A new directional stability transformation method of chaos control for first order reliability analysis

Meng, Zeng; Li, Gang; Yang, Dan; Zhan, Lichao

doi:10.1007/s00158-016-1525-z

Cited by 119 publications

(36 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…( ) and ( ) are, respectively, probability distribution function and cumulative distribution function of random variable at point . For searching the MPP, there are various FORM algorithms such as Hasofer-Lind method [16,17], stability transformation method [8,15], and conjugate gradient [9,12], finite-step length [18], relaxed HL-RF method [10,13], and chaotic conjugate search direction [7,13]. The main effort to develop the FORM formula is to improve the efficiency and robustness of FORM.…”

Section: First-order Reliability Methods (Form)mentioning

confidence: 99%

“…In addition, the HL-RF method is similar to the gradient method with step size of 1 for reliability analysis. These methods may provide unstable results for highly nonlinear reliability problems [7,8,15,18]. However, the gradient and HL-RF method are FORM algorithms with a fast convergence rate because the step size in these approaches is selected equivalent to one, while the step size in the modified versions of FORMbased steepest descent search direction such as improved HL-RF [1,19], RHL-RF [11], and STM [8] is given less than 1 to achieve the stabilization.…”

Section: Gradient Methodmentioning

confidence: 99%

“…The STM [8] using small step size and relaxed HL-RF [11] using a dynamic relaxed factor less than 1 can provide stable results for highly nonlinear performance function but are formulated with complicated formulations [9]. The drawback of the STM is enhanced by the conjugate search direction with chaotic step size using logistic map [7,13] and the directional search direction [15]. The new modified FORM formulas have been developed based on a complicated formulation to search MPP.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Comparative Study of First-Order Reliability Method-Based Steepest Descent Search Directions for Reliability Analysis of Steel Structures

Makhduomi

Keshtegar

Shahraki

2017

Advances in Civil Engineering

View full text Add to dashboard Cite

Three algorithms of first-order reliability method (FORM) using steepest descent search direction are compared to evaluate the reliability index of structural steel problems which are designed by the Iranian National Building code. The FORM formula is modified based on a dynamic step size which is computed based on the merit functions named modified Hasofer-Lind and Rackwitz-Fiessler (MHL-RF) method. The efficiency of the gradient, HL-RF, and MHL-RF method was compared for a bar structure under tensile capacity, a multispan beam under bending capacity, a connection under tension load, and a column under axial force. The results illustrated that the MHL-RF method is more efficient than the HL-RF and gradient method. The designed steel components by the Iranian National Building code showed good confidence levels with the reliability index in the range from 2.5 to 3.0.

show abstract

Section: First-order Reliability Methods (Form)mentioning

confidence: 99%

Section: Gradient Methodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Comparative Study of First-Order Reliability Method-Based Steepest Descent Search Directions for Reliability Analysis of Steel Structures

Makhduomi

Keshtegar

Shahraki

2017

Advances in Civil Engineering

View full text Add to dashboard Cite

show abstract

“…Reliability index calculated by Wang and Grandhi [36] and Gong et al [6] is 2.2983. Meng et al [31] and Keshtegar and Miri [29] obtain that the result of the reliability index is 2.2983. In the reliability analysis of example 1, the reliability index obtained by Monte Carlo simulation using 10 6 samples is 2.5265. e computation results and iterative process of reliability index using the different methods in example 1 are shown in Table 1 and Figure 2, respectively.…”

Section: Nonlinear Numerical Examplementioning

confidence: 96%

“…Keshtegar [30] developed a new FORM which controls instability solutions using chaotic conjugate map. Meng et al [31] proposed a new directional stability transformation method of chaos control for first-order reliability analysis. Besides, Keshtegar and Chakraborty [32] improved FORM by introducing a conjugate search direction approach.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive First-Order Reliability Analysis Method for Nonlinear Problems

Wang

Zhang

Song

2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The HL-RF algorithm of the first-order reliability method (FORM) is a widely useful tool in structural reliability analysis. However, the iteration results of HL-RF algorithm may not converge due to periodic cycles for some highly nonlinear reliability problems. In this paper, an adaptive first-order reliability method (AFORM) is proposed to improve solution efficiency for some highly nonlinear reliability problems by introducing an adaptive factor. In AFORM, based on the two-parameter approximate first-order reliability method, the new iteration point and the previous iteration point are used to obtain the corresponding angle, and the result of convergence is judged by angle condition. According to the convergence degree of the results, two iteration parameters of the approximate reliability method are adjusted continuously by adaptive factor. Moreover, iteration step size is adjusted by changing the parameters to improve the efficiency and robustness of FORM. Finally, four numerical examples and one mechanical reliability analysis example are used to verify the proposed method. Compared with the different algorithms, the results show that AFORM has better efficiency and robustness for some highly nonlinear reliability problems.

show abstract

An efficient and robust structural reliability analysis method with mixed variables based on hybrid conjugate gradient direction

Huang

et al. 2021

Numerical Meth Engineering

View full text Add to dashboard Cite

Traditional reliability analysis is based on probability theory with precise distributions. However, determining the distribution of all variables precisely is impossible due to insufficient information. Therefore, random and interval variables may be encountered, and probabilistic reliability methods are hard to use. The existing interval variables make reliability analysis more difficult. In this article, an efficient and robust hybrid reliability analysis method is proposed for structures with both random and interval variables. Firstly, a single-loop procedure is proposed by performing probabilistic analysis and interval analysis simultaneously in each most probable point search process. Then an improved conjugate sensitivity factor method based on hybrid conjugate gradient direction and adaptive finite step length is developed for probabilistic analysis. Meanwhile, the hybrid conjugate gradient direction together with active set is introduced into the projected gradient method for interval analysis. Finally, a comparison analysis with six numerical examples is provided to validate the performance of the proposed method. The results demonstrate that the proposed method is better than the existing methods in terms of efficiency and robustness for hybrid reliability analysis with random and interval variables.

show abstract

A new directional stability transformation method of chaos control for first order reliability analysis

Cited by 119 publications

References 31 publications

A Comparative Study of First-Order Reliability Method-Based Steepest Descent Search Directions for Reliability Analysis of Steel Structures

A Comparative Study of First-Order Reliability Method-Based Steepest Descent Search Directions for Reliability Analysis of Steel Structures

An Adaptive First-Order Reliability Analysis Method for Nonlinear Problems

An efficient and robust structural reliability analysis method with mixed variables based on hybrid conjugate gradient direction

Contact Info

Product

Resources

About