Small datasets are often challenging due to their limited sample size.This research introduces a novel solution to these problems:average linkage virtual sample generation(ALVSG).ALVSG leverages the underlying data st...Small datasets are often challenging due to their limited sample size.This research introduces a novel solution to these problems:average linkage virtual sample generation(ALVSG).ALVSG leverages the underlying data structure to create virtual samples,which can be used to augment the original dataset.The ALVSG process consists of two steps.First,an average-linkage clustering technique is applied to the dataset to create a dendrogram.The dendrogram represents the hierarchical structure of the dataset,with each merging operation regarded as a linkage.Next,the linkages are combined into an average-based dataset,which serves as a new representation of the dataset.The second step in the ALVSG process involves generating virtual samples using the average-based dataset.The research project generates a set of 100 virtual samples by uniformly distributing them within the provided boundary.These virtual samples are then added to the original dataset,creating a more extensive dataset with improved generalization performance.The efficacy of the ALVSG approach is validated through resampling experiments and t-tests conducted on two small real-world datasets.The experiments are conducted on three forecasting models:the support vector machine for regression(SVR),the deep learning model(DL),and XGBoost.The results show that the ALVSG approach outperforms the baseline methods in terms of mean square error(MSE),root mean square error(RMSE),and mean absolute error(MAE).展开更多
Signals are often of random character since they cannot bear any information if they are predictable for any time t, they are usually modelled as stationary random processes .On the other hand, because of the inertia ...Signals are often of random character since they cannot bear any information if they are predictable for any time t, they are usually modelled as stationary random processes .On the other hand, because of the inertia of the measurement apparatus, measured sampled values obtained in practice may not be the precise value of the signal X(t) at time tk (k∈Z), but only local averages of X(t) near tk. In this paper, it is presented that a wide (or weak ) sense stationary stochastic process can be approximated by generalized sampling series with local average samples.展开更多
By analyzing the theory of over-sampling and averaging, the conclusion is educed that white noise accompanies the signal and the addition of each bit of resolution can be achieved via a fourfold sampling frequency. Th...By analyzing the theory of over-sampling and averaging, the conclusion is educed that white noise accompanies the signal and the addition of each bit of resolution can be achieved via a fourfold sampling frequency. The addition of each bit will approximately increase the SNR （signal to noise ratio） to 6dB.展开更多
A novel adaptive multiple dependent state sampling plan(AMDSSP)was designed to inspect products from a continuous manufacturing process under the accelerated life test(ALT)using both double sampling plan(DSP)and multi...A novel adaptive multiple dependent state sampling plan(AMDSSP)was designed to inspect products from a continuous manufacturing process under the accelerated life test(ALT)using both double sampling plan(DSP)and multiple dependent state sampling plan(MDSSP)concepts.Under accelerated conditions,the lifetime of a product follows the Weibull distribution with a known shape parameter,while the scale parameter can be determined using the acceleration factor(AF).The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive.An economic design of the proposed sampling plan was also considered for the ALT.A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number(ASN)and total cost of inspection(TC)under both producer’s and consumer’s risks.Numerical results are presented to support the AMDSSP for the ALT,while performance comparisons between the AMDSSP,the MDSSP and a single sampling plan(SSP)for the ALT are discussed.Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions.The AMDSSP also had a higher operating characteristic(OC)curve than both the existing sampling plans.Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.展开更多
In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were disc...In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the Legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems.展开更多
In this paper, we study optimal recovery （reconstruction） of functions on the sphere in the average case setting. We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a G...In this paper, we study optimal recovery （reconstruction） of functions on the sphere in the average case setting. We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞.展开更多
This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of t...This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.展开更多
Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in un...Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)problems.However,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)problems.To address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind power.PSAA partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled sets.When approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being introduced.Finally,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by SAA.Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.展开更多
Let B^pΩ,1≤Р≤∞,be the set of all bounded functions in L^p（R）which can be extended to entire unctions of exponential typeΩ. The unitbrm bounds for truncation error of Shannon sampling expansion fromlocal averag...Let B^pΩ,1≤Р≤∞,be the set of all bounded functions in L^p（R）which can be extended to entire unctions of exponential typeΩ. The unitbrm bounds for truncation error of Shannon sampling expansion fromlocal averages are obtained for functions f∈BpΩwith the decay condition f（t）≤A/t^δ,t≠0,where A and δare positive constants. Furthermore we also establish similar results for non-bandlimit functions in Besov classes with the same decay condition as above.展开更多
<正> The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace sat...<正> The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.展开更多
基金funding support from the National Science and Technology Council(NSTC),under Grant No.114-2410-H-011-026-MY3.
文摘Small datasets are often challenging due to their limited sample size.This research introduces a novel solution to these problems:average linkage virtual sample generation(ALVSG).ALVSG leverages the underlying data structure to create virtual samples,which can be used to augment the original dataset.The ALVSG process consists of two steps.First,an average-linkage clustering technique is applied to the dataset to create a dendrogram.The dendrogram represents the hierarchical structure of the dataset,with each merging operation regarded as a linkage.Next,the linkages are combined into an average-based dataset,which serves as a new representation of the dataset.The second step in the ALVSG process involves generating virtual samples using the average-based dataset.The research project generates a set of 100 virtual samples by uniformly distributing them within the provided boundary.These virtual samples are then added to the original dataset,creating a more extensive dataset with improved generalization performance.The efficacy of the ALVSG approach is validated through resampling experiments and t-tests conducted on two small real-world datasets.The experiments are conducted on three forecasting models:the support vector machine for regression(SVR),the deep learning model(DL),and XGBoost.The results show that the ALVSG approach outperforms the baseline methods in terms of mean square error(MSE),root mean square error(RMSE),and mean absolute error(MAE).
基金National Natural Science Foundation of China (No60572113,No10501026) and Liuhui Center for Applied Mathematics
文摘Signals are often of random character since they cannot bear any information if they are predictable for any time t, they are usually modelled as stationary random processes .On the other hand, because of the inertia of the measurement apparatus, measured sampled values obtained in practice may not be the precise value of the signal X(t) at time tk (k∈Z), but only local averages of X(t) near tk. In this paper, it is presented that a wide (or weak ) sense stationary stochastic process can be approximated by generalized sampling series with local average samples.
文摘By analyzing the theory of over-sampling and averaging, the conclusion is educed that white noise accompanies the signal and the addition of each bit of resolution can be achieved via a fourfold sampling frequency. The addition of each bit will approximately increase the SNR （signal to noise ratio） to 6dB.
基金This research was supported by The Science,Research and Innovation Promotion Funding(TSRI)(Grant No.FRB650070/0168)This research block grants was managed under Rajamangala University of Technology Thanyaburi(FRB65E0634M.3).
文摘A novel adaptive multiple dependent state sampling plan(AMDSSP)was designed to inspect products from a continuous manufacturing process under the accelerated life test(ALT)using both double sampling plan(DSP)and multiple dependent state sampling plan(MDSSP)concepts.Under accelerated conditions,the lifetime of a product follows the Weibull distribution with a known shape parameter,while the scale parameter can be determined using the acceleration factor(AF).The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive.An economic design of the proposed sampling plan was also considered for the ALT.A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number(ASN)and total cost of inspection(TC)under both producer’s and consumer’s risks.Numerical results are presented to support the AMDSSP for the ALT,while performance comparisons between the AMDSSP,the MDSSP and a single sampling plan(SSP)for the ALT are discussed.Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions.The AMDSSP also had a higher operating characteristic(OC)curve than both the existing sampling plans.Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.
文摘In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the Legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems.
基金supported by the National Natural Science Foundation of China(No.11426179)the National Natural Science Foundation of China(Nos.10871132,11271263)+4 种基金the Key Scientific Research Fund of Xihua University(No.z1312624)the Foundation of Sichuan Educational Committee(No.14ZA0112)the Preeminent Youth Fund for School of Science in Xihua Universitythe Beijing Natural Science Foundation(No.1132001)BCMIIS
文摘In this paper, we study optimal recovery （reconstruction） of functions on the sphere in the average case setting. We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞.
基金the Science,Research and Innovation Promotion Funding(TSRI)(Grant No.FRB660012/0168)managed under Rajamangala University of Technology Thanyaburi(FRB66E0646O.4).
文摘This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.
基金supported by the National Natural Science Foundation of China(No.51977042)。
文摘Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)problems.However,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)problems.To address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind power.PSAA partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled sets.When approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being introduced.Finally,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by SAA.Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.
基金Supported by the National Natural Science Foundation of China(Nos.61379014 and 11271199)
文摘Let B^pΩ,1≤Р≤∞,be the set of all bounded functions in L^p（R）which can be extended to entire unctions of exponential typeΩ. The unitbrm bounds for truncation error of Shannon sampling expansion fromlocal averages are obtained for functions f∈BpΩwith the decay condition f（t）≤A/t^δ,t≠0,where A and δare positive constants. Furthermore we also establish similar results for non-bandlimit functions in Besov classes with the same decay condition as above.
文摘<正> The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.
