Reliability sensitivity of multi-degree-of-freedom uncertain nonlinear systems with independent failure modes

Zhang, Yimin; Liu, Qiaoling; Wen, Bangchun

doi:10.1007/bf03027067

Cited by 9 publications

(6 citation statements)

References 6 publications

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“…According to References, 35,36,[40][41][42] the arbitrary distribution function of standard random variable Y can be closely represented by the standard normal distribution function via Edgeworth series…”

Section: Reliability Analysis Methods Of Matched Bearingsmentioning

confidence: 99%

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Dynamic reliability analysis of angular contact ball bearings in positioning precision

Zhang

2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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Bearings are the core components in various kinds of rotating machineries. With the increasing demand of reliable bearings in precision equipment, it is of great significance to analyze the motion error of bearings. In this article, a nonlinear dynamic model of angular contact ball bearings installed in pairs is constructed to describe its response characteristics. The definition of a failure mode in matched bearings is that the dynamic response of each inner race is larger than the allowed axial runout. This article introduces a feasible approach to evaluate the reliability of positioning precision of matched bearings with random geometric parameters. The statistical moments of dynamic response are calculated using stochastic perturbation method. The probability distribution function of state function relating to positioning precision is approached by Edgeworth series, from which the reliability and sensitivity are obtained. A pair of 7206B bearings is taken as an application instance of the proposed method. Monte Carlo simulation is employed to provide a benchmark on which to verify the precision and efficiency of the proposed method. In addition, the effects of mean values and variances of random geometric parameters on the positioning precision are analyzed, respectively.

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Section: Reliability Analysis Methods Of Matched Bearingsmentioning

confidence: 99%

“…where Φ ( · ) and φ ( · ) are the probability distribution function and probability density function of standard normal distribution, respectively. H 2 ( Y ) , H 3 ( Y ) and H 5 ( Y ) are the Hermit polynomials, 42 and their recurrence relations are listed as below…”

Section: Dynamic Reliability Model Of Matched Bearingsmentioning

confidence: 99%

Dynamic reliability analysis of angular contact ball bearings in positioning precision

Zhang

2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…Song et al [12] developed a method based on a matrix to transform the solution of system reliability into matrix operation and analyzed the sensitivity of each distributed parameter under system reliability on this basis. Zhang et al [13][14][15] dealt with the reliability sensitivity problem of single degree-of-freedom nonlinear vibration systems with random parameters and put forward a numerical method for reliability sensitivity analysis of mechanical parts with multiple failure modes. Yuan et al [16] developed two reliability sensitivity analysis methods under the non-normal random variables for non-linear limit state equations.…”

Section: Introductionmentioning

confidence: 99%

Dynamic reliability sensitivity analysis for inter-story isolation structure under stochastic excitations

Zhang¹,

Liu²,

Xiao³

et al. 2020

J. vibroeng.

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Considering the uncertainties of seismic excitation and stochastic parameters of the Inter-story Isolation Structure, the implicit structural response function is transformed into an explicit one by the Stochastic Response Surface Method (SRSM), combined with a probabilistic collocation method based on the linear independence principle. By using the reliability analysis method based on the first-passage failure, the reliability of isolation structure is analyzed and the sensitivity of the reliability of each sub-structure is further analyzed. The results show that conducting sensitivity research based on reliability analysis can provide an important theoretical basis for an optimized and robust design of a random vibration system. The changes of the stiffness and damping ratio of the Isolation Layer have a great influence on the reliability of the system and have different effects on the reliability of different parts of the system. The analysis results of reliability sensitivity could provide system reliability indexes to rank stochastic parameters by their importance, thus improving the efficiency of the structure reliability analysis and optimization design.

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“…7–9 In order to assess the effects of the uncertain parameters on the reliability of the vibration systems and to determine the main factors influencing the systems reliability, structural reliability sensitivity analysis methods have been widely applied. 10–13 A source of difficulties for solving the vibration reliability and reliability sensitivity problems by means of approximate methods, for example, first-order reliability method (FORM) and second-order reliability method (SORM), is the structural nonlinearity. It is due to the fact that the surrogate of the limit state functions built by approximate methods may be inaccurate when the systems have strong nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

Study on the application of dimensionality reduction method on reliability and reliability sensitivity analysis of random vibration systems

Sun

Yan

et al. 2015

Advances in Mechanical Engineering

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The application of dimensionality reduction method on the reliability and reliability sensitivity analysis of vibration systems was examined. The dimensionality of a vibration reliability problem was reduced to only two independent dimensions by the means of polar transformation. As the safe and failure classes of samples are clearly distinguishable and occupy a standard position in a two-dimensional plot in the case that the important direction exists, the relevant samples are selected visually. The reliability and reliability sensitivity problems were solved using the position of the relevant samples. Before the reliability and reliability sensitivity estimation, an essential visualization analysis is conducted to examine the capacity of the method in terms of the existence of the important direction which is used to reduce the dimensionality of the reliability problem. In order to calculate the design point correctly, the improved Hasofer-Lind-RackwitzFiessler method was extended with a procedure for determining the perturbation in the calculation of the gradient vector by finite differences according to the numerical precision of the limit state function. The dimensionality reduction method saves the numbers of calling limit state function a lot and has the same accuracy as Monte Carlo method. Examples involving single and multiple degree-of-freedom nonlinear vibration systems were used to demonstrate the approach.

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Reliability sensitivity of multi-degree-of-freedom uncertain nonlinear systems with independent failure modes

Cited by 9 publications

References 6 publications

Dynamic reliability analysis of angular contact ball bearings in positioning precision

Dynamic reliability analysis of angular contact ball bearings in positioning precision

Dynamic reliability sensitivity analysis for inter-story isolation structure under stochastic excitations

Study on the application of dimensionality reduction method on reliability and reliability sensitivity analysis of random vibration systems

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