Monte Carlo Integration Technique Research Articles

Research on three-dimensional wake model of horizontal axis wind turbine based on Weibull function

In wind turbine wake models, Gaussian models depend on multidimensional integration to ascertain the distribution of wake velocity deficits. These integrations, which often involve complex boundary conditions, significantly enhance the complexity of mathematical computations. Due to the difficulty of obtaining analytical solutions, numerical integration methods such as Monte Carlo or other numerical integration techniques are commonly employed. This study presents a three-dimensional wake model (3DJW) for horizontal axis wind turbines, utilizing the Weibull function to simplify wake deficit characterization instead of traditional Gaussian distribution methods. The 3DJW model considers wind shear effects and mass conservation laws to enhance predictions of vertical wake velocities. By integrating incoming wind conditions and turbine parameters, the model efficiently computes downstream wake velocities, improving computational efficiency. To enhance predictions in the ultra-far wake region, an improved three-dimensional Weibull wake model is proposed using the exponential fitting method. Validation through wind tunnel experiments and wind farm data demonstrates the model's accuracy in predicting wake deficits at the hub height, with relative errors in horizontal and vertical profiles mostly within 5% and 3%, respectively. The proposed model enables accurate and rapid calculation of wake velocities at any spatial location downstream, facilitating enhanced energy utilization and reduced costs.

Adaptive Dynamic Programming for Nonlinear-Constrained H∞ Control

This article considers the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> control problem of nonlinear systems having unavailable dynamics and asymmetric saturating actuators. Initially, such an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> control problem is converted into the zero-sum game with a nonquadratic cost function being introduced. Then, in order to solve the Hamilton–Jacobi–Isaacs equation arising in the zero-sum game, a simultaneous policy iteration (SPI) algorithm is developed under the adaptive dynamic programming framework. Meanwhile, it is proved that the convergence of the SPI algorithm in essence amounts to the convergence of the sequential PI algorithm. To implement the SPI algorithm, the critic, the actor, and the perturbation neural networks (NNs) are, respectively, constructed to estimate the cost function, the control policy, and the perturbation. The three NNs’ weights are simultaneously determined by using the least-squares method together with the Monte Carlo integration technique. A remarkable characteristic of such an SPI algorithm is that arbitrary control policies and perturbations are applicable in the learning process. This makes system’s information be able to be replaced by the data collected along system’s trajectories in advance. More importantly, the persistence of the excitation condition is not required. Finally, simulations of two nonlinear examples are given to validate the present SPI algorithm.

Sequential Monte Carlo: A Unified Review

Sequential Monte Carlo methods—also known as particle filters—offer approximate solutions to filtering problems for nonlinear state-space systems. These filtering problems are notoriously difficult to solve in general due to a lack of closed-form expressions and challenging expectation integrals. The essential idea behind particle filters is to employ Monte Carlo integration techniques in order to ameliorate both of these challenges. This article presents an intuitive introduction to the main particle filter ideas and then unifies three commonly employed particle filtering algorithms. This unified approach relies on a nonstandard presentation of the particle filter, which has the advantage of highlighting precisely where the differences between these algorithms stem from. Some relevant extensions and successful application domains of the particle filter are also presented.

Reinforcement learning for robust stabilization of nonlinear systems with asymmetric saturating actuators

We study the robust stabilization problem of a class of nonlinear systems with asymmetric saturating actuators and mismatched disturbances. Initially, we convert such a robust stabilization problem into a nonlinear-constrained optimal control problem by constructing a discounted cost function for the auxiliary system. Then, for the purpose of solving the nonlinear-constrained optimal control problem, we develop a simultaneous policy iteration (PI) in the reinforcement learning framework. The implementation of the simultaneous PI relies on an actor–critic architecture, which employs actor and critic neural networks (NNs) to separately approximate the control policy and the value function. To determine the actor and critic NNs’ weights, we use the approach of weighted residuals together with the typical Monte-Carlo integration technique. Finally, we perform simulations of two nonlinear plants to validate the established theoretical claims.

Effect of Dependency on the Estimation of P[Y&lt;X] in Exponential Stress-strength Models

We consider an expression for the probability R=P(Y&lt;X) where the random variables X and Y denote strength and stress, respectively. Our aim is to study the effect of the dependency between X and Y on R. We assume that X and Y follow exponential distributions and their dependency is modeled by a copula with the dependency parameter theta. We obtain a closed-form expression for R for Farlie-Gumbel-Morgenstern (FGM), Ali-Mikhail-Haq (AMH), Gumbel's bivariate exponential copulas and compute R for Gumbel-Hougaard (GH) copula using a Monte-Carlo integration technique. We plot a graph of R versus theta to study the effect of dependency on R. We estimate R by plugging in the estimates of the marginal parameters and theta in its expression. The estimates of the marginal parameters are based on the marginal likelihood. The estimates of theta are obtained from two different methods; one is based on the conditional likelihood and the other on the method of moments using Blomqvist's beta. Asymptotic distribution of both the estimators of R is obtained. For illustration purpose, we apply our results to a real data set.

Quantum Monte Carlo formulation of the second order algebraic diagrammatic construction: Toward a massively parallel correlated excited state method.

The quantum Monte Carlo (QMC) algebraic diagrammatic construction (ADC) method is introduced, which solves the eigenvalue problem of the second-order ADC scheme for the polarization propagator stochastically within the framework of QMC methodology allowing for massively parallel computations. As common virtue of the Monte Carlo integration techniques, quantum Monte Carlo algebraic diagrammatic construction (QMCADC) enables exploitation of the sparsity of the effective ADC matrix, and it reduces the memory requirements by storing only a portion of configurations at each iteration. Furthermore, distributing memory and processing loads to different computing nodes enables the use of fast developing parallel computing resources. Here, the theory and implementation of QMCADC is reported and its viability is demonstrated by the first proof-of-principle calculations. The focus lies on the first excited state and the reproduction of the corresponding lowest vertical excitation energy of various molecular systems. QMCADC is shown to be a genuine stochastic solution of the ADC eigenvalue problem, and exact ADC values can be obtained with a marginal controllable error.

Approximate Dynamic Programming for Nonlinear-Constrained Optimizations.

In this paper, we study the constrained optimization problem of a class of uncertain nonlinear interconnected systems. First, we prove that the solution of the constrained optimization problem can be obtained through solving an array of optimal control problems of constrained auxiliary subsystems. Then, under the framework of approximate dynamic programming, we present a simultaneous policy iteration (SPI) algorithm to solve the Hamilton-Jacobi-Bellman equations corresponding to the constrained auxiliary subsystems. By building an equivalence relationship, we demonstrate the convergence of the SPI algorithm. Meanwhile, we implement the SPI algorithm via an actor-critic structure, where actor networks are used to approximate optimal control policies and critic networks are applied to estimate optimal value functions. By using the least squares method and the Monte Carlo integration technique together, we are able to determine the weight vectors of actor and critic networks. Finally, we validate the developed control method through the simulation of a nonlinear interconnected plant.

Double Electron–Positron Pair Production with Two-electron Capture in Relativistic Heavy-ion Collisions

We calculated the cross section of double electron-positron pair production with two-electron capture for the collisions of Pb+Pb ions and we did our calculations at LHC energies. We applied a similar methodology for the calculation of bound-free electron-positron pair production. We used perturbation theory and implemented Monte Carlo integration techniques to calculate the lowest order Feynman diagrams. We also compared our double electron-positron pair production with two-electron capture cross section results obtained in the literature. These calculations may help us to learn more about strong QED.

Assimilation of Satellite Microwave Observations over the Rainbands of Tropical Cyclones

AbstractA novel Bayesian Monte Carlo integration (BMCI) technique was developed to retrieve geophysical variables from satellite microwave radiometer data in the presence of tropical cyclones. The BMCI technique includes three steps: generating a stochastic database, simulating satellite brightness temperatures using a radiative transfer model, and retrieving geophysical variables such as profiles of temperature, relative humidity, and cloud liquid and ice water content from real observations. The technique also provides uncertainty estimates for each retrieval and can output the error covariance matrix of selected parameters. The measurements from the Advanced Technology Microwave Sounder (ATMS) on board Suomi National Polar-Orbiting Partnership (Suomi NPP) and the Global Precipitation Measurement (GPM) Microwave Imager (GMI) were used as input. A new technique was developed to correct the ATMS and GMI observations for the beam-filling effect, which is due to small-scale variability of precipitation and clouds when compared with the instrument footprint and also the nonlinear relation between the brightness temperature and precipitation. In addition, the assimilation of the BMCI retrievals into the NASA GEOS model is discussed for Hurricane Maria. The results show that assimilating the BMCI retrievals can influence the dynamical features of the cyclone, including a stronger warm core, a symmetric eye, and vertically aligned wind columns. Two possible factors that may limit the impact of the BMCI retrievals include 1) the resolution of the model (about 25 km), which was too coarse to show the potential of the BMCI data in improving the representation of tropical storms in the model forecast, and 2) the data assimilation system not being able to consider vertically correlated observation errors.

VegasFlow: Accelerating Monte Carlo simulation across multiple hardware platforms

We present VegasFlow, a new software for fast evaluation of high dimensional integrals based on Monte Carlo integration techniques designed for platforms with hardware accelerators. The growing complexity of calculations and simulations in many areas of science have been accompanied by advances in the computational tools which have helped their developments. VegasFlow enables developers to delegate all complicated aspects of hardware or platform implementation to the library so they can focus on the problem at hand. This software is inspired on the Vegas algorithm, ubiquitous in the particle physics community as the driver of cross section integration, and based on Google’s powerful TensorFlow library. We benchmark the performance of this library on many different consumer and professional grade GPUs and CPUs. Program summaryProgram Title:VegasFlowCPC Library link to program files:http://dx.doi.org/10.17632/rpgcbzzhdt.1Developer’s repository link:https://github.com/N3PDF/vegasflowLicensing provisions: GPLv3Programming language: PythonNature of problem: The solution of high dimensional integrals requires the implementation of Monte Carlo algorithms such as Vegas. Monte Carlo algorithms are known to require long computation times.Solution method: Implementation of the Vegas algorithm using the dataflow graph infrastructure provided by the TensorFlow framework. Extension of the algorithm to take advantage of multi-threading CPU and multi-GPU setups.

In silico analysis of argon adsorption and porous properties of Fe-soc-MOF pre-adsorbed with nonpolar and polar fluids

Abstract In this molecular simulation work, we provide a profound insight into the textural and adsorptive properties of a microporous metal-organic framework with soc topology (soc-MOF) using combined argon physisorption and pre-adsorption with fluids having different polarities (CCl4, NH3, and H2O) at 87 K. With different amounts of pre-adsorbed molecules added to the framework, the adsorption isotherms, snapshots, and isosteric heats of argon at 87 K are investigated using the grand canonical Monte Carlo simulation (GCMC), whereas the porous properties are obtained by using the Monte Carlo integration technique (MCI). It is found that insertion of pre-adsorbed molecules has a substantial effect on argon adsorption uptake in the regions of Henry's law and saturation capacity since the accessible pore space becomes smaller in volume and size. By observing the pre-adsorption mechanisms of non-polar (CCl4) and mildly polar (NH3) fluids, it is clear that the pre-adsorbed molecules mainly prefer to locate at the cages due to stronger interaction between Fe sites and pre-adsorbed molecules, followed by pre-adsorption in the channels when the cages are utterly or nearly fulfilled. Therefore, post-adsorption of argon initially occurs in the cages because of the enhancement of interactions between pre-adsorbed molecules existing in the framework, as confirmed by isosteric heat at low loading. Conversely, for highly polar fluids like H2O, pre-adsorption is proceeded by non-selective pore filling. From the analysis at the molecular level, it can be concluded that pre-adsorption could be used as another tool for advanced surface characterization to provide a better understanding of the structural and adsorptive properties of other soc-MOFs and MOFs that have different topological framework types.

Baropodometric quantification and implications of muscle coactivation in the lower limbs caused by head movement: A prospective study

BackgroundIn healthy young adults, muscle coactivation can sometimes be induced by remote voluntary contractions when the motor task is forceful, maximal, tiring, or cyclic and brief. ObjectivesTo show that a change in plantar pressure is an unequivocal response to backward movement of the head, and to contribute to a better understanding of physiotherapy methods that involve remote muscle activation. MethodsInvoluntary coactivation was quantified as a percentage of the anteroposterior plantar pressure distribution, using a baropodometric platform in a population of young adults. The baropodometric data were collected from a 1s recording after 30 s in the reference condition, and from 1s recordings during the first second and then during the 120th second in the test condition. The results were analyzed with Bayesian statistics (Markov chains and Monte Carlo integration techniques). Results90 adults participated in the study (age range: 19–26; 38 males and 52 females). The forefoot plantar pressure increased in all cases, by a mean multiplicative factor (on a logit scale) of 1.12 (from 72.24% to 74.45%) when the head was aligned over the trunk. ConclusionsThis 90-participant trial confirmed our initial hypothesis: a increase in forefoot plantar pressure is a systematic response to the motor task (head movement), and suggests greater recruitment of the plantar flexor muscles. A spinal reflex and/or a previously unknown form of motor overflow might be involved in this phenomenon. These results support the development of inductive physiotherapy techniques based on remote muscle activation in the treatment of musculoskeletal disorders. Clinicalstrial.gov identifierNCT02320097.

Experimental Verification of Force and Stiffness Between Two Ring Magnets Calculated by Monte Carlo Integration Technique

This paper presents the calculation and experimental verification of force and stiffness between two concentric ring-shaped rare earth magnets. This kind of magnet configuration is invariably used in magnetic bearing, micromass measurement system, turbomachineries and space applications. Estimation of magnetic force and stiffness is always important in any application of permanent magnet as it influences the stability and performance of the system. Some analytical methods are available which involve direct solution of elliptic integral, which made the calculation tedious, complex, time- and space consuming. In this work, a simple approach based on Monte Carlo integration technique is proposed to calculate the force and stiffness. Monte Carlo integration technique is preferred to calculate the multidimensional elliptic integrals due to simplicity of the method, less computational time and memory requirement. The result is compared with existing finite element method and verified with experimental result. The verification process indicates that there is a small deviation in result of the proposed method from experimentally obtained result, but taking into account simplicity, space and time requirement, this approach may be considered to be a useful alternative method to calculate force and stiffness of a magnetic system. The proposed method is one of the best examples of utilizing an old computational concept in modern complicated problem solution.

Adaptive Dynamic Programming for Decentralized Stabilization of Uncertain Nonlinear Large-Scale Systems With Mismatched Interconnections

This paper presents a novel decentralized control strategy for a class of uncertain nonlinear large-scale systems with mismatched interconnections. First, it is shown that the decentralized controller for the overall system can be represented by an array of optimal control policies of auxiliary subsystems. Then, within the framework of adaptive dynamic programming, a simultaneous policy iteration (SPI) algorithm is developed to solve the Hamilton–Jacobi–Bellman equations associated with auxiliary subsystem optimal control policies. The convergence of the SPI algorithm is guaranteed by an equivalence relationship. To implement the present SPI algorithm, actor and critic neural networks are applied to approximate the optimal control policies and the optimal value functions, respectively. Meanwhile, both the least squares method and the Monte Carlo integration technique are employed to derive the unknown weight parameters. Furthermore, by using Lyapunov’s direct method, the overall system with the obtained decentralized controller is proved to be asymptotically stable. Finally, the effectiveness of the proposed decentralized control scheme is illustrated via simulations for nonlinear plants and unstable power systems.

Cosmographic analysis with Chebyshev polynomials

The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parameterize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Pad\'e series. In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Pad\'e approximations. We thus focus on regions in which convergence of Chebyshev rational functions is better than standard approaches. With this recipe, as high-redshift data are employed, rational Chebyshev polynomials remain highly stable and enable one to derive highly accurate analytical approximations of Hubble's rate in terms of the cosmographic series. Finally, we check our theoretical predictions by setting bounds on cosmographic parameters through Monte Carlo integration techniques, based on the Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic data, using the JLA supernovae sample and the most recent versions of Hubble parameter and baryon acoustic oscillation measurements. We find that cosmography with Taylor series fails to be predictive with the aforementioned data sets, while turns out to be much more stable using the Chebyshev approach.

Nonlinear Kalman Filtering With Divergence Minimization

We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper we propose novel algorithms to optimize the forward and reverse forms of the KL divergence, as well as the alpha-divergence which contains these two as limiting cases. Unlike previous approaches, our algorithms do not make approximations to the divergences being optimized, but use Monte Carlo integration techniques to derive unbiased algorithms for direct optimization. We assess performance on radar and sensor tracking, and options pricing problems, showing general improvement over the UKF and EKF, as well as competitive performance with particle filtering.

The characterization of Monte Carlo errors for the quantification of the value of forensic evidence

ABSTRACTRecent developments in forensic science have lead to a proliferation of methods for quantifying the probative value of evidence by constructing a Bayes Factor that allows a decision-maker to select between the prosecution and defense models. Unfortunately, the analytical form of a Bayes Factor is often computationally intractable. A typical approach in statistics uses Monte Carlo integration to numerically approximate the marginal likelihoods composing the Bayes Factor. This article focuses on developing a generally applicable method for characterizing the numerical error associated with Monte Carlo integration techniques used in constructing the Bayes Factor. The derivation of an asymptotic Monte Carlo standard error (MCSE) for the Bayes Factor will be presented and its applicability to quantifying the value of evidence will be explored using a simulation-based example involving a benchmark data set. The simulation will also explore the effect of prior choice on the Bayes Factor approximations and corresponding MCSEs.

Solution of the Bartels-Kwiecinski-Praszalowicz equation via Monte Carlo integration

We present a method of solution of the Bartels-Kwiecinski-Praszalowicz (BKP) equation based on the numerical integration of iterated integrals in transverse momentum and rapidity space. As an application, our procedure, which makes use of Monte Carlo integration techniques, is applied to obtain the gluon Green function in the odderon case at leading order. The same approach can be used for more complicated scenarios.

Monte Carlo simulation for stochastic calculus of far‐field radiation from open‐ended waveguide arrays

SummaryIn this paper, Monte Carlo (MC) simulation has been applied for the analysis and stochastic calculus of far‐field radiation from the small, large, and infinite open‐ended waveguide arrays. Elements of the arrays are excited by the fundamental TE10 mode and with equal amplitude and linear phase. The simulated results from MC are compared closely with the finite element method (FEM). Numerical analysis based on FEM is performed using Ansoft High Frequency Structural Simulator to calculate the far‐field radiation characteristics of the arrays. The accuracy and the effectiveness of the aforesaid method, which is based on Monte Carlo integration technique, are also demonstrated in uniformly and nonuniformly spaced waveguide arrays for pattern synthesis or achieving side lobe level reduction. The arrays with arbitrary shapes are simply evaluated by MC method in equal spacing array. It is found that by applying MC simulation, the open‐ended waveguide arrays have the ability to produce the desired radiation pattern and could satisfy requirements for many applications. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Hadron fragmentation inside jets in hadronic collisions

We present an analytical next-to-leading order QCD calculation of the partonic cross sections for the process $pp\rightarrow ({\text{jet}} \,h)X$, for which a specific hadron is observed inside a fully reconstructed jet. In order to obtain the analytical results, we assume the jet to be relatively narrow. We show that the results can be cast into a simple and systematic form based on suitable universal jet functions for the process. We confirm the validity of our calculation by comparing to previous results in the literature for which the next-to-leading order cross section was treated entirely numerically by Monte-Carlo integration techniques. We present phenomenological results for experiments at the LHC and at RHIC. These suggest that $pp\rightarrow ({\text{jet}} \,h)X$ should enable very sensitive probes of fragmentation functions, especially of the one for gluons.