Time-variant reliability model and its measure index of structures based on a non-probabilistic interval process

Abstract

The study on reliability of an aging structure requires taking into account the influence of time. Typical approaches for performing time-variant reliability assessment are always based upon the random process model, where the dynamic distributions of uncertain parameters are determined by a substantial number of samples. In this paper, a new time-variant reliability measurement based on a non-probabilistic interval process model is proposed, in which we describe the time-varying uncertain variables at any time as intervals and define the corresponding auto-covariance function and correlation coefficient function to characterize the correlation between limit states at different times. By combining with the set-theory approach and the classical first-passage theory, a new non-probabilistic model of safety evaluation for time-dependent structures is established, and its measure index is then analytically calculated. The proposed model of timevariant reliability is suitable for both the cases of stationary process and non-stationary process. Moreover, the Monte Carlo method is also presented as a means of verification. The comparison between the presented model and the Monte Carlo-based model is eventually carried out on two application examples; the usage, efficiency and accuracy of the developed approach can be demonstrated.

Non-probabilistic time-dependent kinematic reliability assessment for function generation mechanisms with joint clearances

“…To obtain the time-dependent reliability of function generation mechanism, we need to propose the concept of interval process, and discuss the time-varying properties of interval process [32]. Considering that the motion error function e(a, θ) is an interval process, the upper and lower bounds of e(a, θ) are described as eða; θÞ and eða; θÞ.…”

Failure-based sealing reliability analysis considering dynamic interval and hybrid uncertainties

“…For the time 12 ,, , n tt t … , the joint distribution region composed of interval variables is a hypercube domain. Therefore, the uncertainty process is defined as a dynamic interval process [38].…”

“…In recent years, more and more engineers and statisticians have acquired and processed degradation data through the measurement of performance parameters of several products in order to predict their reliability. Mathematical and other solutions built on the basis of the reliability methodology are still up-to-date [22,41], especially when it is necessary to take into account a particular degree of uncertainty [22,38,46].…”

“…According to [10], different typologies of uncertainty and analysis, methods for reliability can be divided into two main categories: time-variant and time invariant methods. Therefore, the analysis of machines and devices reliability is focused on the identification and evaluation of various types of uncertainty, their effects and the assessment of the probability of a component failure [38].…”

Analytic Interval Prediction of Power System Dynamic under Interval Uncertainty

“…The analysis of interval disturbance has been widely studied in structural mechanics and many other systems [15]. When interval disturbance is injected, the system often has a complicated dynamic response which may affect the system security [16]. From a mathematical point of view, the interval model often needs to consider the solution of ordinary differential equations (ODE) with intervals, which is different from the SDE model and lacks a theoretical basis [17]- [20].…”