Efficient response surface method for high-dimensional structural reliability analysis

Hadidi, Ali; Azar, Bahman Farahmand; Rafiee, Amin

doi:10.1016/j.strusafe.2017.03.006

Cited by 69 publications

(29 citation statements)

References 28 publications

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“…To reduce the number of fitting points, an adaptive interpolation scheme was proposed in [72], where a new centre point for interpolation is chosen on a straight line from the mean vector to the design point * obtained from the first constructed response surface: * * (22) This adaptive interpolation scheme ensures that the new center point is closer to the exact limit surface 0. The RSM has been continuously improved over the years, and the improvements include the adaptive iteration procedure [73], the gradient projection method to select sampling points [74], the coupled RSM and moment method [75], the adoption of the moving least-squares method for better response surface fitting [76], the use of exponential response surface [77], the artificial neural network based RSM and the support vector machine based RSM [78][79][80][81], among others.…”

Section: Response Surface Methodsmentioning

confidence: 99%

Structural reliability and stochastic finite element methods

Aldosary

Wang

2018

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Purpose This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely encountered in engineering practice, arising from such diverse sources as heterogeneity of materials, variability in measurement, lack of data and ambiguity in knowledge. Academia and industries have long been researching for uncertainty quantification (UQ) methods to quantitatively account for the effects of various input uncertainties on the system response. Despite the rich literature of relevant research, UQ is not an easy subject for novice researchers/practitioners, where many different methods and techniques coexist with inconsistent input/output requirements and analysis schemes. Design/methodology/approach This confusing status significantly hampers the research progress and practical application of UQ methods in engineering. In the context of engineering analysis, the research efforts of UQ are most focused in two largely separate research fields: structural reliability analysis (SRA) and stochastic finite element method (SFEM). This paper provides a state-of-the-art review of SRA and SFEM, covering both technology and application aspects. Moreover, unlike standard survey papers that focus primarily on description and explanation, a thorough and rigorous comparative study is performed to test all UQ methods reviewed in the paper on a common set of reprehensive examples. Findings Over 20 uncertainty quantification methods in the fields of structural reliability analysis and stochastic finite element methods are reviewed and rigorously tested on carefully designed numerical examples. They include FORM/SORM, importance sampling, subset simulation, response surface method, surrogate methods, polynomial chaos expansion, perturbation method, stochastic collocation method, etc. The review and comparison tests comment and conclude not only on accuracy and efficiency of each method but also their applicability in different types of uncertainty propagation problems. Originality/value The research fields of structural reliability analysis and stochastic finite element methods have largely been developed separately, although both tackle uncertainty quantification in engineering problems. For the first time, all major uncertainty quantification methods in both fields are reviewed and rigorously tested on a common set of examples. Critical opinions and concluding remarks are drawn from the rigorous comparative study, providing objective evidence-based information for further research and practical applications.

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Section: Response Surface Methodsmentioning

confidence: 99%

Structural reliability and stochastic finite element methods

Aldosary

Wang

2018

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“…This example is a polynomial with division, which is studied by many researchers [9,13,20,27,28]. Some of the results are shown in Table 3.…”

Section: Example Two: a Cantilevermentioning

confidence: 99%

“…Then the RSM, with Bucher experimental design, starts to work from the seedbed. Ali Hadidi et al [20] proposed an improved RSM with the exponential RSF instead of quadratic polynomial without cross terms. The sample points are selected through a novel approach and an experimental updating technique is applied.…”

Section: Introductionmentioning

confidence: 99%

Reliability Analysis on Structures Based on a Modified Iterative Response Surface Method

Wei

Bai

Wang

et al. 2018

Mathematical Problems in Engineering

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In order to improve the computational accuracy and efficiency of response surface method for reliability analysis on structures, a modified iterative response surface method (called as NDIRSM) is proposed. Firstly, a new starting center point, which is closer to design point, is calculated out as the starting center point instead of the point at mean values of input variables and a dynamic factor vector f1, which is inversely proportional to the change rate of performance function with respect to variance, is calculated out for the first iteration. Then the arbitrary factors fk are determined according to the design matrix condition number for the subsequent iteration. Thus the sample points are close to limit state function and the response surface function can approximate the limit state function accurately and efficiently. Two examples are employed to validate the advantages of NDIRSM and the results show that NDIRSM improves the computational accuracy and efficiency of response surface method. At last, NDIRSM is applied to the reliability analysis on low cycle fatigue life of a gas turbine disc, which provides a useful reference for reliability analysis on low cycle fatigue life of gas turbine disc and demonstrates the high computational accuracy and efficiency of NDIRSM.

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“…Response surface method (RSM) [4] is among the most popular surrogate models. Some researchers combine RSM with other approaches to refine the model parameters so that the model becomes more efficient [5]. Support vector machine (SVM) has also gained much attention recently.…”

Section: Introductionmentioning

confidence: 99%

Mechanical Reliability Assessment by Ensemble Learning

et al. 2020

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Reliability assessment plays a significant role in mechanical design and improvement processes. Uncertainties in structural properties as well as those in the stochatic excitations have made reliability analysis more difficult to apply. In fact, reliability evaluations involve estimations of the so-called conditional failure probability (CFP) that can be seen as a regression problem taking the structural uncertainties as input and the CFPs as output. As powerful ensemble learning methods in a machine learning (ML) domain, random forest (RF), and its variants Gradient boosting (GB), Extra-trees (ETs) always show good performance in handling non-parametric regressions. However, no systematic studies of such methods in mechanical reliability are found in the current published research. Another more complex ensemble method, i.e., Stacking (Stacked Generalization), tries to build the regression model hierarchically, resulting in a meta-learner induced from various base learners. This research aims to build a framework that integrates ensemble learning theories in mechanical reliability estimations and explore their performances on different complexities of structures. In numerical simulations, the proposed methods are tested based on different ensemble models and their performances are compared and analyzed from different perspectives. The simulation results show that, with much less analysis of structural samples, the ensemble learning methods achieve highly comparable estimations with those by direct Monte Carlo simulation (MCS).

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Efficient response surface method for high-dimensional structural reliability analysis

Cited by 69 publications

References 28 publications

Structural reliability and stochastic finite element methods

Structural reliability and stochastic finite element methods

Reliability Analysis on Structures Based on a Modified Iterative Response Surface Method

Mechanical Reliability Assessment by Ensemble Learning

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