Statistical simulation procedures
Statistical simulation procedures utilizing Monte Carlo stratification technique
Oglesby, J. L.↗
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Direct statistical simulation of the Lorenz96 system in model reduction approaches
Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimensions than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal-time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems. Published by the American Physical Society 2025
Li, Kuan↗
Chrono-Validation of Near-Real-Time Landslide Susceptibility Models via Plugin Statistical Simulations
The idea behind any validation scheme in landslide susceptibility studies is to test whether a model calibrated on a certain data can predict an unknown dataset of the same nature (landslide presences/absences and covariates). Almost the entirety of landslide susceptibility studies are validated by subsetting a single dataset into a training and test sets. This dataset usually corresponds either to event-specific or to historical inventories. Very rarely, a multi-temporal inventory is available and, in the few cases where this condition is met, the validation practices involve training a model on a specific landslide inventory, deriving a single predictive equation and validating it on a subsequent landslide inventory. This commonly leads landslide predictive studies, even those with a strong statistical rigor, to neglect the uncertainty estimation in their modeling scheme. In statistics, validation can also be performed via statistical simulations. This means that after fitting a given model, one can generate any number of predictive functions and test their predictive skills on any type and number of unknown datasets. In this work, we take a similar direction and we apply it to model and validate three separate co-seismic inventories, including an uncertainty estimation phase. We mapped these inventories within the same area in Indonesia, for three earthquakes occurred in 2012, 2017 and 2018. Specifically, we build three event-specific Bayesian Generalize Additive Models of the binomial family. From each model we then simulate 1000 predictive realizations over the remaining two inventories, by using a plug-in scheme where all the morphometric covariates are kept fixed and only the ground motion is replaced according to the prediction target. By doing so, we introduce a new analytical tool for near-real-time landslide predictive purposes, which is able to produce a probabilistic model which stands in between the definitions of susceptibility and hazard. In fact, our model is able to accurately estimate “where” and “when” - although not “how frequently” - landslide have occurred by featuring the multitemporal information of the trigger. In our findings, the simulations are quite similar to the fitted models; and the nine combinations we analyse produce excellent performance. This result confirms the assumption that “the past is the key to the future”, as we show that the relative contribution of each variable and their interactions in each probabilistic model remains practically the same across temporal replicates. This information is not trivial because it supports the routines implemented in global near-real-time applications.
Temporal validation↗
Mars 2020 Perseverance Entry Descent and Landing Simulation Statistical Analysis and Operations
On February 18, 2021, the Perseverance rover and Ingenuity helicopter demonstra- tion landed at Jezero Crater. The Entry, Descent, and Landing (EDL) architecture, largely the same used to land Curiosity at Gale Crater on August 6, 2012, required high-fidelity flight dynamics simulation with two independent tools to verify per- formance. The process for creating the EDL simulation using the Dynamics Sim- ulator for Entry, Descent and Surface landing (DSENDS) tool will be discussed, along with its use for for independent verification of the EDL statistical analy- sis results and reference trajectory simulation. Analysis and usage details both in development and cruise, along with post-landing assessment of the prediction performance of the simulation, will also be discussed.
"O'Farrell, Clara"↗
Statistical simulations of clusters of galaxies
By comparing observed and simulated rich clusters of galaxies, it is shown that the observed clusters actually possess physical cores. The accuracy with which core radii can be determined is found. It is also shown that the observations of density profiles of galaxies in the clusters give no significant evidence for a dynamical reason as the cause of the anomalously close resemblance found previously between such density profiles and the isothermal gas distribution.
Avni, Y.↗
Observations and statistical simulations of a proposed solar cycle/QBO/weather relationship
The 10.7-cm solar flux is observed to be highly correlated with North Pole stratospheric temperatures when partitioned according to the phase of the equatorial stratospheric winds (the quasi-biennial oscillation, or QBO). Calculations show that temperatures over most of the Northern Hemisphere are highly correlated or anticorrelated with North Pole temperatures. The observed spatial pattern of solar-cycle correlations at high latitudes is shown to be not unique to the solar cycle.
Baldwin, Mark P.↗
A Statistical Simulation Approach to Safe Life Fatigue Analysis of Redundant Metallic Components
This paper introduces a dual active load path fail-safe fatigue design concept analyzed by Monte Carlo simulation. The concept utilizes the inherent fatigue life differences between selected pairs of components for an active dual path system, enhanced by a stress level bias in one component. The design is applied to a baseline design; a safe life fatigue problem studied in an American Helicopter Society (AHS) round robin. The dual active path design is compared with a two-element standby fail-safe system and the baseline design for life at specified reliability levels and weight. The sensitivity of life estimates for both the baseline and fail-safe designs was examined by considering normal and Weibull distribution laws and coefficient of variation levels. Results showed that the biased dual path system lifetimes, for both the first element failure and residual life, were much greater than for standby systems. The sensitivity of the residual life-weight relationship was not excessive at reliability levels up to R = 0.9999 and the weight penalty was small. The sensitivity of life estimates increases dramatically at higher reliability levels.
Matthews, William T.↗
Mars 2020 Perseverance Entry, Descent, and Landing Simulation Statistical Analysis and Operations
No abstract provided
"O'Farrell, Clara"↗
On the convergence of statistics in simulations of stationary incompressible turbulent flows
When reporting statistics from simulations of statistically stationary chaotic phenomenon, it is important to verify that the simulations are time-converged. This condition is connected with the statistical error or number of digits with which statistics can be reliably reported. In this work we consider numerical experiments of low Reynolds number incompressible homogeneous and isotropic turbulence as a model problem to investigate statistical convergence over finite simulation times. Specifically, we investigate the time integration requirements that allow meaningful reporting of the statistical error associated with finiteness of the temporal domain. We address two key questions: (1) How long should a simulation be performed in terms of large eddy time, and (2) How should the simulation time be divided among temporal windows over which a quantity of interest is estimated so that its statistical error could be reliably reported? We find that reliable reporting of statistical errors requires simulations on the order of 10 4 large eddy times, which is orders of magnitude longer than typically performed. Additionally, data post-processing should employ windows of at least ten times the large eddy time scale, with the most robust computation of statistical error of the mean requiring window sizes of an additional factor of ten. For practical simulations, we demonstrate that it is possible to estimate the statistical error within a factor of two under a less stringent condition in which a minimum of four windows with size at least ten large eddy times are used. In conclusion, our observations for homogeneous isotropic turbulence are also shown to hold in turbulent channel flow.
42 ENGINEERING↗
Estimating Uncertainty in Simulated ENSO Statistics
Abstract Large ensembles of model simulations are frequently used to reduce the impact of internal variability when evaluating climate models and assessing climate change induced trends. However, the optimal number of ensemble members required to distinguish model biases and climate change signals from internal variability varies across models and metrics. Here we analyze the mean, variance and skewness of precipitation and sea surface temperature in the eastern equatorial Pacific region often used to describe the El Niño–Southern Oscillation (ENSO), obtained from large ensembles of Coupled model intercomparison project phase 6 climate simulations. Leveraging established statistical theory, we develop and assess equations to estimate, a priori, the ensemble size or simulation length required to limit sampling‐based uncertainties in ENSO statistics to within a desired tolerance. Our results confirm that the uncertainty of these statistics decreases with the square root of the time series length and/or ensemble size. Moreover, we demonstrate that uncertainties of these statistics are generally comparable when computed using either pre‐industrial control or historical runs. This suggests that pre‐industrial runs can sometimes be used to estimate the expected uncertainty of statistics computed from an existing historical member or ensemble, and the number of simulation years (run duration and/or ensemble size) required to adequately characterize the statistic. This advance allows us to use existing simulations (e.g., control runs that are performed during model development) to design ensembles that can sufficiently limit diagnostic uncertainties arising from simulated internal variability. These results may well be applicable to variables and regions beyond ENSO.
54 ENVIRONMENTAL SCIENCES↗
Spectral irradiance measurements of large solar simulators
Statistical extrapolation of spectral irradiance measurements of large solar simulators
Redman, R. S.↗
Testing the thermal Sunyaev-Zel’dovich power spectrum of a halo model using hydrodynamical simulations
Statistical properties of large-scale cosmological structures serve as powerful tools for constraining the cosmological properties of our Universe. Tracing the gas pressure, the thermal Sunyaev-Zel’dovich (tSZ) effect is a biased probe of mass distribution and, hence, can be used to test the physics of feedback or cosmological models. Therefore, it is crucial to develop robust modelling of hot gas pressure for applications to tSZ surveys. Since gas collapses into bound structures, it is expected that most of the tSZ signal is within halos produced by cosmic accretion shocks. Hence, simple empirical halo models can be used to predict the tSZ power spectra. In this study, we employed the HMx halo model to compare the tSZ power spectra with those of several hydrodynamical simulations: the Horizon suite and the Magneticum simulation. We examine various contributions to the tSZ power spectrum across different redshifts, including the one- and two-halo term decomposition, the amount of bound gas, the importance of different masses, and the electron pressure profiles. Our comparison of the tSZ power spectrum reveals discrepancies between the halo model and cosmological simulations that increase with redshift. We find a 20% to 50% difference between the measured and predicted tSZ angular power spectrum over the multipole range ℓ = 10 3 − 10 4 . Our analysis reveals that these differences are driven by the excess of power in the predicted two-halo term at low k and in the one-halo term at high k . At higher redshifts ( z ∼ 3), simulations indicate that more power comes from outside the virial radius than from inside, suggesting a limitation in the applicability of the halo model. We also observe differences in the pressure profiles, despite the fair level of agreement on the tSZ power spectrum at low redshift with the default calibration of the halo model. In conclusion, our study suggests that the properties of the halo model need to be carefully controlled against real or mock data to be proven useful for cosmological purposes.
Ayçoberry, Emma (ORCID:0000000292351195)↗
A Numerical Simulation and Statistical Modeling of High Intensity Radiated Fields Experiment Data
Tests are conducted on a quad-redundant fault tolerant flight control computer to establish upset characteristics of an avionics system in an electromagnetic field. A numerical simulation and statistical model are described in this work to analyze the open loop experiment data collected in the reverberation chamber at NASA LaRC as a part of an effort to examine the effects of electromagnetic interference on fly-by-wire aircraft control systems. By comparing thousands of simulation and model outputs, the models that best describe the data are first identified and then a systematic statistical analysis is performed on the data. All of these efforts are combined which culminate in an extrapolation of values that are in turn used to support previous efforts used in evaluating the data.
Smith, Laura J.↗
Hierarchical Statistical 3D ' Atomistic' Simulation of Decanano MOSFETs: Drift-Diffusion, Hydrodynamic and Quantum Mechanical Approaches
When MOSFETs are scaled to deep submicron dimensions the discreteness and randomness of the dopant charges in the channel region introduces significant fluctuations in the device characteristics. This effect, predicted 20 year ago, has been confirmed experimentally and in simulation studies. The impact of the fluctuations on the functionality, yield, and reliability of the corresponding systems shifts the paradigm of the numerical device simulation. It becomes insufficient to simulate only one device representing one macroscopical design in a continuous charge approximation. An ensemble of macroscopically identical but microscopically different devices has to be characterized by simulation of statistically significant samples. The aims of the numerical simulations shift from predicting the characteristics of a single device with continuous doping towards estimating the mean values and the standard deviations of basic design parameters such as threshold voltage, subthreshold slope, transconductance, drive current, etc. for the whole ensemble of 'atomistically' different devices in the system. It has to be pointed out that even the mean values obtained from 'atomistic' simulations are not identical to the values obtained from continuous doping simulations. In this paper we present a hierarchical approach to the 'atomistic' simulation of aggressively scaled decanano MOSFETs. A full scale 3D drift-diffusion'atomostic' simulation approach is first described and used for verification of the more economical, but also more restricted, options. To reduce the processor time and memory requirements at high drain voltage we have developed a self-consistent option based on a thin slab solution of the current continuity equation only in the channel region. This is coupled to the Poisson's equation solution in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison with the full self-consistent solution. At low drain voltage only single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. A pilot version of a hydrodynamic 'atomistic' simulator has been developed in order to study the effect of the nonequilibrium, non local transport in decanano MOSFETs on the random dopant induced current fluctuations. For the first time we have also applied the density gradient approach in 3D to investigate the effect of the quantum confinement on the threshold voltage fluctuations. The developed 'atomistic' simulation techniques have been applied to study various fluctuation resistant MOSFET architectures including epitaxial and delta doped devices.
Asenov, Asen↗
Stokes-dependent droplet collection efficiency on a NACA 0012 airfoil from droplet-informed simulations with statistical overloading
Accurate modelling of ice accretion on aircraft wings requires analysing droplet impingement on the surface to optimize the design of ice-protection systems. We perform Euler–Lagrange simulations of a droplet-laden flow impinging on a NACA 0012 airfoil. Our study includes water droplets with eight discrete sizes ranging from 1 to 160 microns. We vary the free-stream velocity of the incoming airflow in the range 60 ≤ U ≤ 240 m s −1 and the chord length of the airfoil in the range 0.5 ≤ c ≤ 2 m. Due to the dilute nature of supercooled clouds, one-way coupling is used in the simulations. The effects of droplet breakup and collision are also neglected. To reduce the computational cost, we employ statistical overloading of droplets, allowing us to simulate millions of impinging droplets in a time span on the order of milliseconds. Our results show that the droplet collection efficiency, which measures the likelihood of droplet impingement on the airfoil surface, increases with droplet size and free-stream velocity but decreases with airfoil size. We demonstrate that collection efficiency, impingement velocity and impingement angle are primarily dictated by a single non-dimensional parameter, the droplet Stokes number. We also identify a critical stagnation-streamline Stokes number below which impingements do not occur and use it to estimate the minimum droplet size for impingement. In addition, we observe droplet behaviour to become Stokes number independent at large values of the Stokes number. This article is part of the theme issue ‘Heat and mass transfer in frost and ice’.
Science & Technology - Other Topics↗
Λ Baryon Production in ν¯µ Interactions in the MicroBooNE Detector
The Cabibbo suppressed production of $\Lambda$ baryons in anti-neutrino interactions with nuclei is a rare process that is yet to be measured with a modern neutrino detector with automated reconstruction. The cross section for this process is sensitive to a number of unique nuclear effects, most notably the secondary interactions of the produced hyperon while attempting to escape from the nucleus. Other interactions within the nuclear remnant can impact the estimation of neutrino energy in oscillation measurements, and thus an accurate description of the nuclear environment is required. The strangeness violating hyperon production process is only available to anti-neutrinos. The model of this interaction is implemented into the NuWro neutrino interaction Monte Carlo simulation, and some predictions are presented, focusing on the role of nuclear effects. This model introduces a hyperon-nucleus potential, which calculations from hypernuclear theory permit to be strongly repulsive in th e case of $\Sigma$ baryons. The presence of this potential is found to sculpt the shape of the differential cross section in some variables. The MicroBooNE detector will be described, followed by a description of a measurement of the flux averaged, restricted phase space cross section of Cabibbo suppressed $\Lambda$ baryon production. A sophisticated event selection is employed, as a very large quantity of background neutrino interactions must be removed to perform the measurement with any sensitivity. This selection introduces some novel techniques such as the island finding method, and achieves a background reduction of $\sim 10^6$, with an efficiency of around 7\%. The calculation of the systematic uncertainties will be explained, including two procedures explored to handle sources of background with extremely poor simulation statistics: an in-situ constraint using data from sidebands, and a visual inspection of the data and simulation to remove the troublesome background events. The sensitivity to the $\Lambda$ baryon production cross section is calculated in the form of Bayesian posterior probability distributions, combining the systematic uncertainties with data and simulation statistical uncertainties. As a rare process, the statistical uncertainties are highly non-Gaussian, and the Bayesian approach is applied to include the full shapes of these uncertainties. Data corresponding to $2.2 \times 10^{20}$ protons on target of neutrino mode running and $4.9 \times 10^{20}$ protons on target of anti-neutrino running is analysed. When the data was unblinded, five $\Lambda$ production candidates were selected from the data, consistent with the MC simulation prediction of $5.3 \pm 1.1$ events. The final estimated cross section is $1.8^{+2.0}_{-1.6} \times 10^{-40}$cm$^2/$Ar when employing the sideband constraint procedure. A similar result of $2.0^{+2.2}_{-1.8} \times 10^{-40}$cm$^2/$Ar is obtained when performing the visual scan instead. The methods used in t his analysis are intended to be easily exported to other LArTPC detectors such as the Short Baseline Near Detector.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Statistical modeling of software reliability
This working paper discusses the statistical simulation part of a controlled software development experiment being conducted under the direction of the System Validation Methods Branch, Information Systems Division, NASA Langley Research Center. The experiment uses guidance and control software (GCS) aboard a fictitious planetary landing spacecraft: real-time control software operating on a transient mission. Software execution is simulated to study the statistical aspects of reliability and other failure characteristics of the software during development, testing, and random usage. Quantification of software reliability is a major goal. Various reliability concepts are discussed. Experiments are described for performing simulations and collecting appropriate simulated software performance and failure data. This data is then used to make statistical inferences about the quality of the software development and verification processes as well as inferences about the reliability of software versions and reliability growth under random testing and debugging.
Miller, Douglas R.↗
Statistical Ensemble of Large Eddy Simulations
A statistical ensemble of large eddy simulations (LES) is run simultaneously for the same flow. The information provided by the different large scale velocity fields is used to propose an ensemble averaged version of the dynamic model. This produces local model parameters that only depend on the statistical properties of the flow. An important property of the ensemble averaged dynamic procedure is that it does not require any spatial averaging and can thus be used in fully inhomogeneous flows. Also, the ensemble of LES's provides statistics of the large scale velocity that can be used for building new models for the subgrid-scale stress tensor. The ensemble averaged dynamic procedure has been implemented with various models for three flows: decaying isotropic turbulence, forced isotropic turbulence, and the time developing plane wake. It is found that the results are almost independent of the number of LES's in the statistical ensemble provided that the ensemble contains at least 16 realizations.
Carati, Daniele↗