To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) ...To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) of X(0) as the starting condition of the grey differential model. It optimizes a modified β value and the background value, and takes two times fitting optimization. The new model extends equal intervals to non-equal-intervals and is suitable for general data modelling and estimating parameters of the direct Verhulst GM(1,1). The new model does not need to pre-process the primitive data, nor accumulate generating operation (AGO) and inverse accumulated generating operation (IAGO). It is not only suitable for equal interval data modelling, but also for non-equal interval data modelling. As the new information is fully used and two times fitting optimization is taken, the fitting accuracy is the highest in all existing models. The example shows that the new model is simple and practical. The new model is worth expanding on and applying in data processing or on-line monitoring for tests, social sciences and other engineering sciences.展开更多
Applying the modeling method of Grey system and accumulated generating operation of reciprocal number for the problem of lower precision as well as lower adaptability in non-equidistant GM (1, 1) model, the calculatio...Applying the modeling method of Grey system and accumulated generating operation of reciprocal number for the problem of lower precision as well as lower adaptability in non-equidistant GM (1, 1) model, the calculation formulas were deduced and a non-equidistant GRM (1, 1) model generated by accumulated generating operation of reciprocal number was put forward .The grey GRM (1, 1) model can be used in non-equal interval & equal interval time series and has the characteristic of high precision as well as high adaptability. Example validates the practicability and reliability of the proposed model.展开更多
The transit time difference of fluid particles moving along the upper and lower surfaces of a lift-producing airfoil is studied here both theoretically and numerically.We show that,under thin airfoil assumption and fo...The transit time difference of fluid particles moving along the upper and lower surfaces of a lift-producing airfoil is studied here both theoretically and numerically.We show that,under thin airfoil assumption and for potential flow,the transit time difference is equal to the circulation divided by the square of the inflow velocity and the lift coefficient is equal to half of the number of chords travelled by the airfoil during the transit time difference.An analysis of transit time difference for very thick airfoil(c.f.very large angle of attack)suggests the transit time may change sign beyond thin airfoil assumption,a conclusion supported by an example of flow with an attached vortex.Thus,fluid particles may transit the upper surface with less,equal and more time than those transiting the lower surface for lift producing airfoils,depending on the configuration of flow structure and geometry.展开更多
A novel time-span input neural network was developed to accurately predict the trend of the main steam temperature of a 750-t/d waste incineration boiler.Its historical operating data were used to retrieve sensitive p...A novel time-span input neural network was developed to accurately predict the trend of the main steam temperature of a 750-t/d waste incineration boiler.Its historical operating data were used to retrieve sensitive parameters for the boiler output steam temperature by correlation analysis.Then,the 15 most sensitive parameters with specified time spans were selected as neural network inputs.An external testing set was introduced to objectively evaluate the neural network prediction capability.The results show that,compared with the traditional prediction method,the time-span input framework model can achieve better prediction performance and has a greater capability for generalization.The maximum average prediction error can be controlled below 0.2°C and 1.5°C in the next 60 s and 5 min,respectively.In addition,setting a reasonable terminal training threshold can effectively avoid overfitting.An importance analysis of the parameters indicates that the main steam temperature and the average temperature around the high-temperature superheater are the two most important variables of the input parameters;the former affects the overall prediction and the latter affects the long-term prediction performance.展开更多
基金The 11th Five-Year Plan for Key Constructing Academic Subject of Hunan Province(No.XJT2006180)Natural Science Foundation of Hunan Province (No.07JJ3093)Hunan Province Foundation Research Program (No.2007FJ3030,2007GK3058)
文摘To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) of X(0) as the starting condition of the grey differential model. It optimizes a modified β value and the background value, and takes two times fitting optimization. The new model extends equal intervals to non-equal-intervals and is suitable for general data modelling and estimating parameters of the direct Verhulst GM(1,1). The new model does not need to pre-process the primitive data, nor accumulate generating operation (AGO) and inverse accumulated generating operation (IAGO). It is not only suitable for equal interval data modelling, but also for non-equal interval data modelling. As the new information is fully used and two times fitting optimization is taken, the fitting accuracy is the highest in all existing models. The example shows that the new model is simple and practical. The new model is worth expanding on and applying in data processing or on-line monitoring for tests, social sciences and other engineering sciences.
文摘Applying the modeling method of Grey system and accumulated generating operation of reciprocal number for the problem of lower precision as well as lower adaptability in non-equidistant GM (1, 1) model, the calculation formulas were deduced and a non-equidistant GRM (1, 1) model generated by accumulated generating operation of reciprocal number was put forward .The grey GRM (1, 1) model can be used in non-equal interval & equal interval time series and has the characteristic of high precision as well as high adaptability. Example validates the practicability and reliability of the proposed model.
基金supported partly by the National Key Project of China(No.GJXM92579)the National Science and Technology Major Project of China(No.2017-II-003-0015)the National Natural Science Foundation of China(No.11721202)。
文摘The transit time difference of fluid particles moving along the upper and lower surfaces of a lift-producing airfoil is studied here both theoretically and numerically.We show that,under thin airfoil assumption and for potential flow,the transit time difference is equal to the circulation divided by the square of the inflow velocity and the lift coefficient is equal to half of the number of chords travelled by the airfoil during the transit time difference.An analysis of transit time difference for very thick airfoil(c.f.very large angle of attack)suggests the transit time may change sign beyond thin airfoil assumption,a conclusion supported by an example of flow with an attached vortex.Thus,fluid particles may transit the upper surface with less,equal and more time than those transiting the lower surface for lift producing airfoils,depending on the configuration of flow structure and geometry.
基金Project supported by the National Key Research and Development Program of China(No.2018YFC1901300)the Research Project of Multi-data Fusion and Strategy of Intelligent Control and Optimization for Large Scale Industrial Combustion System,China。
文摘A novel time-span input neural network was developed to accurately predict the trend of the main steam temperature of a 750-t/d waste incineration boiler.Its historical operating data were used to retrieve sensitive parameters for the boiler output steam temperature by correlation analysis.Then,the 15 most sensitive parameters with specified time spans were selected as neural network inputs.An external testing set was introduced to objectively evaluate the neural network prediction capability.The results show that,compared with the traditional prediction method,the time-span input framework model can achieve better prediction performance and has a greater capability for generalization.The maximum average prediction error can be controlled below 0.2°C and 1.5°C in the next 60 s and 5 min,respectively.In addition,setting a reasonable terminal training threshold can effectively avoid overfitting.An importance analysis of the parameters indicates that the main steam temperature and the average temperature around the high-temperature superheater are the two most important variables of the input parameters;the former affects the overall prediction and the latter affects the long-term prediction performance.
