Variate Method Research Articles

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.

Disturbance Detection of a Power Transmission System Based on the Enhanced Canonical Variate Analysis Method

Aiming at the characteristics of dynamic correlation, periodic oscillation, and weak disturbance symptom of power transmission system data, this paper proposes an enhanced canonical variate analysis (CVA) method, called SLCVAkNN, for monitoring the disturbances of power transmission systems. In the proposed method, CVA is first used to extract the dynamic features by analyzing the data correlation and establish a statistical model with two monitoring statistics T2 and Q. Then, in order to handling the periodic oscillation of power data, the two statistics are reconstructed in phase space, and the k-nearest neighbor (kNN) technique is applied to design the statistics nearest neighbor distance DT2 and DQ as the enhanced monitoring indices. Further considering the detection difficulty of weak disturbances with the insignificant symptoms, statistical local analysis (SLA) is integrated to construct the primary and improved residual vectors of the CVA dynamic features, which are capable to prompt the disturbance detection sensitivity. The verification results on the real industrial data show that the SLCVAkNN method can detect the occurrence of power system disturbance more effectively than the traditional data-driven monitoring methods.

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 method combining ELM and PLSR (ELM-P) for estimating chlorophyll content in rice with feature bands extracted by an improved ant colony optimization algorithm

Using spectral information to detect chlorophyll content in rice canopy leaves quickly, non-destructively and accurately has a great practical significance for rice growth evaluation, precise fertilization and scientific management. In this paper, Japonica rice in northeast China is taken as the research object, and rice canopy hyperspectral data of key growth stages are obtained through plot experiments. Firstly, the standard normal variate (SNV) and SG smoothing method is used to preprocess the hyperspectral data, and based on the processed spectral data and ant colony optimization algorithm (ACO), an improved adaptive updating ant colony optimization algorithm (AU-ACO) is proposed to select feature bands of chlorophyll content by introducing an adaptive adjustment strategy of volatilization coefficient and optimal pheromone updating strategy in different stages, and compared with the standard ACO algorithm and full-band modeling method. Then, taking the extracted feature band and full-band as input, considering the advantages of linear model and nonlinear model, a hybrid prediction model (ELM-P) combining extreme learning machine (ELM) with partial least squares regression (PLSR) is proposed. In this model, PLSR is used to obtain the preliminary prediction of the chlorophyll content in rice, and the linear trend is obtained, and then the ELM with strong nonlinear approximation ability is used to predict the deviation of PLSR model, the final prediction value is obtained by superposition of the two outputs. In order to verify the superiority of the proposed model, PLSR and ELM prediction models are also established by taking the full-band and the feature bands by different extraction methods as input. The simulation experiment results show that under the same prediction model conditions, the feature bands extracted by proposed AU-ACO algorithm as input can reduce the complexity of the model and improve the prediction performance of the model. The determination coefficient (R2-P) of testing set and the determination coefficient (R2-C) of training set for each model are greater than 0.6785, among them, the ELM-P model with the feature band extracted by AU-ACO algorithm as input has the highest prediction accuracy, R2-C and R2-P are 0.7969 and 0.7918 respectively, RMSE-C and RMSE-P are 1.2969 and 1.1293 mg/L respectively, which can provide valuable reference for detecting and evaluating chlorophyll content in Japonica rice.

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).

ON-LINE DETECTION OF CERASUS HUMILIS FRUIT BASED ON VIS/NIR SPECTROSCOPY COMBINED WITH VARIABLE SELECTION METHODS AND GA-BP MODEL

In order to realize the rapid and non-destructive detection of fresh Cerasus Humilis’ (CH) classification, and promote the deep-processing of post-harvest fresh fruit and improve market competitiveness, this study proposed a nonlinear identification method based on genetic algorithm (GA) optimized back propagation (BP) neural network of different varieties of fresh CH fruit. “Nongda-4”, “Nongda-5”, and “Nongda-7” fresh CH fruit were selected as research objects to collect their visible/near-infrared spectral data dynamically. The original spectra were preprocessed by moving smoothing (MS) and standard normal variate (SNV) methods, for the characteristic wavelengths were extracted with four dimension-reducing methods, namely principal components analysis (PCA), competitive adaptive reweighed sampling (CARS), CARS-mean impact value (CARS-MIV), and random frog (RF) algorithm. Finally, the BP prediction models were established based on full-spectrum and characteristic wavelengths. At the same time, the GA optimization was used to optimize the initial weight and threshold of the BP neural network and compared with the partial least squares’ discrimination analysis (PLS-DA) linear model. Through comparing the MS (7)+SNV was proved to be the best preprocessing method, the CARS-MIV-GA-BP model had the best discriminant accuracy, the prediction set accuracy was 98.76%, of which the variety “Nongda-4” and “Nongda-5” recognition rate were 100%, the variety “Nongda-7” recognition rate was 96.29%. The results show that the GA can effectively optimize the initial weights and threshold randomization of the BP neural network, improve the discrimination accuracy of CH varieties, and the CARS-MIV algorithm can effectively reduce the number of input nodes of the BP neural network model, simplify the structure of BP neural network. This study provides a new theoretical basis for the detection of fresh CH fruit classification.

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.

Simultaneous quantification of chemical constituents in matcha with visible-near infrared hyperspectral imaging technology

This study aimed to assess the feasibility of identifying multiple chemical constituents in matcha using visible-near infrared hyperspectral imaging (VNIR-HSI) technology. Regions of interest (ROIs) were first defined in order to calculate the representative mean spectrum of each sample. Subsequently, the standard normal variate (SNV) method was applied to correct the characteristic spectra. Competitive adaptive reweighted sampling (CARS) and bootstrapping soft shrinkage (BOSS) were used to optimize the models. They were built based on partial least squares (PLS), creating two models referred to as CARS-PLS and BOSS-PLS. The BOSS-PLS models achieved best predictive accuracy, with coefficients of determination predicted to be 0.8077 for caffeine, 0.7098 for tea polyphenols (TPs), 0.7942 for free amino acids (FAAs), 0.8314 for the ratio of TPs to FAAs, and 0.8473 for chlorophyll. These findings highlight the potential of VNIR-HSI technology as a rapid and nondestructive alternative for simultaneous quantification of chemical constituents in matcha.

Identification of Weeds Based on Hyperspectral Imaging and Machine Learning.

Weeds can be major environmental and economic burdens in New Zealand. Traditional methods of weed control including manual and chemical approaches can be time consuming and costly. Some chemical herbicides may have negative environmental and human health impacts. One of the proposed important steps for providing alternatives to these traditional approaches is the automated identification and mapping of weeds. We used hyperspectral imaging data and machine learning to explore the possibility of fast, accurate and automated discrimination of weeds in pastures where ryegrass and clovers are the sown species. Hyperspectral images from two grasses (Setaria pumila [yellow bristle grass] and Stipa arundinacea [wind grass]) and two broad leaf weed species (Ranunculus acris [giant buttercup] and Cirsium arvense [Californian thistle]) were acquired and pre-processed using the standard normal variate method. We trained three classification models, namely partial least squares-discriminant analysis, support vector machine, and Multilayer Perceptron (MLP) using whole plant averaged (Av) spectra and superpixels (Sp) averaged spectra from each weed sample. All three classification models showed repeatable identification of four weeds using both Av and Sp spectra with a range of overall accuracy of 70–100%. However, MLP based on the Sp method produced the most reliable and robust prediction result (89.1% accuracy). Four significant spectral regions were found as highly informative for characterizing the four weed species and could form the basis for a rapid and efficient methodology for identifying weeds in ryegrass/clover pastures.

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.

Polynomial Chaos as a Control Variate Method

We introduce a control variate Monte Carlo method to estimate $E[f(X)]$ based on a polynomial chaos expansion for $f(X)$. We analyze the mean square error of the control variate estimator when the ...

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, namely dominant linear and small nonlinear PDEs. Then, we apply 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.

Application of hyperspectral imaging to detect toxigenic Fusarium infection on cornmeal

AbstractOne of the most important food safety issues is the detection of mycotoxins, the ubiquitous, natural contaminants in cereals. Hyperspectral imaging (HSI) is a new method in food science, it can be used to predict non-destructively the changes in composition and distribution of compounds. That is why, in the last decade, the potential of HSI has been evaluated in many fields of food science, including mycotoxin research.The aim of the recent study was to test the feasibility of HSI for the differentiation according to the toxin content of cornmeal samples inoculated with Fusarium graminearum, Fusarium verticillioides and Fusarium culmorum and samples with natural levels of mycotoxins. Samples were measured in the near infrared wavelength range of 900–1,700 nm and mean spectra of selected regions of interest of each image were pre-treated using Savitzky-Golay smoothing and standard normal variate (SNV) method. On the spectra, partial least squares discriminant analysis (PLS-DA) was carried out according to the level of contamination. Partial least squares regression (PLSR) method was used to predict deoxynivalenol (DON) content of samples and the cumulative toxin content: the sum of fumonisins (FB1, FB2) and DON content of samples. Based on the promising results of the study, HSI has the potential to be used as a preliminary testing method for mycotoxin content in feed materials.

Rapid Detection of the Quality of Miso (Japanese Fermented Soybean Paste) Using Visible/Near-Infrared Spectroscopy

Miso, the Japanese fermented soybean paste, an essential seasoning for preparing washoku, is gaining increased international recognition. Miso quality is normally evaluated by a panel of sensory assessors, which is a time-consuming and costly procedure. The final quality of miso products depends on the complex interactions of color, taste, flavor, and aroma. This study aimed to use visible/near-infrared (Vis/NIR) spectroscopy combined with a partial least-square regression (PLSR) algorithm to develop a rapid method for predicting the sensory qualities of miso products. The full Vis/NIR spectrum with nine different pretreatment methods was used to build calibration, cross validation and prediction models. The best performance was achieved by a PLSR model with the first derivative pretreatment of the spectra, giving the root mean square error of prediction (RMSEP) and bias values of 25 and 13, respectively, for the validation test. This model effectively classified miso products into different grades. An investigation of particular spectral regions revealed that a similar performance to the best PLSR model was obtained using just the spectra from 400 to 1100 nm with first derivative pretreatment or combined with multiplicative scatter correction (MSC), and standard normal variate (SNV) methods. The study demonstrated that Vis/NIR spectroscopy has the potential for evaluating miso quality with the advantages of being rapid, accurate, low cost, and nondestructive.