photovoltaic performance, operation, and reliability from several leading R&D centers, universities, and industrial companies, is developing a framework for the calculation of performance loss rates of a large number of commercial and research photovoltaic (PV) power plants and their related weather data coming across various climatic zones. The general steps to calculate the performance loss rate are (i) input data cleaning and grading; (ii) data filtering; (iii) performance metric selection, corrections, and aggregation; and finally, (iv) application of a statistical modeling method to determine the performance loss rate value. In this study, several high‐quality power and irradiance datasets have been shared, and the participants of the study were asked to calculate the performance loss rate of each individual system using their preferred methodologies. The data are used for benchmarking activities and to define capabilities and uncertainties of all the various methods. The combination of data filtering, metrics (performance ratio or power based), and statistical modeling methods are benchmarked in terms of (i) their deviation from the average value and (ii) their uncertainty, standard error, and confidence intervals. It was observed that careful data filtering is an essential foundation for reliable performance loss rate calculations. Furthermore, the selection of the calculation steps filter/metric/statistical method is highly dependent on one another, and the steps should not be assessed individually.

14 SOLAR ENERGY↗

DOE OSTI2021

Snowmass2021 - Letter of interest cosmology intertwined II: The hubble constant tension

The current cosmological probes have provided a fantastic confirmation of the standard Λ Cold Dark Matter cosmological model, which has been constrained with unprecedented accuracy. However, with the increase of the experimental sensitivity, a few statistically significant tensions between different independent cosmological datasets emerged. While these tensions can be in part the result of systematic errors, the persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the need for new physics. In this Letter of Interest we will focus on the 4.4σ tension between the Planck estimate of the Hubble constant H0 and the SH0ES collaboration measurements. After showing the H0 evaluations made from different teams using different methods and geometric calibrations, we will list a few interesting models of new physics that could solve this tension and discuss how the next decade’s experiments will be crucial.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Chemoradiation With Concomitant Boosts Followed by Radical Surgery in Locally Advanced Cervical Cancer: Long-term Results of the ROMA-2 Prospective Phase 2 Study

Purpose: This prospective, phase 2 study aimed at assessing the efficacy of accelerated fractionation radiation therapy by concomitant boosts (CBs) associated with chemoradiation therapy (CRT) of the whole pelvis, in improving the rate of pathological complete response (pCR) to treatment in patients with International Federation of Gynaecology and Obstetrics (FIGO) stage IB2-IVA locally advanced cervical cancer. Methods and Materials: Neoadjuvant CRT included conformal irradiation of the whole pelvis with a total dose of 39.6 Gy (1.8 cGy/fraction, 22 fractions), plus additional irradiation of primary tumor and parametria with 10.8 Gy administered with CBs (0.9 cGy/fraction, 12 fractions, every other day). Concomitant chemotherapy included cisplatin (20 mg/m{sup 2}, days 1-4 and 26-30 of treatment), and capecitabine (1300 mg/m{sup 2}/daily, orally) during the first 2 and the last 2 weeks of treatment. Radical hysterectomy plus pelvic with or without aortic lymphadenectomy was performed within 6 to 8 weeks from CRT. Toxicity was recorded according to Radiation Therapy Oncology Group toxicity criteria and Chassagne grading system. Based on the Simon design, 103 cases were required, and the regimen would be considered active if >45 pCR were registered (α error = 0.05; β error = 0.1). Results: pCR was documented in 51 cases (50.5%), and the regimen was considered active, according to the planned statistical assumptions. At median follow-up of 36 months (range: 7-85 months), the 3-year local failure rate was 7%, whereas the 3-year disease-free and overall survival rates were 73.0% and 86.1%, respectively. Grade 3 leukopenia and neutropenia were reported in only 1 and 2 cases, respectively. Gastrointestinal toxicity was always grade 1 or 2. Conclusions: Addition of CBs in the accelerated fractionation modality to the whole pelvis chemoradiation followed by radical surgery results in a high rate of pathologically assessed complete response to CRT and a very encouraging local control rate, with acceptable toxicity.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2017

Treatment Planning System Calculation Errors Are Present in Most Imaging and Radiation Oncology Core-Houston Phantom Failures

Purpose: The anthropomorphic phantom program at the Houston branch of the Imaging and Radiation Oncology Core (IROC-Houston) is an end-to-end test that can be used to determine whether an institution can accurately model, calculate, and deliver an intensity modulated radiation therapy dose distribution. Currently, institutions that do not meet IROC-Houston's criteria have no specific information with which to identify and correct problems. In the present study, an independent recalculation system was developed to identify treatment planning system (TPS) calculation errors. Methods and Materials: A recalculation system was commissioned and customized using IROC-Houston measurement reference dosimetry data for common linear accelerator classes. Using this system, 259 head and neck phantom irradiations were recalculated. Both the recalculation and the institution's TPS calculation were compared with the delivered dose that was measured. In cases in which the recalculation was statistically more accurate by 2% on average or 3% at a single measurement location than was the institution's TPS, the irradiation was flagged as having a “considerable” institutional calculation error. The error rates were also examined according to the linear accelerator vendor and delivery technique. Results: Surprisingly, on average, the reference recalculation system had better accuracy than the institution's TPS. Considerable TPS errors were found in 17% (n=45) of the head and neck irradiations. Also, 68% (n=13) of the irradiations that failed to meet the IROC-Houston criteria were found to have calculation errors. Conclusions: Nearly 1 in 5 institutions were found to have TPS errors in their intensity modulated radiation therapy calculations, highlighting the need for careful beam modeling and calculation in the TPS. An independent recalculation system can help identify the presence of TPS errors and pass on the knowledge to the institution.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Dual particle imaging using time-of-flight neutron classification

Fast-neutron imaging technology is well-suited for passive nuclear material monitoring, secondary inspection of flagged cargo, and wide-area search for lost neutron sources. However, imaging systems that use pulse shape discrimination for event classification require complex pulse waveform analysis. In this work, we evaluate time-of-flight (TOF) based particle classification as an alternative solution for fast-neutron imaging by classifying all events with a TOF above a maximum threshold as neutrons. We measured a Cf-252 source next to Cs-137 using a 12-bar organic-glass scintillator array. By varying the TOF thresholds for neutron identification, we demonstrate a clear trade-off between event yield and backprojection image fidelity, with stricter thresholds improving precision at the cost of statistics, TOF thresholded data generated an image that predicted the neutron source direction with 20% reduced mean central angle prediction error compared to a traditional pulse shape discrimination (PSD) method with comparable event count. Time-of-flight particle classification shows promise as an alternative to pulse shape discrimination systems for fast neutron imaging systems looking to minimize costs and size of electronics with comparable imaging quality. The sources used demonstrate that the method is effective in classifying measured neutrons in a measurement environment with 150 μCi Cs-137 and 1.6 × 10 6 n/s Cf-252 sources positioned at distances of 66 cm and 81 cm from the detector. Additionally, the method classifies low-energy neutron events that pulse shape discrimination removes, so a combination of both methods would result in a higher overall neutron event efficiency.

Heriot, William [Univ. of Michigan, Ann Arbor, MI ↗

DOE OSTI2020

Deeply uncertain: comparing methods of uncertainty quantification in deep learning algorithms

We present a comparison of methods for uncertainty quantification (UQ) in deep learning algorithms in the context of a simple physical system. Three of the most common uncertainty quantification methods - Bayesian Neural Networks (BNN), Concrete Dropout (CD), and Deep Ensembles (DE) - are compared to the standard analytic error propagation. We discuss this comparison in terms endemic to both machine learning ("epistemic" and "aleatoric") and the physical sciences ("statistical" and "systematic"). The comparisons are presented in terms of simulated experimental measurements of a single pendulum - a prototypical physical system for studying measurement and analysis techniques. Our results highlight some pitfalls that may occur when using these UQ methods. For example, when the variation of noise in the training set is small, all methods predicted the same relative uncertainty independently of the inputs. This issue is particularly hard to avoid in BNN. On the other hand, when the test set contains samples far from the training distribution, we found that no methods sufficiently increased the uncertainties associated to their predictions. This problem was particularly clear for CD. In light of these results, we make some recommendations for usage and interpretation of UQ methods.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Machine learning for neutron reflectometry data analysis of two-layer thin films

Neutron reflectometry (NR) is a powerful tool for probing thin films at length scales down to nanometers. We investigated the use of a neural network to predict a two-layer thin film structure to model a given measured reflectivity curve. Application of this neural network to predict a thin film structure revealed that it was accurate and could provide an excellent starting point for traditional fitting methods. Employing prediction-guided fitting has considerable potential for more rapidly producing a result compared to the labor-intensive but commonly-used approach of trial and error searches prior to refinement. A deeper look at the stability of the predictive power of the neural network against statistical fluctuations of measured reflectivity profiles showed that the predictions are stable. We conclude that the approach presented here can provide valuable assistance to users of NR and should be further extended for use in studies of more complex n-layer thin film systems. This result also opens up the possibility of developing adaptive measurement systems in the future.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Block Lanczos algorithm for lattice QCD spectroscopy and matrix elements

Recent work introduced a new framework for analyzing correlation functions with improved convergence and signal-to-noise properties, as well as rigorous quantification of excited-state effects, based on the Lanczos algorithm and spurious eigenvalue filtering with the Cullum-Willoughby test. Here, we extend this framework to the analysis of correlation-function matrices built from multiple interpolating operators in lattice quantum chromodynamics (QCD) by constructing an oblique generalization of the block Lanczos algorithm, as well as a new physically motivated reformulation of the Cullum-Willoughby test that generalizes to block Lanczos straightforwardly. The resulting block Lanczos method directly extends generalized eigenvalue problem (GEVP) methods, which can be viewed as applying a single iteration of block Lanczos. Block Lanczos provides qualitative and quantitative advantages over GEVP methods analogous to the benefits of Lanczos over the standard effective mass, including faster convergence to ground- and excited-state energies, explicitly computable two-sided error bounds, straightforward extraction of matrix elements of external currents, and asymptotically constant signal-to-noise. No fits or statistical inference are required. Proof-of-principle calculations are performed for noiseless mock-data examples as well as two-by-two proton correlation-function matrices in lattice QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Robust Medium-Voltage Distribution System State Estimation using Multi-Source Data

Due to the lack of sufficient online measurements for distribution system observability, pseudo-measurements from short-term load or distributed renewable energy resources (DERs) forecasting are used. However, the accuracy of them is low and thus significantly limits the performance of distribution system state estimation (DSSE). In this paper, a robust DSSE that integrates multi-source measurement data is proposed. Specifically, the historical low-voltage (LV) side smart meters are used to forecast load and DERs injections via the support vector machine (SVM) with optimally tuned parameters. By contrast, the online smart meters at LV side are utilized to derive equivalent power injections at the MV/LV transformers, yielding more accurate pseudo-measurements compared to the forecasted injections. Furthermore, to deal with bad data caused by communication loss, instrumental errors and cyber attacks, robust DSSE that relies on generalized maximum-likelihood (GM)-estimation criterion is developed. The projection statistics are developed to adjust the weights of each measurement, leading to better balance between pseudo- and real-time measurements. Numerical results conducted on modified IEEE 33-bus system with DG integration demonstrate the effectiveness and robustness of the proposed method.

distribution system state estimation↗

DOE OSTI2015

SU-E-T-550: Modulation Index for VMAT

Purpose: To present modulation indices (MIs) for volumetric modulated arc therapy (VMAT). Methods: A total of 40 VMAT plans were retrospectively selected. To investigate the delivery accuracy of each VMAT plan, gamma passing rates, differences in modulating parameters between plans and log files, and differences between the original plans and the plans reconstructed with the log files were acquired. A modulation index (MIt) was designed by multiplications of the weighted quantifications of MLC speeds, MLC accelerations, gantry accelerations and dose-rate variations. Textural features including angular second moment, inverse difference moment, contrast, variance, correlation and entropy were calculated from the fluences of each VMAT plan. To test the performance of suggested MIs, Spearman’s rank correlation coefficients (r) with the plan delivery accuracy were calculated. Conventional modulation indices for VMAT including the modulation complexity score for VMAT (MCSv), leaf travel modulation complexity score (LTMCS) and MI by Li & Xing were calculated, and their correlations were also analyzed in the same way. Results: The r values of contrast (particular displacement distance, d = 1), variance (d = 1), MIt, MCSv, LTMCS and MI by Li&Xing to the local gamma passing rates with 2%/2 mm were 0.547 (p < 0.001), 0.519 (p < 0.001), −0.658 (p < 0.001), 0.186 (p = 0.251), 0.312 (p = 0.05) and −0.455 (p = 0.003), respectively. The r values of those to the MLC errors were −0.863, −0.828, 0.917, −0.635, − 0.857 and 0.795, respectively (p < 0.001). For dose-volumetric parameters, MIt showed higher statistically significant correlations than did the conventional modulation indices. Conclusion: The MIt, contrast (d = 1) and variance (d = 1) showed good performance to predict the VMAT delivery accuracy showing higher correlations to the results of various types of verification methods for VMAT. This work was in part supported by the National Research Foundation of Korea (NRF) grant (no. 490-20140029 and no. 490-20130047) funded by the Korea government.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2016

SU-C-BRB-05: Determining the Adequacy of Auto-Contouring Via Probabilistic Assessment of Ensuing Treatment Plan Metrics in Comparison with Manual Contours

Purpose: To determine if auto-contour and manual-contour—based plans differ when evaluated with respect to probabilistic coverage metrics and biological model endpoints for prostate IMRT. Methods: Manual and auto-contours were created for 149 CT image sets acquired from 16 unique prostate patients. A single physician manually contoured all images. Auto-contouring was completed utilizing Pinnacle’s Smart Probabilistic Image Contouring Engine (SPICE). For each CT, three different 78 Gy/39 fraction 7-beam IMRT plans are created; PD with drawn ROIs, PAS with auto-contoured ROIs, and PM with auto-contoured OARs with the manually drawn target. For each plan, 1000 virtual treatment simulations with different sampled systematic errors for each simulation and a different sampled random error for each fraction were performed using our in-house GPU-accelerated robustness analyzer tool which reports the statistical probability of achieving dose-volume metrics, NTCP, TCP, and the probability of achieving the optimization criteria for both auto-contoured (AS) and manually drawn (D) ROIs. Metrics are reported for all possible cross-evaluation pairs of ROI types (AS,D) and planning scenarios (PD,PAS,PM). Bhattacharyya coefficient (BC) is calculated to measure the PDF similarities for the dose-volume metric, NTCP, TCP, and objectives with respect to the manually drawn contour evaluated on base plan (D-PD). Results: We observe high BC values (BC≥0.94) for all OAR objectives. BC values of max dose objective on CTV also signify high resemblance (BC≥0.93) between the distributions. On the other hand, BC values for CTV’s D95 and Dmin objectives are small for AS-PM, AS-PD. NTCP distributions are similar across all evaluation pairs, while TCP distributions of AS-PM, AS-PD sustain variations up to %6 compared to other evaluated pairs. Conclusion: No significant probabilistic differences are observed in the metrics when auto-contoured OARs are used. The prostate auto-contour needs improvement to achieve clinically equivalent plans.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

Efficient design of random metasurfaces

Random media introduce large degrees of freedom in device design and can thus address challenges in manipulating optical waves. Wave shaping with metasurfaces has mainly utilized periodic or quasi-periodic grids, and the potential of random arrangement of particles for devices has only come under investigation recently. The main difficulty in pursuing random metasurfaces is the identification of the degrees of freedom that optimize their efficiencies and functions. They can also encode information using the statistics of particle distribution. We propose a phase-map that accounts for the statistical nature of random media. The method takes into account effects of random near-field couplings that introduce phase errors by affecting the phase shift of elements. The proposed approach increases the efficiency of our random metasurface devices by up to ~20%. Furthermore, this work paves the way toward the efficient design of random metasurfaces with potential applications in highly secure optical cryptography and information encoding.

Nasari, Hadiseh↗

DOE OSTI2024

High-resolution hypernuclear decay pion spectroscopy at MAMI and future

Hypernuclear decay pion spectroscopy was established in 2012 at MAMI as a mass spectroscopy method for light hypernuclei. A monochromatic pion peak from $^4_Λ$H was successfully observed, and the Λ binding energy was determined to be B Λ = 2.157±0.005(stat.)±0.077(syst.) MeV in the 2014 run. In 2022, an upgrade experiment for $^3_Λ$H spectroscopy was conducted using a newly developed Li target. The absolute electron beam energy will be measured by the synchrotron radiation interferometry, which will be applied with the spectrometer calibration to improve the systematic error. The decay pion spectroscopy is planned to be performed at JLab Hall-C, which would significantly increase the statistics thanks to the higher energy beam, the better K + identification, and the faster data acquisition system. This experiment has been submitted as a Letter of Intent in JLab PAC51. The upgraded decay pion spectroscopy method is expected to provide new, accurate hypernuclear data, which will contribute to the advancement of our understanding of hypernuclear physics

47 OTHER INSTRUMENTATION↗

DOE OSTI2013

Analysis and Synthesis of Load Forecasting Data for Renewable Integration Studies: Preprint

As renewable energy constitutes greater portions of the generation fleet, the importance of modeling uncertainty as part of integration studies also increases. In pursuit of optimal system operations, it is important to capture not only the definitive behavior of power plants, but also the risks associated with systemwide interactions. This research examines the dependence of load forecast errors on external predictor variables such as temperature, day type, and time of day. The analysis was utilized to create statistically relevant instances of sequential load forecasts with only a time series of historic, measured load available. The creation of such load forecasts relies on Bayesian techniques for informing and updating the model, thus providing a basis for networked and adaptive load forecast models in future operational applications.

17 WIND ENERGY↗

DOE OSTI2022

Model-Form Epistemic Uncertainty Quantification for Modeling with Differential Equations: Application to Epidemiology

Modeling real-world phenomena to any degree of accuracy is a challenge that the scientific research community has navigated since its foundation. Lack of information and limited computational and observational resources necessitate modeling assumptions which, when invalid, lead to model-form error (MFE). The work reported herein explored a novel method to represent model-form uncertainty (MFU) that combines Bayesian statistics with the emerging field of universal differential equations (UDEs). The fundamental principle behind UDEs is simple: use known equational forms that govern a dynamical system when you have them; then incorporate data-driven approaches – in this case neural networks (NNs) – embedded within the governing equations to learn the interacting terms that were underrepresented. Utilizing epidemiology as our motivating exemplar, this report will highlight the challenges of modeling novel infectious diseases while introducing ways to incorporate NN approximations to MFE. Prior to embarking on a Bayesian calibration, we first explored methods to augment the standard (non-Bayesian) UDE training procedure to account for uncertainty and increase robustness of training. In addition, it is often the case that uncertainty in observations is significant; this may be due to randomness or lack of precision in the measurement process. This uncertainty typically manifests as “noisy” observations which deviate from a true underlying signal. To account for such variability, the NN approximation to MFE is endowed with a probabilistic representation and is updated using available observational data in a Bayesian framework. By representing the MFU explicitly and deploying an embedded, data-driven model, this approach enables an agile, expressive, and interpretable method for representing MFU. In this report we will provide evidence that Bayesian UDEs show promise as a novel framework for any science-based, data-driven MFU representation; while emphasizing that significant advances must be made in the calibration of Bayesian NNs to ensure a robust calibration procedure.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Selecting registration schemes in case of interstitial lung disease follow-up in CT

Purpose: Primary goal of this study is to select optimal registration schemes in the framework of interstitial lung disease (ILD) follow-up analysis in CT. Methods: A set of 128 multiresolution schemes composed of multiresolution nonrigid and combinations of rigid and nonrigid registration schemes are evaluated, utilizing ten artificially warped ILD follow-up volumes, originating from ten clinical volumetric CT scans of ILD affected patients, to select candidate optimal schemes. Specifically, all combinations of four transformation models (three rigid: rigid, similarity, affine and one nonrigid: third order B-spline), four cost functions (sum-of-square distances, normalized correlation coefficient, mutual information, and normalized mutual information), four gradient descent optimizers (standard, regular step, adaptive stochastic, and finite difference), and two types of pyramids (recursive and Gaussian-smoothing) were considered. The selection process involves two stages. The first stage involves identification of schemes with deformation field singularities, according to the determinant of the Jacobian matrix. In the second stage, evaluation methodology is based on distance between corresponding landmark points in both normal lung parenchyma (NLP) and ILD affected regions. Statistical analysis was performed in order to select near optimal registration schemes per evaluation metric. Performance of the candidate registration schemes was verified on a case sample of ten clinical follow-up CT scans to obtain the selected registration schemes. Results: By considering near optimal schemes common to all ranking lists, 16 out of 128 registration schemes were initially selected. These schemes obtained submillimeter registration accuracies in terms of average distance errors 0.18 ± 0.01 mm for NLP and 0.20 ± 0.01 mm for ILD, in case of artificially generated follow-up data. Registration accuracy in terms of average distance error in clinical follow-up data was in the range of 1.985–2.156 mm and 1.966–2.234 mm, for NLP and ILD affected regions, respectively, excluding schemes with statistically significant lower performance (Wilcoxon signed-ranks test, p < 0.05), resulting in 13 finally selected registration schemes. Conclusions: Selected registration schemes in case of ILD CT follow-up analysis indicate the significance of adaptive stochastic gradient descent optimizer, as well as the importance of combined rigid and nonrigid schemes providing high accuracy and time efficiency. The selected optimal deformable registration schemes are equivalent in terms of their accuracy and thus compatible in terms of their clinical outcome.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

An algebraic method for constructing stable and consistent autoregressive filters

In this paper, we introduce an algebraic method to construct stable and consistent univariate autoregressive (AR) models of low order for filtering and predicting nonlinear turbulent signals with memory depth. By stable, we refer to the classical stability condition for the AR model. By consistent, we refer to the classical consistency constraints of Adams–Bashforth methods of order-two. One attractive feature of this algebraic method is that the model parameters can be obtained without directly knowing any training data set as opposed to many standard, regression-based parameterization methods. It takes only long-time average statistics as inputs. The proposed method provides a discretization time step interval which guarantees the existence of stable and consistent AR model and simultaneously produces the parameters for the AR models. In our numerical examples with two chaotic time series with different characteristics of decaying time scales, we find that the proposed AR models produce significantly more accurate short-term predictive skill and comparable filtering skill relative to the linear regression-based AR models. These encouraging results are robust across wide ranges of discretization times, observation times, and observation noise variances. Finally, we also find that the proposed model produces an improved short-time prediction relative to the linear regression-based AR-models in forecasting a data set that characterizes the variability of the Madden–Julian Oscillation, a dominant tropical atmospheric wave pattern.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗