A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linea...A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.展开更多
For structures that only the predicted bounds of uncertainties are available,this study proposes a Bayesianmethod to logically evaluate the nonprobabilistic reliability of structures based on multi-ellipsoid convex mo...For structures that only the predicted bounds of uncertainties are available,this study proposes a Bayesianmethod to logically evaluate the nonprobabilistic reliability of structures based on multi-ellipsoid convex model and performance test data.According to the given interval ranges of uncertainties,we determine the initial characteristic parameters of a multi-ellipsoid convex set.Moreover,to update the plausibility of characteristic parameters,a Bayesian network for the information fusion of prior uncertainty knowledge and subsequent performance test data is constructed.Then,an updated multi-ellipsoid set with the maximum likelihood of the performance test data can be achieved.The credible non-probabilistic reliability index is calculated based on the Kriging-based surrogate model of the performance function.Several numerical examples are presented to validate the proposed Bayesian updating method.展开更多
A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, u...A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures.展开更多
It is very difficult to know the exact boundaries of the variable domain for problems with small sample size,and the traditional convex set model is no longer applicable.In view of this,a novel reliability model was p...It is very difficult to know the exact boundaries of the variable domain for problems with small sample size,and the traditional convex set model is no longer applicable.In view of this,a novel reliability model was proposed on the basis of the fuzzy convex set(FCS)model.This new reliability model can account for different relations between the structural failure region and variable domain.Key computational algorithms were studied in detail.First,the optimization strategy for robust reliability is improved.Second,Monte Carlo algorithms(i.e.,uniform sampling method)for hyper-ellipsoidal convex sets were studied in detail,and errors in previous reports were corrected.Finally,the Gauss-Legendre integral algorithm was used for calculation of the integral reliability index.Three numerical examples are presented here to illustrate the rationality and feasibility of the proposed model and its corresponding algorithms.展开更多
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
Aerostat capsule is small sample data,so designing reliability is very difficult to be obtained accurately by conventional probabilistic reliability method. Based on the interval non-probabilistic reliability theory,a...Aerostat capsule is small sample data,so designing reliability is very difficult to be obtained accurately by conventional probabilistic reliability method. Based on the interval non-probabilistic reliability theory,an instability mathematics model of envelope structure is studied,and the calculation formula of interval reliability index is put forward. Through the mechanical experiments of three capsule structures,the experimental results of the interval reliability are obtained. By comparing the theoretical and measured values,it is found that the theoretical reliability index is more conservative. Non-probabilistic reliability method can reflect the reliability degree of the capsule body under different loading conditions,which can provide some guidance for engineering application.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
The aim of this paper is to evaluate the fatigue reliability with hybrid uncertain parameters based on a residual strength model. By solving the non-probabilistic setbased reliability problem and analyzing the reliabi...The aim of this paper is to evaluate the fatigue reliability with hybrid uncertain parameters based on a residual strength model. By solving the non-probabilistic setbased reliability problem and analyzing the reliability with randomness, the fatigue reliability with hybrid parameters can be obtained. The presented hybrid model can adequately consider all uncertainties affecting the fatigue reliability with hybrid uncertain parameters. A comparison among the presented hybrid model, non-probabilistic set-theoretic model and the conventional random model is made through two typical numerical examples. The results show that the presented hybrid model, which can ensure structural security, is effective and practical.展开更多
Probabilistic reliability model established by insufficient data is inaccessible. The convex model was applied to model the uncertainties of variables. A new non-probabilistic reliability model was proposed based on t...Probabilistic reliability model established by insufficient data is inaccessible. The convex model was applied to model the uncertainties of variables. A new non-probabilistic reliability model was proposed based on the robustness of system to uncertainty. The non-probabilistic reliability model,the infinite norm model,and the probabilistic model were used to assess the reliability of a steel beam,respectively. The results show that the resistance is allowed to couple with the action effect in the non-probabilistic reliability model. Additionally,the non-probabilistic reliability model becomes the same accurate as probabilistic model with the increase of the bounded uncertain information. The model is decided by the available data and information.展开更多
The non-probabilistic reliability in higher dimensional situations cannot be calcu- lated efficiently using traditional methods, which either require a large amount of calculation or cause significant error. In this s...The non-probabilistic reliability in higher dimensional situations cannot be calcu- lated efficiently using traditional methods, which either require a large amount of calculation or cause significant error. In this study, an efficient computational method is proposed for the cal- culation of non-probabilistic reliability based on the volume ratio theory, specificMly for linear structural systems. The common expression for non-probabilistic reliability is obtained through formula derivation with the amount of computation considerably reduced. The compatibility be- tween non-probabilistic and probabilistic safety measures is demonstrated through the Monte Carlo simulation. The high efficiency of the presented method is verified by several numerical examples.展开更多
It is essential to consider the effects of incomplete measurement,inaccurate information and inadequate cognition on structural topology optimization.For the multi-material structural topology optimization with non-pr...It is essential to consider the effects of incomplete measurement,inaccurate information and inadequate cognition on structural topology optimization.For the multi-material structural topology optimization with non-probability uncertainty,the multi-material interpolation model is represented by the ordered rational approximation of mat erial properties(ordered RAMP).Combined with structural compliance minimization,the multi-material topology optimization with reliability constraints is established.The corresponding non-probability uncertainties are described by the evidence theory,and the uniformity processing method is introduced to convert the evidence variables into random variables.The first-order reliability method is employed to search the most probable point under the reliability index constraint,and then the random variables are equivalent to the deterministic variables according to the geometric meaning of the reliability index and sensitivity information.Therefore,the non-probabilistic reliability-based multi-material topology optimization is transformed into the conventional deterministic optimization format,followed by the ordered RAMP method to solve the optimization problem.Finally,through numerical examples of 2D and 3D structures,the feasibility and effectiveness of the proposed method are verified to consider the geometrical dimensions and external loading uncertainties.展开更多
Based on the interval mathematics and possibility theory, the variables existing in hydraulic turbine blade are described. Considering the multi-failure mode in turbine blade, multi-variable model is established to me...Based on the interval mathematics and possibility theory, the variables existing in hydraulic turbine blade are described. Considering the multi-failure mode in turbine blade, multi-variable model is established to meet the actual situation. Thus, non-probabilistic reliability index is presented by comparing with the output range and the given range.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
The paper discusses non-probabilistic approaches for uncertainty treatment in structure reliability analysis. Based on rough set theory, the uncertain parameters of structures are expressed by rough variables, the str...The paper discusses non-probabilistic approaches for uncertainty treatment in structure reliability analysis. Based on rough set theory, the uncertain parameters of structures are expressed by rough variables, the structure reliability index is computed by rough function and metric. This new methodology for structural reliability is proved to be valid and efficient using theory analysis and examples of practical application.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
基金Project supported by the National Natural Science Foundation of China (Nos.12072007,12072006,12132001,and 52192632)the Ningbo Natural Science Foundation of Zhejiang Province of China (No.202003N4018)the Defense Industrial Technology Development Program of China (Nos.JCKY2019205A006,JCKY2019203A003,and JCKY2021204A002)。
文摘A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.
基金This work was supported financially by the National Key R&D Program of China(2017YFB0203604)the National Natural Science Foundation of China(11972104,11772077)the Liaoning Revitalization Talents Program(XLYC1807187).
文摘For structures that only the predicted bounds of uncertainties are available,this study proposes a Bayesianmethod to logically evaluate the nonprobabilistic reliability of structures based on multi-ellipsoid convex model and performance test data.According to the given interval ranges of uncertainties,we determine the initial characteristic parameters of a multi-ellipsoid convex set.Moreover,to update the plausibility of characteristic parameters,a Bayesian network for the information fusion of prior uncertainty knowledge and subsequent performance test data is constructed.Then,an updated multi-ellipsoid set with the maximum likelihood of the performance test data can be achieved.The credible non-probabilistic reliability index is calculated based on the Kriging-based surrogate model of the performance function.Several numerical examples are presented to validate the proposed Bayesian updating method.
基金supported by the National Natural Science Foundation of China (No.10972084)
文摘A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures.
基金funded by National Natural Science Foundation of China(No.51509254).
文摘It is very difficult to know the exact boundaries of the variable domain for problems with small sample size,and the traditional convex set model is no longer applicable.In view of this,a novel reliability model was proposed on the basis of the fuzzy convex set(FCS)model.This new reliability model can account for different relations between the structural failure region and variable domain.Key computational algorithms were studied in detail.First,the optimization strategy for robust reliability is improved.Second,Monte Carlo algorithms(i.e.,uniform sampling method)for hyper-ellipsoidal convex sets were studied in detail,and errors in previous reports were corrected.Finally,the Gauss-Legendre integral algorithm was used for calculation of the integral reliability index.Three numerical examples are presented here to illustrate the rationality and feasibility of the proposed model and its corresponding algorithms.
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Supported by the National High Technology Research and Development Program of China(2015AA8098085E)
文摘Aerostat capsule is small sample data,so designing reliability is very difficult to be obtained accurately by conventional probabilistic reliability method. Based on the interval non-probabilistic reliability theory,an instability mathematics model of envelope structure is studied,and the calculation formula of interval reliability index is put forward. Through the mechanical experiments of three capsule structures,the experimental results of the interval reliability are obtained. By comparing the theoretical and measured values,it is found that the theoretical reliability index is more conservative. Non-probabilistic reliability method can reflect the reliability degree of the capsule body under different loading conditions,which can provide some guidance for engineering application.
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 (90816024, 10872017 and 10876100)the 111 Project (B07009)the Innovation Foundation of Beihang University for PhD Graduates
文摘The aim of this paper is to evaluate the fatigue reliability with hybrid uncertain parameters based on a residual strength model. By solving the non-probabilistic setbased reliability problem and analyzing the reliability with randomness, the fatigue reliability with hybrid parameters can be obtained. The presented hybrid model can adequately consider all uncertainties affecting the fatigue reliability with hybrid uncertain parameters. A comparison among the presented hybrid model, non-probabilistic set-theoretic model and the conventional random model is made through two typical numerical examples. The results show that the presented hybrid model, which can ensure structural security, is effective and practical.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51008100)the Ministry of Science and Technology(Grant No.2011CB013604)+2 种基金the Natural Science Foundation of Shandong Province,China(Grant No.ZR2001EEQ028)the Science and Technology Planning Project of Weihai(Grant No.2010-3-96)the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology(Grant No.HIT.NSRIF.201009)
文摘Probabilistic reliability model established by insufficient data is inaccessible. The convex model was applied to model the uncertainties of variables. A new non-probabilistic reliability model was proposed based on the robustness of system to uncertainty. The non-probabilistic reliability model,the infinite norm model,and the probabilistic model were used to assess the reliability of a steel beam,respectively. The results show that the resistance is allowed to couple with the action effect in the non-probabilistic reliability model. Additionally,the non-probabilistic reliability model becomes the same accurate as probabilistic model with the increase of the bounded uncertain information. The model is decided by the available data and information.
基金Project supported by the major research project(No.MJ-F-2012-04)Defense Industrial Technology Development Program(No.JCKY2013601B001)the National Natural Science Foundation of China(Nos.11372025,11432002and 11572024)
文摘The non-probabilistic reliability in higher dimensional situations cannot be calcu- lated efficiently using traditional methods, which either require a large amount of calculation or cause significant error. In this study, an efficient computational method is proposed for the cal- culation of non-probabilistic reliability based on the volume ratio theory, specificMly for linear structural systems. The common expression for non-probabilistic reliability is obtained through formula derivation with the amount of computation considerably reduced. The compatibility be- tween non-probabilistic and probabilistic safety measures is demonstrated through the Monte Carlo simulation. The high efficiency of the presented method is verified by several numerical examples.
基金supported by the Natural Science Foundation of China(Grant No.51705268)Shandong Provincial Natural Science Foundation,China(Grant No.ZR2016EEB20)China Postdoctoral Science Foundation Funded Project(Grant No.2017M612191)。
文摘It is essential to consider the effects of incomplete measurement,inaccurate information and inadequate cognition on structural topology optimization.For the multi-material structural topology optimization with non-probability uncertainty,the multi-material interpolation model is represented by the ordered rational approximation of mat erial properties(ordered RAMP).Combined with structural compliance minimization,the multi-material topology optimization with reliability constraints is established.The corresponding non-probability uncertainties are described by the evidence theory,and the uniformity processing method is introduced to convert the evidence variables into random variables.The first-order reliability method is employed to search the most probable point under the reliability index constraint,and then the random variables are equivalent to the deterministic variables according to the geometric meaning of the reliability index and sensitivity information.Therefore,the non-probabilistic reliability-based multi-material topology optimization is transformed into the conventional deterministic optimization format,followed by the ordered RAMP method to solve the optimization problem.Finally,through numerical examples of 2D and 3D structures,the feasibility and effectiveness of the proposed method are verified to consider the geometrical dimensions and external loading uncertainties.
基金the Key Scientific Research Fund Project of Xihua University(No.Z1320406)the National Natural Science Foundation of China(No.51379179)
文摘Based on the interval mathematics and possibility theory, the variables existing in hydraulic turbine blade are described. Considering the multi-failure mode in turbine blade, multi-variable model is established to meet the actual situation. Thus, non-probabilistic reliability index is presented by comparing with the output range and the given range.
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 National Natural Science Foundation of China under Grant No.61373112Special Project of Scientific Research of Education Department of Shaanxi Provincial Government No.11JK0967
文摘The paper discusses non-probabilistic approaches for uncertainty treatment in structure reliability analysis. Based on rough set theory, the uncertain parameters of structures are expressed by rough variables, the structure reliability index is computed by rough function and metric. This new methodology for structural reliability is proved to be valid and efficient using theory analysis and examples of practical application.
基金supported by the Defense Industrial Technology Development Program (Grant Nos.JCKY2018601B001,JCKY2019209C004,and JCKY2019205A006)the National Natural Science Foundation of China (Grant Nos.11432002,11772026,and 12002015)+1 种基金the Aeronautical Science Foundation of China (Grant No.20182951014)the Beijing Municipal Science and Technology Commission (Grant No.Z191100004619006).
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.