Time-dependent Structural Reliability Research Articles

An improved analytical solution to outcrossing rate for scalar nonstationary and non-gaussian processes

For time-dependent reliability methods, there is a lack of analytical solutions to outcrossing rates of nonstationary and non-Gaussian processes. This paper aims to propose an analytical method to determine this type of outcrossing rate with improved accuracy and efficiency. The novelty of this proposed method is that it can consider the probabilistic properties of non-Gaussian processes by combining a two-component parallel system model with higher-order moments-based reliability indexes. The main contributions of this method are: (1) compared with PHI2+ method, it is more accurate for the calculation of the outcrossing rate of nonstationary and non-Gaussian processes with nonlinear limit state functions; (2) compared with MPHI2 method, it is analytical and not only applicable for the nonstationary stochastic processes but also insensitive to time increments; and (3) it is not only more accurate than the existing methods for nonstationary and non-Gaussian processes but also more computation efficient than the Monte Carlo simulation method. The proposed method has shown its advantages for practical structures with neither Gaussian processes nor linear limit state functions, which are beneficial for both researchers and asset managers to evaluate the time-dependent reliability of structures accurately and to develop risk-informed maintenance schemes with a view to prolonging their service life.

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 reliability of structures under consideration of epistemic uncertainty

Time-dependent reliability of structures under consideration of epistemic uncertainty

A closed-form solution to time-dependent reliability of aging structures described by gamma-based deterioration models

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.

Performance decay analysis of cementitious composite cladding structure under stochastic aging

Façade cladding structure made of cementitious composite is prone to cracking due to its brittle characteristics, despite being a non-load-bearing member. Served as building exteriors, aging of cementitious composite may further raise the risk of fracture failure under accidental loads, causing both financial loss and safety hazards. To address this issue, a computational approach, fusing together a novel physics-based stochastic aging model and phase field fracture model, is developed to assess the mechanical performance decay of aging cladding structure. In this study, stochastic leaching under inherent material uncertainty is taken as the primary aging concern, and the analysis is assisted with extended support vector regression for substantial efficiency enhancements. The proposed method is carefully validated against two designed benchmark problems and a real-life application. It is demonstrated to be able to predict the time-dependent reliability of cementitious composite cladding structures precisely and efficiently under stochastic leaching-induced aging.

Time-dependent structural reliability under nonstationary and non-Gaussian processes

With the increasing recognition of random and time-variant nature in structural responses, time-dependent reliability methods have become popular for structural reliability assessment in recent decades. This paper proposes a method that can determine the time-dependent reliability with accuracy and robustness under general stochastic processes, which are neither stationary nor Gaussian. It presents a detailed derivation of the first passage probability and upcrossing rate with a view to better understanding the time-dependent reliability theory. An idea is proposed to determine the upcrossing rate for any stochastic processes by combining the Rice formula with transformation of the stochastic processes. The proposed method is verified with both analytical solution and Monte Carlo simulation, and further tested with two practical examples. It is found in the paper that the proposed method is more accurate than the only existing analytical solution and yet more efficient than the Monte Carlo simulation with the same accuracy. It is also found that the proposed method is robust for any type of stochastic processes with a range of barrier levels and band widths. The significance of this proposed method is that it widens the application of time-dependent reliability methods to the assessment of practical structures during their service life.

Koopman operator for time-dependent reliability analysis

Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work, we propose a Koopman operator based approach for time-dependent reliability analysis of nonlinear dynamical systems. Since the Koopman representations can transform any nonlinear dynamical system into a linear dynamical system, the time evolution of dynamical systems can be obtained by Koopman operators seamlessly regardless of the nonlinear or chaotic behavior. Despite the fact that the Koopman theory has been in vogue a long time back, identifying intrinsic coordinates is a challenging task; to address this, we propose an end-to-end deep learning architecture that learns the Koopman observables and then use it for time marching the dynamical response. Unlike purely data-driven approaches, the proposed approach is robust even in the presence of uncertainties; this renders the proposed approach suitable for time-dependent reliability analysis. We propose two architectures; one suitable for time-dependent reliability analysis when the system is subjected to random initial condition and the other suitable when the underlying system have uncertainties in system parameters. The proposed approach is robust and generalizes to unseen environment (out-of-distribution prediction). Efficacy of the proposed approached is illustrated using four numerical examples. Results obtained indicate supremacy of the proposed approach as compared to purely data-driven auto-regressive neural network, long short- term memory network, and DeepONet.

Time-dependent reliability and resilience of aging structures exposed to multiple hazards in a changing environment

Engineering structures are often subjected to the influences of performance deterioration and multiple hazards during their service lives, and consequently may suffer from damage/failure as a result of external loads. Structural reliability and resilience assessment is a powerful tool for quantifying the structural ability to withstand these environmental or operational attacks. This paper proposes new formulas for structural time-dependent reliability and resilience analyses in the presence of multiple hazards, which are functions of the duration of the reference period of interest. The joint impacts of nonstationarities in multiple hazards due to a changing environment, as well as the deterioration of structural performance, are explicitly incorporated. The correlation between the structural resistances/capacities associated with different hazard types is modeled by employing a copula function. It is observed that, under the context of multiple hazards and aging effects, the time-dependent resilience takes a generalized form of time-dependent reliability. The proposed formulas can be used to guide the adaptive design of structures, where adaptive strategies are identified across a range of possible future service conditions. An example is presented to demonstrate the applicability of the proposed method for structural reliability and resilience analyses.

Time-Dependent Resilience of Repairable Structures Subjected to Nonstationary Load and Deterioration for Analysis and Design

Civil structures and infrastructures are often subjected by design to the impacts of natural and human-caused hazardous events, and accordingly may suffer from damages, functionality loss, and failure. In order to quantitatively measure the associated likelihood and consequences for quantifying risks, an appropriate measure of structural reliability and resilience is essentially required. This paper presents an explicit measure for the time-dependent resilience of repairable structures as a natural extension of time-invariant and time-dependent structural reliability concepts, taking into account the effects of structural performance deterioration and nonstationary external loads. First, the resilience measure associated with a single load event is discussed, and an integral-free expression is developed for a special case of structural robustness and recovery. Subsequently, the resilience measure for a planning horizon, which is a function of the duration of considered service period, is proposed in a closed form. Remarkably, the time-dependent resilience can be treated as a generalized form of the time-dependent reliability. Motivated by this, the resilience-based design and cost optimization of structures are also discussed. A numerical example is presented to demonstrate the accuracy and applicability of the proposed resilience measure.

Study on the Time-dependent Reliability of Corroded Reinforced Concrete Bridge Structures due to Ship Impact

The cumulative damage caused by chloride ion erosion to coastal bridge structures reduces the ship impact resistance of channel bridge structures and leads to changes in reliability of bridge structures on ship impact. It is of great theoretical and practical significance to study the performance degradation change law of corroded bridge structures and to evaluate the ship impact time-dependent reliability of in-service corrosion-damaged bridge structures. Based on the durability decay model of reinforced concrete structures in a chloride ion erosion environment, the time-dependent resistance analysis of bridge structures is carried out considering the reduction of yield strength of longitudinal reinforcement and hoop reinforcement in pile sections and the decay of compressive strength of protective layer concrete. Based on the study of the probabilistic model and parameters of random variables affecting the time-dependent reliability of ship-bridge collision, the typical damage modes of bridge structures under ship impact are analyzed, the time-dependent reliability analysis model of bridge structures under ship impact is established based on the structural damage criterion, the ship-bridge crash limit state functional function is given, and the time-dependent reliability analysis of ship-bridge collision is carried out based on the response surface method.

Time-Dependent Reliability of Aging Structures: Overview of Assessment Methods

Reliability assessment of engineered structures is a powerful and useful concept to estimate the structural capacity of withstanding hazardous events during their service lives. Taking into account the time variation of both structural resistance and the external load processes, the structural safety level is dependent on the duration of service period of interest, due to the accumulation of hazards by exposure in time. This paper presents an overview on the nonempirical assessment methods for time-dependent reliability of deteriorating structures. Generally, these methods can be classified into two types, namely simulation-based and analytical methods. The former is usually brute, and is especially suitable for solving high-dimensional reliability problems. Conversely, analytical solutions may improve the calculation efficiency significantly, and offer insights into the reliability problem that otherwise could be difficult to achieve through Monte Carlo simulation. Both the simulation-based and analytical methods will be reviewed in this paper. Furthermore, the application of time-dependent reliability methods in practical engineering is discussed. Recommendations for future research efforts are also presented.

Bayesian Updating of Time-Dependent Structural Reliability Using the Method of Moment

AbstractBayesian updating of the reliability of deteriorating engineering structures based on inspection data has been attracting a lot of attention recently because it can provide more accurate es...

Random field-based reliability updating framework for existing RC structures incorporating the effect of spatial steel corrosion distribution

In recent years, interest in the effect of the spatial variability associated with steel corrosion on the safety and reliability of reinforced concrete (RC) structures in harsh environments has increased. However, updating the reliability based on observations of existing RC structures remains a challenge. In this paper, an advanced framework for updating the time-dependent reliability incorporating the effect of the spatial steel corrosion distribution in existing RC members is presented. Probabilistic concepts are adopted to model random variables associated with material corrosion as random fields. With the application of a particle filter, spatially observed information obtained at discrete locations on RC members can be utilized to update the associated random variables. This reduces the epistemic uncertainty associated with structural performance assessments. In an illustrative example, time-dependent reliability updating is conducted on a RC bridge girder with the inspection results of the steel corrosion crack width. The effects of the number and space interval of observed locations on the updated structural reliability are investigated. The results demonstrate that the accuracy of the estimation of the time-dependent reliability of RC structures can be improved by using spatial observation information with a greater number of observed locations.

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

For the widely existing time-dependent structural system (TDSS), the current model ignores the interaction among multiple modes in the minimum transformation of the performance function of each mode w.r.t. the time, it may misjudge the state of the system at some instants and result in the error of estimating the reliability. To avoid this possible mistake, this paper proposes an improved reliability analysis model for the TDSS. In the proposed model, the TDSS performance function is transformed into the single-mode time-dependent performance function firstly according to the relationship of multiple modes. Then the failure probability of the TDSS can be estimated by the single-mode time-dependent performance function. The relationship of multiple modes is strictly considered in the proposed model. On the basis of the improved model, this paper also presents the Kriging surrogate model combined with the Monte Carlo simulation method to estimate the failure probability of the TDSS. In this Kriging method, the initial training samples are uniformly selected in the sample space and a new extremum learning function is proposed. Theoretical analysis verifies the rationality of the proposed reliability analysis model, and the efficiency of the proposed method is illustrated by the results of numerical examples.

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.

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.

The Effect of Stochastic Properties of Strength Reduction Function on The Time-Dependent Reliability of RC Structures

Quantitative calculation of structural safety using its specific limit-states is of great importance. Due to the stochastic properties of strength, loading, and environmental reduction functions, these parameters cannot be considered as deterministic variables. In this paper, a probabilistic model including the stochastic properties of the strength reduction factor was proposed to calculate the time-dependent reliability of concrete structures. In this model, the statistical properties of applied loads were also considered. The strength reduction model was calculated quantitatively using the statistical properties of the reducing agent. In this research, the major factor contributing to the strength reduction is the reduction in the cross‐section of the steel bars, reduction of bonding strength, and the spalling of the concrete cover due to reinforcement corrosion induced by chloride ingress. The results of this model were compared to the calculation of reliability using the direct implementation of strength values and another simplified method that only considers initial strength as a random variable. In the methods under investigation, the effect of the uncertainty of reducing factor on the mean and coefficient of variation of results was also studied. The results showed that the probability of failure increases between 25% to 50% when the uncertainty of the reducing factor is taken into account. The proposed model has more realistic results than the simplified model, and these results could be improved for achieving more exact outcomes with lower uncertainty.

Estimation of time-dependent reliability of aging structures under correlated load and autocorrelation in resistance deterioration

This paper proposes explicit approaches for time-dependent reliability assessment of aging structures, taking into account the correlation associated with the load process and that arising from the resistance deterioration process. For the load process, temporal correlation may arise due to the impacts of underlying common causes. With this regard, a closed-form solution is developed for structural reliability, which models the sequence of load effects as a Markov process. Furthermore, the resistance deterioration is by nature a non-increasing stochastic process with autocorrelation on the temporal scale. The Gamma process is used to describe the stochastic behaviour of resistance deterioration, based on which an explicit reliability method is derived. The proposed reliability methods are straightforward to implement and thus are promising to be adopted in practical engineering regarding the safety evaluation of aging structures. Illustrative examples are presented to demonstrate the accuracy and applicability of the proposed approaches.

Time-Dependent Structural Reliability Assessment for Nonstationary Non-Gaussian Performance Functions

AbstractIn this paper, a new analytical formula is proposed to determine the mean outcrossing rate of nonstationary non-Gaussian performance functions. The performance function is firstly transform...

In-situ NDT investigation to estimate degraded quality of concrete on existing structure considering time-variant uncertainties

Concrete structures may be affected due to degradation of stiffness or strength originated from severe environmental stressors or unsystematic variations in the loads and resistances of the structure beyond the baseline conditions of the existing design. Therefore, physical changes in the performing system should be considered for assessing the future reliability and safety of the structure. In this paper an improved approach for the evaluation of time-dependent structural reliability of aged structure has been presented. Experimental investigation has been carried out using two different Non-Destructive testing (NDT) methods, such as ‘Rebound hammer (RH)’ and Ultrasonic pulse velocity (UPV) methods to check the deterioration of the existing structure with respect to age and load processes, however, the results have been used for the evaluation of failure probability of the structure with respect to time or ages. The quality of the degraded concrete is suitably represented by a normalized index called Concrete Quality Designation (CQD). Considering non-stationarity in the process of load and time-dependent structural resistance, the assessment for time-dependent structural reliability is performed to investigate and assess the structural degradation characteristics reliably for safety evaluation of the remaining service life of structure.