A numerical integration method in affine space and a method with high accuracy for computing structural system reliability

Song, Bi Feng

doi:10.1016/0045-7949(92)90209-i

Cited by 20 publications

(8 citation statements)

References 3 publications

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“…These sample points are pseudorandom numbers, which has a certain correlation. The distribution of the sample points is not uniform and the deviation can reach

[ 23 ]. For the calculation of small probability events represented by the structural failure probability, the convergence speed and accuracy are affected by PRN sampling points.…”

Section: Reliability Analysis Systemmentioning

confidence: 99%

A New Reliability Analysis Model of the Chegongzhuang Heat-Supplying Tunnel Structure Considering the Coupling of Pipeline Thrust and Thermal Effect

Zhang

Wang

et al. 2018

Materials

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Based on the operating Chegongzhuang heat-supplying tunnel in Beijing, the reliability of its lining structure under the action of large thrust and thermal effect is studied. According to the characteristics of a heat-supplying tunnel service, a three-dimensional numerical analysis model was established based on the mechanical tests on the in-situ specimens. The stress and strain of the tunnel structure were obtained before and after the operation. Compared with the field monitoring data, the rationality of the model was verified. After extracting the internal force of the lining structure, the improved method of subset simulation was proposed as the performance function to calculate the reliability of the main control section of the tunnel. In contrast to the traditional calculation method, the analytic relationship between the sample numbers in the subset simulation method and Monte Carlo method was given. The results indicate that the lining structure is greatly influenced by coupling in the range of six meters from the fixed brackets, especially the tunnel floor. The improved subset simulation method can greatly save computation time and improve computational efficiency under the premise of ensuring the accuracy of calculation. It is suitable for the reliability calculation of tunnel engineering, because “the lower the probability, the more efficient the calculation.”

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“…These sample points are pseudorandom numbers, which has a certain correlation. The distribution of the sample points is not uniform and the deviation can reach

[ 23 ]. For the calculation of small probability events represented by the structural failure probability, the convergence speed and accuracy are affected by PRN sampling points.…”

Section: Reliability Analysis Systemmentioning

confidence: 99%

A New Reliability Analysis Model of the Chegongzhuang Heat-Supplying Tunnel Structure Considering the Coupling of Pipeline Thrust and Thermal Effect

Zhang

Wang

et al. 2018

Materials

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“…In Table I Tables I and I1 also include some solutions reported by Song (1992) and Zhu (1994), which were obtained from the affine integration method.…”

Section: Example 1: a System With 3 Equicorrelated Elementsmentioning

confidence: 99%

“…(7) can be further simplified to These special cases have been commonly used to assess the numerical accuracy of various approximate solutions. Song (1992) and Zhu (1993) presented a numerical integration method in affine space formed by the failure function equations (3). Civil Engineering and Environmental Systems 1998.15:89-105. .…”

Section: Numerical Integrationmentioning

confidence: 99%

A Simple Approach to Multinormal Integration With Applications to the System Reliability Computation

Pandey

1998

Civil Engineering and Environmental Systems

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The paper presents an cfkclive approximation for evalutaling multinormal integrals commonly encountered in system reliability computations. Conceptually, the method attempts to approximate a multinormal integral by a product of one-dimensional normal integrals, which are easy to evaluate.Examples considered in the paper illustrate a remarkable accuracy of the approximation in comparison with exact integration and simulation solutions. Unlike other approximations, this method does not involve any iterative linearization, minimization or integration. Computational simplicity with high accuracy is the major advantage of the proposed method, which also highlights its potential for estimating reliability of structural systems.

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“…The reliability sensitivity curves with the forcing frequency (Ω) are depicted in Figs. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In order to find the variation of reliability sensitivity, in figures there are some key points in x direction (Ω), those are (1-γ) u ωx , u ωx , (1＋γ) u ωx , (1-γ) u ωy , u ωy and (1+γ) u ωy .…”

Section: Numerical Examplementioning

confidence: 99%

“…The two-order joint failure probability P ij can be obtained by the numerical integration method [17]. Assume the state function of two failure modes is…”

Section: Computation Of P Ijmentioning

confidence: 99%

Vibration reliability sensitivity analysis of general system with correlation failure modes

Zhang

Zhao

2011

J Mech Sci Technol

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The vibration problem of the general system is the main object of research. The material properties and geometry of general system are random parameters because of the manufacturing environment, technical conditions, manufacturing and installation errors, multiphase materials, features and other factors. According to the relation criterion that the difference between the natural frequency and the driving frequency of general systems is not beyond a specific value, the vibration reliability mode and vibration reliability of general systems are defined considering the correlation of the multi-order natural frequency and the random characteristics of structure size and material, and the vibration reliability analysis method for avoiding the resonant is carried out. The second-order joint failure probability is obtained by using the numerical integration method. Based on the reliability design theory and sensitivity analysis method, the vibration reliability sensitivity of the general system with correlation failure modes is extensively discussed and a numerical method for vibration reliability sensitivity design is presented. The variation regularities of vibration reliability sensitivity are obtained and the effects of random parameters on vibration reliability of the general system are studied. The presented method provided the theoretic basis for the reliability design of the general system. A numerical example demonstrated that the proposed method is effective.

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A numerical integration method in affine space and a method with high accuracy for computing structural system reliability

Cited by 20 publications

References 3 publications

A New Reliability Analysis Model of the Chegongzhuang Heat-Supplying Tunnel Structure Considering the Coupling of Pipeline Thrust and Thermal Effect

A New Reliability Analysis Model of the Chegongzhuang Heat-Supplying Tunnel Structure Considering the Coupling of Pipeline Thrust and Thermal Effect

A Simple Approach to Multinormal Integration With Applications to the System Reliability Computation

Vibration reliability sensitivity analysis of general system with correlation failure modes

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