Time-dependent Reliability Research Articles

Evaluating the Impact of Highway-Railway Grade Crossings on Travel Time Reliability on a Highway Network Level

Highway-rail grade crossings (HRGCs) have a range of safety and operational impacts on highway traffic networks. This paper illustrates a methodology for evaluating travel-time reliability for the routes and networks affected by trains traveling through HRGCs. A sub-area network including three HRGCs is used as the study network, and a simulation model calibrated to local traffic conditions and signal preemption strategies using field data is used as the platform to generate travel time data for analysis. Time-dependent reliability intervals for route travel time are generated based on route travel-time means and standard deviations. OD level reliability is calculated using a generic reliability engineering approach for parallel and series systems. The route travel time reliability results can be provided as real-time traffic information to assist drivers’ route-choice decisions. The OD level reliability is a way to quantify the impact of HRGCs on highway network operation. This effort fills the gap of reliability research for HRGCs on the route and sub-area network level, and contributes to improving the efficiency of decision-making for both traffic engineers and drivers.

Time dependent reliability analysis of railway sleepers subjected to corrosion

Prestressed concrete sleepers, as a major component of railway infrastructure, are prone to many environmental deterioration or load induced damages during their service lives. Therefore, an accurate prediction of their remaining service life is of paramount importance for proper allocation of maintenance management budgets. In this study, the remaining cross sectional area of corrosion affected prestressing wires is modeled as a nonstationary Gaussian process while other time‐invariant uncertainties, that is, geometrical properties and load affects, are modeled as random variables. Hence, the timed‐dependent reliability of these assets are calculated using the first passage theory and the corresponding outcrossing rate of the stochastic process from the safe domain. The merit of this analytical method is its efficiency and accuracy in perdition of remaining service life. The applicability of this method is shown on a B70 PSC sleeper designed based on UIC‐713 code and it is found that pitting corrosion in chloride‐laden environment extremely diminishes the service life of these assets.

Preventive maintenance of wood-framed buildings for hurricane preparedness

This paper presents a time-dependent reliability modeling and optimal maintenance planning approach for residential buildings subject to hurricane winds. A gamma process is employed to model the stochastic degradation of building components. The time-dependent fragility function and the failure probability of the roof system obtained from the degradation model are used to determine the retrofit timing of components that optimize an average cost per cycle time. The method is illustrated on determining the retrofit times of roof-to-wall connections based on actual component failure and hurricane wind load data. Effectiveness of the optimal retrofit age is compared to a replacement based on time-invariant failure probabilities. A simulation approach is presented to quantify the effect of wind speed uncertainty on maintenance cost.

An effective approach for kinematic reliability analysis of steering mechanisms

The paper presents an effective surrogate model for system reliability analysis of mechanisms based on an extreme-value kinematic error model and the Kriging approximation. In this regard, two types of kinematic reliability problems are considered, i.e., the system reliability that requires the kinematic error remains within an accuracy threshold along an entire output trajectory, whereas the time-dependent reliability accounts for gradually propagated system failure domain due to the varied pseudo-time parameter from its beginning to the current realization. Both kinematic reliability problems need to evaluate the extreme-valued error function presented in the mixture of absolute and maximum operators. By contrast, the simple position-based error function allows developing accurate surrogate models with a rather small number of training samples. Therefore, an approximation model was proposed to deal with kinematic reliability problems of steering mechanisms. Compared to available reliability methods in the literature, results have demonstrated high accuracy of the proposed method for various kinematic reliability problems. Note that the proposed method for time-dependent reliability analysis requires only one round of design of experiment, rather than repeatedly running the kinematic model like the first-order reliability method. It therefore provides an effective simulation tool for kinematic reliability analysis of mechanisms.

Structural reliability of corroded pipeline using the so-called Separable Monte Carlo method

The evaluation of the failure probability of corroded pipelines is an important calculation to quantify the risk assessment and integrity of pipelines. Traditional Monte Carlo simulation method has been widely used to solve this type of problems, where it generates a very large number of simulations and takes longer time in computing. In this study, enhanced computational method called Separable Monte Carlo is employed to evaluate the time-dependent reliability of pipeline segments containing active corrosion defects, where a practical example was used. The results show that the Separable Monte Carlo simulation method not only minimizes the computational cost strongly but also improves the calculation precision.

Assessment of existing civil engineering structures

The upcoming CEN Technical Specification (TS) on assessment of existing structures is to be related to the probabilistic concepts and fundamental requirements of the EN Eurocodes. The document should concern all types structures made of concrete, steel and other materials, exposed to all kinds of actions. The final draft of the Technical specification was already submitted to the technical committee CEN TC250. It contains requirements, general framework of operational assessment, data updating, structural analysis (linear, nonlinear, dynamic), verifications (partial factors, probabilistic methods, risk assessment), past performance, interventions, annexes (flowchart, time-dependent reliability, assessment of heritage structures). The submitted contribution provides background information on the principles included in TS. Particular attention is paid to specifying appropriate target reliability levels and application of these values in engineering practice through adjustment of partial factors. It is shown that the operational assessment of existing concrete structures provides prediction of the remaining working life of a structure using a convenient reference period (commonly 50 years) taking into account durability aspects and mutual dependence of the failures in subsequent basic time periods (usually considered as one year).

Life-Cycle Reliability Evaluation of Semi-Rigid Materials Based on Modulus Degradation Model

The dynamic modulus of semi-rigid material is one of the important material parameters widely used in the design and evaluate of asphalt pavement, which has a great effect on the reliability, healthy condition and service life of pavement. To show the three-phase degradation process of dynamic modulus accurately and calculate the time-dependent reliability based on fatigue damage, the degradation models based on non-linear fatigue damage and improved Wei-bull distribution modulus degradation are established and testified in this paper, considering the threshold of normalized modulus. Then the reliability models based on the two above degradation process models are evaluated. Finally, the reliability analysis procedure is established using Monte Carlo (MC) method and the corresponding calculation is conducted using Matlab. Cement stabilized macadam is used as an example in this paper. Results show that non-linear fatigue damage and improved Wei-bull distribution modulus degradation models can indicate threephase degradation process of semi-rigid material modulus better and the reliability based on the proposed two models was more accurate to the actual situation.

Corrosion non-uniformity of steel bars and reliability of corroded RC beams

To study the non-uniform distribution of cross-sectional areas and mechanical properties of corroded steel bars under a chloride environment, 19 concrete slabs embedded with steel bars were exposed to a chloride environment to achieve accelerated corrosion. A 3D measurement technique was employed to create geometric models of corroded steel bars, and their cross-sectional areas of a corroded steel bar, a probability distribution model of the spatial variability factor R, was developed through signal processing and statistical analysis methods. The R factor is the ratio of the average cross-sectional area to the minimum one and was applied to analyze the mechanical behavior response to the non-uniform corrosion of steel bars under tensile loading. In addition, the relationship between the mechanical properties and R factor of a corroded steel bar was established to predict its critical state of brittle failure. Our novel approach to this analysis enabled the calculation of the time-dependent reliability of a simply supported corroded reinforced concrete beam. The results showed that non-uniform corrosion is the critical factor affecting the time-dependent reliability of a reinforced concrete beam; moreover, changes in the failure mode of a corroded steel bar may severely impair the reliability of a reinforced concrete beam.

Time-Dependent Reliability-Based Dimensional Synthesis for Planar Linkages With Unknown but Bounded Joint Clearances

Linkage mechanisms are typically designed to generate a specific functional relationship or path. Because the uncertain dimensions and joint clearances severely affect the output motion accuracy, designers urgently need a reliability-based design approach with high confidence and efficiency. However, the traditional kinematic reliability synthesis, which focuses on several discrete time points, cannot satisfy the accuracy requirement over a continuous time interval. Accordingly, to ensure high accuracy over a time period, this study presents a reliability synthesis approach that considers the time-dependency effect of motion error. The exact statistical characteristics of clearances and dimensions may be unavailable because of the limited sample information in practical engineering. Thus, by qualifying the uncertainties as unknown but bounded variables, the time-dependent reliability index is assessed based on a combination of the nonprobabilistic interval process and first-passage theories. Two engineering examples are presented to demonstrate the validity and applicability of the developed methodology.

Combination of line sampling and important sampling for reliability assessment of buried pipelines

In this article, a novel approach for estimating the time-dependent reliability of a buried pipe under the impact of internal and external stresses by combining line sampling and important sampling is proposed. The stresses are analysed given the severe effect of corrosion on the performance of underground pipeline. The effect of corrosion during the design life of buried pipe decreases the capability of the pipe wall to sustain the stresses that occur internally or externally. Herein, the failure conditions of total axial stress and the ovality–stress due to point load in conjunction with the adverse effect of corrosion are examined using the proposed computational framework. The quantification of pipe failure due to these stresses is usually challenging because of the imprecision in the determination of the structural parameters. Therefore, the approach is used to capture and evaluate the influence of randomness behaviour of the parameters of pipe and soil in estimating the structural reliability. The proposed method can be applied to any structural engineering problems. In this study, a buried pipe under a roadway is examined and the effect of the underground water table on the performance of buried pipe over time is investigated. The outcome shows that a continuous increase in underground water table can aggravate the likelihood of the buried pipeline to fail. A parametric and sensitivity assessment of corrosion parameters shows their significant contribution to the probability of failure.

Quantifying multi-modal public transit accessibility for large metropolitan areas: a time-dependent reliability modeling approach

ABSTRACTThe temporal dimensions of public transit accessibility have recently garnered an increasing amount of interest. However, the existing literature on transit accessibility is heavily based on oversimplified assumptions that transit services operate at deterministic speeds using predetermined timetables. These measurements may overestimate transit accessibility, especially for large metropolitan areas where inter- and intra-modal transfers are frequent. To handle travel time uncertainty, a multi-modal transit accessibility modeling approach is proposed to account for realistic variations in travel time and service reliability. The proposed approach is applied to the mapping of transit accessibility in Shenzhen (China), where transit services exhibit significant travel time variations over space and time. Compared to traditional transit accessibility measures, our method has been demonstrated to better capture intrinsic spatial and temporal accessibility variations with complex multi-modal transit networks. Normal distribution of inter-stop travel times and constant travel speed between GPS sampling points are assumed to simply the computation, which we consider to adjust in future studies to better quantify the dynamics of transit accessibility across space and time.

Variation of Time Domain Failure Probabilities of Jack-up with Wave Return Periods

This study evaluated failure probabilities of jack up units on the framework of time dependent reliability analysis using uncertainty from different sea states representing different return period of the design wave. Surface elevation for each sea state was represented by Karhunen-Loeve expansion method using the eigenfunctions of prolate spheroidal wave functions in order to obtain the wave load. The stochastic wave load was propagated on a simplified jack up model developed in commercial software to obtain the structural response due to the wave loading. Analysis of the stochastic response to determine the failure probability in excessive deck displacement in the framework of time dependent reliability analysis was performed by developing Matlab codes in a personal computer. Results from the study indicated that the failure probability increases with increase in the severity of the sea state representing a longer return period. Although the results obtained are in agreement with the results of a study of similar jack up model using time independent method at higher values of maximum allowable deck displacement, it is in contrast at lower values of the criteria where the study reported that failure probability decreases with increase in the severity of the sea state.

Time-dependent reliability assessment of fatigue crack growth modeling based on perturbation series expansions and interval mathematics

A novel method of the time-dependent reliability, which combines the perturbation series expansions with the interval mathematics, is presented in this study for life prediction of fatigue crack growth problems. Distinct from the treatment in statistical analysis, characteristic parameters that exist in structural crack propagation model are described as unknown-but-bounded (UBB) variables with perturbation terms owing to the fact of variability of geometric sizes, material properties, and loading conditions. Then, based on the perturbation principle and the Taylor extension approach, a new interval perturbation series expansion method (PSEM) to predict boundary rules of the fatigue crack length a(t) is derived. Meanwhile, the auto-correlation features between a(tk) and a(tk+1) are also confirmed by employing the interval process theory. Additionally, inspired by the classical out-crossing approach in random process issues, a non-probabilistic time-dependent reliability (NTR) index Rs(T), as a safety measure for in-service engineering structures with crack, is defined, and its solution algorithm is expounded in details. Numerical examples are eventually proposed to demonstrate the validity of the developed methodology of uncertainty quantification and reliability evaluation.

Efficient Solution for Calculation of Upcrossing Rate of Nonstationary Gaussian Process

AbstractAlmost all engineering systems are not only uncertain, but also time-variant. As such, it is most appropriate to use a time-dependent reliability method, e.g., first passage probability, in...

Time-dependent reliability assessment of ship structures under progressive and shock deteriorations

The aim of this paper is to provide a rational reliability assessment of ship structures under multiple hazards during their lifetime. These hazards cause both progressive and shock deteriorations of structural performance. Time-dependent estimation of structural reliability must consider multiple failure modes. In this paper, the safety margins under progressive and shock hazards are evaluated separately for the associated failure modes. Considering the cumulative effect of multiple hazards during the lifetime, probabilistic structural deterioration process is represented by using cumulative-time approach. To present the multi-hazard analysis, corrosion and extreme lateral pressure are adopted as progressive and shock type hazards, respectively. Failure modes of buckling and permanent set are considered for safety and serviceability of a ship structure component. Side shell plating structure in a tanker is used to illustrate the evaluation of lifetime structural performance deterioration in multi-hazard environment.

Evaluation of Time Dependent Reliability Analyses for Human Errors in Development of Bridge Network System

Evaluation of Time Dependent Reliability Analyses for Human Errors in Development of Bridge Network System

FORM and Out-Crossing Combined Time-Variant Reliability Analysis Method for Ship Structures

In view of the varying characteristics of material properties, environmental conditions, and loading effects randomly with long time, the random and temporal characters of different variables should take into account when the structural reliability analysis methods are adopted to estimate the reliability of ship structures. Therefore, a time-variant reliability analysis method combined the out-crossing approach and the first-order reliability method is proposed. In this paper, the research is conducted on the time-variant feature of ship structures under the corrosive action according to the environmental testing data. Furthermore, the limit state function is derived based on the time-variant feature analysis results in which the strength and stress of ship structures are both regarded as variables with respect to time. Then, the time-dependent reliability model of ship structures is established based on this combined method, and the solving process of parameters in this model is illustrated. Finally, a case of a ship grillage structure under marine environment is given to prove that the proposed method has a good application in evaluating the reliability of ship structures. The comparison analysis using different methods is also conducted to study the accuracy and efficiency of this method.

Time-Dependent System Reliability Analysis for Bivariate Responses

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

Reliability Analysis of Nonlinear Vibratory Systems Under Non-Gaussian Loads

A general methodology is presented for time-dependent reliability and random vibrations of nonlinear vibratory systems with random parameters excited by non-Gaussian loads. The approach is based on polynomial chaos expansion (PCE), Karhunen–Loeve (KL) expansion, and quasi Monte Carlo (QMC). The latter is used to estimate multidimensional integrals efficiently. The input random processes are first characterized using their first four moments (mean, standard deviation, skewness, and kurtosis coefficients) and a correlation structure in order to generate sample realizations (trajectories). Characterization means the development of a stochastic metamodel. The input random variables and processes are expressed in terms of independent standard normal variables in N dimensions. The N-dimensional input space is space filled with M points. The system differential equations of motion (EOM) are time integrated for each of the M points, and QMC estimates the four moments and correlation structure of the output efficiently. The proposed PCE–KL–QMC approach is then used to characterize the output process. Finally, classical MC simulation estimates the time-dependent probability of failure using the developed stochastic metamodel of the output process. The proposed methodology is demonstrated with a Duffing oscillator example under non-Gaussian load.

Time-dependent reliability method for service life prediction of reinforced concrete shield metro tunnels

Ageing and deterioration of underground tunnels is inevitable after their long-time in service. This necessitates a rigorous assessment of the probability of failure due to deterioration with a view to predicting remaining safe life. In the light of considerable research undertaken on prediction of service life of the aboveground structures, e.g. bridges, few such studies dealing with the underground structures, e.g. tunnels, have been carried out. The intention of this paper is to present a time-dependent reliability method to assess the tunnel probability failure due to different mechanisms of deterioration. Stochastic models are developed for four common failure modes of tunnel structures as identified by strength and serviceability criteria. Application of the proposed methodology is demonstrated in a case study. It is found in the paper that the reinforcement corrosion is a key factor that affects the probability of deterioration failure and that all deterioration scenarios need to be considered in the assessment of tunnel failures and prediction of their remaining safe life. The proposed method can help the asset managers and practitioners in developing rehabilitation or replacement strategy for existing tunnels with a view for better management of the valuable tunnel asset.