During environment testing, the estimation of random vibration signals （RVS） is an important technique for the airborne platform safety and reliability. However, the available meth- ods including extreme value envel...During environment testing, the estimation of random vibration signals （RVS） is an important technique for the airborne platform safety and reliability. However, the available meth- ods including extreme value envelope method （EVEM）, statistical tolerances method （STM） and improved statistical tolerance method （ISTM） require large samples and typical probability distri- bution. Moreover, the frequency-varying characteristic of RVS is usually not taken into account. Gray bootstrap method （GBM） is proposed to solve the problem of estimating frequency-varying RVS with small samples. Firstly, the estimated indexes are obtained including the estimated inter- val, the estimated uncertainty, the estimated value, the estimated error and estimated reliability. In addition, GBM is applied to estimating the single flight testing of certain aircraft. At last, in order to evaluate the estimated performance, GBM is compared with bootstrap method （BM） and gray method （GM） in testing analysis. The result shows that GBM has superiority for estimating dynamic signals with small samples and estimated reliability is proved to be 100% at the given confidence level.展开更多
To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an impr...To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.展开更多
This paper introduced a bootstrap method called truncated geometric bootstrap method for time series stationary process. We estimate the parameters of a geometric distribution which has been truncated as a probability...This paper introduced a bootstrap method called truncated geometric bootstrap method for time series stationary process. We estimate the parameters of a geometric distribution which has been truncated as a probability model for the bootstrap algorithm. This probability model was used in resampling blocks of random length, where the length of each blocks has a truncated geometric distribution. The method was able to determine the block sizes b and probability p attached to its random selections. The mean and variance were estimated for the truncated geometric distribution and the bootstrap algorithm developed based on the proposed probability model.展开更多
This article introduces a resampling procedure called the truncated geometric bootstrap method for stationary time series process. This procedure is based on resampling blocks of random length, where the length of eac...This article introduces a resampling procedure called the truncated geometric bootstrap method for stationary time series process. This procedure is based on resampling blocks of random length, where the length of each blocks has a truncated geometric distribution and capable of determining the probability p and number of block b. Special attention is given to problems with dependent data, and application with real data was carried out. Autoregressive model was fitted and the choice of order determined by Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The normality test was carried out on the residual variance of the fitted model using Jargue-Bera statistics, and the best model was determined based on root mean square error of the forecasting values. The bootstrap method gives a better and a reliable model for predictive purposes. All the models for the different block sizes are good. They preserve and maintain stationary data structure of the process and are reliable for predictive purposes, confirming the efficiency of the proposed method.展开更多
In 2023,a multivariate normality test based on a chi-square approximation was developed.This method assumes independence among Gaussian random variables,and defines the test statistic,denoted by Q,as the sum of square...In 2023,a multivariate normality test based on a chi-square approximation was developed.This method assumes independence among Gaussian random variables,and defines the test statistic,denoted by Q,as the sum of squared values.This study aims to develop R scripts that implement the Q-test for mul-tivariate normality using either the Shapiro-Wilk W statistic(QSWa)or the Shapiro-Francia W’statistic(QSFa).A bootstrap version of the Q-test(QSWb and QSFb),which does not assume independence,is also included.Addition-ally,it incorporates Royston’s H-test.The use of the scripts is illustrated with a sample of 50 participants assessed on a variable across four yearly admin-istrations.The sampling distribution generated by the bootstrap method dif-fers from the chi-square distribution and corresponds to a generalized chisquare distribution-namely,the distribution of a sum of squares of correlated variables.This distribution is less peaked and has a heavier right tail than the chi-square distribution.It is concluded that the bootstrap approach is con-servative under the null hypothesis of multivariate normality;however,it is theoretically more appropriate than the chi-square approximation.To ap-proximate the distributions of the two versions of the Q-test,it is recom-mended that the z or z’values set to zero in the calculation of the Q statistic not be subtracted when determining the degrees of freedom in the chi-square approximation.Moreover,a significance level of 10%is suggested for the bootstrap approach,rather than the conventional 5%.展开更多
基金supported by Aviation Science Foundation of China (No. 20100251006)the Technological Foundation Project (No. J132012C001)
文摘During environment testing, the estimation of random vibration signals （RVS） is an important technique for the airborne platform safety and reliability. However, the available meth- ods including extreme value envelope method （EVEM）, statistical tolerances method （STM） and improved statistical tolerance method （ISTM） require large samples and typical probability distri- bution. Moreover, the frequency-varying characteristic of RVS is usually not taken into account. Gray bootstrap method （GBM） is proposed to solve the problem of estimating frequency-varying RVS with small samples. Firstly, the estimated indexes are obtained including the estimated inter- val, the estimated uncertainty, the estimated value, the estimated error and estimated reliability. In addition, GBM is applied to estimating the single flight testing of certain aircraft. At last, in order to evaluate the estimated performance, GBM is compared with bootstrap method （BM） and gray method （GM） in testing analysis. The result shows that GBM has superiority for estimating dynamic signals with small samples and estimated reliability is proved to be 100% at the given confidence level.
基金supported by the National Natural Science Foundation of China(No.42174011 and No.41874001).
文摘To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.
文摘This paper introduced a bootstrap method called truncated geometric bootstrap method for time series stationary process. We estimate the parameters of a geometric distribution which has been truncated as a probability model for the bootstrap algorithm. This probability model was used in resampling blocks of random length, where the length of each blocks has a truncated geometric distribution. The method was able to determine the block sizes b and probability p attached to its random selections. The mean and variance were estimated for the truncated geometric distribution and the bootstrap algorithm developed based on the proposed probability model.
文摘This article introduces a resampling procedure called the truncated geometric bootstrap method for stationary time series process. This procedure is based on resampling blocks of random length, where the length of each blocks has a truncated geometric distribution and capable of determining the probability p and number of block b. Special attention is given to problems with dependent data, and application with real data was carried out. Autoregressive model was fitted and the choice of order determined by Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The normality test was carried out on the residual variance of the fitted model using Jargue-Bera statistics, and the best model was determined based on root mean square error of the forecasting values. The bootstrap method gives a better and a reliable model for predictive purposes. All the models for the different block sizes are good. They preserve and maintain stationary data structure of the process and are reliable for predictive purposes, confirming the efficiency of the proposed method.
文摘In 2023,a multivariate normality test based on a chi-square approximation was developed.This method assumes independence among Gaussian random variables,and defines the test statistic,denoted by Q,as the sum of squared values.This study aims to develop R scripts that implement the Q-test for mul-tivariate normality using either the Shapiro-Wilk W statistic(QSWa)or the Shapiro-Francia W’statistic(QSFa).A bootstrap version of the Q-test(QSWb and QSFb),which does not assume independence,is also included.Addition-ally,it incorporates Royston’s H-test.The use of the scripts is illustrated with a sample of 50 participants assessed on a variable across four yearly admin-istrations.The sampling distribution generated by the bootstrap method dif-fers from the chi-square distribution and corresponds to a generalized chisquare distribution-namely,the distribution of a sum of squares of correlated variables.This distribution is less peaked and has a heavier right tail than the chi-square distribution.It is concluded that the bootstrap approach is con-servative under the null hypothesis of multivariate normality;however,it is theoretically more appropriate than the chi-square approximation.To ap-proximate the distributions of the two versions of the Q-test,it is recom-mended that the z or z’values set to zero in the calculation of the Q statistic not be subtracted when determining the degrees of freedom in the chi-square approximation.Moreover,a significance level of 10%is suggested for the bootstrap approach,rather than the conventional 5%.
