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At least 199 records · Page 11

Dealing with Measurement Uncertainties as Nuisance Parameters in Bayesian Model Calibration

In the presence of model discrepancy, the calibration of physics-based models for physical parameter inference is a challenging problem. Lack of identifiability between calibration parameters and model discrepancy requires additional identifiability constraints to be placed on the model discrepancy to obtain unique physical parameter estimates. If these assumptions are violated, the inference for the calibration parameters can be systematically biased. In many applications, such as in dynamic material property experiments, many of the calibration inputs refer to measurement uncertainties. Here, we develop a metric for identifying overfitting of these measurement uncertainties, propose a prior capable of reducing this overfitting, and show how this leads to a diagnostic tool for validation of physical parameter inference. The approach is demonstrated for a benchmark example and applied for a material property application to perform inference on the equation of state parameters of tantalum.

97 MATHEMATICS AND COMPUTING↗

A Bayesian Approach for Characterizing and Mitigating Gate and Measurement Errors

Various noise models have been developed in quantum computing study to describe the propagation and effect of the noise that is caused by imperfect implementation of hardware. Identifying parameters such as gate and readout error rates is critical to these models. We use a Bayesian inference approach to identify posterior distributions of these parameters such that they can be characterized more elaborately. By characterizing the device errors in this way, we can further improve the accuracy of quantum error mitigation. Experiments conducted on IBM’s quantum computing devices suggest that our approach provides better error mitigation performance than existing techniques used by the vendor. Also, our approach outperforms the standard Bayesian inference method in some scenarios.

97 MATHEMATICS AND COMPUTING↗

Process Anomaly Detection for Sparsely Labeled Events in Nuclear Power Plants

An essential aspect of online monitoring, subtle anomaly detection increases the detection lead time for equipment failure and enables a nuclear power plant (NPP) to mitigate unexpected partial or full outages, resulting in significant cost saving to the plant. Once an anomaly is detected by plant staff, its cause and severity are investigated. Because the vast majority of anomalies require some level of investigation, including some that require time-consuming examination, before they are passed over to the engineering organization for further analysis, plants are often equipped with tools to assist the staff in performing anomaly detection. Those tools operate as a black box and are often based on statistical methods that establish sensor correlations using preconfigured mathematical models and flag correlation deviations as anomalies. Due to the number of anomalies detected at a given NPP on a daily basis, a significant number of flagged anomalies usually await examination for days or weeks. A primary cause of this backlog is that the methods used by the tools generate many false positives. Though this is usually attributed to oversensitive model settings due to very narrow normal operation bands, it can also be associated with the model development being inadequate for the process being monitored, or with missing model inputs that could have explained misclassified positives. The performance of anomaly detection tools impacts their plant acceptance and utilization, especially when the effort to address false positives generated by the tool depletes the value or cost saved by using that tool. Thus, means to advance anomaly detection performance have been investigated by the Department of Energy’s Light Water Reactor Sustainability program. Previous and ongoing efforts have targeted unsupervised machine-learning (ML) methods, which do not require the labeling of any data fed into the ML model. By contrast, in supervised anomaly detection methods, every data point is labeled as either a normal or abnormal process condition, and the model is trained to replicate the classification process. Supervised methods usually outperform unsupervised methods, due to the added value in differentiating normal from anomalous states of the monitored process. An NPP’s corrective action program requires it to track and document, via a dedicated report, the resolution of any issues that occur within the plant. Once created, each report is reviewed by a plant screening committee, and several classifications and decisions are made. Recently, a collaborating NPP developed an artificial intelligence and ML-based classifier to categorize a condition report (CR) into classes that can serve to label the data as normal or anomalous. Applying CRs as labels represents a semi-supervised use case. Semi-supervised ML assumes that labels exist for some data points (i.e., labeled anomalies, in this case) but not for the rest. In this effort, semi-supervised ML methods were used to fuse data from CRs with anomaly detection methods in order to test the hypothesis that partially labeled anomalies would improve the accuracy of the anomaly detection methods. Specifically, two methods were used. The first is the deep Semi-supervised Anomaly Detection (deep SAD) method, which can handle labels ranging from fully unsupervised to fully supervised cases. The second is a newly designed ML method developed specifically for this effort and referred to as the high-order feature (HOF)-based method. To evaluate these two methods in controlled environments, synthetic data generators were developed and used. The first datasets used a spring-mass-damper (SMD) system simulator commonly found in mechanical engineering references. This was used to create two use cases: a one- and a three-mass system. Anomalies were introduced by changing the spring and damper coefficients while the system was actuated by random forces. The second datasets used the commercial Dymola-Modelica software to build a simplified nuclear reactor model. Anomalies were added in the form of corrupted sensor readings and/or control commands. The deep SAD method was tested using the SMD system, while the HOF method was tested using both datasets. Application of the deep SAD semi-supervised ML method demonstrated that labels can generate increased confidence in detecting true anomalies. This helped increase the number of true positives and decrease the number of false negatives—something that would aid in addressing the backlog of possible anomalies. Application of the HOF method demonstrated that labels can aid in down selecting from a candidate set of features to a more optimal subset in order to better differentiate between normal and anomalous conditions.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Disentangling the Black Hole Mass Spectrum with Photometric Microlensing Surveys

Abstract From the formation mechanisms of stars and compact objects to nuclear physics, modern astronomy frequently leverages surveys to understand populations of objects to answer fundamental questions. The population of dark and isolated compact objects in the Galaxy contains critical information related to many of these topics, but is only practically accessible via gravitational microlensing. However, photometric microlensing observables are degenerate for different types of lenses, and one can seldom classify an event as involving either a compact object or stellar lens on its own. To address this difficulty, we apply a Bayesian framework that treats lens type probabilistically and jointly with a lens population model. This method allows lens population characteristics to be inferred despite intrinsic uncertainty in the lens class of any single event. We investigate this method’s effectiveness on a simulated ground-based photometric survey in the context of characterizing a hypothetical population of primordial black holes (PBHs) with an average mass of 30 M ⊙ . On simulated data, our method outperforms current black hole (BH) lens identification pipelines and characterizes different subpopulations of lenses while jointly constraining the PBH contribution to dark matter to ≈25%. Key to robust inference, our method can marginalize over population model uncertainty. We find the lower mass cutoff for stellar origin BHs, a key observable in understanding the BH mass gap, particularly difficult to infer in our simulations. This work lays the foundation for cutting-edge PBH abundance constraints to be extracted from current photometric microlensing surveys.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Response of linear dynamic systems with random coefficients

Numerous models of physical systems contain parameters whose values are not known exactly. The physical and mathematical complexities arising in the prediction of the statistical behavior of such systems are discussed. Although the discussions are far from providing a satisfactory solution to such problems, they perhaps, by utilization of simple examples, will create a greater awareness of the statistical effect of random parameters.

Dickerson, J.↗

Social network structure and the spread of complex contagions from a population genetics perspective

Ideas, behaviors, and opinions spread through social networks. If the probability of spreading to a new individual is a non-linear function of the fraction of the individuals’ affected neighbors, such a spreading process becomes a “complex contagion”. This non-linearity does not typically appear with physically spreading infections, but instead can emerge when the concept that is spreading is subject to game theoretical considerations (e.g. for choices of strategy or behavior) or psychological effects such as social reinforcement and other forms of peer influence (e.g. for ideas, preferences, or opinions). Here we study how the stochastic dynamics of such complex contagions are affected by the underlying network structure. Motivated by simulations of complex contagions on real social networks, we present a framework for analyzing the statistics of contagions with arbitrary non-linear adoption probabilities based on the mathematical tools of population genetics. The central idea is to use an effective lower-dimensional diffusion process to approximate the statistics of the contagion. This leads to a tradeoff between the effects of ”selection” (microscopic tendencies for an idea to spread or die out), random drift, and network structure. Our framework illustrates intuitively several key properties of complex contagions: stronger community structure and network sparsity can significantly enhance the spread, while broad degree distributions dampen the effect of selection compared to random drift. Finally, we show that some structural features can exhibit critical values that demarcate regimes where global contagions become possible for networks of arbitrary size. Our results draw parallels between the competition of genes in a population and memes in a world of minds and ideas. Our tools provide insight into the spread of information, behaviors, and ideas via social influence, and highlight the role of macroscopic network structure in determining their fate.

59 BASIC BIOLOGICAL SCIENCES↗

Physiological time-series analysis: what does regularity quantify?

Approximate entropy (ApEn) is a recently developed statistic quantifying regularity and complexity that appears to have potential application to a wide variety of physiological and clinical time-series data. The focus here is to provide a better understanding of ApEn to facilitate its proper utilization, application, and interpretation. After giving the formal mathematical description of ApEn, we provide a multistep description of the algorithm as applied to two contrasting clinical heart rate data sets. We discuss algorithm implementation and interpretation and introduce a general mathematical hypothesis of the dynamics of a wide class of diseases, indicating the utility of ApEn to test this hypothesis. We indicate the relationship of ApEn to variability measures, the Fourier spectrum, and algorithms motivated by study of chaotic dynamics. We discuss further mathematical properties of ApEn, including the choice of input parameters, statistical issues, and modeling considerations, and we conclude with a section on caveats to ensure correct ApEn utilization.

NASA Discipline Cardiopulmonary↗

Statistical Theory of the Ideal MHD Geodynamo

A statistical theory of geodynamo action is developed, using a mathematical model of the geodynamo as a rotating outer core containing an ideal (i.e., no dissipation), incompressible, turbulent, convecting magnetofluid. On the concentric inner and outer spherical bounding surfaces the normal components of the velocity, magnetic field, vorticity and electric current are zero, as is the temperature fluctuation. This allows the use of a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity, current and the temperature fluctuation. The resulting dynamical system, based on the Boussinesq form of the magnetohydrodynamic (MHD) equations, represents MHD turbulence in a spherical domain. These basic equations (minus the temperature equation) and boundary conditions have been used previously in numerical simulations of forced, decaying MHD turbulence inside a sphere [1,2]. Here, the ideal case is studied through statistical analysis and leads to a prediction that an ideal coherent structure will be found in the form of a large-scale quasistationary magnetic field that results from broken ergodicity, an effect that has been previously studied both analytically and numerically for homogeneous MHD turbulence [3,4]. The axial dipole component becomes prominent when there is a relatively large magnetic helicity (proportional to the global correlation of magnetic vector potential and magnetic field) and a stationary, nonzero cross helicity (proportional to the global correlation of velocity and magnetic field). The expected angle of the dipole moment vector with respect to the rotation axis is found to decrease to a minimum as the average cross helicity increases for a fixed value of magnetic helicity and then to increase again when average cross helicity approaches its maximum possible value. Only a relatively small value of cross helicity is needed to produce a dipole moment vector that is aligned at approx.10deg with the rotation axis.

Shebalin, J. V.↗

Validating an Air Traffic Management Concept of Operation Using Statistical Modeling

Validating a concept of operation for a complex, safety-critical system (like the National Airspace System) is challenging because of the high dimensionality of the controllable parameters and the infinite number of states of the system. In this paper, we use statistical modeling techniques to explore the behavior of a conflict detection and resolution algorithm designed for the terminal airspace. These techniques predict the robustness of the system simulation to both nominal and off-nominal behaviors within the overall airspace. They also can be used to evaluate the output of the simulation against recorded airspace data. Additionally, the techniques carry with them a mathematical value of the worth of each prediction-a statistical uncertainty for any robustness estimate. Uncertainty Quantification (UQ) is the process of quantitative characterization and ultimately a reduction of uncertainties in complex systems. UQ is important for understanding the influence of uncertainties on the behavior of a system and therefore is valuable for design, analysis, and verification and validation. In this paper, we apply advanced statistical modeling methodologies and techniques on an advanced air traffic management system, namely the Terminal Tactical Separation Assured Flight Environment (T-TSAFE). We show initial results for a parameter analysis and safety boundary (envelope) detection in the high-dimensional parameter space. For our boundary analysis, we developed a new sequential approach based upon the design of computer experiments, allowing us to incorporate knowledge from domain experts into our modeling and to determine the most likely boundary shapes and its parameters. We carried out the analysis on system parameters and describe an initial approach that will allow us to include time-series inputs, such as the radar track data, into the analysis

Statistical emulation↗

Finding Bounded Rational Equilibria: Iterative Focusing - Part 1

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights from the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.

Wolpert, David H.↗

Finding Bounded Rational Equilibria: Alternative Lagrangians and Uncountable Move Spaces - Part 2

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights &om the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.

Wolpert, David H.↗

Solar activity prediction

A statistical study of formulas for predicting the sunspot number several years in advance is reported. By using a data lineup with cycle maxima coinciding, and by using multiple and nonlinear predictors, a new formula which gives better error estimates than former formulas derived from the work of McNish and Lincoln is obtained. A statistical analysis is conducted to determine which of several mathematical expressions best describes the relationship between 10.7 cm solar flux and Zurich sunspot numbers. Attention is given to the autocorrelation of the observations, and confidence intervals for the derived relationships are presented. The accuracy of predicting a value of 10.7 cm solar flux from a predicted sunspot number is dicussed.

Slutz, R. J.↗

Investigation of the performance characteristics of Doppler radar technique for aircraft collision hazard warning, phase 3

System studies, equipment simulation, hardware development and flight tests which were conducted during the development of aircraft collision hazard warning system are discussed. The system uses a cooperative, continuous wave Doppler radar principle with pseudo-random frequency modulation. The report presents a description of the system operation and deals at length with the use of pseudo-random coding techniques. In addition, the use of mathematical modeling and computer simulation to determine the alarm statistics and system saturation characteristics in terminal area traffic of variable density is discussed.

Source record↗

Diagnostics of sources of disturbances and distribution of vibrations over the width of a tape in tape-feed mechanisms

Disturbances created by certain assemblies and components of tape-feed mechanisms (TFM) and acting on a moving magnetic tape are studied. The method, based on elements of digital logic, is established by stress-strain diagrams of the longitudinal deformations and vibrations across the width of a magnetic tape. Experimental studies were carried out for determination of the functional relationships of longitudinal deformations in a section of magnetic tape to the magnitude of roller play, tension vibrations rate of movement, and elasticity of magnetic tapes. A block diagram of the measurements is shown. Appropriate digital computer algorithms and programs were proposed for statistical analysis of the data obtained. Estimates of the mathematical expectation, dispersion, intercorrelation function, energy spectral density, and distribution pattern of the random process values were calculated.

Kenstavichyus, A. B. B.↗

Enhancement effects in polarimetric radar returns: Phase difference statistics

The probability density functions (pdfs) of the co- and cross-polarized phase differences are derived for backscatter from vegetation using the coherent and incoherent scattering theories. Unlike previous derivations, no assumptions or observations other than the applicability of the Central Limit Theorem (CLT), the low fractional volume of the medium, the reciprocity of the scatterers, and the azimuthal symmetry of the scatterer's orientation statistics are employed. Everything else follows logically via the mathematics. The difference between the coherent theory and the incoherent theory is referred to as the backscatter enhancement effect. The influence of this enhancement effect on the phase difference pdfs is examined and found to be important under combined conditions of scatterer anisotropy and appropriate reflection coefficient values.

Lang, R. H.↗

Associated with aerospace vehicles development of methodologies for the estimation of thermal properties

Thermal stress analyses are an important aspect in the development of aerospace vehicles at NASA-LaRC. These analyses require knowledge of the temperature distributions within the vehicle structures which consequently necessitates the need for accurate thermal property data. The overall goal of this ongoing research effort is to develop methodologies for the estimation of the thermal property data needed to describe the temperature responses of these complex structures. The research strategy undertaken utilizes a building block approach. The idea here is to first focus on the development of property estimation methodologies for relatively simple conditions, such as isotropic materials at constant temperatures, and then systematically modify the technique for the analysis of more and more complex systems, such as anisotropic multi-component systems. The estimation methodology utilized is a statistically based method which incorporates experimental data and a mathematical model of the system. Several aspects of this overall research effort were investigated during the time of the ASEE summer program. One important aspect involved the calibration of the estimation procedure for the estimation of the thermal properties through the thickness of a standard material. Transient experiments were conducted using a Pyrex standard at various temperatures, and then the thermal properties (thermal conductivity and volumetric heat capacity) were estimated at each temperature. Confidence regions for the estimated values were also determined. These results were then compared to documented values. Another set of experimental tests were conducted on carbon composite samples at different temperatures. Again, the thermal properties were estimated for each temperature, and the results were compared with values obtained using another technique. In both sets of experiments, a 10-15 percent off-set between the estimated values and the previously determined values was found. Another effort was related to the development of the experimental techniques. Initial experiments required a resistance heater placed between two samples. The design was modified such that the heater was placed on the surface of only one sample, as would be necessary in the analysis of built up structures. Experiments using the modified technique were conducted on the composite sample used previously at different temperatures. The results were within 5 percent of those found using two samples. Finally, an initial heat transfer analysis, including conduction, convection and radiation components, was completed on a titanium sandwich structural sample. Experiments utilizing this sample are currently being designed and will be used to first estimate the material's effective thermal conductivity and later to determine the properties associated with each individual heat transfer component.

Scott, Elaine P.↗