In the evaluation of some simulation systems, only small samples data are gotten due to the limited conditions. In allusion to the evaluation problem of small sample data, an interval estimation approach with the impr...In the evaluation of some simulation systems, only small samples data are gotten due to the limited conditions. In allusion to the evaluation problem of small sample data, an interval estimation approach with the improved grey confidence degree is proposed.On the basis of the definition of grey distance, three kinds of definition of the grey weight for every sample element in grey estimated value are put forward, and then the improved grey confidence degree is designed. In accordance with the new concept, the grey interval estimation for small sample data is deduced. Furthermore,the bootstrap method is applied for more accurate grey confidence interval. Through resampling of the bootstrap, numerous small samples with the corresponding confidence intervals can be obtained. Then the final confidence interval is calculated from the union of these grey confidence intervals. In the end, the simulation system evaluation using the proposed method is conducted. The simulation results show that the reasonable confidence interval is acquired, which demonstrates the feasibility and effectiveness of the proposed method.展开更多
In this paper, a new method for mobile robot map building based on grey system theory is presented, by which interpretation and integration of sonar readings can be solved robustly and efficiently. The conception of &...In this paper, a new method for mobile robot map building based on grey system theory is presented, by which interpretation and integration of sonar readings can be solved robustly and efficiently. The conception of 'grey number is introduced to model and handle the uncertainty of sonar reading. A new data fusion approach based on grey system theory is proposed to construct environment model. Map building experiments are performed both on a platform of simulation and a real mobile robot. Experimental results show that our method is robust and accurate.展开更多
Based on the variation of discrete surface,a new grey relational analysis model,called the grey variation relational ana-lysis(GVRA)model,is proposed in this paper.Meanwhile,the proposed model avoids the inconsistent ...Based on the variation of discrete surface,a new grey relational analysis model,called the grey variation relational ana-lysis(GVRA)model,is proposed in this paper.Meanwhile,the proposed model avoids the inconsistent results caused by diffe-rent construction of discrete surface of panel data or the change in the order of indicators or objects in existing grey relational analysis models.Firstly,the submatrix of the sample matrix is given according to the permutation and combination theory.Secondly,the amplitude of the submatrix is calculated and the variation of discrete surface is obtained.Then,a grey relational coefficient is presented by variation difference,and the GVRA model is established.Furthermore,the properties of the pro-posed model,such as normality,symmetry,reflexivity,transla-tion invariant,and number multiplication invariant,are also veri-fied.Finally,the proposed model is used to identify the driving factors of haze in the cities along the Yellow River in Shandong Province,China.The result reveals that the proposed model can effectively measure the relationship between panel data.展开更多
In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.B...In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.展开更多
This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on th...This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.展开更多
This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h ...This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model （GM （1, h））, always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method （abbreviated as FDGM （1, h））, is proposed accordingly. Then the feedback control equation and the parameters＇ solution of the FDGM （1, h） model are given. Finally, a real application is used to test the modelling accuracy of the FDGM （1, h） model. Results show that the FDGM （1, h） model is much better than the nonhomogeneous discrete grey forecasting model （NDGM） and the GM （1, h） model.展开更多
Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous Poisson process(NHPP) is the most ...Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous Poisson process(NHPP) is the most used one.However, the failure behavior of software does not follow the NHPP in a statistically rigorous manner, and the pure random method might be not enough to describe the software failure behavior. To solve these problems, this paper proposes a new integrated approach that combines stochastic process and grey system theory to describe the failure behavior of software. A grey NHPP software reliability model is put forward in a discrete form, and a grey-based approach for estimating software reliability under the NHPP is proposed as a nonlinear multi-objective programming problem. Finally, four grey NHPP software reliability models are applied to four real datasets, the dynamic R-square and predictive relative error are calculated. Comparing with the original single NHPP software reliability model, it is found that the modeling using the integrated approach has a higher prediction accuracy of software reliability. Therefore, there is the characteristics of grey uncertain information in the NHPP software reliability models, and exploiting the latent grey uncertain information might lead to more accurate software reliability estimation.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
A combination method of optimization of the back-ground value and optimization of the initial item is proposed. The sequences of the unbiased exponential distribution are simulated and predicted through the optimizati...A combination method of optimization of the back-ground value and optimization of the initial item is proposed. The sequences of the unbiased exponential distribution are simulated and predicted through the optimization of the background value in grey differential equations. The principle of the new information priority in the grey system theory and the rationality of the initial item in the original GM（1,1） model are ful y expressed through the improvement of the initial item in the proposed time response function. A numerical example is employed to il ustrate that the proposed method is able to simulate and predict sequences of raw data with the unbiased exponential distribution and has better simulation performance and prediction precision than the original GM（1,1） model relatively.展开更多
For the classical GM(1,1)model,the prediction accuracy is not high,and the optimization of the initial and background values is one-sided.In this paper,the Lagrange mean value theorem is used to construct the backgrou...For the classical GM(1,1)model,the prediction accuracy is not high,and the optimization of the initial and background values is one-sided.In this paper,the Lagrange mean value theorem is used to construct the background value as a variable related to k.At the same time,the initial value is set as a variable,and the corresponding optimal parameter and the time response formula are determined according to the minimum value of mean relative error(MRE).Combined with the domestic natural gas annual consumption data,the classical model and the improved GM(1,1)model are applied to the calculation and error comparison respectively.It proves that the improved model is better than any other models.展开更多
Crimping is widely adopted in the production of large-diameter submerged-arc welding pipes. Traditionally, designers obtain the technical parameters for crimping from experience or by trial and error through experimen...Crimping is widely adopted in the production of large-diameter submerged-arc welding pipes. Traditionally, designers obtain the technical parameters for crimping from experience or by trial and error through experiments and the finite element(FE) method. However, it is difficult to achieve ideal crimping quality by these approaches. To resolve this issue, crimping parameter design was investigated by multi-objective optimization. Crimping was simulated using the FE code ABAQUS and the FE model was validated experimentally. A welding pipe made of X80 high-strength pipeline steel was considered as a target object and the optimization problem for its crimping was formulated as a mathematical model and crimping was optimized. A response surface method based on the radial basis function was used to construct a surrogate model; the genetic algorithm NSGA-II was adopted to search for Pareto solutions; grey relational analysis was used to determine the most satisfactory solution from the Pareto solutions. The obtained optimal design of parameters shows good agreement with the initial design and remarkably improves the crimping quality. Thus, the results provide an effective approach for improving crimping quality and reducing design times.展开更多
文摘In the evaluation of some simulation systems, only small samples data are gotten due to the limited conditions. In allusion to the evaluation problem of small sample data, an interval estimation approach with the improved grey confidence degree is proposed.On the basis of the definition of grey distance, three kinds of definition of the grey weight for every sample element in grey estimated value are put forward, and then the improved grey confidence degree is designed. In accordance with the new concept, the grey interval estimation for small sample data is deduced. Furthermore,the bootstrap method is applied for more accurate grey confidence interval. Through resampling of the bootstrap, numerous small samples with the corresponding confidence intervals can be obtained. Then the final confidence interval is calculated from the union of these grey confidence intervals. In the end, the simulation system evaluation using the proposed method is conducted. The simulation results show that the reasonable confidence interval is acquired, which demonstrates the feasibility and effectiveness of the proposed method.
基金This project was supported by the National High-Tech Research and Development Plan (2001AA422140) National Science Foundation (69889501, 60105005).
文摘In this paper, a new method for mobile robot map building based on grey system theory is presented, by which interpretation and integration of sonar readings can be solved robustly and efficiently. The conception of 'grey number is introduced to model and handle the uncertainty of sonar reading. A new data fusion approach based on grey system theory is proposed to construct environment model. Map building experiments are performed both on a platform of simulation and a real mobile robot. Experimental results show that our method is robust and accurate.
基金supported by the National Natural Science Foundation of China(72271124,72071111)Shandong Natural Science Foundation(ZR2023MG070)the Social Science Planning Project of Shandong Province(23CGLJ03,21CTJJ01).
文摘Based on the variation of discrete surface,a new grey relational analysis model,called the grey variation relational ana-lysis(GVRA)model,is proposed in this paper.Meanwhile,the proposed model avoids the inconsistent results caused by diffe-rent construction of discrete surface of panel data or the change in the order of indicators or objects in existing grey relational analysis models.Firstly,the submatrix of the sample matrix is given according to the permutation and combination theory.Secondly,the amplitude of the submatrix is calculated and the variation of discrete surface is obtained.Then,a grey relational coefficient is presented by variation difference,and the GVRA model is established.Furthermore,the properties of the pro-posed model,such as normality,symmetry,reflexivity,transla-tion invariant,and number multiplication invariant,are also veri-fied.Finally,the proposed model is used to identify the driving factors of haze in the cities along the Yellow River in Shandong Province,China.The result reveals that the proposed model can effectively measure the relationship between panel data.
基金supported by the National Natural Science Foundation of China(7084001290924022)the Ph.D.Thesis Innovation and Excellent Foundation of Nanjing University of Aeronautics and Astronautics(2010)
文摘In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.
基金supported by the National Natural Science Foundation of China(7090104171171113)the Aeronautical Science Foundation of China(2014ZG52077)
文摘This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.
基金supported by the National Natural Science Foundation of China(7117111370901041)
文摘This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model （GM （1, h））, always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method （abbreviated as FDGM （1, h））, is proposed accordingly. Then the feedback control equation and the parameters＇ solution of the FDGM （1, h） model are given. Finally, a real application is used to test the modelling accuracy of the FDGM （1, h） model. Results show that the FDGM （1, h） model is much better than the nonhomogeneous discrete grey forecasting model （NDGM） and the GM （1, h） model.
基金supported by the National Natural Science Foundation of China (71671090)the Fundamental Research Funds for the Central Universities (NP2020022)the Qinglan Project of Excellent Youth or Middle-Aged Academic Leaders in Jiangsu Province。
文摘Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous Poisson process(NHPP) is the most used one.However, the failure behavior of software does not follow the NHPP in a statistically rigorous manner, and the pure random method might be not enough to describe the software failure behavior. To solve these problems, this paper proposes a new integrated approach that combines stochastic process and grey system theory to describe the failure behavior of software. A grey NHPP software reliability model is put forward in a discrete form, and a grey-based approach for estimating software reliability under the NHPP is proposed as a nonlinear multi-objective programming problem. Finally, four grey NHPP software reliability models are applied to four real datasets, the dynamic R-square and predictive relative error are calculated. Comparing with the original single NHPP software reliability model, it is found that the modeling using the integrated approach has a higher prediction accuracy of software reliability. Therefore, there is the characteristics of grey uncertain information in the NHPP software reliability models, and exploiting the latent grey uncertain information might lead to more accurate software reliability estimation.
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supported by the Key Project of National Social Science Foundation(12AZD111)the National Project for Education Science Planning(EFA110351)+2 种基金the Humanities and Social Science Foundation of Ministry of Education of China(12YJCZH207)the Key Project for Jiangsu Province Social Science Foundation(12DDA011)the Jiangsu College of Humanities and Social Sciences outside Campus Research Base:Chinese Development of Strategic Research Base for Internet of Things
文摘A combination method of optimization of the back-ground value and optimization of the initial item is proposed. The sequences of the unbiased exponential distribution are simulated and predicted through the optimization of the background value in grey differential equations. The principle of the new information priority in the grey system theory and the rationality of the initial item in the original GM（1,1） model are ful y expressed through the improvement of the initial item in the proposed time response function. A numerical example is employed to il ustrate that the proposed method is able to simulate and predict sequences of raw data with the unbiased exponential distribution and has better simulation performance and prediction precision than the original GM（1,1） model relatively.
基金supported by the National Natural Science Foundation of China (71871106)the Blue and Green Project in Jiangsu Provincethe Six Talent Peaks Project in Jiangsu Province (2016-JY-011)
文摘For the classical GM(1,1)model,the prediction accuracy is not high,and the optimization of the initial and background values is one-sided.In this paper,the Lagrange mean value theorem is used to construct the background value as a variable related to k.At the same time,the initial value is set as a variable,and the corresponding optimal parameter and the time response formula are determined according to the minimum value of mean relative error(MRE).Combined with the domestic natural gas annual consumption data,the classical model and the improved GM(1,1)model are applied to the calculation and error comparison respectively.It proves that the improved model is better than any other models.
基金Project(Y2012035)supported by the Natural Science Foundation of Hebei Provincial Education Department,ChinaProject(12211014)supported by the Natural Science Foundation of Hebei Provincial Technology Department,China+2 种基金Project(NJZY14006)supported by the Inner Mongolia Higher School Science and Technology Research Program,ChinaProject(2014BS0502)supported by the Natural Science Foundation of Inner Mongolia,ChinaProject(135143)supported by the Program of Higher-level Talents Fund of Inner Mongolia University,China
文摘Crimping is widely adopted in the production of large-diameter submerged-arc welding pipes. Traditionally, designers obtain the technical parameters for crimping from experience or by trial and error through experiments and the finite element(FE) method. However, it is difficult to achieve ideal crimping quality by these approaches. To resolve this issue, crimping parameter design was investigated by multi-objective optimization. Crimping was simulated using the FE code ABAQUS and the FE model was validated experimentally. A welding pipe made of X80 high-strength pipeline steel was considered as a target object and the optimization problem for its crimping was formulated as a mathematical model and crimping was optimized. A response surface method based on the radial basis function was used to construct a surrogate model; the genetic algorithm NSGA-II was adopted to search for Pareto solutions; grey relational analysis was used to determine the most satisfactory solution from the Pareto solutions. The obtained optimal design of parameters shows good agreement with the initial design and remarkably improves the crimping quality. Thus, the results provide an effective approach for improving crimping quality and reducing design times.
