Objective Any natural system is constantly exchanging material, energy and information with the environment, and all tkese processes follow the basic law of thermodynamics, with no exception of groundwater recharge a...Objective Any natural system is constantly exchanging material, energy and information with the environment, and all tkese processes follow the basic law of thermodynamics, with no exception of groundwater recharge and discharge process. On the basis of the principle of the first law of thermodynamics, the reverse geochemical simulation method is widely used in the study of groundwater recharge, runoff and drainage process. However, some studies only consider the material conservation in theprocess, but ignore the probability of the transformation.展开更多
The electric submersible pump(ESP) is a crucial apparatus utilized for lifting in the oil extraction process.Its lifting capacity is enhanced by the multi-stage tandem structure, but variations in energy characteristi...The electric submersible pump(ESP) is a crucial apparatus utilized for lifting in the oil extraction process.Its lifting capacity is enhanced by the multi-stage tandem structure, but variations in energy characteristics and internal flow across stages are also introduced. In this study, the inter-stage variability of energy characteristics in ESP hydraulic systems is investigated through entropy production(EP) analysis,which incorporates numerical simulations and experimental validation. The EP theory facilitates the quantification of energy loss in each computational subdomain at all ESP stages, establishing a correlation between microscopic flow structure and energy dissipation within the system. Furthermore, the underlying causes of inter-stage variability in ESP hydraulic systems are examined, and the advantages and disadvantages of applying the EP theory in this context are evaluated. Consistent energy characteristics within the ESP, aligned with the distribution of internal flow structure, are provided by the EP theory, as demonstrated by our results. The EP theory also enables the quantitative analysis of internal flow losses and complements existing performance analysis methods to map the internal flow structure to hydraulic losses. Nonetheless, an inconsistency between the energy characterization based on EP theory and the traditional efficiency index when reflecting inter-stage differences is identified. This inconsistency arises from the exclusive focus of the EP theory on flow losses within the flow field, disregarding the quantification of external energy input to the flow field. This study provides a reference for the optimization of EP theory in rotating machinery while deeply investigating the energy dissipation characteristics of multistage hydraulic system, which has certain theoretical and practical significance.展开更多
The centrifugal pump is a prevalent power equipment widely used in different engineering patterns,and the impeller blade wrap angle significantly impacts its performance.A numerical investigation was conducted to anal...The centrifugal pump is a prevalent power equipment widely used in different engineering patterns,and the impeller blade wrap angle significantly impacts its performance.A numerical investigation was conducted to analyze the influence of the blade wrap angle on flow characteristics and energy distribution of a centrifugal pump evaluated as a low specific speed with a value of 69.This study investigates six impellermodels that possess varying blade wrap angles(95°,105°,115°,125°,135°,and 145°)that were created while maintaining the same volute and other geometrical characteristics.The investigation of energy loss was conducted to evaluate the values of total and entropy generation rates(TEG,EGR).The fluid-structure interaction was considered numerically using the software tools ANSYS Fluent and ANSYSWorkbench.The elastic structural dynamic equation was used to estimate the structural response,while the shear stress transport k–ωturbulence model was utilized for the fluid domain modeling.The findings suggest that the blade wrap angle has a significant influence on the efficiency of the pump.The impeller featuring a blade wrap angle of 145°exhibits higher efficiency,with a notable increase of 3.76%relative to the original model.Variations in the blade wrap angle impact the energy loss,shaft power,and pump head.The model with a 145°angle exhibited a maximum equivalent stress of 14.8MPa and a total deformation of 0.084 mm.The results provide valuable insights into the intricate flow mechanism of the centrifugal pump,particularly when considering various blade wrap angles.展开更多
In this paper a parameterization of nonuniform distribution of precipitation has been made from the aspect of the maximum entropy theory.Results from theory and observation show that, the density function of precipita...In this paper a parameterization of nonuniform distribution of precipitation has been made from the aspect of the maximum entropy theory.Results from theory and observation show that, the density function of precipitation depth on the subgrid scale over the grid area of a climate model is the function of the gamma distribution.On this basis,the relative coverage of snow in the region occupied by vegetation in the grid area of a model is parameterized.Meanwhile the calculated results from the parameterizations are also compared with those from the empirical formulas by some other meteorologists.Results show that it is feasible to parameterize the nonuniform distribution of precipitation over the grid area at the angle of entropy theory.展开更多
Interactions among different landforms and varied complicated physical processes cause sediment transport in coastal regions being the interest of ocean management planning studies. In coastal zones, the derivation of...Interactions among different landforms and varied complicated physical processes cause sediment transport in coastal regions being the interest of ocean management planning studies. In coastal zones, the derivation of the bedload sediment transport rate and the flow velocity distribution is done by entropy theory which assumes the modified spatiotemporal disorder power index(MSTDPI) and the time-averaged flow velocity(as a random variable). Studying the deposition trend of bedload sediment transport rate for the sand particle(BLSTRS) and estimating the coastal erosion rate as a case study, the Makran coast is selected. To analyze the spatiotemporal patterns, the disorder power index(entropy-power) method is applied in this study where the monthly data of six Makran coastal sections from January 1970 to December 2015 are used. The studied data are mainly focused on the correlation of the flow rate of the sediment from the Makran River, and the spatiotemporal patterns of BLSTRS.Despite their meaningful spatiotemporal variability, it is not very easy to explain how the abovementioned variables perform together;the entropy-power index allows a better understanding of the combined performance of such parameters as the flow velocity and sediment transport by showing clearer signals for the assessment of coastal engineering issues at very large(coastal) scales.展开更多
Local site conditions play an important role in the effective application of strong motion recordings.In the China National Strong Motion Observation Network System（NSMONS）,some of the stations do not provide boreho...Local site conditions play an important role in the effective application of strong motion recordings.In the China National Strong Motion Observation Network System（NSMONS）,some of the stations do not provide borehole information,and correspondingly,do not assign the site classes yet.In this paper,site classification methodologies for free-field strong motion stations are reviewed and the limitations and uncertainties of the horizontal-to-vertical spectral ratio（HVSR） methods are discussed.Then,a new method for site classification based on the entropy weight theory is proposed.The proposed method avoids the head or tail joggle phenomenon by providing the objective and subjective weights.The method was applied to aftershock recordings from the 2008 Wenchuan earthquake,and 54 free-field NSMONS stations were selected for site classification and the mean HVSRs were calculated.The results show that the improved HVSR method proposed in this paper has a higher success rate and could be adopted in NSMONS.展开更多
The thermodynamic properties of Zn Se are obtained by using quasi-harmonic Debye model embedded in Gibbscode for pressure range 0–10 GPa and for temperature range 0–1000 K. Helmholtz free energy, internal energy, en...The thermodynamic properties of Zn Se are obtained by using quasi-harmonic Debye model embedded in Gibbscode for pressure range 0–10 GPa and for temperature range 0–1000 K. Helmholtz free energy, internal energy, entropy,Debye temperature, and specific heat are calculated. The thermal expansion coefficient along with Gruneisen parameter are also calculated at room temperature for the pressure range. It is found that internal energy is pressure dependent at low temperature, whereas entropy and Helmholtz free energy are pressure sensitive at high temperature. At ambient conditions,the obtained results are found to be in close agreement to available theoretical and experimental data.展开更多
This article applies the basic principles of the general and special entropy, puts forward the concept of High\|entropy system and its entropies. Sometimes, the entropy functions have been defined, and their mathemati...This article applies the basic principles of the general and special entropy, puts forward the concept of High\|entropy system and its entropies. Sometimes, the entropy functions have been defined, and their mathematical models have been constructred, and methods of quantification. Specially. Taking the Mining System as an example, the quantification method of the operating entropy is given under the synthetic action of the man\|made entropy, machine entropy, natural entropy and environmnet entropy. Therefore it enriches the theoretical and applied systems of the general and special entropy.展开更多
High entropy bulk metallic glasses show promising mechanical and physical properties.Dynamic mechanical properties of Ti_（16.7）Zr_（16.7）Hf_（16.7）Cu_（16.7）Ni_（16.7）Be_（16.7）high entropy bulk metallic glass ...High entropy bulk metallic glasses show promising mechanical and physical properties.Dynamic mechanical properties of Ti_（16.7）Zr_（16.7）Hf_（16.7）Cu_（16.7）Ni_（16.7）Be_（16.7）high entropy bulk metallic glass were investigated by mechanical spectroscopy（or called dynamic mechanical analysis）.The main（α）relaxation was observed in the framework of the loss modulus G″,which is related to the dynamic glass transition behaviour for the glassy materials.From physical model point of view,dynamic mechanical properties of the Ti_（16.7）Zr_（16.7）Hf_（16.7）Cu_（16.7）Ni_（16.7）Be_（16.7）high entropy bulk metallic glass show good agreement compared with the quasi-point defects theory.展开更多
A group multiattribute decision-making model was proposed by implementing prospect theory,multi-attribute decision-making,group decision-making and entropy methods for the optimization in commercial space investment.F...A group multiattribute decision-making model was proposed by implementing prospect theory,multi-attribute decision-making,group decision-making and entropy methods for the optimization in commercial space investment.First,the decision-making function was decided using prospect theory by the preference of each expert to reach the comprehensive prospect value based on different investment options;second,expert decision weights were reached according to entropy method;third,the expert group decision-making information was congregated according to the group decision-making congregation algorithm to reach the most optimized investment option;finally,an example was given to demonstrate the feasibility and effectiveness of the method.This model com-prehensively takes the advantages of many methods to congregate experts'experiences and avoid the subjective influences,thus providing a scientific decision-making approach for the commercial space investment.展开更多
This paper presents a distribution free method for predicting the extreme wind velocity from wind monitoring data at the site of the Runyang Suspension Bridge (RSB), China using the maximum entropy theory. The maximum...This paper presents a distribution free method for predicting the extreme wind velocity from wind monitoring data at the site of the Runyang Suspension Bridge (RSB), China using the maximum entropy theory. The maximum entropy theory is a rational approach for choosing the most unbiased probability distribution from a small sample, which is consistent with available data and contains a minimum of spurious information. In this paper, the theory is used for estimating a joint probability density function considering the combined action of wind speed and direction based on statistical analysis of wind monitoring data at the site of the RSB. The joint probability distribution model is further used to estimate the extreme wind velocity at the deck level of the RSB. The results of the analysis reveal that the probability density function of the maximum entropy method achieves a result that fits well with the monitoring data. Hypothesis testing shows that the distributions of the wind velocity data collected during the past three years do not obey the Gumbel distribution. Finally, our comparison shows that the wind predictions of the maximum entropy method are higher than that of the Gumbel distribution, but much lower than the design wind speed.展开更多
In this paper, a novel stochastic method named as the moment-based stochastic edge-based finite element method(MSES-FEM)is proposed to deal with the uncertain electromagnetic problems. First, electromagnetic and mecha...In this paper, a novel stochastic method named as the moment-based stochastic edge-based finite element method(MSES-FEM)is proposed to deal with the uncertain electromagnetic problems. First, electromagnetic and mechanical field are formulated by smoothed Galerkin Weak Form under edge-based smoothed finite element method(ES-FEM) scheme. The moment analysis is then applied to obtain the first four moments of the responses and to observe the effects of each random variable on electromagnetic field responses. The maximum entropy theory is employed to calculate the probability density functions(PDFs) of the responses. A quasi-static electromagnetic problem and a practical electromagnetic forming problem(EMF) are performed. The proposed method successfully solves stochastic electromagnetic forming analysis under the uncertain parameters. Numerical results obtained by the proposed MSES-FEM are quite satisfactory with the ones by the Monte Carlo simulation(MCS).展开更多
In this paper,a novel evolutionary algorithm(EA),called pseudo-derivative EA(called PDEA),is proposed.The basic idea of PDEA is to use pseudo-derivative,which is obtained based on the information produced during the e...In this paper,a novel evolutionary algorithm(EA),called pseudo-derivative EA(called PDEA),is proposed.The basic idea of PDEA is to use pseudo-derivative,which is obtained based on the information produced during the evolution,and to help search the solution of optimization problem.The pseudo-derivative drives the search process in a more informed direction.That makes PDEA different from the random optimization methods.The convergence of PDEA is first analyzed based on systems theory.The convergence condition of PDEA is then derived though this condition is too strong to be satisfied.Next,this condition is relaxed based on the entropy theory.Finally,performances of PDEA are evaluated on the benchmark functions and an adaptive liquid level control system of a surge tank.The numeric simulation results show that PDEA is capable of finding the solutions to the optimization problems with good accuracy,reliability,and speed.展开更多
Interval-valued data appear as a way to represent the uncertainty affecting the observed values. Dealing with interval-valued information systems is helpful to generalize the applications of rough set theory. Attribut...Interval-valued data appear as a way to represent the uncertainty affecting the observed values. Dealing with interval-valued information systems is helpful to generalize the applications of rough set theory. Attribute reduction is a key issue in analysis of interval-valued data. Existing attribute reduction methods for single-valued data are unsuitable for interval-valued data. So far, there have been few studies on attribute reduction methods for interval-valued data. In this paper, we propose a framework for attribute reduction in interval-valued data from the viewpoint of information theory. Some information theory concepts, including entropy, conditional entropy, and joint entropy, are given in interval-valued information systems. Based on these concepts, we provide an information theory view for attribute reduction in interval-valued information systems. Consequently, attribute reduction algorithms are proposed. Experiments show that the proposed framework is effective for attribute reduction in interval-valued information systems.展开更多
基金granted by the National Natural Science Fund of China(Grant no.51578212)
文摘Objective Any natural system is constantly exchanging material, energy and information with the environment, and all tkese processes follow the basic law of thermodynamics, with no exception of groundwater recharge and discharge process. On the basis of the principle of the first law of thermodynamics, the reverse geochemical simulation method is widely used in the study of groundwater recharge, runoff and drainage process. However, some studies only consider the material conservation in theprocess, but ignore the probability of the transformation.
基金financially supported by the China Postdoctoral Science Foundation(Grant No.2023M732979 and No.2022TQ0127)the Cooperative Research Project of the Ministry of Education's "Chunhui Program"(Grant No.HZKY20220117)+1 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20220587)the National Natural Science Foundation of China(Grant No.52309112)。
文摘The electric submersible pump(ESP) is a crucial apparatus utilized for lifting in the oil extraction process.Its lifting capacity is enhanced by the multi-stage tandem structure, but variations in energy characteristics and internal flow across stages are also introduced. In this study, the inter-stage variability of energy characteristics in ESP hydraulic systems is investigated through entropy production(EP) analysis,which incorporates numerical simulations and experimental validation. The EP theory facilitates the quantification of energy loss in each computational subdomain at all ESP stages, establishing a correlation between microscopic flow structure and energy dissipation within the system. Furthermore, the underlying causes of inter-stage variability in ESP hydraulic systems are examined, and the advantages and disadvantages of applying the EP theory in this context are evaluated. Consistent energy characteristics within the ESP, aligned with the distribution of internal flow structure, are provided by the EP theory, as demonstrated by our results. The EP theory also enables the quantitative analysis of internal flow losses and complements existing performance analysis methods to map the internal flow structure to hydraulic losses. Nonetheless, an inconsistency between the energy characterization based on EP theory and the traditional efficiency index when reflecting inter-stage differences is identified. This inconsistency arises from the exclusive focus of the EP theory on flow losses within the flow field, disregarding the quantification of external energy input to the flow field. This study provides a reference for the optimization of EP theory in rotating machinery while deeply investigating the energy dissipation characteristics of multistage hydraulic system, which has certain theoretical and practical significance.
文摘The centrifugal pump is a prevalent power equipment widely used in different engineering patterns,and the impeller blade wrap angle significantly impacts its performance.A numerical investigation was conducted to analyze the influence of the blade wrap angle on flow characteristics and energy distribution of a centrifugal pump evaluated as a low specific speed with a value of 69.This study investigates six impellermodels that possess varying blade wrap angles(95°,105°,115°,125°,135°,and 145°)that were created while maintaining the same volute and other geometrical characteristics.The investigation of energy loss was conducted to evaluate the values of total and entropy generation rates(TEG,EGR).The fluid-structure interaction was considered numerically using the software tools ANSYS Fluent and ANSYSWorkbench.The elastic structural dynamic equation was used to estimate the structural response,while the shear stress transport k–ωturbulence model was utilized for the fluid domain modeling.The findings suggest that the blade wrap angle has a significant influence on the efficiency of the pump.The impeller featuring a blade wrap angle of 145°exhibits higher efficiency,with a notable increase of 3.76%relative to the original model.Variations in the blade wrap angle impact the energy loss,shaft power,and pump head.The model with a 145°angle exhibited a maximum equivalent stress of 14.8MPa and a total deformation of 0.084 mm.The results provide valuable insights into the intricate flow mechanism of the centrifugal pump,particularly when considering various blade wrap angles.
文摘In this paper a parameterization of nonuniform distribution of precipitation has been made from the aspect of the maximum entropy theory.Results from theory and observation show that, the density function of precipitation depth on the subgrid scale over the grid area of a climate model is the function of the gamma distribution.On this basis,the relative coverage of snow in the region occupied by vegetation in the grid area of a model is parameterized.Meanwhile the calculated results from the parameterizations are also compared with those from the empirical formulas by some other meteorologists.Results show that it is feasible to parameterize the nonuniform distribution of precipitation over the grid area at the angle of entropy theory.
文摘Interactions among different landforms and varied complicated physical processes cause sediment transport in coastal regions being the interest of ocean management planning studies. In coastal zones, the derivation of the bedload sediment transport rate and the flow velocity distribution is done by entropy theory which assumes the modified spatiotemporal disorder power index(MSTDPI) and the time-averaged flow velocity(as a random variable). Studying the deposition trend of bedload sediment transport rate for the sand particle(BLSTRS) and estimating the coastal erosion rate as a case study, the Makran coast is selected. To analyze the spatiotemporal patterns, the disorder power index(entropy-power) method is applied in this study where the monthly data of six Makran coastal sections from January 1970 to December 2015 are used. The studied data are mainly focused on the correlation of the flow rate of the sediment from the Makran River, and the spatiotemporal patterns of BLSTRS.Despite their meaningful spatiotemporal variability, it is not very easy to explain how the abovementioned variables perform together;the entropy-power index allows a better understanding of the combined performance of such parameters as the flow velocity and sediment transport by showing clearer signals for the assessment of coastal engineering issues at very large(coastal) scales.
基金National Key Technology R&D Program Under Grant No.2009BAK55B05Nonprofit Industry Research Project of CEA Under Grant No.201108003Science Foundation of Institute of Engineering Mechanics,CEA Under Grant No.2010C01
文摘Local site conditions play an important role in the effective application of strong motion recordings.In the China National Strong Motion Observation Network System（NSMONS）,some of the stations do not provide borehole information,and correspondingly,do not assign the site classes yet.In this paper,site classification methodologies for free-field strong motion stations are reviewed and the limitations and uncertainties of the horizontal-to-vertical spectral ratio（HVSR） methods are discussed.Then,a new method for site classification based on the entropy weight theory is proposed.The proposed method avoids the head or tail joggle phenomenon by providing the objective and subjective weights.The method was applied to aftershock recordings from the 2008 Wenchuan earthquake,and 54 free-field NSMONS stations were selected for site classification and the mean HVSRs were calculated.The results show that the improved HVSR method proposed in this paper has a higher success rate and could be adopted in NSMONS.
文摘The thermodynamic properties of Zn Se are obtained by using quasi-harmonic Debye model embedded in Gibbscode for pressure range 0–10 GPa and for temperature range 0–1000 K. Helmholtz free energy, internal energy, entropy,Debye temperature, and specific heat are calculated. The thermal expansion coefficient along with Gruneisen parameter are also calculated at room temperature for the pressure range. It is found that internal energy is pressure dependent at low temperature, whereas entropy and Helmholtz free energy are pressure sensitive at high temperature. At ambient conditions,the obtained results are found to be in close agreement to available theoretical and experimental data.
文摘This article applies the basic principles of the general and special entropy, puts forward the concept of High\|entropy system and its entropies. Sometimes, the entropy functions have been defined, and their mathematical models have been constructred, and methods of quantification. Specially. Taking the Mining System as an example, the quantification method of the operating entropy is given under the synthetic action of the man\|made entropy, machine entropy, natural entropy and environmnet entropy. Therefore it enriches the theoretical and applied systems of the general and special entropy.
基金Item Sponsored by National Natural Science Foundation of China(51401192,51301136)Fundamental Research Funds for the Central Universities of China(3102015ZY027,3102015BJ(Ⅱ)JGZ019)+2 种基金Aerospace Technology Foundation of China(N2014KC0068,2015ZF53072)Space Technology Foundation of China(N2014KC0073)Project of State Key Laboratory of Materials Processing and Die & Mould Technology,Huazhong University of Science and Technology(P2016-12)
文摘High entropy bulk metallic glasses show promising mechanical and physical properties.Dynamic mechanical properties of Ti_（16.7）Zr_（16.7）Hf_（16.7）Cu_（16.7）Ni_（16.7）Be_（16.7）high entropy bulk metallic glass were investigated by mechanical spectroscopy（or called dynamic mechanical analysis）.The main（α）relaxation was observed in the framework of the loss modulus G″,which is related to the dynamic glass transition behaviour for the glassy materials.From physical model point of view,dynamic mechanical properties of the Ti_（16.7）Zr_（16.7）Hf_（16.7）Cu_（16.7）Ni_（16.7）Be_（16.7）high entropy bulk metallic glass show good agreement compared with the quasi-point defects theory.
文摘A group multiattribute decision-making model was proposed by implementing prospect theory,multi-attribute decision-making,group decision-making and entropy methods for the optimization in commercial space investment.First,the decision-making function was decided using prospect theory by the preference of each expert to reach the comprehensive prospect value based on different investment options;second,expert decision weights were reached according to entropy method;third,the expert group decision-making information was congregated according to the group decision-making congregation algorithm to reach the most optimized investment option;finally,an example was given to demonstrate the feasibility and effectiveness of the method.This model com-prehensively takes the advantages of many methods to congregate experts'experiences and avoid the subjective influences,thus providing a scientific decision-making approach for the commercial space investment.
基金Project supported by the National Natural Science Foundation of China (Nos. 50725828 and 50808041)Scientific Research Foundation of Graduate School of Southeast University (No. YBJJ0923)the Teaching and Research Foundation for Excellent Young Teacher of Southeast University,China
文摘This paper presents a distribution free method for predicting the extreme wind velocity from wind monitoring data at the site of the Runyang Suspension Bridge (RSB), China using the maximum entropy theory. The maximum entropy theory is a rational approach for choosing the most unbiased probability distribution from a small sample, which is consistent with available data and contains a minimum of spurious information. In this paper, the theory is used for estimating a joint probability density function considering the combined action of wind speed and direction based on statistical analysis of wind monitoring data at the site of the RSB. The joint probability distribution model is further used to estimate the extreme wind velocity at the deck level of the RSB. The results of the analysis reveal that the probability density function of the maximum entropy method achieves a result that fits well with the monitoring data. Hypothesis testing shows that the distributions of the wind velocity data collected during the past three years do not obey the Gumbel distribution. Finally, our comparison shows that the wind predictions of the maximum entropy method are higher than that of the Gumbel distribution, but much lower than the design wind speed.
基金supported by the National Key R&D Program of China(Grant No. 2017YFB1002704)the Hunan Provincial Innovation Foundation for Postgraduate of China (Grant No. CX2018B202)+1 种基金the National Natural Science Foundation of China (Grant No. 11872177)the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51621004)。
文摘In this paper, a novel stochastic method named as the moment-based stochastic edge-based finite element method(MSES-FEM)is proposed to deal with the uncertain electromagnetic problems. First, electromagnetic and mechanical field are formulated by smoothed Galerkin Weak Form under edge-based smoothed finite element method(ES-FEM) scheme. The moment analysis is then applied to obtain the first four moments of the responses and to observe the effects of each random variable on electromagnetic field responses. The maximum entropy theory is employed to calculate the probability density functions(PDFs) of the responses. A quasi-static electromagnetic problem and a practical electromagnetic forming problem(EMF) are performed. The proposed method successfully solves stochastic electromagnetic forming analysis under the uncertain parameters. Numerical results obtained by the proposed MSES-FEM are quite satisfactory with the ones by the Monte Carlo simulation(MCS).
文摘In this paper,a novel evolutionary algorithm(EA),called pseudo-derivative EA(called PDEA),is proposed.The basic idea of PDEA is to use pseudo-derivative,which is obtained based on the information produced during the evolution,and to help search the solution of optimization problem.The pseudo-derivative drives the search process in a more informed direction.That makes PDEA different from the random optimization methods.The convergence of PDEA is first analyzed based on systems theory.The convergence condition of PDEA is then derived though this condition is too strong to be satisfied.Next,this condition is relaxed based on the entropy theory.Finally,performances of PDEA are evaluated on the benchmark functions and an adaptive liquid level control system of a surge tank.The numeric simulation results show that PDEA is capable of finding the solutions to the optimization problems with good accuracy,reliability,and speed.
基金Project supported by the National Natural Science Foundation of China(Nos.61473259,61502335,61070074,and60703038)the Zhejiang Provincial Natural Science Foundation(No.Y14F020118)the PEIYANG Young Scholars Program of Tianjin University,China(No.2016XRX-0001)
文摘Interval-valued data appear as a way to represent the uncertainty affecting the observed values. Dealing with interval-valued information systems is helpful to generalize the applications of rough set theory. Attribute reduction is a key issue in analysis of interval-valued data. Existing attribute reduction methods for single-valued data are unsuitable for interval-valued data. So far, there have been few studies on attribute reduction methods for interval-valued data. In this paper, we propose a framework for attribute reduction in interval-valued data from the viewpoint of information theory. Some information theory concepts, including entropy, conditional entropy, and joint entropy, are given in interval-valued information systems. Based on these concepts, we provide an information theory view for attribute reduction in interval-valued information systems. Consequently, attribute reduction algorithms are proposed. Experiments show that the proposed framework is effective for attribute reduction in interval-valued information systems.
