B. Kriegesmann¹, R. Rolfes¹, E. L. Jansen¹, I. Elishakoff², C. Hühne³, A. Kling³

CMC-Computers, Materials & Continua, Vol.32, No.3, pp. 177-200, 2012, DOI:10.3970/cmc.2012.032.177

Abstract Four different approaches for the design of axially compressed cylindrical shells are presented, namely (1) the knockdown factor (KDF) concept, (2) the single perturbation load approach, (3) a probabilistic design procedure and (4) the convex anti-optimization approach. The different design approaches take the imperfection sensitivity and the scatter of input parameters into account differently. In this paper, the design of a composite cylinder is optimized considering the ply angles as design variables. The KDF concept provides a very conservative design load and in addition an imperfection sensitive design, whereas the other approaches lead to a significantly less conservative design load… More >

C. Jiang^1,2, X. Han¹, D. Li³

CMC-Computers, Materials & Continua, Vol.27, No.3, pp. 275-304, 2012, DOI:10.3970/cmc.2011.027.275

Abstract For optimization or decision-making problems with interval uncertainty, the interval comparison relation plays a very important role, as only based on it a better or best decision can be determined. In this paper, a new kind of interval comparison relation termed as reliability-based possibility degree of interval is proposed to give quantitative evaluations on "how much better" of one interval than another, which is more suitable for engineering reliability analysis and numerical computation than the existing relations. In the new relation, the range of the comparing values is extended into the whole real number field, and the precise comparison is… More >

W. Zhang¹, X. Han^1,2, J. Liu¹, Z. H. Tan¹

CMC-Computers, Materials & Continua, Vol.26, No.3, pp. 201-226, 2011, DOI:10.3970/cmc.2011.026.201

Abstract The uncertainty inverse problems with insufficiency and imprecision in the input and/or output parameters are widely existing and unsolved in the practical engineering. The insufficiency refers to the partly known parameters in the input and/or output, and the imprecision refers to the measurement errors of these ones. In this paper, a combined method is proposed to deal with such problems. In this method, the imprecision of these known parameters can be described by probability distribution with a certain mean value and variance. Sensitive matrix method is first used to transform the insufficient formulation in the input and/or output to a… More >

Yong Li^1,*, Joel P. Conte², Philip E. Gill³

CMES-Computer Modeling in Engineering & Sciences, Vol.120, No.3, pp. 517-543, 2019, DOI:10.32604/cmes.2019.06269

Abstract In the field of earthquake engineering, the advent of the performance-based design philosophy, together with the highly uncertain nature of earthquake ground excitations to structures, has brought probabilistic performance-based design to the forefront of seismic design. In order to design structures that explicitly satisfy probabilistic performance criteria, a probabilistic performance-based optimum seismic design (PPBOSD) framework is proposed in this paper by extending the state-of-the-art performance-based earthquake engineering (PBEE) methodology. PBEE is traditionally used for risk evaluation of existing or newly designed structural systems, thus referred to herein as forward PBEE analysis. In contrast, its use for design purposes is limited… More >

Meng Li¹, Kanhua Su¹, Zijian Li², Dongjie Li³, Lifu Wan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.113, No.4, pp. 475-495, 2017, DOI:10.3970/cmes.2017.113.475

Abstract With the consideration of the randomness of complex geologic parameters for ultra-deep wells, an uncertainty analysis method is presented for the extrusion load on casing in ultra-deep wells through complex formation at a certain confidence level. Based on the extrusion load model for casing in ultra-deep wells and the prerequisite of integrity of formation-cement ring-casing, the probability and statistics theory is introduced and the sensitivity analysis on the uncertainty of extrusion load on casing is conducted. The distribution types of each formation parameters are determined statistically. The distribution type and distribution function of the extrusion load on casing are derived.… More >

J.C. Tang¹, C.M. Fu^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.113, No.3, pp. 239-259, 2017, DOI:10.3970/cmes.2017.113.249

Abstract In this paper, an efficient interval analysis method called dimension-reduction interval analysis (DRIA) method is proposed to calculate the bounds of response functions with interval variables, which provides a kind of solution method for uncertainty analysis problems of complex structures and systems. First, multi-dimensional function is transformed into multiple one-dimensional functions by extending dimension reduction method to the interval analysis problem. Second, all the one-dimensional functions are transformed to standard quadratic form by second order Taylor expansion method. As a result, the multi-dimensional function is approximately represented by the functions that each interval variable occurs once, and interval power arithmetic… More >

Rongxing Duan¹, Yanni Lin¹, Longfei Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.113, No.1, pp. 17-34, 2017, DOI:10.3970/cmes.2017.113.015

Abstract Fault tolerant technology has greatly improved the reliability of modern systems on one hand and makes their failure mechanisms more complex on the other. The characteristics of dynamics of failure, diversity of distribution and epistemic uncertainty always exist in these systems, which increase the challenges in the reliability assessment of these systems significantly. This paper presents a novel reliability analysis framework for complex systems within which the failure rates of components are expressed in interval numbers. Specifically, it uses a dynamic fault tree (DFT) to model the dynamic fault behaviors and copes with the epistemic uncertainty using Dempster- Shafer (D-S)… More >

Ryan Weisman³, Manoranjan Majji⁴, Kyle T. Alfriend⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.3, pp. 269-304, 2016, DOI:10.3970/cmes.2016.111.269

Abstract This paper presents a closed form solution to Liouville's equation governing the evolution of the probability density function associated with the motion of a body in a central force field and subject to J2. It is shown that the application of transformation of variables formula for mapping uncertainties is equivalent to the method of characteristics for computing the time evolution of the probability density function that forms the solution of the Liouville's partial differential equation. The insights derived from the nature of the solution to Liouville's equation are used to reduce the dimensionality of uncertainties in orbital element space. It… More >

V. Vittaldev¹, R. P. Russell²

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 83-117, 2016, DOI:10.3970/cmes.2016.111.083

Abstract Monte Carlo simulations are an accurate but computationally expensive procedure for approximating the resultant non-Gaussian probability density function (PDF) after propagation of an initial Gaussian PDF through a nonlinear function. Univariate splitting libraries for Gaussian Mixture Models (GMMs) exist with up to five elements in the literature. The number of splits are extended in the present work by generating three homoscedastic univariate splitting libraries with up to 39 elements. Mulitvariate GMMs are typically handled with splits along a single direction. Instead, we generate a regular multidirectional grid over the initial multivariate Gaussian distribution by recursively applying the splitting library along… More >

Di Wu¹, Wei Gao^1,2, Chongmin Song¹, Zhen Luo³

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.5, pp. 331-373, 2015, DOI:10.3970/cmes.2015.108.331

Abstract Two novel mathematical programming approaches are proposed to separately assess non-deterministic behaviour and stability of engineering structures against disparate uncertainties. Within the proposed computational schemes, uncertainties attributed by the material properties, loading regimes, as well as environmental influences are simultaneously incorporated and modelled by the interval approach. The proposed mathematical programming approaches proficiently transform the uncertain structural analyses into deterministic mathematical programs. Two essential aspects of structural analysis, namely linear structural behaviour and bifurcation buckling, have been explicitly investigated. Diverse verifications have been implemented to justify the accuracy and computational efficiency of the proposed approaches through practically motivated numerical examples. More >