Time-variant Structural Reliability Research Articles

Application of ANN for Estimating Time-Variant Structural Reliability of Reinforced Concrete Structures Using Approximate Approach

Application of ANN for Estimating Time-Variant Structural Reliability of Reinforced Concrete Structures Using Approximate Approach

An estimation variance reduction-guided adaptive Kriging method for efficient time-variant structural reliability analysis

Adaptive Kriging surrogate model is becoming an effective technique to significantly reduce the computational cost for time-variant reliability analysis (TRA). But the existing Kriging adaptive sampling methods for TRA do not consider the correlation between time trajectories and the maximum error-based stopping criterion may be too conservative, both of which will waste some computationally expensive samples. To address the challenges, we propose an estimation variance reduction-guided adaptive Kriging method (VARAK) in this paper. Firstly, we derive the expression for estimation variance of time-variant failure probability and quantify the contribution of a time trajectory to the estimation variance, which includes not only the individual contribution of the time trajectory but also the contribution of correlation between time trajectories. Based on this, the adaptive sampling strategy selects the candidate that has the maximum contribution to the estimation variance as the new training sample, thereby resulting in high efficiency. To accelerate the training approach, the well-known U function is utilized to identify time trajectories with large uncertainty. Moreover, by taking the Kriging prediction uncertainty into account, a new error-based stopping criterion that approximates the relative error between the estimated time-variant failure probability and its expectation is proposed. Since the computation of the proposed stopping criterion may be time-consuming at the initial stage of the adaptive sampling approach, we use the maximum relative error to identify the initial stage and only calculate the stopping criterion after this stage. Four case studies including three numerical examples and an engineering example are presented to demonstrate the good capability and applicability of the proposed VARAK method. The examples illustrate that VARAK can allow the estimated failure probability to converge to the true value at a fast rate with small fluctuations and the procedure can terminate appropriately to avoid oversampling when accuracy is high enough.

Roles of load temporal correlation and deterioration-load dependency in structural time-dependent reliability

Aging of structural performance and significant external loads may impair structural safety and serviceability and cause potential economic losses. In the presence of uncertainties associated with both resistance deterioration and external loads, structural safety shall be estimated quantitatively under a probability-based framework. A stochastic load process is often auto-correlated on the temporal scale, with correlations arising from both the occurrence times and intensities. Moreover, a deterioration process is physically dependent on the load magnitudes. This paper investigates the impacts of load temporal correlation and deterioration-load dependency on time-variant structural reliability. The load occurrence process is modeled as a Poisson point process with correlated separation time between two load events. The correlation between the intensities of load events is described by the multi-variate Gaussian copula function. The resistance aging process is considered to be a combination of both gradual and shock deteriorations. Four candidate copula functions, namely Gaussian, Clayton, Gumbel and Frank, are considered to model the dependency of shock deterioration on load intensity. Two types of failure mechanisms are considered: the first is due to the load effect exceeding the resistance, and the second occurs when the cumulative damage within the considered service period reaches the permissible level. A simulation-based method is developed to estimate structural reliability considering the two failure modes. Illustrative examples are presented to demonstrate the applicability of the proposed method. Parametric studies are conducted to investigate the impacts of temporal correlation in loads and deterioration-load dependency on structural failure probability.

Effects of the axial force eccentricity on the time-variant structural reliability of aging r.c. cross-sections subjected to chloride-induced corrosion

Reinforced concrete structures are generally affected by degradation phenomena, which may include changes in strength and stiffness beyond the baseline conditions which are assumed in structural design. Some of these aging effects may cause component or system strengths to degrade over time, particularly when the concrete is exposed to an aggressive environment which may increase the risk of structural failure. For r.c. structures, due to the uncertainties in material and geometrical properties, in the magnitude and distribution of the loads, in the physical parameters which define the deterioration process, the structural safety should realistically be considered time-variant. In this context, this paper implements a computational probabilistic approach to predict the time-evolution of the mechanical and geometrical properties of a r.c. structural element (i.e., bridge pier) subjected to corrosion-induced deterioration as a consequence of the diffusive attack of chlorides in order to evaluate its service life. Adopting appropriate degradation models of the material properties, concrete and reinforcing steel, as well as assuming appropriate probability density functions related to mechanical and deterioration parameters, the proposed sectional approach is based on Monte Carlo simulations in order to evaluate time-variant axial force-bending moment resistance domains, with the aim to estimate the time-variant reliability index β for different axial force eccentricity values. Finally, an application of the proposed methodology to estimate the expected lifetime of a deteriorating r.c. bridge pier is described and discussed.

Time-variant reliability analysis considering parameter uncertainties

It has been realised that the effect of system parameter uncertainties may be very important, even dominant, in time-variant structural reliability. In this study, currently available methods are reviewed, and general performance functions corresponding to dynamic reliability analysis considering parameter uncertainties are investigated. A moment method for time-variant reliability analysis considering parameter uncertainties is developed, and its application is demonstrated through reliability assessment of a prestressed concrete containment. Point estimation is applied to evaluate the first few moments of the general performance function of a structure, from which the moment-based reliability index based on the fourth moment standardisation function can be evaluated without Monte Carlo simulations. The procedure does not require the computation of derivatives or the determination of the design point; thus, it should be computationally effective for time-variant structural reliability assessment.

Feasibility of FORM in finite element reliability analysis

The context for this paper is the growing need for reliability analysis in conjunction with advanced finite element models. This type of analysis is useful in many civil engineering applications to account for uncertainties by estimating the probability of response events, with all input parameters given as random variables. Compared with traditional structural reliability applications, such analyses carry unique opportunities and challenges. In this paper, emphasis is placed on the first-order reliability method due to its appealing tradeoff between accuracy and computational efficiency. The viability of this reliability method is studied in the context of both static and dynamic finite element problems. For static problems, a list of hypotheses is put forward to help the analyst identify potential pitfalls and remedies. Additional challenges appear in dynamic problems. In this paper, a novel limit-state formulation is considered in conjunction with dynamic loading and inelastic material models. The formulation is based on cumulative response measures, which arguably are the governing measures of structural performance in many applications. The new approach effectively addresses the time-variant structural reliability problem.

Time-variant structural reliability analysis using bivariate diffusive crack growth models

A method to estimate the reliability of structural components by which the time-variant properties of the structural resistance are taken into account is presented. Among the various deterioration mechanisms, which may cause this time variance, the present paper concentrates on the fatigue process, which is described by a bivariate diffusive surface crack growth model. The probability density function of the crack growth is derived by solving a Fokker-Planck-type equation. For updating the hazard rate following load applications, importance sampling simulation procedures are employed. The method is then applied to a piping problem. A sensitivity analysis shows the initial crack size as well as the loading stress amplitude to affect the reliability estimates most significantly.