Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear ...Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.展开更多
The Tanggula （唐古拉） thrust system and the Tuotuohe （沱沱河） foreland basin, which represent major Cenozoic tectonic units of the central Tibetan plateau, have been recently studied. Field investigation, analyse...The Tanggula （唐古拉） thrust system and the Tuotuohe （沱沱河） foreland basin, which represent major Cenozoic tectonic units of the central Tibetan plateau, have been recently studied. Field investigation, analyses of deformation and construction of two restored balanced structural sections suggest 75-100 km （51%-64%） of N-S shortening in the Tanggula thrust system and 55-114 km （42%-47%） of N-S shortening in the Tuotuohe basin. The shortening ratios indicate that the Tanggula- Tuotuohe area has undergone intensive deformation and crustal shortening during the Early Tertiary, resulting not only in crustal thickening, but also in large scale volcanism and in rapid uplift of the Tanggula Mountains.展开更多
The paper presents modeling approach of a Single Ended Primary Inductance Converter (SEPIC) system. The complete model derivation of the SEPIC converter system has been presented in different modes of operation. Stead...The paper presents modeling approach of a Single Ended Primary Inductance Converter (SEPIC) system. The complete model derivation of the SEPIC converter system has been presented in different modes of operation. Steady state and small signal analysis was carried out on the converter dynamic equations using the method of Harmonic balance Technique. The steady state variables and their respective ripple quantities obtained were plotted against duty ratio D. The results obtained for a supply input voltage of 60 volts to the converter at a duty ratio of D = 0.8 , compares well with simulation results.展开更多
In this paper,an improved method,which is based on the harmonic-balance tech-nique,for speeding up the convergence iteration procedure is presented.As an example,it isapplied to the nonlinear analysis of microwave mix...In this paper,an improved method,which is based on the harmonic-balance tech-nique,for speeding up the convergence iteration procedure is presented.As an example,it isapplied to the nonlinear analysis of microwave mixer,in which a simple time domain to fre-quency domain transformation technique for the mixer diode is firstly introduced.The use of thistechnique saves computing time dramatically.And the analyzed results are in good agreementwith the results published.The improved method can also be extended to the CAA of nonlinearcircuits with multi-devices.展开更多
In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate...In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate solution in terms of the automatic differentiation(AD)algorithm.To overcome the deficiency of CAT that demands high computation cost for implementation,a set of ordinary differential equations(ODEs)entailed from CAT based discretized population balance equation(PBE)are solved by using the AD based high-order Taylor expansion.Moreover,an AD based trust-region reflective(TRR)algorithm and another interior-point(IP)algorithm are established for estimating the kinetic parameters associated with particle growth,aggregation and breakage.As a result,the estimation accuracy can be further improved while the computation cost can be significantly reduced,compared to the existing algorithms.Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT,TRR and IP algorithms in comparison with the existing algorithms.Moreover,seeded batch cooling crystallization experiments ofβform L-glutamic acid are performed to validate the proposed method.展开更多
Short-term traffic flow prediction is one of the essential issues in intelligent transportation systems(ITS). A new two-stage traffic flow prediction method named AKNN-AVL method is presented, which combines an advanc...Short-term traffic flow prediction is one of the essential issues in intelligent transportation systems(ITS). A new two-stage traffic flow prediction method named AKNN-AVL method is presented, which combines an advanced k-nearest neighbor(AKNN)method and balanced binary tree(AVL) data structure to improve the prediction accuracy. The AKNN method uses pattern recognition two times in the searching process, which considers the previous sequences of traffic flow to forecast the future traffic state. Clustering method and balanced binary tree technique are introduced to build case database to reduce the searching time. To illustrate the effects of these developments, the accuracies performance of AKNN-AVL method, k-nearest neighbor(KNN) method and the auto-regressive and moving average(ARMA) method are compared. These methods are calibrated and evaluated by the real-time data from a freeway traffic detector near North 3rd Ring Road in Beijing under both normal and incident traffic conditions.The comparisons show that the AKNN-AVL method with the optimal neighbor and pattern size outperforms both KNN method and ARMA method under both normal and incident traffic conditions. In addition, the combinations of clustering method and balanced binary tree technique to the prediction method can increase the searching speed and respond rapidly to case database fluctuations.展开更多
OBJECTIVE:To investigate the difference in gut microbiota between population with damp-heat constitution(DHC)and balanced constitution(BC).METHODS:A multi-centered cross-sectional casecontrol study was conducted,which...OBJECTIVE:To investigate the difference in gut microbiota between population with damp-heat constitution(DHC)and balanced constitution(BC).METHODS:A multi-centered cross-sectional casecontrol study was conducted,which included 249 participants with damp-heat constitution or balanced constitution.Baseline information of participants was collected,and stool samples were collected for gut microbiota analysis.Principal coordinate analysis,linear discriminant analysis effect size analysis,receiver operating characteristic,random forest model,and phylogenetic investigation of communities by reconstruction of unobserved states methods were used to reveal the relationship between gut microbiota and the damp-heat constitution.RESULTS:Compared to those in the BC group,the richness and diversity of the microbiota,specifically those of several short-chain fatty acid producing genera such as Barnesiella,Coprobacter,and Butyricimonas,were significantly decreased in the DHC group.Regarding biological functions,flavonoid biosynthesis,propanoate metabolism,and nucleotide sugar metabolism were suppressed,while arachidonic acid metabolism and glutathione metabolism were enriched in the DHC group.Finally,a classifier based on the microbiota was constructed to discriminate between the DHC and BC populations.CONCLUSION:The gut microbiota of the DHC population exhibits significantly reduced diversity and is closely related to inflammation,metabolic disorders,and liver steatosis,which is consistent with clinical observations,thus serving as a potential diagnostic tool for traditional Chinese medicine constitution discrimination.展开更多
The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to ...The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to complex symbolic operations.Many variants have been developed to improve the HB method,among which the time domain HB-like methods are regarded as crucial improvements because of their fast computation and simple derivation.So far,there are two problems remaining to be addressed.i)A dozen of different versions of HB-like methods,in frequency domain or time domain or in hybrid,have been developed;unfortunately,misclassification pervades among them due to the unclear borderlines of different methods.ii)The time domain HB-like methods suffer from non-physical solutions,which have been shown to be caused by aliasing(mixture of the high-order into the low-order harmonics).Although a series of dealiasing techniques have been developed over the past two decades,the mechanism of aliasing and the final solution to dealiasing are still not well known to the academic community.This paper aims to provide a comprehensive review of the development of HB-like methods and enunciate their principal differences.In particular,the time domain methods are emphasized with the famous aliasing phenomenon clearly addressed.展开更多
Although ultrasound measurements have been used in previous studies on carpal tunnel syndrome to visualize injury to the median nerve, whether such ultrasound data can indicate the severity of carpal tunnel syndrome r...Although ultrasound measurements have been used in previous studies on carpal tunnel syndrome to visualize injury to the median nerve, whether such ultrasound data can indicate the severity of carpal tunnel syndrome remains controversial. The cross-sectional areas of the median nerve at the tunnel inlet and outlet can show swelling and compression of the nerve at the carpal. We hypothesized that the ratio of the cross-sectional areas of the median nerve at the carpal tunnel inlet to outlet accurately reflects the severity of carpal tunnel syndrome. To test this, high-resolution ultrasound with a linear array transducer at 5–17 MHz was used to assess 77 patients with carpal tunnel syndrome. The results showed that the cut-off point for the inlet-to-outlet ratio was 1.14. Significant differences in the inlet-to-outlet ratio were found among patients with mild, moderate, and severe carpal tunnel syndrome. The cut-off point in the ratio of cross-sectional areas of the median nerve was 1.29 between mild and more severe（moderate and severe） carpal tunnel syndrome patients with 64.7% sensitivity and 72.7% specificity. The cut-off point in the ratio of cross-sectional areas of the median nerve was 1.52 between the moderate and severe carpal tunnel syndrome patients with 80.0% sensitivity and 64.7% specificity. These results suggest that the inlet-to-outlet ratio reflected the severity of carpal tunnel syndrome.展开更多
Using hybrid perturbatin_Galerkin technique,a crcular cross_section tube model with sinusoidal wall is studied.This technique can remove the limitation of small parameters for perturbation and the difficulty of select...Using hybrid perturbatin_Galerkin technique,a crcular cross_section tube model with sinusoidal wall is studied.This technique can remove the limitation of small parameters for perturbation and the difficulty of selecting good coordinate functions about Galerkin technique.The effects caused by the boundary conditions and the Reynolds number on the flow were discussed.The position of the separate and reattachment points was obtained.The tendency of the variation about the shear stress on the wall and friction factor along the axis direction were also analyzed.The results at a small parameter have good agreements with the perturbation ones.展开更多
This paper presents an efficient algorithm for optimization of radial distribution systems by a network reconfiguration to balance feeder loads and eliminate overload conditions. The system load-balancing index is use...This paper presents an efficient algorithm for optimization of radial distribution systems by a network reconfiguration to balance feeder loads and eliminate overload conditions. The system load-balancing index is used to determine the loading conditions of the system and maximum system loading capacity. The index value has to be minimum in the optimal network reconfiguration of load balancing. The tabu search algorithm is employed to search for the optimal network reconfiguration. The basic idea behind the search is a move from a current solution to its neighborhood by effectively utilizing a memory to provide an efficient search for optimality. It presents low computational effort and is able to find good quality configurations. Simulation results for a radial 69-bus system. The study results show that the optimal on/off patterns of the switches can be identified to give the best network reconfiguration involving balancing of feeder loads while respecting all the constraints.展开更多
A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Pe...A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Periodic solutions are obtained through harmonic balance method with alternating frequency/time domain(HB-AFT) technique, and then compared with the results of numerical simulation. Good agreement confirms the feasibility of HB-AFT scheme. Moreover, the Floquet theory is adopted to analyze motion stability of the system when rotor runs at different speed intervals. A simple strategy to determine the monodromy matrix is introduced and two ways towards unstability are found for periodic solutions: the period doubling bifurcation and the secondary Hopf bifurcation. The results obtained will contribute to the global response analysis and dynamic optimal design of rotor systems.展开更多
Background:Human immunodeficiency virus(HIV)is spreading rapidly among men who have sex with men(MSM)in China.Anonymous questionnaires or direct interviews have been frequently used to study their behavior.The aim of ...Background:Human immunodeficiency virus(HIV)is spreading rapidly among men who have sex with men(MSM)in China.Anonymous questionnaires or direct interviews have been frequently used to study their behavior.The aim of the study was to describe the behavioral risk profile of the MSM in Beijing using the randomized response techniques(RRTs).Methods:A cross-sectional survey of sexual behavior among a sample of MSM was conducted in two HIV counseling and testing clinics in Beijing.The survey was carried out with an anonymous questionnaire containing sensitive questions on sexual behavior.To obtain the honest responses to the sensitive questions,three distinctive RRTs were used in the questionnaire:(1)Additive randomized response model for quantitative questions,(2)randomized response model for multiple choice questions,and(3)Simmons randomized response model for binomial questions.Formulae for the point estimate,variance,and confidence interval(CI)were provided for each specific model.Results:Using RRTs in a sample of 659 participants,the mean age at first homosexual encounter was estimated to be 21.7 years(95%CI:21.2-22.2),and each had sex with about three(2.9,95%CI:2.4-3.4)male partners on average in the past month.The estimated rate for consistent condom use was 56.4%(95%CI:50.1-62.8%).In addition,condom was estimated to be used among 80.0%(95%CI:74.1-85.9%)of the population during last anal sex with a male partner.Conclusions:Our study employed RRTs in a survey containing questions on sexual behavior among MSM,and the results showed that RRT might be a useful tool to obtain truthful feedback on sensitive information such as sexual behavior from the respondents,especially in traditional Chinese cultural settings.展开更多
基金supported by the National Natural Science Foundation of China(No.10632040)
文摘Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.
基金supported by the National Natural Science Foundation of China (No. 40672086)the Ministry of Science and Technology of China (No. 2006CB701400)
文摘The Tanggula （唐古拉） thrust system and the Tuotuohe （沱沱河） foreland basin, which represent major Cenozoic tectonic units of the central Tibetan plateau, have been recently studied. Field investigation, analyses of deformation and construction of two restored balanced structural sections suggest 75-100 km （51%-64%） of N-S shortening in the Tanggula thrust system and 55-114 km （42%-47%） of N-S shortening in the Tuotuohe basin. The shortening ratios indicate that the Tanggula- Tuotuohe area has undergone intensive deformation and crustal shortening during the Early Tertiary, resulting not only in crustal thickening, but also in large scale volcanism and in rapid uplift of the Tanggula Mountains.
文摘The paper presents modeling approach of a Single Ended Primary Inductance Converter (SEPIC) system. The complete model derivation of the SEPIC converter system has been presented in different modes of operation. Steady state and small signal analysis was carried out on the converter dynamic equations using the method of Harmonic balance Technique. The steady state variables and their respective ripple quantities obtained were plotted against duty ratio D. The results obtained for a supply input voltage of 60 volts to the converter at a duty ratio of D = 0.8 , compares well with simulation results.
文摘In this paper,an improved method,which is based on the harmonic-balance tech-nique,for speeding up the convergence iteration procedure is presented.As an example,it isapplied to the nonlinear analysis of microwave mixer,in which a simple time domain to fre-quency domain transformation technique for the mixer diode is firstly introduced.The use of thistechnique saves computing time dramatically.And the analyzed results are in good agreementwith the results published.The improved method can also be extended to the CAA of nonlinearcircuits with multi-devices.
基金supported in part by the National Natural Science Foundation of China(61633006)the Fundamental Research Funds for the Central Universities of China(DUT2018TB06)National Key Research and Development Program of China(2017YFA0700300)。
文摘In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate solution in terms of the automatic differentiation(AD)algorithm.To overcome the deficiency of CAT that demands high computation cost for implementation,a set of ordinary differential equations(ODEs)entailed from CAT based discretized population balance equation(PBE)are solved by using the AD based high-order Taylor expansion.Moreover,an AD based trust-region reflective(TRR)algorithm and another interior-point(IP)algorithm are established for estimating the kinetic parameters associated with particle growth,aggregation and breakage.As a result,the estimation accuracy can be further improved while the computation cost can be significantly reduced,compared to the existing algorithms.Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT,TRR and IP algorithms in comparison with the existing algorithms.Moreover,seeded batch cooling crystallization experiments ofβform L-glutamic acid are performed to validate the proposed method.
基金Project(2012CB725403)supported by the National Basic Research Program of ChinaProjects(71210001,51338008)supported by the National Natural Science Foundation of ChinaProject supported by World Capital Cities Smooth Traffic Collaborative Innovation Center and Singapore National Research Foundation Under Its Campus for Research Excellence and Technology Enterprise(CREATE)Programme
文摘Short-term traffic flow prediction is one of the essential issues in intelligent transportation systems(ITS). A new two-stage traffic flow prediction method named AKNN-AVL method is presented, which combines an advanced k-nearest neighbor(AKNN)method and balanced binary tree(AVL) data structure to improve the prediction accuracy. The AKNN method uses pattern recognition two times in the searching process, which considers the previous sequences of traffic flow to forecast the future traffic state. Clustering method and balanced binary tree technique are introduced to build case database to reduce the searching time. To illustrate the effects of these developments, the accuracies performance of AKNN-AVL method, k-nearest neighbor(KNN) method and the auto-regressive and moving average(ARMA) method are compared. These methods are calibrated and evaluated by the real-time data from a freeway traffic detector near North 3rd Ring Road in Beijing under both normal and incident traffic conditions.The comparisons show that the AKNN-AVL method with the optimal neighbor and pattern size outperforms both KNN method and ARMA method under both normal and incident traffic conditions. In addition, the combinations of clustering method and balanced binary tree technique to the prediction method can increase the searching speed and respond rapidly to case database fluctuations.
基金National Nonprofit Institute Research Grant for the Institute of Basic Theory for Chinese Medicine,China Academy of Chinese Medical Sciences:Mechanism of Regulating Phlegm-Dampness Constitution to Prevent Metabolic Diseases based on Gut Microbiota-host DNA Methylation(No.YZ-202151)。
文摘OBJECTIVE:To investigate the difference in gut microbiota between population with damp-heat constitution(DHC)and balanced constitution(BC).METHODS:A multi-centered cross-sectional casecontrol study was conducted,which included 249 participants with damp-heat constitution or balanced constitution.Baseline information of participants was collected,and stool samples were collected for gut microbiota analysis.Principal coordinate analysis,linear discriminant analysis effect size analysis,receiver operating characteristic,random forest model,and phylogenetic investigation of communities by reconstruction of unobserved states methods were used to reveal the relationship between gut microbiota and the damp-heat constitution.RESULTS:Compared to those in the BC group,the richness and diversity of the microbiota,specifically those of several short-chain fatty acid producing genera such as Barnesiella,Coprobacter,and Butyricimonas,were significantly decreased in the DHC group.Regarding biological functions,flavonoid biosynthesis,propanoate metabolism,and nucleotide sugar metabolism were suppressed,while arachidonic acid metabolism and glutathione metabolism were enriched in the DHC group.Finally,a classifier based on the microbiota was constructed to discriminate between the DHC and BC populations.CONCLUSION:The gut microbiota of the DHC population exhibits significantly reduced diversity and is closely related to inflammation,metabolic disorders,and liver steatosis,which is consistent with clinical observations,thus serving as a potential diagnostic tool for traditional Chinese medicine constitution discrimination.
基金supported by National Key Research and Development Program of China(No.2021YFA0717100)NationalNatural Science Foundation of China(Nos.12072270,U2013206).
文摘The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to complex symbolic operations.Many variants have been developed to improve the HB method,among which the time domain HB-like methods are regarded as crucial improvements because of their fast computation and simple derivation.So far,there are two problems remaining to be addressed.i)A dozen of different versions of HB-like methods,in frequency domain or time domain or in hybrid,have been developed;unfortunately,misclassification pervades among them due to the unclear borderlines of different methods.ii)The time domain HB-like methods suffer from non-physical solutions,which have been shown to be caused by aliasing(mixture of the high-order into the low-order harmonics).Although a series of dealiasing techniques have been developed over the past two decades,the mechanism of aliasing and the final solution to dealiasing are still not well known to the academic community.This paper aims to provide a comprehensive review of the development of HB-like methods and enunciate their principal differences.In particular,the time domain methods are emphasized with the famous aliasing phenomenon clearly addressed.
基金supported by a grant from the Shanghai Key Laboratory of Peripheral Nerve and Microsurgery in China,No.14DZ2273300the Natural Science Foundation of Shanghai in China,No.13ZR1404600a grant from the National Key Basic Research Program of China(973 Program),No.2014CB542201
文摘Although ultrasound measurements have been used in previous studies on carpal tunnel syndrome to visualize injury to the median nerve, whether such ultrasound data can indicate the severity of carpal tunnel syndrome remains controversial. The cross-sectional areas of the median nerve at the tunnel inlet and outlet can show swelling and compression of the nerve at the carpal. We hypothesized that the ratio of the cross-sectional areas of the median nerve at the carpal tunnel inlet to outlet accurately reflects the severity of carpal tunnel syndrome. To test this, high-resolution ultrasound with a linear array transducer at 5–17 MHz was used to assess 77 patients with carpal tunnel syndrome. The results showed that the cut-off point for the inlet-to-outlet ratio was 1.14. Significant differences in the inlet-to-outlet ratio were found among patients with mild, moderate, and severe carpal tunnel syndrome. The cut-off point in the ratio of cross-sectional areas of the median nerve was 1.29 between mild and more severe（moderate and severe） carpal tunnel syndrome patients with 64.7% sensitivity and 72.7% specificity. The cut-off point in the ratio of cross-sectional areas of the median nerve was 1.52 between the moderate and severe carpal tunnel syndrome patients with 80.0% sensitivity and 64.7% specificity. These results suggest that the inlet-to-outlet ratio reflected the severity of carpal tunnel syndrome.
文摘Using hybrid perturbatin_Galerkin technique,a crcular cross_section tube model with sinusoidal wall is studied.This technique can remove the limitation of small parameters for perturbation and the difficulty of selecting good coordinate functions about Galerkin technique.The effects caused by the boundary conditions and the Reynolds number on the flow were discussed.The position of the separate and reattachment points was obtained.The tendency of the variation about the shear stress on the wall and friction factor along the axis direction were also analyzed.The results at a small parameter have good agreements with the perturbation ones.
文摘This paper presents an efficient algorithm for optimization of radial distribution systems by a network reconfiguration to balance feeder loads and eliminate overload conditions. The system load-balancing index is used to determine the loading conditions of the system and maximum system loading capacity. The index value has to be minimum in the optimal network reconfiguration of load balancing. The tabu search algorithm is employed to search for the optimal network reconfiguration. The basic idea behind the search is a move from a current solution to its neighborhood by effectively utilizing a memory to provide an efficient search for optimality. It presents low computational effort and is able to find good quality configurations. Simulation results for a radial 69-bus system. The study results show that the optimal on/off patterns of the switches can be identified to give the best network reconfiguration involving balancing of feeder loads while respecting all the constraints.
基金supported by the National Basic Research Program of China("973" Project)(Grant No.2015CB057400)the National Natural Science Foundation of China(Grant No.11302058)
文摘A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Periodic solutions are obtained through harmonic balance method with alternating frequency/time domain(HB-AFT) technique, and then compared with the results of numerical simulation. Good agreement confirms the feasibility of HB-AFT scheme. Moreover, the Floquet theory is adopted to analyze motion stability of the system when rotor runs at different speed intervals. A simple strategy to determine the monodromy matrix is introduced and two ways towards unstability are found for periodic solutions: the period doubling bifurcation and the secondary Hopf bifurcation. The results obtained will contribute to the global response analysis and dynamic optimal design of rotor systems.
基金the National Natural Science Foundation of Chinathe Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institutions
文摘Background:Human immunodeficiency virus(HIV)is spreading rapidly among men who have sex with men(MSM)in China.Anonymous questionnaires or direct interviews have been frequently used to study their behavior.The aim of the study was to describe the behavioral risk profile of the MSM in Beijing using the randomized response techniques(RRTs).Methods:A cross-sectional survey of sexual behavior among a sample of MSM was conducted in two HIV counseling and testing clinics in Beijing.The survey was carried out with an anonymous questionnaire containing sensitive questions on sexual behavior.To obtain the honest responses to the sensitive questions,three distinctive RRTs were used in the questionnaire:(1)Additive randomized response model for quantitative questions,(2)randomized response model for multiple choice questions,and(3)Simmons randomized response model for binomial questions.Formulae for the point estimate,variance,and confidence interval(CI)were provided for each specific model.Results:Using RRTs in a sample of 659 participants,the mean age at first homosexual encounter was estimated to be 21.7 years(95%CI:21.2-22.2),and each had sex with about three(2.9,95%CI:2.4-3.4)male partners on average in the past month.The estimated rate for consistent condom use was 56.4%(95%CI:50.1-62.8%).In addition,condom was estimated to be used among 80.0%(95%CI:74.1-85.9%)of the population during last anal sex with a male partner.Conclusions:Our study employed RRTs in a survey containing questions on sexual behavior among MSM,and the results showed that RRT might be a useful tool to obtain truthful feedback on sensitive information such as sexual behavior from the respondents,especially in traditional Chinese cultural settings.
