Harmonic transform-based non-parametric density estimation method for forward uncertainty propagation and reliability analysis

Cai, 2022, An equivalent expectation evaluation method for approximating the probability distribution of performance functions, Struct Saf, 95, 10.1016/j.strusafe.2021.102180 Zhao, 2001, Moment methods for structural reliability, Struct Saf, 23, 47, 10.1016/S0167-4730(00)00027-8 Napa-García, 2017, Reliability analyses of underground openings with the point estimate method, Tunn Undergr Space Technol, 64, 154, 10.1016/j.tust.2016.12.010 Zhao, 2000, New point estimates for probability moments, J Eng Mech, 126, 433, 10.1061/(ASCE)0733-9399(2000)126:4(433) Xu, 2004, A generalized dimension-reduction method for multidimensional integration in stochastic mechanics, Internat J Numer Methods Engrg, 10.1002/nme.1135 Chao-Huang, 2019, Efficient algorithm for evaluation of statistical moments of performance functions, J Eng Mech, 145 Rahman, 2004, A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics, Probab Eng Mech, 19, 393, 10.1016/j.probengmech.2004.04.003 Xu, 2004, A generalized dimension-reduction method for multidimensional integration in stochastic mechanics, Internat J Numer Methods Engrg, 10.1002/nme.1135 Zhang, 2021, Efficient reliability analysis with a CDA-based dimension-reduction model and polynomial chaos expansion, Comput Methods Appl Mech Engrg, 373, 10.1016/j.cma.2020.113467 He, 2019, A novel structural reliability analysis method via improved maximum entropy method based on nonlinear mapping and sparse grid numerical integration, Mech Syst Signal Process, 133, 10.1016/j.ymssp.2019.106247 Choi, 2010, The Hermite moment model for highly skewed response with application to tension leg platforms, J Offshore Mech Arct Eng, 132, 950, 10.1115/1.4000398 Zhang, 2019, Unified Hermite polynomial model and its application in estimating non-Gaussian processes, J Eng Mech, 145, 10.1061/(ASCE)EM.1943-7889.0001577 Huang, 2008, Probabilistic uncertainty analysis by mean-value first order saddlepoint approximation, Reliab Eng Syst Saf, 93, 325, 10.1016/j.ress.2006.10.021 Guo, 2014, An efficient third-moment saddlepoint approximation for probabilistic uncertainty analysis and reliability evaluation of structures, Appl Math Model, 38, 221, 10.1016/j.apm.2013.06.026 Lu, 2020, An improved high order moment-based saddlepoint approximation method for reliability analysis, Appl Math Model, 82, 836, 10.1016/j.apm.2020.02.006 Karl, 1895, Contributions to the mathematical theory of evolution. II. Skew variation in homogeneous material, Philos Trans R Soc Lond Low, 2013, A new distribution for fitting four moments and its applications to reliability analysis, Struct Saf, 42, 12, 10.1016/j.strusafe.2013.01.007 Tagliani, 2013, Determination of the probability of ultimate ruin by maximum entropy applied to fractional moments, Insurance Math Econom, 53, 457, 10.1016/j.insmatheco.2013.07.011 Xu, 2017, Efficient reliability analysis of structures with the rotational quasi-symmetric point- and the maximum entropy methods, Mech Syst Signal Process, 95, 58, 10.1016/j.ymssp.2017.03.019 He W, Zeng Y, Li G. A novel structural reliability analysis method via improved maximum entropy method based on nonlinear mapping and sparse grid numerical integration - ScienceDirect. Mech Syst Signal Process 133:106247–106247. Zhang, 2013, Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method, Struct Saf, 43, 28, 10.1016/j.strusafe.2013.03.001 Xu, 2016, A new method for reliability assessment of structural dynamic systems with random parameters, Struct Saf, 60, 130, 10.1016/j.strusafe.2016.02.005 Xu, 2019, A novel fractional moments-based maximum entropy method for high-dimensional reliability analysis, Appl Math Model, 75, 749, 10.1016/j.apm.2019.06.037 Li, 2018, An improved maximum entropy method via fractional moments with Laplace transform for reliability analysis, Struct Multidiscip Optim, 59 Zhang, 2020, Maximum entropy distribution with fractional moments for reliability analysis, Struct Saf, 83, 10.1016/j.strusafe.2019.101904 McCloud, 2020, Determining the number of effective parameters in kernel density estimation, Comput Statist Data Anal, 143, 10.1016/j.csda.2019.106843 Majdara, 2019, Nonparametric density estimation using copula transform, Bayesian sequential partitioning and diffusion-based kernel estimator, IEEE Trans Knowl Data Eng, PP, 1 Pan, 2022, Research on output distribution modeling of photovoltaic modules based on kernel density estimation method and its application in anomaly identification, Sol Energy, 235, 1, 10.1016/j.solener.2022.02.020 Bhattacharya, 2008, Higher order moments generation by mellin transform for compound models of clutter, Comput Sci Matteo, 2014, Probabilistic characterization of nonlinear systems under Poisson white noise via complex fractional moments, Nonlinear Dynam, 77, 10.1007/s11071-014-1333-1 Cottone, 2010, Fractional calculus approach to the statistical characterization of random variables and vectors, Phys A, 389, 909, 10.1016/j.physa.2009.11.018 Di Paola, 2014, Fokker Planck equation solved in terms of complex fractional moments, Probab Eng Mech, 38, 70, 10.1016/j.probengmech.2014.09.003 Dai, 2018, An improved complex fractional moment-based approach for the probabilistic characterization of random variables, Probab Eng Mech, 53, 52, 10.1016/j.probengmech.2018.05.005 Li, 2006, The dimension-reduction strategy via mapping for probability density evolution analysis of nonlinear stochastic systems, Probab Eng Mech, 21, 442, 10.1016/j.probengmech.2006.02.004 Li, 2009 Wan, 2020, An efficient new PDEM-COM based approach for time-variant reliability assessment of structures with monotonically deteriorating materials, Struct Saf, 82, 10.1016/j.strusafe.2019.101878 Peng, 2021, Surrogate modeling immersed probability density evolution method for structural reliability analysis in high dimensions, Mech Syst Signal Process, 152, 10.1016/j.ymssp.2020.107366 Li, 2008, The principle of preservation of probability and the generalized density evolution equation, Struct Saf, 30, 65, 10.1016/j.strusafe.2006.08.001 Chen, 2019, Direct probability integral method for stochastic response analysis of static and dynamic structural systems, Comput Methods Appl Mech Engrg, 357, 10.1016/j.cma.2019.112612 Cottone, 2009, Fractional calculus approach to the statistical characterization of random variables and vectors, Physica A, 389, 909, 10.1016/j.physa.2009.11.018 Chen, 2016, A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters, Struct Saf, 59, 20, 10.1016/j.strusafe.2015.11.001 Marelli S, Sudret B. UQLab: A Framework for Uncertainty Quantification in Matlab. In: Int conf on vulnerability, risk analysis & management. 2014, p. 2554–63. Yang, 2014, Reliability analysis of structures with complex limit state functions using probability density evolution method, Struct Multidiscip Optim, 50, 275, 10.1007/s00158-014-1048-4 Zhou, 2019, A new surrogate modeling method combining polynomial chaos expansion and Gaussian kernel in a sparse Bayesian learning framework, Internat J Numer Methods Engrg, 120 Xu, 2022, An adaptive mixture of normal-inverse Gaussian distributions for structural reliability analysis, J Eng Mech, 148, 10.1061/(ASCE)EM.1943-7889.0002088 Chao DA, Jxa B. A mixture distribution with fractional moments for efficient seismic reliability analysis of nonlinear structures. Eng Struct 208. Wen, 1976, Method for random vibration of hysteretic systems, J Eng Mech Div, 102, 249, 10.1061/JMCEA3.0002106 Wen, 1980, Equivalent linearization for hysteretic systems under random excitation, J Appl Mech, 47, 150, 10.1115/1.3153594 Chen, 2009, Partition of the probability-assigned space in probability density evolution analysis of nonlinear stochastic structures, Probab Eng Mech, 24, 27, 10.1016/j.probengmech.2007.12.017 Aurenhammer, 1991, Voronoi diagrams—a survey of a fundamental geometric data structure, ACM Comput Surv, 23, 345, 10.1145/116873.116880 Li, 2010 Li, 2021, Reliability analysis of structures with multimodal distributions based on direct probability integral method, Reliab Eng Syst Saf