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Towards a Theory of Sampled-Data Piecewise-Deterministic Markov Processes

The analysis and design of practical control systems requires that stochastic models be employed. Analysis and design tools have been developed, for example, for Markovian jump linear continuous and discrete-time systems, piecewise-deterministic processes (PDP's), and general stochastic hybrid systems (GSHS's). These model classes have been used in many applications, including fault tolerant control and networked control systems. This paper presents initial results on the analysis of a sampled-data PDP representation of a nonlinear sampled-data system with a jump linear controller. In particular, it is shown that the state of the sampled-data PDP satisfies the strong Markov property. In addition, a relation between the invariant measures of a sampled-data system driven by a stochastic process and its associated discrete-time representation are presented. As an application, when the plant is linear with no external input, a sufficient testable condition for the convergence in distribution to the invariant delta Dirac measure is given.

Herencia-Zapana, Heber

Quasi-Static Probabilistic Structural Analyses Process and Criteria

Current deterministic structural methods are easily applied to substructures and components, and analysts have built great design insights and confidence in them over the years. However, deterministic methods cannot support systems risk analyses, and it was recently reported that deterministic treatment of statistical data is inconsistent with error propagation laws that can result in unevenly conservative structural predictions. Assuming non-nal distributions and using statistical data formats throughout prevailing stress deterministic processes lead to a safety factor in statistical format, which integrated into the safety index, provides a safety factor and first order reliability relationship. The embedded safety factor in the safety index expression allows a historically based risk to be determined and verified over a variety of quasi-static metallic substructures consistent with the traditional safety factor methods and NASA Std. 5001 criteria.

Goldberg, B.

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

Vanel, Florence O.

Proposed Reliability-Based Damage Tolerance Guidelines for Space Systems

Deterministic damage tolerance guidelines for highly reusable and efficiently designed launch systems can be challenging to meet and result in overly conservative assessments for tightly controlled manufacturing processes. Deterministic approaches may be unconservative when the structure is workmanship sensitive and there is a wide spread in fracture properties. Reliability-based damage tolerance assessments targeting a component reliability over the service life commensurate to mission risk posture is a promising alternative. Low production rates, short fleets, and lack of standards or guidance has slowed down widespread adoption of this method. Guidance for the robust application of reliability-based damage tolerance for space systems are proposed. These guidelines cover the treatment of uncertainty in damage tolerance analysis, the collection of data to develop probabilistic distributions, uncertainty propagation methods, and types of hardware.

Reliability-Based Damage Tolerance

Horizontal wind estimates deterministically derived from the STS-1 entry flight date--a comparison with available meteorology data

Two wind profiles were determined from STS-1 entry flight data based on preliminary best estimate trajectory (BET). The deterministic process used in deriving the atmospheric winds requires inertial estimates of the spacecraft angle-of-attack (alpha) and side-slip angle (beta) from the BET in conjunction with some air data system measurements of the actual angles. The current orbiter air data system (OADS) provides the necessary alpha information. Two beta profiles were adopted. The first profile assumed that the spacecraft would weathervane into any prevailing wind. The second assumed a conservative side-slip history computed from measured accelerations in the spacecraft body axes. It is shown that there are no major differences between the deterministic winds computed using both methods. Further, comparisons of these winds with raw measurements from Tehachapi, California, and preliminary winds obtained from the LaRC LAIRS file and the JSC/TRW descent BET are presented.

Kelly, G. M.

Protostars and planets - Overview from a planetary perspective

Today the simultaneous formation of a star and planetary system is understood to be natural and coupled consequences of the collapse of an interstellar cloud of molecular gas and dust. Ideas put forward to account for the existence of the solar system seem generally applicable to star formation throughout the universe. If this is indeed the case, then planetary systems should be present in large numbers throughout the universe. Even the gross structural features of the planetary system in the solar system seem largely to be the result of nearly deterministic processes, rather than the result of chance alone; many planetary systems throughout the universe may resemble this one. This chapter summarizes and examines some of the implications of ideas about the formation of stars and planetary systems.

Levy, E. H.

An introduction to chaotic and random time series analysis

The origin of chaotic behavior and the relation of chaos to randomness are explained. Two mathematical results are described: (1) a representation theorem guarantees the existence of a specific time-domain model for chaos and addresses the relation between chaotic, random, and strictly deterministic processes; (2) a theorem assures that information on the behavior of a physical system in its complete state space can be extracted from time-series data on a single observable. Focus is placed on an important connection between the dynamical state space and an observable time series. These two results lead to a practical deconvolution technique combining standard random process modeling methods with new embedded techniques.

Scargle, Jeffrey D.

Pre-Finishing of SiC for Optical Applications

13 Manufacturing & Prototyping A method is based on two unique processing steps that are both based on deterministic machining processes using a single-point diamond turning (SPDT) machine. In the first step, a high-MRR (material removal rate) process is used to machine the part within several microns of the final geometry. In the second step, a low-MRR process is used to machine the part to near optical quality using a novel ductile regime machining (DRM) process. DRM is a deterministic machining process associated with conditions under high hydrostatic pressures and very small depths of cut. Under such conditions, using high negative-rake angle cutting tools, the high-pressure region near the tool corresponds to a plastic zone, where even a brittle material will behave in a ductile manner. In the high-MRR processing step, the objective is to remove material with a sufficiently high rate such that the process is economical, without inducing large-scale subsurface damage. A laser-assisted machining approach was evaluated whereby a CO2 laser was focused in advance of the cutting tool. While CVD (chemical vapor deposition) SiC was successfully machined with this approach, the cutting forces were substantially higher than cuts at room temperature under the same machining conditions. During the experiments, the expansion of the part and the tool due to the heating was carefully accounted for. The higher cutting forces are most likely due to a small reduction in the shear strength of the material compared with a larger increase in friction forces due to the thermal softening effect. The key advantage is that the hybrid machine approach has the potential to achieve optical quality without the need for a separate optical finishing step. Also, this method is scalable, so one can easily progress from machining 50-mm-diameter samples to the 250-mm-diameter mirror that NASA desires.

Rozzi, Jay

Propulsion Airframe Aeroacoustics Technology Evaluation and Selection Using a Multi-Attribute Decision Making Process and Non-Deterministic Design

The Systems Analysis Branch at NASA Langley Research Center has investigated revolutionary Propulsion Airframe Aeroacoustics (PAA) technologies and configurations for a Blended-Wing-Body (BWB) type aircraft as part of its research for NASA s Quiet Aircraft Technology (QAT) Project. Within the context of the long-term NASA goal of reducing the perceived aircraft noise level by a factor of 4 relative to 1997 state of the art, major configuration changes in the propulsion airframe integration system were explored with noise as a primary design consideration. An initial down-select and assessment of candidate PAA technologies for the BWB was performed using a Multi-Attribute Decision Making (MADM) process consisting of organized brainstorming and decision-making tools. The assessments focused on what effect the PAA technologies had on both the overall noise level of the BWB and what effect they had on other major design considerations such as weight, performance and cost. A probabilistic systems analysis of the PAA configurations that presented the best noise reductions with the least negative impact on the system was then performed. Detailed results from the MADM study and the probabilistic systems analysis will be published in the near future.

Burg, Cecile M.

Study of random process theory aids digital data processing

Study of techniques for all random process technology, including stationary, nonstationary, and Gaussian bivariate, aids digital data processing. It presents material on digital filtering, correlation function, optimal spectral smoothing, deterministic data processing, and nonstationary spectrum and correlation analyses.

Bordner, G. W.

Temporal Coarse Graining for Classical Stochastic Noise in Quantum Systems

Simulations of quantum systems with Hamiltonian classical stochastic noise can be challenging when the noise exhibits temporal correlations over a multitude of time scales, such as for 1/f noise in solid-state quantum information processors. Here we present an approach for simulating Hamiltonian classical stochastic noise that performs temporal coarse-graining by effectively integrating out the high-frequency components of the noise. We focus on the case where the stochastic noise can be expressed as a sum of Ornstein-Uhlenbeck processes. Temporal coarse-graining is then achieved by conditioning the stochastic process on a coarse realization of the noise, expressing the conditioned stochastic process in terms of a sum of smooth, deterministic functions and bridge processes with boundaries fixed at zero, and performing the ensemble average over the bridge processes. For Ornstein-Uhlenbeck processes, the deterministic components capture all dependence on the coarse realization, and the stochastic bridge processes are not only independent but taken from the same distribution with correlators that can be expressed analytically, allowing the associated noise propagators to be precomputed once for all simulations. This combination of noise trajectories on a coarse time grid and ensemble averaging over bridge processes has practical advantages, such as a simple concatenation rule, that we highlight with numerical examples.

Albash, Tameem [Sandia National Lab. (SNL-NM), Alb

A Practical Approach to Uncertainty Quantification Using Probability Boxes

To date, while the use of CFD for aerospace vehicle design and development is prevalent, the documentation of uncertainties associated with the simulations are rare. Instead, the current state-of-the-art relies heavily on the experience of the CFD practitioner to estimate the uncertainty associated with their simulations through simple sensitivity studies or subject matter expertise. This practice will have to be replaced with a formal uncertainty quantification (UQ) process if CFD is to play an expanded role in the research and engineering design community, test and evaluation community, and ultimately certification for flight. Accounting for uncertainties in a formal manner is a tedious process. Moreover, the typical CFD practitioner is not likely to be familiar with formal UQ methods. These factors have prevented the adoption of UQ methods in the engineering design and development cycle. This presentation will outline a credible approach to UQ using Probability Boxes that is straightforward to apply, and can readily be automated using existing UQ tool sets such as the DAKOTA packaged developed at Sandia. The added expense incurred when moving away from a deterministic CFD process to a stochastic one that captures uncertainties to enable risk-informed decision making will be discussed, as well as effective ways to reduce the computational costs.

Uncertainty Quantification

Data and scripts associated with “Non-random processes impacting organic matter chemistry are maximized in mid-order streams”

NOTE: The manuscript associated with this data package is currently in review. The data may be revised based on reviewer feedback. Upon manuscript acceptance, this data package will be updated with the final dataset and additional metadata. This data package is associated with the publication “Non-random processes impacting organic matter chemistry are maximized in mid-order streams” submitted to Limnology and Oceanography (L&O) by Danczak et al. (in review). This package contains data and scripts used to investigate dissolved organic matter (DOM) molecular chemistry and diversification processes across 47 surface-water sampling sites in the Yakima River Basin, Washington, USA, during an August 2021 sampling campaign. The package contains analyses of ultrahigh-resolution Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS), geochemical measurements, geospatial attributes, molecular diversity, and meta-metabolome ecological null models needed to reproduce the main manuscript results. The underlying field data were pulled from exising data packages at https://doi.org/10.15485/1892052 (Fulton et al., 2022) and https://doi.org/10.15485/1898914 (Grieger et al., 2022). For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. We thank the following organizations for providing access to field locations for sample collection: the United States Forest Service, Washington Department of Fish and Wildlife, Washington Department of Natural Resources, the Confederated Tribes and Bands of the Yakama Nation, and the Cowiche Canyon Conservatory. Research was conducted under Washington State Parks and Recreation Commission Scientific Research Permit #210901. We are grateful to the Yakama Nation Tribal Council and Yakama Nation Fisheries for their collaboration in facilitating sample collection and ensuring data usage aligns with their values and worldview. This data package contains an R-Markdown file for analyses and five folders: (1) Data, (2) Geospatial Data, (3) Supplemental_Files, (5) Figures_pdf, (4) and src. The Data folder contains tabular inputs and derived files used in the manuscript analysis. The Geospatial Data folder contains climate and water-balance, hydrologic, land-cover, population/regional water-use, stream, topographic, and stream-order attribute CSV files. The src folder contains scripts used to process data, run analyses, and generate figures. The Figures_pdf folder contains manuscript figure outputs. The Supplemental_Files folder contains supplemental analysis products. All files are .csv, .pdf, .html, .png, .R, .Rmd, .svg, or .tre. This data package is associated with the rcfsa-RC2-SPS_Null_Modeling repository found at https://github.com/river-corridors-sfa/rcfsa-RC2-SPS_Null_Modeling.

54 ENVIRONMENTAL SCIENCES

Real-time plasma monitoring framework for advanced plasma control and ML-research in DIII-D

Real-time and adaptive plasma control is crucial for robust tokamak operation, requiring sensitivity and tolerance measurements of the plasma state. This paper presents the implementation of an integrated real-time plasma monitoring framework on the DIII-D tokamak to support advanced control approaches, including machine-learning (ML) methods. The system is built on the SHIELD framework, a high-performance modular architecture that provides a unified pipeline for integrating diverse diagnostics. The framework leverages high-bandwidth digitizers, fast numerical processing, and deterministic, low-latency interconnects to stream high-fidelity data from diagnostics such as electron cyclotron emission (ECE), beam emission spectroscopy (BES), CO interferometers, and a visible tangential divertor camera (TangTV). The system’s validity is demonstrated through direct comparisons of real-time and offline data. Furthermore, we present two key applications of the developed plasma monitoring system with ML-based plasma control strategies, including real-time divertor detachment and active Alfvén Eigenmode control. As a result, this work presents a robust and scalable approach for integrating high-frequency, multidimensional diagnostics into advanced control algorithms for future fusion devices.

AI/ML

High spectral resolution remote sensing of the land

Spectral remote sensing has been practiced on a large scale since the launch of Landsat 1 in 1972. The limited information contained in this spectrally undersampled data set has led to the development of sophisticated statistical-inferential methods for data analysis. The results are usually limited by the availability of ground truth information. Recent technological developments have made it feasible to create narrow-band, contiguous, spectral image data sets that make possible the identification of surface cover materials based on the complete reflectance spectrum for each picture element. This capability will revolutionize the use of remote sensing data and require new deterministic image processing techniques to extract the full information content from the data. Sensors, based on the concept of imaging spectrometry and the new technology of area array infrared detectors, have been constructed and are candidates for Shuttle and space platform flights.

Goetz, A. F. H.

An experiment in hurricane track prediction using parallel computing methods

The barotropic model is used to explore the advantages of parallel processing in deterministic forecasting. We apply this model to the track forecasting of hurricane Elena (1985). In this particular application, solutions to systems of elliptic equations are the essence of the computational mechanics. One set of equations is associated with the decomposition of the wind into irrotational and nondivergent components - this determines the initial nondivergent state. Another set is associated with recovery of the streamfunction from the forecasted vorticity. We demonstrate that direct parallel methods based on accelerated block cyclic reduction (BCR) significantly reduce the computational time required to solve the elliptic equations germane to this decomposition and forecast problem. A 72-h track prediction was made using incremental time steps of 16 min on a network of 3000 grid points nominally separated by 100 km. The prediction took 30 sec on the 8-processor Alliant FX/8 computer. This was a speed-up of 3.7 when compared to the one-processor version. The 72-h prediction of Elena's track was made as the storm moved toward Florida's west coast. Approximately 200 km west of Tampa Bay, Elena executed a dramatic recurvature that ultimately changed its course toward the northwest. Although the barotropic track forecast was unable to capture the hurricane's tight cycloidal looping maneuver, the subsequent northwesterly movement was accurately forecasted as was the location and timing of landfall near Mobile Bay.

Song, Chang G.