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At least 559 records · Page 31

Towards Measurement of Confidence in Safety Cases

Arguments in safety cases are predominantly qualitative. This is partly attributed to the lack of sufficient design and operational data necessary to measure the achievement of high-dependability targets, particularly for safety-critical functions implemented in software. The subjective nature of many forms of evidence, such as expert judgment and process maturity, also contributes to the overwhelming dependence on qualitative arguments. However, where data for quantitative measurements is systematically collected, quantitative arguments provide far more benefits over qualitative arguments, in assessing confidence in the safety case. In this paper, we propose a basis for developing and evaluating integrated qualitative and quantitative safety arguments based on the Goal Structuring Notation (GSN) and Bayesian Networks (BN). The approach we propose identifies structures within GSN-based arguments where uncertainties can be quantified. BN are then used to provide a means to reason about confidence in a probabilistic way. We illustrate our approach using a fragment of a safety case for an unmanned aerial system and conclude with some preliminary observations

Denney, Ewen↗

Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets

A novel extension of the Probabilistic Learning on Manifolds (PLoM) is presented. It makes it possible to synthesize solutions to a wide range of nonlinear stochastic boundary value problems described by partial differential equations (PDEs) for which a stochastic computational model (SCM) is available and which depend on a vector-valued random control parameter. The cost of a single numerical evaluation of this SCM is assumed to be such that only a limited number of points can be computed for constructing the training dataset (small data). Each point of the training dataset is made up of realizations from a vector-valued stochastic process (the stochastic solution) and the associated random control parameter on which it depends. The presented PLoM constrained by PDE allows for generating a large number of learned realizations of the stochastic process and its corresponding random control parameter. These learned realizations are generated so as to minimize the vector-valued random residual of the PDE in the mean-square sense. Appropriate novel methods are developed to solve this challenging problem. Three applications are presented. The first one is a simple uncertain nonlinear dynamical system with a nonstationary stochastic excitation. The second one concerns the 2D nonlinear unsteady Navier–Stokes equations for incompressible flows in which the Reynolds number is the random control parameter. Here, the last one deals with the nonlinear dynamics of a 3D elastic structure with uncertainties. The results obtained make it possible to validate the PLoM constrained by stochastic PDE but also provide further validation of the PLoM without constraint.

Machine learning↗

A probabilistic fatigue analysis of multiple site damage

The variability in initial crack size and fatigue crack growth is incorporated in a probabilistic model that is used to predict the fatigue lives for unstiffened aluminum alloy panels containing multiple site damage (MSD). The uncertainty of the damage in the MSD panel is represented by a distribution of fatigue crack lengths that are analytically derived from equivalent initial flaw sizes. The variability in fatigue crack growth rate is characterized by stochastic descriptions of crack growth parameters for a modified Paris crack growth law. A Monte-Carlo simulation explicitly describes the MSD panel by randomly selecting values from the stochastic variables and then grows the MSD cracks with a deterministic fatigue model until the panel fails. Different simulations investigate the influences of the fatigue variability on the distributions of remaining fatigue lives. Six cases that consider fixed and variable conditions of initial crack size and fatigue crack growth rate are examined. The crack size distribution exhibited a dominant effect on the remaining fatigue life distribution, and the variable crack growth rate exhibited a lesser effect on the distribution. In addition, the probabilistic model predicted that only a small percentage of the life remains after a lead crack develops in the MSD panel.

Rohrbaugh, S. M.↗

Probabilistic Data Association for Orbital-Element Estimation Using Multistage Expectation–Maximization

Tracking space objects is important for managing space traffic and predicting collisions, but is difficult in part due to data association and orbit model uncertainty. Expectation–maximization (EM) is a commonly used tracking method that has not been widely considered for tracking space objects. The technique consists of iteratively computing data association probabilities with a set of current element estimates, and updating estimates of the elements by solving a nonlinear weighted least-squares regression problem where the weights are the data association probabilities. In this paper, we demonstrate the use of EM for probabilistic data association and orbital-element estimation by applying the technique to simulated data from two angles-only tracking scenarios. In both scenarios, EM provides correct data associations and accurate maximum likelihood estimates of orbital elements. One scenario considers tracking a single object in clutter and quantifies the improvement of the orbital-element estimates and data associations as the detection probability increases. However, standard application of EM requires knowing the number of objects or may fail when a large number of objects are present. To address these issues, this paper employs a multistage version of EM that is applicable when there are a large and possibly unknown number of objects.

97 MATHEMATICS AND COMPUTING↗

It Depends - An Overview of Probabilistic Risk Analysis Concepts

How do you understand the data and assumptions in your probabilistic analysis? The PRA analyst needs to understand the data and input assumptions to effectively communicate the system/mission's risks. The decision maker also needs to understand conservatisms and how to interpret uncertainty in the PRA results. Properties such as assumptions on the distributions, uncertainty, use of test data, and common cause modeling can be the subject of much discussion, but often are the leading drivers of a risk profile.

risk assessment↗

UQpy: A general purpose Python package and development environment for uncertainty quantification

In this paper, we present the UQpy software toolbox, an open-source Python package for general uncertainty quantification (UQ) in mathematical and physical systems. The software serves as both a user-ready toolbox that includes many of the latest methods for UQ in computational modeling and a convenient development environment for Python programmers advancing the field of UQ. The paper presents an introduction to the software's architecture and existing capabilities, divided in the code in a set of modules centered around different UQ tasks such as sampling methods, generation of random processes and random fields, probabilistic inverse modeling, reliability analysis, surrogate modeling, and active learning. The paper also highlights the importance of the RunModel module, which is used to drive simulations in the uncertainty analyses performed in UQpy. This module conveniently allows the user to define computational models directly in Python, or to run simulations from a third-party software in serial or in parallel. To illustrate the various capabilities, two examples are tracked throughout the paper and analyzed repeatedly for various UQ tasks. The first is a Python model solving a nonlinear structural dynamics problem, used to illustrate UQpy's capabilities in sampling and forward propagation of high dimensional random vectors (stochastic processes), and probabilistic inference. The second model is a third-party Abaqus finite element model solving the thermomechanical response of a beam structure. This example is used to illustrate UQpy's capabilities in variance reduction sampling techniques, reliability analysis, surrogate modeling and active learning techniques.

97 MATHEMATICS AND COMPUTING↗

A Bayesian Approach for Estimating Uncertainty in Stochastic Economic Dispatch considering Wind Power Penetration

The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To estimate the uncertainty in this stochastic economic dispatch problem for forecasting purposes, the conventional Monte-Carlo method is prohibitively time-consuming for practical applications. To overcome this problem, here we propose a novel Gaussian-process-emulator-based approach to quantify the uncertainty in the stochastic economic dispatch considering wind power penetration. Facing high-dimensional real-world data representing the correlated uncertainties from wind generation, a manifold-learning-based Isomap algorithm is proposed to efficiently represent the low-dimensional hidden probabilistic structure of the data. In this low-dimensional latent space, with Latin hypercube sampling as the computer experimental design, a Gaussian-process emulator is used, for the first time, to serve as a nonparametric, surrogate model for the original complicated stochastic economic dispatch model. This reduced-order representative allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus test system reveal the impressive performance of the proposed method.

17 WIND ENERGY↗

Scalable probabilistic estimates of electric vehicle charging given observed driver behavior

To prepare for rapid growth in global electric vehicle adoption, grid and policy planners depend on detailed forecasts of future charging demand. In this paper we propose a novel holistic, scalable, probabilistic framework to produce large-scale estimates of electric vehicle charging load for long-term planning that capture real drivers’ charging patterns. Our framework captures the uncertainty and stochasticity in charging demand by taking a graphical modeling approach. It has three core elements: driver groups, charging segment choices, and charging session time and energy requirements. The framework uses hierarchical clustering to group drivers by their charging histories, capturing their heterogeneous behaviors and preferences across different segments or types of charging. The framework uses probabilistic mixture models for each driver group’s sessions to identify the unique charging behaviors observed within each segment. We illustrate its application with a large data set from California, profiling the charging patterns and unique driver clusters it identifies. Using the model knobs representing drivers’ battery capacities, behavior, and segment access we present scenarios for California’s charging demand in 2030 with 8 million passenger electric vehicles. Peak charging demand ranged from 3.3 to 8.7 GW across scenarios. Furthermore, each was calculated in under 45 s on a laptop computer.

33 ADVANCED PROPULSION SYSTEMS↗

On the Accuracy of Probabilistic Bucking Load Prediction

The buckling strength of thin-walled stiffened or unstiffened, metallic or composite shells is of major concern in aeronautical and space applications. The difficulty to predict the behavior of axially compressed thin-walled cylindrical shells continues to worry design engineers as we enter the third millennium. Thanks to extensive research programs in the late sixties and early seventies and the contributions of many eminent scientists, it is known that buckling strength calculations are affected by the uncertainties in the definition of the parameters of the problem such as definition of loads, material properties, geometric variables, edge support conditions, and the accuracy of the engineering models and analysis tools used in the design phase. The NASA design criteria monographs from the late sixties account for these design uncertainties by the use of a lump sum safety factor. This so-called 'empirical knockdown factor gamma' usually results in overly conservative design. Recently new reliability based probabilistic design procedure for buckling critical imperfect shells have been proposed. It essentially consists of a stochastic approach which introduces an improved 'scientific knockdown factor lambda(sub a)', that is not as conservative as the traditional empirical one. In order to incorporate probabilistic methods into a High Fidelity Analysis Approach one must be able to assess the accuracy of the various steps that must be executed to complete a reliability calculation. In the present paper the effect of size of the experimental input sample on the predicted value of the scientific knockdown factor lambda(sub a) calculated by the First-Order, Second-Moment Method is investigated.

Arbocz, Johann↗

Probabilistic reliability assessment and case studies for predicted energy savings in residential buildings

This study aims to (1) investigate the key influential parameters (KIPs) in estimating the uncertainty of energy savings using a residential building energy simulation model and (2) perform uncertainty quantification for energy savings for several different scenarios. The proposed methodology was successfully applied to the calculation of uncertainties associated with residential energy retrofits using two test houses designed for pre- and post-retrofit cases. Uncertainties were determined using basic parameters that might be supplied to an energy model and then reevaluated based on an audit of the KIPs identified, resulting in substantially reduced uncertainty. Of four different scenarios, the most uncertain scenario estimated the annual energy savings from the retrofit would be between 18% and 51% at a 95% confidence level, and the least uncertain scenario estimated the annual savings would be between 26% and 40% at a 95% confidence level. The actual measured annual savings from the two test houses was 28%, which shows an agreement with the uncertainty analysis.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evaluation of probabilistic photometric redshift estimation approaches for The Rubin Observatory Legacy Survey of Space and Time (LSST)

Many scientific investigations of photometric galaxy surveys require redshift estimates, whose uncertainty properties are best encapsulated by photometric redshift (photo-z) posterior probability density functions (PDFs). A plethora of photo-z PDF estimation methodologies abound, producing discrepant results with no consensus on a preferred approach. We present the results of a comprehensive experiment comparing twelve photo-z algorithms applied to mock data produced forLarge Synoptic Survey Telescope The Rubin Observatory Legacy Survey of Space and Time (lsst) Dark Energy Science Collaboration (desc). By supplying perfect prior information, in the form of the complete template library and a representative training set as inputs to each code, we demonstrate the impact of the assumptions underlying each technique on the output photo-z PDFs. In the absence of a notion of true, unbiased photo-z PDFs, we evaluate and interpret multiple metrics of the ensemble properties of the derived photo-z PDFs as well as traditional reductions to photo-z point estimates. Additionally, we report systematic biases and overall over/under-breadth of the photo-z PDFs of many popular codes, which may indicate avenues for improvement in the algorithms or implementations. Furthermore, we raise attention to the limitations of established metrics for assessing photo-z PDF accuracy; though we identify the conditional density estimate (CDE) loss as a promising metric of photo-z PDF performance in the case where true redshifts are available but true photo-z PDFs are not, we emphasize the need for science-specific performance metrics.

79 ASTRONOMY AND ASTROPHYSICS↗

Yesterday’s extremes, today’s new normal: flood risk in the Kathmandu Valley, Nepal

Unplanned urban growth has left many cities increasingly vulnerable to extreme rainfall events, particularly in regions with inadequate drainage infrastructures and development encroaching on natural floodplains. Here, in this perspective paper, we examine the September 2024 floods that struck Central Nepal, triggered by a persistent low-pressure system and enhanced by converging moisture flows from the Arabian Sea and the Bay of Bengal which led to widespread catastrophic damage. In the Kathmandu Valley, floodwaters expanded to more than 2.5 times the bankfull water extent, causing significant damage to housing, transportation network, and critical infrastructure, displacing thousands of residents, and severely disrupting urban services. This event highlights the urgent need for improved flood management strategies that integrate both structural and non-structural measures into the infrastructure development. While early warning systems provided critical lead time, challenges remain in reducing forecasting uncertainties and improving communication across government agencies and with local communities. A forward-looking approach is essential, including probabilistic flood forecasting systems, sustainable floodplain management, risk-sensitive land use planning, climate- and disaster- resilient infrastructure development, and the integration of nature-based solutions like urban green and blue spaces to mitigate flood impacts. By involving local communities in planning and preparedness efforts, particularly through citizen science initiatives, and engagement with underserved and disadvantaged communities, Nepal can better adapt to the growing risks posed by extreme rainfall and urban flooding and enhance long-term disaster resilience in rapidly urbanizing areas like Kathmandu Valley.

Kathmandu Valley↗

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↗

Probabilistic structural analysis of a truss typical for space station

A three-bay, space, cantilever truss is probabilistically evaluated using the computer code NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) to identify and quantify the uncertainties and respective sensitivities associated with corresponding uncertainties in the primitive variables (structural, material, and loads parameters) that defines the truss. The distribution of each of these primitive variables is described in terms of one of several available distributions such as the Weibull, exponential, normal, log-normal, etc. The cumulative distribution function (CDF's) for the response functions considered and sensitivities associated with the primitive variables for given response are investigated. These sensitivities help in determining the dominating primitive variables for that response.

Pai, Shantaram S.↗

Correlated Trajectory Uncertainty for Adaptive Sequential Decision Making

One of the great challenges with decision making tasks on real world systems is the fact that data is sparse and acquiring additional data is expensive. In these cases, it is often crucial to make a model of the environment to assist in making decisions. At the same time, limited data means that learned models are erroneous, making it just as important to equip the model with good predictive uncertainties. In the context of learning sequential decision making policies, these uncertainties can prove useful for informing which data to collect for the greatest improvement in policy performance \citep{mehta2021experimental, mehta2022exploration} or informing the policy about unsure regions of state and action space to avoid during test time \citep{yu2020mopo}. Additionally, assuming that realistic samples of the environment can be drawn, an adaptable policy can be trained that attempts to make optimal decisions for any given possible instance of the environment \citep{ghosh2022offline, chen2021offline}. In this work, we examine the so-called ``probabilistic neural network'' (PNN) model that is ubiquitous in model-based reinforcement learning (MBRL) works. We argue that while PNN models may have good marginal uncertainties, they form a distribution of non-smooth transition functions. Not only are these samples unrealistic and may hamper adaptability, but we also assert that this leads to poor uncertainty estimates when predicting multiple step trajectory estimates. To address this issue, we propose a simple sampling method that can be implemented on top of pre-existing models.We evaluate our sampling technique on a number of environments, including a realistic nuclear fusion task, and find that, not only do smooth transition function samples produce more calibrated uncertainties, but they also lead to better downstream performance for an adaptive policy.

Offline Reinforcement Learning↗

Airburst & Blast Damage Modeling Sensitivities for Asteroid Impact Risk Assessment

Blast overpressure from a high-energy airburst or surface impact is the primary source of damage from potentially hazardous asteroid strikes. There are many sources of uncertainty in evaluating these potential damage risks, both in the approaches used to model the entry, breakup, and airburst behaviors of diverse asteroid properties, and in the blast modeling approaches used to estimate the ground damage from these very large-scale, high-energy events. In this study, we use NASA’s Probabilistic Asteroid Impact Risk (PAIR) model to investigate trends and sensitivities in asteroid airburst altitudes and the resulting blast damage estimates across a range of asteroid sizes. In particular, we show how uncertainties in asteroid breakup behavior and effective airburst altitudes combine with height-of-burst (HOB) blast damage models to produce key sensitivities and trends in the amount of damage expected from different asteroid sizes and airburst altitudes. We show airburst altitude ranges and probabilities stemming from asteroid entry and breakup modeling uncertainties, compare differences between traditional nuclear-based HOB blast models and simulation-based HOB models for larger asteroid energies, and show how the resulting interplay between likely burst altitudes and optimal burst heights affects blast damage trends across different asteroid sizes. Finally, we combine the relative likelihoods of asteroid sizes, airburst altitudes, and resulting blast damage severity to evaluate what airburst regimes pose the highest overall level of risk (when considering both the relative likelihood and scale of potential damage) for a mid-sized asteroid threat scenario. Results show what asteroid size regimes are most sensitive to airburst and blast modeling uncertainties, provide insight into nonintuitive trends in the size and severity of blast damage expected from different airburst events, and highlight where additional blast modeling studies or refinements may help improve future impact risk estimates

ATAP↗

Aircraft Conflict Analysis and Real-Time Conflict Probing Using Probabilistic Trajectory Modeling

Methods for maintaining separation between aircraft in the current airspace system have been built from a foundation of structured routes and evolved procedures. However, as the airspace becomes more congested and the chance of failures or operational error become more problematic, automated conflict alerting systems have been proposed to help provide decision support and to serve as traffic monitoring aids. The problem of conflict detection and resolution has been tackled from a number of different ways, but in this thesis, it is recast as a problem of prediction in the presence of uncertainties. Much of the focus is concentrated on the errors and uncertainties from the working trajectory model used to estimate future aircraft positions. The more accurate the prediction, the more likely an ideal (no false alarms, no missed detections) alerting system can be designed. Additional insights into the problem were brought forth by a review of current operational and developmental approaches found in the literature. An iterative, trial and error approach to threshold design was identified. When examined from a probabilistic perspective, the threshold parameters were found to be a surrogate to probabilistic performance measures. To overcome the limitations in the current iterative design method, a new direct approach is presented where the performance measures are directly computed and used to perform the alerting decisions. The methodology is shown to handle complex encounter situations (3-D, multi-aircraft, multi-intent, with uncertainties) with relative ease. Utilizing a Monte Carlo approach, a method was devised to perform the probabilistic computations in near realtime. Not only does this greatly increase the method's potential as an analytical tool, but it also opens up the possibility for use as a real-time conflict alerting probe. A prototype alerting logic was developed and has been utilized in several NASA Ames Research Center experimental studies.

Yang, Lee C.↗

Bayesian stability and force modeling for uncertain machining processes

Accurately simulating machining operations requires knowledge of the cutting force model and system frequency response. However, this data is collected using specialized instruments in an ex-situ manner. Bayesian statistical methods instead learn the system parameters using cutting test data, but to date, these approaches have only considered milling stability. This paper presents a physics-based Bayesian framework which incorporates both spindle power and milling stability. Initial probabilistic descriptions of the system parameters are propagated through a set of physics functions to form probabilistic predictions about the milling process. The system parameters are then updated using automatically selected cutting tests to reduce parameter uncertainty and identify more productive cutting conditions, where spindle power measurements are used to learn the cutting force model. The framework is demonstrated through both numerical and experimental case studies. Results show that the approach accurately identifies both the system natural frequency and cutting force model.

42 ENGINEERING↗