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All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

Guidebook for Assessing Similarity and Implementing Empirical Transfer Functions for Probability of Detection (POD) Demonstrations for Signal Based Nondestructive Evaluation (NDE) Methods

This document provides guidance for assessing similarity relative to nondestructive evaluation (NDE) detectability based on Probability of Detection demonstrations when comparing different NDE inspection situations. Differences in inspection situations addressed by the similarity assessment methodology herein can include differences in the component being inspected, and differences in the conditions for the inspection. Additional differences in the inspection situation relative to differences in the method or procedure are not addressed in this document but can be assessed using NDE calibration or instrument standardization specimens.

Probability of Detection↗
NASA NTRS2018

Effect of Cross-Correlation of Orbital Error on Probability of Collision Determination

This paper discusses the effect of global model error on probability of collision (Pc) determination. Modifications to the Pc formulation for cross-correlation of orbital error in prediction are developed and assessed for recent conjunctions. While specific geometries can be identified or constructed to produce significant change in Pc for the modified formulation, it is of operational interest to quantify the relative occurrence of such cases for satellite conjunction risk assessment. Such analysis is feasible per data collections in place over the past year.

Cross-correlation↗
NASA NTRS2022

Guidebook for the Design and Analysis of a NASA Standard Nondestructive Evaluation (NDE) Probability of Detection (POD) Study

Purpose: This document provides guidance on the design and analysis of a NASA Standard nondestructive evaluation (NDE) probability of detection (POD) study. A Standard NDE flaw size is considered to be conservative such that most inspectors, trained and certified in the specific NDE method, are expected to provide at least 90/95 POD for that flaw size to inspect fracture-critical hardware. Scope: This document is specifically applicable to NASA Technical Standards that establish the NDE requirements for any NASA system or component, flight or ground, where fracture control and a quantitative demonstration of POD is a requirement, including NASA-STD-5009B, Nondestructive Evaluation Requirements for Fracture-Critical Metallic Components, and NASA-STD-5019A,Fracture Control Requirements for Spaceflight Hardware.

Probability of Detection↗
NASA NTRSDate not supplied

Setting the Bar for the Replacement of the Probability of Collision Metric

Recent research in satellite conjunction risk assessment has levelled a number of criticisms at the probability of collision (Pc) parameter as a durable statement of satellite collision likelihood, and a number of different alternatives to this calculation have been proposed. Many of these proposals, however, stop at the outlining of the theory and do not discuss the additional philosophical and practical issues that must be confronted in evaluating such proposals for adoption. The present work seeks to outline some of these philosophical and practical considerations, and therefore the kinds of analyses and profiling that will be needed before the Pc, which is at present nearly universally adopted in the conjunction risk mitigation community, can be replaced with a new (and superior) paradigm and associated metric.

conjunction assessment↗
DOE OSTI2024

Evaluation of the Simplified Assessment Peak Equivalent Stress Design Limit Probability of Failure

The ASME Boiler and Pressure Vessel Code Section III Division 5 Subsection HH Subpart A (HHA) outlines requirements and qualification methods for graphite core components in high temperature reactor environments. One such structural qualification method is the Simplified Assessment outlined in HHA-3220, which represents a comparison of service level specific equivalent stresses to allowable stress values derived from target probability of failures (POFs). The target POF is based on the structural reliability class (SRC) for the components and service condition of interest, and is used to establish design limits for combined membrane and peak equivalent stresses. Combined membrane stress limits are derived from two parameter Weibull distribution fits of the graphite grade specific tensile strength data and the target POF. The combined membrane stress limits are then scaled based on the ratio of flexural strength to tensile strength (referred hereinafter as Rtf) to establish the corresponding peak equivalent stress limits. It is desired that the target POF is at least maintained for both combined membrane and peak equivalent design limits, especially with the use of Rtf. The assessment presented herein examines tensile and flexural data for medium and fine grade graphites relative to the calculated combined membrane and peak equivalent stress limits per HHA-3220 and illustrates the simplified assessment method results in anticipated, or at least conservative, peak equivalent design stress limits.

36 - MATERIALS SCIENCE↗
DOE OSTI2016

Vertical overlap of probability density functions of cloud and precipitation hydrometeors: CLOUD AND PRECIPITATION PDF OVERLAP

Coarse-resolution climate models increasingly rely on probability density functions (PDFs) to represent subgrid-scale variability of prognostic variables. While PDFs characterize the horizontal variability, a separate treatment is needed to account for the vertical structure of clouds and precipitation. When sub-columns are drawn from these PDFs for microphysics or radiation parameterizations, appropriate vertical correlations must be enforced via PDF overlap specifications. This study evaluates the representation of PDF overlap in the Subgrid Importance Latin Hypercube Sampler (SILHS) employed in the assumed PDF turbulence and cloud scheme called the Cloud Layers Unified By Binormals (CLUBB). PDF overlap in CLUBB-SILHS simulations of continental and tropical oceanic deep convection is compared with overlap of PDF of various microphysics variables in cloud-resolving model (CRM) simulations of the same cases that explicitly predict the 3D structure of cloud and precipitation fields. CRM results show that PDF overlap varies significantly between different hydrometeor types, as well as between PDFs of mass and number mixing ratios for each species, - a distinction that the current SILHS implementation does not make. In CRM simulations that explicitly resolve cloud and precipitation structures, faster falling species, such as rain and graupel, exhibit significantly higher coherence in their vertical distributions than slow falling cloud liquid and ice. These results suggest that to improve the overlap treatment in the sub-column generator, the PDF correlations need to depend on hydrometeor properties, such as fall speeds, in addition to the currently implemented dependency on the turbulent convective length scale.

58 GEOSCIENCES↗
DOE OSTI2021

Survey on stochastic distribution systems: A full probability density function control theory with potential applications

Complex systems seen either in general engineering practice or economics are subjected to ever increased uncertainties that are mostly represented as random variables or parameters, and the characteristics of random variables are represented by their probability density functions (PDFs). Controlling their PDFs means to shape their stochastic distributions and in general it would provide a full treatment for system analysis and operational control and optimization. This leads to the development of stochastic distribution control (SDC) systems theory in the past decades, where the original aim of the controller design is to realize a shape control of the distributions of certain random variables in their PDFs sense for some engineering processes. Indeed, once the PDFs of these random variables or parameters are used to describe their distribution characters, the control task is to obtain control signals so that the output PDFs of stochastic systems are made to follow their target PDFs. The subject of SDC was initially originated for non-Gaussian stochastic control systems design but has found a wide spectrum of applications in general systems in terms of data-driven modeling, analysis, signal processing (filtering), data mining via multivariable statistics, decision-making (optimization) for systems subjected to uncertainties and even in economics. In this context, SDC constitutes an effective primer tool for complex system analysis, control and operational optimizations. In this review paper, a detailed survey of the developments on the research of SDC systems will be made together with their wide spectrum applications and future perspectives.

42 ENGINEERING↗
DOE OSTI2019

Modeling of the Flows of Admixtures in a Random Layered Strip with Probable Arrangement of Inclusions Near the Boundaries of the Body

We study the random flow of admixtures in a two-phase stochastically inhomogeneous strip with the most probable arrangement of inclusions in the vicinity of the surfaces of the body. A mathematical model is formulated for the function of diffusion flow with nonzero constant initial concentration. A random diffusion flow is represented in the form of a Neumann series. The procedure of averaging of the random mass flow over the ensemble of phase configurations with arcsine distribution function is performed. The influence of the characteristics of the medium on the distribution of mass flow is analyzed. It is shown that if the diffusion coefficient of admixtures in the inclusion is higher than for the matrix, then the increase in the characteristic thickness of the layers causes a decrease in the value of the diffusion flow, whereas the mass flow in the entire body increases with the volume fraction of the inclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Outage probability and average BER estimation of FSO system employing wavelength diversity

Free space optical (FSO) communication has gained significant attention among researchers for high bandwidth and secured data transfer applications. However, its performance is limited by the local atmospheric conditions. This paper focusses on an FSO system employing a diversity method to compensate signal loss occurred due to atmospheric turbulence conditions varying from moderate to strong. We derive a closed-form expression for two important parameters, viz.: average bit error rate (BER) and outage probability over gamma–gamma distribution channel. The numerical results for different combining schemes are presented in this paper. Enhancement in reliability and performance of FSO communication system with wavelength diversity is investigated. Effect of different wavelengths 850 nm, 1310 nm and 1550 nm on average BER is analysed and minimum BER is achieved for optimal combining at 1550 nm at diversity order R=3.

42 ENGINEERING↗
DOE OSTI2018

BI-RADS 3: Current and Future Use of Probably Benign

Purpose of Review: Probably benign (BI-RADS 3) causes confusion for interpreting physicians and referring physicians and can induce significant patient anxiety. The best uses and evidence for using this assessment category in mammography, breast ultrasound, and breast MRI will be reviewed; the reader will have a better understanding of how and when to use BI-RADS 3. Recent Findings: Interobserver variability in the use of BI-RADS 3 has been documented. The 5th edition of the BI-RADS atlas details the appropriate use of BI-RADS 3 for diagnostic mammography, ultrasound, and MRI, and discourages its use in screening mammography. Data mining, elastography, and diffusion weighted MRI have been evaluated to maximize the accuracy of BI-RADS 3. Summary: BI-RADS 3 is an evolving assessment category. When used properly, it reduces the number of benign biopsies while allowing the breast imager to maintain a high sensitivity for the detection of early stage breast cancer.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2023

The neutron number probability distribution in coupled lumped assemblies

Here, the validity of the gamma distribution in describing the neutron number probability distribution function for both isolated and coupled multiplying assemblies when constrained to reproduce the true mean and variance is investigated in lumped geometry by numerical comparison with kinetic Monte Carlo simulations. The mean and variance are obtained from numerical solution of moment equations constructed from the relevant forward Master equation with assembly coupling coefficients obtained from a view factor method. Numerical results for a two-group, two coupled assemblies model, with static and dynamic reactivity insertion, show that except for subcritical assemblies, the gamma distribution well-approximates the number distribution. Differences in the fast and thermal neutron population shapes are explained in terms of effective source strengths due to downscatter and coupling.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices

Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied in this paper have all their degrees of freedom coupled to each other. Thus, the problem of linearized small oscillations of such systems involves two full positive-definite and non-commuting matrices, as opposed to the sparse matrices associated with disordered crystals. Consequently, the familiar methods for determining the averaged vibrational spectra of disordered crystals, introduced many years ago by Dyson and Schmidt, are inapplicable for highly connected disordered systems. In this paper we apply random matrix theory (RMT) to calculate the averaged vibrational spectra of such systems, in the limit of infinitely large system size. At the heart of our analysis lies a calculation of the average spectrum of the product of two positive definite random matrices by means of free probability theory techniques. We also show that this problem is intimately related with quasi-hermitian random matrix theory (QHRMT), which means that the ‘hamiltonian’ matrix is hermitian with respect to a non-trivial metric. This extends ordinary hermitian matrices, for which the metric is simply the unit matrix. The analytical results we obtain for the spectrum agree well with our numerical results. The latter also exhibit oscillations at the high-frequency band edge, which fit well the Airy kernel pattern. We also compute inverse participation ratios of the corresponding amplitude eigenvectors and demonstrate that they are all extended, in contrast with conventional disordered crystals. Finally, we compute the thermodynamic properties of the system from its spectrum of vibrations. In addition to matrix model analysis, we also study the vibrational spectra of various multi-segmented disordered pendula, as concrete realizations of highly connected mechanical systems. A universal feature of the density of vibration modes, common to both pendula and the matrix model, is that it tends to a non-zero constant at vanishing frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Angular momentum eigenstates of the isotropic 3-D harmonic oscillator: Phase-space distributions and coalescence probabilities

The isotropic 3-dimensional harmonic oscillator potential can serve as an approximate description of many systems in atomic, solid state, nuclear, and particle physics. In particular, the question of 2 particles binding (or coalescing) into angular momentum eigenstates in such a potential has interesting applications. Here we compute the probabilities for coalescence of two distinguishable, non-relativistic particles into such a bound state, where the initial particles are represented by generic wave packets of given average positions and momenta. We use a phase-space formulation and hence need the Wigner distribution functions of angular momentum eigenstates in isotropic 3-dimensional harmonic oscillators. These distribution functions have been discussed in the literature before but we utilize an alternative approach to obtain these functions. Along the way, we derive a general formula that expands angular momentum eigenstates in terms of products of 1-dimensional harmonic oscillator eigenstates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Converting sWeights to probabilities with density ratios

The use of machine learning approaches continues to have many benefits in experimental nuclear and particle physics. One common issue is generating training data which is sufficiently realistic to give reliable results. Here we advocate using real experimental data as the source of training data and demonstrate how one might subtract background contributions through the use of probabilistic weights which can be readily applied to training data. The sPlot formalism is a common tool used to isolate distributions from different sources. However, the negative sWeights produced by the sPlot technique can cause training problems and poor predictive power. This article demonstrates how density ratio estimation can be applied to convert sWeights to event probabilities, which we call drWeights. The drWeights can then be applied to produce the distributions of interest and are consistent with direct use of the sWeights. This article will also show how decision trees are particularly well suited to convert sWeights, with the benefit of fast prediction rates and adaptability to aspects of experimental data such as the data sample size and proportions of different event sources. We also show that a density ratio product approach in which the initial drWeights are reweighted by an additional converter gives substantially better results.

Glazier, Derek I. [Univ. of Glasgow, Scotland (Uni↗
DOE OSTI2013

Multivariate Normal Tissue Complication Probability Modeling of Heart Valve Dysfunction in Hodgkin Lymphoma Survivors

Purpose: To establish a multivariate normal tissue complication probability (NTCP) model for radiation-induced asymptomatic heart valvular defects (RVD). Methods and Materials: Fifty-six patients treated with sequential chemoradiation therapy for Hodgkin lymphoma (HL) were retrospectively reviewed for RVD events. Clinical information along with whole heart, cardiac chambers, and lung dose distribution parameters was collected, and the correlations to RVD were analyzed by means of Spearman's rank correlation coefficient (Rs). For the selection of the model order and parameters for NTCP modeling, a multivariate logistic regression method using resampling techniques (bootstrapping) was applied. Model performance was evaluated using the area under the receiver operating characteristic curve (AUC). Results: When we analyzed the whole heart, a 3-variable NTCP model including the maximum dose, whole heart volume, and lung volume was shown to be the optimal predictive model for RVD (Rs = 0.573, P<.001, AUC = 0.83). When we analyzed the cardiac chambers individually, for the left atrium and for the left ventricle, an NTCP model based on 3 variables including the percentage volume exceeding 30 Gy (V30), cardiac chamber volume, and lung volume was selected as the most predictive model (Rs = 0.539, P<.001, AUC = 0.83; and Rs = 0.557, P<.001, AUC = 0.82, respectively). The NTCP values increase as heart maximum dose or cardiac chambers V30 increase. They also increase with larger volumes of the heart or cardiac chambers and decrease when lung volume is larger. Conclusions: We propose logistic NTCP models for RVD considering not only heart irradiation dose but also the combined effects of lung and heart volumes. Our study establishes the statistical evidence of the indirect effect of lung size on radio-induced heart toxicity.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Predicting the 5-Year Risk of Biochemical Relapse After Postprostatectomy Radiation Therapy in ≥PT2, pN0 Patients With a Comprehensive Tumor Control Probability Model

Purpose: To fit the individual biochemical recurrence-free survival (bRFS) data from patients treated with postprostatectomy radiation therapy (RT) with a comprehensive tumor control probability (TCP) model. Methods and Materials: Considering pre-RT prostate-specific antigen (PSA) as a surrogate of the number of clonogens, bRFS may be expressed as a function of dose-per-fraction–dependent radiosensitivity (α{sub eff}), the number of clonogens for pre-RT PSA = 1 ng/mL (C), and the fraction of patients who relapse because of clonogens outside the treated volume (K), assumed to depend (linearly or exponentially) on pre-RT PSA and Gleason score (GS). Data from 894 node-negative, ≥pT2, pN0 hormone-naive patients treated with adjuvant (n=331) or salvage (n=563) intent were available: 5-year bRFS data were fitted grouping patients according to GS (<7:392, =7:383, >7:119). Results: The median follow-up time, pre-RT PSA, and dose were 72 months, 0.25 ng/mL, and 66.6 Gy (range 59.4-77.4 Gy), respectively. The best-fit values were 0.23 to 0.26 Gy{sup −1} and 10{sup 7} for α{sub eff} and C for the model considering a linear dependence between K and PSA. Calibration plots showed good agreement between expected and observed incidences (slope: 0.90-0.93) and moderately high discriminative power (area under the curve [AUC]: 0.68-0.69). Cross-validation showed satisfactory results (average AUCs in the training/validation groups: 0.66-0.70). The resulting dose-effect curves strongly depend on pre-RT PSA and GS. bRFS rapidly decreases with PSA: the maximum obtainable bRFS (defined as 95% of the maximum) declined by about 2.7% and 4.5% for each increment of 0.1 ng/mL for GS <7 and ≥7, respectively. Conclusions: Individual data were fitted by a TCP model, and the resulting best-fit parameters were radiobiologically consistent. The model suggests that relapses frequently result from clonogens outside the irradiated volume, supporting the choice of lymph-node irradiation, systemic therapy, or both for specific subgroups (GS <7: PSA >0.8-1.0 ng/mL; GS ≥7: PSA >0.3 ng/mL). Early RT should be preferred over delayed RT; the detrimental effect of PSA increase can never be fully compensated by increasing the dose, especially for patients with GS ≥7.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Methods for Reducing Normal Tissue Complication Probabilities in Oropharyngeal Cancer: Dose Reduction or Planning Target Volume Elimination

Purpose: Strategies to reduce the toxicities of head and neck radiation (ie, dysphagia [difficulty swallowing] and xerostomia [dry mouth]) are currently underway. However, the predicted benefit of dose and planning target volume (PTV) reduction strategies is unknown. The purpose of the present study was to compare the normal tissue complication probabilities (NTCP) for swallowing and salivary structures in standard plans (70 Gy [P70]), dose-reduced plans (60 Gy [P60]), and plans eliminating the PTV margin. Methods and Materials: A total of 38 oropharyngeal cancer (OPC) plans were analyzed. Standard organ-sparing volumetric modulated arc therapy plans (P70) were created and then modified by eliminating the PTVs and treating the clinical tumor volumes (CTVs) only (C70) or maintaining the PTV but reducing the dose to 60 Gy (P60). NTCP dose models for the pharyngeal constrictors, glottis/supraglottic larynx, parotid glands (PGs), and submandibular glands (SMGs) were analyzed. The minimal clinically important benefit was defined as a mean change in NTCP of >5%. The P70 NTCP thresholds and overlap percentages of the organs at risk with the PTVs (56-59 Gy, vPTV{sub 56}) were evaluated to identify the predictors for NTCP improvement. Results: With the P60 plans, only the ipsilateral PG (iPG) benefited (23.9% vs 16.2%; P<.01). With the C70 plans, only the iPG (23.9% vs 17.5%; P<.01) and contralateral SMG (cSMG) (NTCP 32.1% vs 22.9%; P<.01) benefited. An iPG NTCP threshold of 20% and 30% predicted NTCP benefits for the P60 and C70 plans, respectively (P<.001). A cSMG NTCP threshold of 30% predicted for an NTCP benefit with the C70 plans (P<.001). Furthermore, for the iPG, a vPTV{sub 56} >13% predicted benefit with P60 (P<.001) and C70 (P=.002). For the cSMG, a vPTV{sub 56} >22% predicted benefit with C70 (P<.01). Conclusions: PTV elimination and dose-reduction lowered the NTCP of the iPG, and PTV elimination lowered the NTCP of the cSMG. NTCP thresholds and the percentage of overlap of the PTV with organs at risk can predict which patients will benefit and inform future clinical trial design.

62 RADIOLOGY AND NUCLEAR MEDICINE↗