Land use structure optimization(LUSO) is an important issue for land use planning. In order for land use planning to have reasonable flexibility, uncertain optimization should be applied for LUSO. In this paper, the r...Land use structure optimization(LUSO) is an important issue for land use planning. In order for land use planning to have reasonable flexibility, uncertain optimization should be applied for LUSO. In this paper, the researcher first expounded the uncertainties of LUSO. Based on this, an interval programming model was developed, of which interval variables were to hold land use uncertainties. To solve the model, a heuristics based on Genetic Algorithm was designed according to Pareto Optimum principle with a confidence interval under given significance level to represent LUSO result. Proposed method was applied to a real case of Yangzhou, an eastern city in China. The following conclusions were reached. 1) Different forms of uncertainties ranged from certainty to indeterminacy lay in the five steps of LUSO, indicating necessary need of comprehensive approach to quantify them. 2) With regards to trade-offs of conflicted objectives and preferences to uncertainties, our proposed model displayed good ability of making planning decision process transparent, therefore providing an effective tool for flexible land use planning compiling. 3) Under uncertain conditions, land use planning effectiveness can be primarily enhanced by flexible management with reserved space to percept and hold uncertainties in advance.展开更多
The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the int...The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the interval of effective step size（IES） has not been thoroughly explored theoretically.In this paper,by using a general estimation for the total error of the numerical solutions of ODEs,a method is proposed for determining an approximate IES by translating the functions for truncation and rounding errors.It also illustrates this process with an example.Moreover,the relationship between the IES and its approximation is found,and the relative error of the approximation with respect to the IES is given.In addition,variation in the IES with increasing integration time is studied,which can provide an explanation for the observed numerical results.The findings contribute to computational step-size choice for reliable numerical solutions.展开更多
Aimed at the uncertain characteristics of discrete logistics network design,an interval hierarchical triangular uncertain OD demand model based on interval demand and network flow is presented.Under consideration of t...Aimed at the uncertain characteristics of discrete logistics network design,an interval hierarchical triangular uncertain OD demand model based on interval demand and network flow is presented.Under consideration of the system profit,the uncertain demand of logistics network is measured by interval variables and interval parameters,and an interval planning model of discrete logistics network is established.The risk coefficient and maximum constrained deviation are defined to realize the certain transformation of the model.By integrating interval algorithm and genetic algorithm,an interval hierarchical optimal genetic algorithm is proposed to solve the model.It is shown by a tested example that in the same scenario condition an interval solution[3275.3,3 603.7]can be obtained by the model and algorithm which is obviously better than the single precise optimal solution by stochastic or fuzzy algorithm,so it can be reflected that the model and algorithm have more stronger operability and the solution result has superiority to scenario decision.展开更多
In the traditional Markov chain model (MCM), aleatory uncertainty because of inherent randomness and epistemic uncertainty due to the lack of knowledge are not differentiated. Generalized interval probability provides...In the traditional Markov chain model (MCM), aleatory uncertainty because of inherent randomness and epistemic uncertainty due to the lack of knowledge are not differentiated. Generalized interval probability provides a concise representation for the two kinds of uncertainties simultaneously. In this paper, a generalized Markov chain model (GMCM), based on the generalized interval probability theory, is proposed to improve the reliability of prediction. In the GMCM, aleatory uncertainty is represented as probability; interval is used to capture epistemic uncertainty. A case study for predicting the average dynamic compliance in machining processes is provided to demonstrate the effectiveness of proposed GMCM. The results show that the proposed GMCM has a better prediction performance than that of MCM.展开更多
Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject...Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject to variation. In the study, the collocation interval analysis method based on the first class Chebyshev polynomial approximation is presented to investigate the least favorable responses and the most favorable responses of interval-parameter structures under random excitations. Compared with the interval analysis method based on the first order Taylor expansion, in which only information including the function value and derivative at midpoint is used, the collocation interval analysis method is a non-gradient algorithm using several collocation points which improve the precision of results owing to better approximation of a response function. The pseudo excitation method is introduced to the solving procedure to transform the random problem into a deterministic problem. To validate the procedure, we present numerical results concerning a building under seismic ground motion and aerofoil under continuous atmosphere turbulence to show the effectiveness of the collocation interval analysis method.展开更多
This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.Thi...This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.展开更多
Hydrological risk is highly dependent on the occurrence of extreme rainfalls.This fact has led to a wide range of studies on the estimation and uncertainty analysis of the extremes.In most cases,confidence intervals(C...Hydrological risk is highly dependent on the occurrence of extreme rainfalls.This fact has led to a wide range of studies on the estimation and uncertainty analysis of the extremes.In most cases,confidence intervals(CIs)are constructed to represent the uncertainty of the estimates.Since the accuracy of CIs depends on the asymptotic normality of the data and is questionable with limited observations in practice,a Bayesian highest posterior density(HPD)interval,bootstrap percentile interval,and profile likelihood(PL)interval have been introduced to analyze the uncertainty that does not depend on the normality assumption.However,comparison studies to investigate their performances in terms of the accuracy and uncertainty of the estimates are scarce.In addition,the strengths,weakness,and conditions necessary for performing each method also must be investigated.Accordingly,in this study,test experiments with simulations from varying parent distributions and different sample sizes were conducted.Then,applications to the annual maximum rainfall(AMR)time series data in South Korea were performed.Five districts with 38-year(1973–2010)AMR observations were fitted by the three aforementioned methods in the application.From both the experimental and application results,the Bayesian method is found to provide the lowest uncertainty of the design level while the PL estimates generally have the highest accuracy but also the largest uncertainty.The bootstrap estimates are usually inferior to the other two methods,but can perform adequately when the distribution model is not heavy-tailed and the sample size is large.The distribution tail behavior and the sample size are clearly found to affect the estimation accuracy and uncertainty.This study presents a comparative result,which can help researchers make decisions in the context of assessing extreme rainfall uncertainties.展开更多
Based on the traditional finite volume method, a new numerical technique is presented for the transient temperature field prediction with interval uncertainties in both the physical parameters and initial/boundary con...Based on the traditional finite volume method, a new numerical technique is presented for the transient temperature field prediction with interval uncertainties in both the physical parameters and initial/boundary conditions. New stability theory applicable to interval discrete schemes is developed. Interval ranges of the uncertain temperature field can be approximately yielded by two kinds of parameter perturbation methods. Different order Neumann series are adopted to approximate the interval matrix inverse. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed model and methods.展开更多
The general characteristics of climate changes over the past 2000 years in China,regional differences and uncertainties were analyzed based on the recently peer-reviewed high time-resolution climatic reconstructions.T...The general characteristics of climate changes over the past 2000 years in China,regional differences and uncertainties were analyzed based on the recently peer-reviewed high time-resolution climatic reconstructions.The results showed that there exists four warm periods of the temperature variation in China since the Qin Dynasty,including the western and eastern Han Dynasties(200 BC-AD 180),the Sui and Tang dynasties(541-810),the Song and Yuan dynasties(931-1320),and the 20th century,and three cold phases involving the Wei,Jin,and North-South Dynasties(181-540),the late Tang Dynasty(811-930),and the Ming and Qing dynasties(1321-1920).The Song and Yuan warm period is consistent with the Medieval Warm Period over the Northern Hemisphere,and the cold phases of the North-South Dynasties and the Ming and Qing dynasties are paralleled to the Dark Ages Cold Period and the Little Ice Age,respectively.The 13th-15th century could be a shift to the wet condition of the climate,and the low precipitation variability is exhibited in western China prior to 1500.In the context of the climate warming,the pattern of the drought in north and flood in south is prevalent over the eastern China.In addition,the published reconstructions have a high level of confidence for the past 500 years,but large uncertainties exist prior to the 16th century.展开更多
In summary,the interval uncertainty is introduced to the acoustic metamaterial with Helmholtz resonators.And then,new descriptions(the conservative approximation,the unsafe approximation and the approximation precisio...In summary,the interval uncertainty is introduced to the acoustic metamaterial with Helmholtz resonators.And then,new descriptions(the conservative approximation,the unsafe approximation and the approximation precision)on uncertainties of physical properties of this interval acoustic metamaterial are defined.Lastly,an optimization model for this interval acoustic metamaterial is proposed.The organization of this paper is listed as follows.The acoustic transmission line method(ATLM)for an acoustic metamaterial with Helmholtz resonators is described in Section 2.In Section3,uncertain analysis of the interval acoustic metamaterial is presented.In Section 4,optimization model of the interval acoustic metamaterial is proposed.The discussion on optimization results is shown in Section 5.In section 6,some conclusions are given.展开更多
This paper addresses the issue of security alliances in Northeast Asia--their origins and current status. It observes some fundamental changes of such alliances in the region with the change of time, and concludes tha...This paper addresses the issue of security alliances in Northeast Asia--their origins and current status. It observes some fundamental changes of such alliances in the region with the change of time, and concludes that the present alliances are still hedging against uncertainty. In particular, it elaborates the legitimacy of alliance due to collective defense, rather than cooperative aggressiveness that erodes the credibility of alliance and leads to distrust of nations. The paper raises the Taiwan Question and DPRK issue as key examples to analyze how China and the US have entered a strategically distrustful relationship and how these two issues have been intertwined. It also discusses how to de-link them and build a more stable and secure relationship between China and the US through forward-looking cooperation.展开更多
A Newton iteration-based interval uncertainty analysis method(NI-IUAM) is proposed to analyze the propagating effect of interval uncertainty in multidisciplinary systems. NI-IUAM decomposes one multidisciplinary syste...A Newton iteration-based interval uncertainty analysis method(NI-IUAM) is proposed to analyze the propagating effect of interval uncertainty in multidisciplinary systems. NI-IUAM decomposes one multidisciplinary system into single disciplines and utilizes a Newton iteration equation to obtain the upper and lower bounds of coupled state variables at each iterative step.NI-IUAM only needs to determine the bounds of uncertain parameters and does not require specific distribution formats. In this way, NI-IUAM may greatly reduce the necessity for raw data. In addition, NI-IUAM can accelerate the convergence process as a result of the super-linear convergence of Newton iteration. The applicability of the proposed method is discussed, in particular that solutions obtained in each discipline must be compatible in multidisciplinary systems. The validity and efficiency of NI-IUAM is demonstrated by both numerical and engineering examples.展开更多
基金Under the auspices of National Natural Science Foundation of China(No.41401627,41471144)Foundation Research Project of Jiangsu Province(No.BK20140236)
文摘Land use structure optimization(LUSO) is an important issue for land use planning. In order for land use planning to have reasonable flexibility, uncertain optimization should be applied for LUSO. In this paper, the researcher first expounded the uncertainties of LUSO. Based on this, an interval programming model was developed, of which interval variables were to hold land use uncertainties. To solve the model, a heuristics based on Genetic Algorithm was designed according to Pareto Optimum principle with a confidence interval under given significance level to represent LUSO result. Proposed method was applied to a real case of Yangzhou, an eastern city in China. The following conclusions were reached. 1) Different forms of uncertainties ranged from certainty to indeterminacy lay in the five steps of LUSO, indicating necessary need of comprehensive approach to quantify them. 2) With regards to trade-offs of conflicted objectives and preferences to uncertainties, our proposed model displayed good ability of making planning decision process transparent, therefore providing an effective tool for flexible land use planning compiling. 3) Under uncertain conditions, land use planning effectiveness can be primarily enhanced by flexible management with reserved space to percept and hold uncertainties in advance.
基金supported by the National Natural Science Foundation of China[grant numbers 41375110,11471244]
文摘The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the interval of effective step size（IES） has not been thoroughly explored theoretically.In this paper,by using a general estimation for the total error of the numerical solutions of ODEs,a method is proposed for determining an approximate IES by translating the functions for truncation and rounding errors.It also illustrates this process with an example.Moreover,the relationship between the IES and its approximation is found,and the relative error of the approximation with respect to the IES is given.In addition,variation in the IES with increasing integration time is studied,which can provide an explanation for the observed numerical results.The findings contribute to computational step-size choice for reliable numerical solutions.
基金Project(51178061)supported by the National Natural Science Foundation of ChinaProject(2010FJ6016)supported by Hunan Provincial Science and Technology,China+1 种基金Project(12C0015)supported by Scientific Research Fund of Hunan Provincial Education Department,ChinaProject(13JJ3072)supported by Hunan Provincial Natural Science Foundation of China
文摘Aimed at the uncertain characteristics of discrete logistics network design,an interval hierarchical triangular uncertain OD demand model based on interval demand and network flow is presented.Under consideration of the system profit,the uncertain demand of logistics network is measured by interval variables and interval parameters,and an interval planning model of discrete logistics network is established.The risk coefficient and maximum constrained deviation are defined to realize the certain transformation of the model.By integrating interval algorithm and genetic algorithm,an interval hierarchical optimal genetic algorithm is proposed to solve the model.It is shown by a tested example that in the same scenario condition an interval solution[3275.3,3 603.7]can be obtained by the model and algorithm which is obviously better than the single precise optimal solution by stochastic or fuzzy algorithm,so it can be reflected that the model and algorithm have more stronger operability and the solution result has superiority to scenario decision.
基金supported by the National Key Basic Research Program of China (973 Program) (Grant No. 2011CB706803)the National Natural Science Foundation of China (Grant Nos. 51175208, 51075161)
文摘In the traditional Markov chain model (MCM), aleatory uncertainty because of inherent randomness and epistemic uncertainty due to the lack of knowledge are not differentiated. Generalized interval probability provides a concise representation for the two kinds of uncertainties simultaneously. In this paper, a generalized Markov chain model (GMCM), based on the generalized interval probability theory, is proposed to improve the reliability of prediction. In the GMCM, aleatory uncertainty is represented as probability; interval is used to capture epistemic uncertainty. A case study for predicting the average dynamic compliance in machining processes is provided to demonstrate the effectiveness of proposed GMCM. The results show that the proposed GMCM has a better prediction performance than that of MCM.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10872017, 90816024 and 10876100)111 Project (Grant No. B07009)
文摘Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject to variation. In the study, the collocation interval analysis method based on the first class Chebyshev polynomial approximation is presented to investigate the least favorable responses and the most favorable responses of interval-parameter structures under random excitations. Compared with the interval analysis method based on the first order Taylor expansion, in which only information including the function value and derivative at midpoint is used, the collocation interval analysis method is a non-gradient algorithm using several collocation points which improve the precision of results owing to better approximation of a response function. The pseudo excitation method is introduced to the solving procedure to transform the random problem into a deterministic problem. To validate the procedure, we present numerical results concerning a building under seismic ground motion and aerofoil under continuous atmosphere turbulence to show the effectiveness of the collocation interval analysis method.
文摘This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.
基金supported by Hanyang University(Grant No.HY-2014)
文摘Hydrological risk is highly dependent on the occurrence of extreme rainfalls.This fact has led to a wide range of studies on the estimation and uncertainty analysis of the extremes.In most cases,confidence intervals(CIs)are constructed to represent the uncertainty of the estimates.Since the accuracy of CIs depends on the asymptotic normality of the data and is questionable with limited observations in practice,a Bayesian highest posterior density(HPD)interval,bootstrap percentile interval,and profile likelihood(PL)interval have been introduced to analyze the uncertainty that does not depend on the normality assumption.However,comparison studies to investigate their performances in terms of the accuracy and uncertainty of the estimates are scarce.In addition,the strengths,weakness,and conditions necessary for performing each method also must be investigated.Accordingly,in this study,test experiments with simulations from varying parent distributions and different sample sizes were conducted.Then,applications to the annual maximum rainfall(AMR)time series data in South Korea were performed.Five districts with 38-year(1973–2010)AMR observations were fitted by the three aforementioned methods in the application.From both the experimental and application results,the Bayesian method is found to provide the lowest uncertainty of the design level while the PL estimates generally have the highest accuracy but also the largest uncertainty.The bootstrap estimates are usually inferior to the other two methods,but can perform adequately when the distribution model is not heavy-tailed and the sample size is large.The distribution tail behavior and the sample size are clearly found to affect the estimation accuracy and uncertainty.This study presents a comparative result,which can help researchers make decisions in the context of assessing extreme rainfall uncertainties.
基金supported by the National Special Fund for Major Research Instrument Development(Grant No.2011YQ140145)111 Project(Grant No.B07009)+1 种基金National Natural Science Foundation of China(Grant No.11002013)Defense Industrial Technology Development Program(Grant Nos.A2120110001 and B2120110011)
文摘Based on the traditional finite volume method, a new numerical technique is presented for the transient temperature field prediction with interval uncertainties in both the physical parameters and initial/boundary conditions. New stability theory applicable to interval discrete schemes is developed. Interval ranges of the uncertain temperature field can be approximately yielded by two kinds of parameter perturbation methods. Different order Neumann series are adopted to approximate the interval matrix inverse. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed model and methods.
基金supported by grants to IGSNRR from China Global Change Research Program of MOST (Grant No. 2010CB950101)the Chinese Academy of Sciences (Grant No. XDA05080100)National Natural Science Foundation of China (Grant No. 41071029)
文摘The general characteristics of climate changes over the past 2000 years in China,regional differences and uncertainties were analyzed based on the recently peer-reviewed high time-resolution climatic reconstructions.The results showed that there exists four warm periods of the temperature variation in China since the Qin Dynasty,including the western and eastern Han Dynasties(200 BC-AD 180),the Sui and Tang dynasties(541-810),the Song and Yuan dynasties(931-1320),and the 20th century,and three cold phases involving the Wei,Jin,and North-South Dynasties(181-540),the late Tang Dynasty(811-930),and the Ming and Qing dynasties(1321-1920).The Song and Yuan warm period is consistent with the Medieval Warm Period over the Northern Hemisphere,and the cold phases of the North-South Dynasties and the Ming and Qing dynasties are paralleled to the Dark Ages Cold Period and the Little Ice Age,respectively.The 13th-15th century could be a shift to the wet condition of the climate,and the low precipitation variability is exhibited in western China prior to 1500.In the context of the climate warming,the pattern of the drought in north and flood in south is prevalent over the eastern China.In addition,the published reconstructions have a high level of confidence for the past 500 years,but large uncertainties exist prior to the 16th century.
基金supported by National Natural Science Foundation of China(Grant Nos.11402083&11572121)Independent Research Project of State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body in Hunan University(Grant No.51375002)Fundamental Research Funds for the Central Universities,Collaborative Innovation Center of Intelligent New Energy Vehicle,and the Hunan Collaborative Innovation Center of Green Automobile
文摘In summary,the interval uncertainty is introduced to the acoustic metamaterial with Helmholtz resonators.And then,new descriptions(the conservative approximation,the unsafe approximation and the approximation precision)on uncertainties of physical properties of this interval acoustic metamaterial are defined.Lastly,an optimization model for this interval acoustic metamaterial is proposed.The organization of this paper is listed as follows.The acoustic transmission line method(ATLM)for an acoustic metamaterial with Helmholtz resonators is described in Section 2.In Section3,uncertain analysis of the interval acoustic metamaterial is presented.In Section 4,optimization model of the interval acoustic metamaterial is proposed.The discussion on optimization results is shown in Section 5.In section 6,some conclusions are given.
文摘This paper addresses the issue of security alliances in Northeast Asia--their origins and current status. It observes some fundamental changes of such alliances in the region with the change of time, and concludes that the present alliances are still hedging against uncertainty. In particular, it elaborates the legitimacy of alliance due to collective defense, rather than cooperative aggressiveness that erodes the credibility of alliance and leads to distrust of nations. The paper raises the Taiwan Question and DPRK issue as key examples to analyze how China and the US have entered a strategically distrustful relationship and how these two issues have been intertwined. It also discusses how to de-link them and build a more stable and secure relationship between China and the US through forward-looking cooperation.
基金supported by the National Natural Science Foundation of China(Grant No.11602012)the 111 Project(Grant No.B07009)+1 种基金the Defense Industrial Technology Development Program(Grant No.JCKY2016601B001)and the China Postdoctoral Science Foundation(Grant No.2016M591038)
文摘A Newton iteration-based interval uncertainty analysis method(NI-IUAM) is proposed to analyze the propagating effect of interval uncertainty in multidisciplinary systems. NI-IUAM decomposes one multidisciplinary system into single disciplines and utilizes a Newton iteration equation to obtain the upper and lower bounds of coupled state variables at each iterative step.NI-IUAM only needs to determine the bounds of uncertain parameters and does not require specific distribution formats. In this way, NI-IUAM may greatly reduce the necessity for raw data. In addition, NI-IUAM can accelerate the convergence process as a result of the super-linear convergence of Newton iteration. The applicability of the proposed method is discussed, in particular that solutions obtained in each discipline must be compatible in multidisciplinary systems. The validity and efficiency of NI-IUAM is demonstrated by both numerical and engineering examples.
