Time-dependent Reliability Research Articles

A single-loop Kriging coupled with subset simulation for time-dependent reliability analysis

Time-dependent reliability analysis (TRA) plays an important role in improving the validity and practicability of product reliability evaluation over an interested life interval. Conventional TRA for high-reliability product, however, requires tackling two main challenges: (1) the inaccurate analysis of small failure probability problem and (2) the computationally expensive time-variant performance function. In this paper, a single-loop Kriging coupled with subset simulation (SLK-co-SS) method is proposed to address these challenges. By introducing time-dependent intermediate failure events, the estimation of small failure probability is first converted into a product of larger condition probabilities, which can be estimated by a proposed most probable extreme value method based on the trained Kriging model. We then develop an improved maximum error-guided adaptive sampling strategy to sequentially train and update the Kriging model in every intermediate failure event. To make more training samples located at the high potential region of time-dependent limit state surface, the error-tolerance threshold of updating stopping criterion varies with the intermediate failure events. The comparison results on four examples demonstrate the good capability and applicability of proposed SLK-co-SS method.

Advanced surrogate-based time-dependent reliability analysis method by an effective strategy of reducing the candidate sample pool

Advanced surrogate-based time-dependent reliability analysis method by an effective strategy of reducing the candidate sample pool

Time-Dependent Reliability Analysis of Plate-Stiffened Prismatic Pressure Vessel with Corrosion

In this study, the structural reliability of plate-stiffened prismatic pressure vessels was analyzed over time. A reliability analysis was performed using a time-dependent structural reliability method based on the response surface method (RSM). The plate-stiffened prismatic pressure vessel had a rectangular cross-section with repeated internal load-bearing structures. For the structural analysis, this repeated structure was modeled as a strip, and a structural reliability analysis was performed to identify changes in the reliability index when general corrosion and pitting corrosion occurred in the outer shell. Pitting corrosion was assumed to be randomly distributed on the outer shell, and the reliability index according to the degree of pit (DOP) and time was analyzed. Analysis results confirmed that the change in the reliability index was larger when pitting corrosion was applied compared with when only general corrosion was applied. Additionally, it was confirmed that above a certain DOP, the reliability index was affected.

Parallel efficient global optimization method: A novel approach for time-dependent reliability analysis and applications

Time-dependent failure may result from material properties deterioration, random load, and other uncertain factors, which are widespread among practical engineering applications. However, in previous studies of time-dependent reliability analysis (TRA), parallel computing, which can speed up the optimization process significantly, has not been fully considered. Therefore, this study proposed a parallel efficient global optimization (PEGO) integrated with the adaptive Kriging-Monte Carlo simulation (AK-MCS) for the TRA problems. It was shown that the proposed method was superior to the existing TRA methods in computing efficiency and maintained a high accuracy to solve the high-dimension of the TRA problems. Besides, it exhibited an extensive application scope due to the excellent performances (i.e., efficiency, accuracy), which were verified via six representative cases, including four low-dimension and two high-dimension, by comparing with the existing TRA methods.

Time-dependent reliability analysis for a set of RC T-beam bridges under realistic traffic considering creep and shrinkage

Reinforced concrete bridges constitute the major part of existing bridges. The purpose of this paper is to present a serviceability evaluation methodology for RC bridges under probabilistic conditions. It will be based on analytical calculations with no need to complex modeling or advanced software. For this purpose, a realistic traffic model is simulated based on existing weigh-in-motion WIM data from some European sites. The probabilistic distributions of the time-dependent load effects, moment and deflection, are then deduced after hundreds of simulations. The degradation effects are introduced in the analysis by considering the concrete creep and shrinkage. A simplified model to introduce creep effect under variable traffic load is also proposed. The time dependent reliability indices are then calculated for a set of 21 simply supported RC T-beam bridges with varying parameters such as span lengths, number of girders, girder spacing and number of design lanes. The first order reliability method FORM, is used in the reliability calculation in order to evaluate the structural performance under the considered failure scenario.

Time-dependent reliability and optimal design of scraper chains based on fretting wear process

PurposeThis paper aims to present a dynamic reliability model of scraper chains based on the fretting wear process and propose a reasonable structural optimization method.Design/methodology/approachFirst, the dynamic tension of the scraper chain is modeled by considering the polygon effect of the scraper conveyor. Then, the numerical wear model of the scraper chain is established based on the tangential and radial fretting wear modes. The scraper chain wear process is introduced based on the diameter wear rate. Furthermore, the time-dependent reliability of scraper chains based on the fretting wear process is addressed by the third-moment saddlepoint approximation (TMSA) method. Finally, the scraper chain is optimized based on the reliability optimization design theory.FindingsThere is a correlation between the wear and the dynamic tension of the scraper conveyor. The unit sliding distance of fretting wear is affected by the dynamic tension of the scraper conveyor. The reliability estimation of the scraper chain with incomplete probability information is achieved by using the TMSA for the method needs only the first three statistical moments of the state variable. From the perspective of the chain drive system, the reliability-based optimal design of the scraper chain can effectively extend its service life and reduce its linear density.Originality/valueThe innovation of the work is that the physical model of the scraper chain wear is established based on the dynamic analysis of the scraper conveyor. And based on the physical model of wear, the time-dependent reliability and optimal design of scraper chains are carried out.

A new non-probabilistic time-dependent reliability model for mechanisms with interval uncertainties

This paper proposes a new non-probabilistic time-dependent reliability model for evaluating the kinematic reliability of mechanisms when the input uncertainties are characterized by intervals. Based on the introduction of the non-probabilistic interval process of motion error, the most probable point of an outcrossing is defined to transform the complicated time-dependent problem into a concisely time-independent problem. A non-probabilistic time-dependent reliability index is proposed to evaluate the kinematic reliability of various mechanisms, and two computational strategies are designed to calculate the index. Then, the proposed reliability model is applied to a numerical example, a typical four-bar linkage mechanism and a car rack-and-pinion steering linkage mechanism, to demonstrate the significance of the proposed reliability model. The results show that the proposed model provides an effective tool for making reliability evaluation of time-dependent problems.

Copula-based reliability and sensitivity analysis of aging dams: Adaptive Kriging and polynomial chaos Kriging methods

Time-dependent reliability and sensitivity analysis, in which the nature of demand, capacity and the limit state function varies over the life cycle of the structural system, is a challenging task. Meta-models are a suitable tool to construct inexpensive-to-evaluate and accurate surrogates in analysis of modern engineering problems. The paper’s contribution is threefold: First, the superiority of polynomial chaos Kriging (PCK) meta-model in terms of efficiency and accuracy is depicted in comparison to two other state-of-the-art methods in an explicit representation of a pilot gravity dam. Second, the problem of aging dams is analytically studied. Adaptive reliability approaches which benefit from Kriging and PCK meta-models are also investigated in a comparative analysis with classical reliability methods. Third, the importance of considering nonlinear dependency between random variables by copula theory is investigated under the reliability and sensitivity concepts. The results show that PCK meta-model can be used as an effective technique in uncertainty quantification (UQ) of dams. Furthermore, Kriging and PCK-assisted reliability methods can establish fairly accurate meta-models to perform reliability analysis in structural UQ with low computational efforts. Finally, the concept of UQ is propagated to ”dam class” in which the dam shape and its age are assumed to be variable. A generalized program is developed to assist dam owners and decision-makers in approximate failure probability estimation of gravity dams. This paper paves the road for global risk assessment of dams.

Maintenance Management Research of a Large-span Continuous Rigid Frame Bridge Based on Reliability Assessment by Using Strain Monitored Data

When the bridge components needing maintenance are the world problem at present, and the health monitoring system is considered to be a very helpful tool for solving this problem. In this paper, a large number of strain data acquired from the structural health monitoring system (SHMS) installed on a continuous rigid frame bridge are adopted to do reliability assessment. Firstly, a calculation method of punctiform time-dependent reliability is proposed based on the basic reliability theory, and introduced how to calculate reliability of the bridge by using the stress data transformed from the strain data. Secondly, combined with “Three Sigma” principle and the basic pressure safety reserve requirement, the critical load effects distribution function of the bridge is defined, and then the maintenance reliability threshold for controlling the unfavorable load state which appears in the early operation stage of this type bridge is suggested, and then the combination of bridge maintenance management and health monitoring system is realized. Finally, the transformed stress distribution certifies that the load effects of concrete bridges practically have a normal distribution; as for the concrete continuous rigid frame bridge with C50 strength grade concrete, the retrofit reliability threshold should be valued at 6.13. The methodology suggested in this article can help bridge engineers do effective maintenance of bridges, which can effectively extend the service life of the bridge and bring better economic and social benefits.

Time-Dependent Stress-Strength Reliability Model with Phase-Type Cycle Time Based on Finite Mixture Models

This paper deals with the estimation of the stress-strength reliability of time-dependent models. Suppose that a system is allowed to run continuously and is subjected to random stress at random time points. Then we can assume a decrease in the strength of the system during the completion of each run. Let the strength of the system decreases by a constant and the stress on the system increases by a constant over each run. Time taken for completion of a run is assumed to have continuous phase-type distribution, the initial strength of the system, as well as, initial stress on the system are assumed to have a finite mixture of either Weibull distributions or power transformed half logistic distributions. A detailed numerical illustration of the results is also carried out.

Time-Dependent Reliability Algorithm Based on Kriging and Monte Carlo

Time-Dependent Reliability Algorithm Based on Kriging and Monte Carlo

Time-dependent reliability of corroded circular steel tube structures: Characterization of statistical models for material properties

The tubular steel structure is one of the most commonly used structural forms exposed in corrosive environments and its structural reliability should be addressed accordingly. However, the materials properties of corroded steel tubes were implicitly represented by those of corroded steel plates in previous studies. Experimental data and reliability analysis regarding the properties of corroded steel tubes (rather than plates) are still inadequate for reliability study. In response to these issues, this study conducted 96 tensile tests with respect to the different degrees of corrosion in circular steel tubes. Results demonstrated that the fracture mode of the corroded steel coupons changed to brittle fracture, and the necking phenomenon in the failure area gradually disappeared. Ultimate strength, yield strength and corresponding strain were remarkably degraded, and the yield plateau shortened and even disappeared as the degree of corrosion increased. Moreover, normal distribution can represent the yield strength of corroded steel tubes, and this distribution was verified by five hypothesis tests in this study. The mean yield strength of corroded steel presented a quadratic declining tendency at increasing corrosion rates. The time-dependent reliability analysis of corroded steel tubes was conducted in two corrosion scenarios (i.e. atmospheric and marine environments) and six levels of applied loadings (reflecting different safety levels). Finally, a set of trial material safety factors for ensuring sufficient safety margin was assessed, which can provide a reference for related specifications of steel tube structures subjected to atmospheric corrosion and/or marine environments.

Time-dependent reliability analysis of recycled aggregate concrete beams

This paper investigates the time-dependent reliability of recycled aggregate concrete (RAC) beams made with 50% incorporation of recycled coarse aggregates. A basic method based on the series system model is adopted to calculate the reliability index, and the case studies show that the reliability index decreases with the service time: the reliability indices decrease from the values of 3.27 and 3.70 to 3.02 and 3.55 for RAC beams and normal aggregate concrete (NAC) beams during the service period of 50 years (target reliability index is 3.2 according to Chinese code) in the first case study, also indicating that the reliability index of RAC beams is lower than that of the NAC beams. Then, influencing factors such as the compressive strength , reinforcement ratio, thickness of concrete cover, carbonation rate and corrosion rate are analyzed based on a parametric study . All these factors affect the time to surface cracking and the time to reach the limit crack width of concrete cover. Finally, this investigation concludes that the methods, such as increasing the compressive strength or appropriately increasing the strength of concrete and reinforcement ratio at the same time, are feasible methods for meeting the requirements of the time-dependent reliability of concrete beams. • The reliability index of RAC beams is lower than that of NAC beams. • Factors influencing the reliability index of concrete beams are analyzed based on a parametric study. • Feasible methods for improving the time-dependent reliability of concrete beams are proposed.

An Efficient Library for Reliability Block Diagram Evaluation

Reliability Block Diagrams (RBDs) are widely used in reliability engineering to model how the system reliability depends on the reliability of components or subsystems. In this paper, we present librbd, a C library providing a generic, efficient and open-source solution for time-dependent reliability evaluation of RBDs. The library has been developed as a part of a project for reliability evaluation of complex systems through a layered approach, combining different modeling formalisms and solution techniques at different system levels. The library achieves accuracy and efficiency comparable to, and mostly better than, those of other well-established tools, and it is well designed so that it can be easily used by other libraries and tools.

Reliability assessment framework of deteriorating reinforced concrete bridges subjected to earthquake and pier scour

This study assesses the life-cycle probability of survival of a deteriorating reinforced concrete girder bridge subjected to earthquake and pier scour. Adopting a component level approach, the framework of reliability assessment of bridge is established for its service life. The framework is established by the following three steps: 1) establish the probabilistic models of natural hazards; 2) capture the responses of bridge subjected to multiple hazards using SAP2000; 3) utilize methods of time-dependent reliability to assess the probability of survival of the bridge during its service life. The result shows that comparing to the pier scour, deterioration affects the seismic fragility of the bridge more significantly; however, pier scour could lengthen the natural period of bridge, and reduce the seismic response of the bridge, when the scour depth is under a specific level. It would underestimate the effects of multi-hazard to consider the hazards individually, when the correlation of structural effects induced by multi-hazards is negative, and the effects could be overestimated when the correlation is positive. This study reveals the two types of the correlations for the seismic fragility analysis of the reinforced concrete bridge, which should be noticed when design and operate a bridge subjected to multi-hazard.

Time-Dependent Reliability Analysis of Reinforced Concrete Beams Subjected to Uniform and Pitting Corrosion and Brittle Fracture.

Reinforced concrete (RC) beams are basic elements used in the construction of various structures and infrastructural systems. When exposed to harsh environmental conditions, the integrity of RC beams could be compromised as a result of various deterioration mechanisms. One of the most common deterioration mechanisms is the formation of different types of corrosion in the steel reinforcements of the beams, which could impact the overall reliability of the beam. Existing classical reliability analysis methods have shown unstable results when used for the assessment of highly nonlinear problems, such as corroded RC beams. To that end, the main purpose of this paper is to explore the use of a structural reliability method for the multi-state assessment of corroded RC beams. To do so, an improved reliability method, namely the three-term conjugate map (TCM) based on the first order reliability method (FORM), is used. The application of the TCM method to identify the multi-state failure of RC beams is validated against various well-known structural reliability-based FORM formulations. The limit state function (LSF) for corroded RC beams is formulated in accordance with two corrosion types, namely uniform and pitting corrosion, and with consideration of brittle fracture due to the pit-to-crack transition probability. The time-dependent reliability analyses conducted in this study are also used to assess the influence of various parameters on the resulting failure probability of the corroded beams. The results show that the nominal bar diameter, corrosion initiation rate, and the external loads have an important influence on the safety of these structures. In addition, the proposed method is shown to outperform other reliability-based FORM formulations in predicting the level of reliability in RC beams.

Subset simulation-based reliability analysis of the corroding natural gas pipeline

In this study, a subset simulation-based methodology is developed to evaluate the time-dependent reliability of the corroding pipeline with multiple correlated corrosion defects. Two competing failure modes, namely small leak and burst, are considered in the methodology. Firstly, the time-dependent structural reliability model of the two competing failure modes is established. Then, the computational framework for implementing subset simulation for failure probability estimation of the individual corrosion defect is presented. Thereafter, a procedure to calculate the system reliability of the entire pipeline with correlated corrosion defects is proposed. Moreover, a numerical example based on a real natural gas pipeline is proposed, and the time-dependent failure probabilities of both the small leak and burst are predicted, which are compared with the evaluation results produced by the direct Monte Carlo simulation and Kriging method. By means of numerical example, the accuracy and efficiency of our methodology are demonstrated. Furthermore, a sensitivity analysis is performed to investigated the effect of the correlation of the corrosion defects on the system reliability, and the results indicate that the correlation exert great impact on system reliability.

Efficient and Comprehensive Time-Dependent Reliability Analysis of Complex Structures by a Parameter State Model

AbstractA major challenge in a time-dependent reliability analysis is to find a good balance between computational effort, accuracy, and comprehension of the analysis. In this contribution, computa...

An efficient importance sampling approach for reliability analysis of time-variant structures subject to time-dependent stochastic load

Structural performance is affected by deterioration processes and external loads. Both effects may change over time, posing a challenge for conducting reliability analysis. In such context, this contribution aims at assessing the reliability of structures where some of its parameters are modeled as random variables, possibly including deterioration processes, and which are subjected to stochastic load processes. The approach is developed within the framework of importance sampling and it is based on the concept of composite limit states, where the time-dependent reliability problem is transformed into a series system with multiple performance functions. Then, an efficient two-step importance sampling density function is proposed, which splits time-invariant parameters (random variables) from the time-variant ones (stochastic processes). This importance sampling scheme is geared towards a particular class of problems, where the performance of the structural system exhibits a linear dependency with respect to the stochastic load for fixed time. This allows calculating the reliability associated with the series system most efficiently. Practical examples illustrate the performance of the proposed approach.

Time-dependent reliability of (weighted) k-out-of-n systems with identical component deterioration

The performance of civil infrastructure systems is vital in supporting a community’s functionalities. Reliability assessment of these systems is a powerful approach to evaluate whether the system performance is desirably safe under the impacts of resistance degradation and non-stationary loads. A k-out-of-n system is a widely-used logic model for a system with n components, which survives (works) if at least k components work. Its special cases include a series or a parallel system. Furthermore, a weighted k-out-of-n system has components with positive integer weights and the system survives if the total weight of working components reaches the predefined threshold k. This paper proposes a method for estimating the time-dependent reliability of both ordinary and weighted k-out-of-n systems, taking into account the effects of resistance deterioration, resistance correlation and load non-stationarity, for which a mathematical solution is derived. The applicability of the proposed method is illustrated through reliability evaluation of a representative k-out-of-n system.