Monte Carlo Sampling Method Research Articles

A hard look at the X-ray spectral variability of NGC 7582

ABSTRACT NGC 7582 (z = 0.005264; D = 22.5 Mpc) is a highly variable, changing-look AGN. In this work, we explore the X-ray properties of this source using XMM–Newton and NuSTAR archival observations in the 3 – 40 keV range, from 2001 to 2016. NGC 7582 exhibits a long-term variability between observations but also a short-term variability in two observations that has not been studied before. To study the variability, we perform a time-resolved spectral analysis using a phenomenological model and a physically motivated model (uxclumpy). The spectral fitting is achieved using a nested sampling Monte Carlo method. uxclumpy enables testing various geometries of the absorber that may fit AGN spectra. We find that the best model is composed of a fully covering clumpy absorber. From this geometry, we estimate the velocity, size, and distance of the clumps. The column density of the absorber in the line of sight varies from Compton-thin to Compton-thick between observations. Variability over the time-scale of a few tens of kiloseconds is also observed within two observations. The obscuring clouds are consistent with being located at a distance not larger than 0.6 pc, moving with a transverse velocity exceeding ∼700 km s−1. We could put only a lower limit on the size of the obscuring cloud being larger than 1013 cm. Given the sparsity of the observations, and the limited exposure time per observation available, we cannot determine the exact structure of the obscuring clouds. The results are broadly consistent with comet-like obscuring clouds or spherical clouds with a non-uniform density profile.

Reliability analysis of flap deflection angle based on collaborative intelligent moving Kriging model

To effectively monitor the reliability of civil aircraft flap deflection angle, combined with the quick access recorder(QAR), the collaborative intelligent moving Kriging(CIMK) method is proposed by absorbing the Kriging model, decomposition and co-ordination strategy, equilibrium optimizer(EO), and moving least square(MLS). Among them, the decomposition coordination strategy is used to deal with the relationship between the flaps left and right deflection angles. MLS is employed to select effective modeling samples and solve the undetermined coefficients of Kriging model. EO method is applied to determine optimizing the local compact support region radius of MLS. Firstly, the fault reason for flap left-right asymmetry is analyzed to clarify the main characteristic parameters in QAR data. Secondly, combined with the QAR data of relevant influencing parameters, the civil aircraft flap deflection model(limit state function) is constructed by using CIMK. Then, the reliability and influence of civil aircraft flap deflection angle are analyzed by Monte Carlo(MC) sampling method. The results show that when the flap deflection angle is 3°, the reliability is 0.450 2, and the important factors affecting the flap deflection angle are Mach number, left angle of attack, right angle of attack, etc. Compared with the response surface method(RSM), Kriging, support vector machine(SVM), and back-propagation-artificial neural network(BP-ANN), the average absolute error accuracy of the proposed method is relative improved by 53.02%, 51.43%, 49.03%, and 44.04%, the average relative error accuracy is relative improved by 68.36%, 66.76%, 64.41%, and 62.64%, and the modeling efficiency is relative improved by 50.62%, 26.35%, and 43.01% respectively compared with Kriging, SVM and BP-ANN. When the number of simulations is 103, the analysis accuracy is relative improved by 8.82%, 7.25%, 6.22%, and 3.98% respectively.

Optimization design of a parallel surgical robot with remote center of motion

This paper proposes a parallel surgical robot with a remote center of motion, and the kinematic optimization design is studied. The surgical robot is composed of two branches, each of which is a planar mechanism. The kinematics model of the robot is established through spatial geometric analysis. A modified Monte-Carlo sampling method is presented to greatly increase the sampling rate during the workspace calculation of the parallel surgical robot. Further, through the boundary sampling method, the boundary of the workspace is encrypted and sampled, and the accurate workspace is obtained. A dexterity index with clear physical meaning is proposed and the corresponding solution is found. Based on the effective workspace volume index and global dexterity index, a multi-objective optimization is carried out on the parallel surgical robot by using the quantum particle swarm optimization. The optimized robot has a large effective workspace and good dexterity, which meets the needs of surgical robots.

Bayesian Analysis of Multivariate Longitudinal Ordinal Data Using Multiple Multivariate Probit Models

Multivariate longitudinal ordinal data are often involved in longitudinal studies with each individual having more than one longitudinal ordinal measure. However, due to complicated correlation structures within each individual and no explicit likelihood functions, analyzing multivariate longitudinal ordinal data is quite challenging. In this paper, Markov chain Monte Carlo (MCMC) sampling methods are developed to analyze multivariate longitudinal ordinal data by extending multivariate probit (MVP) models for univariate longitudinal ordinal data to multiple multivariate probit models (MMVP) for multivariate longitudinal ordinal data. The identifiable MVP models require the covariance matrix of the latent multivariate normal variables underlying the longitudinal ordinal variables to be a correlation matrix, thus a Metropolis-Hastings (MH) algorithm is usually necessitated, which brings a rigorous task to develop efficient MCMC sampling methods. In contrast to the identifiable MVP models, the non-identifiable MVP models can be constructed to circumvent a MH algorithm to sample a correlation matrix by a Gibbs sampling to sample a covariance matrix, and hence improve the mixing and convergence of the MCMC components. Therefore, both the identifiable MMVP models and the non-identifiable MMVP models for multivariate longitudinal ordinal data are presented, and their corresponding MCMC sampling methods are developed. The performances of these methods are illustrated through simulation studies and an application using data from the Russia Longitudinal Monitoring Survey-Higher School of Economics (RLMS-HSE).

A Bayesian inference approach for parametric identification through optimal control method

AbstractThe objective of the research is to obtain deterministic and probabilistic resolution of material parameters from full field measurements of kinematic data acquired from digital image correlation. The deterministic inverse problem involves formulation of an optimal control approach where the complete knowledge of the boundary conditions and the measurement data are not required. The probabilistic framework inculcates this optimal control method in a Bayesian inference framework. A Markov chain Monte Carlo sampling method is applied to obtain the posterior probability density function, along with a radial basis function network for the numerical frugality of the samplings.

Probabilistic Failure Risk of Aeroengine Life-Limited Parts Considering the Random Load Interference Effect

Probabilistic failure risk analysis of aeroengine life-limited parts is of great significance for flight safety. Current probabilistic failure risk analysis uses equal amplitude load calculations for conservative estimation, avoiding inclusion of the interference effect analyzing random loads due to its massive computational complexity and leading to reduced analysis accuracy. Here, an efficient algorithm is established to solve this computational problem, and an analytical framework is established to consider the interference effect of variable amplitude load. The corresponding probabilistic failure risk analysis is performed for the centrifugal compressor disk. The results show that considering the interference effect of random variable amplitude loads causes a significant decrease in the risk of failure, and the efficient algorithm has advantages over the Monte Carlo sampling method in accuracy and efficiency when considering load interference. This work provides a reference for exploring the probabilistic damage tolerance method under complex loads and supports the optimal design of life-limited parts.

On Filtering and Smoothing Algorithms for Linear State-Space Models Having Quantized Output Data

The problem of state estimation of a linear, dynamical state-space system where the output is subject to quantization is challenging and important in different areas of research, such as control systems, communications, and power systems. There are a number of methods and algorithms to deal with this state estimation problem. However, there is no consensus in the control and estimation community on (1) which methods are more suitable for a particular application and why, and (2) how these methods compare in terms of accuracy, computational cost, and user friendliness. In this paper, we provide a comprehensive overview of the state-of-the-art algorithms to deal with state estimation subject to quantized measurements, and an exhaustive comparison among them. The comparison analysis is performed in terms of the accuracy of the state estimation, dimensionality issues, hyperparameter selection, user friendliness, and computational cost. We consider classical approaches and a new development in the literature to obtain the filtering and smoothing distributions of the state conditioned to quantized data. The classical approaches include the extended Kalman filter/smoother, the quantized Kalman filter/smoother, the unscented Kalman filter/smoother, and the sequential Monte Carlo sampling method, also called particle filter/smoother, with its most relevant variants. We also consider a new approach based on the Gaussian sum filter/smoother. Extensive numerical simulations—including a practical application—are presented in order to analyze the accuracy of the state estimation and the computational cost.

Random Traffic Flow Simulation of Heavy Vehicles Based on R-Vine Copula Model and Improved Latin Hypercube Sampling Method

The rationality of heavy vehicle models is crucial to the structural safety assessment of bridges. To establish a realistic heavy vehicle traffic flow model, this study proposes a heavy vehicle random traffic flow simulation method that fully considers the vehicle weight correlation based on the measured weigh-in-motion data. First, a probability model of the key parameters in the actual traffic flow is established. Then, a random traffic flow simulation of heavy vehicles is realized using the R-vine Copula model and improved Latin hypercube sampling (LHS) method. Finally, the load effect is calculated using a calculation example to explore the necessity of considering the vehicle weight correlation. The results indicate that the vehicle weight of each model is significantly correlated. Compared to the Monte Carlo method, the improved LHS method better considers the correlation between high-dimensional variables. Furthermore, considering the vehicle weight correlation using the R-vine Copula model, the random traffic flow generated by the Monte Carlo sampling method ignores the correlation between parameters, leading to a weaker load effect. Therefore, the improved LHS method is preferred.

HOLISMOKES

Modeling of strong gravitational lenses is a necessity for further applications in astrophysics and cosmology. With the large number of detections in current and upcoming surveys, such as the Rubin Legacy Survey of Space and Time (LSST), it is pertinent to investigate automated and fast analysis techniques beyond the traditional and time-consuming Markov chain Monte Carlo sampling methods. Building upon our (simple) convolutional neural network (CNN), we present here another CNN, specifically a residual neural network (ResNet), that predicts the five mass parameters of a singular isothermal ellipsoid (SIE) profile (lens center x and y, ellipticity ex and ey, Einstein radius θE) and the external shear (γext, 1, γext, 2) from ground-based imaging data. In contrast to our previous CNN, this ResNet further predicts the 1σ uncertainty for each parameter. To train our network, we use our improved pipeline to simulate lens images using real images of galaxies from the Hyper Suprime-Cam Survey (HSC) and from the Hubble Ultra Deep Field as lens galaxies and background sources, respectively. We find very good recoveries overall for the SIE parameters, especially for the lens center in comparison to our previous CNN, while significant differences remain in predicting the external shear. From our multiple tests, it appears that most likely the low ground-based image resolution is the limiting factor in predicting the external shear. Given the run time of milli-seconds per system, our network is perfectly suited to quickly predict the next appearing image and time delays of lensed transients. Therefore, we use the network-predicted mass model to estimate these quantities and compare to those values obtained from our simulations. Unfortunately, the achieved precision allows only a first-order estimate of time delays on real lens systems and requires further refinement through follow-up modeling. Nonetheless, our ResNet is able to predict the SIE and shear parameter values in fractions of a second on a single CPU, meaning that we are able to efficiently process the huge amount of galaxy-scale lenses expected in the near future.

The Research of Reliability Evaluation Method Based on PoF

Combining with the practical engineering case, this paper decomposed and analyzed the process of electronic products’ reliability assessment based on the Physics of Failure (PoF) method. The first step is to build a digital prototype model and then a PoF model. The second step is to use the Monte Carlo sampling method to obtain the failure samples of different fault points based on the PoF model. The third step is forming the failure DFs by fitting the failure samples. The fourth step is using the failure DF to calculate the Time to Failure (TTF)of the components. Finally, the paper can obtain the time of the TTF and the failure DF by applying the competitive failure principle. Compared with the reliability evaluation method based on test data, the reliability evaluation method based on PoF is more economical and efficient.

Bayesian optimization of hyperparameters from noisy marginal likelihood estimates

SummaryBayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is an iterative method where a Gaussian process posterior of the underlying function is sequentially updated by new function evaluations. We propose a novel Bayesian optimization framework for situations where the user controls the computational effort and therefore the precision of the function evaluations. This is a common situation in econometrics where the marginal likelihood is often computed by Markov chain Monte Carlo or importance sampling methods. The new acquisition strategy gives the optimizer the option to explore the function with cheap noisy evaluations and therefore find the optimum faster. The method is applied to estimating the prior hyperparameters in two popular models on US macroeconomic time series data: the steady‐state Bayesian vector autoregressive (BVAR) and the time‐varying parameter BVAR with stochastic volatility.

A State-of-the-Art Review of Probabilistic Portfolio Management for Future Stock Markets

Portfolio management has long been one of the most significant challenges in large- and small-scale investments alike. The primary objective of portfolio management is to make investments with the most favorable rate of return and the lowest amount of risk. On the other hand, time series prediction has garnered significant attention in recent years for predicting the trend of stock prices in the future. The combination of these two approaches, i.e., predicting the future stock price and adopting portfolio management methods in the forecasted time series, has turned out to be a novel research line in the past few years. That is, to have a better understanding of the future, various researchers have attempted to predict the future behavior of stocks and subsequently implement portfolio management techniques on them. However, due to the uncertainty in predicting the future, the reliability of these methodologies is in question, and it is unclear to what extent their results can be relied upon. Therefore, probabilistic approaches have also entered the research arena, and attempts have been made to incorporate uncertainty into future forecasting and portfolio management. This issue has led to the development of probabilistic portfolio management for future data. This review paper begins with a discussion of various time-series prediction methods for stock market data. Next, a classification and evaluation of portfolio management approaches are provided. Afterwards, the Monte Carlo sampling method is discussed as the most prevalent technique for probabilistic analysis of stock market data. The probabilistic portfolio management method is applied to future Shanghai Stock Exchange data in the form of a case study to measure the applicability of this method to real-world projects. The results of this research can serve as a benchmark example for the analysis of other stock market data.

Sampling constrained continuous probability distributions: A review

AbstractThe problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Markov Chain Monte Carlo (MCMC) sampling methods have been adapted to handle different types of constraints on random variables. Among these methods, Hamilton Monte Carlo (HMC) and the related approaches have shown significant advantages in terms of computational efficiency compared with other counterparts. In this article, we first review HMC and some extended sampling methods, and then we concretely explain three constrained HMC‐based sampling methods, reflection, reformulation, and spherical HMC. For illustration, we apply these methods to solve three well‐known constrained sampling problems, truncated multivariate normal distributions, Bayesian regularized regression, and nonparametric density estimation. In this review, we also connect constrained sampling with another similar problem in the statistical design of experiments with constrained design space.This article is categorized under: Applications of Computational Statistics > Computational Mathematics Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC) Statistical and Graphical Methods of Data Analysis > Sampling

Comparative study on peak power prediction methods during start-up and power-up of heat pipe reactor based on neural network and decision tree

The effective control of start-up and power-up processes is essential if thermal power reactors are operated autonomously. The decision-making processes of an autonomous operating system must anticipate and suppress unwanted power fluctuations in a timely manner. The rapid and accurate predictions of the peak power to be expected in a surge can help an autonomous operating system to make more appropriate and timely decisions. This paper compares the predictive performance of the neural network with that of the decision tree, where both are based on peak power datasets for start-up and power-up processes. We explain how the datasets are constructed, i.e., by coupling the Monte Carlo sampling methods with the analysis of the system analysis procedure. We introduce a framework for the comprehensive evaluation of both prediction algorithms. We conclude that the neural network has better intrinsic predictive accuracy than the decision tree for the control of start-up and power-up processes. With further expansion of the datasets, it is expected that the predictive advantage of the neural network will become more evident. However, predictive accuracy is not the only criterion by which different predictive algorithms can be compared. The poor interpretability and high training costs of the neural network limit its application in practice while the accuracy of the decision tree can be improved via ensemble strategies. Therefore, deciding an algorithm to use is a complex selection process that should reflect the constraints of the specific application.

Efficient gravitational wave searches with pulsar timing arrays using Hamiltonian Monte Carlo

Pulsar timing arrays (PTAs) detect low-frequency gravitational waves (GWs) by looking for correlated deviations in pulse arrival times. Current Bayesian searches use Markov Chain Monte Carlo (MCMC) methods, which struggle to sample the large number of parameters needed to model the PTA and GW signals. As the data span and number of pulsars increase, this problem will only worsen. An alternative Monte Carlo sampling method, Hamiltonian Monte Carlo (HMC), utilizes Hamiltonian dynamics to produce sample proposals informed by first-order gradients of the model likelihood. This in turn allows it to converge faster to high dimensional distributions. We implement HMC as an alternative sampling method in our search for an isotropic stochastic GW background, and show that this method produces equivalent statistical results to similar analyses run with standard MCMC techniques, while requiring 100-200 times fewer samples. We show that the speed of HMC sample generation scales as $\mathcal{O}(N_\mathrm{psr}^{5/4})$ where $N_\mathrm{psr}$ is the number of pulsars, compared to $\mathcal{O}(N_\mathrm{psr}^2)$ for MCMC methods. These factors offset the increased time required to generate a sample using HMC, demonstrating the value of adopting HMC techniques for PTAs.

A novel deep learning based probabilistic power flow method for Multi-Microgrids distribution system with incomplete network information

With the massive deployment of microgrids (MGs) and energy communities, various stakeholders have been involved in distribution networks. Due to the underdeveloped information infrastructure, especially in rural distribution networks, there is an increasing number of “blind areas” in the operation of distribution networks. The calculation of probabilistic power flow (PPF) with incomplete parameters have become an urgent issue to be solved for ensuring safe operation. Based on the deep learning and mechanism models, a novel PPF method is proposed for multi-microgrids distribution systems considering incomplete network information. Firstly, accessible power exchange data as well as public and independent information are utilized to realize equivalent modeling for microgrids area with incomplete parameters, based on a novel Kriging surrogate enhanced Gate Recurrent Unit-Temporal Convolutional Network (GRU-TCN). Then, the PPF calculation is effectively conducted by the distribution system operator (DSO) through the point estimation method (PEM), in which the equivalent GRU-TCN models and model-based power flow are integrated. Therefore, the complicated interactive iteration of the power flow equation is avoided, and the PPF calculation efficiency is effectively improved. In addition, user privacy is protected because only the trained GRU-TCN deep learning models will be used by DSO for the PPF calculation. The proposed method is validated in a modified IEEE 33-node distribution network, a modified American PG&E 69-node distribution network as well as the modified three-phase unbalanced IEEE 123-node distribution network including several MGs with unknown internal network parameters. The results show that the proposed method can improve the PPF calculation efficiency greatly while ensuring high-precision calculation results. The required evaluation time can be reduced by 64.01% and 99.31% compared with the DNN-based Monte Carlo sampling method and the traditional mechanism model-based Monte Carlo sampling method with complete information, respectively.

Market profitability of CSP-biomass hybrid power plants: Towards a firm supply of renewable energy

CSP-biomass hybrid power plants are promising options for displacing electricity from flexible fossil systems and increasing the share of dispatchable renewable energy in power grids. However, they are investment-intensive technologies whose competitiveness in electricity markets is still uncertain. This paper explores for the first time the profitability of CSP-biomass hybrid systems, assuming their participation as price-taking technologies in the Iberian day-ahead electricity market. For this purpose, a new economic evaluation metric called the Profitability Factor is proposed to extend the scope of the levelized cost of electricity (LCOE) by including the variability of market electricity prices. Besides, a stochastic approach integrating uncertainty related to investment costs, electricity prices and biomass costs through Monte-Carlo sampling methods has been applied. Results show that CSP-biomass schemes have up to 33% probability of being profitable in the electricity market before considering external financial support. High biomass share (approx. 76%) leads to a profitability increase of up to 0.11 USD/kWh (median value) compared to an equivalent CSP stand-alone plant. In addition, best-performing hybrid configurations would require a maximum add-in tariff between 0.040 and 0.071 USD/kWh (95% probability) to achieve grid parity. The resulting external financial support is significantly lower than those set through Power Purchase Agreements for the first generation CSP stand-alone plants (still in operation). Thus, CSP-biomass hybrid plants could provide flexibility and other services to power grids, which, if valued in the electricity market, would further increase the technology's competitiveness.

Simulation of a TRISO MiniFuel irradiation experiment with data-informed uncertainty quantification

An irradiation experiment using tristructural isotropic (TRISO) fuel particles and the miniature fuel (MiniFuel) irradiation vehicle was performed in Oak Ridge National Laboratory’s High Flux Isotope Reactor (HFIR) to support development of the Kairos Power fluoride salt–cooled, high-temperature reactor (KP-FHR). This paper describes modeling predictions of temperatures and fuel burnup for the as-built experiment. An uncertainty quantification (UQ) analysis was performed to determine the effect of TRISO particle volume and position on the temperature predictions at various fuel heat generation rates (HGRs). This UQ study utilized fuel kernel position and volume measurements previously collected using X-ray computed tomography (XCT) techniques and Monte Carlo sampling methods to generate fuel compact cases that were then analyzed using a finite element thermal model. The UQ analysis indicated that uncertainty in calculated temperatures caused by varying TRISO particle arrangement is relatively small, even at high fuel HGR. Final predictions of particle temperatures throughout the irradiation are shown to be relevant to KP-FHR normal and off-normal operating conditions and to previous TRISO irradiation experiments. The combination of XCT with UQ analyses will inform post-irradiation examination (PIE) of the irradiated fuel compacts, and these analyses can be used to develop fuel performance models for coated particle fuel forms. Both PIE of separate-effects irradiation data and enhanced fuel performance modeling support accelerated qualification of TRISO fuels for a broad range of advanced reactor applications. The novel approach demonstrated here of measuring TRISO particle configurations with XCT methods and generating representative fuel compacts for finite element modeling and UQ analysis could be leveraged by the broader particle fuel community in the development of other TRISO fuel experiments in which these variables may have a significant impact on key outcomes.

Data-driven model-based flow measurement uncertainty quantification for building central cooling systems using a probabilistic approach

Uncertainties inevitably exist in measurements and may lead to biases in making management and control decisions, and thus affect the energy performance of building central cooling systems. Water flow meters are essential for the monitoring and operational control of building central cooling systems, but they often suffer from significant measurement uncertainties due to site constraints and unfavorable working environment. An effective method to quantify the flow measurement uncertainties is urgently needed. This study proposes a data-driven model-based flow measurement uncertainty quantification strategy using Bayesian inference and Markov chain Monte Carlo sampling methods. The proposed strategy is tested and validated systematically on an air-cooled chiller. Four case studies with different levels of flow measurement uncertainties are conducted. The test results show that both systematic and random uncertainties of flow measurements are quantified accurately by this strategy. The 95% Bayesian credible intervals of systematic and random uncertainties contain their pre-set (actual) values, and their posterior means (estimated values) are very close to their pre-set values. The relative errors in quantifying flow measurement uncertainties are within 10%. The performance of the proposed method is quite satisfactory. This study provides a cost-effective and promising alternative for on-site flow meter calibration in engineering practice.

Simulation Study of New Buckling Restraint Bracing Based on Bayesian Optimization Algorithm to Identify the Parameters of Modified Bouc–Wen Model

The introduction of new materials can significantly improve the performance of existing dampers, but the constitutive model of new materials is difficult to be obtained in a short time, which makes its numerical simulation difficult. Bouc–Wen–Baber–Noori (BWBN) model can well describe the stress-strain relationship of materials, and it is helpful to introduce new materials into numerical simulation. In this paper, a new high manganese steel material is used to fabricate buckling restrained brace, and based on the improved Transition Markov Chain Monte Carlo (iTMCMC) sampling method and Bayesian reasoning, a new parameter identification of BWBN model is completed; model parameters are introduced into OpenSees to complete the response analysis of the new steel damper in the structure. It provides a new method and approach for introducing new materials into structural seismic resistance and proves its reliability.