Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories o...Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.展开更多
Prediction of vibration energy responses of structures with uncertainties is of interest in many fields. The energy density control equation for one-dimensional structure is provided firstly. Interval analysis method ...Prediction of vibration energy responses of structures with uncertainties is of interest in many fields. The energy density control equation for one-dimensional structure is provided firstly. Interval analysis method is applied to the control equation to obtain the range of energy density responses of structures with interval parameters. A cantilever beam with interval-valued damping coefficient is exemplified to carry out a simulation. The result shows that the mean value of energy density from the interval analysis method is the same as that from a probabilistic method which validates the interval analysis method. Besides, the response range from the interval analysis method is wider and includes that from the probabilistic method which indicates the interval analysis method is a more conservative method and is safer in realistic engineering structures.展开更多
This paper proposes a sensitivity analysis method for engineering parameters using interval analyses.This method substantially extends the application of interval analysis method.In this scheme,parameter intervals and...This paper proposes a sensitivity analysis method for engineering parameters using interval analyses.This method substantially extends the application of interval analysis method.In this scheme,parameter intervals and decision-making target intervals are determined using the interval analysis method.As an example,an inverse analysis method for uncertainty is presented.The intervals of unknown parameters can be obtained by sampling measured data.Even for limited measured data,robust results can also be obtained with the inverse analysis method,which can be intuitively evaluated by the uncertainty expressed in terms of an interval.For complex nonlinear problems,an iteratively optimized inverse analysis model is proposed.In a given set of loose parameter intervals,all the unknown parameter intervals that satisfy the measured information can be obtained by an iteratively optimized inverse analysis model.The influences of measured precisions and the number of parameters on the results of the inverse analysis are evaluated.Finally,the uniqueness of the interval inverse analysis method is discussed.展开更多
Interval analysis is a new uncertainty analysis method for engineering structures. In this paper, a new sensitivity analysis method is presented by introducing interval analysis which can expand applications of the in...Interval analysis is a new uncertainty analysis method for engineering structures. In this paper, a new sensitivity analysis method is presented by introducing interval analysis which can expand applications of the interval analysis method. The interval analysis process of sensitivity factor matrix of soil parameters is given. A method of parameter intervals and decision-making target intervals is given according to the interval analysis method. With FEM, secondary developments are done for Marc and the Duncan-Chang nonlinear elastic model. Mutual transfer between FORTRAN and Marc is implemented. With practial examples, rationality and feasibility are validated. Comparison is made with some published results.展开更多
Uncertainty is extensively involved in the rotor systems of rotating machinery, which may cause an unstable vibrational response. To take the uncertainty into consideration for the uncertain rotor-bearing system, an i...Uncertainty is extensively involved in the rotor systems of rotating machinery, which may cause an unstable vibrational response. To take the uncertainty into consideration for the uncertain rotor-bearing system, an improved unified interval analysis method based on the Chebyshev expansion is established in this paper. Firstly, the Chebyshev Interval Method(CIM) to calculate not only the critical speeds but also the dynamic response of rotor with uncertain parameters is introduced. Then, the numerical investigation is carried out based on the developed double disk rotor model and computation procedure, and the results demonstrate the validity. But when the uncertainty is sufficiently large to influence critical speeds, the upper and lower bounds are far from the actual bounds. In order to overcome the defects, a Bound Correction Interval analysis Method(BCIM) is proposed based on the Chebyshev expansion and the modal superposition. In use of the improved method, the bounds of the interval responses, especially the upper bound,are corrected, and the comparison with other methods demonstrates that the higher accuracy and a wider application range.展开更多
Based on measured natural frequencies and acceleration responses,a non-probabilistic information fusion technique is proposed for the structural damage detection by adopting the set-membership identification(SMI) an...Based on measured natural frequencies and acceleration responses,a non-probabilistic information fusion technique is proposed for the structural damage detection by adopting the set-membership identification(SMI) and twostep model updating procedure.Due to the insufficiency and uncertainty of information obtained from measurements,the uncertain problem of damage identification is addressed with interval variables in this paper.Based on the first-order Taylor series expansion,the interval bounds of the elemental stiffness parameters in undamaged and damaged models are estimated,respectively.The possibility of damage existence(PoDE) in elements is proposed as the quantitative measure of structural damage probability,which is more reasonable in the condition of insufficient measurement data.In comparison with the identification method based on a single kind of information,the SMI method will improve the accuracy in damage identification,which reflects the information fusion concept based on the non-probabilistic set.A numerical example is performed to demonstrate the feasibility and effectiveness of the proposed technique.展开更多
基金The project supported by the National Outstanding Youth Science Foundation of China (10425208)the National Natural Science Foundation of ChinaInstitute of Engineering Physics of China (10376002) The English text was polished by Keren Wang
文摘Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11072066)
文摘Prediction of vibration energy responses of structures with uncertainties is of interest in many fields. The energy density control equation for one-dimensional structure is provided firstly. Interval analysis method is applied to the control equation to obtain the range of energy density responses of structures with interval parameters. A cantilever beam with interval-valued damping coefficient is exemplified to carry out a simulation. The result shows that the mean value of energy density from the interval analysis method is the same as that from a probabilistic method which validates the interval analysis method. Besides, the response range from the interval analysis method is wider and includes that from the probabilistic method which indicates the interval analysis method is a more conservative method and is safer in realistic engineering structures.
基金Supported by the National Natural Science Foundation of China(50978083)the Fundamental Research Funds for the Central Universities(2010B02814)
文摘This paper proposes a sensitivity analysis method for engineering parameters using interval analyses.This method substantially extends the application of interval analysis method.In this scheme,parameter intervals and decision-making target intervals are determined using the interval analysis method.As an example,an inverse analysis method for uncertainty is presented.The intervals of unknown parameters can be obtained by sampling measured data.Even for limited measured data,robust results can also be obtained with the inverse analysis method,which can be intuitively evaluated by the uncertainty expressed in terms of an interval.For complex nonlinear problems,an iteratively optimized inverse analysis model is proposed.In a given set of loose parameter intervals,all the unknown parameter intervals that satisfy the measured information can be obtained by an iteratively optimized inverse analysis model.The influences of measured precisions and the number of parameters on the results of the inverse analysis are evaluated.Finally,the uniqueness of the interval inverse analysis method is discussed.
基金supported by the Science and Technology Innovation Foundation of Hohai University(No. 2013-406096)
文摘Interval analysis is a new uncertainty analysis method for engineering structures. In this paper, a new sensitivity analysis method is presented by introducing interval analysis which can expand applications of the interval analysis method. The interval analysis process of sensitivity factor matrix of soil parameters is given. A method of parameter intervals and decision-making target intervals is given according to the interval analysis method. With FEM, secondary developments are done for Marc and the Duncan-Chang nonlinear elastic model. Mutual transfer between FORTRAN and Marc is implemented. With practial examples, rationality and feasibility are validated. Comparison is made with some published results.
文摘Uncertainty is extensively involved in the rotor systems of rotating machinery, which may cause an unstable vibrational response. To take the uncertainty into consideration for the uncertain rotor-bearing system, an improved unified interval analysis method based on the Chebyshev expansion is established in this paper. Firstly, the Chebyshev Interval Method(CIM) to calculate not only the critical speeds but also the dynamic response of rotor with uncertain parameters is introduced. Then, the numerical investigation is carried out based on the developed double disk rotor model and computation procedure, and the results demonstrate the validity. But when the uncertainty is sufficiently large to influence critical speeds, the upper and lower bounds are far from the actual bounds. In order to overcome the defects, a Bound Correction Interval analysis Method(BCIM) is proposed based on the Chebyshev expansion and the modal superposition. In use of the improved method, the bounds of the interval responses, especially the upper bound,are corrected, and the comparison with other methods demonstrates that the higher accuracy and a wider application range.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education (20091102120023)the Aeronautical Science Foundation of China (2012ZA51010)+1 种基金the National Natural Science Foundation of China (11002013)Defense Industrial Technology Development Program (A2120110001 and B2120110011)
文摘Based on measured natural frequencies and acceleration responses,a non-probabilistic information fusion technique is proposed for the structural damage detection by adopting the set-membership identification(SMI) and twostep model updating procedure.Due to the insufficiency and uncertainty of information obtained from measurements,the uncertain problem of damage identification is addressed with interval variables in this paper.Based on the first-order Taylor series expansion,the interval bounds of the elemental stiffness parameters in undamaged and damaged models are estimated,respectively.The possibility of damage existence(PoDE) in elements is proposed as the quantitative measure of structural damage probability,which is more reasonable in the condition of insufficient measurement data.In comparison with the identification method based on a single kind of information,the SMI method will improve the accuracy in damage identification,which reflects the information fusion concept based on the non-probabilistic set.A numerical example is performed to demonstrate the feasibility and effectiveness of the proposed technique.