Stochastic Calculations Research Articles

A FULL REFERENCE APOLLO3® DETERMINISTIC SCHEME FOR THE JHR MATERIAL TESTING REACTOR

JHR is a new material testing reactor under construction at CEA Cadarache. Its high flux core contains 37 fuel assemblies loaded along concentric rings into alveolus of an aluminum matrix. For the operation of the reactor, twenty-seven of these fuel assemblies hovnst hafnium rods in their center while the other ones but also the beryllium radial reflector can accommodate experimental devices. In order to accurately predict its operating core characteristics but also its irradiation performance, a recently developed scheme based on the APOLLO3® platform is being developed which uses the sub-group method for spatial self-shielding, the 2D method of characteristics and the 3D unstructured conform MINARET Sn transport solver. A 2D model of JHR has been built and optimized for calculating, at the lattice step, the self-shielded and condensed cross sections thanks to the sub-group method and the method of characteristics. Results are benchmarked against a TRIPOLI-4® stochastic reference calculation. A more refined spatial mesh gives better results on fission rates and reactivity compared to the ones of the former APOLLO2 scheme. The classical 2-step calculations use the hypothesis of infinite lattice configuration, which is reasonable for the assemblies close to the center but not for peripheral ones. Hence, a new approach is being set up taking into account the surrounding of each assembly. The newly 3-step scheme uses the Sn solver MINARET and gives better results than the traditional 2-step scheme. This approach will be applied to a 3D modelling of the heterogeneous JHR core configurations incorporating experimental devices and enabling burn up calculations.

The Mini Labyrinth – a Simple Benchmark for Radiation Protection and Shielding Analysis

The Mini Labyrinth experiment is a simple neutron and gamma shielding experiment developed at STU, inspired by the ALARM-CF-AIR-LAB-001 ICSBEP benchmark experiment. The STU Mini Labyrinth is approximately ten times smaller and consists of NEUTRONSTOP shielding blocks. This paper describes the second version of the Mini Labyrinth experiment and presents the results of the neutron and gamma fields simulation and measurement. The PuBe neutron source with the emission rate of 1.0E7 n.s-1 was utilized in the experiment. The measurement of gamma ambient dose equivalent H*(10) and neutron count rates is performed by the Thermo Scientific RadEye portable survey meter. The simulation part was carried out using the state-of-the-art MCNP6 and SCALE6 MONACO stochastic calculation tools taking into account the detailed geometry of the labyrinth and a combined neutron and gamma source of particles. The comparisons were performed between codes and an experiment, based on the dose rate in the unique detection positions and using a 2D map of neutron and photon fluxes. The propagation of cross-section uncertainties was investigated through the shielding analysis. Partial agreement between codes and measurement was achieved, however serious discrepancies near the PuBe source were identified.

Coherent transfer of topological interface states.

We demonstrate the controlled coherent transfer of topological interface states in a one-dimensional non-Hermitian chain of interacting Bose-Einstein condensates. The topological protection stems from a spatially patterned pump in an open-dissipative system. As a test bed setup of the proposed phenomenon, we consider a chain of coupled micropillars with embedded quantum wells, possessing exciton-polariton resonances. The transfer of an interface state is driven by spatially localised, adiabatic pump modulation in the vicinity of the interface state. The stochastic calculations prove the coherent nature of the interface state transfer. For appropriate system parameters the coherence degree is preserved after multiple transitions, paving the way towards long-range transfer of a coherent quantum state.

The role of the diffusion process in bimolecular reactions with neighborhood

AbstractWe performed stochastic and deterministic calculations to study simple bimolecular chemical kinetics with a neighborhood, necessary for solid‐state and viscous medium reactions. Regarding the standard deterministic method using ordinary differential equations (ODEs) to describe a bimolecular reaction with the neighborhood, we established a comparison that indicates, in this method, an implicit diffusion process. For example, the reaction is processed in a homogeneous medium, differently from the stochastic method without diffusion. The two methods coincide at the thermodynamic limit (containing little relative fluctuation) when added with the explicit diffusion process on the stochastic model. The irreversible reaction without diffusion was emulated using the ODEs of a reversible reaction, and the inherent residual concentration of the reactions with low or no diffusion occurring in solids or strong viscous media was obtained from pseudochemical equilibrium.

Probabilistic Approaches to the Security Analysis of Smart Grid with High Wind Penetration: The Case of Jeju Island’s Power Grids

As the importance of renewable generating resources has grown around the world, South Korea is also trying to expand the proportion of renewable generating resources in the power generation sector. Among the various renewable energy sources, wind generating resources are emerging as a key alternative to conventional power generations in the electricity sector in Korea accounted for 17.7 GW of total capacity by 2030. As wind generating resources are gradually replacing traditional generating resources, the system security and reliability are negatively affected because of the variability, due to intermittent outputs. Therefore, existing power grids will need to be correctly re-measured to cover the large scale of renewable energy, including wind generation. To expand the grid, we must understand the characteristics of renewable energy and the impact of its adoption in the grid. In this paper, we analyze various characteristics of wind power generation, and then we propose a probabilistic power output modeling method to consider the uncertainty of wind power generation. For the probabilistic approach, Monte-Carlo simulation is used in the modeling method. The modeled wind power outputs can help planning for the reinforcement and expansion of power systems to expand the capacity for large-scale renewable energy in the future. To verify the proposed method, some case studies were performed using empirical data, and probabilistic power flow calculation was performed by integrating large-scale wind power generation to the Jeju Island power system. The probabilistic method proposed in this paper can efficiently plan power system expansion and play a key strategy of evaluating the security of the power system through the results of stochastic power flow calculation.

Comparison of Deterministic and Stochastic Depletions in Graphite-Filled MOX Fuel Assembly Design

A comparison between stochastic and deterministic depletion calculations based on a graphite-filled MOX fuel assembly configuration is presented in this paper. The infinite multiplication factors and isotope inventory changes as a function of burnup obtained by Monte Carlo method module SCALE/KENO and deterministic method module SCALE/NEWT are compared with those obtained by deterministic code HELIOS. The impact in calculation results by using different nuclear data library is also investigated. The SCALE/KENO results show a good agreement with SCALE/NEWT results in the eigenvalue as a function of burnup (less than 0.1%). However, the absolute difference in the initial k¥ between SCALE/KENO and NEWT modules and HELIOS results is quite large (around 1.1%) and the isotope inventory changes show quite differently at the end of cycle. The uranium and plutonium depletion rates calculated by SCALE/KENO and SCALE/NEWT have quite good agreement. By using the same data library, the good agreement between stochastic and deterministic code’s results were confirmed.

River network alteration of C-N-P dynamics in a mesoscale agricultural catchment

The majority of freshwater ecosystems worldwide suffer from eutrophication, particularly because of agriculture-derived nutrient sources. In the European Union, a discrepancy exists between the scale of regulatory assessment and the size of research catchments. The Water Framework Directive sets water quality objectives at the mesoscale (50–500 km2), a scale at which both hillslope and in-stream processes influence carbon (C), nitrogen (N) and phosphorus (P) dynamics. Conversely, research catchments focus on headwaters to investigate hillslope processes while minimising the influence of river processes on C-N-P dynamics. Because hillslope and river processes have common hydro-climatic drivers, the relative influence of each on C-N-P dynamics is difficult to disentangle at the mesoscale. In the present study, we used repeated synoptic sampling throughout the river network of a 300 km2 intensively farmed catchment, spatial stochastic modelling and mass balance calculations to analyse this mesoscale conundrum. The main objective was to quantify how river processes altered C-N-P hydrochemical dynamics in different flow, concentration and temperature conditions. Our results show that flow was the main control of alterations of C-N-P dynamics in the river network, while temperature and source concentration had little or no influence. The influence of river processes peaked during low flow, with up to 50% of dissolved organic carbon (DOC) production, up to 100% of nitrate (NO3) retention and up to 50% of total phosphorus (TP) retention. Despite high percentages of river processes at low flow, their influence on annual loads was low for NO3 (median of −10%) and DOC (median of +25%) but too variable to draw conclusions for TP. Because of the differing river alteration rates among carbon and nutrients, stoichiometric ratios varied greatly from headwaters to the outlet, especially during the eutrophication-sensitive low-flow season.

Bi-fidelity stochastic gradient descent for structural optimization under uncertainty

The presence of uncertainty in material properties and geometry of a structure is ubiquitous. The design of robust engineering structures, therefore, needs to incorporate uncertainty in the optimization process. Stochastic gradient descent (SGD) method can alleviate the cost of optimization under uncertainty, which includes statistical moments of quantities of interest in the objective and constraints. However, the design may change considerably during the initial iterations of the optimization process which impedes the convergence of the traditional SGD method and its variants. In this paper, we present two SGD based algorithms, where the computational cost is reduced by employing a low-fidelity model in the optimization process. In the first algorithm, most of the stochastic gradient calculations are performed on the low-fidelity model and only a handful of gradients from the high-fidelity model is used per iteration, resulting in an improved convergence. In the second algorithm, we use gradients from the low-fidelity models to be used as control variate, a variance reduction technique, to reduce the variance in the search direction. These two bi-fidelity algorithms are illustrated first with a conceptual example. Then, the convergence of the proposed bi-fidelity algorithms is studied with two numerical examples of shape and topology optimization and compared to popular variants of the SGD method that do not use low-fidelity models. The results show that the proposed use of a bi-fidelity approach for the SGD method can improve the convergence. Two analytical proofs are also provided that show linear convergence of these two algorithms under appropriate assumptions.

Stochastic Power Flow Calculation of High-Density Correlation Input Power Grid Based on Hybrid Gaussian Model

Traditional stochastic power flow calculation assumes that the input variables are uncorrelated and directly used to calculate high-density correlation input variables has certain errors. To this end, this paper proposes a stochastic power flow algorithm based on mixed Gaussian models that takes into account input correlation. First, a mixed Gaussian model is established based on load data, then uniform sampling and Naf transformation are used to process random variables, and the high-density correlation in the original space is converted into independent random variables, and the piecewise linear Monte Carlo method is used to carry out random power flow. Calculation can greatly reduce the calculation time and reduce the truncation error as much as possible. Finally, combined with the actual calculation examples of IEEE-30, the results show that the algorithm can simplify the actual calculation process, improve the calculation efficiency, and has certain practical value in engineering.

SAOSA: Stable Adaptive Optimization for Stacked Auto-encoders

The stacked auto-encoders are considered deep learning algorithms automatically extracting meaningful unsupervised features from the input data using a hierarcfhical learning process. The parameters are learnt layer-by-layer in each auto-encoder (AE). As optimization is one of the main components of the neural networks and auto-encoders, the learning rate is one of the crucial hyper-parameters of neural networks and AE. This issue on a large scale and especially sparse data sets is more important. In this paper, we adapt the learning rate for special AE corresponding to various components of AE networks in each stochastic gradient calculation and analyze the theoretical convergence of back-propagation learning for the proposed method. We also promote our methodology for online adaptive optimizations suitable for deep learning. We obtain promising results compared to constant learning rates on the (1) MNIST digit, (2) blogs-Gender-100 text, (3) smartphone based recognition of human activities and postural transitions time series, and (4) EEG brainwave feeling emotions time series classification tasks using a single machine.

Decomposition of stochastic flow and an averaging principle for slow perturbations

In this work we use the stochastic flow decomposition technique to get components that represent the dynamics of the slow and fast motion of a stochastic differential equation with a random perturbation. Assuming a Lipschitz condition for vector fields and an average principle we get an approximation for the slow motion. To obtain the estimate for the rate of convergence we use a distance function which is defined in terms of the height functions associated to an isometric embedding of the manifold into the Euclidean space. This metric is topologically equivalent to the Riemannian distance given by the infimum of the lengths of all admissible curves between two points and works well with stochastic calculation tools. Finally, we get an estimate for the approximation between the solution of perturbed system and the original process provided by the unperturbed.

Stochastic equation of motion approach to fermionic dissipative dynamics. II. Numerical implementation

This paper provides a detailed account of the numerical implementation of the stochastic equation of motion (SEOM) method for the dissipative dynamics of fermionic open quantum systems. To enable direct stochastic calculations, a minimal auxiliary space (MAS) mapping scheme is adopted, with which the time-dependent Grassmann fields are represented by c-number noises and a set of pseudo-operators. We elaborate on the construction of the system operators and pseudo-operators involved in the MAS-SEOM, along with the analytic expression for the particle current. The MAS-SEOM is applied to study the relaxation and voltage-driven dynamics of quantum impurity systems described by the single-level Anderson impurity model, and the numerical results are benchmarked against those of the highly accurate hierarchical equations of motion method. The advantages and limitations of the present MAS-SEOM approach are discussed extensively.

Multiagent Reinforcement Learning for Energy Management in Residential Buildings

The aim of this article is to explore the multiagent reinforcement learning approach for residential multicarrier energy management. Defining the multiagents system not only enhances the possibility of dedicating separate demand response programs for different components but also accelerates the computational calculations. We employ the Q -learning to provide the optimum solution in solving the presented residential energy management problem. Furthermore, to address uncertainties, a scenario-based method with the real data and proper probability density functions is used. Deterministic and stochastic numerical calculations are made to justify the effectiveness and robustness of the proposed method. The simulated results indicate that the application of the proposed reinforcement learning-based method leads to lower cost schemes for consumers rather than the conventional optimization-based energy management programs.

Storm surge risk assessment for the insurance system: A case study in Tokyo Bay, Japan

With the renewal of the basic disaster management plan in Japan, the transferring flood risk itself to insurance carriers is promoted by the Japanese government. An insurance company to which flood risks are transferred must assess infrequent flood risks to manage the overall risk of the company. Insurance systems may reach peak risk condition when a high wind coincides with a high storm surge level. However, there are few studies on the assessment of storm surges using stochastic approaches for Japan. This study suggests the procedure of stochastic storm surge risk assessment with low calculation load and applies it to the Tokyo Bay coast in Japan, a region exposed to large storm surges.Risk mapping and economic losses on the Tokyo Bay coast due to extreme flooding caused by storm surges are predicted for exceedance probability using stochastic approaches. Data on one thousand modeled typhoons passing through Tokyo Bay are extracted using a probabilistic tropical cyclone model over 10,000 years. Flooding due to storm surges is calculated with a validated numerical storm surge model. Next, a storm surge risk map that indicates inundation depth for a representative exceedance probability is created from the results of a series of stochastic hazard calculations. The inundation depth data sets for 1000 typhoons—along with the spatially distributed assets and values and damage functions provided by the Japanese government for Tokyo Bay—are used to estimate the economic loss from typhoons for corresponding exceedance probability. From the risk mapping, it was found that the storm surge risk in Chiba and Kanagawa prefectures is relatively high for exceedance probabilities and the economic losses estimated for the exceedance probability of 0.005 are 158.4 and 91.5 billion Japanese yen for the private and commercial sectors respectively along the Tokyo Bay coast. Moreover, the effect of the astronomical tide on the exceedance probability is evaluated using a neural network. However, it was found that the randomly determined astronomical tide does not have a significant influence on the exceedance probability targeted for insurance purposes when losses over 10,000 years are investigated.

The analytical dynamics of the finite population evolution games

We study the dynamics of a finite number of replicators with different strategies in evolutionary games, using the moment closure approximation for the master equation and the Hamilton–Jacobi equation approach. These methods give finite population corrections to the results of the replicator equation. The model under investigation has two strategies N overall replicators with constant payoff matrix and the Moran process as the update mechanism. Our results are compared with the results of the deterministic replicator equation and the results of numerical stochastic calculations.

High-level Stochastic Project Cost and Duration Planning Methodology Integrating Earned Duration, Schedule and Value, Criticality, Cruciality and Downside Risk Metrics

A high-level methodology is described to integrate deterministic and stochastic calculations of project networks with parallel pathways of work items. It provides the systematic integration of earned value, earned schedule and earned duration metrics and derivative to-completion forecasts of project cost and duration with stochastically-derived quantitative measures of criticality, cruciality, uncertainty and downside risk measures at project, work item and budget levels. A project network consisting of up to about 50 high-level project work items (rather than hundreds of activities) is evaluated applying critical path analysis using a matrix template that derives the fraction of the project completed at regular intervals (e.g., 2% to 5%) along a baseline planned project schedule – the work-progress-breakdown diagram. This matrix is evaluated for each deterministic and stochastic case providing the key information to derive a spectrum established and novel earned value metrics, and to quantify uncertainty, down-side risk and criticality at the work-item, pathway and project levels.

Development of methods and algorithms for a stochastic biomedical signal period calculation in medical computer diagnostic systems

An method and algorithm for a stochastic biomedical signal period calculation is developed, which characterized by high resolution and performance, suitable for using in biomedical computer diagnostic systems. The method and algorithm is implemented on the basis of determination a minimum of a centered biomedical signal mean values functional variation procedure. The results of existing algorithms operation for biomedical signals period calculation by known methods based on: averaging of time intervals between a biosignal realization maximum values, averaging of intervals between a biosignal amplitude spectra maximum values, averaging of time intervals between a biosignal autocorrelation function maximum values and averaging of time intervals between maximum values of a power spectral density are analyzed. The calculation results obtained by different methods differ, which in turn leads to ambiguous results of the biomedical signal processing. Algorithmic and software designed to calculate the stochastic biomedical signal period makes it possible to reduce the calculation estimates blur in medical computer diagnostic systems, because, unlike the known methods, the developed one has a small scatter of the standard deviation at the biomedical signal ensemble realizations synchronization and lower algorithmic complexity, which leads to calculations performance increasing. The software is implemented in the Matlab environment. The developed algorithm verification procedure is carried out by means of simulation. The verification results 100% confirmed the accuracy of a priori known test signal period determination.

Project Scheduling using Event Based Scheduler with ABC

Scheduling is the first and foremost step for every project implementation. Project scheduling could be a mechanism to communicate what tasks has to be compelled to get done and which resources are going to be allotted to finish those tasks in what timeframe. Project scheduling occurs during the planning phase of the project. The problem comprises the correct assignment of employees to the various tasks that frame a software project, casing in time and cost limitations. To accomplish this objective, this paper presents and discusses the EBS with ACO, FCM clustering and EBS with ABC and the conclusions are drawn from it. First, to schedule human resources to tasks we implement Event based scheduler with the Ant colony optimization algorithm (ACO) for probabilistic optimization, second, for fast scheduling we implemented Fuzzy c means clustering to assign similar data points of employees to clusters so that the searching space will be reduced. Third, for optimum scheduling we apply Artificial Bee Colony algorithm with Event Based Scheduler. Artificial bee colony (ABC) is an optimization algorithm based on stochastic calculation which has demonstrated good search capacities on numerous advancement issues. Based on these findings we briefly describe the scheduling with FCM-EBS with ABC prompt optimum values.

STOCHASTIC CALCULATION OF A QUASI-HOMOGENEOUS BOLTED JOINTS OF THE BODY SHEETS OF THE STEEL SILOS

This paper deals with the study of reliability of quasi-homogeneous bolted joints of the body of thin-walled constructions ofthe steel silos. Heterogeneity of this unit can be caused by number of reasons, in particular by presence of bolts of differentstrength in joint. In such case the reliability of the system is determined trough the probability of trouble-free work of the coefficient of the critical factor. The general conception of stochastic calculation consists in using the Monte-Karlo simulationprocedure for the samples of random values of the large volume. It was formed the system of conditions, under which the reliability of joints is provided and analytical expressions for the value of coefficient of the critical factor is got, and also madepractical calculation example with the following graphic presentation on a special coordinate plane – a critical stochasticscale. It was illustrated that random presence of bolts of less strength in field joint rapidly increases the risk of refusal.

Pleione: A tool for statistical and multi-objective calibration of Rule-based models

Mathematical models based on Ordinary Differential Equations (ODEs) are frequently used to describe and simulate biological systems. Nevertheless, such models are often difficult to understand. Unlike ODE models, Rule-Based Models (RBMs) utilise formal language to describe reactions as a cumulative number of statements that are easier to understand and correct. They are also gaining popularity because of their conciseness and simulation flexibility. However, RBMs generally lack tools to perform further analysis that requires simulation. This situation arises because exact and approximate simulations are computationally intensive. Translating RBMs into ODEs is commonly used to reduce simulation time, but this technique may be prohibitive due to combinatorial explosion. Here, we present the software called Pleione to calibrate RBMs. Parameter calibration is essential given the incomplete experimental determination of reaction rates and the goal of using models to reproduce experimental data. The software distributes stochastic simulations and calculations and incorporates equivalence tests to determine the fitness of RBMs compared with data. The primary features of Pleione were thoroughly tested on a model of gene regulation in Escherichia coli. Pleione yielded satisfactory results regarding calculation time and error reduction for multiple simulators, models, parameter search strategies, and computing infrastructures.