Time-dependent Reliability Problem Research Articles

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 reliability analysis of corroded RC beams based on the phase-type fitting method

It remains an important challenge to quantitatively describe the corrosion of reinforced concrete (RC) structures under chloride penetration. When considering the uncertainties encountered throughout the life cycle of RC structures exposed to a corrosive environment and evaluating their safety and reliability, the complexity of the problem intensifies. To address these issues, this paper focuses on the time-dependent reliability analysis of corroded RC beams, utilizing the phase-type (PH) fitting method. Initially, a model for the time-dependent reliability of corroded RC beams is established, incorporating the time-dependent chloride diffusion coefficient. Subsequently, a novel PH fitting method is proposed. The effectiveness of this new method is demonstrated through numerical examples. Furthermore, the time-dependent reliability analysis of corroded RC beams is compared using both the PH fitting method and the Monte Carlo simulation. The results reveal that the proposed method can accurately and efficiently deal with time-dependent reliability problems.

A generalized index for functionality-sensitive resilience quantification

The resilience index based on the integral of functionality/performance function within a time interval of interest has been widely used in the literature. However, it cannot fully reflect the sensitivity of the resilience of the object (e.g., structure or system) to the variation of functionality. In this paper, a generalized index is proposed to measure the resilience of structures and systems that is sensitive to the instantaneous functionality, as reflected by a generating function involved in the proposed resilience index. The mathematical properties of the proposed resilience model are discussed. It is proven that, the proposed index varies within [0,1], and is a monotone measure. If the generating function is a power function with α being the exponent (called α-fairness function), the additivity property (i.e., superadditivity, additivity, and subadditivity) of the resilience index is dependent on the value of α. It is also observed that the existing resilience index is a special case of the proposed one. A byproduct is that, with a properly selected generating function, the time-dependent reliability problem of an aging structure can also be described by the proposed resilience index. The applicability of the proposed resilience model is demonstrated through four examples.

An efficient method for time-dependent reliability problems with high-dimensional outputs based on adaptive dimension reduction strategy and surrogate model

Time-dependent reliability analysis with high dimensional outputs is a challenge because of ‘curse of dimensionality’ and accurate reliability estimation over entire time interval is computationally expensive. In this paper, an efficient time-dependent reliability analysis method is proposed for systems with high dimensional outputs based on adaptive dimension reduction strategy and Kriging. The adaptive Kriging model is constructed in low-dimensional space after performing principal component analysis (PCA) on original time-dependent output. A new learning function and corresponding stopping criterion are developed as the guideline for selecting training samples at each iteration. The proposed learning function focuses on prediction accuracy over the entire time interval and the stopping criterion is directly linked to failure probability. Subsequently, fewer number of function evaluations is required compared with existing competitive works. Moreover, the key advantage of the proposed method is that it is a single-loop process, i.e., the selection of training samples, dimension reduction and Kriging modeling have been combined simultaneously at each iteration with adaptive manner. However, the existing competitive methods, generally, have two independent stages, i.e., stage one is collecting training samples and stage two is performing PCA and Kriging modelling for time-dependent reliability analysis. Thus, these methods cannot fully utilize the information provided by PCA to find optimal training samples. It is noteworthy that the dimension reduction is also an adaptive process in the proposed method, i.e., dimension reduction changes with the training samples at each iteration. The applicability, accuracy and efficiency of the proposed method are validated through three numerical examples and one engineering example.

Application of LSTM based on the BAT-MCS for binary-state network approximated time-dependent reliability problems

Reliability is an important tool for evaluating the performance of modern networks. Currently, it is NP-hard and #P-hard to calculate the exact reliability of a binary-state network when the reliability of each component is assumed to be fixed. However, this assumption is unrealistic because the reliability of each component always varies with time. To meet this practical requirement, we propose a new algorithm called the binary-addition-tree algorithm and Monte Carlo simulation based Long Short-Term Memory (LSTM-BAT-MCS), based on long short-term memory (LSTM), the Monte Carlo simulation (MCS), and the binary-addition-tree algorithm (BAT). The superiority of the proposed LSTM-BAT-MCS was demonstrated by experimental results of three benchmark networks with at most 10−4 mean square error.

An envelope-function-based algorithm for time-dependent reliability analysis of structures with hybrid uncertainties

This paper proposes a novel envelope-function-based algorithm for time-dependent reliability analysis considering random and interval uncertainties. First, the envelope function of the bound of the limit-state function is approximated with assistance of the first-order reliability method, thereby transforming time-dependent reliability problem into a time-independent one. Here, the Kriging modeling method is utilized to construct the expansion point determination function for reducing the most probable point search, which significantly accelerates the expansion point determination in constructing the envelope function. After the envelope function is found, the time-dependent reliability in terms of random and interval uncertainties is efficiently calculated by a multivariate Gaussian integral. Finally, five case studies are used to demonstrate the effectiveness of the proposed algorithm. The results indicate it can provide accurate and efficient time-dependent reliability analysis for structures where the random and interval uncertainties coexist.

Time-dependent kinematic reliability analysis of gear mechanism based on sequential decoupling strategy and saddle-point approximation

Accurate and efficient reliability evaluation is critical to ensure the safety of gear mechanism. This paper aims to develop an effective and practical method for time-dependent kinematic reliability of gear mechanism. Firstly, dynamic model of gear mechanism is established, and a surrogate model of kinematic error is obtained based on BP neural network. After that, we employ a sequential decoupling strategy of efficient global optimization to transform the time-dependent reliability problem into a time-independent one, with which the second-order information of the extreme limit-state function can be then obtained. Finally, the saddle-point approximation method is applied to estimate the time-dependent kinematic reliability of the gear mechanism. The accuracy and efficiency of the proposed method are verified by several engineering problems, and comparisons are made against other existing reliability methods. Results of the engineering cases show that the proposed method can effectively reduce the limit-state function call numbers while reaching the same accuracy as Monte Carlo Simulation.

An efficient importance sampling approach for reliability analysis of time-variant structures subject to time-dependent stochastic load

Structural performance is affected by deterioration processes and external loads. Both effects may change over time, posing a challenge for conducting reliability analysis. In such context, this contribution aims at assessing the reliability of structures where some of its parameters are modeled as random variables, possibly including deterioration processes, and which are subjected to stochastic load processes. The approach is developed within the framework of importance sampling and it is based on the concept of composite limit states, where the time-dependent reliability problem is transformed into a series system with multiple performance functions. Then, an efficient two-step importance sampling density function is proposed, which splits time-invariant parameters (random variables) from the time-variant ones (stochastic processes). This importance sampling scheme is geared towards a particular class of problems, where the performance of the structural system exhibits a linear dependency with respect to the stochastic load for fixed time. This allows calculating the reliability associated with the series system most efficiently. Practical examples illustrate the performance of the proposed approach.

Time-dependent reliability analysis of service-proven quay walls subject to corrosion-induced degradation

The assessment of service-proven quay walls subject to corrosion-induced degradation is inherently a time-dependent reliability problem. Two major challenges are the modelling of corrosion and taking into account the decrease of epistemic uncertainty throughout the quay wall's service life. The main objective of this study is to examine the probability of failure, despite successful past performance, when the quay wall is subject to corrosion and randomly imposed variable loads. The development of the annual failure rate is modelled using crude Monte Carlo and by performing a first-order system reliability analysis. The annual failure rates found for service-proven quay walls vary over time. For those with successful service histories and subject to low corrosion rates, the highest reliability indices are observed in the first year of the service life, whereas with higher corrosion rates the final year prevails. In general, it seems more practical to evaluate reliability on an annual basis rather than over longer time periods, since the latter will introduce an iterative procedure to determine the wall's remaining lifetime. The key findings of this study can be crucial for the lifetime extension of existing quay walls, and presumably also for other service-proven geotechnical structures subject to corrosion.

A time-variant reliability analysis method for non-linear limit-state functions with the mixture of random and interval variables

Most of the current time-variant reliability analysis methods are applicable for only random variables. However, some of the uncertain parameters can only be easily modeled by interval variables in many engineering applications. The main contribution of this paper is to propose a new time-variant reliability analysis method for nonlinear limit state function with the coexistence of random variables and interval uncertain variables. Three primary strategies are put forward. Firstly, the stochastic process in the time-variant limit-state function is discretized, equivalently gaining several static limit-state functions at different time. Secondly, each static limit-state function is linearized at the most probable point (MPP) and the worst-case point (WCP) of interval variable, by doing which, the ordinary time-dependent reliability problem is equally transformed into a static reliability one with mixed uncertain variables. Finally, complex nested optimization problems using sequential iterations are effectively solved in mixed reliability calculation. The proposed method can obtain structural reliability considering time effects and mixed uncertainties. The effectiveness and the efficiency of the proposed method are demonstrated by four numerical examples.

A novel extended crossing rate method for time-dependent hybrid reliability analysis under random and interval inputs

With the aim of efficiently estimating the upper bound of time-dependent failure probability for the time-dependent reliability problem involving random and interval inputs (RI-TDFP), an extended crossing rate method is proposed. The proposed method first converts the time-dependent hybrid reliability analysis into a temporal and spatial multi-parameter problem. Then, it uses the extended crossing rate strategy to estimate the RI-TDFP. The proposed strategy is a single-loop strategy, which is more efficient than the nested double-loop strategies. The proposed method avoids using discretization or optimization strategies to estimate the global minimum of the time-dependent performance function with respect to the time parameter and interval inputs, and thus the computational cost is further reduced. Finally, the proposed method avoids using the first order reliability method (FORM) for reliability analysis with respect to the random inputs, and thus the proposed method is more accurate than the FORM.

Time-dependent mechanism reliability analysis based on envelope function and vine-copula function

Time-dependent reliability analysis is an important and challenging issue due to the time-dependent motion and loadings of a mechanism. In this paper, a general framework and corresponding methods are proposed to deal with the time-dependent reliability analysis of a mechanism effectively. The envelope function is used to estimate the finite expansion points, which converts the time-dependent reliability problem to the time-independent reliability problem under the general probability distribution. The covariance matrix is then derived with the vine-copula function to describe the correlation of the performance at the obtained expansion points. With the covariance matrix, the joint probability density function (PDF) is acquired based on the kernel density estimation (KDE) method. The time-dependent reliability is finally estimated by the integral. The case study with different conditions is provided to validate the efficiency and accuracy of the proposed approach.

Fast integration algorithms for time-dependent structural reliability analysis considering correlated random variables

During the service life of civil infrastructures, their performance, functionality, and serviceability are essentially time-dependent reliability problems as both structural resistance and load effect are related with time. With respect to the practical engineering, the performance function is usually complicated, multi-dimensional and implicit and involves both correlated and non-correlated random variables; thus the computational process of time-dependent reliability analysis is relatively challenging. To address this issue, the time-dependent failure probability of structures with complicated, multi-dimensional and implicit performance functions involving correlated random variables is mathematically formulated in this paper. A novel and efficient approach is then proposed to compute the time-dependent failure probability. In the proposed method, the integral of time-dependent failure probability with respect to time domain and random-variate space are estimated by Gauss-Legendre quadrature and point-estimate method based on bivariate dimension-reduction integration, respectively. Accordingly, the time-dependent probability of failure within a given period is decomposed into a series of probabilities of failure with time-dependent random variables at specified time points conditioned on the estimating points of the time-independent random variables, which can be evaluated from state-of-the-art techniques for reliability assessment. The efficiency and accuracy of the proposed method are demonstrated by three numerical examples with either explicit or implicit performance functions involving correlated random variables, in which Monte Carlo simulations are employed for comparison.

Reliability sensitivity analysis method for time-dependent problem based on first-passage method

The sensitivity index plays a critical role in the design of product and is used to quantify the impact degree of the uncertainty of the input variable to the uncertainty of the interest output. This paper presents a new local reliability sensitivity method and a global reliability sensitivity analysis method of time-dependent reliability problems. Firstly, according to the Poisson's assumption-based first-passage method, the local reliability sensitivity index is directly obtained by calculating the partial derivative of the failure probability to the distribution parameters of input random variable. Then, the moment-independent global reliability sensitivity index of the time-dependent problems is derived based on the concept of moment-independent. Finally, the efficiency and accuracy of the proposed method are verified with the reference results of Monte Carlo simulation.

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.

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.

LRFD for assessment of deteriorating existing structures

The deterioration of infrastructures is a widespread problem in many countries. In order to assess such structures for continued future service, simple and practical tools need to be developed for evaluating the time-dependent reliability and performance of the structures. This paper describes the concept of a resistance reduction factor due to degradation of a component to approximate a time-dependent reliability problem as a time-independent one. With the factor the time-varying resistance can be equivalently replaced with a time-invariant resistance, and load and resistance factors can be determined for the assessment applying simple AFOSM. An approximation method to determine the factor is proposed, and a numerical example shows that the target reliability level can be achieved fairly accurately using an approximate reduction factor. It is also demonstrated that the approximation method can be applied to estimate a resistance reduction factor including the cases when the strength of a component is restored to some extent by means of inspection and repair, and, accordingly, to evaluate the effect of inspection and repair on the reliability of the component.