The authors firstly evaluate the strain accumulation rate of the Xianshuihe fault zone based on earthquake activity. We calculated the stress and seismic moment accumulation rate for each subsection of the Xianshuihe ...The authors firstly evaluate the strain accumulation rate of the Xianshuihe fault zone based on earthquake activity. We calculated the stress and seismic moment accumulation rate for each subsection of the Xianshuihe fault zone based on the distribution of geological slip rate and GPS survey results. According to the results, we get the recurrence intervals of characterized earthquakes on each subsection respectively. A three-dimensional finite element model for western Sichuan is constructed to discuss the earthquakes triggering among major earthquakes ({ntM}>6.7) that occurred along the Xianshuihe fault zone since 1893. The calculated Coulomb failure stress changes (?CFS) show that 5 of the 6 earthquakes with Ms>6.7 were triggered by positive ?CFS. The interactions between major earthquakes not only influence recurrence intervals of characterized earthquakes on each subsection, but also change recurrence behavior of major earthquakes along the whole fault zone.展开更多
It is significant to consider the effect of uncertainty of the measured modal parameters on the updated finite element(FE) model,especially for updating the FE model of practical bridges,since the uncertainty of the m...It is significant to consider the effect of uncertainty of the measured modal parameters on the updated finite element(FE) model,especially for updating the FE model of practical bridges,since the uncertainty of the measured modal parameters cannot be ignored owing to the application of output-only identification method and the existence of the measured noise.A reasonable method is to define the objective of the FE model updating as the statistical property of the measured modal parameters obtained by conducting couples of identical modal tests,however,it is usually impossible to implement repeated modal test due to the limit of practical situation and economic reason.In this study,a method based on fuzzy finite element(FFM) was proposed in order to consider the effect of the uncertainty of the measured modal parameters on the updated FE model by using the results of a single modal test.The updating parameters of bridges were deemed as fuzzy variables,and then the fuzzification of objective of the FE model updating was proposed to consider the uncertainty of the measured modal parameters.Finally,the effectiveness of the proposed method was verified by updating the FE model of a practical bridge with the measured modal parameters.展开更多
The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on...The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements are given. The sub-interval amount is discussed and the approximate computation formula is given. At the same time, the computational precision is discussed and some measures of improving computational efficiency are given. Finally, based on sub-interval perturbed finite element method and anti-slide stability analysis method, the formula for computing the bounds of stability factor is given. It provides a basis for estimating and evaluating reasonably anti-slide stability of structures.展开更多
We use the Fokas method to analyze the derivative nonlinear Schrodinger （DNLS） equation iqt （x, t） = -qxx （x, t）＋（rq^2）x on the interval [0, L]. Assuming that the solution q（x, t） exists, we show that it ca...We use the Fokas method to analyze the derivative nonlinear Schrodinger （DNLS） equation iqt （x, t） = -qxx （x, t）＋（rq^2）x on the interval [0, L]. Assuming that the solution q（x, t） exists, we show that it can be represented in terms of the solution of a matrix Riemann- Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit （x, t） dependence, and it has jumps across {ξ∈C｜Imξ^4 = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a（ξ）, b（ξ）}, {A（ξ）, B（ξ）}, and {A（ξ）, B（ξ）}, which in turn are defined in terms of the initial data q0（x） = q（x, 0）, the bound- ary data g0（t）= q（0, t）, g1（t） = qx（0, t）, and another boundary values f0（t） = q（L, t）, f1（t） = qx（L, t）. The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.展开更多
Machining and installation errors are unavoidable in mechanical structures. However, the effect of errors on radial stiffness of the mechanical elastic wheel(ME-Wheel) is not considered in previous studies. To this en...Machining and installation errors are unavoidable in mechanical structures. However, the effect of errors on radial stiffness of the mechanical elastic wheel(ME-Wheel) is not considered in previous studies. To this end, the interval mathematical model and interval finite element model of the ME-Wheel were both established and compared with bench test results. The intercomparison of the influence of the machining and installation errors on the ME-Wheel radial stiffness revealed good consistency among the interval mathematical analysis, interval finite element simulation,and bench test results. Within the interval range of the ME-Wheel machining and installation errors, parametric analysis of the combined elastic rings was performed at different initial radial rigidity values. The results showed that the initial radial stiffness of the flexible tire body significantly influenced the ME-Wheel radial stiffness, and the inverse relationship between the hinge unit length or suspension hub and the radial stiffness was nonlinear. The radial stiffness of the ME-Wheel is predicted by using the interval algorithm for the first time, and the regularity of the radial stiffness between the error and the load on the ME-Wheel is studied, which will lay the foundation for the exact study of the ME-Wheel dynamic characteristics in the future.展开更多
Uncertainties are unavoidable in practical engineering,and phononic crystals are no exception.In this paper,the uncertainties are treated as the interval parameters,and an interval phononic crystal beam model is estab...Uncertainties are unavoidable in practical engineering,and phononic crystals are no exception.In this paper,the uncertainties are treated as the interval parameters,and an interval phononic crystal beam model is established.A perturbation-based interval finite element method(P-IFEM)and an affine-based interval finite element method(A-IFEM)are proposed to study the dynamic response of this interval phononic crystal beam,based on which an interval vibration transmission analysis can be easily implemented and the safe bandgap can be defined.Finally,two numerical examples are investigated to demonstrate the effectiveness and accuracy of the P-IFEM and A-IFEM.Results show that the safe bandgap range may even decrease by 10%compared with the deterministic bandgap without considering the uncertainties.展开更多
This work focuses on the design of a sliding mode controller for a class of continuoustime interval type-2 fuzzy-model-based nonlinear systems with unmeasurable state information over a finite-time interval.Aiming at ...This work focuses on the design of a sliding mode controller for a class of continuoustime interval type-2 fuzzy-model-based nonlinear systems with unmeasurable state information over a finite-time interval.Aiming at describing the nonlinearities containing parameter uncertainties that inevitably appear in practice,the interval type-2 fuzzy sets are employed to model the studied system.To improve the designing flexibility,a fuzzy observer model non-parallel distribution compensation scheme is designed to estimate the state information of the plant,i.e.,the observer is allowed to have a mismatching premise structure from the system.On this basis,the appropriate fuzzy sliding surface and fuzzy controller are constructed by following the same premise variables as the designed fuzzy observer.Then,by means of the sliding mode control theory and the Lyapunov function method,some novel sufficient criteria are established to ensure the finite-time boundedness for the studied systems via a partitioning strategy including the reaching phase,the sliding motion phase and the whole time interval.Furthermore,the designed gains are acquired by solving the matrix convex optimization problem.Finally,the effectiveness of the developed method is demonstrated by two simulation examples.展开更多
In this paper, through an information-theoretic approach, we construct estimations and confidence intervals of Z-functionals involving finite population and with the presence of auxiliary information. In particular, w...In this paper, through an information-theoretic approach, we construct estimations and confidence intervals of Z-functionals involving finite population and with the presence of auxiliary information. In particular, we give a method of estimating the variance of finite population with known mean. The modified estimates and confidence intervals for Z-functionals can adequately use the auxiliary information, at least not worse than what the standard ones do. A simulation study is presented to assess the performance of the modified estimates for the finite sample case.展开更多
This paper introduces a non-conventional approach with multi-dimensional random sampling to solve a cocaine abuse model with statistical probability. The mean Latin hypercube finite difference (MLHFD) method is propos...This paper introduces a non-conventional approach with multi-dimensional random sampling to solve a cocaine abuse model with statistical probability. The mean Latin hypercube finite difference (MLHFD) method is proposed for the first time via hybrid integration of the classical numerical finite difference (FD) formula with Latin hypercube sampling (LHS) technique to create a random distribution for the model parameters which are dependent on time t. The LHS technique gives advantage to MLHFD method to produce fast variation of the parameters' values via number of multidimensional simulations (100, 1000 and 5000). The generated Latin hypercube sample which is random or non-deterministic in nature is further integrated with the FD method to complete one cycle of LHS-FD simulation iteration. This process is repeated until n final iterations of LHS-FD are obtained. The means of these n final solutions (MLHFD solutions) are tabulated, graphed and analyzed. The numerical simulation results of MLHFD for the SEIR model are presented side-by-side with deterministic solutions obtained from the classical FD scheme and homotopy analysis method with Pade approximation (HAM-Pade). The present MLHFD results are also compared with the previous non-deterministic statistical estimations from 1995 to 2015. Good agreement between the two is perceived with small errors. MLHFD method can be used to predict future behavior, range and prediction interval for the epidemic model solutions. The expected profiles of the cocaine abuse subpopulations are projected until the year 2045. Both the statistical estimations and the deterministic results of FD and HAM-Pade are found to be within the MLHFD prediction intervals for all the years and for all the subpopulations considered.展开更多
基金the Ministry of Science and Technology of China (Grant No. 2004CB418406)the "Basic Science Research Plan" of the Institute of Earth-quake Science, China Earthquake Administration (Grant No. 2007-03)
文摘The authors firstly evaluate the strain accumulation rate of the Xianshuihe fault zone based on earthquake activity. We calculated the stress and seismic moment accumulation rate for each subsection of the Xianshuihe fault zone based on the distribution of geological slip rate and GPS survey results. According to the results, we get the recurrence intervals of characterized earthquakes on each subsection respectively. A three-dimensional finite element model for western Sichuan is constructed to discuss the earthquakes triggering among major earthquakes ({ntM}>6.7) that occurred along the Xianshuihe fault zone since 1893. The calculated Coulomb failure stress changes (?CFS) show that 5 of the 6 earthquakes with Ms>6.7 were triggered by positive ?CFS. The interactions between major earthquakes not only influence recurrence intervals of characterized earthquakes on each subsection, but also change recurrence behavior of major earthquakes along the whole fault zone.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51008097 and 11172078)the National Key Technology R&D Program (Grant No. 2011BAK02B02)
文摘It is significant to consider the effect of uncertainty of the measured modal parameters on the updated finite element(FE) model,especially for updating the FE model of practical bridges,since the uncertainty of the measured modal parameters cannot be ignored owing to the application of output-only identification method and the existence of the measured noise.A reasonable method is to define the objective of the FE model updating as the statistical property of the measured modal parameters obtained by conducting couples of identical modal tests,however,it is usually impossible to implement repeated modal test due to the limit of practical situation and economic reason.In this study,a method based on fuzzy finite element(FFM) was proposed in order to consider the effect of the uncertainty of the measured modal parameters on the updated FE model by using the results of a single modal test.The updating parameters of bridges were deemed as fuzzy variables,and then the fuzzification of objective of the FE model updating was proposed to consider the uncertainty of the measured modal parameters.Finally,the effectiveness of the proposed method was verified by updating the FE model of a practical bridge with the measured modal parameters.
文摘The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements are given. The sub-interval amount is discussed and the approximate computation formula is given. At the same time, the computational precision is discussed and some measures of improving computational efficiency are given. Finally, based on sub-interval perturbed finite element method and anti-slide stability analysis method, the formula for computing the bounds of stability factor is given. It provides a basis for estimating and evaluating reasonably anti-slide stability of structures.
基金supported by grants from the National Science Foundation of China (10971031 11271079+2 种基金 11075055)Doctoral Programs Foundation of the Ministry of Education of Chinathe Shanghai Shuguang Tracking Project (08GG01)
文摘We use the Fokas method to analyze the derivative nonlinear Schrodinger （DNLS） equation iqt （x, t） = -qxx （x, t）＋（rq^2）x on the interval [0, L]. Assuming that the solution q（x, t） exists, we show that it can be represented in terms of the solution of a matrix Riemann- Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit （x, t） dependence, and it has jumps across {ξ∈C｜Imξ^4 = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a（ξ）, b（ξ）}, {A（ξ）, B（ξ）}, and {A（ξ）, B（ξ）}, which in turn are defined in terms of the initial data q0（x） = q（x, 0）, the bound- ary data g0（t）= q（0, t）, g1（t） = qx（0, t）, and another boundary values f0（t） = q（L, t）, f1（t） = qx（L, t）. The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.
基金Supported by National Natural Science Foundation of China(Grant No.11672127)Major Exploration Project of the General Armaments Department of China(Grant No.NHA13002)+1 种基金Fundamental Research Funds for the Central Universities of China(Grant No.NP2016412,NP2018403,NT2018002)Jiangsu Provincial Innovation Program for Graduate Education and the Fundamental Research Funds for the Central Universities of China(Grant No.KYLX16_0330)
文摘Machining and installation errors are unavoidable in mechanical structures. However, the effect of errors on radial stiffness of the mechanical elastic wheel(ME-Wheel) is not considered in previous studies. To this end, the interval mathematical model and interval finite element model of the ME-Wheel were both established and compared with bench test results. The intercomparison of the influence of the machining and installation errors on the ME-Wheel radial stiffness revealed good consistency among the interval mathematical analysis, interval finite element simulation,and bench test results. Within the interval range of the ME-Wheel machining and installation errors, parametric analysis of the combined elastic rings was performed at different initial radial rigidity values. The results showed that the initial radial stiffness of the flexible tire body significantly influenced the ME-Wheel radial stiffness, and the inverse relationship between the hinge unit length or suspension hub and the radial stiffness was nonlinear. The radial stiffness of the ME-Wheel is predicted by using the interval algorithm for the first time, and the regularity of the radial stiffness between the error and the load on the ME-Wheel is studied, which will lay the foundation for the exact study of the ME-Wheel dynamic characteristics in the future.
基金the National Natural Science Foundation of China(Nos.12272172 and 11847009)the Natural Science Foundation of Jiangsu Higher Education Institutions of China(No.22KJB580005)+1 种基金the Youth Talent Promotion Project from China Association for Science and Technology(No.2022QNRC001)the Priority Academic Program Development of Jiangsu Higher Education Institutions of China。
文摘Uncertainties are unavoidable in practical engineering,and phononic crystals are no exception.In this paper,the uncertainties are treated as the interval parameters,and an interval phononic crystal beam model is established.A perturbation-based interval finite element method(P-IFEM)and an affine-based interval finite element method(A-IFEM)are proposed to study the dynamic response of this interval phononic crystal beam,based on which an interval vibration transmission analysis can be easily implemented and the safe bandgap can be defined.Finally,two numerical examples are investigated to demonstrate the effectiveness and accuracy of the P-IFEM and A-IFEM.Results show that the safe bandgap range may even decrease by 10%compared with the deterministic bandgap without considering the uncertainties.
基金the National Natural Science Foundation of China under Grant Nos.61873002,62173001。
文摘This work focuses on the design of a sliding mode controller for a class of continuoustime interval type-2 fuzzy-model-based nonlinear systems with unmeasurable state information over a finite-time interval.Aiming at describing the nonlinearities containing parameter uncertainties that inevitably appear in practice,the interval type-2 fuzzy sets are employed to model the studied system.To improve the designing flexibility,a fuzzy observer model non-parallel distribution compensation scheme is designed to estimate the state information of the plant,i.e.,the observer is allowed to have a mismatching premise structure from the system.On this basis,the appropriate fuzzy sliding surface and fuzzy controller are constructed by following the same premise variables as the designed fuzzy observer.Then,by means of the sliding mode control theory and the Lyapunov function method,some novel sufficient criteria are established to ensure the finite-time boundedness for the studied systems via a partitioning strategy including the reaching phase,the sliding motion phase and the whole time interval.Furthermore,the designed gains are acquired by solving the matrix convex optimization problem.Finally,the effectiveness of the developed method is demonstrated by two simulation examples.
基金Supported by National Natural Science Foundation of China (Grant Nos.10571093 and 10871104)SRFDP of China (Grant No.20050055038)
文摘In this paper, through an information-theoretic approach, we construct estimations and confidence intervals of Z-functionals involving finite population and with the presence of auxiliary information. In particular, we give a method of estimating the variance of finite population with known mean. The modified estimates and confidence intervals for Z-functionals can adequately use the auxiliary information, at least not worse than what the standard ones do. A simulation study is presented to assess the performance of the modified estimates for the finite sample case.
文摘This paper introduces a non-conventional approach with multi-dimensional random sampling to solve a cocaine abuse model with statistical probability. The mean Latin hypercube finite difference (MLHFD) method is proposed for the first time via hybrid integration of the classical numerical finite difference (FD) formula with Latin hypercube sampling (LHS) technique to create a random distribution for the model parameters which are dependent on time t. The LHS technique gives advantage to MLHFD method to produce fast variation of the parameters' values via number of multidimensional simulations (100, 1000 and 5000). The generated Latin hypercube sample which is random or non-deterministic in nature is further integrated with the FD method to complete one cycle of LHS-FD simulation iteration. This process is repeated until n final iterations of LHS-FD are obtained. The means of these n final solutions (MLHFD solutions) are tabulated, graphed and analyzed. The numerical simulation results of MLHFD for the SEIR model are presented side-by-side with deterministic solutions obtained from the classical FD scheme and homotopy analysis method with Pade approximation (HAM-Pade). The present MLHFD results are also compared with the previous non-deterministic statistical estimations from 1995 to 2015. Good agreement between the two is perceived with small errors. MLHFD method can be used to predict future behavior, range and prediction interval for the epidemic model solutions. The expected profiles of the cocaine abuse subpopulations are projected until the year 2045. Both the statistical estimations and the deterministic results of FD and HAM-Pade are found to be within the MLHFD prediction intervals for all the years and for all the subpopulations considered.
