Traditional econometrics has long employed ＂points＂ to measure time series data. In real life situations, however, it suffers the loss of volatility information, since many variables are bounded by intervals in a gi...Traditional econometrics has long employed ＂points＂ to measure time series data. In real life situations, however, it suffers the loss of volatility information, since many variables are bounded by intervals in a given period. To address this issue, this paper provides a new methodology for interval time series analysis. The concept of ＂interval stochastic process＂ is formally defined as a counterpart of ＂stochastic process＂ in point-based econometrics. The authors introduce the concepts of interval stationarity, interval statistics （including interval mean, interval variance, etc.） and propose an interval linear model to investigate the dynamic relationships between interval processes. A new interval-based optimization approach for estimation is proposed, and corresponding evaluation criteria are derived. To demonstrate that the new interval method provides valid results, an empirical example on the sterling-dollar exchange rate is presented.展开更多
Interval state estimation(ISE)can estimate state intervals of power systems according to confidence intervals of predicted pseudo-measurements,thereby analyzing the impact of uncertain pseudo-measurements on states.Ho...Interval state estimation(ISE)can estimate state intervals of power systems according to confidence intervals of predicted pseudo-measurements,thereby analyzing the impact of uncertain pseudo-measurements on states.However,predicted pseudo-measurements have prediction errors,and their confidence intervals do not necessarily contain the truth values,leading to estimation biases of the ISE.To solve this problem,this paper proposes a pseudo-measurement interval prediction framework based on the Gaussian process regression(GPR)model,thereby improving the prediction accuracy of pseudo-measurement confidence intervals.Besides,a weight assignment strategy for improving the robustness of weighted least squares(WLS)ISE is proposed.This strategy quantifies the deviation between the pseudo-measurement intervals and their estimated intervals and assigns smaller weights to the pseudo-measurement intervals with larger deviations,thereby improving the estimation accuracy and robustness of the ISE.This paper adopts the data from the supervisory control and data acquisition(SCADA)system of the New York Independent System Operator(NYISO).It verifies the advantages of the GPR method for pseudo-measurement interval prediction by comparing it with the quantile regression and neural network methods.In addition,this paper demonstrates the effectiveness of the proposed weight assignment strategy through the IEEE 14-bus case.Finally,the differences in the estimation accuracy and the bad data identification between the robust interval state estimation and deterministic state estimation are discussed.展开更多
Long-memory process has been widely studied in classical financial time series analysis,which has merely been reported in the field of interval-valued financial time series.The aim of this paper is to explore long-mem...Long-memory process has been widely studied in classical financial time series analysis,which has merely been reported in the field of interval-valued financial time series.The aim of this paper is to explore long-memory process in the prediction of interval-valued time series(IvTS).To model the long-memory process,two novel interval-valued time series prediction models named as interval-valued vector autoregressive fractionally integrated moving average(IV-VARFIMA)and ARFIMAX-FIGARCH were established.In the developed long-memory pattern,both of the short term and long-term influences contained in IvTS can be included.As an application of the proposed models,interval-valued form of WTI crude oil futures price series is predicted.Compared to current IvTS prediction models,IV-VARFIMA and ARFIMAX-FIGARCH can provide better in-sample and out-of-sample forecasts.展开更多
In recent years, the authors have extended the traditional interval method into the time dimension to develop a new mathematical tool called the “interval process model” for quantifying time-varying or dynamic uncer...In recent years, the authors have extended the traditional interval method into the time dimension to develop a new mathematical tool called the “interval process model” for quantifying time-varying or dynamic uncertainties. This model employs upper and lower bounds instead of precise probability distributions to quantify uncertainty in a parameter at any given time point. It is anticipated to complement the conventional stochastic process model in the coming years owing to its relatively low dependence on experimental samples and ease of understanding for engineers. Building on our previous work, this paper proposes a spectrum analysis method to describe the frequency domain characteristics of an interval process, further strengthening the theoretical foundation of the interval process model and enhancing its applicability for complex engineering problems. In this approach, we first define the zero midpoint function interval process and its auto/cross-power spectral density(PSD) functions. We also deduce the relationship between the auto-PSD function and the auto-covariance function of the stationary zero midpoint function interval process. Next, the auto/cross-PSD function matrices of a general interval process are defined, followed by the introduction of the concepts of PSD function matrix and cross-PSD function matrix for interval process vectors. The spectrum analysis method is then applied to random vibration problems, leading to the creation of a spectrum-analysis-based interval vibration analysis method that determines the PSD function for the system displacement response under stationary interval process excitations. Finally, the effectiveness of the formulated spectrum-analysis-based interval vibration analysis approach is verified through two numerical examples.展开更多
The efficiency of reconciliation in the continuous key distribution is the main factor which limits the ratio of secret key distribution. However, the efficiency depends on the computational complexity of the algorith...The efficiency of reconciliation in the continuous key distribution is the main factor which limits the ratio of secret key distribution. However, the efficiency depends on the computational complexity of the algorithm. This paper optimizes the two main aspects of the reconciliation process of the continuous key distribution： the partition of interval and the estimation of bit. We use Gaussian approximation to effectively speed up the convergence of algorithm. We design the estimation function as the estimator of the SEC （sliced error correction） algorithm. Therefore, we lower the computational complexity and simplify the core problem of the reconciliation algorithm. Thus we increase the efficiency of the reconciliation process in the continuous key distribution and then the ratio of the secret key distribution is also increased.展开更多
Purpose–The purpose of this paper is to propose a grey clustering evaluation model based on analytic hierarchy process(AHP)and interval grey number(IGN)to solve the clustering evaluation problem with IGNs.Design/meth...Purpose–The purpose of this paper is to propose a grey clustering evaluation model based on analytic hierarchy process(AHP)and interval grey number(IGN)to solve the clustering evaluation problem with IGNs.Design/methodology/approach–First,the centre-point triangular whitenisation weight function with real numbers is built,and then by using interval mean function,the whitenisation weight function is extended to IGNs.The weights of evaluation indexes are determined by AHP.Finally,this model is used to evaluate the flight safety of a Chinese airline.The results indicate that the model is effective and reasonable.Findings–When IGN meets certain conditions,the centre-point triangular whitenisation weight function based on IGN is not multiple-cross and it is normative.It provides a certain standard and basis for obtaining the effective evaluation indexes and determining the scientific evaluation of the grey class.Originality/value–The traditional grey clustering model is extended to the field of IGN.It can make full use of all the information of the IGN,so the result of the evaluation is more objective and reasonable,which provides supports for solving practical problems.展开更多
A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative,...A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.展开更多
The authors recently developed a kind of non-probabilistic analysis method, named as‘non-random vibration analysis’, to deal with the important random vibration problems, in which the excitation and response are bot...The authors recently developed a kind of non-probabilistic analysis method, named as‘non-random vibration analysis’, to deal with the important random vibration problems, in which the excitation and response are both given in the form of interval process rather than stochastic process. Since it has some attractive advantages such as easy to understand, convenient to use and small dependence on samples, the non-random vibration analysis method is expected to be an effective supplement of the traditional random vibration theory. In this paper, we further extend the nonrandom vibration analysis into the general viscous damping system, and formulate a method to calculate the dynamic response bounds of a viscous damping vibration system under uncertain excitations. Firstly, the unit impulse response matrix of the system is obtained by using a complex mode superposition method. Secondly, an analytic formulation of the system dynamic response middle point and radius under uncertain excitations is derived based on the Duhamel’s integral, and thus the upper and lower response bounds of the system can be obtained. Finally, two numerical examples are investigated to demonstrate the effectiveness of the proposed method.展开更多
基金This work was partially supported by the National Natural Science Foundation of China and Research Granting Committee of Hong Kong
文摘Traditional econometrics has long employed ＂points＂ to measure time series data. In real life situations, however, it suffers the loss of volatility information, since many variables are bounded by intervals in a given period. To address this issue, this paper provides a new methodology for interval time series analysis. The concept of ＂interval stochastic process＂ is formally defined as a counterpart of ＂stochastic process＂ in point-based econometrics. The authors introduce the concepts of interval stationarity, interval statistics （including interval mean, interval variance, etc.） and propose an interval linear model to investigate the dynamic relationships between interval processes. A new interval-based optimization approach for estimation is proposed, and corresponding evaluation criteria are derived. To demonstrate that the new interval method provides valid results, an empirical example on the sterling-dollar exchange rate is presented.
基金supported in part by the National Natural Science Foundation of China(No.51677012).
文摘Interval state estimation(ISE)can estimate state intervals of power systems according to confidence intervals of predicted pseudo-measurements,thereby analyzing the impact of uncertain pseudo-measurements on states.However,predicted pseudo-measurements have prediction errors,and their confidence intervals do not necessarily contain the truth values,leading to estimation biases of the ISE.To solve this problem,this paper proposes a pseudo-measurement interval prediction framework based on the Gaussian process regression(GPR)model,thereby improving the prediction accuracy of pseudo-measurement confidence intervals.Besides,a weight assignment strategy for improving the robustness of weighted least squares(WLS)ISE is proposed.This strategy quantifies the deviation between the pseudo-measurement intervals and their estimated intervals and assigns smaller weights to the pseudo-measurement intervals with larger deviations,thereby improving the estimation accuracy and robustness of the ISE.This paper adopts the data from the supervisory control and data acquisition(SCADA)system of the New York Independent System Operator(NYISO).It verifies the advantages of the GPR method for pseudo-measurement interval prediction by comparing it with the quantile regression and neural network methods.In addition,this paper demonstrates the effectiveness of the proposed weight assignment strategy through the IEEE 14-bus case.Finally,the differences in the estimation accuracy and the bad data identification between the robust interval state estimation and deterministic state estimation are discussed.
基金supported by the Humanities and Social Sciences Research Youth Project of the Ministry of Education of China under Grant No.21YJCZH148the Natural Science Foundation of Anhui Province under Grant Nos.2108085MG239,2108085QG290,2008085QG334,and 2008085MG226+2 种基金the National Natural Science Foundation of China under Grant Nos.72001001,71901001,and 72071001the Provincial Natural Science Research Project of Anhui Colleges,China under Grant No.KJ2020A0004The teacher project of Anhui Ecology and Economic Development Research Center in 2021 under Grant No.AHST2021002.
文摘Long-memory process has been widely studied in classical financial time series analysis,which has merely been reported in the field of interval-valued financial time series.The aim of this paper is to explore long-memory process in the prediction of interval-valued time series(IvTS).To model the long-memory process,two novel interval-valued time series prediction models named as interval-valued vector autoregressive fractionally integrated moving average(IV-VARFIMA)and ARFIMAX-FIGARCH were established.In the developed long-memory pattern,both of the short term and long-term influences contained in IvTS can be included.As an application of the proposed models,interval-valued form of WTI crude oil futures price series is predicted.Compared to current IvTS prediction models,IV-VARFIMA and ARFIMAX-FIGARCH can provide better in-sample and out-of-sample forecasts.
基金supported by the National Natural Science Foundation of China (Grant No. 52105253)the State Key Program of National Science Foundation of China (Grant No.52235005)。
文摘In recent years, the authors have extended the traditional interval method into the time dimension to develop a new mathematical tool called the “interval process model” for quantifying time-varying or dynamic uncertainties. This model employs upper and lower bounds instead of precise probability distributions to quantify uncertainty in a parameter at any given time point. It is anticipated to complement the conventional stochastic process model in the coming years owing to its relatively low dependence on experimental samples and ease of understanding for engineers. Building on our previous work, this paper proposes a spectrum analysis method to describe the frequency domain characteristics of an interval process, further strengthening the theoretical foundation of the interval process model and enhancing its applicability for complex engineering problems. In this approach, we first define the zero midpoint function interval process and its auto/cross-power spectral density(PSD) functions. We also deduce the relationship between the auto-PSD function and the auto-covariance function of the stationary zero midpoint function interval process. Next, the auto/cross-PSD function matrices of a general interval process are defined, followed by the introduction of the concepts of PSD function matrix and cross-PSD function matrix for interval process vectors. The spectrum analysis method is then applied to random vibration problems, leading to the creation of a spectrum-analysis-based interval vibration analysis method that determines the PSD function for the system displacement response under stationary interval process excitations. Finally, the effectiveness of the formulated spectrum-analysis-based interval vibration analysis approach is verified through two numerical examples.
基金the National Natural Science Foundation of China (Grant No. 60773085)
文摘The efficiency of reconciliation in the continuous key distribution is the main factor which limits the ratio of secret key distribution. However, the efficiency depends on the computational complexity of the algorithm. This paper optimizes the two main aspects of the reconciliation process of the continuous key distribution： the partition of interval and the estimation of bit. We use Gaussian approximation to effectively speed up the convergence of algorithm. We design the estimation function as the estimator of the SEC （sliced error correction） algorithm. Therefore, we lower the computational complexity and simplify the core problem of the reconciliation algorithm. Thus we increase the efficiency of the reconciliation process in the continuous key distribution and then the ratio of the secret key distribution is also increased.
基金supported by National Natural Science Foundation of China under the project of 71601050 and Civil Aviation Administration of China Science Planned Projects under the project of MHRD20150211.
文摘Purpose–The purpose of this paper is to propose a grey clustering evaluation model based on analytic hierarchy process(AHP)and interval grey number(IGN)to solve the clustering evaluation problem with IGNs.Design/methodology/approach–First,the centre-point triangular whitenisation weight function with real numbers is built,and then by using interval mean function,the whitenisation weight function is extended to IGNs.The weights of evaluation indexes are determined by AHP.Finally,this model is used to evaluate the flight safety of a Chinese airline.The results indicate that the model is effective and reasonable.Findings–When IGN meets certain conditions,the centre-point triangular whitenisation weight function based on IGN is not multiple-cross and it is normative.It provides a certain standard and basis for obtaining the effective evaluation indexes and determining the scientific evaluation of the grey class.Originality/value–The traditional grey clustering model is extended to the field of IGN.It can make full use of all the information of the IGN,so the result of the evaluation is more objective and reasonable,which provides supports for solving practical problems.
基金Supported by Grant No.201/01/1451 of the Grant Agency of Czech Republicthe Council of Czech Government J14/98:153100011
文摘A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.
基金supported by the Science Challenge Project of China (No. TZ2018007)the National Science Fund for Distinguished Young Scholars (No. 51725502)+1 种基金the National Key R&D Program of China (No. 2016YFD0701105)the Open Project Program of Key Laboratory for Precision & Non-traditional Machining of Ministry of Education, Dalian University of Technology of China (No. JMTZ201701)
文摘The authors recently developed a kind of non-probabilistic analysis method, named as‘non-random vibration analysis’, to deal with the important random vibration problems, in which the excitation and response are both given in the form of interval process rather than stochastic process. Since it has some attractive advantages such as easy to understand, convenient to use and small dependence on samples, the non-random vibration analysis method is expected to be an effective supplement of the traditional random vibration theory. In this paper, we further extend the nonrandom vibration analysis into the general viscous damping system, and formulate a method to calculate the dynamic response bounds of a viscous damping vibration system under uncertain excitations. Firstly, the unit impulse response matrix of the system is obtained by using a complex mode superposition method. Secondly, an analytic formulation of the system dynamic response middle point and radius under uncertain excitations is derived based on the Duhamel’s integral, and thus the upper and lower response bounds of the system can be obtained. Finally, two numerical examples are investigated to demonstrate the effectiveness of the proposed method.
