Stochastic Sampling Research Articles

Joint Failure Probability of Dams Based on Probabilistic Flood Hazard Analysis

Probabilistic risk methods are becoming increasingly accepted as a means of carrying out risk-informed decision making regarding the design and operation policy of structures such as dams. Probabilistic risk calculations require the quantification of epistemic and aleatory uncertainties not investigated through deterministic methodologies. In this hydrological study, a stochastic sampling methodology is employed to investigate the joint failure probability of three dams in adjacent similarly sized watersheds within the same hydrologic unit code (HUC) 6 basin. A probabilistic flood hazard analysis (PFHA) framework is used to simulate the hydrologic loading of a range of extreme precipitation events across the combined watershed area of the three studied dams. Precipitation events are characterized by three distinct storm types influential in the Tennessee Valley region with implications for weather variability and climate change. The stochastic framework allows for the simulation of hundreds of thousands of spillway outflows that are used to produce empirical bivariate exceedance probabilities for spillway discharge pairs at selected dams. System response curves that indicate the probability of failure given spillway discharge are referenced for each dam and applied to generate empirical bivariate failure probability (joint failure probability) estimates. The stochastic simulation results indicate the range of spillway discharges for each pair of dams that pose the greatest risk of joint failure. The estimate of joint failure considering the dependence of spillway discharges between dams is shown to be three to four orders of magnitude more likely (7.42 × 102 to 5.68 × 103) than estimates that assume coincident failures are the result of independent hydrologic events.

Evaluation of breeding cost in the French maritime pine breeding program and perspectives for alternative strategies using molecular markers

The economic efficiency of conventional breeding strategies for forest trees based on biparental crosses is compared with that of alternative strategies based on pedigree reconstruction using molecular markers. Analyses of economic efficiency is based on comparisons of breeding scenarios corresponding to the same total investment. The first step is the description and cost evaluation of each basic operation, from crossing to genetic selection and clonal archive establishment. Breeding scenarios are then compared by stochastic sampling with a parametric genetic model (POPSIM), the comparison criteria in this case being genetic gain in the seed orchard for a given level of genetic diversity. Additionally, the economic gain resulting from the use of improved material is estimated for different levels of breeding investment. Our analysis shows that genotyping costs account for a much smaller proportion of total investment than phenotyping costs. We also show that, in comparisons of breeding scenarios corresponding to the same total investment, the three main breeding strategies (biparental crosses, polymix crosses, and open pollination) achieve similar genetic gains provided that sufficiently large numbers of parents are considered. These results open up promising perspectives for the wider integration of molecular markers into forest tree breeding strategies.

Bisphenols in Aquatic Products from South China: Implications for Human Exposure.

In this study, 245 representative samples of aquatic products were selected from local markets in Shenzhen by stochastic sampling. The samples comprised eight species and fell into three aquatic product categories: fish, crustaceans, and bivalves. A total of eight BPs were determined by liquid chromatography coupled with mass spectrometry, namely, bisphenol A (BPA), bisphenol AF (BPAF), bisphenol AP (BPAP), bisphenol B (BPB), bisphenol S (BPS), bisphenol P (BPP), bisphenol Z (BPZ), and bisphenol F (BPF). All BPs were detected in aquatic products, except for BPAF, indicating pervasive contamination by BPs in aquatic products. BPS demonstrated the highest detection rate both before and after enzymatic hydrolysis, whereas BPAP exhibited the lowest detection rate before enzymatic hydrolysis and BPB displayed the lowest detection rate after enzymatic hydrolysis. The concentration difference before and after enzymatic hydrolysis proved to be statistically significant. Moreover, 49-96% of BPs in aquatic products were found in the combined state, underscoring the essentiality of conducting detections on aquatic product samples following enzymatic hydrolysis. While the health risks associated with ingesting BPs residues through aquatic product consumption were found to be minimal for residents at risk of exposure, the results suggest the necessity for more stringent regulations governing the consumption of aquatic products.

Correlation function distributions for O(N) lattice field theories in the disordered phase

Numerical computations in strongly interacting quantum field theories are often performed using Monte Carlo sampling methods. A key task in these calculations is to estimate the value of a given physical quantity from the distribution of stochastic samples that are generated using the Monte Carlo method. Typically, the sample mean and sample variance are used to define the expectation values and uncertainties of computed quantities. However, the Monte Carlo sample distribution contains more information than these basic properties, and it is useful to investigate it more generally. In this work, the exact form of the probability distributions of two-point correlation functions at zero momentum in O(N) lattice field theories in the disordered phase and in infinite volume are determined. These distributions allow for a robust investigation of the efficacy of the Monte Carlo sampling procedure and are shown also to allow for improved estimators of the target physical quantity to be constructed. The theoretical expectations are shown to agree with numerical calculations in the O(2) model. Published by the American Physical Society 2024

Derivative-free search approaches for optimization of well inflow control valves and controls

Decisions regarding problem conceptualization, search approach, and how best to parametrize optimization methods for practical application are key to successful implementation of optimization approaches within georesources field development projects. This work provides decision support regarding the application of derivative-free search approaches for concurrent optimization of inflow control valves (ICVs) and well controls. A set of state-of-the-art approaches possessing different search features is implemented over two reference cases, and their performance, resource requirements, and specific method configurations are compared across multiple problem formulations for completion design. In this study, problem formulations to optimize completion design comprise fixed ICVs and piecewise-constant well controls. The design is optimized by several derivative-free methodologies relying on parallel pattern-search (tAPPS), population-based stochastic sampling (tPSO) and trust-region interpolation-based models (tDFTR). These methodologies are tested on a heterogeneous two-dimensional case and on a realistic case based on a section of the Olympus benchmark model. Three problem formulations are applied in both cases, i.e., one formulation optimizes ICV settings only, while two joint configurations also treat producer and injector controls as variables. Various method parametrizations across the range of cases and problem formulations exploit the different search features to improve convergence, achieve final objectives and infer response surface features. The scope of this particular study treats only deterministic problem formulations. Results outline performance trade-offs between parallelizable algorithms (tAPPS, tPSO) with high total runtime search efficiency and the local-search trust-region approach (tDFTR) providing effective objective gains for a low number of cost function evaluations. tAPPS demonstrates robust performance across different problem formulations that can support exploration efforts, e.g., during a pre-drill design phase while multiple independent tDFTR runs can provide local tuning capability around established solutions in a time-constrained post-drill setting. Additional remarks regarding joint completion design optimization, comparison metrics, and relative algorithm performance given the varying problem formulations are also made.

Similarity Coefficient Generation Using Adjoint-Based Sensitivity and Uncertainty Method and Stochastic Sampling Method

In this study, a similarity coefficient generation code system was established using the Monte Carlo Code for Advanced Reactor Design (McCARD) transport code and the MIG multi-correlated input sampling code. We considered the adjoint-based sensitivity and uncertainty (S/U) and stochastic sampling (S.S.) approaches to the generation of the ck similarity coefficient. To examine the code system, the ck similarity coefficients of 23 relevant critical experiments and the System-Integrated Modular Advanced Reactor (SMART) small modular reactor (SMR) target system were generated using ENDF/B-VII.1 covariance data with the Los Alamos National Laboratory (LANL) 30-group energy group structure. Our results show that the similarity coefficients between the 16 LEU thermal-spectrum-based critical experiments and SMART are more than 0.90, which is the recommended criterion of the U.S. Nuclear Regulatory Commission (NRC). These results are very helpful for licensees and can be used to justify the determination of critical experiment benchmarks for computational bias estimations of the SMART target system. To examine the discrepancy in the similarity coefficient, ck, due to the covariance data, similarity analyses for a 24 × 24 benchmark matrix were performed using ENDF-VIII.0, JENDL-5.0, and JEFF-3.3 covariance data. The results show that the selection of the covariance data used for ck generation significantly impacts the similarity coefficient. Moreover, it was observed that the current results for the SCALE 6.1 covariance data show a consistent trend with the results reported in earlier studies.

Differentiable stochastic halo occupation distribution

ABSTRACT In this work, we demonstrate how differentiable stochastic sampling techniques developed in the context of deep reinforcement learning can be used to perform efficient parameter inference over stochastic, simulation-based, forward models. As a particular example, we focus on the problem of estimating parameters of halo occupation distribution (HOD) models that are used to connect galaxies with their dark matter haloes. Using a combination of continuous relaxation and gradient re-parametrization techniques, we can obtain well-defined gradients with respect to HOD parameters through discrete galaxy catalogue realizations. Having access to these gradients allows us to leverage efficient sampling schemes, such as Hamiltonian Monte Carlo, and greatly speed up parameter inference. We demonstrate our technique on a mock galaxy catalogue generated from the Bolshoi simulation using a standard HOD model and find near-identical posteriors as standard Markov chain Monte Carlo techniques with an increase of ∼8× in convergence efficiency. Our differentiable HOD model also has broad applications in full forward model approaches to cosmic structure and cosmological analysis.

Modeling a domain wall network in BiFeO3 with stochastic geometry and entropy-based similarity measure

A compact and tractable two-dimensional model to generate the topological network structure of domain walls in BiFeO3 thin films is presented in this study. Our method combines the stochastic geometry parametric model of the centroidal Voronoi tessellation optimized using the von Neumann entropy, a novel information-theoretic tool for networks. The former permits the generation of image-based stochastic artificial samples of domain wall networks, from which the network structure is subsequently extracted and converted to the graph-based representation. The von Neumann entropy, which reflects information diffusion across multiple spatiotemporal scales in heterogeneous networks, plays a central role in defining a fitness function. It allows the use of the network as a whole rather than using a subset of network descriptors to search for optimal model parameters. The optimization of the parameters is carried out by a genetic algorithm through the maximization of the fitness function and results in the desired graph-based network connectivity structure. Ground truth empirical networks are defined, and a dataset of network connectivity structures of domain walls in BiFeO3 thin films is undertaken through manual annotation. Both a versatile tool for manual network annotation of noisy images and a new automatic network extraction method for high-quality images are developed.

Reliability analysis and inverse optimization method for floating wind turbines driven by dual meta-models combining transient-steady responses

This study introduces an innovative framework aimed at enhancing the reliability, lifespan, and cost-effectiveness of floating wind turbines. By seamlessly integrating transient and steady-state response surface methods, this approach reduces the dimensionality of high-cost, high-fidelity simulation data for floating wind turbines. It effectively utilizes time-domain stochastic response history samples, addressing two critical aspects in reliability analysis, including statistical properties related to maximum loads relevant for static strength design and the distribution characteristics of vibration amplitudes pertinent to fatigue damage design. The processed data is used to construct a forward 1st metamodel, which is integrated into a multi-objective optimization algorithm. This algorithm determines optimal hyperparameters based on stochastic environmental conditions. Subsequently, an inverse 2nd metamodel is established, working in conjunction with the 1st metamodel, forming a dual structure for reliability analysis. Extensive Monte Carlo simulations and probability density analyses demonstrate the effectiveness of the adaptive flexible controller frequency strategy, obtained using the proposed framework, in reducing vibration-induced blade-tip-tower collision risks and long-term vibration damage, particularly at low to medium wind speeds. This significantly improves turbine stability and safety, enhancing overall performance. The proposed methodology provides valuable insights into the design, manufacturing, and operation of floating wind turbines.

Quantum Vibronic Effects on the Excitation Energies of the Nitrogen-Vacancy Center in Diamond.

We investigated the impact of quantum vibronic coupling on the electronic properties of solid-state spin defects using stochastic methods and first-principles molecular dynamics with a quantum thermostat. Focusing on the negatively charged nitrogen-vacancy center in diamond as an exemplary case, we found a significant dynamic Jahn-Teller splitting of the doubly degenerate single-particle levels within the diamond's band gap, even at 0 K, with a magnitude exceeding 180 meV. This pronounced splitting leads to substantial renormalizations of these levels and, subsequently, of the vertical excitation energies of the doubly degenerate singlet and triplet excited states. Our findings underscore the pressing need to incorporate quantum vibronic effects into first-principles calculations, particularly when comparing computed vertical excitation energies with experimental data. Our study also reveals the efficiency of stochastic thermal line sampling for studying phonon renormalizations of solid-state spin defects.

Efficient Quasiparticle Determination beyond the Diagonal Approximation via Random Compression.

Calculations of excited states in the Green's function formalism often invokes the diagonal approximation, in which the quasiparticle states are taken from a mean-field calculation. In this paper, we extend the stochastic approaches applied in the many-body perturbation theory and overcome this limitation for large systems in which we are interested in a small subset of states. We separate the problem into a core subspace whose coupling to the remainder of the system environment is stochastically sampled. This method is exemplified on computing hole injection energies into CO2 on an extended gold surface with nearly 3000 electrons. We find that in the extended system the size of the problem can be compressed up to 95% using stochastic sampling. This result provides a way forward for self-consistent stochastic methods and determination of Dyson orbitals in large systems.

Attack-tolerant control for Markovian jump systems with stochastic sampling: A sliding mode scheme

This work discusses the sampled-data sliding mode control problem for Markovian jump systems in the presence of Denial-of-Service (DoS) attacks, where the state signals are sampled stochastically and transmitted via vulnerable communication networks. The successful transmitted sequence with double randomness is established, and the probability distribution on both the attacked signals and stochastic delays are given. With the aid of the coordinate transformation, a linear sliding surface is constructed and the mode-dependent sliding mode controller is designed by means of only successfully transmitted state signals. Moreover, the resultant closed-loop systems composed of partial state and sliding mode variable are described as a continuous time-delay system with double randomness depending on the probability distribution characteristics of both the sampling periods and DoS attacks. Both the mean-square exponential ultimate boundedness of the closed-loop system and the reachability of the sliding surface are analyzed and the corresponding sufficient conditions are derived. Meanwhile, an optimization problem with genetic algorithm is formulated for achieving fast convergence of the state trajectory, small ultimate bound of the system state and small sliding bound. Finally, the simulation results via the numerical example are provided to illustrate the proposed sampled-data sliding mode control scheme.

Estimation of informal park-and-ride

Curbside parking in a residential area may be induced by the presence of a public transport stop. Travelers may park their car near the stop and continue their trip to the city center by other means. This is called informal park-and-ride. The magnitude of the phenomenon is estimated by simulation. Parking demand is derived from the history of parking time (tickets) sold at vending machines. For each ticket, an activity location is determined by stochastic sampling from a buildings (facilities) database based on the position of the vending machine. The activity timing is derived from the parking duration specified by the ticket. Suitable parking spots for an activity are determined for the cases (i) drive-park-walk and (ii) drive-park-publicTransport-walk respectively. The generalized cost (based on money and travel duration) is determined for both options. The decision is sampled by means of a behavioural model. Several scenarios are considered and the results allow to evaluate the complaints issued by residents of a study area because microsimulation enables the generation of probability densities for parking occupation in such area in each scenario. This paper reports how the method is applied to a study area in Amsterdam.

Theoretical and kinetic study of the thermal decomposition mechanism of long chain aldehydes

The mechanism of decomposition of the butanal and pentanal long chain aldehydes was investigated using the ab initio transition state theory-based master equation approach. The rate constants of the homolytic bond scission reactions of butanal and pentanol leading to the formation of CHO+C3H7, CH2CHO+C2H5, C2H4CHO+CH3, C3H7CO+H, C2H5ĊHCHO+H and CH2CHO+C3H7, C2H4CHO+C2H5, C3H6CHO+CH3, C4H9CO+H, C3H7ĊHCHO+H, respectively, as well as of the reverse barrierless recombination channels, were determined using Variable Reaction Coordinate Transition State Theory. The potential energy surfaces were determined at the multireference CASPT2/aug-cc-pVTZ level on ωB97X-D/jun-cc-pVTZ structures, while stochastic samplings were performed at the CASPT2 level using a (4e,4o) active space. Rate laws for the alkyl+R-CHO, H+R-ĊHCHO, and H+R-ĊO classes of reactions were then determined. Rate constants of H-abstraction reactions and of the three body butanal →CO+H2+C3H6 channel were determined using ωB97X-D/jun-cc-pVTZ structures and Hessians and CCSD(T) energies, extrapolated to the complete basis set. It was found that the calculated homolytic bond scission reactions are faster by a factor of 2–3 with respect to literature previous estimates. The calculated reaction rates were inserted in the CRECK kinetic scheme and used to simulate literature speciation data of butanal and pentanal pyrolysis in shock tubes and ignition delay times, finding that their inclusion into the kinetic scheme enhances the predictive capabilities of the mechanism. The aldehyde decomposition mechanism and the rate constants determined in this study are suitable to be used to interpret and predict the reactivity of aldehydes in a wide range of temperatures and pressures.

Stochastic sampled-data multi-objective control of active suspension systems for in-wheel motor driven electric vehicles

This paper addresses the sampled-data multi-objective active suspension control problem for an in-wheel motor driven electric vehicle subject to stochastic sampling periods and asynchronous premise variables. The focus is placed on the scenario that the dynamical state of the half-vehicle active suspension system is transmitted over an in-vehicle controller area network that only permits the transmission of sampled data packets. For this purpose, a stochastic sampling mechanism is developed such that the sampling periods can randomly switch among different values with certain mathematical probabilities. Then, an asynchronous fuzzy sampled-data controller, featuring distinct premise variables from the active suspension system, is constructed to eliminate the stringent requirement that the sampled-data controller has to share the same grades of membership. Furthermore, novel criteria for both stability analysis and controller design are derived in order to guarantee that the resultant closed-loop active suspension system is stochastically stable with simultaneous H2 and H∞ performance requirements. Finally, the effectiveness of the proposed stochastic sampled-data multi-objective control method is verified via several numerical cases studies in both time domain and frequency domain under various road disturbance profiles.

Stability and guaranteed cost control for linear impulsive systems with random impulses: Application to stochastic event‐triggered control

SummaryThis paper proposes a systematic framework for stability and guaranteed cost control of linear impulsive systems subject to random time‐ and event‐triggering impulses. Moment stability criteria and design methods of time‐ and event‐triggered controllers with guaranteed quadratic performance for the impulsive system are established. It shows that the proposed event‐triggered controller in the sense that it guarantees at least the same quadratic performance function bound as the designed time‐triggered guaranteed cost controller, however, with a larger, or at most equal, average inter‐transmission time. Based on the proposed framework of random‐impulses systems, a stochastic dynamic event‐triggered control strategy is proposed to solve sampled‐data control systems in the presents of sporadic measurements or stochastic sampling. Numerical simulations illustrate the effectiveness of the proposed theoretical results.

Online Learning for Dual-Index Policies in Dual-Sourcing Systems

Problem definition: We consider a periodic-review dual-sourcing inventory system with a regular source (lower unit cost but longer lead time) and an expedited source (shorter lead time but higher unit cost) under carried-over supply and backlogged demand. Unlike existing literature, we assume that the firm does not have access to the demand distribution a priori and relies solely on past demand realizations. Even with complete information on the demand distribution, it is well known in the literature that the optimal inventory replenishment policy is complex and state dependent. Therefore, we focus our attention on a class of popular, easy-to-implement, and near-optimal heuristic policies called the dual-index policy. Methodology/results: The performance measure is the regret, defined as the cost difference of any feasible learning algorithm against the full-information optimal dual-index policy. We develop a nonparametric online learning algorithm that admits a regret upper bound of [Formula: see text], which matches the regret lower bound for any feasible learning algorithms up to a logarithmic factor. Our algorithm integrates stochastic bandits and sample average approximation techniques in an innovative way. As part of our regret analysis, we explicitly prove that the underlying Markov chain is ergodic and converges to its steady state exponentially fast via coupling arguments, which could be of independent interest. Managerial implications: Our work provides practitioners with an easy-to-implement, robust, and provably good online decision support system for managing a dual-sourcing inventory system. Funding: This work was supported by the Amazon Research Award. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0323 .

Stochastic simulation of earthquake ground motions based on improved finite-fault model

In the seismic reliability analysis of engineering structures, it is often necessary to adopt stochastic ground motions as inputs. However, the current methods used to generate stochastic samples, such as the spectral representation method, the spectral transfer method, the dynamic source method, the physical source method, and the comprehensive method, etc., are not very convincing since they do not contain the complete information of seismic occurrence and propagation. In this study, an improved finite-fault model for stochastic simulation of ground motions is proposed. Compared to existing stochastic finite-fault model, the improved model considers the propagation law of phase spectrum, local site effect, and the impact of wave velocity on the arrival time of seismic waves. Besides, identification and statistics of model parameters are carried out based on ground motion records. Reasonable samples of stochastic ground motions are then obtained. In addition, parameter sensitivity analysis is conducted to determine critical random variables, which reduces the complexity of stochastic simulation. Simulation results are compared with recorded accelerograms from the 1999 Chi-Chi earthquake. It is shown that the improved stochastic finite-fault model is reliable, and the acceleration response spectra of simulated samples are consistent with those of station records collected at various site classes and the design spectra.

Distributed consensus tracking of nonlinear MASs under stochastic switching topologies via aperiodically intermittent control

SummaryIn this article, we investigate the mean‐square consensus tracking problem of nonlinear MASs subjected to external disturbances under stochastic switching topologies. An aperiodically intermittent control strategy is proposed to guarantee consensus tracking in the mean‐square sense, which depends only on the local state information of the neighbors and the leader. The stochastic switching signal of the interaction topologies is modeled as a continuous‐time Markov process, and the aperiodically intermittent control method is driven by a discrete‐time series of stochastic samples, that are independent of each other. Moreover, several sufficient conditions are established to ensure the feasibility of the control strategy. The proofs are given by employing matrix inequality theory and Lyapunov stability theory. Finally, numerical simulations are provided to verify the feasibility of the proposed theoretical results.

Annotating otoliths with a deep generative model

Abstract Otoliths are a central information source for fish ecology and stock management, conveying important data about age and other life history for individual fish. Traditionally, interpretation of otoliths has required skilled expert readers, but recently deep learning classification and regression models have been trained to extract fish age from images of otoliths from a variety of species. Despite high accuracy in many cases, the adoption of such models in fisheries management has been slow. One reason may be that the underlying mechanisms the model uses to derive its results from the data are opaque, and this lack of legibility makes it challenging to build sufficient trust in the results. Here, we implement a deep learning model that instead of age predicts the location of annotation marks for each of the annuli. This allows an expert to evaluate the model’s performance in detail. The quality of the annotations was judged by a panel of four expert otolith readers in a double-blinded randomized survey. Using a scale from 1 to 5, the generated marks received an average quality score of 4.22, whereas expert annotations received an average score of 4.33. By counting the marks to determine fish age, we obtained an agreement between expert and model annotations of 64% on our test set, which running the model stochastically increased to 69%. Stochastic sampling yields further benefits, including an explicit measure of the model’s uncertainty, the post hoc likelihood of the different age classes for each otolith, and a set of alternative annotation sequences that highlight the structure of the annuli.