As environmental concerns drive shifts in construction materials,rock is increasingly considered as an alternative to sand,reinforcing the importance of understanding its dynamic properties.This study investigates the...As environmental concerns drive shifts in construction materials,rock is increasingly considered as an alternative to sand,reinforcing the importance of understanding its dynamic properties.This study investigates the effect of water content on the small-strain dynamic properties of basalt samples using free-free laboratory testing.Free-free testing,which requires minimal equipment and preparation,provides an efficient and low-cost method for determining key dynamic properties,including three wave velocities(V_(s),V_(p),and V_(c)),material damping ratios,and Poisson's ratios.These properties are crucial for numerical modeling in earthquake analyses and geotechnical site characterization.The test consists of three components:(1)direct travel-time measurement,(2)torsional resonance testing,and(3)compressional resonance testing.A total of 20 rock samples were tested under systematically controlled water contents,ranging from fully dried to saturated,to quantify the effects on Poisson's ratio and material damping ratios.The results showed significant increases in both parameters with rising water content.The Poisson's ratio increased by up to 320%for aphanitic basalt and 150%for vesicular basalt,while the damping ratio rose up to 30-fold(D_(c,min))and 16-fold(D_(s,min)).These findings highlight the critical need to incorporate consideration of water content when characterizing dynamic rock properties for seismic and geotechnical analyses.The practical applicability of this research lies in improving in situ property interpretation and enhancing seismic design reliability by providing engineers with precise relationships between water content and dynamic rock behavior.展开更多
In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose ...In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose to the null hypothesis. These expansions are given in series form of beta distributions.展开更多
The effect of structural discontinuities on the progressive failure process of anisotropic rocks should be paid particular attention.The crack damage stress σ_(cd),also considered as the yield strength,and the relati...The effect of structural discontinuities on the progressive failure process of anisotropic rocks should be paid particular attention.The crack damage stress σ_(cd),also considered as the yield strength,and the relationship between σ_(cd) and the uniaxial peak strength σ_(ucs) of anisotropic rocks for different orientations 8 of the isotropy planes with respect to the loading directions were investigated theoretically and experimentally.A theoretical relation of σ_(cd)/σ_(ucs) with the function of the shape parameter m was established.Additionally,uniaxial compression tests of shale samples were conducted for several inclinations θ.The test result of σ_(cd)/σ_(ucs) was close to the theoretical value for a given orientation.Furthermore,both experimental results and theoretical solutions of σ_(cd)/σ_(ucs) were independent of the inclination θ while σ_(cd) andσ_(ucs) were strongly affected by θ.The strength ratio σ_(cd)/σ_(ucs) may therefore be an intrinsic property of anisotropic rocks and could be used to predict the failure of rock samples.展开更多
This paper analyzed the consistency of some parameters of soils in the literature and experimental results from fall cone test and its application to soil plasticity classification.Over 500 data from both literatures ...This paper analyzed the consistency of some parameters of soils in the literature and experimental results from fall cone test and its application to soil plasticity classification.Over 500 data from both literatures and experiments using fall cone and Casagrande methods were compiled to assess the relationships among specified water content,cone penetration index ebT,and plasticity angle eaT of finegrained soils.The results indicate that no unique correlation exists among b,liquid limit of the fall cone test(LLc)and a.The water content at 1 mm cone penetration eC0T correlates well with b,plasticity ratio eRpT(i.e.the ratio of plastic limit to liquid limit),and a.Finally,the potential of using the btan a diagram to classify soil plasticity was also discussed.展开更多
In this article,dynamic method and static method of testing Poisson's ratio of OSB(Oriented Strand Board)were proposed.Through modal and static numerical analyses,the position where the transverse stress is equal ...In this article,dynamic method and static method of testing Poisson's ratio of OSB(Oriented Strand Board)were proposed.Through modal and static numerical analyses,the position where the transverse stress is equal to zero was determined.The binary linear regression method was applied to express the gluing position of the strain gauge as a relational express ion that depended on the length-width ratio and width-thickness ratio of the canti-lever plate.Then the longitudinal and transverse Poisson's ratios of OSB were mea sured by the given dynamic and static methods.In addition,the test results of OSB Poisson's ratio were analyzed with the probability distribution of random variables.The results showed that using the proposed dynamic method and static method,the test results for longitudinal and transverse Poisson's ratios of OSB were quite consistent,despite the gluing position of the strain gauges being different.And these OSB Poisson's ratios were accorded with that obtained by the axial tensile method and the four-point bending method.OSB longitudinal and transverse Poisson's ratios followed Weibull distribution.展开更多
In recent years,there is a scenario in urban tunnel constructions to build super-large-span tunnels for traffic diversion and route optimization purposes.However,the increased size makes tunnel support more difficult....In recent years,there is a scenario in urban tunnel constructions to build super-large-span tunnels for traffic diversion and route optimization purposes.However,the increased size makes tunnel support more difficult.Unfortunately,there are few studies on the failure and support mechanism of the surrounding rocks in the excavation of supported tunnel,while most model tests of super-large-span tunnels focus on the failure characteristics of surrounding rocks in tunnel excavation without supports.Based on excavation compensation method(ECM),model tests of a super-large-span tunnel excavation by different anchor cable support methods in the initial support stage were carried out.The results indicate that during excavation of super-large-span tunnel,the stress and displacement of the shallow surrounding rocks decrease,following a step-shape pattern,and the tunnel failure is mainly concentrated on the vault and spandrel areas.Compared with conventional anchor cable supports,the NPR(negative Poisson’s ratio)anchor cable support is more suitable for the initial support stage of the super-large-span tunnels.The tunnel support theory,model test materials,methods,and the results obtained in this study could provide references for study of similar super-large-span tunnels。展开更多
This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ...This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ratio test is X^2（1）.展开更多
One of the important fields in statistics is testing hypothesis of correlation coefficient. The extension of the idea of testing correlation to fuzzy hypothesis is of great interesting. In this study, we examined the ...One of the important fields in statistics is testing hypothesis of correlation coefficient. The extension of the idea of testing correlation to fuzzy hypothesis is of great interesting. In this study, we examined the use of fuzzy hypothesis testing approach for the Sequential Probability Ratio Test (SPRT) of correlation coefficient. Use of fuzzy hypothesis testing for correlation coefficient with SPRT is illustrated by an example.展开更多
It is well-known that the power of Cochran’s Q test to assess the presence of heterogeneity among treatment effects in a clinical meta-analysis is low due to the small number of studies combined. Two modified tests (...It is well-known that the power of Cochran’s Q test to assess the presence of heterogeneity among treatment effects in a clinical meta-analysis is low due to the small number of studies combined. Two modified tests (PL1, PL2) were proposed by replacing the profile maximum likelihood estimator (PMLE) into the variance formula of logarithm of risk ratio in the standard chi-square test statistic for testing the null common risk ratios across all k studies (i = 1, L, k). The simply naive test (SIM) as another comparative candidate has considerably arisen. The performance of tests in terms of type I error rate under the null hypothesis and power of test under the random effects hypothesis was done via a simulation plan with various combinations of significance levels, numbers of studies, sample sizes in treatment and control arms, and true risk ratios as effect sizes of interest. The results indicated that for moderate to large study sizes (k?≥ 16)?in combination with moderate to large sample sizes?(?≥ 50), three tests (PL1, PL2, and Q) could control type I error rates in almost all situations. Two proposed tests (PL1, PL2) performed best with the highest power when?k?≥ 16?and moderate sample sizes (= 50,100);this finding was very useful to make a recommendation to use them in practical situations. Meanwhile, the standard Q test performed best when?k?≥ 16 and large sample sizes (≥ 500). Moreover, no tests were reasonable for small sample sizes (≤ 10), regardless of study size k. The simply naive test (SIM) is recommended to be adopted with high performance when k = 4 in combination with (≥ 500).展开更多
We prove that any collection which tiles the positive integers must contain one of two types of sub-collections. We then use this result to prove a variation of the Ratio Test for convergence of series. This version o...We prove that any collection which tiles the positive integers must contain one of two types of sub-collections. We then use this result to prove a variation of the Ratio Test for convergence of series. This version of the Ratio Test shows the convergence of certain series for which the Root Test (which is known to be more powerful than the conventional Ratio Test) fails. This version of the Ratio Test is also used to prove a version of the Banach Contraction Principle for self-maps of a complete metric space.展开更多
There are a few statistics testing the homogeneity of odds ratios across strata. Asymptotic statistics lose their power in the “sparse-data” setting. Both asymptotic statistics and exact tests have low power when th...There are a few statistics testing the homogeneity of odds ratios across strata. Asymptotic statistics lose their power in the “sparse-data” setting. Both asymptotic statistics and exact tests have low power when the sample sizes are small. We created a set of U statistics and compared them with some existing statistics in testing homogeneity of OR at different data settings. We evaluated their performance in terms of the empirical size and power via Monto Carlo simulations. Our results showed that two of the U-statistics under our study had higher power for testing homogeneity of odds ratios for 2 by 2 contingency tables. The application of the tests was illustrated in two real examples.展开更多
In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null d...In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.展开更多
In this paper,we consider testing the hypothesis concerning the means of two independent semicontinuous distributions whose observations are zero-inflated,characterized by a sizable number of zeros and positive observ...In this paper,we consider testing the hypothesis concerning the means of two independent semicontinuous distributions whose observations are zero-inflated,characterized by a sizable number of zeros and positive observations from a continuous distribution.The continuous parts of the two semicontinuous distributions are assumed to follow a density ratio model.A new two-part test is developed for this kind of data.The proposed test takes the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution.The test is proved to follow a 2 distribution with two degrees of freedom.Simulation studies show that the proposed test controls the type I error rates at the desired level,and is competitive to,and most of the time more powerful than two popular tests.A real data example from a dietary intervention study is used to illustrate the usefulness of the proposed test.展开更多
We consider an extension to Sequential Probability Ratio Tests for when we have uncertain costs, but also opportunity to learn about these in an adaptive manner. In doing so we demonstrate the effects that allowing un...We consider an extension to Sequential Probability Ratio Tests for when we have uncertain costs, but also opportunity to learn about these in an adaptive manner. In doing so we demonstrate the effects that allowing uncertainty has on observation cost, and the costs associated with Type I and Type II error. The value of information relating to modelled uncertainties is derived and the case of statistical dependence between the parameter affecting decision outcome and the parameter affecting unknown cost is also examined. Numerical examples of the derived theory are provided, along with a simulation comparing this adaptive learning framework to the classical one.展开更多
In this paper, a method to calculate the slope of the ratio restraint characteristic of a transformer differential relay protection is proposed. The method allows using some concise but effective means to get the slop...In this paper, a method to calculate the slope of the ratio restraint characteristic of a transformer differential relay protection is proposed. The method allows using some concise but effective means to get the slope. Modulating the argument of current output from ONLLY testing equipment can make the relay protection device operate, thus, the data used for calculation would be obtained naturally after several trails. In order to make sure how effective that method could be, some experiment data is given as well.展开更多
文摘As environmental concerns drive shifts in construction materials,rock is increasingly considered as an alternative to sand,reinforcing the importance of understanding its dynamic properties.This study investigates the effect of water content on the small-strain dynamic properties of basalt samples using free-free laboratory testing.Free-free testing,which requires minimal equipment and preparation,provides an efficient and low-cost method for determining key dynamic properties,including three wave velocities(V_(s),V_(p),and V_(c)),material damping ratios,and Poisson's ratios.These properties are crucial for numerical modeling in earthquake analyses and geotechnical site characterization.The test consists of three components:(1)direct travel-time measurement,(2)torsional resonance testing,and(3)compressional resonance testing.A total of 20 rock samples were tested under systematically controlled water contents,ranging from fully dried to saturated,to quantify the effects on Poisson's ratio and material damping ratios.The results showed significant increases in both parameters with rising water content.The Poisson's ratio increased by up to 320%for aphanitic basalt and 150%for vesicular basalt,while the damping ratio rose up to 30-fold(D_(c,min))and 16-fold(D_(s,min)).These findings highlight the critical need to incorporate consideration of water content when characterizing dynamic rock properties for seismic and geotechnical analyses.The practical applicability of this research lies in improving in situ property interpretation and enhancing seismic design reliability by providing engineers with precise relationships between water content and dynamic rock behavior.
文摘In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose to the null hypothesis. These expansions are given in series form of beta distributions.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (No.XDB10030302)the National Natural Science Foundation of China (No.41302233)the Project funded by China Postdoctoral Science Foundation (No.2014T70121)
文摘The effect of structural discontinuities on the progressive failure process of anisotropic rocks should be paid particular attention.The crack damage stress σ_(cd),also considered as the yield strength,and the relationship between σ_(cd) and the uniaxial peak strength σ_(ucs) of anisotropic rocks for different orientations 8 of the isotropy planes with respect to the loading directions were investigated theoretically and experimentally.A theoretical relation of σ_(cd)/σ_(ucs) with the function of the shape parameter m was established.Additionally,uniaxial compression tests of shale samples were conducted for several inclinations θ.The test result of σ_(cd)/σ_(ucs) was close to the theoretical value for a given orientation.Furthermore,both experimental results and theoretical solutions of σ_(cd)/σ_(ucs) were independent of the inclination θ while σ_(cd) andσ_(ucs) were strongly affected by θ.The strength ratio σ_(cd)/σ_(ucs) may therefore be an intrinsic property of anisotropic rocks and could be used to predict the failure of rock samples.
文摘This paper analyzed the consistency of some parameters of soils in the literature and experimental results from fall cone test and its application to soil plasticity classification.Over 500 data from both literatures and experiments using fall cone and Casagrande methods were compiled to assess the relationships among specified water content,cone penetration index ebT,and plasticity angle eaT of finegrained soils.The results indicate that no unique correlation exists among b,liquid limit of the fall cone test(LLc)and a.The water content at 1 mm cone penetration eC0T correlates well with b,plasticity ratio eRpT(i.e.the ratio of plastic limit to liquid limit),and a.Finally,the potential of using the btan a diagram to classify soil plasticity was also discussed.
基金This research was sponsored by the Science and Technology Project for Policy Guidance of Jiangsu Province(SZ-LYG 2020016).
文摘In this article,dynamic method and static method of testing Poisson's ratio of OSB(Oriented Strand Board)were proposed.Through modal and static numerical analyses,the position where the transverse stress is equal to zero was determined.The binary linear regression method was applied to express the gluing position of the strain gauge as a relational express ion that depended on the length-width ratio and width-thickness ratio of the canti-lever plate.Then the longitudinal and transverse Poisson's ratios of OSB were mea sured by the given dynamic and static methods.In addition,the test results of OSB Poisson's ratio were analyzed with the probability distribution of random variables.The results showed that using the proposed dynamic method and static method,the test results for longitudinal and transverse Poisson's ratios of OSB were quite consistent,despite the gluing position of the strain gauges being different.And these OSB Poisson's ratios were accorded with that obtained by the axial tensile method and the four-point bending method.OSB longitudinal and transverse Poisson's ratios followed Weibull distribution.
基金supported by the Innovation Fund Research Project of State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology(Grant No.SKLGDUEK202201)the Foundation for the Opening of State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology(Grant No.SKLGDUEK2129)the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(Grant No.Z020007)。
文摘In recent years,there is a scenario in urban tunnel constructions to build super-large-span tunnels for traffic diversion and route optimization purposes.However,the increased size makes tunnel support more difficult.Unfortunately,there are few studies on the failure and support mechanism of the surrounding rocks in the excavation of supported tunnel,while most model tests of super-large-span tunnels focus on the failure characteristics of surrounding rocks in tunnel excavation without supports.Based on excavation compensation method(ECM),model tests of a super-large-span tunnel excavation by different anchor cable support methods in the initial support stage were carried out.The results indicate that during excavation of super-large-span tunnel,the stress and displacement of the shallow surrounding rocks decrease,following a step-shape pattern,and the tunnel failure is mainly concentrated on the vault and spandrel areas.Compared with conventional anchor cable supports,the NPR(negative Poisson’s ratio)anchor cable support is more suitable for the initial support stage of the super-large-span tunnels.The tunnel support theory,model test materials,methods,and the results obtained in this study could provide references for study of similar super-large-span tunnels。
基金Supported by the National Natural Science Foundation of China(10661003)the SRF for ROCS,SEM([2004]527)the NSF of Guangxi(0728092)
文摘This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ratio test is X^2（1）.
文摘One of the important fields in statistics is testing hypothesis of correlation coefficient. The extension of the idea of testing correlation to fuzzy hypothesis is of great interesting. In this study, we examined the use of fuzzy hypothesis testing approach for the Sequential Probability Ratio Test (SPRT) of correlation coefficient. Use of fuzzy hypothesis testing for correlation coefficient with SPRT is illustrated by an example.
文摘It is well-known that the power of Cochran’s Q test to assess the presence of heterogeneity among treatment effects in a clinical meta-analysis is low due to the small number of studies combined. Two modified tests (PL1, PL2) were proposed by replacing the profile maximum likelihood estimator (PMLE) into the variance formula of logarithm of risk ratio in the standard chi-square test statistic for testing the null common risk ratios across all k studies (i = 1, L, k). The simply naive test (SIM) as another comparative candidate has considerably arisen. The performance of tests in terms of type I error rate under the null hypothesis and power of test under the random effects hypothesis was done via a simulation plan with various combinations of significance levels, numbers of studies, sample sizes in treatment and control arms, and true risk ratios as effect sizes of interest. The results indicated that for moderate to large study sizes (k?≥ 16)?in combination with moderate to large sample sizes?(?≥ 50), three tests (PL1, PL2, and Q) could control type I error rates in almost all situations. Two proposed tests (PL1, PL2) performed best with the highest power when?k?≥ 16?and moderate sample sizes (= 50,100);this finding was very useful to make a recommendation to use them in practical situations. Meanwhile, the standard Q test performed best when?k?≥ 16 and large sample sizes (≥ 500). Moreover, no tests were reasonable for small sample sizes (≤ 10), regardless of study size k. The simply naive test (SIM) is recommended to be adopted with high performance when k = 4 in combination with (≥ 500).
文摘We prove that any collection which tiles the positive integers must contain one of two types of sub-collections. We then use this result to prove a variation of the Ratio Test for convergence of series. This version of the Ratio Test shows the convergence of certain series for which the Root Test (which is known to be more powerful than the conventional Ratio Test) fails. This version of the Ratio Test is also used to prove a version of the Banach Contraction Principle for self-maps of a complete metric space.
文摘There are a few statistics testing the homogeneity of odds ratios across strata. Asymptotic statistics lose their power in the “sparse-data” setting. Both asymptotic statistics and exact tests have low power when the sample sizes are small. We created a set of U statistics and compared them with some existing statistics in testing homogeneity of OR at different data settings. We evaluated their performance in terms of the empirical size and power via Monto Carlo simulations. Our results showed that two of the U-statistics under our study had higher power for testing homogeneity of odds ratios for 2 by 2 contingency tables. The application of the tests was illustrated in two real examples.
文摘In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.
基金Supported by the National Natural Science Foundation of China(No.11971433)the First Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics)the Intramural Research Program of the Eunice Kennedy Shriver National Institute of Child Health and Human Development.
文摘In this paper,we consider testing the hypothesis concerning the means of two independent semicontinuous distributions whose observations are zero-inflated,characterized by a sizable number of zeros and positive observations from a continuous distribution.The continuous parts of the two semicontinuous distributions are assumed to follow a density ratio model.A new two-part test is developed for this kind of data.The proposed test takes the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution.The test is proved to follow a 2 distribution with two degrees of freedom.Simulation studies show that the proposed test controls the type I error rates at the desired level,and is competitive to,and most of the time more powerful than two popular tests.A real data example from a dietary intervention study is used to illustrate the usefulness of the proposed test.
文摘We consider an extension to Sequential Probability Ratio Tests for when we have uncertain costs, but also opportunity to learn about these in an adaptive manner. In doing so we demonstrate the effects that allowing uncertainty has on observation cost, and the costs associated with Type I and Type II error. The value of information relating to modelled uncertainties is derived and the case of statistical dependence between the parameter affecting decision outcome and the parameter affecting unknown cost is also examined. Numerical examples of the derived theory are provided, along with a simulation comparing this adaptive learning framework to the classical one.
文摘In this paper, a method to calculate the slope of the ratio restraint characteristic of a transformer differential relay protection is proposed. The method allows using some concise but effective means to get the slope. Modulating the argument of current output from ONLLY testing equipment can make the relay protection device operate, thus, the data used for calculation would be obtained naturally after several trails. In order to make sure how effective that method could be, some experiment data is given as well.
