Time-dependent Reliability Research Articles

Reliability prediction for corroding natural gas pipelines

This paper aims to evaluate time-dependent reliability of a corroding onshore underground natural gas pipeline system over its lifetime. The reliability analysis is segment-based, as opposed to defect-based and the pipe segment is examined with respect to external metal loss corrosion. The non-homogeneous Poisson process (NHPP) and an empirical power law model are employed for generation of corrosion defects over time and for defect growth, respectively. The time-dependent probability of failure is evaluated by employing the limit state function for burst under internal pressure. Internal pressure is modelled using a Poisson square wave process-based method (PSWP). Thereinafter, the study uses the aforementioned analysis, in conjunction with a heuristic model, in order to investigate the influence of imperfect repairs on the reliability prediction of the pipeline system. The heuristic method is known as split system approach and it is used to describe the changes in reliability of the pipeline system over its lifetime with the consideration of multiple maintenance actions. A numerical example of the described methodology is presented based on a chosen maintenance policy. A parametric study is conducted to examine the impact of instantaneous generation rate of NHPP model, PSWP model and reliability control limit on the results of the numerical application. The proposed methodology aims to assist engineers in the decision making with regard to corrosion maintenance strategies.

Time-dependent reliability assessment of aging series systems subjected to non-stationary loads

Civil infrastructure systems provide physical supports to a community’s functionalities and are expected to achieve acceptable safety levels subjected to extreme load effects. However, these systems may deteriorate with time as a result of aggressive environmental or operating conditions in service, implying that the system reliability may decline beyond the baseline as assumed for design. Moreover, the increasing trend of the external loads may also contribute to the reduction of the system reliability. In this paper, a semi-analytical method is proposed for assessing the reliability of aging systems subjected to non-stationary loads. The series system is considered, where the system failure is defined as the failure of any single component (structure) among the system. The application of the proposed method is illustrated using a representative series bridge network with several individual bridges. The role of parameters such as the variations in the load intensity, resistance correlation and number of components under attack in the system reliability are investigated.

Time-Dependent Reliability Analysis Through Response Surface Method

In time-dependent reliability analysis, the first-passage method has been extensively used to evaluate structural reliability under time-variant service circumstances. To avoid computing the outcrossing rate in this method, surrogate modeling may provide an effective alternative for calculating the time-dependent reliability indices in structural analysis. A novel approach, namely time-dependent reliability analysis with response surface (TRARS), is thus introduced in this paper to estimate the time-dependent reliability for nondeterministic structures under stochastic loads. A Gaussian stochastic process is generated by using the expansion optimal linear estimation (EOLE) method which has proven to be more accurate and efficient than some series expansion discretization techniques. The random variables and maximum responses of uncertain structures are treated as the input and output parameters, respectively. Through introducing the response surface (RS) model, a novel iterative procedure is proposed in this study. A Bucher strategy is adopted to generate the initial sample points, and a gradient projection technique is used to generate new sampling points for updating the RS model in each iteration. The time-dependent reliability indices and probabilities of failure are thus obtained efficiently using the first-order reliability method (FORM) over a certain design lifetime. In this study, four demonstrative examples are provided for illustrating the accuracy and efficiency of the proposed method.

An Outcrossing Rate Model and Its Efficient Calculation for Time-Dependent System Reliability Analysis

Time-dependent reliability problems widely appear in the engineering practice when the material properties of the structure deteriorate in time or random loading modeled as random processes is involved. Among existing methods to the time-dependent reliability problems, the most dominating one is the outcrossing rate method. This paper presents an outcrossing rate model and its efficient calculation approach for system problems, and based on the presented model, a time-dependent system reliability analysis method is proposed. The main idea of the method is to transform the evaluation of the system outcrossing rates into the calculation of a time-invariant system reliability. Three numerical examples are used to demonstrate the effectiveness of the proposed method.

Time-dependent reliability analysis of mooring lines for fish cage under corrosion effect

Moored fish cage structures are forced to move into the offshore area due to the shrinking availability of sheltered near-shore sites and increasing environmental impacts of aquaculture, and this provokes a significant challenge for the reliability design of mooring system. The uncertainties involved in the predictions of applied loads and structural strength are analyzed for calculating the reliability level of mooring system. In this study, a probability corrosion model is used to describe the uncertainty of corrosion depth and the joint probability density of significant wave height and spectral peak period is selected to depict the randomness of sea states. The non-linear finite element model is developed to investigate the minimum breaking strength of mooring chains and is validated through comparing with the formulas providing by the International Association of Classification Societies (IACS) Unified Requirements concerning for Materials and Welding. A validated numerical model is applied to calculate the tension force of mooring system for both the single-cage system and the multi-cage system at several sea states, and the response surface method is utilized to display the limit state function to calculate the reliability level in terms of the uncertain metocean variables. The results indicate that the reliability level decreases significantly with the increasing corrosion depth and the correlation of corrosion model for mooring chains has a remarkable impact on the failure probability of mooring system. In addition, the failure probability of mooring system for the four-cage system is much higher than that for the single-cage system.

Cross-entropy-based adaptive importance sampling for time-dependent reliability analysis of deteriorating structures

Time-dependent reliability analysis of deteriorating structures is important in their performance evaluation and maintenance. Various definitions and methods have been used by researchers to predict the time-dependent reliability of structures. In the present study, these methods are first critically reviewed and examined. Among these methods, the stochastic-process-based method is theoretically the most rigorous but also computationally the most expensive. To facilitate the wide application of the stochastic-process-based method in complex problems, an efficient importance sampling method is then proposed in this paper. The proposed method includes a number of improvements formulated to enhance the efficiency and robustness of an existing method proposed by Kurtz and Song, leading to more efficient solutions of time-dependent reliability problems of structural systems with multiple important regions. The validity and efficiency of the new method is demonstrated through three numerical examples.

Evaluating Time-Dependent Reliability and Probability of Failure of Reinforced-Concrete Bridge Components and Predicting Residual Capacity after Subsequent Rehabilitation

AbstractThe load-carrying capacity of reinforced concrete bridges can degrade over their service life through the initiation of deterioration mechanisms induced by fatigue, corrosion, cracks, and s...

Probabilistic durability assessment of concrete structures in marine environments: Reliability and sensitivity analysis

A probabilistic framework for durability assessment of concrete structures in marine environments was proposed in terms of reliability and sensitivity analysis, which takes into account the uncertainties under the environmental, material, structural and executional conditions. A time-dependent probabilistic model of chloride ingress was established first to consider the variations in various governing parameters, such as the chloride concentration, chloride diffusion coefficient, and age factor. Then the Nataf transformation was adopted to transform the non-normal random variables from the original physical space into the independent standard Normal space. After that the durability limit state function and its gradient vector with respect to the original physical parameters were derived analytically, based on which the first-order reliability method was adopted to analyze the time-dependent reliability and parametric sensitivity of concrete structures in marine environments. The accuracy of the proposed method was verified by comparing with the second-order reliability method and the Monte Carlo simulation. Finally, the influences of environmental conditions, material properties, structural parameters and execution conditions on the time-dependent reliability of concrete structures in marine environments were also investigated. The proposed probabilistic framework can be implemented in the decision-making algorithm for the maintenance and repair of deteriorating concrete structures in marine environments.

An approach for time-dependent reliability analysis of Jackup structures

This paper proposes an approach for evaluation of time dependent reliability of Jackup structures. An approach for signal processing using prolate spheroidal wave functions is combined with stochas...

Research on Time-Variant Wear Reliability of Gear Rack

In this paper, a gear rack of a ship lift is taken as an example. This paper presents a method for analyzing the reliability of gear and rack movement under the influence of time-varying wear. The example of large modulus gear rack mechanism for ship lift is verified. Through the wear state of rack and pinion, the time dependent reliability equation of kinematic pair is established with the consideration of the original dimension error, gap error and wear effect. Based on the Archard wear model, the hardness and other factors under the influence of time variation are analyzed and the new kinematic pair model is established. Finally, the Matlab software is used to simulate the wear process of the rack and pinion. The influence degree of the above factors on the motion reliability of mechanism is analyzed. The results of simulation and analysis show that the method is more accurate and suitable for engineering application. It provides an important reference for the life prediction of gear rack and the development of maintenance and maintenance outline.

Time-varying reliability indexes for multi-AUV cooperative system

With the development of multi-autonomous underwater vehicle (AUV) cooperative systems, the evaluation of their reliability is becoming more and more important. Since AUVs are always in motion, the reliability of the system is not stationary, but it varies with time. This paper studies the time-varying reliability evaluation indexes for multi-AUV cooperative systems. Aimed at elucidating the characteristics of the system, by considering the motion of the AUVs, two time dependent reliability evaluation indexes, natural connectivity and all-terminal reliability of the basic reliability indexes, are determined with the graph theory. Then the time-varying reliability of multi-AUV cooperative systems is evaluated combining with an actual example. This paper provides a method to evaluate the time-varying reliability of multi-AUV cooperative systems.

Joint Probability Method to Time-dependent Reliability for Planar Path Mechanisms

Joint Probability Method to Time-dependent Reliability for Planar Path Mechanisms

Stochastic modelling fatigue crack evolution and optimum maintenance strategy for composite blades of wind turbines

The composite blades of offshore wind turbines accumulate structural damage such as fatigue cracking due to harsh operation environments during their service time, leading to premature structural failures. This paper investigates various fatigue crack models for reproducing crack development in composite blades and proposes a stochastic approach to predict fatigue crack evolution and to analyse failure probability for the composite blades. Three typical fatigue models for the propagation of fatigue cracks, i.e., Miner model, Paris model and Reifsnider model, are discussed to reproduce the fatigue crack evolution in composite blades subjected to cyclical loadings. The lifetime probability of fatigue failure of the composite blades is estimated by stochastic deterioration modelling such as gamma process. Based on time-dependent reliability analysis and lifecycle cost analysis, an optimised maintenance policy is determined to make the optimal decision for the composite blades during the service time. A numerical example is employed to investigate the effectiveness of predicting fatigue crack growth, estimating the probability of fatigue failure and evaluating an optimal maintenance policy. The results from the numerical study show that the stochastic gamma process together with the proper fatigue models can provide a useful tool for remaining useful life predictions and optimum maintenance strategies of the composite blades of offshore wind turbines.

DEVELOPED PROBABILISTIC REDUCTION FACTORS FOR LOPHIRA ALATA (EKKI) TIMBER JOISTS SUBJECTED TO CREEP-RUPTURE

Wood experiences a significant loss of strength and stiffness when loaded over period of time. This phenomenon is known as creep-rupture. Several models were developed for the estimation of the reduction of load carrying capacity of timber with time. In this paper, the results of time dependent structural reliability analysis of timber joist produced with Lophiraalata (Ekki) timber specie was presented. Three load duration models were considered in the study, namely: The Model proposed by Wood, Gerhards model, and Nielsen. The timber joist was designed in accordance with the Eurocode 5. The uncertainties in all the basic design variables were fully accommodated in the time dependent reliability analysis. The entire process was implemented using a developed MATLAB program employing First Order Reliability Method (FORM). Time dependent mathematical models for modification of safety index to account for the effect of load duration were proposed. The use of both Gerhards and Nielsen model, for the design of Lophiraalata timber members was recommended. http://dx.doi.org/10.4314/njt.v36i1.6

DEVELOPED PROBABILISTIC REDUCTION FACTORS FOR LOPHIRA ALATA (EKKI) TIMBER JOISTS SUBJECTED TO CREEP-RUPTURE

Wood experiences a significant loss of strength and stiffness when loaded over period of time. This phenomenon is known as creep-rupture. Several models were developed for the estimation of the reduction of load carrying capacity of timber with time. In this paper, the results of time dependent structural reliability analysis of timber joist produced with Lophiraalata (Ekki) timber specie was presented. Three load duration models were considered in the study, namely: The Model proposed by Wood, Gerhards model, and Nielsen. The timber joist was designed in accordance with the Eurocode 5. The uncertainties in all the basic design variables were fully accommodated in the time dependent reliability analysis. The entire process was implemented using a developed MATLAB program employing First Order Reliability Method (FORM). Time dependent mathematical models for modification of safety index to account for the effect of load duration were proposed. The use of both Gerhards and Nielsen model, for the design of Lophiraalata timber members was recommended. http://dx.doi.org/10.4314/njt.v36i1.6

Structural time-dependent reliability assessment of the vibration active control system with unknown-but-bounded uncertainties

The active control system for structural vibration is extremely sensitive to the parametric uncertainty so that more and more concerns of its reliability estimation have been given recently. In view of the insufficiency of the uncertainty information in practical engineering, a non-probabilistic time-dependent reliability method that combines the active vibration control theory with interval analysis is proposed in this paper to effectively estimate the dynamic safety of the controlled structures, in which circumstances the unknown-but-bounded uncertainties in structural parameters are considered. The uncertain structural responses based on the closed-loop control are firstly analyzed and embodied by the interval process model. By virtue of the first-passage theory, an integral procedure of non-probabilistic time-dependent reliability analysis of the active control system for structural vibration is then conducted. Two engineering examples and one experimental application are eventually presented to demonstrate the validity and applicability of the methodology developed.

Reliability estimation of fatigue crack growth prediction via limited measured data

In view of limited uncertainty information, a time-dependent reliability estimation procedure that combines the determined crack growth model with interval mathematics is presented as a theoretical basis for structural damage tolerance design. Firstly, by virtue of the theory of non-probabilistic interval process, an interval process model of fatigue crack propagation is investigated, in which we describe uncertain crack length a(N) at any load cycle N as interval variable and define the corresponding auto-covariance function and the correlation coefficient function to further characterize the correlation of a(N) at different cycles. By comparison of the critical crack length acritical, the uncertainty properties of the time-varying limit-state function can be given as well. Furthermore, inspired by the first-passage approach in random process theory, a new measure index of non-probabilistic time-dependent reliability is proposed as a feasible way for precisely evaluating the safe life of in-service engineering structures with crack. The corresponding solution algorithm is further discussed. Some application examples demonstrate the usage, efficiency and accuracy of the developed methodology eventually.

Time-Dependent Reliability Analysis Using a Vine-ARMA Load Model

A common strategy for the modeling of stochastic loads in time-dependent reliability analysis is to describe the loads as independent Gaussian stochastic processes. This assumption does not hold for many engineering applications. This paper proposes a Vine-autoregressive-moving average (Vine-ARMA) load model for time-dependent reliability analysis, in problems with a vector of correlated non-Gaussian stochastic loads. The marginal stochastic processes are modeled as univariate ARMA models. The correlations among different univariate ARMA models are captured using the Vine copula. The ARMA model maintains the correlation over time. The Vine copula represents not only the correlation among different ARMA models but also the tail dependence of different ARMA models. Therefore, the developed Vine-ARMA model can flexibly model a vector of high-dimensional correlated non-Gaussian stochastic processes with the consideration of tail dependence. Due to the complicated structure of the Vine-ARMA model, new challenges are introduced in time-dependent reliability analysis. In order to overcome these challenges, the Vine-ARMA model is integrated with a single-loop Kriging (SILK) surrogate modeling method. A hydrokinetic turbine blade subjected to a vector of correlated river flow loads is used to demonstrate the effectiveness of the proposed method.

Reliability models for a nonrepairable system with heterogeneous components having a phase-type time-to-failure distribution

This research paper presents practical stochastic models for designing and analyzing the time-dependent reliability of nonrepairable systems. The models are formulated for nonrepairable systems with heterogeneous components having phase-type time-to-failure distributions by a structured continuous time Markov chain (CTMC). The versatility of the phase-type distributions enhances the flexibility and practicality of the systems. By virtue of these benefits, studies in reliability engineering can be more advanced than the previous studies. This study attempts to solve a redundancy allocation problem (RAP) by using these new models. The implications of mixing components, redundancy levels, and redundancy strategies are simultaneously considered to maximize the reliability of a system. An imperfect switching case in a standby redundant system is also considered. Furthermore, the experimental results for a well-known RAP benchmark problem are presented to demonstrate the approximating error of the previous reliability function for a standby redundant system and the usefulness of the current research.

Gaussian copula–Bayesian dynamic linear model–based time-dependent reliability prediction of bridge structures considering nonlinear correlation between failure modes

Bridge structures in service are subjected to long-term ambient environments and continuously increasing traffic demands; therefore, the physical quantities of the existing bridge structures are subjected to changes in both time and space. Through health monitoring for bridges, the data of the load effects of bridge structures, including strain, stress, deflection, and so on, of the specified structural components or structures, can be obtained. The novel monitoring systems installed in bridge structures contain sensors providing a large amount of monitored data. Proper processing of the continuously provided monitored data is one of the main difficulties in the field of structural health monitoring for time-dependent reliability prediction of structural components and/or structures. Under the actions of the common random sources of the time-dependent input load data, the time-dependent nonlinear correlation will exist among the time-dependent output load effect data. The Bayesian dynamic linear models are introduced to predict the time-dependent output variables and model the time-dependent nonlinear correlation coefficients between them. Then, the Gaussian copula–Bayesian dynamic linear models are built based on the Gaussian copula theory and the time-dependent correlation coefficients. The models can better and more feasibly predict the future reliability of bridge structures. Finally, an actual application example is provided to illustrate the feasibility and application of the built Gaussian copula–Bayesian dynamic linear models for structural reliability prediction.