A Novel Algorithm for Structural Reliability Analysis Based on Finite Step Length and Armijo Line Search
This paper presents a novel algorithm for structural reliability analysis based on the finite step length and Armijo line search to remove the drawbacks of the Hasofer–Lind and Rakwitz–Fiessler (HL-RF) algorithm that may be subjected to non-convergence in the first-order reliability method (FORM). I...
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| Published in | Applied sciences Vol. 9; no. 12; p. 2546 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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MDPI AG
01.06.2019
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| ISSN | 2076-3417 2076-3417 |
| DOI | 10.3390/app9122546 |
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| Abstract | This paper presents a novel algorithm for structural reliability analysis based on the finite step length and Armijo line search to remove the drawbacks of the Hasofer–Lind and Rakwitz–Fiessler (HL-RF) algorithm that may be subjected to non-convergence in the first-order reliability method (FORM). Initially, the sensitivity factor with finite step length is introduced for preventing the iterative process of the algorithm from entering a periodic loop. Subsequently, an optimization method based on the sufficient descent condition with the Armijo line search technique is proposed. With that, the initial step length and adjusting coefficient are optimized to enhance the applicability of the algorithm emphatically for highly nonlinear functions. A comparison analysis is carried out between the proposed algorithm and existing FORM-based algorithms to validate the robustness and efficiency of the proposed algorithm. The results of this demonstrate that the proposed algorithm is superior to the HL-RF algorithm in terms of robustness and surpass the other existing FORM-based algorithms in connection to efficiency. |
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| AbstractList | This paper presents a novel algorithm for structural reliability analysis based on the finite step length and Armijo line search to remove the drawbacks of the Hasofer–Lind and Rakwitz–Fiessler (HL-RF) algorithm that may be subjected to non-convergence in the first-order reliability method (FORM). Initially, the sensitivity factor with finite step length is introduced for preventing the iterative process of the algorithm from entering a periodic loop. Subsequently, an optimization method based on the sufficient descent condition with the Armijo line search technique is proposed. With that, the initial step length and adjusting coefficient are optimized to enhance the applicability of the algorithm emphatically for highly nonlinear functions. A comparison analysis is carried out between the proposed algorithm and existing FORM-based algorithms to validate the robustness and efficiency of the proposed algorithm. The results of this demonstrate that the proposed algorithm is superior to the HL-RF algorithm in terms of robustness and surpass the other existing FORM-based algorithms in connection to efficiency. (1) Transform the random variables X into standard normal random variables U by Rosenblatt or Nataf transformation techniques [26], which is expressed as U=Φ−1FXX where Φ−1 is the inverse cumulative distribution function (CDF) of the standard normal distribution, FX is the CDF of X , and U=U1,U2,⋯Un . Uk+1=GUk−∇TGUkUk∇GUkαk where ⋅ is the norm of a vector, k is the counter of iteration, ∇GUk is the gradient of GUk , and αk is the sensitivity factor that can be calculated by αk=−∇GUk∇GUk (3) Estimate the failure probability by Pf≈Φ−β where Φ is the CDF of the standard normal distribution and β=U* is the reliability index. On this basis, the first-order Taylor expansion of the LSFs is used, and Gβk+1 αk=0 is approximated as GUk+∇TGUkβk+1 αk−Uk≈0 The reliability index is accordingly computed as βk+1≈∇TGUkUk−GUk∇TGUkαk Consequently, the iterative formulation can be summarized as Uk+1=∇TGUkUk−GUk∇TGUkαkαk where, αk=Uk−λ∇GUkUk−λ∇GUk Noted that if λ→∞ , Equation (11) becomes limλ→∞αk=limλk→∞Uk/λ−∇GUkUk/λ−∇GUk=−∇GUk∇GUk Equation (12) indicates that the HL-RF algorithm is a special case of the above iterative formulation with infinite step length. [...]it is named as FSL algorithm [29]. According to the sufficient descent condition [33], the adjustment of step length is expressed as λk+1= λkUk+1−Uk<Uk−Uk−1 cλkUk+1−Uk≥Uk−Uk−1 where c is the adjusting coefficient, and a recommended value for c in This paper presents a novel algorithm for structural reliability analysis based on the finite step length and Armijo line search to remove the drawbacks of the Hasofer−Lind and Rakwitz−Fiessler (HL-RF) algorithm that may be subjected to non-convergence in the first-order reliability method (FORM). Initially, the sensitivity factor with finite step length is introduced for preventing the iterative process of the algorithm from entering a periodic loop. Subsequently, an optimization method based on the sufficient descent condition with the Armijo line search technique is proposed. With that, the initial step length and adjusting coefficient are optimized to enhance the applicability of the algorithm emphatically for highly nonlinear functions. A comparison analysis is carried out between the proposed algorithm and existing FORM-based algorithms to validate the robustness and efficiency of the proposed algorithm. The results of this demonstrate that the proposed algorithm is superior to the HL-RF algorithm in terms of robustness and surpass the other existing FORM-based algorithms in connection to efficiency. |
| Author | Huang, Peng Huang, Hong-Zhong Huang, Tudi |
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| SubjectTerms | Algorithms Armijo line search Efficiency Engineering finite step length first-order reliability method HL-RF algorithm Methods Optimization reliability analysis |
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| Title | A Novel Algorithm for Structural Reliability Analysis Based on Finite Step Length and Armijo Line Search |
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