Time-dependent Reliability Assessment Research Articles

Outcrossing Rate Method for Nonstationary Non-Gaussian Performance Functions and Its Application to Time-Dependent Reliability Assessment

Outcrossing Rate Method for Nonstationary Non-Gaussian Performance Functions and Its Application to Time-Dependent Reliability Assessment

Failure assessment of deteriorated steel light poles

Steel poles are extensively used as street light posts and various other applications within the power distribution network. For partially buried pole, the effect of corrosion below and at the ground level significantly controls the overall load capacity. In this study, number of in-service steel pole specimens extracted from field were assessed for the corrosion damage. The level of corrosion was estimated by remaining wall thickness measured using ultrasonic testing and the surface corrosion was estimated using 3D laser scanning to adopt an appropriate existing model for buried steel structures. A relationship between maximum and average corrosion pit depth and loss of embedment depth was then developed. Finally, the corrosion parameters, combined with uncertainty in loading and soil properties were employed to perform time-dependent reliability assessment for steel light poles which can be used to assist the asset maintenance team in planning the replacement or strengthening works for steel pole.

A hybrid physics-informed machine learning approach for time-dependent reliability assessment of electromagnetic relays

Electromagnetic relays (EMRs) are intricate micro-electromechanical systems characterized by nonlinear behavior and coupling effects between electromagnetic and mechanical forces. Accurately modeling degradation and assessing reliability are crucial yet challenging tasks for ensuring their safe and efficient operation. Current data-driven methods for degradation modeling and reliability assessment often neglect the known physical knowledge regarding EMRs, leading to inaccuracies in modeling and assessment outcomes when data is incomplete. While physics-informed machine learning (PIML) approaches offer a potential solution, common regression models like Gaussian processes (GP) and long short-term memory (LSTM) suffer from underfitting and overfitting, respectively. To address these issues, we presents a hybrid PIML approach for time-dependent reliability assessment based on the emerging variational autoencoder (VAE) framework. This approach combines the advantages of GP-based methods that enable probabilistic representation with deep neural network-based methods that are more flexible and computationally efficient. Finally, we validate our proposed approach using real-world engineering data, demonstrating its superior accuracy and computational efficiency compared to state-of-the-art methods.

Reliability assessment of bridge hangers based on fault tree with response surface

Bridge hangers play a crucial role in transmitting forces and supporting bridge structures. The condition of these hangers directly impacts the overall safety of the bridge. However, they are susceptible to fatigue failure due to cyclic loads like wind and vehicle traffic. Therefore, evaluating the fatigue performance of bridge hangers is vital. Typically made up of multiple parallel steel wires, the failure of even one wire can affect the fatigue performance of the entire hanger. This underscores the importance of considering the individual components’ impact on the system as a whole. This study presents a time-dependent reliability assessment model for bridge hangers based on the S-N curve of steel wire. Additionally, a system-level reliability assessment model is developed using fault tree analysis, taking into account the influence of broken wires and stress redistribution on the hanger system. The model is solved using response surface methodology, and through five numerical simulations, the study examines the effect of key parameters, including the number of broken wires, equivalent structural stress, and total cycles on the system’s reliability.

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.

Temporal reliability evolution of a prestressed girder with post-tensioned tendons subjected to corrosion

This paper presents a methodology for the assessment of time-dependent reliability of post-tensioned (PT) girders. As possible lack of consistent maintenance efforts and the constraints of economic and temporal resources become increasingly apparent, there is a need to comprehend their remaining service life, intricately tied to the gradual evolution of their reliability over time. In this study, the primary focus is directed towards a combination of extreme load failure mechanisms and tendon corrosion. The proposed methodology is applied to a scenario involving a simply supported prestressed girder with PT tendons. The analysis takes into account the progressive reduction in bending capacity over time due to the adverse effects of tendon corrosion. Diverging from conventional approaches found in existing literature, the time-to-corrosion model embeds not only the chloride concentration in voids present in the grout injection but also considers the thermodynamic conditions necessary for the development of corrosion. A sensitivity analysis of the input variables is performed to identify the most influential parameters over time. The study shows that considering both chloride concentration and thermodynamic conditions can lead to a more realistic residual structural life. It is concluded that the consideration of the thermodynamic conditions is essential to avoid overly conservative safety assessments, which could lead to a poorly optimized management and sustainability of bridges.

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.

Moment‐based outcrossing rate method for time‐dependent reliability assessment including finite element analysis

AbstractIn practice, structural limit state function (LSF) is often combined with finite element (FE) models, and the corresponding time‐dependent reliability assessment (TRA) inevitably involves dealing with computational inefficiency. In this paper, a general moment‐based outcrossing rate (GMO) method is proposed to conduct TRA efficiently, with no limitation in the form of LSF. There are two innovations of GMO method: firstly, an explicit moment‐based outcrossing rate is developed; secondly, a separate algorithm is proposed that facilitates the separation of FE analysis from TRA cycle. The proposed method minimizes the computational cost associated with FE analysis and enables TRA cycle to be conducted more efficiently with the assistance of an explicit moment‐based outcrossing rate and explicit moment‐based outcrossing rate. Three numerical examples are investigated to examine the accuracy and efficiency of GMO method for TRA cycle. GMO method is found from the results that it can efficient and accurate to conduct TRA. Such improvements in computational efficiency are particularly valuable for complex structures where FE analysis is computationally expensive and time‐consuming.

Time-dependent reliability assessment of existing concrete bridges with varying knowledge levels by proof load testing

In the evaluation of existing bridges and viaducts, relying solely on a desk study is often inadequate for determining their structural reliability. Performing a proof load test provides valuable field data that offers detailed information about the structural integrity. However, the relation between the magnitude of the load and the structural reliability is not immediately clear. This study addresses the challenges associated with determining the target load and highlights the uncertainties that play a key role. A case study is presented that shows the time-dependent character of the structural reliability and the influence of an informative and a weakly informative prior distribution in a Bayesian context. It is shown how both past traffic loads and a proof load test may contribute to the proven strength of a structure. The described method provides a starting point towards a flexible approach for proof load testing in which structure-specific knowledge levels and requirements are considered.

Experimental based time-dependent reliability assessment of corrosion initiation for PC girders in frozen marine environment

Chloride induced corrosion is the main reason for the deterioration of concrete structures in marine environments, and the prediction of corrosion initiation life is one of the greatest challenges for preventative maintenance. To conduct a corrosion initiation assessment of PC girders in frozen marine environment and support preventative maintenance, a time-dependent reliability assessment method is developed. Long-term exposure experiments and in-house tests are combined to calibrate the chloride diffusion model, and then a probabilistic diffusion model is proposed based on the randomness of the key model parameters. Through the analysis of the target reliability index of corrosion initiation, the risk-function based time-dependent reliability assessment method is developed. Finally, a case study is introduced to illustrate the application of the proposed method. It is found that the surface chloride concentration on concrete structures in frozen marine environments increases at the beginning of service life and it tends to be stabilize when the service time is around 9–10 years. The age reduction factor of chloride diffusion can be described as the linear function of cementitious composition. The target reliability indices of corrosion initiation are suggested as 2.46, 1.50 and 1.13 for the referenced periods of 1, 10 and 20 years. The corrosion initiation life is very sensitive to the tensile stress level of concrete, and it decreases linearly with the increasement in tensile stress when the stress is not higher than 2 MPa.

Dynamic reliability analysis of the existing bridges based on probability density evolution method

Existing bridges have experienced time-varying load effects and resistance degradation during the service periods. The complex dynamic loads and diverse failure modes make the existing bridges face high service risks, therefore, it is urgent to make time-dependent reliability assessment for the service bridges. The classical time-varying reliability analysis method is increasingly complex and challenging with the increase of the number about random variables. In this paper, probability density evolution theory is introduced as a more advantageous approach to solve the above problem, which is more advantageous for solving the reliability of complex structures with multiple random variables. The dynamic reliability of the existing bridge in serviceability limit state and ultimate limit state is analyzed by considering the bridge resistance degradation and the increase of load effects, as well as the time-varying factors such as shrinkage and creep effect of concrete bridges. The accuracy and computational efficiency for this method are compared with the Monte Carlo method, and the effectiveness of the proposed method is verified, which has the advantages of higher computational efficiency and better accuracy and can be applied to complex nonlinear structures under various loads.

Time-Dependent Reliability Assessment of Long-Span PSC Box-Girder Bridge Considering Vehicle-Induced Cyclic Creep

The neglect of the cyclic creep of concrete induced by vehicles may overestimate the deflection reliability of long-span prestressed concrete (PSC) box-girder bridges and increase structural safety risks. In this paper, a novel method considering the combined effects of the shrinkage, static creep, and cyclic creep of concrete and the stress relaxation of prestressed tendons is proposed to assess the time-dependent deflection reliability of PSC box-girder bridges. By employing the Kelvin chain model, the conventional integral-type method for calculating the static creep of concrete is converted to rate-type creep analysis, which has a higher computational efficiency and can consider various nonlinear effects. The cyclic creep of concrete is estimated by the fatigue mechanics-based model and integrated into the quasi-elastic incremental constitutive model. The proposed constitutive model is implemented in a general finite-element program DIANA, in which the mechanical behavior of the thin-walled box girder is described by the composite degenerated shell elements. An importance sampling method is applied when estimating the deflection reliability to balance the computational accuracy and efficiency. The proposed method is applied to a long-span PSC box-girder bridge with a main span of 150 m. The results indicate that the cyclic creep of concrete may accelerate the reduction of the deflection reliability indexes, which may fall below the target level before the expected service life of the bridge. In addition, heavy trucks passing in pairs have a significant impact on the deflection reliability. The research findings can be used for the reliable design and optimal maintenance of long-span PSC box-girder bridges.

Structural Time-Dependent Reliability Assessment: Advanced Approaches for Engineered Structures

Structural Time-Dependent Reliability Assessment: Advanced Approaches for Engineered Structures

Time-dependent reliability assessment of a simply supported girder bridge based on the third-moment method

Concrete bridges decay over time due to environmental or operational processes, leading to a reduction in their reliability. In this paper, a new time-dependent reliability evaluation procedure is proposed taking into consideration the simultaneous non-stationarities of vehicle load effect and resistance deterioration. Using the third-moment (3M) method and the second-moment (2M) method, the time-varying reliability of a simply supported girder bridge was investigated. The 3M method is a novel approach to calculate the reliability index requiring neither iteration nor computation of derivatives. As validated by Monte-Carlo simulations, it is shown that the 3M method is more accurate than the 2M method. Based on different moment methods, the effects of parameters such as the growth rate of vehicle load and the time proportions of different operation states in the reliability of the system were investigated. By analyzing the relationship between the time-dependent reliability index and the target reliability index, the time points of maintenance and inspection were predicted.

Adaptive surrogate model coupled with stochastic configuration network strategies for time-dependent reliability assessment

Time-dependent reliability assessment is crucial in enhancing product development economics and product performance sustainability throughout the lifecycle. It is still a challenge to accurately and efficiently evaluate the time-dependent reliability of engineering systems. This paper proposes a novel adaptive surrogate model method combining stochastic configuration network (SCN) and Kriging strategies to evaluate time-dependent reliability. SCN has accurate approximation ability and learning efficiency for strongly nonlinear systems that can overcome the conventional time-dependent reliability calculation, which is time-consuming and characterized by low accuracy. The proposed method first applies SCN to establish the response model of the performance function with respect to time and obtain the extreme value of the performance function. Then, Kriging is used to establish the extreme value model of the performance function with respect to the random variables based on the extreme value of performance function. The adaptive process considering the characteristics of random variables samples is adopted to update the extreme value model until the model meets the confidence target. Lastly, Monte Carlo simulation is employed for time-dependent reliability assessment based on the established extreme value model. Three example studies are used to demonstrate the effectiveness of the proposed approach for time-dependent reliability assessment.

Time-Dependent Reliability Assessment of a Continuous I-shaped Steel Beam Considering Corrosion Effects

Among other fields, climate change has a great influence on metal corrosion that reduces the durability and reliability of steel structures. A time-dependent reliability analysis includes time-dependent climate scenarios and deterioration processes as well as random variables, material properties, and dimensions. The extent of corrosion damage is calculated by tracking the evolution of the corrosion process using Monte Carlo simulations. The current paper presents a time-dependent reliability assessment of a continuous I-shaped steel beam, considering the corrosion effects of climate change in Vietnam. The results showed that the safety probability of a continuous steel beam considering metal corrosion from the pristine to 100 years reduces from 96.77% to 63.08%. These findings can be used to assess and provide a cost-technical analysis of climate adaptation measures.

Time-dependent reliability assessment of corroded metal structures based on Physics of Failure (PoF): With a case study of cast iron pipe

In most metal structures, corrosion has been recognized as the main cause of failure, and fracture often occurs in structures subjected to corrosion, e.g., metal pipes. Since the evolution of a corrosion defect into a crack takes the majority of a structure’s lifespan, accurate quantification of this transition limit state is significant in assessing the probability of failure. This paper aims to propose a methodology for predicting the occurrence of a crack in corroded structures based on the Physics-of-Failure (PoF) theory. The Stress Intensity Factor (SIF) concept and the J-integral-based finite element analysis are used to derive the solution of the SIFs in the corroded structure. A cast iron pipe with a crack-shape corrosion defect is taken as an example. A model for estimating the SIF for a corrosion pit with high aspect ratio has been proposed. The evolution of SIF is modeled by a stochastic process, and an advanced time-dependent method (i.e., upcrossing method) is used to quantify the probability of failure. It is found that combining the concept of Physics-of-Failure with time-dependent reliability method can provide an effective tool for predicting the failure probability of corroded structures. It is also found from the sensitivity analysis that the internal pressure has the highest effect on the probability of failure, followed by the corrosion pit depth. The results from this paper offer a necessary basis for safety and reliability analysis of corroded metal pipes, providing asset managers a cost-effective tool in planning maintenance works.

Failure probability analysis of corroded RC structures considering the effect of spatial variability

A reasonable assessment of the probability of structural failure is essential to ensure the safe performance of corroded reinforced concrete (RC) structures. In this paper, a novel cross-sectional area loss model of corroded steel bars is proposed and the scale of fluctuation of some key parameters is estimated using the semi-variogram function method. A stochastic resistance deterioration model considering the effect of unbalanced corrosion and spatial variability and a time-dependent reliability assessment method of corroded concrete structures (CCSs) are then presented. A simple case analysis of a CCS is used to illustrate the application of the proposed method. The case analysis results show that the cumulative failure probability (CFP) is overestimated using the popular pit area model, while it is underestimated without considering the spatial variability of calculation parameters. Random field parameter analysis shows that an appropriate choice of the element size is very important for the safety evaluation of RC structures. Additionally, compared with a marine atmospheric environment, the CFP of a case study structure in tidal and splash environments was found to be increased by 20.15% and 70.40%, respectively, due to the gradual increase of corrosion current density. Of the three service environments, the splash environment thus has the greatest impact on structural failure probability.

Time-Dependent Reliability Assessment Method for RC Simply Supported T-Beam Bridges Based on Lateral Load Distribution Influenced by Reinforcement Corrosion

The safety and reliability of bridges gradually decrease over time under the influence of disadvantageous environmental factors, primarily due to reinforcement corrosion caused by chloride ingress. The traditional lateral load distribution (LLD) theory does not consider the influence of corrosion, which degrades the accuracy of bridge performance and reliability calculation. A time-dependent reliability assessment method for simply supported T-beam bridges is proposed in this paper, which considers the influence of reinforcement corrosion on LLD. Firstly, the steel corrosion process and degree are predicted based on the chloride ingress model, into which the water/cement ratio and concrete strength are innovatively introduced in order to improve the prediction accuracy. Secondly, the effective stiffness calculation method for corroded reinforcement bridges is established with the moment of inertia and section crack condition employed. Thirdly, the modified eccentric compression method is improved by the effective stiffness and iterative algorithm, which is suitable for the LLD calculation of corroded reinforcement bridges. The time-dependent vehicle load effect can be computed combined with the probability distribution of live load. Finally, the time-dependent reliability of the flexural bearing capacity is obtained by the Monte Carlo method and Bayesian theory without prior information. A simply supported bridge with five T-beams is taken as an example for analysis. It is indicated that the results calculated by the traditional reliability method are conservative, which cannot make a true and accurate evaluation. The method proposed in this paper can effectively reduce the assessment error caused by model uncertainty while considering the interaction between reinforcement corrosion and vehicle live load effect.

An explicit compound Poisson process-based shock deterioration model for reliability assessment of aging structures

Existing structures may suffer from resistance deterioration due to repeated attacks. The modeling of resistance deterioration is a critical ingredient in the reliability assessment and service life prediction of these degraded structures. In this paper, an explicit compound Poisson process-based model is developed to describe the shock deterioration of structural resistance, where the magnitude of each shock deterioration increment is modeled by a Gamma-distributed random variable. The moments (mean value and variance) and the distribution function of the cumulative shock deterioration are derived in a closed form, based on a proposed W-function. A method for the efficient calculation of the W-function is presented, which reduces to the Bessel type I function if the shock deterioration increment is exponentially distributed (a special case of Gamma distribution). The proposed shock deterioration model is applicable to either a stationary or a nonstationary Poisson process of random jumps. Subsequently, the overall resistance deterioration is modeled as the linear combination of gradual and shock deteriorations, based on which the proposed model can be used in the time-dependent reliability assessment of aging structures efficiently. A numerical example is presented to demonstrate the applicability of the proposed deterioration model by estimating the time-dependent reliability of an aging bridge. It is found that a smaller threshold for the degraded resistance leads to greater mean value and standard deviation of the time to failure, and this effect is enhanced by a smaller occurrence rate of the shock deterioration.