Time-variant System Reliability Research Articles

Time-Varying Reliability Analysis of Multi-Cracked Beams Considering Maintenance Dependence

Time-varying reliability models of multi-cracked beam structures are established in this paper, which provide a theoretical method for the safety evaluation of multi-cracked beam structures. The reliability models proposed in this paper consider the interaction between the complex statistical correlations between system parameters during system operation and maintenance correlations, which is a difficult problem in the time-varying reliability modeling that takes into account work mechanisms and maintenance behavior. In the proposed models, multiple cracked elements are regarded as a dependent series system. The stresses, crack extensions, and multiple failure modes between each element constitute the complex failure dependence of the system. The time-varying reliability models of a multi-cracked beam structure are established via the neural network method and failure dependence analysis. Moreover, the failure dependence coefficient is proposed to quantify the time-varying failure dependence. Based on the working principle of the beam structures and the maintenance mechanism for the cracked state of the beams, a time-varying system reliability mode considering the maintenance dependence is proposed. Furthermore, the maintenance dependence coefficient index is proposed to quantitatively measure the interaction between the maintenance dependence and the failure dependence. Finally, the validity of the model is verified through the Monte Carlo simulation method. In the numerical examples, the relationship between maintenance dependence and failure dependence is illustrated and the influences of the statistical characteristics of the maintenance characteristic parameters on the maintainability and failure dependence are analyzed.

BIM–based time-varying system reliability analysis for buildings and infrastructures

In recent decades, building information modelling (BIM) technology has been rapidly developed and applied widely in the building industry. Although BIM technology is crucial for the whole design, construction, operation, and maintenance life cycle of building structures, BIM-based infrastructure time effect analysis still has limitless potential. Nevertheless, the current BIM-based study on time effect focuses mostly on cost and schedule analyses for buildings. The assessment of infrastructure places greater emphasis on component level evaluation and ignores how components affect system safety. In this paper, a BIM-reliability integrated technology for time-varying and system analysis of structural safety is developed. In the developed framework, parameters information for calculating component reliability are first extracted from the BIM model. The BIM model is then transformed into a topology structure and based on the transformed structure, the risk assessment is conducted through stochastic approaches. The suggested framework is demonstrated using two different cases: a long-term corrosion impact analysis example of an underground pipeline network and a short-term seismic load analysis instance of a four-layer frame. In the short-term analysis, the structural analysis is performed by integrating REVIT-Dynamo and OpenSees, taking into account the randomness of the material properties and the fabrication size. The design optimization can be carried out by comparing the reliability of inter-storey displacement under seismic load in different design schemes, and the system failure probability is more sensitive to the changes in the failure probability of each floor. In the long-term analysis, the time-varying reliability and importance index of each pipe during its lifetime are calculated using the transformed topology algorithm and the stochastic corrosion model. It is found that the BIM-reliability integrated technology can effectively evaluate the impact of time effect on the safety of the structures and is of great significance for structures with unknown working environment and working conditions.

Time-Variant Reliability Analysis for a Complex System Based on Active-Learning Kriging Model

The active-learning Kriging (ALK)–based time-variant system reliability analysis has been widely concentrated. Unfortunately, the current time-variant system reliability methods are mostly focused on the series system, parallel system, or series-parallel system; thus, they cannot efficiently deal with the time-variant reliability problem of a complex system such as bridge system, network system, and so on. In view of this issue, the paper proposes an efficient time-variant reliability method for a complex system by introducing the structure function into the ALK-based time-variant reliability analysis. Firstly, similar to the ALK-based time-variant system reliability method, some extreme values corresponding to the initial input samples are optimized, and thus the initial extremum response surface is constructed based on the Kriging model. Then, considering the epistemic uncertainty of the Kriging predictions, the predicted response of system structure function under a particular input sample is viewed as a random variable, and its mean and variance are computed based on the minimal cut sets of a complex system. Lastly, considering the aleatory uncertainty between the different candidate samples, the point corresponding to the maximum prediction variance is selected, the most important component is decided by introducing the structure importance, and its extreme value is correspondingly optimized to update the initial extremum response surface. The stopping criterion is also provided in this paper and the effectiveness of the proposed method is illustrated by several examples.

Time-Variant System Reliability Analysis of Concrete Sewer Pipes under Corrosion Considering Multiple Failure Modes

This paper presents a framework for time-variant system reliability analysis of concrete sewer pipes considering multiple modes of failure. Sewer pipelines are among critical infrastructure systems, designed to collect and transport wastewater away from communities. Such pipes are typically subjected to corrosion and subsequent damage because of continuous contact with corrosive materials. Corrosion is here modeled in terms of the reduction in the pipe wall thickness. In the proposed framework, prevailing uncertainties in the characteristics of wastewater fluid, geometric properties of fluid cross section, and corrosion-related parameters of concrete are quantified as random variables. Next, various modes of failure under bending, shear, excessive cracking, and cover loss are formulated as multiple limit-state functions. This leads to a general system reliability problem defined as a series system of parallel subsystems, i.e., cut sets. Further, by introducing the corrosion model into the limit-state functions, a time-variant system reliability problem is established in which the integration domain is conditioned to the corrosion level at each point in time. By integrating over the conditional probabilities through a rejection sampling method, the failure probability is computed given the corrosion level over the desired time span. The results show that the failure probability increases sharply with time and corrosion level. For instance, the failure probability exceeds 80% for pipes over 50 years and at corrosion levels of over 40%. Moreover, the sensitivity analysis shows that the acid-consumption capacity of the pipe material, the pH-related factor, and the proportion of S2− dissolved highly influence the failure probability. The maximum effects of these parameters occur within 0%–10% corrosion. The results of this study can be used to evaluate the failure probability of sewer pipes given their age and current corrosion level.

Time-Variant Reliability Analysis for a Complex System Based on Active-Learning Kriging Model

The active-learning Kriging (ALK)–based time-variant system reliability analysis has been widely concentrated. Unfortunately, the current time-variant system reliability methods are mostly focused on the series system, parallel system, or series-parallel system; thus, they cannot efficiently deal with the time-variant reliability problem of a complex system such as bridge system, network system, and so on. In view of this issue, the paper proposes an efficient time-variant reliability method for a complex system by introducing the structure function into the ALK-based time-variant reliability analysis. Firstly, similar to the ALK-based time-variant system reliability method, some extreme values corresponding to the initial input samples are optimized, and thus the initial extremum response surface is constructed based on the Kriging model. Then, considering the epistemic uncertainty of the Kriging predictions, the predicted response of system structure function under a particular input sample is viewed as a random variable, and its mean and variance are computed based on the minimal cut sets of a complex system. Lastly, considering the aleatory uncertainty between the different candidate samples, the point corresponding to the maximum prediction variance is selected, the most important component is decided by introducing the structure importance, and its extreme value is correspondingly optimized to update the initial extremum response surface. The stopping criterion is also provided in this paper and the effectiveness of the proposed method is illustrated by several examples.

Cumulative residual Kullback-Leibler divergence based sensor placement using reliability criteria

In the current work, we propose a novel, information theoretic based sensor placement design approach for placing sensors in a steady state linear flow process for reliable estimation of variables. In particular, the optimal sensor placement minimizes the cumulative residual Kullback-Leibler divergence based objective function. Unlike the existing approaches that maximize system reliability corresponding to a fixed time, the proposed approach utilizes the time varying system reliability to compute the objective function. Further, it provides a mechanism to the end-user to tailor the optimal design by specifying her preference as the reference system reliability in the objective function. The sensor placement problem proposed in our current work is an integer non-linear programming problem. We also propose a greedy heuristic algorithm to solve this problem with low computational cost. Finally, we demonstrate the utility of the proposed design approach on a benchmark case study.

Parametric Plots of Limit-State Surfaces as a Design Tool in Time-Variant System Reliability

The ability to accurately determine the temporal safe region in time-variant reliability analysis is seminal for reliability-based design. When stochastic excitations are present and discrete-time approaches are invoked, the errors can be large when one uses only one past safe event (and one new failure event) at each time-step. Furthermore, when all previous safe events are accumulated and used, the calculations can be time consuming and the accuracy not ensured. In this paper, a minimal, or a so-called extreme limit-state, surface is obtained to identify the system temporal safe region in an economical manner. To do this, the limit-state surface motion for each failure mode is recorded as a parametric polar plot that provides both magnitude and relative angle of the vectors from the origin to the most-likely failure points (MLFPs) in standard normal space. The angle differences provide correlation and the magnitude differences provide importance. At the component-level, a few logical policies that compare correlation and the magnitude ensure that the safe region is sufficiently recognized. At the system-level, the temporal average of correlations and the magnitudes at the component-level, along with series or parallel system designations, foretells which failure modes are needed to form the system extreme limit-state surface. The impact of the work includes an immediate recognition of the important failure modes and reduced computation for methods such as multi-normal integration. Case studies of both series-system reliability and parallel-system reliability are presented using structural beams excited by stochastic loads and plagued with degrading material properties and dimensions. The accuracy of the extreme LSS is demonstrated cogently. The use of the polar plots as a design tool becomes evident.

Subset simulation based approach for space-time-dependent system reliability analysis of corroding pipelines

This paper proposes a subset simulation (SS) based approach for space and time-dependent reliability analysis of corroding pipelines. It is assumed that the pipeline can fail either due to leakage and/or burst. We propose two distinct approaches for tackling the problem. In the first approach, we treat the problem as a time-variant system reliability problem. The problem is formulated as a series system where failure at one of the defect locations will result in failure of the pipeline. This approach is particularly suitable when there are only a limited number of corrosion defects. In the second approach, the reliability analysis problem is treated as a ‘space-time variant’ reliability analysis problem. This approach is particularly suitable when exact knowledge about the number of defects is not available. In both the approaches, the time-dependent probability of failure is represented in an auto-regressive form such that the probability of failure at a given time can be computed based on the probability of failure at the previous time and an incremental failure probability. A simple composite limit-state function is proposed for computing the incremental failure probability. SS is used for computing the initial and incremental failure probabilities. To illustrate performance of the proposed approach, four pipeline problems representing different scenarios are considered. For all cases, the proposed approach is found to yield highly accurate results.

Time-variant system reliability analysis method for a small failure probability problem

This paper proposes a time-variant system reliability analysis method by combining multiple response Gaussian process (MRGP) and subset simulation (SS) to solve the small failure probability problem. One common method for time-variant reliability analysis is based on the double-loop procedure where the inner loop is the optimization for extreme values and the outer loop is extreme-value-based reliability analysis. In this paper, a new single-loop strategy is firstly proposed to decouple the double-loop procedure by using the best value in current initial samples to approximate the extreme value, thus the extremal optimization in inner loop can be avoided. Then the MRGP model is used to construct the surrogate model of extreme value response surface for time-variant system reliability analysis based on the approximated extremums. Meanwhile, the Kriging model is also constructed based on the initial samples to assist in searching the new sample point. Furthermore, for selecting the new point that resides as close to the extreme value response surface as possible from the Monte Carlo simulation (MCS) sample pool, three learning functions (U-function, EFF-function and H-function) are respectively used to find the new random variable sample point based on the MRGP model and the expected improvement (EI) function is used to find the new time sample point based on the Kriging model. Finally, for reducing the size of candidate sample pool and the computing burden, the SS method is combined with the MRGP model to deal with the small failure probability problem. The effectiveness of the proposed method is also demonstrated by several examples.

Effects of correlation between the adjacent components on time dependent failure probability of corroded pipelines

This study aims to investigate the effects of correlation of random variables between the adjacent components on time variant system reliability of corroded pipelines. The system reliability analysis is conducted using a combination of Latin Hypercube Sampling and Cholesky decomposition methods for four different failure modes (Composite (C), Corrosion Perforation (CP), Local Burst (LB) and Rupture (R)). Since the multivariate target correlation matrix might be non-positive definite, a combination of two efficient optimization techniques is implemented to find the minimum perturbation for transforming the non-positive definite correlation matrix into a positive definite one. The findings of the paper indicate that there is no monotonic order in either lower or upper bound of the system failure probability of corroded pipelines with uniform variation in target correlation matrix. Furthermore, some correlations can change the upper bound of the system failure probability of corroded pipelines about 10%. In addition, the cumulative upper bounds of the system failure probability of the investigated case study for C, CP, LB and R failure modes reach unity after 9, 10, 11 and 13 years, respectively.

A single-loop strategy for time-variant system reliability analysis under multiple failure modes

This paper proposes a single-loop strategy for time-variant system reliability analysis by combining multiple response Gaussian process (MRGP) and Kriging model. Firstly, a new strategy is provided to decouple the double-loop strategy of extreme-value-based time-variant system reliability analysis, where the extreme value response in the double-loop strategy is approximated by the best value in the initial points to avoid the inner-loop extremal optimization. Then, the extreme value response surface is directly built based on the approximated extreme value using the MRGP model. Meanwhile, a Kriging model based on initial points is also proposed to search a new sample point. Furthermore, in order to update the initial sample points and improve the accuracy of the proposed strategy, three learning functions (U-function, EFF-function and H-function) and expected improvement (EI) function are combined to select a new point that resides as close to the extreme value response surface as possible. Finally, several examples are presented to demonstrate the effectiveness of the proposed strategy.

Reliability-based design optimization of time-dependent systems with stochastic degradation

A major hurdle in the application of reliability-based design optimization (RBDO) to time-dependent systems is the continual interplay between calculating time-variant reliability (to ensure reliability policies are met) and moving the design point to optimize some objective function, such as cost, weight, size and so forth. In most cases the reliability can be obtained readily using so-called fast integration methods. However, this option is not available when certain stochastic processes are invoked to model gradual damage or deterioration. In this case, sampling methods must be used. This paper provides a novel way to obviate this inefficiency. First, a meta-model is built to relate time-variant system reliability to the entire design space (and noise space if required). A design of experiments paradigm and Monte Carlo simulation using the mechanistic model determines the corresponding system reliability accurately. A moving least-squares meta-model relates the data. Then, the optimization process to find the best design point, accesses the meta-model to quickly evaluate objectives and reliability constraints. Case-studies include a parallel Daniel's system and a series servo control system. The meta-model approach is simple, accurate and very fast, suggesting an attractive means for RBDO of time-dependent systems.

Estimation of time-variant system reliability of nonlinear randomly excited systems based on the Girsanov transformation with state-dependent controls

The problem of time-variant system reliability analysis of nonlinear dynamical systems subjected to random excitations is considered. The governing equations are formulated as a set of Ito’s stochastic differential equations. Subsequently, a Monte Carlo simulation strategy, which incorporates Girsanov’s transformation- based variance reduction step, is developed. The novel element of the work lies in the formulation of state-dependent Girsanov’s control forces for estimating the system reliability. The study considers failure modes arranged in series, parallel, or composite configurations. Illustrative examples include studies on a 5-dof Duffing’s system and an inelastic frame subjected to multi-support, non-stationary, Gaussian excitations. The numerical results demonstrate significant variance reduction achieved in estimating low probabilities of failure.

An improved TRPD method for time-variant reliability analysis

In this paper, an improved time-variant reliability analysis method based on stochastic process discretization (iTRPD) is proposed. Firstly, the time-variant reliability problem is transformed into a time-invariant series system reliability problem. Then the first order reliability method (FORM) is employed to analyze the reliability of each component of the system, and a corresponding approach is given to calculate the correlation coefficient matrix of all the components’ performance functions. Finally, the target time-variant reliability can be obtained with the reliability index vector and the correlation coefficient matrix of the involved components. In this study, the iTRPD is further applied to the system reliability problems, and hence a corresponding time-variant system reliability analysis method is also developed. Four numerical examples are investigated to demonstrate the effectiveness of the proposed methods.

Time-Variant System Reliability Assessment by Probability Density Evolution Method

AbstractThe time-variant system reliability analysis is a challenging and significant topic, which also faces the common obstacles of traditional system reliability methods such as combination expl...

System reliability assessment of deteriorating structures subjected to time-invariant loads based on improved moment method

The time-variant system reliability analysis is a significant topic in the field of reliability engineering. Although progress has been made, there remain multiple challenges in the existing methods including the explosive number of possible failure modes, requiring correlation information, and excessive computational efforts.In the present work, an improved moment method with high accuracy, efficiency and robustness is proposed for system reliability analysis of deteriorating structures. First, by introducing the complete system failure process, an equivalent time dependent performance function describing a deteriorating structural system is obtained. Second, a point estimate method based on the adaptive trivariate dimensional decomposition is adopted to calculate the first six moments of the performance function. And third, a saddlepoint approximation involving the first six moments is developed to estimate the system failure probability. Several examples are investigated to verify the accuracy, efficiency and stability of the proposed method.

Statistical Performance Assessment of an NDE-Based SHM-DP Methodology for the Remaining Fatigue Life Prediction of Monitored Structural Components and Systems

Integrated structural health monitoring and damage prognosis (SHM-DP) methodologies, coupled with sensor-based nondestructive evaluation (NDE) techniques, are becoming increasingly important for the near-real-time condition assessment (i.e., SHM) and future performance predictions (i.e., DP) of aging mechanical systems, civil structures, and infrastructure networks, as well as automotive, naval, and aerospace vehicles. A successful SHM-DP strategy, capable of identifying all critical damage mechanisms while accounting for all relevant sources of uncertainty, can be used as an advanced tool to effectively and optimally manage the life-cycle of the monitored system, recursively forecast its remaining useful life (RUL), and ultimately reduce the overall ownership cost through dynamic reliability-based inspection and maintenance (RBIM) plans, system downtime minimization, catastrophic failure prevention, and potential RUL extension. In this perspective, fatigue damage propagation is one of the most critical and unpredictable deterioration processes for a large variety of structural and mechanical systems that are subjected repeatedly to cyclic and/or random operational loading during their service life. Within this limited scope, the authors developed a comprehensive NDE-based SHM-DP framework for recursively predicting the time-varying system reliability and the remaining fatigue life (RFL) of monitored systems subjected to deterioration by multi-site fatigue damage propagation. This paper provides a brief overview of the proposed framework and then uses a set of experimental fatigue test data to perform a thorough statistical performance assessment of the developed methodology at the local reliability component level (i.e., single damage mechanism and single damage location) including NDE detectability and measurement uncertainty as well as both load and model parameter uncertainty.

Probabilistic-based prediction of lifetime performance of RC bridges subject to maintenance interventions

In this paper, a probabilistic- and finite element-based approach to evaluate and predict the lifetime performance of reinforced concrete (RC) bridges undergoing various maintenance actions is proposed with the time-variant system reliability being utilized as a performance indicator. Depending on their structural state during the degradation process, the classical maintenance actions for RC bridges are firstly categorized into four types: Preventive type I, Preventive type II, Strengthening and Replacement. Preventive type I is used to delay the onset of steel corrosion, Preventive type II can suppress the corrosion process of reinforcing steel, Strengthening is the application of various maintenance materials to improve the structural performance and Replacement is performed to restore the individual components or overall structure to their original conditions. The quantitative influence of these maintenance types on structural performance is investigated and the respective analysis modules are written and inputted into the computer program. Accordingly, the time-variant system reliability can be calculated by the use of Monte Carlo simulations and the updated the program. Finally, an existing RC continuous bridge located in Shanghai, China, is used as an illustrative example and the lifetime structural performance with and without each of the maintenance types are discussed. It is felt that the proposed approach can be applied to various RC bridges with different structural configurations, construction methods and environmental conditions.

A time-variant reliability analysis method for structural systems based on stochastic process discretization

In this paper, we propose a new method for analyzing time-variant system reliability based on stochastic process discretization, which provides an effective tool for reliability design of many relatively complex structures considering the whole lifecycle. Within a design lifetime, the stochastic process is discretized into a series of random variables, and meanwhile, we can derive a time-invariant limit-state function in each time interval; the discretized random variables from the stochastic processes and the original random variables are transformed to the independent normal space, and a conventional time-invariant system reliability problem is derived through the linearization to each discretized limit-state functions; by solving this time-invariant system reliability problem, we can obtain the structural reliability or failure probability within the design lifetime. Finally, in this paper, we provide four numerical examples to verify the effectiveness of the method.

A Novel Approach to Evaluate the Time-Variant System Reliability of Deteriorating Concrete Bridges

Bridge time-variant system reliability is a useful measure to evaluate the lifetime performance of deteriorating bridge structures under uncertainty and is an influential performance indicator in bridge maintenance management programs. This paper proposes a computational methodology based on the Monte Carlo simulations for evaluating the time-variant system reliability of concrete bridges under environmental attacks. Methods related to the reduction of concrete sections and the variation of the load effects acting on the components are investigated using a finite element-based computational program, CBDAS (Concrete Bridge Durability Analysis System), to perform the assessment of lifetime structural performance. With regard to system reliability, a practical technique for searching the structural failure mode is also presented and a program, SRMCS (System Reliability by Monte Carlo Simulations), based on the Monte Carlo simulations is written to calculate and evaluate the structural system reliability of deteriorating concrete bridges. Finally, three numerical examples are presented to display the CBDAS and SRMCS functions.