Time-dependent Reliability Analysis Research Articles

Time-dependent reliability analysis for structures under multilevel loads based on fatigue damage theory

This paper proposes an efficient method to evaluate the time-dependent fatigue reliability of structures under complex multilevel loads using a finite set of fatigue test data obtained under single-level loading conditions. The method preserves the simplicity of linear damage accumulation theory while considering the interactions among multiple load levels and the influence of load sequence on reliability. Leveraging the linear damage rule, a cumulative damage probability model was established under single-level constant amplitude loading. This model incorporates a fatigue life degradation function to characterize the cumulative damage effect of load cycles and corrects the fatigue reliability curve under single-level constant amplitude loading. By employing the principle of fatigue damage equivalence, the method determines the damage equivalence at the load switching point using the damage curve method, enabling the conversion of equivalent reliability under multilevel loads. The proposed method was validated by combining the test data obtained under three working conditions, including two-level loads loading, load blocks loading, and changing loads loading. The results demonstrate that the proposed method can accurately and efficiently evaluate the time-dependent fatigue reliability under different types of multilevel loads, using only a limited set of fatigue life data under single constant amplitude loads.

Non-probabilistic time-dependent reliability analysis of mechanism motion accuracy based on extreme value response

Non-probabilistic time-dependent reliability analysis of mechanism motion accuracy based on extreme value response

Time-Dependent Fuzzy Reliability Analysis of Concrete Slab during the Initial Water Storage Period of CFRD: A Case Study

The concrete-faced rockfill dam (CFRD) has been widely constructed worldwide, and the reliability of the concrete panels, the most important containment structure, is critical to the safety of the CFRDs and downstream communities. Several practical projects show that concrete slab cracking usually occurs during the water storage period, which can be attributed to the rapid increase of hydrostatic pressure and uneven settlement of the dam body. In this paper, a time-dependent reliability analysis method considering the fuzziness of the failure criterion is presented to assess the slab cracking risk of the Houziyan CFRD during the water storage period. Based on the observed deformation, the material parameters are calibrated to ensure the fidelity of the numerical simulation. Based on the Drucker–Prager yield criterion and tensile strength criterion, the response surface method is utilized to construct the performance functions at different moments, and then the time-dependent reliability analysis considering the fuzzy failure criteria is implemented for the concrete slab. The case study of the Houziyan CFRD shows that, during the initial period of water storage, the reliability index of the concrete slab decreases with the rise of the water level. With a stable water level, the probability of cracking of the concrete slab slowly decreases as the deformation of the dam body and slab tend to be coordinated. Especially, considering the fuzziness of the failure criteria, the reliability index decreased by about 2%, indicating that the proposed evaluation method is biased toward safety. The method proposed in this paper can reflect the evolution law of concrete slab reliability with the operating environment and provides a new approach to evaluate the performance of the concrete slab during the water storage period.

Time-dependent reliability assessment and optimal design of corroded reinforced concrete beams

It remains a significant challenge to quantitatively describe the corrosion of reinforced concrete (RC) structures under chloride penetration. Moreover, when considering uncertainties throughout the life cycle of corroded RC structures for assessing their safety, reliability, and optimal design, the complexity of the problem intensifies. To address these issues, this paper studies the time-dependent reliability analysis and optimal design of corroded RC beams. At first, the time-dependent reliability of beams is investigated by considering both the serviceability limit state (SLS), which corresponds to the corrosion initiation of the reinforced steel, and the ultimate limit state (ULS), associated with the bending failure of the beam. This analysis takes into account the time-dependent chloride diffusion coefficient and incorporates a stochastic process. The reliability is evaluated using the Monte Carlo Simulation (MCS) method and the cumulative distribution function (CDF) method. Subsequently, a time-dependent reliability-based design optimization (TRBDO) problem is formulated, and the PSO-MCS, a methodology incorporating a particle swarm optimization (PSO) algorithm and MCS is adopted to solve it. After optimization, the initial cost of the specific RC beam is reduced from 1351.879€ to 1247.075€, while the time-dependent reliability within [0, 100] years is improved from 0.6057 to 0.6508. The effectiveness of the CDF, MCS and PSO-MCS methods are demonstrated through reliability analysis and design examples of corroded RC beams.

Time-dependent reliability analysis of structural systems based on parallel active learning Kriging model

Time-dependent reliability analysis quantifies the failures of structural systems due to time-dependent uncertainties, such as material degradation and dynamic loads. The active learning Kriging model methods are widely used in structural reliability analysis to replace extensive time-consuming finite element simulations. However, they can only update one training sample and one failure mode per iteration, which limits their application to time-dependent, parallel computing, and multiple failure modes problems. In this study, we propose a new parallel active learning Kriging model for time-dependent reliability analysis, which can update multiple training samples and multiple failure modes per iteration. It includes the following strategies: (1) a novel parallel learning function is proposed, which combines the correlation function and U learning function to allow for the selection of multiple training samples per iteration; (2) an adaptive adjustment strategy for the number of parallel samples is proposed, which takes into account the prediction probability of parallel samples; (3) the proposed parallel learning function is integrated into time-dependent reliability analysis with multiple failure modes, enabling simultaneous updates of multiple training samples and failure modes, thus greatly reducing the number of iterations and computational time; and (4) a new stopping criterion is proposed to improve the efficiency of the estimation of failure probability. The proposed method can be applied to series or parallel time-dependent structural systems with multiple failure modes. We demonstrate the effectiveness of the proposed method through three examples, and the proposed method can achieve a balance between the computational time and function calls while maintaining a high level of accuracy in the estimation of time-dependent failure probability.

A novel active learning Gaussian process modeling-based method for time-dependent reliability analysis considering mixed variables

The purpose of time-dependent reliability analysis is evaluating the reliability of a system or component within a specified timeframe. Several approaches have been suggested for addressing time-dependent reliability challenges, including analytical methods and methods based on response surrogate models. As a representative of Machine Learning methods, the Active Learning Gaussian process model has gained more and more popularity in time-dependent reliability analysis. In practical applications, certain uncertainties may not be adequately represented by random variables following deterministic distributions. In contrast, these uncertainties can be easily described by interval variables. This article introduces an innovative method based on Active Learning Gaussian process modeling for time-dependent reliability analysis, encompassing both random and interval variables. The initial step involves transforming stochastic processes into random parameters through spectral decomposition. Moreover, a new sampling strategy to manage mixed uncertainties is proposed, where the candidate samples of mixed variables with positive maximum extreme responses and negative minimum extreme responses are identified. These samples are utilized to construct and renew an extreme Gaussian process model. Lastly, we present an improved confidence-based learning function to accelerate the learning process, which is designed to locate the optimal random input and interval input for updating the extreme Gaussian process model. One mathematical example and two engineering examples are conducted to verify the performance of the proposed method. Results illustrate that our method offers high accuracy while reducing the evaluations of true performance functions in addressing time-dependent reliability issues under mixed uncertainties.

On efficient time-dependent reliability analysis method through most probable point-oriented Kriging model combined with importance sampling

On efficient time-dependent reliability analysis method through most probable point-oriented Kriging model combined with importance sampling

Time-dependent reliability of structures under consideration of fuzzy uncertainty

Time-dependent reliability (TDR) is the possibility that a structure or system under consideration can perform the intended function under specified service conditions over a given time instant under fuzzy uncertainty. This paper is mainly concerned to identify fuzzy variables, generate the membership function of the input variables and output quantities, analyze timedependent performance level, estimate the possibility safety index, and evaluate the TDR of the structures. To evaluate TDR by a possibilistic approach, the fuzzy uncertainty that is characterized by membership function is considered. The type of uncertainty defines the method of reliability analysis, i.e., aleatory uncertainty possesses a probabilistic approach, whereas epistemic uncertainty leads to a possibilistic approach. The TDR analysis of the structures subjected to sustained load and corrosion based on probability theory is well developed. On the contrary, the TDR of structures subjected to combined effects sustained load, corrosion, creep, and shrinkage based on possibility theory lack research. Thus, this paper is significant to evaluate the TDR of structures subjected to the aforementioned effects based on possibility theory. However, it requires a rigorous procedure, a single-loop optimization method (SLOM) is employed to evaluate the TDR of structures involving epistemic uncertainty. To enhance the validation of the proposed approach, several examples are thoroughly carried out.

Time-Dependent Unavailability Exploration of Interconnected Urban Power Grid and Communication Network

This paper presents a time-dependent reliability analysis created for a critical energy infrastructure use case, which consists of an interconnected urban power grid and a communication network. By utilizing expert knowledge from the energy and communication sectors and integrating the renewal theory of multi-component systems, a representative reliability model of this interconnected energy infrastructure, based on real network located in the Czech Republic, is established. This model assumes reparable and non-reparable components and captures the topology of the interconnected infrastructure and reliability characteristics of both the power grid and the communication network. Moreover, a time-dependent reliability assessment of the interconnected system is provided. One of the significant outputs of this research is the identification of the critical components of the interconnected network and their interdependencies by the directed acyclic graph. Numerical results indicate that the original design has an unacceptable large unavailability. Thus, to improve the reliability of the interconnected system, a slightly modified design, in which only a limited number of components in the system are modified to keep the additional costs of the improved design limited, is proposed. Consequently, numerical results indicate reducing the unavailability of the improved interconnected system in comparison with the initial reliability design. The proposed unavailability exploration strategy is general and can bring a valuable reliability improvement in the power and communication sectors.

A Subdomain uncertainty-guided Kriging method with optimized feasibility metric for time-dependent reliability analysis

Active learning strategy combined with single-loop Kriging method has attracted much attention for Time-dependent Reliability Analysis (TRA). Large sample pool across all time instants is required to comprehensively cover the failure surface. Identifying training samples with most existing methods requires assessing the response of the entire sample pool, leading to high time costs. Similarly, to assist in identifying critical sampling regions, evaluating failure probability with a large sample pool in each iteration is also time-consuming. Additionally, higher-order uncertainty information is typically ignored, impairing the sampling efficiency. To address these issues, a Subdomain Uncertainty-guided Kriging (SUK) Method is proposed. Stochastic processes are first equivalently converted to random variables. By simultaneously sampling random variables and time parameter, an equivalent sample pool with significantly reduced size is generated for adaptive sampling. With a concise subdomain uncertainty assessment function, critical sampling region, i.e. sensitive subdomain, is distinguished efficiently. By comprehensively considering both the expectation and standard deviation of feasibility function, a novel Optimized Feasibility Metric (OFM) is then proposed for active learning. The proportion of misclassified samples is analytically deduced as stopping criterion. Finally, comparison results on four examples demonstrate the good performances of the proposed subdomain uncertainty-guided Kriging method.

Time-dependent reliability analysis of planar mechanisms considering truncated random variables and joint clearances

The dimension variables and joint clearances are key factors affecting the motion accuracy of a mechanism. The existing time-dependent reliability analysis methods usually assume that the dimension variables follow ideal distribution, ignoring the truncation restrictions due to production and manufacturing. In addition, improper handling of the correlation between joint clearance variables leads to inaccurate calculation results. To address the above issues, this paper proposes a time-dependent kinematic reliability analysis method, in which the truncated random variables and joint clearances are comprehensively considered. Firstly, the complex correlation of clearance variables in the motion error function is processed by the dimension reduction method. Then, the truncated variables are converted into truncated standard normal variables. Furthermore, the envelope function method with expansion at the most probable point (MPP) is used to transform time-dependent reliability into time-independent reliability at multiple time points, greatly reducing computational complexity. On this basis, the saddlepoint method is used to fit the motion error cumulative distribution function at each time point, and the upper and lower bounds of failure probability are obtained through the Copula function and second-order narrow reliability bounds. The effectiveness of the proposed method is verified by a typical 4-bar linkage and a single crank double rocker mechanism.

A novel quantile-based sequential optimization and reliability assessment method for safety life analysis

Safety life analysis under random uncertainty is an effective tool for guiding the maintenance and design of structures. However, existing methods for safety life analysis employ a nested solution strategy by dichotomy, with inner time-dependent reliability analysis, resulting in high computational costs. This paper proposes a quantile-based sequential optimization and reliability assessment (QSORA) method to overcome the shortcoming of nested solution strategy in safety life analysis. In QSORA, the probability constraint is first equivalently transformed into a quantile constraint corresponding to the target time-dependent failure probability (TDFP). Then, the coupling relationship between the search for safety life and the quantile estimation is then eliminated, and the safety life is solved iteratively through a series of cycles. Each cycle contains two independent executions: an equivalent deterministic optimization and quantile estimation of extreme performance function corresponding to the target TDFP. Finally, a sampling-based method combined with a double-loop Kriging model is proposed to efficiently estimate the quantile, and it is embedded into QSORA to improve the efficiency of safety life analysis. Two learning functions are adopted to ensure the accuracy of double-loop Kriging model. Numerical and engineering examples verify the efficiency and accuracy of the proposed method for safety life analysis.

Time-dependent reliability analysis of corroded RC beams based on the phase-type fitting method

It remains an important challenge to quantitatively describe the corrosion of reinforced concrete (RC) structures under chloride penetration. When considering the uncertainties encountered throughout the life cycle of RC structures exposed to a corrosive environment and evaluating their safety and reliability, the complexity of the problem intensifies. To address these issues, this paper focuses on the time-dependent reliability analysis of corroded RC beams, utilizing the phase-type (PH) fitting method. Initially, a model for the time-dependent reliability of corroded RC beams is established, incorporating the time-dependent chloride diffusion coefficient. Subsequently, a novel PH fitting method is proposed. The effectiveness of this new method is demonstrated through numerical examples. Furthermore, the time-dependent reliability analysis of corroded RC beams is compared using both the PH fitting method and the Monte Carlo simulation. The results reveal that the proposed method can accurately and efficiently deal with time-dependent reliability problems.

Mixed Bayesian Network for reliability assessment of RC structures subjected to environmental actions

Under environmental action, reinforced concrete (RC) structures might suffer from reinforcement corrosion caused by the surrounding environment, dramatically reducing structural reliability and threatening social development. However, most of the existing reliability assessment methods for RC structures only focused on the structural performance at the design stage given the original unchanged environment, ignoring the effects of realistic exposure conditions and inspection results on reliability evaluation. Thus, this paper develops a general reliability assessment framework based on a Mixed Bayesian network (MBN), incorporating three modules, i.e., durability assessment, load-bearing capacity analysis, and time-dependent reliability analysis. In MBN, separate sub-BNs are built based on different modules and connected by pinch point variables where probabilistic information is transmitted via soft evidence. Besides, this framework considers time-dependent environmental parameters and two-dimensional chloride transport and their effects on reliability. Meanwhile, adjustment coefficients are applied to improve the results of the analytical mechanical model with respect to different limit states through the finite element model (FEM). The proposed MBN framework is illustrated for a corroded RC beam under a marine atmospheric environment to investigate the effects of environmental modeling, chloride transport patterns, and concrete crack inspection on reliability assessment. The results indicate that under the assumed conditions in the case study, early inspection of large cracks may significantly overestimate the failure probability by about 500%. Besides, failure probability might be underestimated by about 95%, ignoring the time-variant environment and two-dimensional chloride transport.

Time-depending Reliability Analysis of O-ring Sealing Performance

O-rings are commonly used due to their simple structure and excellent performance. However, the time-dependent creep behavior of rubber during usage can significantly impact the working performance and service life of the O-ring. The phenomenological creep constitutive model establishes a relationship between the deformation of rubber materials under creep conditions and time, by incorporating a creep function that considers the significance of damage. Based on the phenomenological creep constitutive model, we establish a simulation model for the contact pressure of an engine O-ring. This model characterizes the time-dependent degradation process of the O-ring’s sealing performance by tracking the variation of contact pressure and contact surface width over time. To account for the randomness of rubber material model parameters and compression amount, we develop a time-dependent reliability analysis model for the O-ring using the first-order second-moment (FOSM) method. The research findings can establish a theoretical foundation for the assessment, analysis, and evaluation of O-ring sealing’s time-dependent reliability.

Reliability analysis of time-dependent problems based on ensemble learning of surrogate models

PurposeSurrogate models are extensively used to substitute real models which are expensive to evaluate in the time-dependent reliability analysis. Normally, different surrogate models have different scopes of application. However, information is often insufficient for analysts to select the most appropriate surrogate model for a specific application. Thus, the result precited by individual surrogate model tends to be suboptimal or even inaccurate. Ensemble model can effectively deal with the above concern. This work aims to study the application of ensemble model for reliability analysis of time-independent problems.Design/methodology/approachIn this work, a method of reliability analysis for time-dependent problems based on ensemble learning of surrogate models is developed. The ensemble of surrogate models includes Kriging, radial basis function, and support vector machine. The prediction is approximated by the weighted average model. The ensemble learning of surrogate models is updated by finding and adding the sample points with large prediction errors throughout the entire procedure.FindingsThe effectiveness of the proposed method is verified by several examples. The results show that the ensemble of surrogate models can effectively propagate the uncertainty of time-varying problems, and evaluate the reliability with high prediction accuracy and computational efficiency.Originality/valueThis work proposes an adaptive learning framework for the uncertainty propagation of time-dependent problems based on the ensemble of surrogate models. Compared with individual surrogate models, the ensemble model not only saves the effort of selecting an appropriate surrogate model especially when the knowledge of unknown problem is lacking, but also improves the prediction accuracy and computational efficiency.

A double-loop Kriging model algorithm combined with importance sampling for time-dependent reliability analysis

A double-loop Kriging model algorithm combined with importance sampling for time-dependent reliability analysis

Time-Dependent Reliability Analysis of RC Bridges Considering Shrinkage, Creep, Resistance Degradation, and Vehicle Load Flows

Due to concrete shrinkage, concrete creep, resistance degradation, and vehicle load flows, the long-term performance of reinforced concrete bridges exhibits time-varying characteristics. The vehicle-borne process is a nonstationary random process, which interacts with concrete shrinkage, concrete creep, and resistance degradation to cause constant changes in bridge internal force and deformation, further, bridge dynamic reliability occurs. This study presented a reasonable method for calculating the time-varying reliability of simply supported girder bridges under the effects of traffic loads and shrinkage creep. Stochastic truck-load models were simulated based on site-specific weigh-in-motion measurements, then the internal forces of the bridge were calculated when the mean value of vehicle-mounted effects increases by 1% per year. Considering the resistance degradation and load effect increase, the reliability of the RC bridge in serviceability limit state and capacity-carrying ultimate state were analyzed using first-passage probability method and Monte Carlo method, respectively. The accuracy of the proposed method was verified by comparison. The evaluation results show that the failure probability including shrinkage and creep has increased significantly; creep is affected by the bridge span and the number of main girders, and the reliability assessment results are safer for bridges with smaller spans.

Time-Dependent Reliability Analysis of Fracture Failure of Corroded Cast Iron Water Pipes and Bayesian Updating for Lifetime Prediction

Affected by the underground soil environment, buried cast iron pipelines are subject to corrosion during their long-term service, resulting in damage accumulation to the pipe wall and the eventual fracture failure of pipes. This paper aims to propose a probabilistic method to quantitively assess the time-dependent reliability of fracture failure of corroded cast iron pipes. A Gamma-based corrosion process of the pipe wall is derived according to the reported corrosion models. The first-order reliability method and the Monte Carlo simulation are used to cross-validate and conduct the time-dependent reliability analysis based on the fracture failure criterion. Furthermore, uncertain physical parameters of the pipes are updated by the Bayesian Markov Chain Monte Carlo (MCMC) algorithm based on the regional historical data of failed pipes, and lifetime predictions of buried cast iron pipelines are then obtained. A worked example is provided to illustrate the application of the proposed method. It is found that the Gamma process can well simulate the corrosion process hence can be employed to calculate the probability of pipe fracture failure. Sensitivity analysis reveals that the pipe internal water pressure, the fracture toughness, and the geometry of corrosion pits are the most influential parameters to the probability of fracture failure. It is also found that the predicted lifetime of corroded cast iron pipes in the worked example decreases from 110 to 85 years after the Bayesian updating.

Time-Dependent Reliability Analysis for Deflection of a Reinforced Concrete Box Girder Bridge

Prior to casting of concrete, proper supervision and attention to camber provision in bridge construction are required. It is also critical to use an appropriate quality control manual, pay due attention to reinforcement bar placement, and have a high level of formwork design before construction begins. If these issues are not properly addressed, performance of structures will be affected. In this research, performance of a 40.5m box-girder reinforced concrete bridge which was constructed without having proper camber is studied. As camber was the most important issue of the bridge under investigation, the impact on strength and serviceability requirements is compared to the standard. A dynamic load test with an Arduino type accelerometer is performed to assess the bridge's current condition in relation to the serviceability limit requirement. The deterioration of reinforced concrete (RC) sections due to reinforcement corrosion, creep, and an increase in load intensity, as well as the corresponding statistical distributions are considered to estimate the long-term effect of bridge deflection. The time-variant analysis results show that a linear decrease in deflection reliability indices with the bridge's expected service life of 58 years and strengthening it increased to 85 years.