Control Variate Method Research Articles

Preliminary design, thermodynamic analysis and optimization of a novel carbon dioxide based combined power, cooling and distillate water system

The problems of power difficulty, hot weather, and distillate water shortage on the island platform have seriously affected people's production and life. Constructing a multi-energy supply system is an effective method to solve the above problems. Hence, a novel system combined power, cooling and distillate water system is proposed in this paper. The proposed system includes supercritical carbon dioxide recompression Brayton cycle, absorption refrigeration cycle, and multi-effect desalination. According to the energy, mass, and salt balance, the thermodynamic model is established. With the application of the control variate method, the influences of five key variables on the proposed system performance are analyzed. Parametric analysis results reveal that the decrease of compressor pressure ratio or the increase of turbine inlet temperature and heat-end temperature difference in generator contributes to the design thermodynamic performance. In addition, the performance of the proposed system and the stand-alone supercritical carbon dioxide recompression Brayton cycle is compared under the base design case. The proposed system can gain improvements by 4.02% for exergy efficiency and 52.51% for energy utilization factor in comparison with the stand-alone supercritical carbon dioxide recompression Brayton cycle. At the same time, the proposed system can generate 101.8 MW of cooling capacity and 25334 m3/day of distillate water production. Furthermore, objective optimization using a genetic algorithm is carried out to obtain the optimal design performance for the proposed system and stand-alone supercritical carbon dioxide recompression Brayton cycle. The energy utilization factor and exergy efficiency of the proposed system are 49.83% higher and 3.49% higher than those of supercritical carbon dioxide recompression Brayton cycle under the optimal conditions. Finally, this study can provide a new idea for improving the design and performance of power, cooling and distillate water combined system for island platforms.

Experimental and theoretical analysis of large particle\u2013wall collision with different metal plates

The coefficients of restitution are important parameters in the study of particle–wall collision, which is widely used in discrete element modeling in solid–liquid multiphase systems. To improve the accuracy of numerical simulations, correspondingly exact particle–wall collision parameters are needed. The current models used in numerical simulation, however, are mostly suitable for solid–gas systems, in which collision models used to be micro-sized. Millimeter-size particle–wall collision models in wet experimental conditions and research on the influence of plate materials were lacking. In this study, we designed an experimental system focused on the different materials of the particles and collision plates and the dry or wet experimental environment to discuss the change of restitution coefficients in various conditions. We selected millimeter-sized iron 45 particles and glass particles, which represented plastic material and hard brittle material, respectively. We also selected three industrial metals, HT250 gray cast iron, 6061 aluminum alloy, and 316 stainless steel, which are commonly used in hydraulic machinery, for the collision plates. Experiments were performed to measure the incident and rebound velocities of the particle at various impact angles. In this paper, we have provided and compared the results of restitution coefficients of velocity and angle varying with the approach angle. In the processing of the experiment, we used the control variate method and applied an ultra-depth of field three-dimensional microscope to scan the surface of the collision plate. In the analysis of the experimental results, single particle–wall collision was seen as a non-smooth dynamical system to discuss the specific phenomenon. Finally, we obtained the relationship between the restitution of normal velocity and elastic elements of materials and explained the relationship of stick–slip motion with the approach angle and velocity.

Enhancement of applicability of high-efficiency random sampling method using control variates method and sensitivity coefficients

ABSTRACT The CV-S method is a high-efficiency random sampling method to estimate statistical moments of random variables, and it uses an approximated target parameter which are linearly dependent on input as a mockup parameter. In order to enhance the applicability of the CV-S method, we propose to use a mockup parameter which is different from but similar to a target parameter and whose sensitivity coefficients are available. In the present work, nuclear fuel burnup problems are concerned, and standard deviation of k∞ and nuclide number densities at certain fuel burnup are estimated by the CV-S method. Through numerical tests, it is clearly demonstrated that even if sensitivity coefficients of non burnup-related parameters in a simple system like a fuel pin-cell are used as the mockup, the CV-S method has a potential to efficiently estimate statistical moments of burnup-related parameters in a complicated system like a fuel assembly.

A new efficient approximation scheme for solving high-dimensional semilinear PDEs: Control variate method for Deep BSDE solver

This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs). First, we decompose a target semilinear PDE (BSDE) into two parts, linear PDE part and nonlinear PDE part. Then, we employ a Deep BSDE solver with a new control variate method to solve those PDEs, where approximations based on an asymptotic expansion technique are effectively applied to the linear part and also used as control variates for the nonlinear part. Moreover, our theoretical result indicates that errors of the proposed method become much smaller than those of the original Deep BSDE solver. Finally, we show numerical experiments to demonstrate the validity of our method, which is consistent with the theoretical result in this paper.

MEAN-FIELD CONTROL VARIATE METHODS FOR KINETIC EQUATIONS WITH UNCERTAINTIES AND APPLICATIONS TO SOCIOECONOMIC SCIENCES

In this paper, we extend a recently introduced multi-fidelity control variate for the uncertainty quantification of the Boltzmann equation to the case of kinetic models arising in the study of multiagent systems. For these phenomena, where the effect of uncertainties is particularly evident, several models have been developed whose equilibrium states are typically unknown. In particular, we aim to develop efficient numerical methods based on solving the kinetic equations in the phase space by Direct Simulation Monte Carlo (DSMC) coupled to a Monte Carlo sampling in the random space. To this end, exploiting the knowledge of the corresponding mean-field approximation we develop novel mean-field Control Variate (MFCV) methods that are able to strongly reduce the variance of the standard Monte Carlo sampling method in the random space. We verify these observations with several numerical examples based on classical models , including wealth exchanges and opinion formation model for collective phenomena.

Utilizing artificial neural network to simulate and predict the hydraulic performance of free water surface constructed wetlands

Optimizing the hydraulic performance of free water surface constructed wetlands (FWS CWs) is of great economic and ecological value. However, there is a complex nonlinear relationship between the hydraulic performance and design parameters of FWS CWs. In this study, an artificial neural network (ANN) was applied to simulate and predict the hydraulic performance corresponding to different combinations of design parameters, and orthogonal design L9 (34) was used to determine the optimal combination of the important hyperparameters of the ANN. Based on the convenient scenario prediction ability of ANN, sensitivity analysis of different design parameters was carried out by the control variate method and full factor experiment. The results showed that the combination of 3 hidden layers, 15 neural nodes in each hidden layer, 0.001 learning rate, and 8 batch sizes was optimal for the established ANN model, achieving a coefficient of determination of 0.828 in the validation set and a satisfactory prediction effect in the test set. The narrow feature distribution interval in the training set restricted the generalization ability of the ANN model to some extent. Of the four continuous design parameters, the water depth and aspect ratio had an important influence on the effective volume ratio. The layout of inlet and outlet was the most influential design parameter, as confirmed by the full factor experiment of five factors and four levels. The established ANN allowed real-time implementation in an extended scenario at a low cost. This study suggests that the ANN can simultaneously project complex and uncertain effects of several design parameters on wetland performance. In future research, acquiring further comprehensive, impartial, and unbiased experimental datasets is necessary to establish a more robust and generalizing ANN model that can guide the optimal design of FWS CWs.

ANALISIS RISIKO PORTOFOLIO MENGGUNAKAN METODE SIMULASI MONTE CARLO CONTROL VARIATES

Value at Risk (VaR) is a method to measure the maximum loss with a certain level of confidence in a certain period. Monte Carlo simulation is the most popular method of calculating VaR. The purpose of this study is to demonstrate control variates method as a variance reduction method that can be applied to estimate VaR. Moreover, it is to compare the results with the normal VaR method or analytical VaR calculation. Control variates method was used to find new returns from all stocks which are used as estimators of the control variates. The new returns were then used to define parameters needed to generate N random numbers. Furthermore, the generated numbers were used to find the VaR value. The method was then applied to estimate a portfolio of the game and esports company stocks that are EA, TTWO, AESE, TCEHY, and ATVI . The results show Monte Carlo simulation gives VaR of US$41.6428 within 1000 simulation, while the analytical VaR calculation or normal VaR method gives US$30.0949.

Postprocessing of MCMC

Markov chain Monte Carlo is the engine of modern Bayesian statistics, being used to approximate the posterior and derived quantities of interest. Despite this, the issue of how the output from a Markov chain is postprocessed and reported is often overlooked. Convergence diagnostics can be used to control bias via burn-in removal, but these do not account for (common) situations where a limited computational budget engenders a bias-variance trade-off. The aim of this article is to review state-of-the-art techniques for postprocessing Markov chain output. Our review covers methods based on discrepancy minimization, which directly address the bias-variance trade-off, as well as general-purpose control variate methods for approximating expected quantities of interest.

An adaptive prediction method for mechanical properties deterioration of sandstone under freeze\u2013thaw cycles: a case study of Yungang Grottoes

Due to the location of the Yungang Grottoes, freeze–thaw cycles contribute significantly to the degradation of the mechanical properties of the sandstone. The factors influencing the freeze–thaw cycle are classified into two categories: external environmental conditions and the inherent properties of the rock itself. Since the parameters of rock properties are inherent to each rock, the effect of rock properties on freeze–thaw degradation cannot be investigated by the control variates method. An adaptive multi-output gradient boosting decision trees (AMGBDT) algorithm is proposed to fit nonlinear relationships between mechanical properties and physical factors. The hyperparameters in the GBDT algorithm are set as variables, and the Sequential quadratic programming (SQP) algorithm is applied to solve the hyperparameter optimization, which means finding the maximum Score. The case study illustrates that the AMGBDT algorithm can precisely determine the effect of each independent factor on the output. The patterns of mechanical properties are similar when the number of freeze–thaw cycles and porosity are used as variables separately and when both are used simultaneously. The uniaxial compressive strength decay rate is positively correlated with the number of freeze–thaw cycles and porosity. The modulus of elasticity is negatively correlated with the number of freeze–thaw cycles and porosity. The results show that the number of freeze–thaw cycles is the main factor influencing the freeze–thaw cycling action, and the porosity is minor. In addition, the fitting accuracy of the AMGBDT algorithm is generally higher than neural networks (NN) and random forests (RF). Studying the influence of porosity and other rock properties on the freeze–thaw cycle will help to understand the failure mechanism of rock freeze–thaw cycles.

On Multilevel and Control Variate Monte Carlo Methods for Option Pricing under the Rough Heston Model

The rough Heston model is a form of a stochastic Volterra equation, which was proposed to model stock price volatility. It captures some important qualities that can be observed in the financial market—highly endogenous, statistical arbitrages prevention, liquidity asymmetry, and metaorders. Unlike stochastic differential equation, the stochastic Volterra equation is extremely computationally expensive to simulate. In other words, it is difficult to compute option prices under the rough Heston model by conventional Monte Carlo simulation. In this paper, we prove that Euler’s discretization method for the stochastic Volterra equation with non-Lipschitz diffusion coefficient E[|Vt−Vtn|p] is finitely bounded by an exponential function of t. Furthermore, the weak error |E[Vt−Vtn]| and convergence for the stochastic Volterra equation are proven at the rate of O(n−H). In addition, we propose a mixed Monte Carlo method, using the control variate and multilevel methods. The numerical experiments indicate that the proposed method is capable of achieving a substantial cost-adjusted variance reduction up to 17 times, and it is better than its predecessor individual methods in terms of cost-adjusted performance. Due to the cost-adjusted basis for our numerical experiment, the result also indicates a high possibility of potential use in practice.

Study on heat transfer characteristics of regenerative shell-and-tube heat exchangers

A new type of regenerative shell-and-tube heat exchanger is designed to solve the problems that the generation load of cogeneration units is limited by the amount of heat supply during the heating period, the peak shaving capacity of units decreases, and the phenomenon of wind and light abandonment in the power system is serious. Considering the advantages of nearly constant temperature and large potential heat release during the heat storage/release process ofphase change materials, paraffin is selected as the phase change material, and the phase change area of the heat exchanger is selected as the heat exchange unit. The control variates method is used to simulate the heat storage/release process of the heat exchange unit according to the key factors such as the flow rate of heat transfer fluid, the thermal conductivity of phase change materials and the thickness of phase change layer. The results show that increasing the flow rate of heat transfer fluid can enhance the heat storage capacity of the heat exchange unit and shorten the complete melting time of phase change materials. In order to control the heat at the output end of the heat exchanger during the heat release process, the flow rate of heat transfer fluid should be appropriately selected; using composite materials to improve the thermal conductivity of phase change materials can enhance the heat transfer capacity of the heat exchange unit, and the average heat transfer coefficient of the heat exchange unit is more than 2 times higher than that of pure paraffin at the same heat transfer fluid flow rate; increasing the thickness of phase change layer can prolong the time of maintaining the outlet temperature of heat transfer fluid in the process of heat release.

Stock Option Pricing by Augmented Monte-Carlo Simulation models

Studying stock options is still a pristine area of research in the Iranian capital market. This is due to the lack of data as well as the complexity of valuation methodologies. In the present paper, using the Monte-Carlo simulation, we have estimated the value of stock options traded on Tehran Stock Exchange and examined whether the use of a control variate or antithetic variate augmented methods can lower the standard error of estimates. Furthermore, the estimated values of the three models under consideration, including crude Monte-Carlo, control variates augmented Monte-Carlo, and antithetic variates augmented Monte-Carlo are compared with each other and with options market prices. The results show that the standard error of the antithetic variate method is less than the crude method and control variate method. However, the control variate augmented Monte-Carlo model is more powerful than the crude Monte-Carlo and antithetic variate augmented Monte-Carlo method. Therefore, we can conclude that the control variate augmented Monte-Carlo model has a better performance in estimating the value of trading stock options and its estimated values are closer to the market prices.

One-pot synthesis of carbon fiber/carbon nanotube hybrid using lanthanum (III) chloride for tensile property enhancement of epoxy composites

This study presents a one-pot method for facile synthesis of carbon fiber (CF) / carbon nanotube (CNT) hybrid, which is achieved by the surface reaction of CF and carboxylated carbon nanotubes (CNT-COOH) in the eco-friendly lanthanum (III) chloride (LaCl3)-urea-ethanol solution. The control variate method is utilized to investigate the formation mechanism of the CF/CNT hybrid. Based on the scanning electron microscopy, X-ray powder diffraction, Fourier transform infrared and X-ray photoelectron spectroscopy results, it is found that La (III) coordinates with two or more atoms from different material surface so as to link different material, and urea serves as lone electron pair donor to provide extra binding sites for La (III), then both La (III) and urea play the role of bridge to connect CF and CNT-COOH. The prepared CF/CNT hybrid improves the tensile strength (modulus) of epoxy composites by 59.0% (78.5%), and corresponding improving mechanism has been revealed. The one-pot synthesis of CF/CNT hybrid is convenient, eco-friendly and thus suitable for green industrial application.

Research on non-intrusive load disaggregation method based on multi-model combination

Non-Intrusive Load Monitoring (NILM) technology is used to obtain the detail of household electricity consumption by analyzing total electricity consumption data without installation of any sensors. It is of great significance to power demand-side management. A new load disaggregation method based on combinatorial optimization is proposed in this paper. Firstly, the particle swarm optimization (PSO) algorithm is improved by applying time probability to the fitness function. Meanwhile, the iterative process of PSO is constrained to avoid falling into local optimal solution. The improvement is verified by experiments on the Reference Energy Disaggregation Data Set (REDD). And then, on the basis of a single model and with the idea of ensemble learning, this paper studies the multi-model combination load disaggregation method that combines the improved PSO mentioned above, integer programming (IP) algorithm and delta feature (DF) model in parallel, and the experimental group is designed through the control variate method. Experimental results show that the multi-model combination method has a good performance with a high average accuracy of 87% for load disaggregation.

The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model

This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black–Scholes (BS) volatility, we instead derive the equivalent constant-elasticity-of-variance (CEV) volatility. Our approach effectively reduces the approximation error in a way similar to the control variate method because the CEV model is the zero vol-of-vol limit of the SABR model. Moreover, the CEV volatility approximation yields a finite value at a zero strike and thus conveniently leads to a small-time asymptotics for the mass at zero. The numerical results compare favorably with the BS volatility approximations in terms of the approximation accuracy, small-strike volatility asymptotics, and no-arbitrage region.

A generalized multi-fidelity simulation method using sparse polynomial chaos expansion

The polynomial chaos expansion (PCE) method has received considerable attention in uncertainty quantification (UQ). Nevertheless, it is well known that the computational cost of PCE becomes expensive, or even unaffordable for high-dimensional problems (i.e., curse of dimensionality). To alleviate the computational burden, many multi-fidelity PCE methods have been proposed, which work by approximating the high-fidelity (HF) model with the sum of a low-fidelity (LF) model and a correction function. Although the current multi-fidelity PCE methods have proven to be effective in the examples they tested, their accuracy has a strong dependence on the LF model selection. Aimed at this issue, we develop a generalized multi-fidelity PCE (GMF-PCE) using the control variate method. Specifically, an adjustable coefficient is assigned to the LF model and its optimal value is theoretically derived. Furthermore, a flexible yet still simple enough way is provided to implement the developed method, i.e., the sparse PCE based on the least angle regression (LAR) is employed to approximate the LF model, and then the subset of LF-PCE expansion is automatically detected using LAR and corrected via HF computations. Two classic algebraic examples for UQ, namely the borehole problem and the Ishigami function, as well as an unsaturated flow and heat transport problem are used to examine the performance of GMF-PCE. The results show that with the same computational cost, GMF-PCE can achieve much higher accuracy compared to the sparse LAR-based PCE and MF-PCE (non-generalized version).

Accurate Structural Reliability Analysis Using an Improved Line-Sampling-Method-Based Slime Mold Algorithm

Line sampling (LS) is a robust and powerful simulation technique to reduce the computational burden provided by Monte Carlo simulation (MCS) for the reliability analysis of engineering structures. However, when dealing with highly nonlinear and implicit limit-state functions, LS yields instable results as nonconvergence or divergence. In this study, a novel framework that integrates the LS method with the slime mold algorithm (LS-SMA) is proposed to solve complex structural reliability problems. SMA is a new metaheuristic population-based algorithm inspired by the behavior and morphological changes in slime molds that can well solve multivariable optimization problems. In the proposed method, the determination of the important direction of LS is formulated as an unconstrained optimization problem according to the LS theory. Then SMA is employed to solve this optimization problem to decrease the computational cost. Thus, the LS-SMA is able to overcome the drawbacks of LS such as the local convergence and divergence. Seven numerical problems were utilized to investigate the LS-SMA applicability, where its performance was compared with MCS, subset simulation (SS), importance sampling (IS), LS, first-order reliability method (FORM), and first-order control variate method (FOCM). The results demonstrate that the proposed LS-SMA can be applied with high efficiency for solving the reliability problems that involve highly nonlinear or dimensional and complex implicit limit-state functions.

An Efficient Frame Optimization Scheme for Low Power Wide Area Networks

In order to support low power wide area networks (LPWANs) with a scarce pilot resource, we discuss the data framing and its corresponding optimization problem. In specific, we design a general pilot-symbol-assisted-modulation (G-PSAM) frame based on the standard PSAM (S-PSAM) frame and derive joint data-aided & non-data-aided Cramer-Rao bounds (DA&NDA CRBs) for carrier frequency offset (CFO), phase offset (PO), and time delay estimation, followed by an approximate DA&NDA CRB for the CFO. With the approximate DA&NDA CRB and the well-known control-variate method (CVM), we then provide an efficient G-PSAM frame optimization scheme, which is asymptotically optimal in terms of the mean-squared-error (MSE) performance. Simulation results show the superiority of the optimized G-PSAM frame over the S-PSAM frame for both the short-packet and long-packet transmissions. Meanwhile, we also present an example verification on the joint DA&NDA aided carrier synchronization (i.e., Turbo synchronization).

A Control Variate Method Driven by Diffusion Approximation

AbstractIn this paper we introduce a control variate estimator for a quantity of interest that can be expressed as the expectation of a function of a random process, that is itself the solution of a differential equation driven by fast mean‐reverting ergodic random forces. The control variate is built with the same function and with the limit diffusion process that approximates the original random process when the mean reversion time of the driving forces goes to 0. We propose a coupling of the original process and the limit diffusion process that gives a control variate estimator with small variance. We show that the correlation between the two processes indeed goes to 1 when the mean reversion time goes to 0 and we quantify the convergence rate, which allows us to characterize the variance reduction of the proposed control variate estimator. The efficiency of the method is illustrated on a few examples. © 2021 Wiley Periodicals LLC.

Geometric modeling of Holocene large-river delta growth patterns, as constrained by environmental settings

Topographic/bathymetric conditions of the continental shelf can significantly influence the long-term growth of river deltas. In particular, these conditions constrain the accommodation space for sedimentation in the deltaic areas. In this study, we use a conceptual geometric model to evaluate the role played by this factor, on the basis of the principle of mass conservation. The Ganges-Brahmaputra, Mekong and Nile deltas are examined as three typical examples, in terms of their different original seabed morphologies. The control variate method is applied to eliminate the effect of the difference in model input variables. The results show that, assuming a constant sediment load, the delta growth rate will decrease with time; a higher value of the original seabed slope leads to a lower shoreline progradation rate for the subaerial delta and a higher growth rate for the subaqueous delta. Thus, the original seabed morphology represented by slope is a critical factor affecting the evolution of Holocene large-river deltas. These results explain the interrelationships between sediment load, deltaic plain area, and the original seabed slopes for the 27 large-river deltas worldwide, located in the middle/low latitudes, with different tectonic backgrounds. In the future, the conceptual geometric model may be combined with sediment dynamic modeling to identify more details of the evolution of these deltas.