This paper focuses on resolving the identification problem of a neuro-fuzzy model(NFM) applied in batch processes. A hybrid learning algorithm is introduced to identify the proposed NFM with the idea of auxiliary erro...This paper focuses on resolving the identification problem of a neuro-fuzzy model(NFM) applied in batch processes. A hybrid learning algorithm is introduced to identify the proposed NFM with the idea of auxiliary error model and the identification principle based on the probability density function(PDF). The main contribution is that the NFM parameter updating approach is transformed into the shape control for the PDF of modeling error. More specifically, a virtual adaptive control system is constructed with the aid of the auxiliary error model and then the PDF shape control idea is used to tune NFM parameters so that the PDF of modeling error is controlled to follow a targeted PDF, which is in Gaussian or uniform distribution. Examples are used to validate the applicability of the proposed method and comparisons are made with the minimum mean square error based approaches.展开更多
We propose a new type of dark energy （DE） model, in which the equation of state of DE wae is a simple function of the fractional energy density Ωde instead of the redshift z. We assume three DE models of this type,...We propose a new type of dark energy （DE） model, in which the equation of state of DE wae is a simple function of the fractional energy density Ωde instead of the redshift z. We assume three DE models of this type, and fit them with present observations to get constraints of DE, which are also compared with the CPL model. It is shown that a suitable wda,（Ωde） model can give smaller X2 or smaller errors of wde than that of the CPL model. This new type of DE model can help to study the essential properties and nature of DE.展开更多
基金Supported by the National Natural Science Foundation of China(61374044)Shanghai Science Technology Commission(12510709400)+1 种基金Shanghai Municipal Education Commission(14ZZ088)Shanghai Talent Development Plan
文摘This paper focuses on resolving the identification problem of a neuro-fuzzy model(NFM) applied in batch processes. A hybrid learning algorithm is introduced to identify the proposed NFM with the idea of auxiliary error model and the identification principle based on the probability density function(PDF). The main contribution is that the NFM parameter updating approach is transformed into the shape control for the PDF of modeling error. More specifically, a virtual adaptive control system is constructed with the aid of the auxiliary error model and then the PDF shape control idea is used to tune NFM parameters so that the PDF of modeling error is controlled to follow a targeted PDF, which is in Gaussian or uniform distribution. Examples are used to validate the applicability of the proposed method and comparisons are made with the minimum mean square error based approaches.
基金Supported in part by the National Natural Science Foundation of China under Grant No. 11147186Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ12A05004 and Grant from Hangzhou Normal University
文摘We propose a new type of dark energy （DE） model, in which the equation of state of DE wae is a simple function of the fractional energy density Ωde instead of the redshift z. We assume three DE models of this type, and fit them with present observations to get constraints of DE, which are also compared with the CPL model. It is shown that a suitable wda,（Ωde） model can give smaller X2 or smaller errors of wde than that of the CPL model. This new type of DE model can help to study the essential properties and nature of DE.
