Time-dependent Reliability Research Articles

Deep learning methods for time-dependent reliability analysis of reservoir slopes in spatially variable soils

The Three Gorges Reservoir Area (TGRA) is one of the most important landslide-prone regions in China, and rational stability evaluation of reservoir slopes in it is of great significance to design mitigation measures and prevent landslide disasters. It is well recognized that seasonal rainfall and periodic reservoir water level fluctuation are the two major factors influencing the stability of reservoir slopes, and thus the reservoir slope stability may be varying with the external triggering factors. Although geotechnical reliability analysis offers a novel means to quantify slope stability in a probabilistic manner, the previous research focuses more on the time-independent slope reliability analysis, ignoring the effects of time-varying factors. How to evaluate the time-dependent reliability of reservoir slopes accurately and efficiently remains an open question. This study proposes deep learning (DL)-based time-dependent reliability analysis approach, and a practical case adapted from the Bazimen landslide in the TGRA is used for illustration. The predictive performances of the three DL algorithms, namely Convolutional Neural Network (CNN), Long short-term memory (LSTM), and Light gradient boosting machine (LightGBM) are systematically investigated. Results show that the proposed DL-based approach can reasonably portray the variation tendency of the Bazimen landslide time-dependent failure probability, which provides a promising way to rationally evaluate the time-dependent failure probability of reservoir slopes considering the spatial variability of soil properties. Among the three DL algorithms, the CNN performs the best in the Bazimen landslide example.

Durability Design of Concrete Structures Under Reinforce-ment Corrosion

Traditionally, the durability design of concrete structures is
 based on implicit rules (minimum concrete cover, maximum
 water/cement ratio, crack width limitation, etc.). The research on
 concrete durability during the last decades has produced a reliable
 basis for information on deterioration processes. Based on this
 knowledge, it is possible to start incorporating durability in the
 design of concrete structures. Standard reliability methods were
 used to evaluate time dependent reliability of concrete structures
 under corrosion attack.

MAntRA: A framework for model agnostic reliability analysis

We propose a novel model-agnostic data-driven reliability analysis framework for time-dependent reliability analysis. The proposed approach – referred to as MAntRA – combines Bayesian inference and stochastic differential equations to evaluate the reliability of stochastically-driven dynamical systems for which the governing physics is a priori unknown. A two-stage approach is adopted: in the first stage, an efficient variational Bayesian equation discovery algorithm is developed to determine the governing physics of an underlying stochastic differential equation (SDE) from measured output-only data. The developed algorithm is efficient and accounts for epistemic uncertainty due to limited and noisy data and aleatoric uncertainty because of environmental effects and external excitation. In the second stage, the discovered SDE is solved using a stochastic integration scheme, and the probability of failure is computed. The efficacy of the proposed approach is illustrated in four numerical examples. The results obtained indicate the possible application of the proposed approach for reliability analysis of in-situ and heritage structures from on-site measurements.

Time-dependent reliability assessment of a simply supported girder bridge based on the third-moment method

Concrete bridges decay over time due to environmental or operational processes, leading to a reduction in their reliability. In this paper, a new time-dependent reliability evaluation procedure is proposed taking into consideration the simultaneous non-stationarities of vehicle load effect and resistance deterioration. Using the third-moment (3M) method and the second-moment (2M) method, the time-varying reliability of a simply supported girder bridge was investigated. The 3M method is a novel approach to calculate the reliability index requiring neither iteration nor computation of derivatives. As validated by Monte-Carlo simulations, it is shown that the 3M method is more accurate than the 2M method. Based on different moment methods, the effects of parameters such as the growth rate of vehicle load and the time proportions of different operation states in the reliability of the system were investigated. By analyzing the relationship between the time-dependent reliability index and the target reliability index, the time points of maintenance and inspection were predicted.

Structural Time-Dependent Reliability Assessment: Advanced Approaches for Engineered Structures

Structural Time-Dependent Reliability Assessment: Advanced Approaches for Engineered Structures

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 innovative method for space-time-dependent reliability analysis

The spatiotemporal variability exists in almost all engineering problems, since the environmental actions and material properties may change both spatially and temporally in a stochastic manner. Therefore, reliability analysis is inherently space–time-dependent. In this study, an innovative space–time-dependent outcrossing rate (STOR) method is proposed for dealing with such reliability problems. The failure probability of a structure is determined based on outcrossing rate which is theoretically derived for the first time, considering the spatiotemporal variability of all basic variables. Then, an efficient numerical algorithm for computing the failure probability is proposed based on Gauss-Legendre quadrature. The application of STOR method is investigated through three examples, including non-Gaussian random processes, non-Gaussian random fields, strong nonlinear limit state functions and small failure probability problems. The proposed STOR method is found to be efficient for space–time-dependent reliability analysis with enough accuracy.

Time-dependent reliability analysis of wellbore stability during drilling in hydrate exploitation

Methane hydrates is regarded as an important alternative energy in the future. Due to the complexity of marine environment, the mechanical parameters and initial stress state of formation have great uncertainties which can affect the wellbore stability in hydrate exploitation. In this study, a new time-dependent analytical model is proposed, considering the influence of hydrate dissociation on the mechanical properties and the partial coupling among pore pressure/temperature/mechanical field. The analytical solutions are verified and validated by numerical solutions. Based on the analytical solution and Mogi-Coulomb failure criterion, the reliability of wellbore stability during drilling in hydrate exploitation is analyzed by the Response Surface Method. Through the reliability analysis, the probability of wellbore instability increases and the safe drilling fluid pressure window range is narrowed with time, and finally tended to be stable at t = 12 h. Hydrate dissociation would lead to a more narrowed pressure window range, about by −38.75%. The most significant parameter whose uncertainty affects the instability probability is initial in-situ stress, followed by the initial internal friction angle and Biot’s coefficient.

Adaptive subset simulation for time-dependent small failure probability incorporating first failure time and single-loop surrogate model

High-precision time-dependent reliability analysis (TDRA) is essential for small failure probability estimation and life-cycle design and maintenance for engineering structures of high importance. However, existing small failure probability estimation methods, e.g., subset simulation (SS) and importance sampling (IS), might face challenges in accurate TDRA with relatively low computational costs. Thus, this paper presents a novel TDRA method for small failure probability based on point evolution kernel density (PKDE) and adaptive SS. To efficiently reduce the computational burden, single-loop surrogate modeling (SLSM) is employed, and TDRA is implemented by capturing the cumulative density function (CDF) of the first failure time. The proposed method is called First-failure-Time-PKDE-Adaptive-Surrogate-modeling-based-SS (FT-PASS). In FT-PASS, good-lattice-point-set-Partially-Stratified-Sampling (GLP-PSS) is performed to select uniform initial points and achieve the initial TDRA by PKDE. Subsequently, a Kriging model is built and trained by an advanced learning function to obtain the distribution of the first failure time with SS and revise the initial TDRA. Four different cases, a numerical case, a corroded steel beam, a turbine blade subject to stochastic loads, and a planar steel truss subject to stochastic load and corrosion effect, are used to validate FT-PASS. The results indicate that FT-PASS can accurately estimate time-dependent small failure probability and strike a balance between computational efficiency and accuracy compared with conventional TDRA methods.

Two-stage vibration-suppression framework for optimal robust placements design and reliable PID gains design via set-crossing theory and artificial neural network

• Atwo-stage controlmodelfor design of placements and PID parametersis proposed. • The optimal placementsrobust design of uncertain vibration systemsis proposed. • The optimal PID gainsdesign withtime-dependent reliabilitylimitsis proposed. • The ANNis appliedin vibratory controloptimization to improve the efficiency. Structure vibration control is a significant problem in practical engineering, and Proportional-Integral-Differential (abbreviated as “PID”) control is widely used. The design of a PID controller contains the robust design of placements of actuators and sensors (abbreviated as “ASPD”), and the reliable design of PID gains. Because of the uncertain parameters in practical engineering, the controller designed from the deterministic system has the possibility of failure when applied to a practical system. To solve this problem, this paper proposed a two-stage framework for uncertain vibration active control systems via non-probabilistic time-dependent reliability (abbreviated as “NTDR”) and artificial neutral network (abbreviated as “ANN”). This framework decouples the ASPD and PID gains design as two stages. Considering the insufficient sample data, uncertain parameters are quantified with non-probabilistic interval forms. The optimization objective of ASPD combines the deterministic eigenvalues of controllability gramian or observability gramian, the robust theory and placements constraints to carry out the optimization. In this way the optimization objective can be less affected by uncertain parameters and has practical significance. For the reliable design of PID gains, the NTDR is adapted to evaluate the safety of an uncertain system. Then ANNs from uncertain parameters and PID gains to the optimization objective considering NTDR are established. By carrying out the optimization to the last ANN, the efficiency of optimization is improved while the accuracy is guaranteed. Two numerical examples and one experimental example show the practicability and effectiveness of the proposed method.

Uncertainty-oriented optimal PID control design framework for piezoelectric structures based on subinterval dimension-wise method (SDWM) and non-probabilistic time-dependent reliability (NTDR) analysis

Piezoelectric system is widely used in vibration control, but due to the influence of uncertainty in the system, the control rate designed for determined system may not meet the design requirements in practical application. In order to solve the uncertainty problems in the system, a set of NTDR reliability optimization framework for piezoelectric active control system is proposed in this paper. Taking the most widely used PID controller as an example, a new controller design method is proposed: the response interval of the closed-loop system is calculated by the novel SDWM. Based on the first crossing theory, a new time-dependent reliability index is defined to calculate the time-dependent reliability of the piezoelectric system. Through an example of piezoelectric laminate, the layout of different piezoelectric materials is compared. Then, taking piezoelectric curved shell as an example, the influence of piezoelectric uncertainty and uncertainty parameter radius on vibration control of piezoelectric system is studied. Finally, the accuracy of the method is verified by Monte Carlo algorithm.

Time-Dependent Seismic Reliability of Coastal Bridge Piers Subjected to Nonuniform Corrosion.

Coastal bridge piers suffer random performance deterioration owing to the presence of complex nonuniform corrosion characteristics and material uncertainties. Some of these piers will also be threatened by random earthquakes during a long-term service period, and therefore, structural safety needs to be probabilistically assessed by the seismic reliability method. To deal with this problem, we present a method to calculate the time-dependent reliability of the coastal bridge pier, comprehensively considering the randomness of a seismic event, nonuniform corrosion, and material uncertainty. First, the time-dependent M-N interaction diagrams are established by using the Monte Carlo simulation method. On the basis of the interaction diagrams, the moment resistance reduction function and time-dependent moment resistance distribution are determined. Subsequently, the moment demand under the seismic load is determined using the Poisson model and the response acceleration spectrum. Then, the formulas to calculate the time-dependent reliability of a nonuniform corroded pier are derived on the basis of the theorem of total probability. The proposed method is illustrated with a case study of a coastal bridge pier. It was found that the increase in corrosion damage would obviously increase time-dependent reliability. Furthermore, the increase in submerged zone height delayed the year when the failure section shifts from the pier bottom to the bottom of the splash and tidal zone, and it reduces the failure probability of the coastal pier. The research results presented herein show that the nonuniform corrosion manifestations influence the failure mode-related time-dependent seismic reliability of the coastal bridge pier.

A closed-form solution to time-dependent reliability of aging structures described by gamma-based deterioration models

Structural resistance deterioration is by nature a non-increasing stochastic process with autocorrelation on the temporal scale. The Gamma process is often used to describe the stochastic behavior of resistance deterioration. With Gamma-based deterioration models, the calculation of time-dependent reliability presents a serious challenge, and often Monte Carlo simulation is the only solution to this problem. This paper derives a closed-form solution for time-dependent reliability of aging structures, in which the resistance deterioration is described by a Gamma process and the applied load is modelled as a Gaussian process with a constant standard deviation. The accuracy of the proposed method is verified through a comparison with Monte Carlo simulation results, and its applicability is further illustrated in a time-dependent reliability analysis of an existing highway bridge whose vehicle load is modelled using weigh-in-motion (WIM) data. It is found that the measured vehicle load has a relatively small uncertainty, and the uncertainty associated with resistance deterioration is crucial to the reliability assessment because it dominates the overall uncertainty in the reliability calculation.

Time-dependent reliability calculation method of RC bridges based on the dual neural network

Time-dependent reliability calculation method of RC bridges based on the dual neural network

Probabilistic Double Linear Damage Accumulation Model and Time-dependent Reliability Analysis of Mechanical Structure

Probabilistic Double Linear Damage Accumulation Model and Time-dependent Reliability Analysis of Mechanical Structure

Adaptive surrogate model coupled with stochastic configuration network strategies for time-dependent reliability assessment

Time-dependent reliability assessment is crucial in enhancing product development economics and product performance sustainability throughout the lifecycle. It is still a challenge to accurately and efficiently evaluate the time-dependent reliability of engineering systems. This paper proposes a novel adaptive surrogate model method combining stochastic configuration network (SCN) and Kriging strategies to evaluate time-dependent reliability. SCN has accurate approximation ability and learning efficiency for strongly nonlinear systems that can overcome the conventional time-dependent reliability calculation, which is time-consuming and characterized by low accuracy. The proposed method first applies SCN to establish the response model of the performance function with respect to time and obtain the extreme value of the performance function. Then, Kriging is used to establish the extreme value model of the performance function with respect to the random variables based on the extreme value of performance function. The adaptive process considering the characteristics of random variables samples is adopted to update the extreme value model until the model meets the confidence target. Lastly, Monte Carlo simulation is employed for time-dependent reliability assessment based on the established extreme value model. Three example studies are used to demonstrate the effectiveness of the proposed approach for time-dependent reliability assessment.

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.

Reliability Analysis and Life Prediction of Aging LNG Unloading Arms Based on Non-Destructive Test Data

Unloading arms (ULAs) among seaport infrastructures are susceptible to deterioration posed by the effects of harsh marine environmental conditions. During infrastructure’s service life, the deterioration of structural integrity may increase the risk of failure of infrastructure, and should be taken into account during structural reliability assessment. In this study, a simple non-destructive test (NDT) was employed to examine the structural deterioration of ULAs which were installed over 30 years ago. Then, these aging ULAs were modeled by the finite-element program, using non-destructive test data to update the thickness dimensions of structural members. Next, a reliability assessment was conducted based on the stress distribution of the main structural components under external loads, which are calculated by their relation to wind speed. Moreover, the time-dependent reliability index curve was also built by considering the deterioration function to predict the failure probability of the particular components during the remaining lifetime. The study revealed that the present condition of the ULA system was satisfactory for current loading conditions. A reliability index predicted with deteriorations factors may be a rational and appropriate approach for the assessment of aging structures needed for efficient infrastructure management.

Time-Dependent Reliability Assessment of a Continuous I-shaped Steel Beam Considering Corrosion Effects

Among other fields, climate change has a great influence on metal corrosion that reduces the durability and reliability of steel structures. A time-dependent reliability analysis includes time-dependent climate scenarios and deterioration processes as well as random variables, material properties, and dimensions. The extent of corrosion damage is calculated by tracking the evolution of the corrosion process using Monte Carlo simulations. The current paper presents a time-dependent reliability assessment of a continuous I-shaped steel beam, considering the corrosion effects of climate change in Vietnam. The results showed that the safety probability of a continuous steel beam considering metal corrosion from the pristine to 100 years reduces from 96.77% to 63.08%. These findings can be used to assess and provide a cost-technical analysis of climate adaptation measures.

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.