Time-dependent System Reliability Research Articles

A probabilistic framework for external pitting corrosion growth modelling for buried steel pipelines considering soil properties

This paper introduces a novel framework for developing reliable probabilistic predictive corrosion growth models for buried steel pipelines using pipeline inspection data. The framework adopts a power-law function of time model formulation, accounting for nonconstant damage growth rates, and considers the correlation between defect depth and length growth models. The proposed framework explicitly incorporates local influential soil properties in the model formulation; thus, it requires no segmentation and homogenous defect growth assumption and provides defect-specific growth models. The framework is applicable regardless of the availability of matched or non-matched defect data. For corrosion initiation time estimation, two different approaches are proposed: one is to use a Poisson process to account for defect occurrence, which can also predict newly generated defects since the last inspection, and the other is to use multivariate linear regression of soil and pipe properties. The statistics of unknown model parameters are assessed using a Bayesian updating framework in which the model error can be incorporated. The proposed framework is applied using two different sets of data: one set of inline inspection (ILI) data and one set of field excavation data. A case study is conducted, where time-dependent system reliability of an in-service pipeline is assessed considering small leak and burst failure modes using the developed defect growth models. The impact of the growth model accuracy on the probability of failure is investigated, and the importance analysis is performed to identify the most influential random variables to the probability of failure.

Time-dependent system reliability analysis for mechanical on-load tap-changer with multiple failure modes

To regulate voltage level, the mechanical on-load tap-changer is a crucial series system of the ultra-high-voltage converter transformer. Whether its motion is reliable throughout the whole process is vital for the safe operation of converter transformer. Therefore, the time-dependent system reliability analysis is carried on for the mechanical on-load tap-changer with multiple failure modes based on the first-passage method. First, the failure modes of the mechanical on-load tap-changer are comprehensively analyzed according to the safety requirement, and then, the output error of each failure mode related to the moving mechanism of the system is modeled based on the motion equation to establish the varied limit-state functions of the time intervals over the whole motion. Then, the first-passage method is leveraged to solve this time-dependent reliability problem with multiple failure modes, in which the analytical formula of the outcrossing rate, the crucial element of the first-passage method, is derived by introducing the first-order moment of the doubly truncated multivariate Gaussian distribution. On this basis, the time-dependent system kinematic reliability is calculated using the Simpson integration algorithm. Finally, a numerical case is studied first, and in what follows, the practical engineering application to the mechanical on-load tap-changer is showcased in detail to demonstrate the effectiveness and efficiency of the proposed method by comparison with previous methods.

Time-dependent system reliability analysis using adaptive single-loop Kriging with probability of rejecting classification

Time-dependent system reliability analysis using adaptive single-loop Kriging with probability of rejecting classification

Optimum maintenance strategy for CRTS II slab track based on time-dependent system reliability

CRTS (China Railway Track System) II slab track is a vertical multi-layer and longitudinal anisotropic strip system, which has been widely constructed in China’s high-speed railway. In this study, an innovative optimum maintenance strategy is proposed for CRTS II slab track, based on the concept of time-dependent system reliability and life-cycle cost analysis. System limit state function of the track structure is constructed with consideration of important serviceability failure modes. The time-dependent system reliability of the track structure is investigated and utilized as the indicator of track performance, which is estimated by an innovative outcrossing method based on the system limit state function considering time-dependent correlation among failure modes. At each maintenance time, all critical failure modes and components are identified and repaired to decrease the system failure probability under the acceptable level. Application of the proposed maintenance strategy is demonstrated by a worked example of a track structural system on bridge. It is found that: (1) appropriate maintenance strategy is important to ensure service reliability of the track system and extend the service life; and (2) the proposed maintenance strategy can be utilized to predict when, where, and what failure mode for maintenance and it can help to minimize the expected life-cycle cost without compromising the service reliability of the track structure.

A nested single-loop Kriging model coupled with subset simulation for time-dependent system reliability analysis

Time-dependent system reliability analysis still faces severe challenges including the simultaneous consideration of time-dependent uncertainties under multiple failure modes and the accurate estimation of small failure probability. Therefore, this paper proposes a nested single-loop Kriging (NSLK) model coupled with subset simulation (SS) method, named NSLK-co-SS, for time-dependent system reliability assessment. Firstly, based on the rationale of SS method, the small time-dependent system failure probability is converted into the product of a series of large intermediate failure probabilities by introducing a series of intermediate failure events. Then, by reformulating the time-dependent system reliability problem as a nested system reliability one, the NSLK method is developed to estimate each intermediate failure probability. Meanwhile, a system reliability theory-based U (SYSU) learning function is proposed to identify both the best training sample and mode and sequentially update the Kriging models of multiple modes in a series of small intermediate sample pools. Two numerical examples and an engineering example were investigated to demonstrate the efficiency and accuracy of the proposed method.

LSTM-augmented deep networks for time-variant reliability assessment of dynamic systems

This paper presents a long short-term memory (LSTM)-augmented deep learning framework for time-dependent reliability analysis of dynamic systems. To capture the behavior of dynamic systems under time-dependent uncertainties, multiple LSTMs are trained to generate local surrogate models of dynamic systems in the time-independent system input space. With these local surrogate models, the time-dependent responses of dynamic systems at specific input configurations can be predicted as an augmented dataset accordingly. Then feedforward neural networks (FNN) can be trained as global surrogate models of dynamic systems based on the augmented data. To further enhance the performance of the global surrogate models, the Gaussian process regression technique is utilized to optimize the architecture of the FNNs by minimizing a validation loss. With the global surrogates, the time-dependent system reliability can be directly approximated by the Monte Carlo simulation (MCS). Three case studies are used to demonstrate the effectiveness of the proposed approach.

Conditional time-dependent limit state function model considering damages and its application in reliability evaluation of CRTS II track slab

On-site observations show that several damages have occurred in CRTS II slab-type ballastless track system, such as crack and interface debonding between different structural layers, which will trigger the occurrence of some failure modes of CRTS II track slab. As the damages are the prior for specific failure modes, time-dependent reliability of CRTS II track slab should be conducted considering the uncertainties associated with both the failure mode and the damage, which is defined as the conditional time-dependent reliability in this study. To appropriately express the causal relationship among the failure modes and prior damages, a conditional limit state function (LSF) model is proposed with explicit expressions provided. With the aid of the proposed model, conditional time-dependent reliability of CRTS II track slab for two individual failure modes are investigated, which are the steel yielding failure mode under longitudinal cracking, and the vertical instability failure mode under interface debonding. Furthermore, conditional time-dependent system reliability of the track slab has also been analyzed considering four safety failure modes. The advantage of the proposed method is that prior damages have been accounted in establishing the failure criteria and incorporated in the formulation of time-dependent reliability, which provides a general formwork for structural reliability involving the causal relationship among the failure modes and damages.

Time-dependent reliability analysis for repairable consecutive-k-out-of-n:F system

In a repairable consecutive system, after the system operates for a certain time, some components may fail, some failed components may be repaired and the state of the system may change. The models developed in the existing literature usually assume that the state of the system varies over time depending on the values of n and k and the state of the system is known. Since the system reliability will vary over time, it is of great interest to analyse the time-dependent system reliability. In this paper, we develop a novel and simple method that utilizes the eigenvalues of the transition rate matrix of the system for the computation of time-dependent system reliability when the system state is known. In addition, the transition performance probabilities of the system from a known state to the possible states are also analysed. Computational results are presented to illustrate the applicability and accuracy of the proposed method.

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.

A flexible optimization algorithm for GO-FLOW methodology to deal with shared signals

In this paper, we propose an optimized GO-FLOW algorithm for time-dependent system reliability analysis. The optimized GO-FLOW algorithm is implemented based on recursive calculation of the complete set of minimum path sets. The algorithm is augmented with a cut-off criterion for probabilistic models to offer a much more flexible approach to achieve the trade-off between computational complexity and accuracy. The optimization method and algorithm are tested with an example case study of reliability analysis of auxiliary feedwater system in nuclear power plants. The verification results show that the retrofitting GO-FLOW method is capable of efficient processing of the shared signals and providing accuracy solutions at high speed.

Evaluation of the availability and reliability of a standby repairable system incorporating imperfect switchovers and working breakdowns

This study involves the evaluation of the availability and reliability of a repairable system containing warm standby components and undergoing switching failure under a Markovian environment. A single repairperson is responsible for repairing failed components. As soon as the system is free of failed components, the repairperson takes multiple vacations. The repairperson is also subject to breakdown while repairing failed components. When the repairperson experiences a breakdown, there is a probability of 1−δ that he/she is sent for recovery, or a probability of δ that he/she continues to work at a lower rate. For the Markov model, we establish a finite set of differential equations governing the repairable system. A numerical approach based on the Runge–Kutta method is employed to solve the differential equations. Numerical solutions for the time-dependent availability can then be obtained. For the reliability model, we use the Laplace transform method to find the explicit form of the reliability function and the mean time to failure (MTTF) of the system. Finally, we conduct a numerical sensitivity analysis of the time-dependent availability, system reliability and MTTF with respect to various system parameters.

Time-Dependent System Reliability Analysis With Second-Order Reliability Method

AbstractSystem reliability is quantified by the probability that a system performs its intended function in a period of time without failures. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method using the envelope method and second-order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the second-order component reliability method with an improve envelope approach, which produces a component reliability index. The covariance between component responses is estimated with the first-order approximations, which are available from the second-order approximations of the component reliability analysis. Then, the joint distribution of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples.

An LSTM-Based Ensemble Learning Approach for Time-Dependent Reliability Analysis

Abstract This paper presents a long short-term memory (LSTM)-based ensemble learning approach for time-dependent reliability analysis. An LSTM network is first adopted to learn system dynamics for a specific setting with a fixed realization of time-independent random variables and stochastic processes. By randomly sampling the time-independent random variables, multiple LSTM networks can be trained and leveraged with the Gaussian process (GP) regression to construct a global surrogate model for the time-dependent limit state function. In detail, a set of augmented data is first generated by the LSTM networks and then utilized for GP modeling to estimate system responses under time-dependent uncertainties. With the GP models, the time-dependent system reliability can be approximated directly by sampling-based methods such as the Monte Carlo simulation (MCS). Three case studies are introduced to demonstrate the efficiency and accuracy of the proposed approach.

An Application of Time-Dependent Holding Costs and System Reliability in a Multi-Item Sustainable Economic Energy Efficient Reliable Manufacturing System

Sustainable efficient energy is the key factor of any sustainable manufacturing system. This study addresses a multi-item sustainable economic energy efficient reliable manufacturing quantity (MSEEERMQ) model. The manufacturing system produces defective products during long-runs, where those products may be reworked under the optimum effect of energy and carbon footprint with some costs. As all products are not sold immediately, the holding cost increases based on time. The management decides the system design variable to reduce energy consumption cost and increase system reliability under some time-dependent holding costs, and the optimum energy such that the maximum profit of the production model is obtained with a system reliability as a decision variable. The inflation and time-value of money are considered to calculate the cost of the production model under efficient energy. Using control theory, an Euler–Lagrange method is employed to obtain the sustainable critical path, which gives the optimal solution of the model. There are two lemmas to prove the global optimal solution of the model through the control theory. There is an illustrative example to test the model. Under different conditions there are other two examples with graphical representation and sensitivity analysis. Numerical studies reveal that maximum profit is obtained at the optimal value of the decision variable.

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.

Sequential time-dependent reliability analysis for the lower extremity exoskeleton under uncertainty

This paper proposes a sequential time-dependent reliability analysis method by considering time sequence and correlation of failure processes for the lower extremity exoskeleton under uncertainty, which will provide an approach to improving the comfort and safety for the wearer. A kernel density function based uncertainty quantification method is provided for precisely quantitatively estimating the time-dependent reliability of joints and the position of the end-effector firstly. After decoupling time sequence and failures correlation due to error propagation, the original reliability problem is then transferred to a series time-dependent reliability model. The time-dependent system reliability analysis is finally realized by calculating conditional probability. A case study is implemented to testify the effectiveness of the proposed method.

Importance sampling-based system reliability analysis of corroding pipelines considering multiple failure modes

The importance sampling (IS) technique is employed to evaluate the time-dependent system reliability of corroding pipeline segments containing multiple active corrosion defects by considering two competing failure modes, small leak and burst. The IS density functions in the standard normal space for incremental probabilities of small leak and burst of the pipe segment over a short time period are established as the weighted averages of the IS density functions for small leak and burst, respectively, at individual corrosion defects. The IS density functions for incremental probabilities of small leak and burst of individual defects are centred at the design points in the corresponding failure domains. Four numerical examples that are representative of the onshore gas transmission pipelines in the US are used to illustrate the application of the proposed methodology. The results demonstrate the excellent accuracy and efficiency of the methodology.

Sensitivity of system reliability of corroding pipelines to modeling of stochastic growth of corrosion defects

The time-dependent system reliability of pressurized pipeline segments containing multiple active corrosion defects is evaluated to investigate the sensitivity of the system reliability to various modeling options regarding the corrosion growth. The gamma and inverse Gaussian processes are employed to model the defect growth, whereas the dependence among the growths of different defects is characterized using the Gaussian copula and sum-of-stochastic-process approach. The analysis results indicate that all else being equal the system reliability is insensitive to using the Gaussian copula or sum-of-stochastic-process approach to model the dependence among the growths of different defects. Furthermore, using the inverse Gaussian process to model the defect growth leads to slightly higher failure probabilities than using the gamma process. Finally, the results suggest that the use of one year as the time increment to simulate Gaussian copula-based dependent defect growths in the reliability analysis is adequate for the relatively slow corrosion growth that is typical for buried pipelines.

Time-Dependent Series System Reliability Analysis Method and Application to Gear Transmission Systems

A gear transmission system such as a gear train is a series system in sense of reliability evaluation, while it is different from a traditional series system such as a chain. Therefore, the conventional series system reliability model is not appropriate for gear transmission system. Based on the time-dependent configuration and the time-dependent loading path of a gear train, system specific reliability modeling technique is presented, by which a gear train is taken as a time-dependent series system, consisting of different components (gear teeth) in different time intervals. To illustrate the application of the reliability analysis method, several time-dependent series system reliability models are developed for different types of gear trains, the reliability estimation results are compared with those obtained by traditional series system reliability model.

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.