Time-dependent Reliability Research Articles

Time-dependent reliability analysis of flood defenses under cumulative internal erosion

Internal erosion is a significant cause of failure in dams, levees and other hydraulic structures. This article studies the time-dependent reliability of such structures under Backward Erosion Piping (BEP), a form of internal erosion in the foundation. First, a physics-based time-dependent piping failure model is presented. Second, a time-variant reliability analysis method is presented which allows to quantify how the reliability evolves over the years due to cumulative pipe growth over multiple flood events. Finally, these models are used to study the importance of time-dependence for reliability estimates of flood defenses in The Netherlands. The findings show that, particularly in coastal areas, incorporating time-dependence significantly reduces the computed failure probability. Reductions vary widely, ranging from a factor of 5 to more than 10 6 , depending on flood duration and levee properties. Therefore, reliability estimates for levees can be improved by incorporating time-dependent pipe development in the BEP failure model, and thereby contribute to avoiding unnecessary reinforcements.

Time-Dependent Failure Assessment of Ceramic Receivers

The outlet temperature targets for Gen 3 Concentrating Solar Power (CSP) systems pose a significant challenge to the structural reliability of high temperature metallic components, including those manufactured from nickel-based superalloys. Advanced ceramics present a potential solution due to their excellent high-temperature strength. However, accurate assessment of ceramic components requires an entirely different approach compared to metallic components. This paper describes the implementation of time-dependent reliability analysis of ceramic components in srlife – an open-source software package for estimating the life of high temperature CSP components. This new capability will allow high temperature CSP designers to make fair comparisons between competing metallic and ceramic designs and accurately assess the performance of different ceramic materials for CSP receivers and other components. The current version of the tool is available at https://github.com/Argonne-National-Laboratory/srlife.

Application of Binary Decision Diagrams in Time-Dependent Reliability Analysis

Binary Decision Diagrams (BDDs) are often used in specific types of reliability analysis known as topological (or structure) analysis and time-independent analysis. The previous focuses only on the analysis of system topology, which is defined by structure function. The latter takes into account the structure function together with the time-independent reliabilities of components that the system is composed of. However, the most interesting type of reliability analysis is time-dependent analysis in which reliabilities of the components are time-dependent functions. In this paper, we first present the development of a mathematical model of a non-repairable system composed of independent non-repairable components and explain the properties of this model from the point of view of time-dependent, time-independent, and topological reliability analysis. In the second part of the paper, we present and experimentally compare two methods for time-dependent reliability analysis of the considered mathematical model. The first method is based on the direct application of BDDs and we label it as a basic approach. The second, symbolic approach, combines BDDs with expression trees. The experimental comparison implemented using opensource C++ libraries TeDDy and GiNaC shows that the first method based on the basic approach is much faster than the second method using expression trees.

Outcrossing Rate Method for Nonstationary Non-Gaussian Performance Functions and Its Application to Time-Dependent Reliability Assessment

Outcrossing Rate Method for Nonstationary Non-Gaussian Performance Functions and Its Application to Time-Dependent Reliability Assessment

Nonprobabilistic time-dependent reliability analysis for uncertain structures under interval process loads

In this paper, a novel nonprobabilistic analysis framework is proposed to evaluate the time-dependent reliability of uncertain structures under time-varying loads. Firstly, a novel uncertainty propagation method is developed by combining interval process integration and surrogate-based interval analysis and the correlation coefficient between responses of adjacent time steps is further analyzed. Subsequently, the nonprobabilistic time-dependent reliability is analyzed base on the first-passage theory and the established interval model. Unlike existing nonprobabilistic methods that consider time-invariant external loads, the proposed method applies an interval process to describe time-varying external loads, thereby offering a broader range of applicability. Compared to existing nonprobabilistic methods that consider time-varying loads, the proposed method establishes a more refined nonprobabilistic time-dependent reliability model based on the first passage theory, achieving higher accuracy. The effectiveness and superiority of the proposed method are validated through a numerical example and an engineering application.

Time-dependent reliability analysis of aerospace electromagnetic relay considering hybrid uncertainties quantification of probabilistic and interval variables

Reliability is a crucial metric in aerospace engineering. The results of reliability assessments for components like aerospace electromagnetic relays directly impact the development and operational reliability of aerospace engineering systems. Current methods for analyzing the reliability of aerospace electromagnetic relays have limitations, such as neglecting the combined effects of multiple uncertain factors, degradation of key component properties, and the influence of fluctuations in aerospace environments. Additionally, these methods often assume a single-type uncertainty in the manufacturing process, leading to significant deviations between the analysis results and actual measurement results. To address these issues, this study proposes an efficient time-dependent reliability analysis method based on the HL-RF algorithm, considering a hybrid of probabilistic and interval uncertainty that accounts for degradation and environmental conditions. The proposed method is applied to the reliability analysis of actual aerospace electromagnetic relay products and compared with traditional methods, demonstrating significant advantages. The proposed method has been applied to the time-dependent reliability analysis of actual aerospace electromagnetic relay products under different environmental conditions. The analysis results exhibit an error margin within 5.12% compared to actual measurement results. Compared to analysis methods solely based on probabilistic uncertainty quantification or interval uncertainty quantification, this method reduces the analysis error by 52% and 67% respectively. When compared to two other state-of-the-art methods that integrate probabilistic and interval uncertainty quantification, the error reduction is 23%. These demonstrate the superiority of the proposed method and validates its effectiveness. The presented approach has the potential to be extended for reliability analysis in other aerospace electromechanical systems.

Subset simulation based simplified approach for pipeline with multiple irregular corrosion defects in time-dependent reliability analysis

Pipeline system plays an important role in the natural gas and petroleum transportation, and it is widely employed in the engineering application. However, the pipeline system is subjected to corrosion given the industry environment condition, or soil condition when it is buried. In this case, it is important to assess the remaining life of corroded pipeline. Consequently, it is important to predict the failure probability considering the corrosion growth over time and operating pressure. Nevertheless, the prediction of failure probability in corroded pipeline in not an easy task, due to the fact that a realistic corrosion usually has an irregular geometry, especially, when multiple irregular corrosion is involved in the analysis. To simplify the problem, this work presents a simplified procedure for time-dependent reliability analysis to predict the failure probability in pipeline with multiple irregular corrosion defects, considering two failure modes, the burst and leak mode. The approach is based on Subset Simulation and Weighted Depth Difference method, where the multiple irregular corrosion is treated by a discretization procedure and a weighting coefficient is evaluated in every discretization points. Then, this weighting coefficient is introduced into burst pressure assessment, which is employed by burst failure mode limit state function. In this work, the corrosion growth is modelled by power function corrosion model, and initial corrosion depth is generated randomly. The Subset Simulation is employed to evaluate the failure probability, where the Markov Chain Monte Carlo is adopted to evaluate the conditional probability and Metropolis-Hasting algorithm is employed to solve the problem. Finally, several scenarios with single and multiple irregular corrosion defects are analyzed to demonstrate the effectiveness of presented procedure.

Failure assessment of deteriorated steel light poles

Steel poles are extensively used as street light posts and various other applications within the power distribution network. For partially buried pole, the effect of corrosion below and at the ground level significantly controls the overall load capacity. In this study, number of in-service steel pole specimens extracted from field were assessed for the corrosion damage. The level of corrosion was estimated by remaining wall thickness measured using ultrasonic testing and the surface corrosion was estimated using 3D laser scanning to adopt an appropriate existing model for buried steel structures. A relationship between maximum and average corrosion pit depth and loss of embedment depth was then developed. Finally, the corrosion parameters, combined with uncertainty in loading and soil properties were employed to perform time-dependent reliability assessment for steel light poles which can be used to assist the asset maintenance team in planning the replacement or strengthening works for steel pole.

A hybrid physics-informed machine learning approach for time-dependent reliability assessment of electromagnetic relays

Electromagnetic relays (EMRs) are intricate micro-electromechanical systems characterized by nonlinear behavior and coupling effects between electromagnetic and mechanical forces. Accurately modeling degradation and assessing reliability are crucial yet challenging tasks for ensuring their safe and efficient operation. Current data-driven methods for degradation modeling and reliability assessment often neglect the known physical knowledge regarding EMRs, leading to inaccuracies in modeling and assessment outcomes when data is incomplete. While physics-informed machine learning (PIML) approaches offer a potential solution, common regression models like Gaussian processes (GP) and long short-term memory (LSTM) suffer from underfitting and overfitting, respectively. To address these issues, we presents a hybrid PIML approach for time-dependent reliability assessment based on the emerging variational autoencoder (VAE) framework. This approach combines the advantages of GP-based methods that enable probabilistic representation with deep neural network-based methods that are more flexible and computationally efficient. Finally, we validate our proposed approach using real-world engineering data, demonstrating its superior accuracy and computational efficiency compared to state-of-the-art methods.

Time-Dependent Reliability Analysis of Anhydrite Rock Tunnels under Swelling Conditions: A Study on Stress, Deformation, and Engineering Solutions

This study presents an analytical approach for evaluating the reliability of anhydrite rock tunnels, focusing on their characteristic swelling behavior. Anhydrite rocks, prone to significant expansion upon moisture exposure, pose a challenge in tunnel construction, potentially leading to structural issues such as floor heave and lining damage. To address this, this research develops an elastic swelling analytical solution based on humidity stress field theory, enabling the assessment of time-dependent stress and deformation changes in anhydrite tunnels. The solution’s applicability is demonstrated through its application to the Lirang tunnel. The investigation into the effects of support pressure, swelling time, and reserved deformation on tunnel reliability reveals that circumferential stress at the tunnel wall increases by 13.94% and 21.86% for swelling periods of 30 and 365 days, respectively. Similarly, radial displacement escalates by 22.97% and 35.93% over these periods, highlighting the significant impact of swelling behavior. Using a spreadsheet-based First Order Reliability Method (FORM) for analysis, this study finds that the original design of the Lirang tunnel did not meet the desired reliability standards under swelling conditions. However, strategic adjustments in construction variables, such as increasing support pressure to 1.2 MPa or enhancing reserved deformation to 59 mm, elevated the tunnel’s reliability to meet safety requirements. This research provides a vital framework for assessing and enhancing the reliability of anhydrite rock tunnels, considering the long-term effects of swelling. It underscores the importance of incorporating swelling behavior in the design and construction of tunnels in anhydrite rock formations, offering valuable insights for optimizing tunnel stability in such challenging geological conditions.

A single-loop reliability sensitivity analysis strategy for time-dependent rare events with both random variables and stochastic processes

To deal with the time-dependent reliability sensitivity (TDRS) analysis of rare events with both random variables and stochastic processes, a single-loop sampling procedure combined with the cross entropy-based importance sampling strategy (CEIS), namely SCEIS, is derived to lighten the computational burden without loss of precision. Firstly, the TDRS indices are derived to make them implementable by a single-loop importance sampling (IS) procedure. Then, the quasi-optimal IS density is obtained through the extension of the cross-entropy method, which is an adaptive procedure that overcomes the challenges of determining the position and number of design points in traditional IS. Furthermore, the SCEIS can be easily implemented to estimate the TDRS indices for problems with small failure probability. Three examples involving numerical and engineering problems are analyzed to demonstrate the performance of the proposed method. The results obtained from comparing with other existing methods reveal that the proposed method provides satisfactory TDRS analysis for rare events while significantly reducing computational costs.

Multi-fidelity wavelet neural operator surrogate model for time-independent and time-dependent reliability analysis

Operator learning frameworks have recently emerged as an effective scientific machine learning tool for learning complex nonlinear operators of differential equations. Since neural operators learn an infinite-dimensional functional mapping, it is useful in applications requiring rapid prediction of solutions for a wide range of input functions. A task of a similar nature arises in many applications of uncertainty quantification, including reliability estimation and design under uncertainty, each of which demands thousands of samples subjected to a wide range of possible input conditions, an aspect to which neural operators are specialized. Although the neural operators are capable of learning complex nonlinear solution operators, they require an extensive amount of data for successful training. Unlike the applications in computer vision, the computational complexity of the numerical simulations and the cost of physical experiments contributing to the synthetic and real training data compromise the performance of the trained neural operator model, thereby directly impacting the accuracy of uncertainty quantification results. We aim to alleviate the data bottleneck by using multi-fidelity learning in neural operators, where a neural operator is trained by using a large amount of inexpensive low-fidelity data along with a small amount of expensive high-fidelity data. We propose the multi-fidelity wavelet neural operator, capable of learning solution operators from a multi-fidelity dataset, for efficient and effective data-driven reliability analysis of dynamical systems. We illustrate the performance of the proposed framework on bi-fidelity data simulated on coarse and refined grids for spatial and spatiotemporal systems.

C0–Semigroups Approach to the Reliability Model Based on Robot-Safety System

This paper considers a system with one robot and n safety units (one of which works while the others remain on standby), which is described by an integro-deferential equation. The system can fail in the following three ways: fails with an incident, fails safely and fails due to the malfunction of the robot. Using the C0–semigroups theory of linear operators, we first show that the system has a unique non-negative, time-dependent solution. Then, we obtain the exponential convergence of the time-dependent solution to its steady-state solution. In addition, we study the asymptotic behavior of some time-dependent reliability indices and present a numerical example demonstrating the effects of different parameters on the system.

Interval uncertainty-oriented impedance force control for space manipulator with time-dependent reliability

For specific missions of spacecraft including on-orbit assembly, docking, grasp, etc., the presence of uncertainties leads to difficulties in the analysis of impedance force control systems and evaluations of safety for space manipulators. Therefore, in this study, a novel interval uncertainty-oriented impedance force control method for space manipulators with time-dependent reliability was established. The proposed method can accurately and rapidly characterize uncertainties. Additionally, it can reflect the reliability of a control system based on an overall time history. Once the uncertainties of the dynamic models and state responses are known, their uncertainty bounds can be obtained using an established non-probabilistic propagation method with high accuracy. An interval process model and the first passage theory are employed in the non-probabilistic time-dependent model. A joint reliability index is established based on the single reliability indexes, which can more efficiently evaluate the control system reliability than the individual indexes. A numerical example related to space manipulator is used to study the developed impedance force control method and verify the effectiveness of the method. The results from the response curves reveal validity of the proposed method, while the reduction in time proves efficiency of the method.

Reliability modeling of pre-stressed composite structures subject to interlayer slip failure under multi-axial random impact and vibration loads

A time-dependent reliability model for pre-stressed metal/polymer/metal composite structures subject to interlayer slip failure is developed in this study, allowing for predicting the probability of failure of the whole structure under multi-axial random multi-peak impact loads and transport vibration. A multi-Gaussian envelope model with uniform modulations is proposed to model random multi-peak impact loads, and the inverse sampling method is employed to model random transport vibration. An interlayer slip physics model is developed based on the contact surface friction mechanism under multi-axial vibration load and the stress-relaxation constitutive model. By implementing the interlayer slip physics model in the finite element method framework via the user-material routine, the geometry effect of the structure can be dealt with, and the reliabilities at an arbitrary location of the structure can be obtained. The proposed method is demonstrated using engineering examples. The results show that the proposed reliability assessment method provides a viable and systematical procedure of computing the time-dependent reliability of composite structures as a whole under multi-axial impact loads and vibrations.

Stochastic Analysis and Time-Dependent Reliability of Reinforced Concrete Beams Considering Spatially Distributed Corrosion Deterioration

Stochastic Analysis and Time-Dependent Reliability of Reinforced Concrete Beams Considering Spatially Distributed Corrosion Deterioration

Efficient time-dependent reliability analysis for a railway bridge model

Efficient time-dependent reliability analysis for a railway bridge model

Upcrossing‐based time‐dependent resilience of aging structures

The time-dependent resilience of an in-service aging structure provides quantitative measure of the structural ability to prepare for, adapt to, withstand and recover from disruptive events. Resilience models have been proposed in the literature to evaluate the resilience of aging structures subjected to discrete load processes, which are, however, not applicable to handle resilience problems considering continuous load processes. In this paper, a new method is developed to evaluate the time-dependent resilience of aging structures subjected to a continuous load process. The proposed method serves as the complement of the existing resilience models addressing discrete load processes, and takes into account the aging effects of the structural resistance/capacity and the nonstationarity in loads as a result of climate change. A structure suffers from a damage state upon the occurrence of an upcrossing of the load effect with respect to the resistance/capacity, leading to the reduction of the performance function, followed by a recovery process that restores the performance. The proposed method enables the time-dependent resilience to be evaluated via a closed form solution. It is also revealed that, the proposed resilience model takes an extended form of the existing formula for upcrossing-based time-dependent reliability, thus establishing a unified framework for the two quantities. The applicability of the proposed method is demonstrated through examining the time-dependent resilience of a residential building subjected to wind load. The effects of key factors on resilience, including the nonstationarity and correlation structure of the load process, as well as the resistance/capacity deterioration scenario, are investigated through an example. In particular, the structural resilience would be overestimated if ignoring the potential impacts of climate change, which is a relatively non-conservative evaluation.

Efficient reliability analysis of stochastic dynamic first-passage problems by probability density evolution analysis with subset supported point selection

This study introduces a novel point selection procedure for the Probability Density Evolution Method (PDEM) to estimate time-dependent reliability and failure probabilities in dynamic systems under first-passage failure conditions. The method integrates and modifies features of the Subset simulation procedure to adaptively generate dependent sample sets suitable for a reliability analysis by a direct probability integration approach levering PDEM. Performance function assessments are used as weighting factors in the Subset supported Point Selection (S-PS), enhancing the ultimate failure probability estimation accuracy. The presented approach effectively identifies samples in the failure region, particularly benefiting for dynamic systems under stochastic excitation, tested with random dimensions up to 60. It also offers a computationally efficient structural reliability estimation procedure by analyzing full time–history responses. The proposed method provides deeper insights into rare failure events and mechanisms through the visualization of intermediate results. This research presents an advanced framework for estimating structural reliability and understanding critical events in dynamic systems.

Reliability assessment of bridge hangers based on fault tree with response surface

Bridge hangers play a crucial role in transmitting forces and supporting bridge structures. The condition of these hangers directly impacts the overall safety of the bridge. However, they are susceptible to fatigue failure due to cyclic loads like wind and vehicle traffic. Therefore, evaluating the fatigue performance of bridge hangers is vital. Typically made up of multiple parallel steel wires, the failure of even one wire can affect the fatigue performance of the entire hanger. This underscores the importance of considering the individual components’ impact on the system as a whole. This study presents a time-dependent reliability assessment model for bridge hangers based on the S-N curve of steel wire. Additionally, a system-level reliability assessment model is developed using fault tree analysis, taking into account the influence of broken wires and stress redistribution on the hanger system. The model is solved using response surface methodology, and through five numerical simulations, the study examines the effect of key parameters, including the number of broken wires, equivalent structural stress, and total cycles on the system’s reliability.