Randomness and fuzziness are among the attributes of the influential factors for stability assessment of pile foundation. According to these two characteristics, the triangular fuzzy number analysis approach was intro...Randomness and fuzziness are among the attributes of the influential factors for stability assessment of pile foundation. According to these two characteristics, the triangular fuzzy number analysis approach was introduced to determine the probability-distributed function of mechanical parameters. Then the functional function of reliability analysis was constructed based on the study of bearing mechanism of pile foundation, and the way to calculate interval values of the functional function was developed by using improved interval-truncation approach and operation rules of interval numbers. Afterwards, the non-probabilistic fuzzy reliability analysis method was applied to assessing the pile foundation, from which a method was presented for non- probabilistic fuzzy reliability analysis of pile foundation stability by interval theory. Finally, the probability distribution curve of non- probabilistic fuzzy reliability indexes of practical pile foundation was concluded. Its failure possibility is 0.91%, which shows that the pile foundation is stable and reliable.展开更多
The aim of this paper is to propose a theoretical approach for performing the nonprobabilistic reliability analysis of structure.Due to a great deal of uncertainties and limited measured data in engineering practice,t...The aim of this paper is to propose a theoretical approach for performing the nonprobabilistic reliability analysis of structure.Due to a great deal of uncertainties and limited measured data in engineering practice,the structural uncertain parameters were described as interval variables.The theoretical analysis model was developed by starting from the 2-D plane and 3-D space.In order to avoid the loss of probable failure points,the 2-D plane and 3-D space were respectively divided into two parts and three parts for further analysis.The study pointed out that the probable failure points only existed among extreme points and root points of the limit state function.Furthermore,the low-dimensional analytical scheme was extended to the high-dimensional case.Using the proposed approach,it is easy to find the most probable failure point and to acquire the reliability index through simple comparison directly.A number of equations used for calculating the extreme points and root points were also evaluated.This result was useful to avoid the loss of probable failure points and meaningful for optimizing searches in the research field.Finally,two kinds of examples were presented and compared with the existing computation.The good agreements show that the proposed theoretical analysis approach in the paper is correct.The efforts were conducted to improve the optimization method,to indicate the search direction and path,and to avoid only searching the local optimal solution which would result in missed probable failure points.展开更多
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
A method named interval analysis method, which solves the buckling load of composite laminate with uncertainties, is presented. Based on interval mathematics and Taylor series expansion, the interval analysis method i...A method named interval analysis method, which solves the buckling load of composite laminate with uncertainties, is presented. Based on interval mathematics and Taylor series expansion, the interval analysis method is used to deal with uncertainties. Not necessarily knowing the probabilistic statistics characteristics of the uncertain variables, only little information on physical properties of material is needed in the interval analysis method, that is, the upper bound and lower bound of the uncertain variable. So the interval of response of the structure can be gotten through less computational efforts. The interval analysis method is efficient under the condition that probability approach cannot work well because of small samples and deficient statistics characteristics. For buckling load of a special cross-ply laminates and antisymmetric angle-ply laminates with all edges simply supported, calculations and comparisons between interval analysis method and probability method are performed.展开更多
A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and vi...A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.展开更多
In this paper,an efficient interval analysis method called dimension-reduction interval analysis(DRIA)method is proposed to calculate the bounds of response functions with interval variables,which provides a kind of s...In this paper,an efficient interval analysis method called dimension-reduction interval analysis(DRIA)method is proposed to calculate the bounds of response functions with interval variables,which provides a kind of solution method for uncertainty analysis problems of complex structures and systems.First,multi-dimensional function is transformed into multiple one-dimensional functions by extending dimension reduction method to the interval analysis problem.Second,all the one-dimensional functions are transformed to standard quadratic form by second order Taylor expansion method.As a result,the multi-dimensional function is approximately represented by the functions that each interval variable occurs once,and interval power arithmetic can be used to efficiently calculate the bounds of response functions in restricted overestimation.Finally,three numerical examples and an engineering application are investigated to demonstrate the validity of the proposed method.展开更多
The importance analysis method represents a powerful tool for quantifying the impact of input uncertainty on the output uncertainty.When an input variable is described by a specific interval rather than a certain prob...The importance analysis method represents a powerful tool for quantifying the impact of input uncertainty on the output uncertainty.When an input variable is described by a specific interval rather than a certain probability distribution,the interval importance measure of input interval variable can be calculated by the traditional non-probabilistic importance analysis methods.Generally,the non-probabilistic importance analysis methods involve the Monte Carlo simulation(MCS)and the optimization-based methods,which both have high computational cost.In order to overcome this problem,this study proposes an interval important analytical method avoids the time-consuming optimization process.First,the original performance function is decomposed into a combination of a series of one-dimensional subsystems.Next,the interval of each variable is divided into several subintervals,and the response value of each one-dimensional subsystem at a specific input point is calculated.Then,the obtained responses are taken as specific values of the new input variable,and the interval importance is calculated by the approximated performance function.Compared with the traditional non-probabilistic importance analysis method,the proposed method significantly reduces the computational cost caused by the MCS and optimization process.In the proposed method,the number of function evaluations is equal to one plus the sum of the subintervals of all of the variables.The efficiency and accuracy of the proposed method are verified by five examples.The results show that the proposed method is not only efficient but also accurate.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
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
Uncertain parameters are widespread in engineering systems.This study investigates the modal analysis of a fluid-conveying pipe subjected to elastic supports with unknown-but-bound parameters.The governing equation fo...Uncertain parameters are widespread in engineering systems.This study investigates the modal analysis of a fluid-conveying pipe subjected to elastic supports with unknown-but-bound parameters.The governing equation for the elastically supported fluid-conveying pipe is transformed into ordinary differential equations using the Galerkin truncation method.The Chebyshev interval approach,integrated with the assumed mode method is then used to investigate the effects of uncertainties of support stiffness,fluid speed,and pipe length on the natural frequencies and mode shapes of the pipe.Additionally,both symmetrical and asymmetrical support stiffnesses are discussed.The accuracy and effectiveness of the Chebyshev interval approach are verified through comparison with the Monte Carlo method.The results reveal that,for the same deviation coefficient,uncertainties in symmetrical support stiffness have a greater impact on the first four natural frequencies than those of the asymmetrical one.There may be significant differences in the sensitivity of natural frequencies and mode shapes of the same order to uncertain parameters.Notably,mode shapes susceptible to uncertain parameters exhibit wider fluctuation intervals near the elastic supports,requiring more attention.展开更多
The dynamic influence of joints in aero-engine rotor systems is investigated in this paper.Firstly,the tangential stiffness and loss factor are obtained from an isolated lap joint setup with dynamic excitation experim...The dynamic influence of joints in aero-engine rotor systems is investigated in this paper.Firstly,the tangential stiffness and loss factor are obtained from an isolated lap joint setup with dynamic excitation experiments.Also,the influence of the normal contact pressure and the excitation level are examined,which revel the uncertainty in joints.Then,the updated Thin Layer Elements(TLEs)method with fitted parameters based on the experiments is established to simulate the dynamic properties of joints on the interface.The response of the rotor subjected to unbalance excitation is calculated,and the results illustrate the effectiveness of the proposed method.Meanwhile,using the Chebyshev inclusion function and a direct iteration algorithm,a nonlinear interval analysis method is established to consider the uncertainty of parameters in joints.The accuracy is proved by comparison with results obtained using the Monte-Carlo method.Combined with the updated TLEs,the nonlinear Chebyshev method is successfully applied on a finite model of a rotor.The study shows that substantial attention should be paid to the dynamical design for the joint in rotor systems,the dynamic properties of joints under complex loading and the corresponding interval analysis method need to be intensively studied.展开更多
Considering that the uncertain information has serious influences on the safety of structural systems and is always limited, it is reasonable that the uncertainties are generally described as interval sets. Based on t...Considering that the uncertain information has serious influences on the safety of structural systems and is always limited, it is reasonable that the uncertainties are generally described as interval sets. Based on the non-probabilistic set-theoretic theory, which is applied to measuring the safety of structural components and further combined with the branch-and-bound method for the probabilistic reliability analysis of structural systems, the non-probabilistic branch-and-bound method for determining the dominant failure modes of an uncertain structural system is given. Meanwhile, a new system safety measuring index obtained by the non-probabilistic set-theoretic model is investigated. Moreover, the compatibility between the classical probabilistic model as well as the proposed interval-set model will be discussed to verify the physical meaning of the safety measure in this paper. Some numerical examples are utilized to illustrate the validity and feasibility of the developed method.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
In engineering applications, probabilistic reliability theory appears to be presently the most important method, however, in many cases precise probabilistic reliability theory cannot be considered as adequate and cre...In engineering applications, probabilistic reliability theory appears to be presently the most important method, however, in many cases precise probabilistic reliability theory cannot be considered as adequate and credible model of the real state of actual affairs. In this paper, we developed a hybrid of probabilistic and non-probabilistic reliability theory, which describes the structural uncertain parameters as interval variables when statistical data are found insufficient. By using the interval analysis, a new method for calculating the interval of the structural reliability as well as the reliability index is introduced in this paper, and the traditional probabilistic theory is incorporated with the interval analysis. Moreover, the new method preserves the useful part of the traditional probabilistic reliability theory, but removes the restriction of its strict requirement on data acquisition. Example is presented to demonstrate the feasibility and validity of the proposed theory.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
In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indi...In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.展开更多
This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This...This paper proposes a new non-intrusive hybrid interval method using derivative information 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 polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.展开更多
A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D F...A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.展开更多
With the fast growth of Chinese economic, more and more capital will be invested in environmental projects. How to select the environmental investment projects （alternatives） for obtaining the best environmental qua...With the fast growth of Chinese economic, more and more capital will be invested in environmental projects. How to select the environmental investment projects （alternatives） for obtaining the best environmental quality and economic benefits is an important problem for the decision makers. The purpose of this paper is to develop a decision-making model to rank a finite number of alternatives with several and sometimes conflicting criteria. A model for ranking the projects of municipal sewage treatment plants is proposed by using exports＇ information and the data of the real projects. And, the ranking result is given based on the PROMETHEE method. Furthermore, by means of the concept of the weight stability intervals （WSI）, the sensitivity of the ranking results to the size of criteria values and the change of weights value of criteria are discussed. The result shows that some criteria, such as “proportion of benefit to project cost”, will influence the ranking result of alternatives very strong while others not. The influence are not only from the value of criterion but also from the changing the weight of criterion. So, some criteria such as “proportion of benefit to project cost” are key critera for ranking the projects. Decision makers must be cautious to them.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
基金Project(50378036) supported by the National Natural Science Foundation of ChinaProject(03JJY5024) supported by the Natural Science Foundation of Hunan Province, China
文摘Randomness and fuzziness are among the attributes of the influential factors for stability assessment of pile foundation. According to these two characteristics, the triangular fuzzy number analysis approach was introduced to determine the probability-distributed function of mechanical parameters. Then the functional function of reliability analysis was constructed based on the study of bearing mechanism of pile foundation, and the way to calculate interval values of the functional function was developed by using improved interval-truncation approach and operation rules of interval numbers. Afterwards, the non-probabilistic fuzzy reliability analysis method was applied to assessing the pile foundation, from which a method was presented for non- probabilistic fuzzy reliability analysis of pile foundation stability by interval theory. Finally, the probability distribution curve of non- probabilistic fuzzy reliability indexes of practical pile foundation was concluded. Its failure possibility is 0.91%, which shows that the pile foundation is stable and reliable.
基金the National Natural Science Foundation of China (51408444, 51708428)
文摘The aim of this paper is to propose a theoretical approach for performing the nonprobabilistic reliability analysis of structure.Due to a great deal of uncertainties and limited measured data in engineering practice,the structural uncertain parameters were described as interval variables.The theoretical analysis model was developed by starting from the 2-D plane and 3-D space.In order to avoid the loss of probable failure points,the 2-D plane and 3-D space were respectively divided into two parts and three parts for further analysis.The study pointed out that the probable failure points only existed among extreme points and root points of the limit state function.Furthermore,the low-dimensional analytical scheme was extended to the high-dimensional case.Using the proposed approach,it is easy to find the most probable failure point and to acquire the reliability index through simple comparison directly.A number of equations used for calculating the extreme points and root points were also evaluated.This result was useful to avoid the loss of probable failure points and meaningful for optimizing searches in the research field.Finally,two kinds of examples were presented and compared with the existing computation.The good agreements show that the proposed theoretical analysis approach in the paper is correct.The efforts were conducted to improve the optimization method,to indicate the search direction and path,and to avoid only searching the local optimal solution which would result in missed probable failure points.
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.
文摘A method named interval analysis method, which solves the buckling load of composite laminate with uncertainties, is presented. Based on interval mathematics and Taylor series expansion, the interval analysis method is used to deal with uncertainties. Not necessarily knowing the probabilistic statistics characteristics of the uncertain variables, only little information on physical properties of material is needed in the interval analysis method, that is, the upper bound and lower bound of the uncertain variable. So the interval of response of the structure can be gotten through less computational efforts. The interval analysis method is efficient under the condition that probability approach cannot work well because of small samples and deficient statistics characteristics. For buckling load of a special cross-ply laminates and antisymmetric angle-ply laminates with all edges simply supported, calculations and comparisons between interval analysis method and probability method are performed.
基金This work was supported by the National Natural Science Foundation of China(Nos.51405370&51421004)the National Key Basic Research Program of China(No.2015CB057400)+2 种基金the project supported by Natural Science Basic Plan in Shaanxi Province of China(No.2015JQ5184)the Fundamental Research Funds for the Central Universities(xjj2014014)Shaanxi Province Postdoctoral Research Project.
文摘A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.
文摘In this paper,an efficient interval analysis method called dimension-reduction interval analysis(DRIA)method is proposed to calculate the bounds of response functions with interval variables,which provides a kind of solution method for uncertainty analysis problems of complex structures and systems.First,multi-dimensional function is transformed into multiple one-dimensional functions by extending dimension reduction method to the interval analysis problem.Second,all the one-dimensional functions are transformed to standard quadratic form by second order Taylor expansion method.As a result,the multi-dimensional function is approximately represented by the functions that each interval variable occurs once,and interval power arithmetic can be used to efficiently calculate the bounds of response functions in restricted overestimation.Finally,three numerical examples and an engineering application are investigated to demonstrate the validity of the proposed method.
文摘The importance analysis method represents a powerful tool for quantifying the impact of input uncertainty on the output uncertainty.When an input variable is described by a specific interval rather than a certain probability distribution,the interval importance measure of input interval variable can be calculated by the traditional non-probabilistic importance analysis methods.Generally,the non-probabilistic importance analysis methods involve the Monte Carlo simulation(MCS)and the optimization-based methods,which both have high computational cost.In order to overcome this problem,this study proposes an interval important analytical method avoids the time-consuming optimization process.First,the original performance function is decomposed into a combination of a series of one-dimensional subsystems.Next,the interval of each variable is divided into several subintervals,and the response value of each one-dimensional subsystem at a specific input point is calculated.Then,the obtained responses are taken as specific values of the new input variable,and the interval importance is calculated by the approximated performance function.Compared with the traditional non-probabilistic importance analysis method,the proposed method significantly reduces the computational cost caused by the MCS and optimization process.In the proposed method,the number of function evaluations is equal to one plus the sum of the subintervals of all of the variables.The efficiency and accuracy of the proposed method are verified by five examples.The results show that the proposed method is not only efficient but also accurate.
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(Grant Nos.12272211,12072181,and 12121002).
文摘Uncertain parameters are widespread in engineering systems.This study investigates the modal analysis of a fluid-conveying pipe subjected to elastic supports with unknown-but-bound parameters.The governing equation for the elastically supported fluid-conveying pipe is transformed into ordinary differential equations using the Galerkin truncation method.The Chebyshev interval approach,integrated with the assumed mode method is then used to investigate the effects of uncertainties of support stiffness,fluid speed,and pipe length on the natural frequencies and mode shapes of the pipe.Additionally,both symmetrical and asymmetrical support stiffnesses are discussed.The accuracy and effectiveness of the Chebyshev interval approach are verified through comparison with the Monte Carlo method.The results reveal that,for the same deviation coefficient,uncertainties in symmetrical support stiffness have a greater impact on the first four natural frequencies than those of the asymmetrical one.There may be significant differences in the sensitivity of natural frequencies and mode shapes of the same order to uncertain parameters.Notably,mode shapes susceptible to uncertain parameters exhibit wider fluctuation intervals near the elastic supports,requiring more attention.
基金supported by the National Natural Science Foundation of China(Nos.51575022,11772022 and 51475021).
文摘The dynamic influence of joints in aero-engine rotor systems is investigated in this paper.Firstly,the tangential stiffness and loss factor are obtained from an isolated lap joint setup with dynamic excitation experiments.Also,the influence of the normal contact pressure and the excitation level are examined,which revel the uncertainty in joints.Then,the updated Thin Layer Elements(TLEs)method with fitted parameters based on the experiments is established to simulate the dynamic properties of joints on the interface.The response of the rotor subjected to unbalance excitation is calculated,and the results illustrate the effectiveness of the proposed method.Meanwhile,using the Chebyshev inclusion function and a direct iteration algorithm,a nonlinear interval analysis method is established to consider the uncertainty of parameters in joints.The accuracy is proved by comparison with results obtained using the Monte-Carlo method.Combined with the updated TLEs,the nonlinear Chebyshev method is successfully applied on a finite model of a rotor.The study shows that substantial attention should be paid to the dynamical design for the joint in rotor systems,the dynamic properties of joints under complex loading and the corresponding interval analysis method need to be intensively studied.
基金National Nature Science Foundation of China(No.11002013)Defense Industrial Technology Development Program(Nos.A2120110001,B2120110011)the Aeronautical Science Foundation of China(No.2012ZA51010)
文摘Considering that the uncertain information has serious influences on the safety of structural systems and is always limited, it is reasonable that the uncertainties are generally described as interval sets. Based on the non-probabilistic set-theoretic theory, which is applied to measuring the safety of structural components and further combined with the branch-and-bound method for the probabilistic reliability analysis of structural systems, the non-probabilistic branch-and-bound method for determining the dominant failure modes of an uncertain structural system is given. Meanwhile, a new system safety measuring index obtained by the non-probabilistic set-theoretic model is investigated. Moreover, the compatibility between the classical probabilistic model as well as the proposed interval-set model will be discussed to verify the physical meaning of the safety measure in this paper. Some numerical examples are utilized to illustrate the validity and feasibility of the developed method.
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the National Outstanding Youth Science Foundation of China (10425208)Civil 863 Program (2006AA04Z410)111 Project (B07009)
文摘In engineering applications, probabilistic reliability theory appears to be presently the most important method, however, in many cases precise probabilistic reliability theory cannot be considered as adequate and credible model of the real state of actual affairs. In this paper, we developed a hybrid of probabilistic and non-probabilistic reliability theory, which describes the structural uncertain parameters as interval variables when statistical data are found insufficient. By using the interval analysis, a new method for calculating the interval of the structural reliability as well as the reliability index is introduced in this paper, and the traditional probabilistic theory is incorporated with the interval analysis. Moreover, the new method preserves the useful part of the traditional probabilistic reliability theory, but removes the restriction of its strict requirement on data acquisition. Example is presented to demonstrate the feasibility and validity of the proposed theory.
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.
基金Project(50774095) supported by the National Natural Science Foundation of ChinaProject(200449) supported by the National Outstanding Doctoral Dissertations Special Funds of China
文摘In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.
文摘This paper proposes a new non-intrusive hybrid interval method using derivative information 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 polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.
基金supported by the National Natural Science Foundation of China (51109029,51178081,51138001,and 51009020)the State Key Development Program for Basic Research of China (2013CB035905)
文摘A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.
基金Shanghai Leading Academic Discipline Project (T0502)Shanghai Municipal Educational Commission Project (05EZ32).
文摘With the fast growth of Chinese economic, more and more capital will be invested in environmental projects. How to select the environmental investment projects （alternatives） for obtaining the best environmental quality and economic benefits is an important problem for the decision makers. The purpose of this paper is to develop a decision-making model to rank a finite number of alternatives with several and sometimes conflicting criteria. A model for ranking the projects of municipal sewage treatment plants is proposed by using exports＇ information and the data of the real projects. And, the ranking result is given based on the PROMETHEE method. Furthermore, by means of the concept of the weight stability intervals （WSI）, the sensitivity of the ranking results to the size of criteria values and the change of weights value of criteria are discussed. The result shows that some criteria, such as “proportion of benefit to project cost”, will influence the ranking result of alternatives very strong while others not. The influence are not only from the value of criterion but also from the changing the weight of criterion. So, some criteria such as “proportion of benefit to project cost” are key critera for ranking the projects. Decision makers must be cautious to them.
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.
