In order to improve the strength and stiffness of shield cutterhead, the method of fuzzy mathematics theory in combination with the finite element analysis is adopted. An optimal design model of structural parameters ...In order to improve the strength and stiffness of shield cutterhead, the method of fuzzy mathematics theory in combination with the finite element analysis is adopted. An optimal design model of structural parameters for shield cutterhead is formulated,based on the complex engineering technical requirements. In the model, as the objective function of the model is a composite function of the strength and stiffness, the response surface method is applied to formulate the approximate function of objective function in order to reduce the solution scale of optimal problem. A multi-objective genetic algorithm is used to solve the cutterhead structure design problem and the change rule of the stress-strain with various structural parameters as well as their optimal values were researched under specific geological conditions. The results show that compared with original cutterhead structure scheme, the obtained optimal scheme of the cutterhead structure can greatly improve the strength and stiffness of the cutterhead, which can be seen from the reduction of its maximum equivalent stress by 21.2%, that of its maximum deformation by 0.75%, and that of its mass by 1.04%.展开更多
Grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized an...Grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized and redefined. This paper includes the fundamental definitions and calculation rules of the grey hazy set, grey number, grey matrix and grey function. Grey mathematics includes four types of operation, i.e. the grey operation, the whitened operation, the covered operation and the only potential true operation. According to its intrinsic quality, the covered operation, which differs from the interval one, is called as the whole-proximate calculation that means the proximate calculation spreads through the whole range of the covered set of every grey number, and we confirm that it may be a new branch of computational or applied mathematics. The overview should develop the grey system theory and grey mathematics.展开更多
To apply the fire modelling for the fire engineer with symbolic mathematics,the key equations of a zone model were demonstrated. There were thirteen variables with nine constraints,so only four ordinary differential e...To apply the fire modelling for the fire engineer with symbolic mathematics,the key equations of a zone model were demonstrated. There were thirteen variables with nine constraints,so only four ordinary differential equations (ODEs) were required to solve. A typical fire modelling with two-room structure was studied. Accordingly,the source terms included in the ODEs were simplified and modelled,and the fourth Runge-Kutta method was used to solve the ordinary differential equations (ODEs) with symbolic mathematics. Then a zone model could be used with symbolic mathematics. It is proposed that symbolic mathematics is possible for use by fire engineer.展开更多
The purpose of this award is to recognize work of lasting significance and impact in advancing mathematics education as an interdisciplinary field,linking mathematics,educational studies and practice.In particular,the...The purpose of this award is to recognize work of lasting significance and impact in advancing mathematics education as an interdisciplinary field,linking mathematics,educational studies and practice.In particular,the award recognizes major contributions to new knowledge and scholarship,and as well,exemplary contributions in promoting interdisciplinary collaboration in mathematics education.展开更多
It focuses on that students must be developed the ability to solve the practical problem by building the mathematics models and the ability to combine the theory with the practice. It also states that students must be...It focuses on that students must be developed the ability to solve the practical problem by building the mathematics models and the ability to combine the theory with the practice. It also states that students must be improved the learning interests and practical experience.展开更多
The problem on the stability of motion for a generalized Birkhoffian system was studied. The disturbed equations of motion and their first approximation for the system were established. The criterion of stability of m...The problem on the stability of motion for a generalized Birkhoffian system was studied. The disturbed equations of motion and their first approximation for the system were established. The criterion of stability of motion for the system was set up by using Liapunov's first approximation theory. Based on the theory of Noether symmetry,the Liapunov's function was constructed,and the criterion of stability of motion for the system was also set up by using Liapunov's direct method. Two examples were given to illustrate the application of the results.展开更多
In order to accurately forecast the load of power system and enhance the stability of the power network, a novel unascertained mathematics based recurrent neural network (UMRNN) for power intelligence center (PIC) was...In order to accurately forecast the load of power system and enhance the stability of the power network, a novel unascertained mathematics based recurrent neural network (UMRNN) for power intelligence center (PIC) was created through three steps. First, by combining with the general project uncertain element transmission theory (GPUET), the basic definitions of stochastic, fuzzy, and grey uncertain elements were given based on the principal types of uncertain information. Second, a power dynamic alliance including four sectors: generation sector, transmission sector, distribution sector and customers was established. The key factors were amended according to the four transmission topologies of uncertain elements, thus the new factors entered the power intelligence center as the input elements. Finally, in the intelligence handing background of PIC, by performing uncertain and recursive process to the input values of network, and combining unascertained mathematics, the novel load forecasting model was built. Three different approaches were put forward to forecast an eastern regional power grid load in China. The root mean square error (ERMS) demonstrates that the forecasting accuracy of the proposed model UMRNN is 3% higher than that of BP neural network (BPNN), and 5% higher than that of autoregressive integrated moving average (ARIMA). Besides, an example also shows that the average relative error of the first quarter of 2008 forecasted by UMRNN is only 2.59%, which has high precision.展开更多
To solve the problems that exist in the color morphological sieves, a new fuzzy color morphological sieve is proposed.The method adopts color fuzzy model to define extrema and selects more rational regional merging wa...To solve the problems that exist in the color morphological sieves, a new fuzzy color morphological sieve is proposed.The method adopts color fuzzy model to define extrema and selects more rational regional merging way to produce better results.It can deal with the maxima or the minima areas respectively and the approach is simple and agile in design.The color fuzzy model and the steps of the algorithm are discussed.The evaluation of the performance shows the new method can produce the best synthetical performance.展开更多
In the process of evaluating,the weights of indicators are firstly determined by AHP and Delphi methods;and the values of indicators are normalized by grey correlative coefficient method.A suit of means were put forwa...In the process of evaluating,the weights of indicators are firstly determined by AHP and Delphi methods;and the values of indicators are normalized by grey correlative coefficient method.A suit of means were put forward,by which a qualitative and quantitative evaluation indicator system suitable for the situation of China and uncertainties can be established.Both idiographic and operable methods and process were presented.Following the principle of elasticity,hiberarchy and maneuverability,a three-layer evaluation indicator system was established by AHP in Jiuyi ecological residential community,which includes 5 subsystems and 24 indicatiors.The weights of indicators are measured by AHP and expert estimate and their best indicators values up to par were determined by fuzzy mathematics and optimization.The whole evaluation indicator system not only has an active and practical effect on estimating ecological residential community,but also guides ecological residential community planning.展开更多
In this paper, a theoretical model of multi-level, non-spherical scatterers is developed for fully polarimetric scattering from tree canopy in SAR imaging at C band. The amplitude functions of non-spherical particles ...In this paper, a theoretical model of multi-level, non-spherical scatterers is developed for fully polarimetric scattering from tree canopy in SAR imaging at C band. The amplitude functions of non-spherical particles with randomly spatial orientation are derived by the generalized Rayleigh-Gans (GRG) approximation. The non-diagonal extinction matrix and the Mueller matrix solution are constructed. Numerical solutions of polarimetric scattering of four Stokes parameters from random, non-spherical scatterers are obtained. To physically identify polarimetric scattering of the Mueller matrix solution, the coherency matrix and its eigen-analysis are discussed. Functional dependence of the coherency matrix and entropy upon various parameters are obtained. As an application, the analysis of AirSAR images at P, L, C bands is discussed.展开更多
Lifting scheme is a second-generation wavelet transform which is easier to understand than the first-generation wavelet transform. Fourier analysis is not necessary for the construction, and inverse transform can natu...Lifting scheme is a second-generation wavelet transform which is easier to understand than the first-generation wavelet transform. Fourier analysis is not necessary for the construction, and inverse transform can naturally be realized. Furthermore, it is faster than the first-generation wavelet transform. In terms of compression ratio and compression efficiency, SPIHT is the best algorithm based on EZW, but its theory is difficult to understand and come true. We carry out the SPIHT algorithm, and propose a reformed algorithm based on SPIHT, making the realization more easier. In the end, LSS algorithm composed of lifting scheme and SPIHT algorithm is presented, whose compression efficiency is the same as SPIHT, but running is 10% faster than SPIHT.展开更多
基金Project(51074180) supported by the National Natural Science Foundation of ChinaProject(2012AA041801) supported by the National High Technology Research and Development Program of China+2 种基金Project(2007CB714002) supported by the National Basic Research Program of ChinaProject(2013GK3003) supported by the Technology Support Plan of Hunan Province,ChinaProject(2010FJ1002) supported by Hunan Science and Technology Major Program,China
文摘In order to improve the strength and stiffness of shield cutterhead, the method of fuzzy mathematics theory in combination with the finite element analysis is adopted. An optimal design model of structural parameters for shield cutterhead is formulated,based on the complex engineering technical requirements. In the model, as the objective function of the model is a composite function of the strength and stiffness, the response surface method is applied to formulate the approximate function of objective function in order to reduce the solution scale of optimal problem. A multi-objective genetic algorithm is used to solve the cutterhead structure design problem and the change rule of the stress-strain with various structural parameters as well as their optimal values were researched under specific geological conditions. The results show that compared with original cutterhead structure scheme, the obtained optimal scheme of the cutterhead structure can greatly improve the strength and stiffness of the cutterhead, which can be seen from the reduction of its maximum equivalent stress by 21.2%, that of its maximum deformation by 0.75%, and that of its mass by 1.04%.
基金supported by the China Postdoctoral Science Foundation(200902321)a Marie Curie International Incoming Fellowship within the 7th European Community Framework Program(FP7-PIIFGA-2013-629051)
文摘Grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized and redefined. This paper includes the fundamental definitions and calculation rules of the grey hazy set, grey number, grey matrix and grey function. Grey mathematics includes four types of operation, i.e. the grey operation, the whitened operation, the covered operation and the only potential true operation. According to its intrinsic quality, the covered operation, which differs from the interval one, is called as the whole-proximate calculation that means the proximate calculation spreads through the whole range of the covered set of every grey number, and we confirm that it may be a new branch of computational or applied mathematics. The overview should develop the grey system theory and grey mathematics.
基金Project(PolyU B-Q01e) supported by the Research Project "Onsetting of Internal Fire Whirls in Buildings and Associated Safet Provision"
文摘To apply the fire modelling for the fire engineer with symbolic mathematics,the key equations of a zone model were demonstrated. There were thirteen variables with nine constraints,so only four ordinary differential equations (ODEs) were required to solve. A typical fire modelling with two-room structure was studied. Accordingly,the source terms included in the ODEs were simplified and modelled,and the fourth Runge-Kutta method was used to solve the ordinary differential equations (ODEs) with symbolic mathematics. Then a zone model could be used with symbolic mathematics. It is proposed that symbolic mathematics is possible for use by fire engineer.
文摘The purpose of this award is to recognize work of lasting significance and impact in advancing mathematics education as an interdisciplinary field,linking mathematics,educational studies and practice.In particular,the award recognizes major contributions to new knowledge and scholarship,and as well,exemplary contributions in promoting interdisciplinary collaboration in mathematics education.
文摘It focuses on that students must be developed the ability to solve the practical problem by building the mathematics models and the ability to combine the theory with the practice. It also states that students must be improved the learning interests and practical experience.
基金Sponsored by the National Natural Science Foundation of China( 10972151)the Natural Science Foundation of Higher Education Institution of Jiangsu Province,China ( 08KJB130002)
文摘The problem on the stability of motion for a generalized Birkhoffian system was studied. The disturbed equations of motion and their first approximation for the system were established. The criterion of stability of motion for the system was set up by using Liapunov's first approximation theory. Based on the theory of Noether symmetry,the Liapunov's function was constructed,and the criterion of stability of motion for the system was also set up by using Liapunov's direct method. Two examples were given to illustrate the application of the results.
基金Projects(70572090, 70373017) supported by the National Natural Science Foundation of China
文摘In order to accurately forecast the load of power system and enhance the stability of the power network, a novel unascertained mathematics based recurrent neural network (UMRNN) for power intelligence center (PIC) was created through three steps. First, by combining with the general project uncertain element transmission theory (GPUET), the basic definitions of stochastic, fuzzy, and grey uncertain elements were given based on the principal types of uncertain information. Second, a power dynamic alliance including four sectors: generation sector, transmission sector, distribution sector and customers was established. The key factors were amended according to the four transmission topologies of uncertain elements, thus the new factors entered the power intelligence center as the input elements. Finally, in the intelligence handing background of PIC, by performing uncertain and recursive process to the input values of network, and combining unascertained mathematics, the novel load forecasting model was built. Three different approaches were put forward to forecast an eastern regional power grid load in China. The root mean square error (ERMS) demonstrates that the forecasting accuracy of the proposed model UMRNN is 3% higher than that of BP neural network (BPNN), and 5% higher than that of autoregressive integrated moving average (ARIMA). Besides, an example also shows that the average relative error of the first quarter of 2008 forecasted by UMRNN is only 2.59%, which has high precision.
基金supported by the National Natural Science Foundation of China(6137301761402241+4 种基金615722606157226161472192)the Scientific&Technological Support Project of Jiangsu Province(BE2014718BE2015702)
基金supported by the Provincial Youth Scientist Fund (2005BS01001)the Provincial Natural Science Fund (Z2006G10)the Scientific Research Foundation for Advanced Talents of Huaihai Institute of Technology
文摘To solve the problems that exist in the color morphological sieves, a new fuzzy color morphological sieve is proposed.The method adopts color fuzzy model to define extrema and selects more rational regional merging way to produce better results.It can deal with the maxima or the minima areas respectively and the approach is simple and agile in design.The color fuzzy model and the steps of the algorithm are discussed.The evaluation of the performance shows the new method can produce the best synthetical performance.
基金Supported by Hunan Provincial Science and Technology Program(05SK3082,2007SK4012)Natural Science Foundation-funded Project(06JJ5147)
文摘In the process of evaluating,the weights of indicators are firstly determined by AHP and Delphi methods;and the values of indicators are normalized by grey correlative coefficient method.A suit of means were put forward,by which a qualitative and quantitative evaluation indicator system suitable for the situation of China and uncertainties can be established.Both idiographic and operable methods and process were presented.Following the principle of elasticity,hiberarchy and maneuverability,a three-layer evaluation indicator system was established by AHP in Jiuyi ecological residential community,which includes 5 subsystems and 24 indicatiors.The weights of indicators are measured by AHP and expert estimate and their best indicators values up to par were determined by fuzzy mathematics and optimization.The whole evaluation indicator system not only has an active and practical effect on estimating ecological residential community,but also guides ecological residential community planning.
文摘In this paper, a theoretical model of multi-level, non-spherical scatterers is developed for fully polarimetric scattering from tree canopy in SAR imaging at C band. The amplitude functions of non-spherical particles with randomly spatial orientation are derived by the generalized Rayleigh-Gans (GRG) approximation. The non-diagonal extinction matrix and the Mueller matrix solution are constructed. Numerical solutions of polarimetric scattering of four Stokes parameters from random, non-spherical scatterers are obtained. To physically identify polarimetric scattering of the Mueller matrix solution, the coherency matrix and its eigen-analysis are discussed. Functional dependence of the coherency matrix and entropy upon various parameters are obtained. As an application, the analysis of AirSAR images at P, L, C bands is discussed.
文摘Lifting scheme is a second-generation wavelet transform which is easier to understand than the first-generation wavelet transform. Fourier analysis is not necessary for the construction, and inverse transform can naturally be realized. Furthermore, it is faster than the first-generation wavelet transform. In terms of compression ratio and compression efficiency, SPIHT is the best algorithm based on EZW, but its theory is difficult to understand and come true. We carry out the SPIHT algorithm, and propose a reformed algorithm based on SPIHT, making the realization more easier. In the end, LSS algorithm composed of lifting scheme and SPIHT algorithm is presented, whose compression efficiency is the same as SPIHT, but running is 10% faster than SPIHT.
