Structural Reliability Analysis of Limit State Functions With Multiple Design Points Using Evolutionary Strategies

In structural reliability analysis there could be several limit state functions with multiple design points. The missing of one or more of these design points can be responsible for significant errors on the system reliability evaluation. In this paper, a simple version of the Evolutionary Strategies (ES) algorithm is combined with the First Order Second Moment method (FORM) to perform the reliability analysis of systems with multiple design points. The ES algorithm is used to perform a preliminary identification of the design points (local maxima). These design points approximations are used as initial guesses in the HL-RF (Hasofer and Lind–Rackwitz and Fiessler) method in order to calculate the true design points. The system failure probability is then evaluated with FORM approximation for series systems. The proposed methodology is applied to the analysis of three non-linear limit state functions with Normal and non-Normal random variables and the results are compared with those obtained with the Monte Carlo method.

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First-Order Reliability Method for Structural Reliability Analysis in the Presence of Random and Interval Variables

ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg ◽

10.1115/1.4030911 ◽

2015 ◽

Vol 1 (4) ◽

Cited By ~ 6

Author(s):

Umberto Alibrandi ◽

C. G. Koh

Keyword(s):

Reliability Analysis ◽

Structural Reliability ◽

Limit State ◽

Computational Cost ◽

Computational Effort ◽

Stochastic Dynamic ◽

First Order Reliability Method ◽

First Order ◽

Structural Reliability Analysis ◽

Reliability Method

This paper presents a novel procedure based on first-order reliability method (FORM) for structural reliability analysis in the presence of random parameters and interval uncertain parameters. In the proposed formulation, the hybrid problem is reduced to standard reliability problems, where the limit state functions are defined only in terms of the random variables. Monte Carlo simulation (MCS) for hybrid reliability analysis (HRA) is presented, and it is shown that it requires a tremendous computational effort; FORM for HRA is more efficient but still demanding. The computational cost is significantly reduced through a simplified procedure, which gives good approximations of the design points, by requiring only three classical FORMs and one interval analysis (IA), developed herein through an optimization procedure. FORM for HRA and its simplified formulation achieve a much improved efficiency than MCS by several orders of magnitude, and it can thus be applied to real-world engineering problems. Representative examples of stochastic dynamic analysis and performance-based engineering are presented.

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On the Application of Structural Reliability Analysis

Volume 9: Offshore Geotechnics; Torgeir Moan Honoring Symposium ◽

10.1115/omae2017-62717 ◽

2017 ◽

Author(s):

Torfinn Hørte ◽

Gudfinnur Sigurdsson

Keyword(s):

Reliability Analysis ◽

Structural Engineering ◽

Structural Reliability ◽

Limit State ◽

Design Analysis ◽

Ultimate Limit State ◽

Hull Girder ◽

Structural Reliability Analysis ◽

Code Calibration ◽

Calculated Probability

Structural Reliability Analysis (SRA) is a useful tool in structural engineering. Uncertainty in input parameters and model uncertainties in the analysis predictions are explicitly modelled by random variables. With this methodology, the uncertainties involved are handled in a consistent and transparent way. Compared to a deterministic analysis, SRA provides improved insight in how the various uncertainties involved influence the results. The main results from SRA is the calculated probability of structural failure, but other useful results such as uncertainty importance factors and design points being the most likely combination of all variables at failure represent helpful information. The present paper illustrates some the features using SRA for two different types of application. The first application is the use of SRA as a tool for code calibration and the second shows the application of SRA to a problem where common practice is likely to be rather conservative and therefore leading to unacceptable results, but where the degree of conservatism is not known. Two examples are chosen to illustrate code calibration; i.e. hull girder ultimate limit state (ULS) for tankers and ULS for mooring design in the ULS for floating offshore vessels. Code calibration involves both SRA and design analysis following the code. It is shown how the design analysis can be modified in order to better reflect a chosen target reliability level across a selected set of test cases representative for what the code should cover. Fatigue of subsea wellhead systems is selected as an example of a special case when application of existing rules may lead to unsatisfactory results which are likely to be rather conservative. It is shown how results can be presented in terms of the accumulated probability of fatigue failure as a function of time. This may be a more suitable basis for decision making than a calculated fatigue life from a standard analysis. It is also illustrated how importance factors from the SRA can be used as guidance on how to prioritize effort in order to improve prediction of the fatigue damage. The present paper is not intended to be detailed in all input and analysis methodology, but draw the attention towards the possibilities and benefits of applying SRA in structural engineering, where the examples are used to illustrate this potential.

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NorMoor JIP, Structural Reliability Analysis for Mooring Lines in Ultimate and Accidental Limit State

10.4043/27734-ms ◽

2017 ◽

Author(s):

Torfinn Hørte ◽

Siril Okkenhaug ◽

Øivind Paulshus

Keyword(s):

Reliability Analysis ◽

Structural Reliability ◽

Limit State ◽

Mooring Lines ◽

Structural Reliability Analysis

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The structural reliability analysis using explicit neural state functions

MATEC Web of Conferences ◽

10.1051/matecconf/201926210002 ◽

2019 ◽

Vol 262 ◽

pp. 10002 ◽

Cited By ~ 2

Author(s):

Agnieszka Dudzik ◽

Beata Potrzeszcz-Sut

Keyword(s):

Reliability Analysis ◽

Reliability Index ◽

Structural Reliability ◽

Limit State ◽

Random Variables ◽

Transformation Method ◽

Stability Loss ◽

Cross Sectional ◽

Component Reliability ◽

State Functions

The present study considers the problems of stability and reliability of spatial truss susceptible to stability loss from the condition of node snapping. In the reliability analysis of structure, uncertain parameters, such us load magnitudes, cross-sectional area, modulus of elasticity are represented by random variables. Random variables are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier. In the performed analyses explicit form of the random variables function were used. To formulate explicit limit state functions the neural networks is used. In the paper only the time independent component reliability analysis problems are considered. The NUMPRESS software, created at the IFTR PAS, was used in the reliability analysis. The Hasofer-Lind index in conjunction with transformation method in the FORM was used as a reliability measure. The primary research method is the FORM method. In order to verify the correctness of the calculation SORM and Monte Carlo methods are used. The values of reliability index for different descriptions of mathematical model of the structure were determined. The sensitivity of reliability index to the random variables is defined.

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Structural Reliability Analysis of Ship Hulls Accounting for Collision or Grounding Damage

Journal of Marine Science and Application ◽

10.1007/s11804-020-00176-w ◽

2020 ◽

Author(s):

Branka Bužančić Primorac ◽

Joško Parunov ◽

C. Guedes Soares

Keyword(s):

Reliability Analysis ◽

Structural Reliability ◽

Limit State ◽

Random Variables ◽

Bending Moment ◽

State Equation ◽

Limit States ◽

Moment Capacity ◽

Ship Hulls ◽

Structural Reliability Analysis

AbstractClassical structural reliability analysis of intact ship hulls is extended to the case of ships with collision or grounding damages. Still water load distribution and residual bending moment capacity are included as random variables in the limit state equation. The probability density functions of these random variables are defined based on random damage parameters given by the Marine Environment Protection Committee of the International Maritime Organization, while the proposed reliability formulation is consistent with international recommendations and thus may be valuable in the development of rules for accidental limit states. The methodology is applied on an example of an Aframax oil tanker. The proposed approach captures in a rational way complex interaction of different pertinent variables influencing safety of damaged ship structure.

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Bayesian Approach for Structural Reliability Analysis and Optimization Using the Kriging Dimension Reduction Method

Journal of Mechanical Design ◽

10.1115/1.4001377 ◽

2010 ◽

Vol 132 (5) ◽

Cited By ~ 21

Author(s):

Jooho Choi ◽

Dawn An ◽

Junho Won

Keyword(s):

Dimension Reduction ◽

Reliability Analysis ◽

Bayesian Approach ◽

Structural Reliability ◽

Reduction Method ◽

Epistemic Uncertainty ◽

Limit State ◽

State Function ◽

Dimension Reduction Method ◽

Structural Reliability Analysis

An efficient method for a structural reliability analysis is proposed under the Bayesian framework, which can deal with the epistemic uncertainty arising from a limited amount of data. Until recently, conventional reliability analyses dealt mostly with the aleatory uncertainty, which is related to the inherent physical randomness and its statistical properties are completely known. In reality, however, epistemic uncertainties are prevalent, which makes the existing methods less useful. In the Bayesian approach, the probability itself is treated as a random variable of a beta distribution conditional on the provided data, which is determined by conducting a double loop of reliability analyses. The Kriging dimension reduction method is employed to promote efficient implementation of the reliability analysis, which can construct the PDF of the limit state function with favorable accuracy using a small number of analyses. Mathematical examples are used to demonstrate the proposed method. An engineering design problem is also addressed, which is to find an optimum design of a pigtail spring in a vehicle suspension, taking material uncertainty due to limited test data into account.

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A modified downhill simplex algorithm interpolation response surface method for structural reliability analysis

Engineering Computations ◽

10.1108/ec-03-2019-0085 ◽

2019 ◽

Vol 37 (4) ◽

pp. 1423-1450

Author(s):

Hailiang Su ◽

Fengchong Lan ◽

Yuyan He ◽

Jiqing Chen

Keyword(s):

Reliability Analysis ◽

Response Surface ◽

Response Surface Method ◽

Structural Reliability ◽

Limit State ◽

Simplex Algorithm ◽

Content Type ◽

Structural Reliability Analysis ◽

Surface Method ◽

Downhill Simplex

Purpose Because of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM). Design/methodology/approach In DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis. Findings The computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy. Originality/value This paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

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