A robust iterative algorithm for structural reliability analysis

Gong, Jinxin; Yi, Ping

doi:10.1007/s00158-010-0582-y

Cited by 101 publications

(39 citation statements)

References 17 publications

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“…This is a very important point since usually full characterization methods are considered to be computationally expensive; 3. the implementation and solution of the full characterization method using the collocation approach is rather simple as described in Section 3: one needs only to call the limit state function ns times, assemble the matrix whose coefficients depend on the chosen polynomials (N X ) and solve a ns Â N X system of linear equations. This procedure is much simpler than implementing an optimization algorithm to solve the FORM problem, not to mention convergence issues frequently observed [33].…”

Section: Discussionmentioning

confidence: 99%

Overcoming the drawbacks of the FORM using a full characterization method

López¹,

Torii²,

Miguel³

et al. 2015

Structural Safety

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Section: Discussionmentioning

confidence: 99%

Overcoming the drawbacks of the FORM using a full characterization method

López¹,

Torii²,

Miguel³

et al. 2015

Structural Safety

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“…( ) 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%

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

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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.

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“…For the control system discussed above, the settling time can be calculated through equations (6), (25), and (27)…”

Section: Reliability Calculationmentioning

confidence: 99%

Methodology to evaluate reliability of performance of second-order automatic control system

Yang

Tan

Suo

2017

Advances in Mechanical Engineering

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Reliability evaluation plays a more and more important role in nuclear engineering, aviation industry, and so on. Due to the special integrity of a control system, traditional reliability methods, such as the reliability block diagram and fault tree analysis, are not proper to make a reasonable and accurate reliability evaluation on a control system. However, a systematic methodology to predict performance reliability of a control system is rarely reported. In this article, a methodology of performance reliability based on the performance requirement for an automatic control system, not just limited to the stability reliability or probabilistic robustness evaluation, is first proposed. A solution to evaluate control performance reliability is introduced with analytical approximation approach called first-order second-moment method. Also, a robust iterative algorithm is adopted to overcome the bifurcation and chaos problems encountered when searching the most probable point for highly nonlinear limit state function. An elaborate example based on a servo motor control system is presented to calculate performance reliability of the settling time of the control system with first-order secondmoment method. Its numerical approximation is demonstrated to be accurate through Monte Carlo simulation.

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A robust iterative algorithm for structural reliability analysis

Cited by 101 publications

References 17 publications

Overcoming the drawbacks of the FORM using a full characterization method

Overcoming the drawbacks of the FORM using a full characterization method

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

Methodology to evaluate reliability of performance of second-order automatic control system

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