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Statistical estimation of service cracks and maintenance cost for aircraft structures

A method is developed for the statistical estimation of the number of cracks to be repaired in service as well as the repair and the maintenance costs. The present approach accounts for the statistical distribution of the initial crack size, the statistical nature of the NDI technique used for detecting the crack, and the renewal process for the crack propagation of repaired cracks. The mean and the standard deviation of the cumulative number of cracks to be repaired are computed as a function of service time. The statistics of the costs of repair and maintenance, expressed in terms of the percentage of the cost of replacement, are estimated as a function of service time. The results of the present study provide relevant information for the decision of fleet management, the estimation of life cycle cost, and procurement specifications. The present study is essential to the design and cost optimization of aircraft structures.

Yang, J.-N.↗

Highly accelerated life testing (HALT): A review from a statistical perspective

Despite its use in one form or another for at least four decades, HALT and related techniques [e.g., highly accelerated-stress screening (HASS) and stress audits (HASA)] are not well understood within the statistical community and remain controversial. This largely reflects a conflict in motivation between engineers, testing under harsh conditions to discover and eliminate failure modes, and statisticians, taking a more cautious approach to develop quantitative estimates of parameters such as mean time between failures (MTBF). Here, this review article will clarify HALT concepts and methods and explain where it fits within the universe of methods that involve the application of accelerating factors to compress the time required to evaluate or enhance product reliability. A major distinction is between methods such as HALT, a high-stress test-analyze-fix-test iterative process directed at improving reliability by discovering and fixing weak points in a design, and quantitative accelerated life testing (QALT), whose goal is the estimation of product life for a fixed design. We discuss methods such as physics of failure that offer some hope of bridging the gap between the qualitative nature of HALT, and purely quantitative statistical methods. We present a variety of engineering applications of HALT including metal fatigue, piping and pressure vessels, structural damage, radiation damage, and rotating machinery. We also discuss potential synergies between HALT and QALT, such as rapid identification, through HALT, of failure modes requiring quantitative analysis. For further study, extensive references to the applicable literature are provided as well as an appendix that describes related methods.

97 MATHEMATICS AND COMPUTING↗

Measuring representative volume elements from high-resolution grain-scale strain fields

Most crystalline materials present a highly heterogeneous response at the microscale, which can be affected by both internal factors (such as microstructural parameters) and external factors (such as loading). Relating microscale inhomogeneities to the macroscale response of a material requires the use of homogenisation techniques, usually based on the concept of a representative volume element (RVE)—the smallest volume of material that represents the global average response. Here, in this work, we present a new and robust experimental method of measuring the size of a strain-based RVE from high-resolution grain-scale strain fields obtained using digital image correlation (DIC). The proposed method is based on the statistical (stereological) nature of the RVE, which has been widely adopted in numerical studies, and involves dividing a strain field into randomly selected regions of varying sizes and statistically analysing the distributions of average strains within them. To validate the new method, we generate a large number of synthetic strain fields from a fractional Gaussian noise algorithm. The proposed stereological method is shown to be capable of producing reliable RVE measurements from a very large range of possible microscale strain fields while at the same time being robust in that it can produce RVE measurement results even in cases where other existing methods may be unable to do so. The proposed method has a low field-of-view requirement, only needing a field-of-view about 1.2 times as large as the RVE to produce reliable measurements. In addition, the stereological method offers significant flexibility since its statistical nature allows for control over how strict the RVE measurement should be in each case.

36 MATERIALS SCIENCE↗

Upper Subcritical Limit Calculations with Correlated Integral Experiments

The American National Standards Institute (ANSI) and American Nuclear Society (ANS) standard for Validation of Neutron Transport Methods for Nuclear Criticality Safety Calculations defines the Upper Subcritical Limit (USL) as “a limit on the calculated k effective value established to ensure that conditions calculated to be subcritical will actually be subcritical.” Often, USL calculations are based on statistical techniques that infer information about a nuclear system of interest (application) from a set of known/well characterized similar systems (experiments). In determining a USL, it is common to statistically determine a calculation bias and bias uncertainty. Bias is “the systematic difference between calculated results and experimental data.” The bias uncertainty is “the uncertainty that accounts for the combined effects of uncertainties in the benchmarks, the calculational models of the benchmarks, and the calculational methods.” Both the bias and the bias uncertainty are often inferred through statistical methods applied to the selected set of experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Interpolation of a surface from sets of discrete height data of different statistical characteristics

This paper presents and analyzes a method for the interpolation of a unique surface from two sets of independent digital height data of differing statistical characteristics. This method is based on linear prediction and thus relies on the concepts of auto- and cross-covariance functions. The linear prediction algorithm for two sets of digital height measurements is first derived and then evaluated using the method of moving averages and bilinear interpolation for comparison. It is found that the overall root mean square interpolation errors of linear prediction are similar to those from moving averages and bilinear interpolation. This accuracy performance, together with the well known potential for controlled filtering of measuring errors and good-behavior in areas of poor control, makes linear prediction a versatile and general method for interpolating a unique surface from two sets of digital height data, with applications in photogrammetric mapping, remote sensing, and other fields.

Leberl, F.↗

Validating Nuclear Data Uncertainties Obtained from a Statistical Analysis of Experimental Data with the “Physical Uncertainty Bounds” Method

Concerns within the nuclear data community led to substantial increases of Neutron Data Standards (NDS) uncertainties from its previous to the current version. For example, those associated with the NDS reference cross section 239 Pu(n,f) increased from 0.6–1.6% to 1.3–1.7% from 0.1–20 MeV. These cross sections, among others, were adopted, e.g., by ENDF/B-VII.1 (previous NDS) and ENDF/B-VIII.0 (current NDS). There has been a strong desire to be able to validate these increases based on objective criteria given their impact on our understanding of various application uncertainties. Here, the “Physical Uncertainty Bounds” method (PUBs) by Vaughan et al. is applied to validate evaluated uncertainties obtained by a statistical analysis of experimental data. We investigate with PUBs whether ENDF/B-VII.1 or ENDF/B-VIII.0 239 Pu(n,f) cross-section uncertainties are more realistic given the information content used for the actual evaluation. It is shown that the associated conservative (1.5–1.8%) and minimal realistic (1.1–1.3%) uncertainty bounds obtained by PUBs enclose ENDF/B-VIII.0 uncertainties and indicate that ENDF/B-VII.1 uncertainties are underestimated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Hawai‘i Play Fairway (Final Report)

Most of Hawai'i's geothermal resources are blind—their manifestations, such as hot springs and steam vents, do not appear on the ground surface because the heated water flows far below. With the exception of $K\bar{i}lauea East Rift Zone$, in most areas of Hawai'i, high lateral permeability in the first kilometer below ground surface prevents surface thermal features from developing. As a methodology for discovering these blind resources, Play Fairway Analysis (PFA) involves finding potential locations of blind hydrothermal systems and describing potential geothermal sources in rift-zone settings. Using the PFA to find Hawai'i's geothermal resources, the University of Hawai'i (UH) conducted the Hawai‘i Play Fairway Project, Hawai'i's first statewide geothermal resource assessment since 1985. Sponsored by the U.S. Department of Energy, the Hawai'i Play Fairway Project provided an updated resource assessment, a roadmap for additional exploration activities, and the identification of areas for further exploration. Benefitting from UH's core competency in earth sciences and experienced geothermal researchers, the project comprised three phases. During the first phase, the team identified, compiled, and ranked existing geologic, groundwater, and geophysical datasets relevant to subsurface heat, fluid and permeability. Using a Bayesian statistical approach, the team developed a statistical methodology to integrate these data into a resource probability map. The team evaluated the confidence in the probability value and considered development viability of areas with geothermal resources. With these analyses, the team identified 10 locations in the Hawaiian Islands for exploration activities. For the second phase, the team collected new groundwater data in 10 locations across the state and new geophysical data on $L\bar{a}na‘i, Maui$, and central Hawai'i Island and modeled topographically induced stress to better characterize subsurface permeability. Analyzing the subsurface stresses, the team evaluated the potential for fracture-induced permeability. The team inverted the MT and gravity data to produce 3D models of resistivity and density, respectively, on $L\bar{a}na‘i$, across $Haleakal\bar{a}'s$ SW rift (Maui), and surrounding Mauna Kea (Hawai‘i Island). The team developed and applied a new method for incorporating depth information about resistivity, density, and potential for fracture-induced permeability into the statistical method for computing resource probability in these three focus areas. The team incorporated the new groundwater results with the new geophysical results and the calculations of potential for fracture-induced permeability to produce updated maps of resource probability and confidence. Through combining data from the first and second phases, the team determined locations for further exploration during the third phase. For MT and gravity surveys, the team recommended $Kaua'i's$ $L\bar{i}hu'e$ $Basin$, the east rift of $Maui's$ $Haleakal\bar{a}$ volcano, and the southwest rift of Hawai'i Island's Mauna Loa volcano. The MT and gravity surveys aimed to enable improved confidence in the resource potential in these locations. For drilling deep groundwater well(s), the team recommended Southeast Mauna Kea and $L\bar{a}na's$ $P\bar{a}l\bar{a}wai$ $Basin$. During the third phase, further exploration involved drilling a groundwater well in $L\bar{a}na's$ $P\bar{a}l\bar{a}wai$ $Basin$ and performing more geophysical surveys. We deepened an existing water well proximal to our target area on $L\bar{a}na'i$ due to funding constraints that precluded us from spudding a new well that would exceed 1km depth. Drilling was preceded by a number of substantial elements including: writing an Environmental Assessment and the subsequent legal process, performance of deviation logging, lowering a camera down the well, coordinating site preparation with $P\bar{u}lama$ $L\bar{a}na'i$, shipping the UH-owned rig interisland, procuring supplies, and leading 3 community meetings on $L\bar{a}na'i$. Drilling occurred 24/7 the entire month of June 2019 over which time $L\bar{a}na'i$ $Well$ 10 was deepened from 427 m to 1057 m, with continuous core collected. We measured a roughly linear temperature gradient averaging 42°C/km and a maximum bottom hole temperature of 66°C. This gradient is more than twice the background for Hawai'i and within a range of gradients measured in this depth range for some exploration wells within KERZ. We consider these results encouraging for $L\bar{a}na'i's$ resource potential and recommend following with a slim hole within $L\bar{a}na'i's$ caldera (our target zone) to ~ 2 km. Further, the positive implications such results have for the island of O‘ahu are substantial - the shield stage of O'ahu's volcanoes ended 1-2 My earlier. However, O'ahu uses more electricity than the rest of the islands combined, and the utility recently called for 500-700MW of firm, dispatchable renewable electricity on O'ahu by 2033. In Phase 3, we also collected limited new encouraging groundwater data, and updated our thoughts on the probabilities of fluid and permeability at resource depths (Pr F = 1; Pr P = mostly unconstrained). Ultimately, we advocate for using our final probability of heat, and confidence in this probability, to drive the next phase of exploration. We contend further development of geothermal in Hawai‘i will enable the state to achieve its 100% renewable policy objective and Hawai'i to transition off of fossil fuels through geothermal discovery and development. The project not only produced a large amount of data and expanded the existing knowledge of Hawai'i's geothermal resources, but also produced publications, theses, presentations, core photos, datasets, media reports, television interviews, community events, and a blog. Students and new professionals benefitted from the project's hands-on research experiences and educational opportunities and earned awards and recognition.

15 GEOTHERMAL ENERGY↗

Enhanced Co-Expression Extrapolation (COXEN) Gene Selection Method for Building Anti-Cancer Drug Response Prediction Models

The co-expression extrapolation (COXEN) method has been successfully used in multiple studies to select genes for predicting the response of tumor cells to a specific drug treatment. Here, we enhance the COXEN method to select genes that are predictive of the efficacies of multiple drugs for building general drug response prediction models that are not specific to a particular drug. The enhanced COXEN method first ranks the genes according to their prediction power for each individual drug and then takes a union of top predictive genes of all the drugs, among which the algorithm further selects genes whose co-expression patterns are well preserved between cancer cases for building prediction models. We apply the proposed method on benchmark in vitro drug screening datasets and compare the performance of prediction models built based on the genes selected by the enhanced COXEN method to that of models built on genes selected by the original COXEN method and randomly picked genes. Models built with the enhanced COXEN method always present a statistically significantly improved prediction performance (adjusted p-value ≤ 0.05). Our results demonstrate the enhanced COXEN method can dramatically increase the power of gene expression data for predicting drug response.

60 APPLIED LIFE SCIENCES↗

Probability of initiation and extinction in the Mercury Monte Carlo code

A Monte Carlo method for computing the probability of initiation has previously been implemented in Mercury. Recently, a new method based on the probability of extinction has been implemented as well. The methods have similarities from counting progeny to cycling in time, but they also have differences such as population control and statistical uncertainty reporting. The two methods agree very well for several test problems. Since each method has advantages and disadvantages, we currently recommend that both methods are used to compute the probability of criticality. (authors)

97 MATHEMATICS AND COMPUTING↗

MODELING THE Ly α FOREST IN COLLISIONLESS SIMULATIONS

Cosmological hydrodynamic simulations can accurately predict the properties of the intergalactic medium (IGM), but only under the condition of retaining the high spatial resolution necessary to resolve density fluctuations in the IGM. This resolution constraint prohibits simulating large volumes, such as those probed by BOSS and future surveys, like DESI and 4MOST. To overcome this limitation, we present “Iteratively Matched Statistics” (IMS), a novel method to accurately model the Ly α forest with collisionless N -body simulations, where the relevant density fluctuations are unresolved. We use a small-box, high-resolution hydrodynamic simulation to obtain the probability distribution function (PDF) and the power spectrum of the real-space Ly α forest flux. These two statistics are iteratively mapped onto a pseudo-flux field of an N -body simulation, which we construct from the matter density. We demonstrate that our method can reproduce the PDF, line of sight and 3D power spectra of the Ly α forest with good accuracy (7%, 4%, and 7% respectively). We quantify the performance of the commonly used Gaussian smoothing technique and show that it has significantly lower accuracy (20%–80%), especially for N -body simulations with achievable mean inter-particle separations in large-volume simulations. In addition, we show that IMS produces reasonable and smooth spectra, making it a powerful tool for modeling the IGM in large cosmological volumes and for producing realistic “mock” skies for Ly α forest surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Method of Determining the Reliability of Real-Time In-reactor Monitoring of VVER

A methodological approach and the basic tenets for evaluating the reliability of in-reactor monitoring of VVER are presented. The method is based on the statistical analysis of indications in real time and includes methods for evaluating the admissible maximum error of the measurement channels used for monitoring as well as the average value and admissible deviation of indications in groups of parallel monitoring channels, as well as a method of evaluating reliability by comparing the values of a parameter with the regime values. In comparing the indications of a monitoring channel with the indications of other parallel channels, the median value is proposed as the baseline value. The developed method is implemented in the Diagnostika SVRK special software, which has been successfully tested during the commissioning of the No. 1 unit at the Novovoronezh NPP-2.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Using Satellite Data to Characterize the Temporal Thermal Behavior of an Active Volcano: Mount St. Helens, WA

ASTER thermal infrared data over Mt. St Helens were used to characterize its thermal behavior from Jun 2000 to Feb 2006. Prior to the Oct 2004 eruption, the average crater temperature varied seasonally between -12 and 6 C. After the eruption, maximum single-pixel temperature increased from 10 C (Oct 2004) to 96 C (Aug 2005), then showed a decrease to Feb 2006. The initial increase in temperature was correlated with dome morphology and growth rate and the subsequent decrease was interpreted to relate to both seasonal trends and a decreased growth rate/increased cooling rate, possibly suggesting a significant change in the volcanic system. A single-pixel ASTER thermal anomaly first appeared on Oct 1, 2004, eleven hours after the first eruption - 10 days before new lava was exposed at the surface. By contrast, an automated algorithm for detecting thermal anomalies in MODIS data did not trigger an alert until Dec 18. However, a single-pixel thermal anomaly first appeared in MODIS channel 23 (4 um) on Oct 13, 12 days after the first eruption - 2 days after lava was exposed. The earlier thermal anomaly detected with ASTER data is attributed to the higher spatial resolution (90 m) compared with MODIS (1 m) and the earlier visual observation of anomalous pixels compared to the automated detection method suggests that local spatial statistics and background radiance data could improve automated detection methods.

Advanced Spaceborne Thermal Emission and Reflectio↗

SU-E-T-769: T-Test Based Prior Error Estimate and Stopping Criterion for Monte Carlo Dose Calculation in Proton Therapy

Purpose: The Monte Carlo (MC) method is a gold standard for dose calculation in radiotherapy. However, it is not a priori clear how many particles need to be simulated to achieve a given dose accuracy. Prior error estimate and stopping criterion are not well established for MC. This work aims to fill this gap. Methods: Due to the statistical nature of MC, our approach is based on one-sample t-test. We design the prior error estimate method based on the t-test, and then use this t-test based error estimate for developing a simulation stopping criterion. The three major components are as follows.First, the source particles are randomized in energy, space and angle, so that the dose deposition from a particle to the voxel is independent and identically distributed (i.i.d.).Second, a sample under consideration in the t-test is the mean value of dose deposition to the voxel by sufficiently large number of source particles. Then according to central limit theorem, the sample as the mean value of i.i.d. variables is normally distributed with the expectation equal to the true deposited dose.Third, the t-test is performed with the null hypothesis that the difference between sample expectation (the same as true deposited dose) and on-the-fly calculated mean sample dose from MC is larger than a given error threshold, in addition to which users have the freedom to specify confidence probability and region of interest in the t-test based stopping criterion. Results: The method is validated for proton dose calculation. The difference between the MC Result based on the t-test prior error estimate and the statistical Result by repeating numerous MC simulations is within 1%. Conclusion: The t-test based prior error estimate and stopping criterion are developed for MC and validated for proton dose calculation. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)

60 APPLIED LIFE SCIENCES↗

Guidelines for Design and Analysis of Large, Brittle Spacecraft Components

There were two related parts to this work. The first, conducted at The Aerospace Corporation was to develop and define methods for integrating the statistical theory of brittle strength with conventional finite element stress analysis, and to carry out a limited laboratory test program to illustrate the methods. The second part, separately funded at Aerojet Electronic Systems Division, was to create the finite element postprocessing program for integrating the statistical strength analysis with the structural analysis. The second part was monitored by Capt. Jeff McCann of USAF/SMC, as Special Study No.11, which authorized Aerojet to support Aerospace on this work requested by NASA. This second part is documented in Appendix A. The activity at Aerojet was guided by the Aerospace methods developed in the first part of this work. This joint work of Aerospace and Aerojet stemmed from prior related work for the Defense Support Program (DSP) Program Office, to qualify the DSP sensor main mirror and corrector lens for flight as part of a shuttle payload. These large brittle components of the DSP sensor are provided by Aerojet. This document defines rational methods for addressing the structural integrity and safety of large, brittle, payload components, which have low and variable tensile strength and can suddenly break or shatter. The methods are applicable to the evaluation and validation of such components, which, because of size and configuration restrictions, cannot be validated by direct proof test.

Robinson, E. Y.↗

Data compression

An approach to data compression is discussed in which the effect achieved by compression is evaluated by the closeness of the approach to the minimum possible volume. An attempt is made to systematize the known results on data compression. The review contains: description of methods of data compression based on statistical coding and information theory; application of methods of interpolation and extrapolation; a specific compression method (related to description of the histogram of a sample); some criteria of effectiveness and methods of service information representation; and discussion of models suggested for theoretical analysis.

Babkin, V. F.↗

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