On reliability analysis method through rotational sparse grid nodes

Abstract This study aims to develop a rotational sparse grid (R-SPGR) method for statistical moment evaluation and structural reliability analysis with enhanced accuracy and efficiency. The optimal rotational angle in the proposed R-SPGR method is determined by an optimization approach, in which the objective function is constructed in terms of discrepancy between the marginal moments of each input uncertain variables calculated from these rotational sparse grid nodes and their exact values. The R-SPGR nodes allow capturing more information of exact probability distribution for the system response, which is considered critically important to the calculation of statistical moments accurately. Following this, the probability density function (PDF) and failure probability of system response can be efficiently determined by using the saddlepoint approximation technique. To demonstrate the effectiveness of the proposed method, four benchmark examples, one structural analysis example and one practical example of industrial robot are provided here, in which the results obtained from the proposed R-SPGR method are compared with those calculated from the conventional sparse grid (SPGR) method, the maximum entropy problem with fractional moments (ME-FM) method and Monte Carlo simulation (MCS) method. From these illustrative examples involving a wide range of complexity, it is demonstrated that the proposed R-SPGR method has fairly high accuracy and efficiency for structural reliability analysis.

[1]  M. Pandey,et al.  Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method , 2013 .

[2]  Zhen Hu,et al.  First order reliability method for time-variant problems using series expansions , 2015 .

[3]  Jie Liu,et al.  Extending SORA method for reliability-based design optimization using probability and convex set mixed models , 2018, Structural and Multidisciplinary Optimization.

[4]  Baotong Li,et al.  Construction of probability box model based on maximum entropy principle and corresponding hybrid reliability analysis approach , 2020, Structural and Multidisciplinary Optimization.

[5]  Chao Dang,et al.  A novel hybrid cubature formula with Pearson system for efficient moment-based uncertainty propagation analysis , 2020, Mechanical Systems and Signal Processing.

[6]  Gang Li,et al.  An active weight learning method for efficient reliability assessment with small failure probability , 2020 .

[7]  A. Sudjianto,et al.  First-order saddlepoint approximation for reliability analysis , 2004 .

[8]  Zhonglai Wang,et al.  Time-dependent mechanism reliability analysis based on envelope function and vine-copula function , 2019, Mechanism and Machine Theory.

[9]  Jianbing Chen,et al.  Probability density evolution analysis of engineering structures via cubature points , 2012 .

[10]  Z. Zhang,et al.  A new uncertainty propagation method considering multimodal probability density functions , 2019, Structural and Multidisciplinary Optimization.

[11]  Shui Yu,et al.  Time-variant reliability assessment for multiple failure modes and temporal parameters , 2018 .

[12]  Xu Han,et al.  Kinematic Reliability Analysis of Robotic Manipulator , 2020, Journal of Mechanical Design.

[13]  Chao Dang,et al.  A new bivariate dimension reduction method for efficient structural reliability analysis , 2019 .

[14]  Tong Zhou,et al.  Adaptive Bayesian quadrature based statistical moments estimation for structural reliability analysis , 2020, Reliab. Eng. Syst. Saf..

[15]  M. Pandey,et al.  System reliability analysis of the robotic manipulator with random joint clearances , 2012 .

[16]  Gang Li,et al.  Maximum Entropy Method-Based Reliability Analysis With Correlated Input Variables via Hybrid Dimension-Reduction Method , 2019, Journal of Mechanical Design.

[17]  B. Keshtegar,et al.  A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis , 2018 .

[18]  Ying Xiong,et al.  A new sparse grid based method for uncertainty propagation , 2010 .

[19]  Xu Han,et al.  A Moment Approach to Positioning Accuracy Reliability Analysis for Industrial Robots , 2020, IEEE Transactions on Reliability.

[20]  Ming Jian Zuo,et al.  A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis , 2018, Reliab. Eng. Syst. Saf..

[21]  Bo Yu,et al.  An importance learning method for non-probabilistic reliability analysis and optimization , 2018, Structural and Multidisciplinary Optimization.

[22]  Zeng Meng,et al.  An active learning method combining Kriging and accelerated chaotic single loop approach (AK-ACSLA) for reliability-based design optimization , 2019 .

[23]  Gang Li,et al.  An improved maximum entropy method via fractional moments with Laplace transform for reliability analysis , 2018, Structural and Multidisciplinary Optimization.

[24]  Jie Liu,et al.  Forward and inverse structural uncertainty propagations under stochastic variables with arbitrary probability distributions , 2018, Computer Methods in Applied Mechanics and Engineering.

[25]  Liang Gao,et al.  A general failure-pursuing sampling framework for surrogate-based reliability analysis , 2019, Reliab. Eng. Syst. Saf..

[26]  Ning-Cong Xiao,et al.  Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables , 2020 .

[27]  S. Rahman,et al.  A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics , 2004 .

[28]  Sarangapani Jagannathan,et al.  Event-Sampled Output Feedback Control of Robot Manipulators Using Neural Networks , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Jie Liu,et al.  Evidence-Based Structural Uncertainty Quantification by Dimension Reduction Decomposition and Marginal Interval Analysis , 2020, Journal of Mechanical Design.

[30]  Qing Li,et al.  Robust optimization of foam-filled thin-walled structure based on sequential Kriging metamodel , 2014 .

[31]  João Cardoso,et al.  Review and application of Artificial Neural Networks models in reliability analysis of steel structures , 2015 .

[32]  Robert E. Melchers,et al.  General multi-dimensional probability integration by directional simulation , 1990 .

[33]  Zhonglai Wang,et al.  A general decoupling approach for time- and space-variant system reliability-based design optimization , 2019 .

[34]  Qiujing Pan,et al.  An efficient reliability method combining adaptive Support Vector Machine and Monte Carlo Simulation , 2017 .

[35]  B. Kang,et al.  Stochastic approach to kinematic reliability of open-loop mechanism with dimensional tolerance , 2010 .

[36]  Xu Han,et al.  A time-variant extreme-value event evolution method for time-variant reliability analysis , 2019, Mechanical Systems and Signal Processing.

[37]  B. Y. Ni,et al.  Uncertainty propagation analysis by an extended sparse grid technique , 2019 .

[38]  Yudong Zhang,et al.  A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications , 2015 .

[39]  Xiaoping Du,et al.  A Saddlepoint Approximation Based Simulation Method for Uncertainty Analysis , 2006 .

[40]  Xiaoping Du,et al.  Efficient reliability-based design with second order approximations , 2019 .

[41]  Chao Jiang,et al.  Parallelotope-formed evidence theory model for quantifying uncertainties with correlation , 2020 .

[42]  Mahesh D. Pandey,et al.  Computationally Efficient Reliability Analysis of Mechanisms Based on a Multiplicative Dimensional Reduction Method , 2014 .

[43]  Jie Liu,et al.  Time-Variant Reliability Analysis through Response Surface Method , 2017 .

[44]  Yan Zeng,et al.  A novel structural reliability analysis method via improved maximum entropy method based on nonlinear mapping and sparse grid numerical integration , 2019, Mechanical Systems and Signal Processing.

[45]  Liang Gao,et al.  A combined projection-outline-based active learning Kriging and adaptive importance sampling method for hybrid reliability analysis with small failure probabilities , 2019, Computer Methods in Applied Mechanics and Engineering.

[46]  D. Novák,et al.  CORRELATION CONTROL IN SMALL-SAMPLE MONTE CARLO TYPE SIMULATIONS I: A SIMULATED ANNEALING APPROACH , 2009 .

[47]  Hong-Zhong Huang,et al.  A novel single-loop procedure for time-variant reliability analysis based on Kriging model , 2019, Applied Mathematical Modelling.

[48]  T. N. Patterson.  Modified optimal quadrature extensions , 1993 .

[49]  Xu Han,et al.  New efficient and robust method for structural reliability analysis and its application in reliability-based design optimization , 2020 .

[50]  Jun He,et al.  A Sparse Grid Stochastic Collocation Method for Structural Reliability Analysis , 2014, 8th International Symposium on Reliability Engineering and Risk Management.

[51]  Dirk Nuyens,et al.  Quasi-Monte Carlo based uncertainty analysis: Sampling efficiency and error estimation in engineering applications , 2019, Reliab. Eng. Syst. Saf..

[52]  Hong-shuang Li,et al.  A sampling-based method for high-dimensional time-variant reliability analysis , 2019, Mechanical Systems and Signal Processing.

[53]  Chen Jiang,et al.  An active failure-pursuing Kriging modeling method for time-dependent reliability analysis , 2019, Mechanical Systems and Signal Processing.

[54]  Xiaoping Du,et al.  Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations , 2005, DAC 2005.

[55]  Minglu Zhang,et al.  Dynamic Parameter Identification for a Manipulator with Joint Torque Sensors Based on an Improved Experimental Design , 2019, Sensors.

[56]  Zeng Meng,et al.  A novel experimental data-driven exponential convex model for reliability assessment with uncertain-but-bounded parameters , 2020 .

[57]  Yan Wang,et al.  A Convex Optimization-Based Dynamic Model Identification Package for the da Vinci Research Kit , 2019, IEEE Robotics and Automation Letters.

[58]  Jun Xu,et al.  An adaptive trivariate dimension-reduction method for statistical moments assessment and reliability analysis , 2020, Applied Mathematical Modelling.

[59]  Jianbing Chen,et al.  Improving Point Selection in Cubature by a New Discrepancy , 2013, SIAM J. Sci. Comput..

[60]  Jing Liu,et al.  Time-variant reliability prediction for dynamic systems using partial information , 2020, Reliab. Eng. Syst. Saf..

[61]  Chao Dang,et al.  Efficient reliability analysis of structures with the rotational quasi-symmetric point- and the maximum entropy methods , 2017 .

[62]  Jun Xu,et al.  An efficient method for statistical moments and reliability assessment of structures , 2018, Structural and Multidisciplinary Optimization.

[63]  Hao Wu,et al.  A novel non-probabilistic reliability-based design optimization algorithm using enhanced chaos control method , 2017 .

[64]  Jan Swevers,et al.  Optimal robot excitation and identification , 1997, IEEE Trans. Robotics Autom..

[65]  C. Bucher.  Asymptotic sampling for high-dimensional reliability analysis , 2009 .

[66]  Hans Petter Langtangen,et al.  Chaospy: An open source tool for designing methods of uncertainty quantification , 2015, J. Comput. Sci..

[67]  Jie Liu,et al.  A computational framework of kinematic accuracy reliability analysis for industrial robots , 2020 .