Interval K-L expansion of interval process model for dynamic uncertainty analysis

Ni, Bingyu; Jiang, Chao; Li, J.W.; Tian, Wenya

doi:10.1016/j.jsv.2020.115254

Cited by 27 publications

(9 citation statements)

References 38 publications

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“…Jiang et al (2019a, b) have made significant improvements to the interval process model and the nonrandom vibration analysis method, improving its applicability in the engineering field. Ni et al (2020) developed a novel expansion method for the interval process model by reference to the Karhunen-Lo eve (K-L) expansion for stochastic process and random field models. The dynamic reliability analysis method based on stochastic process discretization and its improved method is explored by Jiang et al (2014aJiang et al ( , b, 2018.…”

Section: Monte Carlomentioning

confidence: 99%

“…(2019a, b) have made significant improvements to the interval process model and the nonrandom vibration analysis method, improving its applicability in the engineering field. Ni et al. (2020) developed a novel expansion method for the interval process model by reference to the Karhunen-Loève (K-L) expansion for stochastic process and random field models.…”

Section: Dynamic Reliability Analysis Of Single-objective Structurementioning

confidence: 99%

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Structural dynamic reliability analysis: review and prospects

Teng

Feng

Chen

et al. 2022

IJSI

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PurposeThe purpose of this paper is to briefly summarize and review the theories and methods of complex structures’ dynamic reliability. Complex structures are usually assembled from multiple components and subjected to time-varying loads of aerodynamic, structural, thermal and other physical fields; its reliability analysis is of great significance to ensure the safe operation of large-scale equipment such as aviation and machinery.Design/methodology/approachIn this paper for the single-objective dynamic reliability analysis of complex structures, the calculation can be categorized into Monte Carlo (MC), outcrossing rate, envelope functions and extreme value methods. The series-parallel and expansion methods, multi-extremum surrogate models and decomposed-coordinated surrogate models are summarized for the multiobjective dynamic reliability analysis of complex structures.FindingsThe numerical complex compound function and turbine blisk are used as examples to illustrate the performance of single-objective and multiobjective dynamic reliability analysis methods. Then the future development direction of dynamic reliability analysis of complex structures is prospected.Originality/valueThe paper provides a useful reference for further theoretical research and engineering application.

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Section: Monte Carlomentioning

confidence: 99%

Section: Dynamic Reliability Analysis Of Single-objective Structurementioning

confidence: 99%

Structural dynamic reliability analysis: review and prospects

Teng

Feng

Chen

et al. 2022

IJSI

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“…Up to now, most of the existing methods are only applicable for linear systems. For nonlinear systems, except MC simulation [30], only a Karhunen-Loève (K-L) expansion method [31] has been proposed, in which an interval process in time domain is described by superposition of infinite deterministic time-related functions with uncorrelated interval coefficients. For an interval process with weak time-correlation and long-duration, the K-L method may be computationally prohibitive due to 'dimension disaster'.…”

Section: Introductionmentioning

confidence: 99%

A novel linear uncertainty propagation method for nonlinear dynamics with interval process

Zhang

et al. 2022

Nonlinear Dyn

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Interval process is a preferable model for time-varying uncertainty propagation of dynamic systems when only the range of uncertainties can be obtained. However, for nonlinear systems, except Monte Carlo (MC) simulation, there are still few efficient uncertainty propagation methods under the interval process model. This paper develops a non-intrusive and semi-analytical uncertainty propagation method, named 'Convex Model Linearization Method (CMLM)', by constructing a linearization formulation of a nonlinear system in a non-probabilistic sense. First, the criterion to evaluate the difference between the original system and the linearization formulation is derived, represented by discrepancy of middle-point, radius, and correlations of response. By minimizing these three parameters, the coefficients of linear equations will be optimized to obtain the linearization formulation of the original system. Then, the analytical equations are built to calculate uncertainty response under the interval process, without time-consuming analysis of the original system. To further improve the efficiency of the linearization process, Chebyshev-polynomial is introduced to approximate the nonlinear dynamic analysis. Two numerical examples that duffing oscillator and vehicle ride are set to tested the proposed CMLM. Compared to MC method, with comparable uncertainty response precision, the CMLM just need 1%-10% times of dynamic analysis of the nonlinear system. Furthermore, a practical launch vehicle ascent trajectory problem with black-box dynamics is solved by, respectively, the CMLM and MC method. The results verify the capacity of the CMLM to deal with black-box problems and show that the CMLM performs better in terms of accuracy, efficiency and robustness.

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“…Also, other expansions can be used as an Expansion Optimal Linear Estimator [20]. This approach is applied on several cases, e.g., structural dynamics [21,22], electromagnetic [23] and a Euler-Bernoulli beam [24].…”

Section: Introductionmentioning

confidence: 99%