Control Variate Method Research Articles

An improved method for statistics estimation of out-of-plane load resistance of masonry walls using design-code models and mechanics-based finite element models

The susceptibility of masonry walls to out-of-plane failure under seismic loading presents a significant engineering concern. In adherence to contemporary limit state design philosophy and as mandated by performance-based design guidelines, it is crucial to accurately estimate statistics parameters such as the mean and variance of out-of-plane resistance. To achieve this, two deterministic models are often considered within the Monte Carlo simulation framework: design-code models, known for their computational efficiency but potential for significant model error, and mechanics-based finite element models, noted for their accuracy but computational intensity. Relying solely on either model for statistics estimation presents challenges due to their respective inherent limitations. This study introduces an improved strategy that synergizes the strengths of both models, resulting in enhanced statistics estimators for the out-of-plane resistance of masonry walls. The proposed methodology involves the use of the control variate method by integrating numerous design-code model evaluations to boost computational efficiency while incorporating a limited number of finite element model evaluations to ensure accuracy. The constructions of the proposed estimators follow rigorous optimization procedures to minimize associated errors and variances. Theoretical derivations are provided for essential elements in the estimator constructions, such as model evaluation numbers for finite element and design-code models and control variate coefficients. Moreover, the accuracy of the proposed estimators is compared with that of the crude Monte Carlo estimator. A key benefit of the proposed estimators is their unbiased nature, and their accuracy is not compromised by the discrepancies between the finite element model and the design-code model. To demonstrate the practicality of these estimators, two case studies are illustrated: one focusing on unreinforced masonry walls and the other on reinforced masonry walls. The results indicate that design-code model-based estimators exhibit large bias, and compared to the estimators that solely rely on the finite element model, the proposed estimators achieve higher accuracy given the same computational budget.

Effects of drilling parameters on stress relief performance during mining

Abstract This study investigated the effects of borehole diameter and borehole interval on the stress relief performance of coal seams during mining. A discrete element numerical model was established based on the Voronoi and block models, and the stress relief performance was investigated in terms of axial stress, vertical displacement, and plastic zone development using the control variates method. The results showed that a decrease in the distance from the workface was accompanied by an increase in the effects of mining, the stress concentration, and the vertical displacement of the roof. Coal mining had positive effects on fracture propagation in front of the workface. As the borehole interval increased, the density of boreholes in the coal seams decreased, reducing the stress concentration and fracture propagation in front of the workface. The stress relief performance of the boreholes in the coal seams was improved at an borehole interval of 8 m. However, as the borehole diameter increased, the stress concentration near the boreholes decreased, reducing the effects of the workface mining on stress relief through the boreholes. Meanwhile, increasing the borehole diameter decreased the vertical displacement of the roof but exacerbated fracture propagation in front of the workface, which improved the stress relief performance of the boreholes in the coal seams. This study provides a reference for arranging boreholes in coal seams during mining.

Improving compressed matrix multiplication using control variate method

The seminal work by Pagh [1] proposed a matrix multiplication algorithm for real-valued squared matrices called Compressed Matrix Multiplication (CMM) having a sparse matrix output product. The algorithm is based on a popular sketching technique called Count-Sketch [2] and Fast Fourier Transform (FFT). For input square matrices A and B of order n and the product matrix AB with Frobenius norm ||AB||F, the algorithm offers an unbiased estimate for each entry, i.e., (AB)i,j of the product matrix AB with a variance bounded by ||AB||F2/b, where b is the compressed bucket size. Thus, the variance will eventually become high for a small bucket size. In this work, we address the high variance problem of CMM with the help of a simple and practical technique based on classical variance reduction methods in statistics. Our techniques rely on the Control Variate (CV) method. We suggest rigorous theoretical analysis for variance reduction and complement it via supporting empirical evidence.

Multi-fidelity reinforcement learning with control variates

In many computational science and engineering applications, the output of a system of interest corresponding to a given input can be queried at different levels of fidelity with different costs. Typically, low-fidelity data is cheap and abundant, while high-fidelity data is expensive and scarce. In this work we study the reinforcement learning (RL) problem in the presence of multiple environments with different levels of fidelity for a given control task. We focus on improving the RL agent’s performance with multifidelity data. Specifically, a multifidelity estimator that exploits the cross-correlations between the low- and high-fidelity returns is proposed to reduce the variance in the estimation of the state–action value function. The proposed estimator, which is based on the method of control variates, is used to design a multifidelity Monte Carlo RL (MFMCRL) algorithm that improves the learning of the agent in the high-fidelity environment. The impacts of variance reduction on policy evaluation and policy improvement are theoretically analyzed by using probability bounds. Our theoretical analysis and numerical experiments demonstrate that for a finite budget of high-fidelity data samples, our proposed MFMCRL agent attains superior performance compared with that of a standard RL agent that uses only the high-fidelity environment data for learning the optimal policy. 22This article is an extended version of a paper originally presented at the ESANN (European Symposium on Artificial Neural Networks) conference in 2023.

Research on Aerodynamic characteristics of Lightweight Spheres Suspended in Vertical Airflow

Experimenting to obtain data about the drag force is usually difficult and expensive. In this paper, an experiment is conducted using a hair dryer as a provision of a controllable airflow, and two ping pong balls as the object in an airflow to find out the factors that affect the stability of an object in an airflow by using the control variate method and use the turbulent jets theory to calculate the drag force. The result of this experiment is that when the balls have the same mass, as the wind speed increases, the vertical stability of the ball becomes better and the horizontal stability becomes better as well. When the wind speed is the same, as the mass of the ball increases, the vertical stability of the ball becomes better. The equations to calculate the drag force are correct and can simulate and calculate the result of the track of an object. The value of this experiment is that it provides an easy way to experiment with the drag force.

Dynamic analysis of a tensegrity-based traction structure

Purpose This study proposes a tensegrity-based traction structure with D-bar dual cable units. It is used to connect the airship and the ground to stabilize the airship.Design/methodology/approach The mathematical models and dynamic models of the D-bar dual cable (hereafter referred to as DD cable) unit of the tensegrity-based traction structure are established. Based on the minimum mass method, the mass of the DD cable unit in the critical state (cable member is yielding, or bar member is buckling or yielding) is analyzed. Then, the tensile strength of the DD cable unit and single cable unit under the same condition is compared using the control variate method. Finally, based on ANSYS dynamic simulation, the stability of the two structures under the same external force disturbance was tested.Findings Expressions for the minimum mass of the DD cable unit under different failure conditions are solved. Dynamic simulation results show that the capacity of resisting disturbance of the DD cable unit is much better than that of the single cable unit under the same wind speed. So, we find a structure more suitable for the fixed connection of an airship.Originality/value This study helps to provide theoretical reference and thinking for the practical application of the traction structure with a D-bar dual cable unit.

New “Walk on Equations” Monte Carlo Algorithm for Linear Systems

A novel version of Monte Carlo algorithm for solving systems of linear algebraic equations is presented and studied. The algorithm is similar to the “Walk on Equations” Monte Carlo method recently developed by Ivan Dimov, Sylvain Maire and Jean Michel Sellier. It is done a comparison with the Gauss-Seidel method for matrices up to size of 212. The algorithm could be drastically improved by choosing appropriate values for the relaxation parameters, which in turn leads to dramatic reduction in time and lower relative errors for a given number of iterations. What is more, a sequential Monte Carlo method of John Halton based on an iterative use of the control variate method has been applied. Some of the most important numerical applications are the large system, coming from a finite element approximation of problems, describing a beam structure in constructive mechanics, and the block-diagonal matrices, which come from discretization of models in a regime-switching economy.

Modified control variates method based on second-order saddle-point approximation for practical reliability analysis

Abstract. A novel method is presented for efficiently analyzing the reliability of engineering components and systems with highly nonlinear complex limit state functions. The proposed method begins by transforming the integral of the limit state function into an integral of a highly correlated limit state function using the control variates method. The second-order reliability method is then employed within the control variates framework to approximate the highly correlated limit state function as a quadratic polynomial. Subsequently, the probability of failure is obtained through the estimation of the saddle-point approximation and a small number of samples generated by Latin hypercube sampling. To demonstrate the effectiveness of the proposed method, four examples involving mathematical functions and mechanical problems are solved. The results are compared with those obtained using the second-order reliability method (SORM), control variates based on Monte Carlo simulation (CVMCS) with second-order saddle-point approximation (SOSPA), importance sampling (IS) and Monte Carlo simulation (MCS). The findings demonstrate that, while maintaining high-precision reliability results, the proposed method significantly reduces the number of evaluations of the limit state function through a small number of initial samples. The method is capable of efficiently and accurately solving complex practical engineering reliability problems.

Reliability analysis of regenerative chatter stability in turning tool systems by modified control variate method

Reliability analysis of regenerative chatter stability in turning tool systems by modified control variate method

DETERMINING THE VALUE OF DOUBLE BARRIER OPTION USING STANDARD MONTE CARLO, ANTITHETIC VARIATE, AND CONTROL VARIATE METHODS

In this paper, we applied the standard Monte Carlo, antithetic variate, and control variates methods to value the double barrier knock-in option price. The underlying asset used in the calculation of double barrier knock-in option is the share of ANTM from April 1, 2019 until March 1, 2022. The value of the double barrier knock-in option is simulated using standard Monte Carlo, antithetic variate, and control variates methods. The results showed that all the methods converge to the exact solution, with the control variate method to be the fastest. Standard Monte Carlo method has the least computational time, followed by control variate and antithetic variate method. Compared to the other methods, control variate is the most effective and efficient in determining the value of double barrier knock-in option, based on the option value, relative error and computational time. Antithetic variate method converges faster to the exact solution compared to standard Monte Carlo. However it has the longest computation time compared to the other methods.

Multi-parameters study on underwater coil launch

The projectile launched by electromagnetic weapon has strong kinetic energy. In order to study the laws and characteristics of electromagnetic induction coilgun launching underwater, a multi-stage coilgun model was established in this paper. Based on the control variates method, the effects of trigger position, coil turns, capacitance value and other parameters on the launching process were studied, then the effects of above factors on the launching efficiency and exit speed were analyzed. The results show that the optimal trigger position offsets to the direction of the breech with the increase of the projectile speed; the optimal coil turns for a certain projectile and launching occurs when the trigger position is determined; the increase of the capacitance value can increase the exit speed of projectile, and the capacitance value should be selected according to the efficiency-speed curve when the launch efficiency is considered; the seawater resistance has little influence on the acceleration of the projectile, and comparatively large influence when there is no driving force. The research results of this paper can provide theoretical support for the manufacture of underwater coilgun prototype.

Revealing Variable Dependences in Hexagonal Boron Nitride Synthesis via Machine Learning.

Wafer-scale monolayer two-dimensional (2D) materials have been realized by epitaxial chemical vapor deposition (CVD) in recent years. To scale up the synthesis of 2D materials, a systematic analysis of how the growth dynamics depend on the growth parameters is essential to unravel its mechanisms. However, the studies of CVD-grown 2D materials mostly adopted the control variate method and considered each parameter as an independent variable, which is not comprehensive for 2D materials growth optimization. Herein, we synthesized a representative 2D material, monolayer hexagonal boron nitride (hBN), on single-crystalline Cu (111) by epitaxial chemical vapor deposition and varied the growth parameters to regulate the hBN domain sizes. Furthermore, we explored the correlation between two growth parameters and provided the growth windows for large flake sizes by the Gaussian process. This new analysis approach based on machine learning provides a more comprehensive understanding of the growth mechanism for 2D materials.

Open-Circuit Fault-Tolerant Vector Control for Five-Phase SPMSM Based on Five-Phase Six-Leg Inverter

Five-phase permanent-magnet synchronous motor (PMSM) has the ability of fault-tolerant operation, which is beneficial for high reliability occasions. A fault-tolerant current vector control strategy based on five-phase six-leg inverter is proposed for open-circuit fault in this article. It deals with single-, double-, and triple-phase fault conditions. First, the overall control scheme is established based on the mathematical model of five-phase surface-mounted PMSM. To release more control degrees of freedom, the constraint for the sum of fault-tolerant phase currents is removed, and the control variates method is used to calculate the optimal fault-tolerant currents. Furthermore, to achieve the current tracking, the corresponding reduced-order current transformation matrices are derived, and the corresponding main power topology, the five-phase six-leg voltage source inverter (VSI), is established. The unbalanced operation of the topology is investigated, the equivalence to the full-bridge VSI is proved, and the voltage utilization and voltage unbalance of five phase half-bridge, full-bridge, and six-leg inverter are compared. Then, the corresponding carrier-based PWM control strategy based on zero-sequence injection has been proposed, which is equivalent with the three-dimensional space vector PWM algorithm and is computationally efficient. The experimental results confirm the effectiveness of the proposed fault-tolerant control strategy.

Joint Physical Layer Frame Optimization and Carrier Synchronization for Satellite Communications

In this paper, we discuss general data-framing and optimization, parallel frequency-phase estimation, and powerful frequency estimator for satellite communications. Based on the standard pilot-symbol-assisted-modulation (S-PSAM) frame, we design a general PSAM (G-PSAM) frame, whose corresponding data-aided & non-data-aided Cramér-Rao bound (DA&NDA CRB) is derived with respect to carrier frequency offset, time delay and phase offset, followed by its approximate form. Also, we provide a simple solution to the G-PSAM frame optimization by means of the approximate DA&NDA CRB and the control-variate method. With an unbiased auto-correlation (AC) value, we then propose a frequency-phase decoupler and develop a parallel frequency-phase estimation (PFPE) mode in terms of the serial frequency-phase estimation (SFPE) mode, where a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">serial-to-parallel</i> estimation conversion can be implemented. Furthermore, we extend the AC frequency estimator in the PFPE mode as a powerful stepwise correlation-based one aiming at the target performance. Theoretical analysis and numerical results are provided to show the superiority of the optimized frames, the robustness of the PFPE mode, and the adaptability of the proposed frequency estimator with the optimized frames under different transmission systems.

Fashion-MNIST Classification Based on CNN Image Recognition

Image classification is an important part of Artificial Intelligence (AI) and involves several tasks such as image normalization, image segmentation, feature extraction etc. Convolutional Neural Network (CNN) has been proved to be an effective network in image classification. According to this study, we had used a relatively small dataset named Fashion-MNIST (i.e. 70,000 images, 10 categories) to find out the model that can have a higher accuracy with limited training samples. We have trained three classic CNN models which are DenseNet121, MobileNet, ResNet 50 respectively. After that, we comprehensively measured the performance by several norms that comes from these three different models. Finally, we had a conclusion on which could be the most efficient one in this scenario based on the test results, in order to discovery which models are the most powerful one, and worth training. Human always deal with many types of images, so people need a powerful AI to help them to recognize and categorize these images. After this study, the DenseNet121 is the most powerful model in these three - DenseNet121, MobileNet, ResNet 50, the method to determine this result is that in the whole study we used a method called control variate method, we use the same amount of images, same amount of training times, then compared the final output of these three models, in the end we discovered that the DenseNet121 is the most powerful one.

Economic Representative Scenarios for Variable Annuity Dynamic Hedging of GMMB and GMDB

Variable annuities introduce significant risk for the insurers. To control this risk, insurers generally use dynamic hedging models. In practice, calculations for dynamic hedging models for variable annuities are computationally intensive since they require many nested stochastic scenario projections with outer and inner loops. In this article, we study the relationship between the hedging errors and the descriptive statistics of economic scenarios. Then, using the relationships between the hedging errors and the descriptive statistics of the economics scenarios, we present two novel scenario selection algorithms to determine economic representative scenarios (ERS) to run for dynamic risk hedging models. We do this for guaranteed minimum maturity benefit (GMMB) and guaranteed minimum death benefit (GMDB). We also benchmark these new algorithms against a control variate algorithm and Monte Carlo simulations. One of the two proposed novel scenario selection algorithms, the adapted Clara algorithm gives a lower mean absolute deviation of the conditional tail expectation (CTE) than the control variate method and Monte Carlo simulations for the same number of scenarios. Also, 500 representative scenarios selected by the adapted Clara algorithm generate a mean absolute deviation of the CTE95 of the hedging errors approximately equivalent to 1000 (or more in some cases) Monte Carlo simulations for 5 years GMMB and GMDB.

A general control variate method for time-changed Lévy processes: an application to options pricing

A general control variate method for time-changed Lévy processes: an application to options pricing

Variance reduction in feature hashing using MLE and control variate method

Variance reduction in feature hashing using MLE and control variate method

Optimization of urban rail transit station spacing for minimizing passenger travel time

Urban rail transit, regarded as the backbone of urban public transportation, can effectively solve the problems of urban traffic congestion and automobile exhaust pollution. However, due to improper planning, unreasonable station location often appears, which seriously affects the service access and mobility of rail transit. In order to improve the station spacing and passenger transport efficiency, a calculation model of station spacing for minimizing passenger travel time was established. In order to enhance the adaptability of the model in different cities, the grid road network and radial road network are considered when establishing the model. The results show that the station spacing is related to the passenger access/egress speed, the passenger travel distance, the maximum train running speed, the train stop time and the train acceleration. The influence of these parameters on the station spacing is obtained through the control variate method, and there are indeed obvious differences under different road network conditions. The research results can provide theoretical reference for station planning of new lines. Since the station spacing of the operated lines cannot be changed, this study can provide reference for skip-stop operation.

Post-Processing 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 post-processed 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 post-processing Markov chain output. Our review covers methods based on discrepancy minimisation, which directly address the bias-variance trade-off, as well as general-purpose control variate methods for approximating expected quantities of interest.