A Stewart platform is introduced in thc 500 m aperture spherical radio telescope（FAST） as an accuracy adjustable mechanism for teed receivers. Accuracy analysis is the basis of accuracy design. However, a rapid and ...A Stewart platform is introduced in thc 500 m aperture spherical radio telescope（FAST） as an accuracy adjustable mechanism for teed receivers. Accuracy analysis is the basis of accuracy design. However, a rapid and effective accuracy analysis method for parallel manipulator is still needed. In order to enhance solution efficiency, an interval analysis method（lA method） is introduced to solve the terminal error bound of the Stewart platform with detailed solution path. Taking a terminal pose of the Stewart platform in FAST as an example, the terminal error is solved by the Monte Carlo method（MC method） by 4 980 s, the stochastic mathematical method（SM method） by 0.078 s, and the IA method by 2.203 s. Compared with MC method, the terminal error by SM method leads a 20% underestimate while the IA method can envelop the real error bound of the Stewart platform. This indicates that the IA method outperforms the other two methods by providing quick calculations and enveloping the real error bound of the Stewart platform. According to the given structural error of the dimension parameters of the Stewart platform, the IA method gives a maximum position error of 19.91 mm and maximum orientation error of 0.534°, which suggests that the IA method can be used for accuracy design of the Stewart platfbnn in FAST. The 1A method presented is a rapid and effective accuracy analysis method for Stewart platform.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
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
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
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
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
In recent years,growing attention has been paid to the interval investigation of uncertainty problems.However,the contradiction between accuracy and efficiency always exists.In this paper,an iterative interval analysi...In recent years,growing attention has been paid to the interval investigation of uncertainty problems.However,the contradiction between accuracy and efficiency always exists.In this paper,an iterative interval analysis method based on Kriging-HDMR(IIAMKH)is proposed to obtain the lower and upper bounds of uncertainty problems considering interval variables.Firstly,Kriging-HDMR method is adopted to establish the meta-model of the response function.Then,the Genetic Algorithm&Sequential Quadratic Programing(GA&SQP)hybrid optimization method is applied to search for the minimum/maximum values of the meta-model,and thus the corresponding uncertain parameters can be obtained.By substituting them into the response function,we can acquire the predicted interval.Finally,an iterative process is developed to improve the accuracy and stability of the proposed method.Several numerical examples are investigated to demonstrate the effectiveness of the proposed method.Simulation results indicate that the presented IIAMKH can obtain more accurate results with fewer samples.展开更多
Based on the failure rate and design features allocation method,considering the multiple influential factors which affect electric multiple unit( EMU) bogies,maintainability allocation on EMU bogie was presented by in...Based on the failure rate and design features allocation method,considering the multiple influential factors which affect electric multiple unit( EMU) bogies,maintainability allocation on EMU bogie was presented by interval analytic hierarchy analysis and fuzzy comprehensive assessment. The maintainability allocation model was established. Weight based on the influence degree of each factor on maintenance was assigned. Fuzzy interval numbers were used to substitute real numbers and express uncertain information.The maintenance weighting factors for each subsystem were calculated by fuzzy comprehensive assessment. Then the allocation method was applied to EMU bogie. The results show that the method is feasible. The problem difficult to quantify for EMU bogie maintenance allocation is solved effectively.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
The influences of uncertainties in structural parameters on the flutter speed of wing are studied. On the basis of the deterministic flutter analysis model of wing, the uncertainties in structural parameters are consi...The influences of uncertainties in structural parameters on the flutter speed of wing are studied. On the basis of the deterministic flutter analysis model of wing, the uncertainties in structural parameters are considered and described by interval numbers. By virtue of first-order Taylor series expansion, the lower and upper bound curves of the transient decay rate coefficient versus wind velocity are given. So the interval estimation of the flutter critical wind speed of wing can be obtained, which is more reasonable than the point esti- mation obtained by the deterministic flutter analysis and provides the basis for the further non-probabilistic interval reliability analysis of wing flutter. The flow chart for interval fmite element model of flutter analysis of wing is given. The proposed interval finite element model and the stochastic finite element model for wing flutter analysis are compared by the examples of a three degrees of freedom airfoil and fuselage and a 15° sweptback wing, and the results have shown the effectiveness and feasibility of the presented model. The prominent advantage of the proposed interval finite element model is that only the bounds of uncertain parameters are required, and the probabilistic distribution densities or other statistical characteristics are not needed.展开更多
Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject...Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject to variation. In the study, the collocation interval analysis method based on the first class Chebyshev polynomial approximation is presented to investigate the least favorable responses and the most favorable responses of interval-parameter structures under random excitations. Compared with the interval analysis method based on the first order Taylor expansion, in which only information including the function value and derivative at midpoint is used, the collocation interval analysis method is a non-gradient algorithm using several collocation points which improve the precision of results owing to better approximation of a response function. The pseudo excitation method is introduced to the solving procedure to transform the random problem into a deterministic problem. To validate the procedure, we present numerical results concerning a building under seismic ground motion and aerofoil under continuous atmosphere turbulence to show the effectiveness of the collocation interval analysis method.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
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
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
A Newton iteration-based interval uncertainty analysis method(NI-IUAM) is proposed to analyze the propagating effect of interval uncertainty in multidisciplinary systems. NI-IUAM decomposes one multidisciplinary syste...A Newton iteration-based interval uncertainty analysis method(NI-IUAM) is proposed to analyze the propagating effect of interval uncertainty in multidisciplinary systems. NI-IUAM decomposes one multidisciplinary system into single disciplines and utilizes a Newton iteration equation to obtain the upper and lower bounds of coupled state variables at each iterative step.NI-IUAM only needs to determine the bounds of uncertain parameters and does not require specific distribution formats. In this way, NI-IUAM may greatly reduce the necessity for raw data. In addition, NI-IUAM can accelerate the convergence process as a result of the super-linear convergence of Newton iteration. The applicability of the proposed method is discussed, in particular that solutions obtained in each discipline must be compatible in multidisciplinary systems. The validity and efficiency of NI-IUAM is demonstrated by both numerical and engineering examples.展开更多
This study introduces a new approach utilizing an interval finite element method combined with a bilevel Kriging model to determine the bounds of structural responses in the presence of spatial uncertainties.A notable...This study introduces a new approach utilizing an interval finite element method combined with a bilevel Kriging model to determine the bounds of structural responses in the presence of spatial uncertainties.A notable benefit of this approach is its ability to determine the response bounds across all degrees of freedom with a small sample size,which means that it has high efficiency.Firstly,the spatially varying uncertain parameters are quantified using an interval field model,which is described by a series of standard interval variables within a truncated interval Karhunen-Loe`ve(K-L)series expansion.Secondly,considering that the bound of structural response is a function of spatial position with the property of continuity,a surrogate model for the response bound is constructed,namely the first-level Kriging model.The training samples required for this surrogate model are obtained by establishing the second-level Kriging model.The second-level Kriging model is established to describe the structural responses at particular locations relative to the interval variables so as to facilitate the upper and lower bounds of the node response required by the first-level Kriging model.Finally,the accuracy and effectiveness of the method are verified through examples.展开更多
In electrical circuit analysis, it is often necessary to find the set of all direct current （d.c.） operating points （either voltages or currents） of nonlinear circuits. In general, these nonlinear equations are of...In electrical circuit analysis, it is often necessary to find the set of all direct current （d.c.） operating points （either voltages or currents） of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.展开更多
The vertex solution for estimation on the static displacement bounds of structures with uncertain-but-bounded parameters is studied in this paper. For the linear static problem, when there are uncertain interval param...The vertex solution for estimation on the static displacement bounds of structures with uncertain-but-bounded parameters is studied in this paper. For the linear static problem, when there are uncertain interval parameters in the stiffness matrix and the vector of applied forces, the static response may be an interval. Based on the interval operations, the interval solution obtained by the vertex solution is more accurate and more credible than other methods （such as the perturbation method）. However, the vertex solution method by traditional serial computing usually needs large computational efforts, especially for large structures. In order to avoid its disadvantages of large calculation and much runtime, its parallel computing which can be used in large-scale computing is presented in this paper. Two kinds of parallel computing algorithms are proposed based on the vertex solution. The parallel computing will solve many interval problems which cannot be resolved by traditional interval analysis methods.展开更多
A squirrel cage induction generator （SCIG） offers many advantages for wind energy conversion systems but suffers from poor voltage regulation under varying operating conditions. The value of excitation capacitance ...A squirrel cage induction generator （SCIG） offers many advantages for wind energy conversion systems but suffers from poor voltage regulation under varying operating conditions. The value of excitation capacitance （C exct ） is very crucial for the selfexcitation and voltage build-up as well as voltage regulation in SCIG. Precise calculation of the value of C exct is, therefore, of considerable practical importance. Most of the existing calculation methods make use of the steady-state model of the SCIG in conjunction with some numerical iterative method to determine the minimum value of C exct . But this results in over estimation, leading to poor transient dynamics. This paper presents a novel method, which can precisely calculate the value of C exct by taking into account the behavior of the magnetizing inductance during saturation. Interval analysis has been used to solve the equations. In the proposed method, a range of magnetizing inductance values in the saturation region are included in the calculation of C exct , required for the self-excitation of a 3-φ induction generator. Mathematical analysis to derive the basic equation and application of interval method is presented. The method also yields the magnetizing inductance value in the saturation region which corresponds to an optimum C exct（min） value. The proposed method is experimentally tested for a 1.1 kW induction generator and has shown improved results.展开更多
For improving the method of finding maintenance windows under uncertain parameters, an algorithm of maintenance window under uncertainties is presented using interval analysis and sensitivity analysis. Age replacement...For improving the method of finding maintenance windows under uncertain parameters, an algorithm of maintenance window under uncertainties is presented using interval analysis and sensitivity analysis. Age replacement model is selected to demonstrate how to use this new algorithm. Considered the uncertainties, the optimal maintenance interval of preventive maintenance is not only a single value, but a possible range. The requirement from maintenance engineers is also considered, the maintenance window is made as a symmetrical interval format, like(100 ± 10) day. Comparing with the methods using in the literatures, the new algorithm is without requirement of distribution assumption of uncertain parameter values and computer simulation.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 10973023,11103046,11203048)
文摘A Stewart platform is introduced in thc 500 m aperture spherical radio telescope（FAST） as an accuracy adjustable mechanism for teed receivers. Accuracy analysis is the basis of accuracy design. However, a rapid and effective accuracy analysis method for parallel manipulator is still needed. In order to enhance solution efficiency, an interval analysis method（lA method） is introduced to solve the terminal error bound of the Stewart platform with detailed solution path. Taking a terminal pose of the Stewart platform in FAST as an example, the terminal error is solved by the Monte Carlo method（MC method） by 4 980 s, the stochastic mathematical method（SM method） by 0.078 s, and the IA method by 2.203 s. Compared with MC method, the terminal error by SM method leads a 20% underestimate while the IA method can envelop the real error bound of the Stewart platform. This indicates that the IA method outperforms the other two methods by providing quick calculations and enveloping the real error bound of the Stewart platform. According to the given structural error of the dimension parameters of the Stewart platform, the IA method gives a maximum position error of 19.91 mm and maximum orientation error of 0.534°, which suggests that the IA method can be used for accuracy design of the Stewart platfbnn in FAST. The 1A method presented is a rapid and effective accuracy analysis method for Stewart platform.
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 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 National Natural Science Foundation of China(Grant No.11472137)the Fundamental Research Funds for the Central Universities(Grant No.309181A8801 and 30919011204).
文摘In recent years,growing attention has been paid to the interval investigation of uncertainty problems.However,the contradiction between accuracy and efficiency always exists.In this paper,an iterative interval analysis method based on Kriging-HDMR(IIAMKH)is proposed to obtain the lower and upper bounds of uncertainty problems considering interval variables.Firstly,Kriging-HDMR method is adopted to establish the meta-model of the response function.Then,the Genetic Algorithm&Sequential Quadratic Programing(GA&SQP)hybrid optimization method is applied to search for the minimum/maximum values of the meta-model,and thus the corresponding uncertain parameters can be obtained.By substituting them into the response function,we can acquire the predicted interval.Finally,an iterative process is developed to improve the accuracy and stability of the proposed method.Several numerical examples are investigated to demonstrate the effectiveness of the proposed method.Simulation results indicate that the presented IIAMKH can obtain more accurate results with fewer samples.
基金Traction Power State Key Laboratory of Southwest Jiaotong University,China(No.TPL1 312)Key Project of Technology Research and Development Plan of Railway Ministry,China(NO.2012J009-A)+1 种基金National Natural Science Foundation of Liaoning Province,China(No.2014028020)Liaoning Province Education Administration Project,China(No.L20138182)
文摘Based on the failure rate and design features allocation method,considering the multiple influential factors which affect electric multiple unit( EMU) bogies,maintainability allocation on EMU bogie was presented by interval analytic hierarchy analysis and fuzzy comprehensive assessment. The maintainability allocation model was established. Weight based on the influence degree of each factor on maintenance was assigned. Fuzzy interval numbers were used to substitute real numbers and express uncertain information.The maintenance weighting factors for each subsystem were calculated by fuzzy comprehensive assessment. Then the allocation method was applied to EMU bogie. The results show that the method is feasible. The problem difficult to quantify for EMU bogie maintenance allocation is solved effectively.
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National Science Fund for Distinguished Young Scholars of China (10425208)111 Project (B07009)
文摘The influences of uncertainties in structural parameters on the flutter speed of wing are studied. On the basis of the deterministic flutter analysis model of wing, the uncertainties in structural parameters are considered and described by interval numbers. By virtue of first-order Taylor series expansion, the lower and upper bound curves of the transient decay rate coefficient versus wind velocity are given. So the interval estimation of the flutter critical wind speed of wing can be obtained, which is more reasonable than the point esti- mation obtained by the deterministic flutter analysis and provides the basis for the further non-probabilistic interval reliability analysis of wing flutter. The flow chart for interval fmite element model of flutter analysis of wing is given. The proposed interval finite element model and the stochastic finite element model for wing flutter analysis are compared by the examples of a three degrees of freedom airfoil and fuselage and a 15° sweptback wing, and the results have shown the effectiveness and feasibility of the presented model. The prominent advantage of the proposed interval finite element model is that only the bounds of uncertain parameters are required, and the probabilistic distribution densities or other statistical characteristics are not needed.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10872017, 90816024 and 10876100)111 Project (Grant No. B07009)
文摘Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject to variation. In the study, the collocation interval analysis method based on the first class Chebyshev polynomial approximation is presented to investigate the least favorable responses and the most favorable responses of interval-parameter structures under random excitations. Compared with the interval analysis method based on the first order Taylor expansion, in which only information including the function value and derivative at midpoint is used, the collocation interval analysis method is a non-gradient algorithm using several collocation points which improve the precision of results owing to better approximation of a response function. The pseudo excitation method is introduced to the solving procedure to transform the random problem into a deterministic problem. To validate the procedure, we present numerical results concerning a building under seismic ground motion and aerofoil under continuous atmosphere turbulence to show the effectiveness of the collocation interval analysis method.
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supported by the National Natural Science Foundation of China(Grant No.11602012)the 111 Project(Grant No.B07009)+1 种基金the Defense Industrial Technology Development Program(Grant No.JCKY2016601B001)and the China Postdoctoral Science Foundation(Grant No.2016M591038)
文摘A Newton iteration-based interval uncertainty analysis method(NI-IUAM) is proposed to analyze the propagating effect of interval uncertainty in multidisciplinary systems. NI-IUAM decomposes one multidisciplinary system into single disciplines and utilizes a Newton iteration equation to obtain the upper and lower bounds of coupled state variables at each iterative step.NI-IUAM only needs to determine the bounds of uncertain parameters and does not require specific distribution formats. In this way, NI-IUAM may greatly reduce the necessity for raw data. In addition, NI-IUAM can accelerate the convergence process as a result of the super-linear convergence of Newton iteration. The applicability of the proposed method is discussed, in particular that solutions obtained in each discipline must be compatible in multidisciplinary systems. The validity and efficiency of NI-IUAM is demonstrated by both numerical and engineering examples.
基金co-supported by the National Key R&D Program of China(No.2022YFB3403800)the National Natural Science Foundations of China(Nos.52235005 and 52175224)the Hunan Province Agricultural Science and Technology Innovation Fund Project,China(No.2024CX117).
文摘This study introduces a new approach utilizing an interval finite element method combined with a bilevel Kriging model to determine the bounds of structural responses in the presence of spatial uncertainties.A notable benefit of this approach is its ability to determine the response bounds across all degrees of freedom with a small sample size,which means that it has high efficiency.Firstly,the spatially varying uncertain parameters are quantified using an interval field model,which is described by a series of standard interval variables within a truncated interval Karhunen-Loe`ve(K-L)series expansion.Secondly,considering that the bound of structural response is a function of spatial position with the property of continuity,a surrogate model for the response bound is constructed,namely the first-level Kriging model.The training samples required for this surrogate model are obtained by establishing the second-level Kriging model.The second-level Kriging model is established to describe the structural responses at particular locations relative to the interval variables so as to facilitate the upper and lower bounds of the node response required by the first-level Kriging model.Finally,the accuracy and effectiveness of the method are verified through examples.
文摘In electrical circuit analysis, it is often necessary to find the set of all direct current （d.c.） operating points （either voltages or currents） of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.
基金supported by the National Outstanding Youth Science Foundation of China (No.10425208)111 Project(No.B07009)FanZhou Science and Research Foundation for Young Scholars (No.20080503).
文摘The vertex solution for estimation on the static displacement bounds of structures with uncertain-but-bounded parameters is studied in this paper. For the linear static problem, when there are uncertain interval parameters in the stiffness matrix and the vector of applied forces, the static response may be an interval. Based on the interval operations, the interval solution obtained by the vertex solution is more accurate and more credible than other methods （such as the perturbation method）. However, the vertex solution method by traditional serial computing usually needs large computational efforts, especially for large structures. In order to avoid its disadvantages of large calculation and much runtime, its parallel computing which can be used in large-scale computing is presented in this paper. Two kinds of parallel computing algorithms are proposed based on the vertex solution. The parallel computing will solve many interval problems which cannot be resolved by traditional interval analysis methods.
文摘A squirrel cage induction generator （SCIG） offers many advantages for wind energy conversion systems but suffers from poor voltage regulation under varying operating conditions. The value of excitation capacitance （C exct ） is very crucial for the selfexcitation and voltage build-up as well as voltage regulation in SCIG. Precise calculation of the value of C exct is, therefore, of considerable practical importance. Most of the existing calculation methods make use of the steady-state model of the SCIG in conjunction with some numerical iterative method to determine the minimum value of C exct . But this results in over estimation, leading to poor transient dynamics. This paper presents a novel method, which can precisely calculate the value of C exct by taking into account the behavior of the magnetizing inductance during saturation. Interval analysis has been used to solve the equations. In the proposed method, a range of magnetizing inductance values in the saturation region are included in the calculation of C exct , required for the self-excitation of a 3-φ induction generator. Mathematical analysis to derive the basic equation and application of interval method is presented. The method also yields the magnetizing inductance value in the saturation region which corresponds to an optimum C exct（min） value. The proposed method is experimentally tested for a 1.1 kW induction generator and has shown improved results.
文摘For improving the method of finding maintenance windows under uncertain parameters, an algorithm of maintenance window under uncertainties is presented using interval analysis and sensitivity analysis. Age replacement model is selected to demonstrate how to use this new algorithm. Considered the uncertainties, the optimal maintenance interval of preventive maintenance is not only a single value, but a possible range. The requirement from maintenance engineers is also considered, the maintenance window is made as a symmetrical interval format, like(100 ± 10) day. Comparing with the methods using in the literatures, the new algorithm is without requirement of distribution assumption of uncertain parameter values and computer simulation.
