According to the relationships among state transition probability matrixes with different step lengths, an improved Markov chain model based on autocorrelation and entropy techniques was introduced. In the improved Ma...According to the relationships among state transition probability matrixes with different step lengths, an improved Markov chain model based on autocorrelation and entropy techniques was introduced. In the improved Markov chain model, the state transition probability matrixes can be adjusted. The steps of the historical state of the event, which was significantly related to the future state of the event, were determined by the autocorrelation technique, and the impact weights of the event historical state on the event future state were determined by the entropy technique. The presented model was applied to predicting annual precipitation and annual runoff states, showing that the improved model is of higher precision than those existing Markov chain models, and the determination of the state transition probability matrixes and the weights is more reasonable. The physical concepts of the improved model are distinct, and its computation process is simple and direct, thus, the presented model is sufficiently general to be applicable to the prediction problems in hydrology and water resources.展开更多
Fuzzy entropy was designed for non convex fuzzy membership function using well known Hamming distance measure.The proposed fuzzy entropy had the same structure as that of convex fuzzy membership case.Design procedure ...Fuzzy entropy was designed for non convex fuzzy membership function using well known Hamming distance measure.The proposed fuzzy entropy had the same structure as that of convex fuzzy membership case.Design procedure of fuzzy entropy was proposed by considering fuzzy membership through distance measure,and the obtained results contained more flexibility than the general fuzzy membership function.Furthermore,characteristic analyses for non convex function were also illustrated.Analyses on the mutual information were carried out through the proposed fuzzy entropy and similarity measure,which was also dual structure of fuzzy entropy.By the illustrative example,mutual information was discussed.展开更多
In order to meet the strict requirements for information in engineering management, the positive interval (0, 1 ] in Shannon information entropy is extended to the real number interval [ - 1, 1 ]. The information the...In order to meet the strict requirements for information in engineering management, the positive interval (0, 1 ] in Shannon information entropy is extended to the real number interval [ - 1, 1 ]. The information theory and the decision theory are combined effectively, and the deficiencies that the traditional Bayes decision-making methods only consider a single factor are made up for. The multi-factors engineering decision-making methods are proposed, and some critical problems are solved in the practical engineering management decision-making process.展开更多
An optimization model of underground mining method selection was established on the basis of the unascertained measurement theory.Considering the geologic conditions,technology,economy and safety production,ten main f...An optimization model of underground mining method selection was established on the basis of the unascertained measurement theory.Considering the geologic conditions,technology,economy and safety production,ten main factors influencing the selection of mining method were taken into account,and the comprehensive evaluation index system of mining method selection was constructed.The unascertained evaluation indices corresponding to the selected factors for the actual situation were solved both qualitatively and quantitatively.New measurement standards were constructed.Then,the unascertained measurement function of each evaluation index was established.The index weights of the factors were calculated by entropy theory,and credible degree recognition criteria were established according to the unascertained measurement theory.The results of mining method evaluation were obtained using the credible degree criteria,thus the best underground mining method was determined.Furthermore,this model was employed for the comprehensive evaluation and selection of the chosen standard mining methods in Xinli Gold Mine in Sanshandao of China.The results show that the relative superiority degrees of mining methods can be calculated using the unascertained measurement optimization model,so the optimal method can be easily determined.Meanwhile,the proposed method can take into account large amount of uncertain information in mining method selection,which can provide an effective way for selecting the optimal underground mining method.展开更多
The mainstream depth of a return flow can be viewed as an intrinsic depth of horizontal convection. By using a theoretical tube model combined with the application of the Maximum Entropy Production Principle (MaxEPP) ...The mainstream depth of a return flow can be viewed as an intrinsic depth of horizontal convection. By using a theoretical tube model combined with the application of the Maximum Entropy Production Principle (MaxEPP) in thermodynamics, the following statements can be made. Under fixed external forcing, the system chooses a particular depth as the mainstream depth of its return flow, the depth of which not only satisfies the maximum circulation rate and the maximum heat transport, but also satisfies the maximum entropy production rate. A comparison between this intrinsic depth and the container height leads to the definition of a relative partial and full-penetration pattern of the circulation. Moreover, this intrinsic depth is found to vary with the external forcing; the regulation of this variation is related to the Modified Rayleigh number.展开更多
Human visual sense has two aspects in our feeling for blurred image, that is, one is the amount of blur depending on object size, the other is the amount of blur independent of the object size. In the former for examp...Human visual sense has two aspects in our feeling for blurred image, that is, one is the amount of blur depending on object size, the other is the amount of blur independent of the object size. In the former for example, when the image size becomes larger, the author feels smaller amount blur. The quantitative evaluation based on entropy for blurred images is proposed in this paper. The author calls this metric "variation entropy". This metric has two kinds of aspects that coincide with the human visual sense. The first is the absolute evaluation of blur, and the second is the relative evaluation of blur. The former can be quantified by variation entropy for a unit boundary length (or L-type variation entropy: HL ), which is dependent on resolution, and the latter can be quantified by variation entropy for a unit area (or A-type variation entropy: H^A ), which is independent of resolution. These two metrics have complementary properties. At last, two variation entropies are applied to the standard kanji character database, and then the strong relation between variation entropy and accuracy of recognition is discussed. The tendency of writing skills for grades is evaluated by applying the metric to a database collected from school children.展开更多
A multi-objective performance optimization method is proposed, and the problem that single structural parame- ters of small fan balance the optimization between the static characteristics and the aerodynamic noise is ...A multi-objective performance optimization method is proposed, and the problem that single structural parame- ters of small fan balance the optimization between the static characteristics and the aerodynamic noise is solved. In this method, three structural parameters are selected as the optimization variables. Besides, the static pressure efficiency and the aerodynamic noise of the fan are regarded as the multi-objective performance. Furthermore, the response surface method and the entropy method are used to establish the optimization function between the op- timization variables and the multi-objective performances. Finally, the optimized model is found when the opti- mization function reaches its maximttm value. Experimental data shows that the optimized model not only en- hances the static characteristics of the fan but also obviously reduces the noise. The results of the study will provide some reference for the optimization of multi-objective performance of other types of rotating machinery.展开更多
Refractory high-entropy alloys(HEAs) exhibit remarkable mechanical properties desired for high-temperature applications. However, their oxidation resistance at high temperatures received less attention. Recent work in...Refractory high-entropy alloys(HEAs) exhibit remarkable mechanical properties desired for high-temperature applications. However, their oxidation resistance at high temperatures received less attention. Recent work indicates that MoTaTiCrAl alloy exhibits excellent oxidation resistance,but the effects of Al and Cr remain unclear. In this work, we demonstrate that the addition of Al is unnecessary for preventing oxidation of the MoTaTiCrAl alloy and the removal of Al leads to a more oxidation resistant MoTaTiCr medium entropy alloy. Structural and chemical analyses indicate that the excellent oxidation resistance of MoTaTiCr is mainly associated with the formation of continuous CrTaO4 oxide layer.The results indicate that complex oxides can be adopted as effective candidates for enhancement of oxidation resistance,in addition to typical strategy of forming Al2O3, Cr2O3 or SiO2 barrier layer.展开更多
We establish the sharp upper and lower bounds of Gaussian type for the heat kernel in the metric measure space satisfying the RCD(0, N)(equivalently, RCD~*(0, N), condition with N∈N\ {1} and having the maximum volume...We establish the sharp upper and lower bounds of Gaussian type for the heat kernel in the metric measure space satisfying the RCD(0, N)(equivalently, RCD~*(0, N), condition with N∈N\ {1} and having the maximum volume growth, and then show its application on the large-time asymptotics of the heat kernel, sharp bounds on the(minimal) Green function, and above all, the large-time asymptotics of the Perelman entropy and the Nash entropy, where for the former the monotonicity of the Perelman entropy is proved. The results generalize the corresponding ones in the Riemannian manifolds, and some of them appear more explicit and sharper than the ones in metric measure spaces obtained recently by Jiang et al.(2016).展开更多
Enhanced oxidation resistance is a primary demand for the application of refractory high-entropy alloys(RHEAs)at elevated temperatures.In this study,Al was added to a Ti_(2)VZrNb RHEA to partially substitute Nb to imp...Enhanced oxidation resistance is a primary demand for the application of refractory high-entropy alloys(RHEAs)at elevated temperatures.In this study,Al was added to a Ti_(2)VZrNb RHEA to partially substitute Nb to improve its oxidation resistance and mechanical properties.The alloy was found to have an increased oxidation resistance by forming a continuous Al_(2)O_(3)+ZrO_(2)oxide protective surface.At the same time,the room-temperature yield strength was also increased by 66%to 1273 MPa via solid solution strengthening.The low atomic mass of Al also helped to reduce the density of the alloy by 8.2%to 5.44 g cm^(−3).This resulted in a high specific yield strength of 234 MPa cm3 g^(−1) for the alloy.Meanwhile,the Ti_(2)VZrNb_(0.5)-Al_(0.5)alloy also exhibited a high compressive plasticity of>50%.These values are among the best reported so far for RHEAs.展开更多
In nonlinear error growth dynamics,the initial error cannot be accurately determined,and the forecast error,which is also uncertain,can be considered to be a random variable.Entropy in information theory is a natural ...In nonlinear error growth dynamics,the initial error cannot be accurately determined,and the forecast error,which is also uncertain,can be considered to be a random variable.Entropy in information theory is a natural measure of the uncertainty of a random variable associated with a probability distribution.This paper effectively combines statistical information theory and nonlinear error growth dynamics,and introduces some fundamental concepts of entropy in information theory for nonlinear error growth dynamics.Entropy based on nonlinear error can be divided into time entropy and space entropy,which are used to estimate the predictabilities of the whole dynamical system and each of its variables.This is not only applicable for investigating the dependence between any two variables of a multivariable system,but also for measuring the influence of each variable on the predictability of the whole system.Taking the Lorenz system as an example,the entropy of nonlinear error is applied to estimate predictability.The time and space entropies are used to investigate the spatial distribution of predictability of the whole Lorenz system.The results show that when moving around two chaotic attractors or near the edge of system space,a Lorenz system with lower sensitivity to the initial field behaves with higher predictability and a longer predictability limit.The example analysis of predictability of the Lorenz system demonstrates that the predictability estimated by the entropy of nonlinear error is feasible and effective,especially for estimation of predictability of the whole system.This provides a theoretical foundation for further work in estimating real atmospheric multivariable joint predictability.展开更多
基金Under the auspices of Major Special Technological Program of Water Pollution Control and Management (No.2009ZX07106-001)National Natural Science Foundation of China (No. 51079037, 50909063)
文摘According to the relationships among state transition probability matrixes with different step lengths, an improved Markov chain model based on autocorrelation and entropy techniques was introduced. In the improved Markov chain model, the state transition probability matrixes can be adjusted. The steps of the historical state of the event, which was significantly related to the future state of the event, were determined by the autocorrelation technique, and the impact weights of the event historical state on the event future state were determined by the entropy technique. The presented model was applied to predicting annual precipitation and annual runoff states, showing that the improved model is of higher precision than those existing Markov chain models, and the determination of the state transition probability matrixes and the weights is more reasonable. The physical concepts of the improved model are distinct, and its computation process is simple and direct, thus, the presented model is sufficiently general to be applicable to the prediction problems in hydrology and water resources.
基金Work supported by the Second Stage of Brain Korea 21 Projects Work(2010-0020163) supported by the Priority Research Centers Program through the National Research Foundation (NRF) funded by the Ministry of Education,Science and Technology of Korea
文摘Fuzzy entropy was designed for non convex fuzzy membership function using well known Hamming distance measure.The proposed fuzzy entropy had the same structure as that of convex fuzzy membership case.Design procedure of fuzzy entropy was proposed by considering fuzzy membership through distance measure,and the obtained results contained more flexibility than the general fuzzy membership function.Furthermore,characteristic analyses for non convex function were also illustrated.Analyses on the mutual information were carried out through the proposed fuzzy entropy and similarity measure,which was also dual structure of fuzzy entropy.By the illustrative example,mutual information was discussed.
文摘In order to meet the strict requirements for information in engineering management, the positive interval (0, 1 ] in Shannon information entropy is extended to the real number interval [ - 1, 1 ]. The information theory and the decision theory are combined effectively, and the deficiencies that the traditional Bayes decision-making methods only consider a single factor are made up for. The multi-factors engineering decision-making methods are proposed, and some critical problems are solved in the practical engineering management decision-making process.
基金Project(2007CB209402) supported by the National Basic Research Program of China Project(SKLGDUEK0906) supported by the Research Fund of State Key Laboratory for Geomechanics and Deep Underground Engineering of China
文摘An optimization model of underground mining method selection was established on the basis of the unascertained measurement theory.Considering the geologic conditions,technology,economy and safety production,ten main factors influencing the selection of mining method were taken into account,and the comprehensive evaluation index system of mining method selection was constructed.The unascertained evaluation indices corresponding to the selected factors for the actual situation were solved both qualitatively and quantitatively.New measurement standards were constructed.Then,the unascertained measurement function of each evaluation index was established.The index weights of the factors were calculated by entropy theory,and credible degree recognition criteria were established according to the unascertained measurement theory.The results of mining method evaluation were obtained using the credible degree criteria,thus the best underground mining method was determined.Furthermore,this model was employed for the comprehensive evaluation and selection of the chosen standard mining methods in Xinli Gold Mine in Sanshandao of China.The results show that the relative superiority degrees of mining methods can be calculated using the unascertained measurement optimization model,so the optimal method can be easily determined.Meanwhile,the proposed method can take into account large amount of uncertain information in mining method selection,which can provide an effective way for selecting the optimal underground mining method.
基金Supported by the The National Basic Research Program (973 Program) (Nos. 2007CB816004, 2005CB422302)the National Outstanding Youth Natural Science Foundation of China (No. 40725017)
文摘The mainstream depth of a return flow can be viewed as an intrinsic depth of horizontal convection. By using a theoretical tube model combined with the application of the Maximum Entropy Production Principle (MaxEPP) in thermodynamics, the following statements can be made. Under fixed external forcing, the system chooses a particular depth as the mainstream depth of its return flow, the depth of which not only satisfies the maximum circulation rate and the maximum heat transport, but also satisfies the maximum entropy production rate. A comparison between this intrinsic depth and the container height leads to the definition of a relative partial and full-penetration pattern of the circulation. Moreover, this intrinsic depth is found to vary with the external forcing; the regulation of this variation is related to the Modified Rayleigh number.
文摘Human visual sense has two aspects in our feeling for blurred image, that is, one is the amount of blur depending on object size, the other is the amount of blur independent of the object size. In the former for example, when the image size becomes larger, the author feels smaller amount blur. The quantitative evaluation based on entropy for blurred images is proposed in this paper. The author calls this metric "variation entropy". This metric has two kinds of aspects that coincide with the human visual sense. The first is the absolute evaluation of blur, and the second is the relative evaluation of blur. The former can be quantified by variation entropy for a unit boundary length (or L-type variation entropy: HL ), which is dependent on resolution, and the latter can be quantified by variation entropy for a unit area (or A-type variation entropy: H^A ), which is independent of resolution. These two metrics have complementary properties. At last, two variation entropies are applied to the standard kanji character database, and then the strong relation between variation entropy and accuracy of recognition is discussed. The tendency of writing skills for grades is evaluated by applying the metric to a database collected from school children.
基金supported by Open Foundation of Zhejiang Provincial Top Key Academic Discipline of Mechanical EngineeringZhejiang Sci-Tech University Key Laboratory(ZSTUME 01A04)
文摘A multi-objective performance optimization method is proposed, and the problem that single structural parame- ters of small fan balance the optimization between the static characteristics and the aerodynamic noise is solved. In this method, three structural parameters are selected as the optimization variables. Besides, the static pressure efficiency and the aerodynamic noise of the fan are regarded as the multi-objective performance. Furthermore, the response surface method and the entropy method are used to establish the optimization function between the op- timization variables and the multi-objective performances. Finally, the optimized model is found when the opti- mization function reaches its maximttm value. Experimental data shows that the optimized model not only en- hances the static characteristics of the fan but also obviously reduces the noise. The results of the study will provide some reference for the optimization of multi-objective performance of other types of rotating machinery.
基金supported by the National Key Research and Development Program of China (2018YFA0703600)the National Science Fund for Distinguished Young Scholars (51825104)+3 种基金the Key Research Program of Frontier Sciences of Chinese Academy of Sciences (QYZDY-SSW-JSC017)the Strategic Priority Research Program of Chinese Academy of Sciences (XDB30000000)the Key Basic and Applied Research Program of Guangdong Province, China (2019B030302010)the National Natural Science Foundation of China (11790291 and 61888102)。
文摘Refractory high-entropy alloys(HEAs) exhibit remarkable mechanical properties desired for high-temperature applications. However, their oxidation resistance at high temperatures received less attention. Recent work indicates that MoTaTiCrAl alloy exhibits excellent oxidation resistance,but the effects of Al and Cr remain unclear. In this work, we demonstrate that the addition of Al is unnecessary for preventing oxidation of the MoTaTiCrAl alloy and the removal of Al leads to a more oxidation resistant MoTaTiCr medium entropy alloy. Structural and chemical analyses indicate that the excellent oxidation resistance of MoTaTiCr is mainly associated with the formation of continuous CrTaO4 oxide layer.The results indicate that complex oxides can be adopted as effective candidates for enhancement of oxidation resistance,in addition to typical strategy of forming Al2O3, Cr2O3 or SiO2 barrier layer.
基金supported by National Natural Science Foundation of China (Grant No. 11401403)the Australian Research Council (Grant No. DP130101302)
文摘We establish the sharp upper and lower bounds of Gaussian type for the heat kernel in the metric measure space satisfying the RCD(0, N)(equivalently, RCD~*(0, N), condition with N∈N\ {1} and having the maximum volume growth, and then show its application on the large-time asymptotics of the heat kernel, sharp bounds on the(minimal) Green function, and above all, the large-time asymptotics of the Perelman entropy and the Nash entropy, where for the former the monotonicity of the Perelman entropy is proved. The results generalize the corresponding ones in the Riemannian manifolds, and some of them appear more explicit and sharper than the ones in metric measure spaces obtained recently by Jiang et al.(2016).
基金supported by the National Key R&D Program of China(2021YFA1200201)the National Natural Science Foundation of China(52071003,91860202,and 11604006)+4 种基金Beijing Nova Program(Z211100002121170)Beijing Municipal Education Commission Project(PXM2020_014204_000021 and PXM2019_014204_500032)Beijing Outstanding Young Scientists Projects(BJJWZYJH01201910005018)Beijing Natural Science Foundation(Z180014)“111”project(DB18015)。
文摘Enhanced oxidation resistance is a primary demand for the application of refractory high-entropy alloys(RHEAs)at elevated temperatures.In this study,Al was added to a Ti_(2)VZrNb RHEA to partially substitute Nb to improve its oxidation resistance and mechanical properties.The alloy was found to have an increased oxidation resistance by forming a continuous Al_(2)O_(3)+ZrO_(2)oxide protective surface.At the same time,the room-temperature yield strength was also increased by 66%to 1273 MPa via solid solution strengthening.The low atomic mass of Al also helped to reduce the density of the alloy by 8.2%to 5.44 g cm^(−3).This resulted in a high specific yield strength of 234 MPa cm3 g^(−1) for the alloy.Meanwhile,the Ti_(2)VZrNb_(0.5)-Al_(0.5)alloy also exhibited a high compressive plasticity of>50%.These values are among the best reported so far for RHEAs.
基金supported by National Natural Science Foundation of China (Grant No. 40975031)
文摘In nonlinear error growth dynamics,the initial error cannot be accurately determined,and the forecast error,which is also uncertain,can be considered to be a random variable.Entropy in information theory is a natural measure of the uncertainty of a random variable associated with a probability distribution.This paper effectively combines statistical information theory and nonlinear error growth dynamics,and introduces some fundamental concepts of entropy in information theory for nonlinear error growth dynamics.Entropy based on nonlinear error can be divided into time entropy and space entropy,which are used to estimate the predictabilities of the whole dynamical system and each of its variables.This is not only applicable for investigating the dependence between any two variables of a multivariable system,but also for measuring the influence of each variable on the predictability of the whole system.Taking the Lorenz system as an example,the entropy of nonlinear error is applied to estimate predictability.The time and space entropies are used to investigate the spatial distribution of predictability of the whole Lorenz system.The results show that when moving around two chaotic attractors or near the edge of system space,a Lorenz system with lower sensitivity to the initial field behaves with higher predictability and a longer predictability limit.The example analysis of predictability of the Lorenz system demonstrates that the predictability estimated by the entropy of nonlinear error is feasible and effective,especially for estimation of predictability of the whole system.This provides a theoretical foundation for further work in estimating real atmospheric multivariable joint predictability.