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reliability-based design in rock engineering: Application of Bayesian regression methods to rock strength data

Journal of Rock Mechanics and Geotechnical Engineering 2019年第3期11卷 612-627页

作者： Nezam Bozorgzadeh John P.Harrison Department of Civil Engineering GeoEngineering Centre at Queen’s-RMC(Royal Military College of Canada)KingstonCanada Department of Civil and Mineral Engineering University of TorontoTorontoCanada

reliability-based design (RBD) is being adopted by geotechnical design codes worldwide, and it is therefore necessary that rock engineering practice evolves to embrace RBD. This paper examines the Hoek-Brown (H-B) strength criterion within the RBD framework, and presents three distinct analyses using a Bayesian approach. Firstly, a compilation of intact compressive strength test data for six rock types is used to examine uncertainty and variability in the estimated H-B parameters m and σc, and corresponding predicted axial strength. The results suggest that within- and between-rock type variabilities are so large that these parameters need to be determined from rock testing campaigns, rather than reference values being used. The second analysis uses an extensive set of compressive and tensile (both direct and indirect) strength data for a granodiorite, together with a new Bayesian regression model, to develop joint probability distributions of m and σc suitable for use in RBD. This analysis also shows how compressive and indirect tensile strength data may be robustly used to fit an H-B criterion. The third analysis uses the granodiorite data to investigate the important matter of developing characteristic strength criteria. Using definitions from Eurocode 7, a formal Bayesian interpretation of characteristic strength is proposed and used to analyse strength data to generate a characteristic criterion. These criteria are presented in terms of characteristic parameters mk and σck, the values of which are shown to depend on the testing regime used to obtain the strength data. The paper confirms that careful use of appropriate Bayesian statistical analysis allows the H-B criterion to be brought within the framework of RBD. It also reveals that testing guidelines such as the International Society for Rock Mechanics and Rock Engineering (ISRM) suggested methods will require modification in order to support RBD. Importantly, the need to fully understand the implications of

关键词： reliability-based design(RBD) Hoek-Brown(HeB)criterion Bayesian regression Indirect tensile strength Characteristic strength criterion

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Novel decoupled framework for reliability-based design optimization of structures using a robust shifting technique

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Frontiers of Structural and Civil Engineering 2019年第4期13卷 800-820页

作者： Mohammad Reza GHASEMI Charles V. CAMP Babak DIZANGIAN Department of Civil Engineering University of Sistan and Baluchestan Zahedan *** Iran Department of Civil Engineering The University of Memphis Memphis TN 38152 USA Department of Civil Engineering Velayat University Iranshahr *** Iran

In a reliability-based design optimization (RBDO), computation of the failure probability (Pf) at all design points through the process may suitably be avoided at the early stages. Thus, to reduce extensive computations of RBDO, one could decouple the optimization and reliability analysis. The present work proposes a new methodology for such a decoupled approach that separates optimization and reliability analysis into two procedures which significantly improve the computational efficiency of the RBDO. This technique is based on the probabilistic sensitivity approach (PSA) on the shifted probability density function. Stochastic variables are separated into two groups of desired and non-desired variables. The three-phase procedure may be summarized as: Phase 1, apply deterministic design optimization based on mean values of random variables;Phase 2, move designs toward a reliable space using PSA and finding a primary reliable optimum point;Phase 3, applying an intelligent self-adaptive procedure based on cubic B-spline interpolation functions until the targeted failure probability is reached. An improved response surface method is used for computation of failure probability. The proposed RBDO approach could significantly reduce the number of analyses required to less than 10% of conventional methods. The computational efficacy of this approach is demonstrated by solving four benchmark truss design problems published in the structural optimization literature.

关键词： reliability-based design optimization trusses sensitivity analysis shifting technique cubic B-splines response surface method

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Efficient reliability-based Optimization Scheme for Piezoelectric Composite Beams with Delamination under Axial Compression

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Journal of Donghua University(English Edition) 2019年第3期36卷 239-246页

作者： BI Rengui LI Yingli ZHANG Zheng WU Shunxing College of Physics Mechanical and Electrical EngineeringJishou UniversityJishou 416000China School of Traffic and Transportation Engineering Central South UniversityChangsha 410075China

An efficient computational framework for reliability analysis and reliability-based design optimization of piezoelectric composite beam with delamination is *** the proposed approach,the transverse shear deformation,delamination and piezoelectricity of the beam are taken into *** introducing the Heaviside step function into the displacement components and using the Rayleigh-Ritz method,and the buckling governing equations for the piezoelectric composite beams is *** reliability of the beams is obtained by integrating the support vector machine method and first order reliability method,further the reliability-based optimization is executed through employing genetic *** effects of ply style,delamination length and voltage are discussed in *** results indicate that the comprehensive computational scheme provides a unified numerical framework to analysis the nondeterministic buckling and reliability efficiently.

关键词： piezoelectric composite beam delamination buckling reliability-based optimization support vector machine genetic algorithm

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Influence of rock property correlation on reliability analysis of rock slope stability: From property characterization to reliability analysis

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Geoscience Frontiers 2018年第6期9卷 1639-1648页

作者： Adeyemi Emman Aladejare Yu Wang Department of Architecture and Civil Engineering City University of Hong Kong

Cohesion(c) and friction angle(φ) of rock are important parameters required for reliability analysis of rock slope stability. There is correlation between c and φ which affects results of reliability analysis of rock slope stability. However, the characterization of joint probability distribution of c and φ through which their correlation can be estimated requires a large amount of rock property data, which are often not available for most rock engineering projects. As a result, the correlation between c and φ is often ignored or simply assumed during reliability studies, which may lead to bias estimation of failure probability. In probabilistic rock slope stability analysis, the influence of ignoring or simply assuming the correlation of the rock strength parameters(i.e., c and φ) on the reliability of rock slopes has not been fully investigated. In this study, a Bayesian approach is developed to characterize the correlation between c and φ, and an expanded reliability-based design(RBD) approach is developed to assess the influence of correlation between c and φ on reliability of a rock slope. The Bayesian approach characterizes the sitespecific joint probability distribution of c and φ, and quantifies the correlation between c and φ using available limited data pairs of c and φ from a rock project. The expanded RBD approach uses the joint probability distribution of c and φ obtained through the Bayesian approach as inputs, to determine the reliability of a rock slope. The approach gives insight into the propagation of the correlation between c and φ through their joint probability into the reliability analysis, and their influence on the calculated reliability of the rock slope. The approaches may be applied in practice with little additional effort from a conventional analysis. The proposed approaches are illustrated using real c and φ data pairs obtained from laboratory tests of fractured rock at Forsmark, Sweden.

关键词： reliability-based design Rock slope Correlation Failure probability Bayesian approach Joint probability distribution

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Iterative hybrid decoding algorithm for LDPC codes based on attenuation factor

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Frontiers of Electrical and Electronic Engineering in China 2012年第3期7卷 279-285页

作者： Minghua LIU Lijun ZHANG School of Electronic and Information Engineering Beijing JiaotongUniversity Beijing 100044 China

An attenuated iterative reliability-based major- ity-logic （AIML） decoding algorithm for low-density parity-check （LDPC） codes is proposed, which pertains to hybrid decoding schemes. The algorithm is devised based on the orthogonal check-sums of one-step majority- logic （OSMLG） decoding algorithm in conjunction with certain of reliability measures of the received symbols. Computation of reliability measure of the syndrome sum is refined by introducing an attenuation factor. Simulation results show that, in binary-input additive white Gaussian noise （BI-AWGN） channel, the AIML decoding algorithm outperforms other popular iterative reliability-based major- ity-logic （IML） decoding algorithms with a slight increase in computational complexity. Within maximum iteration number of 5, the AIML algorithm can achieve almost identical error performance to sum-product algorithm （SPA）. No error floor effect can be observed for the AIML algorithm down to the bit error rate （BER） of 10- s, while error floor appears for SPA around the BER of 10 7 even with maximum iteration number of 100. Furthermore, the inherent feature of parallel procession for AIML algorithm enforces the decoding speed in contrast to those serial decoding schemes, such as weighted bit-flipping （WBF） algorithm.

关键词： attenuation factor reliability-based iterative,majority-logic low-density parity-check (LDPC) codes

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