Conjunction Time and Collision Probability Calculation Based on Bayesian Optimization

Collision Probability with Gaussian Mixture Orbit Uncertainty

A range of different techniques for determining the unknown coefficients of Polynomial Chaos Expansion (PCE) models for antenna structures, are presented. PCE models offer significant advantages over Monte Carlo analysis, for the modeling of the statistical behavior of structures, but the different approaches for calculating the PCE model coefficients exhibits a large variation in the number of required basis points, that number also being problem specific. A range of model coefficient calculation techniques are evaluated in this article, for the problem of modeling cross-polarization of an inset-fed patch antenna. This structure is one of the most widely used antenna structures, often produced in high-volume, and serves as an excellent example to emphasize the variation in performance between the different techniques, and problem-specific nature of finding an optimal solution. It is shown that the most optimal method requires fewer than 10% analysis points of the least optimal, and a factor of 100 fewer points than Monte-Carlo analysis.

Global sensitivity analysis: A Bayesian learning based polynomial chaos approach

Development of clustered polynomial chaos expansion model for stochastic hydrological prediction

Analytical model for collision probability assessments with large satellite constellations

The method of collision probability is usually used to realize the work of collision assessment and warning of space objects, thus improving accuracy of collision assessment and warning is very important. The collision probability criterion is collision probability threshold. By investigating and analyzing the related bibliography from both domestic and international researchers, a comprehensive description on determination of collision probability threshold of space objects is presented. The determination of covariance matrix, the calculation of collision probability and the flux calculation of debris are introduced in detail. Taking International Space Station (ISS) for instance, of which, the debris flux was calculated and the incidence from space environment was analyzed. The conclusion that collision probability threshold of ISS may be overrated is reached by comparing with previous results.

In this paper, surrogate models are built iteratively using polynomial chaos expansion (PCE) and detailed numerical simulations of a carbon sequestration system. Output variables from a numerical simulator are approximated as polynomial functions of uncertain parameters. Once generated, PCE representations can be used in place of the numerical simulator and often decrease simulation times by several orders of magnitude. However, PCE models are expensive to derive unless the number of terms in the expansion is moderate, which requires a relatively small number of uncertain variables and a low degree of expansion. To cope with this limitation, instead of using a classical full expansion at each step of an iterative PCE construction method, we introduce a mixed-integer programming (MIP) formulation to identify the best subset of basis terms in the expansion. This approach makes it possible to keep the number of terms small in the expansion. Monte Carlo (MC) simulation is then performed by substituting the va...

A new approximation is proposed for calculating the first flight collision probabilities in cluster-type fuel lattices, based on the subcell model. In this method the unit cluster is divided into subregions of fuel pins (with or without cladding) arranged in rings, associated coolant, and homogeneous annular regions surrounding the fuel region. The fuel pins and associated coolant are treated separately, and each is distinguished ringwise as a different subregion. The collision probability is then calculated for a neutron proceeding from one subregion to another. The method treats rigorously the fuel annulus where a neutron starts with consideration given to the non-uniform structure of the annulus. The other fuel annuli, however, are treated approximately as if each annulus were homogeneous. The values of the homogenized cross sections of the annuli are determined in such manner that the number of outgoing neutrons from the homogenized annuli equals that from the actual non-uniform fuel annuli. The colli...

We propose a set of equations for preliminary risk‐targeted seismic design of structures base‐isolated using single friction pendulum (SFP) bearings. The equations offer statistical estimates of the maximum displacement of the superstructure relative to the base and the maximum displacement of the isolated base response quantities of interest (RQIs), given ground motion intensity measures and the essential dynamic properties of the SFP bearing base‐isolated structure. The set of proposed equations enables preliminary seismic design of SFP base‐isolated structures using the mean annual frequency of exceeding displacement‐defined limit states related to the two RQIs. To develop the design equations, we define and use a two‐degree‐of‐freedom (2DOF) surrogate model that features a few essential dynamic parameters of the SFP bearing base‐isolated structure. We first verify that the 2DOF surrogate model is accurate enough to represent the base and superstructure displacements compared to the complete multiple‐degree‐of‐freedom model of the prototype SFP bearing base‐isolated structure. Next, we perform more than 5 million non‐linear dynamical analyses of 4900 distinct 2DOF surrogates subjected to 210 different recorded ground motions scaled five times. We fit the response data of each 2DOF surrogate to a linear model and use two different modeling techniques to derive the design equations. One model is based on Polynomial Chaos Expansion (PCE), and the other model is based on Linear Regression (LR). The PCE model is more accurate than the LR model, with the trade‐off regarding its simplicity. Nevertheless, both the PCE and the LR models are accurate enough to estimate the design quantities of interest of the SFP bearing base‐isolated structure for preliminary design purposes. Lastly, we exemplify the use of the proposed design equations and we show that the estimate of base displacement is conservative in the cases when the superstructure of the SPF bearing base‐isolated structure yields.

Data-driven design shows the promise of accelerating materials discovery but is challenging due to the prohibitive cost of searching the vast design space of chemistry, structure, and synthesis methods. Bayesian Optimization (BO) employs uncertainty-aware machine learning models to select promising designs to evaluate, hence reducing the cost. However, BO with mixed numerical and categorical variables, which is of particular interest in materials design, has not been well studied. In this work, we survey frequentist and Bayesian approaches to uncertainty quantification of machine learning with mixed variables. We then conduct a systematic comparative study of their performances in BO using a popular representative model from each group, the random forest-based Lolo model (frequentist) and the latent variable Gaussian process model (Bayesian). We examine the efficacy of the two models in the optimization of mathematical functions, as well as properties of structural and functional materials, where we observe performance differences as related to problem dimensionality and complexity. By investigating the machine learning models' predictive and uncertainty estimation capabilities, we provide interpretations of the observed performance differences. Our results provide practical guidance on choosing between frequentist and Bayesian uncertainty-aware machine learning models for mixed-variable BO in materials design.

Estimation of internal states in a Li-ion battery using BiLSTM with Bayesian hyperparameter optimization

Bayesian optimization has proven effective for optimizing expensive-to-evaluate functions in Chemical Engineering. However, valuable physical insights from domain experts are often overlooked. This article introduces a collaborative Bayesian optimization approach that re-integrates human input into the data-driven decision-making process. By combining high-throughput Bayesian optimization with discrete decision theory, experts can influence the selection of experiments via a discrete choice. We propose a multi-objective approach togenerate a set of high-utility and distinct solutions, from which the expert selects the desired solution for evaluation at each iteration. Our methodology maintains the advantages of Bayesian optimization while incorporating expert knowledge and improving accountability. The approach is demonstrated across various case studies, including bioprocess optimization and reactor geometry design, demonstrating that even with an uninformed practitioner, the algorithm recovers the regret of standard Bayesian optimization. By including continuous expert opinion, the proposed method enables faster convergence and improved accountability for Bayesian optimization in engineering systems.

This paper examines the legal basis and framework for the United Nations registration process for space objects. UN registration processes are compared against and contrasted with national and regional registration processes to highlight potential adjustments in light of the need for a space traffic management system. While there are shortfalls in compliance and monitoring of States’ responsibility to adhere to UN registration requirements, the growing importance of space traffic management is providing a catalyst for reform and recommitment to the ideals upon which the 1975 UN Registration Convention was based. Since the data provided to national registries and the UN register is not detailed enough and is not sufficient for creating a space traffic management regime, it is recommended that (1) the recommendations concerning the registration of space objects belonging to a large constellation that were agreed by the UNCOPUOS Working Group on the Status and Application of the Five United Nations Treaties on Outer Space in 2023 are implemented to ensure uniformity of registration practice regarding large constellations; (2) States incentivize good registration practices by other States, for instance by requiring that satellites of commercial actors are registered by the relevant launching State as a condition for market access; (3) the importance of furnishing additional information on the subsequent activity and status of objects, as required by the Registration Convention, UN General Assembly resolutions 1721 (XVI) B and 62/101 and Guideline A.5 para 2 of the UNCOPUOS Guidelines on the Long-Term Sustainability of Space Activities, be underlined.

The CompModels package for R provides a suite of computer model test functions that can be used for computer model prediction/emulation, uncertainty quantification, and calibration.Moreover, the CompModels package is especially well suited for the sequential optimization of computer models.The package is a mix of real-world physics problems, known mathematical functions, and black-box functions that have been converted into computer models with the goal of Bayesian (i.e., sequential) optimization in mind.Likewise, the package contains computer models that represent either the constrained or unconstrained optimization case, each with varying levels of difficulty.In this paper, we illustrate the use of the package with both real-world examples and black-box functions by solving constrained optimization problems via Bayesian optimization.Ultimately, the package is shown to provide users with a source of computer model test functions that are reproducible, shareable, and that can be used for benchmarking of novel optimization methods.

Space collision probability computation based on on-board optical cues