Time-dependent structural system reliability analysis model and its efficiency solution

Time-dependent structural systems (TDSSs) in engineering involve high dimensionality, nonlinearity, and complex uncertainties, complicating the reliability analysis compared to time-independent assessments. To address these challenges, this paper proposes an extremum-based back propagation neural network (BPNN) method for TDSS reliability analysis. The method adopts a double-loop structure. Specifically, the inner loop finds the minimum of the time-dependent performance function for a given realization of the random variables. This transformation converts the time-dependent problem into an equivalent time-invariant one. Then, the outer loop constructs a BPNN surrogate model to map the relationship between the random variables and the performance function minima. To improve computational efficiency, an adaptive sample selection strategy is integrated into the training process. This technique selects samples near the failure boundary to iteratively update the BPNN, ensuring high accuracy with a small training set. Once the stopping criterion is satisfied, the failure probability is estimated using Monte Carlo simulation (MCS). The trained BPNN model is used to rapidly predict the extremum for the large-scale sample pool. The proposed method is verified through three practical engineering cases: a four-bar mechanism, an aero-engine turbine disc, and a cantilever tube. Results show that the method remains accurate and efficient. The successful applications confirm the rationality and engineering applicability of the proposed model.

For structural reliability analysis with time-consuming performance functions, an innovative design of experiment (DoE) strategy of the Kriging model is proposed, which is named as the stepwise accuracy-improvement strategy. The epistemic randomness of the performance value at any point provided by the Kriging model is used to derive an accuracy measure of the Kriging model. The basic idea of the proposed strategy is to enhance the accuracy of the Kriging model with the best next point that has the largest improvement with regard to the accuracy measure. An optimization problem is developed to define the best next point. The objective function is the expectation that quantifies how much an untried point could enhance the accuracy of the Kriging model. Markov chain Monte Carlo sampling and Gauss–Hermite quadrature are employed to make several approximations to solve the optimization problem and get the best next point. A structural reliability analysis method is also constructed based on the proposed strategy and the accuracy measure employed. Several examples are studied. The results validate the advantages of the proposed DoE strategy.

Due to multiple implicit limit state functions needed to be surrogated, adaptive Kriging model for system reliability analysis with multiple failure modes meets a big challenge in accuracy and efficiency. In order to improve the accuracy of adaptive Kriging meta-model in system reliability analysis, this paper mainly proposes an improved AK-SYS by using a refined U learning function. The improved AK-SYS updates the Kriging meta-model from the most easily identifiable failure mode among the multiple failure modes, and this strategy can avoid identifying the minimum mode or the maximum mode by the initial and the in-process Kriging meta-models and eliminate the corresponding inaccuracy propagating to the final result. By analyzing three case studies, the effectiveness and the accuracy of the proposed refined U learning function are verified.

Time-dependent system reliability is computed as the probability that the responses of a system do not exceed prescribed failure thresholds over a time duration of interest. In this work, an efficient time-dependent reliability analysis method is proposed for systems with bivariate responses which are general functions of random variables and stochastic processes. Analytical expressions are derived first for the single and joint upcrossing rates based on the first-order reliability method (FORM). Time-dependent system failure probability is then estimated with the computed single and joint upcrossing rates. The method can efficiently and accurately estimate different types of upcrossing rates for the systems with bivariate responses when FORM is applicable. In addition, the developed method is applicable to general problems with random variables, stationary, and nonstationary stochastic processes. As the general system reliability can be approximated with the results from reliability analyses for individual responses and bivariate responses, the proposed method can be extended to reliability analysis of general systems with more than two responses. Three examples, including a parallel system, a series system, and a hydrokinetic turbine blade application, are used to demonstrate the effectiveness of the proposed method.

Direct differentiation method for response sensitivity analysis of a bounding surface plasticity soil model

The Kriging model has been widely explored in structural reliability analysis. Multiple sampling strategies combining the Kriging model are researched to alleviate the computational burden, especially in finite element analysis. In this paper, a novel sampling strategy is proposed to update the Design of Experiments (DoE) by combining Kriging and Maximin design. Maximin design is an experimental design to acquire a spatial distribution matrix. Benefiting from the characteristic of Maximin design, the spatial distance of the selected sample point is taken into account when updating the DoE. The selected sample points are evenly distributed in the sample space, which avoids excessive fitting of the Kriging model. Consequently, the proposed strategy requires relatively few points when constructing the Kriging model, to improve the efficiency of calculation while ensuring accuracy. An explicit example verifys the efficiency and accuracy of the sampling strategy, and a truss structure verifies the outperformance of the proposed method in calculating implicit performance functions.

After an outline of the concept of stochastic (probabilistic / statistical) dependence and of the corresponding models for the structural reliability analysis, two algorithms are presented which may be used in the reliability analysis / seismic risk assessment of structures whose failure can be represented in terms of chains of component or elementary failures. Both of them involve specific matriceal techniques.KeywordsFailure ModeFragility CurveStructural ReliabilityComponent FailureProbabilistic Risk AssessmentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Structural resistance deterioration is by nature a non-increasing stochastic process with autocorrelation on the temporal scale. The Gamma process is often used to describe the stochastic behavior of resistance deterioration. With Gamma-based deterioration models, the calculation of time-dependent reliability presents a serious challenge, and often Monte Carlo simulation is the only solution to this problem. This paper derives a closed-form solution for time-dependent reliability of aging structures, in which the resistance deterioration is described by a Gamma process and the applied load is modelled as a Gaussian process with a constant standard deviation. The accuracy of the proposed method is verified through a comparison with Monte Carlo simulation results, and its applicability is further illustrated in a time-dependent reliability analysis of an existing highway bridge whose vehicle load is modelled using weigh-in-motion (WIM) data. It is found that the measured vehicle load has a relatively small uncertainty, and the uncertainty associated with resistance deterioration is crucial to the reliability assessment because it dominates the overall uncertainty in the reliability calculation.

A probabilistic framework for durability assessment of concrete structures in marine environments was proposed in terms of reliability and sensitivity analysis, which takes into account the uncertainties under the environmental, material, structural and executional conditions. A time-dependent probabilistic model of chloride ingress was established first to consider the variations in various governing parameters, such as the chloride concentration, chloride diffusion coefficient, and age factor. Then the Nataf transformation was adopted to transform the non-normal random variables from the original physical space into the independent standard Normal space. After that the durability limit state function and its gradient vector with respect to the original physical parameters were derived analytically, based on which the first-order reliability method was adopted to analyze the time-dependent reliability and parametric sensitivity of concrete structures in marine environments. The accuracy of the proposed method was verified by comparing with the second-order reliability method and the Monte Carlo simulation. Finally, the influences of environmental conditions, material properties, structural parameters and execution conditions on the time-dependent reliability of concrete structures in marine environments were also investigated. The proposed probabilistic framework can be implemented in the decision-making algorithm for the maintenance and repair of deteriorating concrete structures in marine environments.

A Novel ESN-DeepONet and Kriging Double Layer Model for Time-dependent Reliability Analysis with Random Process

IntroductionMedication adherence is associated with a reduction of adverse outcomes in heart failure (HF). However, this association is complex to estimate accurately because adherence (exposure) can vary during the follow-up period. Adherence can be estimated as a fixed exposure to predict outcomes, and this is known as a landmark analysis. In contrast, adherence can also be estimated as a dynamic exposure which varies over time in the follow-up period. This is known as a time-varying analysis and is expected to be the more precise method.
 Objectives and ApproachWe compared these two methods in a HF cohort. We identified a population-based cohort of 3619 heart failure patients, aged 65-84 years hospitalised in Western Australia from 2003-2007 and who survived to 1-year post-discharge (landmark date). Adherence to renin-angiotensin system inhibitors (RASI) and β-blockers was calculated using proportion of days covered (PDC) expressed either as a fixed time exposure (in landmark analysis) or a varying exposure (in time-dependent analysis). The latter was updated every 30 days after the landmark date. Cox regression models were used to investigate the association between adherence and all-cause death at 1- and 3-years post-landmark date.
 ResultsFor 1-year outcomes, hazard ratios (HR) for every 10% increase in PDC were similar between models from landmark analyses (RASI adherence: 0.93, 0.90-0.97; β-blocker adherence: 0.96, 0.92-1.0) and time-dependent analyses (RASI adherence: 0.94, 0.91-0.97; β-blockers adherence: 0.95, 0.92 -0.99). However, 95% confidence intervals estimated from time-dependent models were narrower than those from landmark analyses. HRs were slightly closer to the null when estimated from time-dependent models. A similar pattern was seen with 3-year outcomes.
 Conclusion / ImplicationsTime-dependent analysis of adherence-outcome associations results in more precise estimates of hazard ratios. Estimates of HRs from landmark analysis models were similar but usually lower than those from time-dependent models.

An analytical method based on stochastic differential equations is presented for the stochastic damage and reliability analysis of hysteretic structures to earthquake excitations. The differential forms of hysteretic constitutive laws and of measures of structural damages are described. The time-dependent joint probability density function of seismic responses including the measures of damages as well as their statistics are evaluated. The seismic reliability functions are directly evaluated from the probability density functions of structural damages.

Failure-mode importance measures in structural system with multiple failure modes and its estimation using copula

The paper presents a hybrid active-learning approach for structural reliability analysis via adaptive Kriging surrogate models. The quasi first-order reliability method is first proposed for characteristic truncation point of a structural performance function. This is used to define a truncation boundary via the joint probability distribution function of input random variables. To reduce simulation time for new training samples, a U-function based criterion is further implemented to refine the candidate sample set. Since the reliability-based expected improvement function and U functions are combined together to evaluate new training samples, it finalizes a hybrid active-learning Kriging (HALK) to develop adaptive surrogate models for the structural reliability analysis. Several numerical examples are presented to demonstrate potential applications of the proposed HALK algorithm. Compared to benchmark results provided by the brutal force Monte-Carlo simulation method, the effectiveness of the HALK approach has been justified by dealing with various structural reliability problems.

Structural reliability analysis with fuzzy random variables using error principle