The construction method of background value is improved in the original multi-variable grey model （MGM（1,m）） from its source of construction errors. The MGM（1,m） with optimized background value is used to elimin...The construction method of background value is improved in the original multi-variable grey model （MGM（1,m）） from its source of construction errors. The MGM（1,m） with optimized background value is used to eliminate the random fluctuations or errors of the observational data of all variables, and the combined prediction model together with the multiple linear regression is established in order to improve the simulation and prediction accuracy of the combined model. Finally, a combined model of the MGM（1,2） with optimized background value and the binary linear regression is constructed by an example. The results show that the model has good effects for simulation and prediction.展开更多
Rock mass rating system （RMR） is based on the six parameters which was defined by Bieniawski （1989） [1]. Experts frequently relate joint and discontinuities and ground water conditions in linguistic terms with rou...Rock mass rating system （RMR） is based on the six parameters which was defined by Bieniawski （1989） [1]. Experts frequently relate joint and discontinuities and ground water conditions in linguistic terms with rough calculation. As a result, there is a sharp transition between two modules which create doubts. So, in this paper the proposed weights technique was applied for linguistic criteria. Then by using the fuzzy inference system and the multi-variable regression analysis, the accurate RMR is predicted. Before the performing of regression analysis, sensitivity analysis was applied for each of Bieniawski parameters. In this process, the best function was selected among linear, logarithmic, exponential and inverse func- tions and finally it was applied in the regression analysis for construction of a predictive equation. From the constructed regression equation the relative importance of the input parameters can also be observed. It should be noted that joint condition was identified as the most important effective parameter upon RMR. Finally, fuzzy and regression models were validated with the test datasets and it was found that the fuzzy model predicts more accurately RMR than reression models.展开更多
This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h ...This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model （GM （1, h））, always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method （abbreviated as FDGM （1, h））, is proposed accordingly. Then the feedback control equation and the parameters＇ solution of the FDGM （1, h） model are given. Finally, a real application is used to test the modelling accuracy of the FDGM （1, h） model. Results show that the FDGM （1, h） model is much better than the nonhomogeneous discrete grey forecasting model （NDGM） and the GM （1, h） model.展开更多
The least squares support vector regression (LS-SVR) is usually used for the modeling of single output system, but it is not well suitable for the actual multi-input-multi-output system. The paper aims at the modeling...The least squares support vector regression (LS-SVR) is usually used for the modeling of single output system, but it is not well suitable for the actual multi-input-multi-output system. The paper aims at the modeling of multi-output systems by LS-SVR. The multi-output LS-SVR is derived in detail. To avoid the inversion of large matrix, the recursive algorithm of the parameters is given, which makes the online algorithm of LS-SVR practical. Since the computing time increases with the number of training samples, the sparseness is studied based on the pro-jection of online LS-SVR. The residual of projection less than a threshold is omitted, so that a lot of samples are kept out of the training set and the sparseness is obtained. The standard LS-SVR, nonsparse online LS-SVR and sparse online LS-SVR with different threshold are used for modeling the isomerization of C8 aromatics. The root-mean-square-error (RMSE), number of support vectors and running time of three algorithms are compared and the result indicates that the performance of sparse online LS-SVR is more favorable.展开更多
基金supported by the National Natural Science Foundation of China(71071077)the Ministry of Education Key Project of National Educational Science Planning(DFA090215)+1 种基金China Postdoctoral Science Foundation(20100481137)Funding of Jiangsu Innovation Program for Graduate Education(CXZZ11-0226)
文摘The construction method of background value is improved in the original multi-variable grey model （MGM（1,m）） from its source of construction errors. The MGM（1,m） with optimized background value is used to eliminate the random fluctuations or errors of the observational data of all variables, and the combined prediction model together with the multiple linear regression is established in order to improve the simulation and prediction accuracy of the combined model. Finally, a combined model of the MGM（1,2） with optimized background value and the binary linear regression is constructed by an example. The results show that the model has good effects for simulation and prediction.
文摘Rock mass rating system （RMR） is based on the six parameters which was defined by Bieniawski （1989） [1]. Experts frequently relate joint and discontinuities and ground water conditions in linguistic terms with rough calculation. As a result, there is a sharp transition between two modules which create doubts. So, in this paper the proposed weights technique was applied for linguistic criteria. Then by using the fuzzy inference system and the multi-variable regression analysis, the accurate RMR is predicted. Before the performing of regression analysis, sensitivity analysis was applied for each of Bieniawski parameters. In this process, the best function was selected among linear, logarithmic, exponential and inverse func- tions and finally it was applied in the regression analysis for construction of a predictive equation. From the constructed regression equation the relative importance of the input parameters can also be observed. It should be noted that joint condition was identified as the most important effective parameter upon RMR. Finally, fuzzy and regression models were validated with the test datasets and it was found that the fuzzy model predicts more accurately RMR than reression models.
基金supported by the National Natural Science Foundation of China(7117111370901041)
文摘This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model （GM （1, h））, always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method （abbreviated as FDGM （1, h））, is proposed accordingly. Then the feedback control equation and the parameters＇ solution of the FDGM （1, h） model are given. Finally, a real application is used to test the modelling accuracy of the FDGM （1, h） model. Results show that the FDGM （1, h） model is much better than the nonhomogeneous discrete grey forecasting model （NDGM） and the GM （1, h） model.
基金Supported by the National Creative Research Groups Science Foundation of China (60721062)the National Basic Research Program of China (2007CB714000)
文摘The least squares support vector regression (LS-SVR) is usually used for the modeling of single output system, but it is not well suitable for the actual multi-input-multi-output system. The paper aims at the modeling of multi-output systems by LS-SVR. The multi-output LS-SVR is derived in detail. To avoid the inversion of large matrix, the recursive algorithm of the parameters is given, which makes the online algorithm of LS-SVR practical. Since the computing time increases with the number of training samples, the sparseness is studied based on the pro-jection of online LS-SVR. The residual of projection less than a threshold is omitted, so that a lot of samples are kept out of the training set and the sparseness is obtained. The standard LS-SVR, nonsparse online LS-SVR and sparse online LS-SVR with different threshold are used for modeling the isomerization of C8 aromatics. The root-mean-square-error (RMSE), number of support vectors and running time of three algorithms are compared and the result indicates that the performance of sparse online LS-SVR is more favorable.
