Time-dependent Failure Probability Research Articles

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.

Sequentially Quadratic Surrogate Algorithm for Time-dependent Reliability and Reliability Sensitivity Analysis

Time-dependent reliability and reliability sensitivity analysis in presence of random uncertainty is widespread in equipment structures. To this end, this paper establishes a sequentially quadratic surrogate method. Firstly, the global reliability sensitivity analysis (GRS) is transformed into the classification problem of the time-dependent performance function outputs by means of conditional probability formula. Secondly, referring to the strategy of the Meta-IS method, the Kriging model of time-dependent performance function is employed to construct the importance sampling function to generate the importance sampling (IS) samples of failure domain efficiently. Furthermore, the Kriging model is updated in the IS samples set through the single-loop adaptive Kriging method to realize the accurate identification of the failure indicator function of IS samples, as well as simulation of time-dependent failure probability. Finally, utilize the information of the failure samples obtained by the estimation of time-dependent reliability to evaluate GRS. The proposed algorithm has excellent computational efficiency and applicability due to the conversion of the conditional probability formula, which enables the computational consumption of the time-dependent reliability and GRS analysis independent of the dimensions of the inputs, as well as the Meta-IS method, which improves the sampling efficiency and is applicable to the case of complex implicit performance function. The given examples fully verify the conclusions.

Two-Phase Adaptive Kriging Model Based Importance Sampling Method for Estimating Time-Dependent Failure Probability

To improve the computational efficiency of the time-dependent failure probability (TDFP) to system with dynamic loads, materials degeneration and other time-varying factors, a two-phase adaptive Kriging model-based importance sampling (IS) method is proposed. The main contribution of this article is that a single Kriging model is established and adaptively refined to gradually approach the optimal IS probability density function (PDF) and estimate TDFP in two sequential phases. In the first phase, a generally approximate IS PDF is constructed by Kriging model based on its prediction characteristic and subsequently updated until convergence. Then, a simple rejection sampling technique is used to robustly generate IS samples for the estimation of TDFP. In the second phase, current Kriging model is subsequently refined for accurately identifying the classification of the IS samples generated in the last phase. Finally, the TDFP can be estimated using the products obtained in the above two phases. As the IS PDF established by Kriging model is used for directly approximating the optimal one, the proposed method has the capacity to deal with the complicated problem containing multiple failure regions. Additionally, since IS procedure can dramatically improve the sampling efficiency, the proposed method is an effective technique to the time-consuming TDFP analysis problems.

Data-Driven Fatigue Failure Probability Updating of OSD by Bayesian Backward Propagation

This study introduces a data-driven approach for updating the fatigue failure probability of the orthotropic steel deck (OSD) using Bayesian backward propagation. The OSD in steel bridges is considered as a parallel system composed of two critical fatigue-prone components, namely, the rib-to-diaphragm and rib-to-deck joints. A probabilistic model for fatigue reliability is established based on the equivalent structural stress method and limit state function. The system-level fatigue reliability model is then constructed, taking into account the correlations between limit states of individual components through Bayesian network forward propagation. The key advantage of the Bayesian network-based framework is its ability to perform backward propagation, allowing for the updating of failure probabilities for critical components when the system-level failure of the OSD is observed. Consequently, the proposed approach enables the identification of vulnerable components through data-driven fatigue failure probability updating. Finally, the approach is applied to a real instrumented steel bridge to determine the time-dependent fatigue failure probability at both the system and component levels over its service life. The results show that the component-level fatigue failure probability model will underestimate the fatigue life in comparison to the system-level model. Meanwhile, the proposed method could identify vulnerable components by quantifying the fatigue failure probability of in-service steel bridges.

Time-dependent reliability analysis of structural systems based on parallel active learning Kriging model

Time-dependent reliability analysis quantifies the failures of structural systems due to time-dependent uncertainties, such as material degradation and dynamic loads. The active learning Kriging model methods are widely used in structural reliability analysis to replace extensive time-consuming finite element simulations. However, they can only update one training sample and one failure mode per iteration, which limits their application to time-dependent, parallel computing, and multiple failure modes problems. In this study, we propose a new parallel active learning Kriging model for time-dependent reliability analysis, which can update multiple training samples and multiple failure modes per iteration. It includes the following strategies: (1) a novel parallel learning function is proposed, which combines the correlation function and U learning function to allow for the selection of multiple training samples per iteration; (2) an adaptive adjustment strategy for the number of parallel samples is proposed, which takes into account the prediction probability of parallel samples; (3) the proposed parallel learning function is integrated into time-dependent reliability analysis with multiple failure modes, enabling simultaneous updates of multiple training samples and failure modes, thus greatly reducing the number of iterations and computational time; and (4) a new stopping criterion is proposed to improve the efficiency of the estimation of failure probability. The proposed method can be applied to series or parallel time-dependent structural systems with multiple failure modes. We demonstrate the effectiveness of the proposed method through three examples, and the proposed method can achieve a balance between the computational time and function calls while maintaining a high level of accuracy in the estimation of time-dependent failure probability.

Time-dependent earthquake-fire coupling fragility analysis under limited prior knowledge: A perspective from type-2 fuzzy probability

Earthquake-triggered fire domino scenarios (E-FDSs) arise frequently from the interaction between earthquakes and chemical installations, resulting in catastrophic multi-hazard coupling events. The complicated mutually amplified phenomena between natural disasters and chemical accidents significantly aggravates the escalation of domino accidents, which has posed great challenges for modeling and preventing E-FDSs. Under this impetus, this work proposes an advanced type-2 fuzzy probabilistic methodology to obtain the time-dependent failure probability of steel cylindrical tanks (SCTs) subjected to the earthquake-fire sequence. To cope with the limited prior knowledge on E-FDSs, a basic universal is established to describe the fire resistance attenuation caused by the seismic damage. The coupling failure criterion of SCTs is formulated by a type-2 fuzzy time-dependent limit state equation. A credibility-based stochastic simulation algorithm is developed for the hybrid uncertainty analysis (combining ambiguity and stochasticity). The proposed methodology is validated by case studies of a 5000 m3 fixed roof tank. Compared to the existing accident probability model, the proposed methodology can not only capture the fire resistance attenuation caused by the seismic damage but also provide a dynamic estimation of tank failure probability with respect to the fire exposure time. The proposed methodology can effectively and dynamically capture the accident evolution process, which in turn helps mitigate and prevent the spatiotemporal propagation of domino effects.

Reliability assessment of stochastic dynamical systems using physics informed neural network based PDEM

In the recent decade, the reliability analysis of a stochastic system coupled with the uncertainty related to the system’s parameter has attracted much attention. Probability density evolution method (PDEM) is one of the viable options that estimates the probability density function of the structural response by solving generalized density evolution equations (GDEEs). The advantage of PDEM is that it is derived based on the principle of probability conservation, where GDEEs are decoupled from the physical system. In general, GDEEs in PDEM are solved using a finite difference scheme in which the accuracy of the numerical solution depends on the number of temporal and spatial discretizations, leading to computationally inefficient for high-fidelity models. With this in view, this study proposes a physics-informed neural network (PINN), a novel deep learning method, based PDEM, for solving the GDEEs. PINN utilizes physical information in the form of differential equations to enhance the performance of the neural networks. This method does not need any interpolation or coordinate transformation, which is often seen in any numerical scheme, thus the computational budget is reduced. Three numerical examples are presented in this study to illustrate the proposed PINN-based PDEM, including a Van-der-Pol oscillator subjected to Gaussian white noise, a one-storey moment resisting frame coupled with a nonlinear energy sink with negative stiffness and sliding friction, and a high-rise timber building coupled with shape memory alloy-based outriggers. The first example is utilized to show the accuracy of the proposed method by comparing results with the Fokker–Planck–Kolmogorov equation and Monte Carlo simulation. The rest two examples are investigated for estimating time-dependent probability of failure. Numerical results show that the proposed PINN-based PDEM can estimate the probability of failure efficiently.

A novel quantile-based sequential optimization and reliability assessment method for safety life analysis

Safety life analysis under random uncertainty is an effective tool for guiding the maintenance and design of structures. However, existing methods for safety life analysis employ a nested solution strategy by dichotomy, with inner time-dependent reliability analysis, resulting in high computational costs. This paper proposes a quantile-based sequential optimization and reliability assessment (QSORA) method to overcome the shortcoming of nested solution strategy in safety life analysis. In QSORA, the probability constraint is first equivalently transformed into a quantile constraint corresponding to the target time-dependent failure probability (TDFP). Then, the coupling relationship between the search for safety life and the quantile estimation is then eliminated, and the safety life is solved iteratively through a series of cycles. Each cycle contains two independent executions: an equivalent deterministic optimization and quantile estimation of extreme performance function corresponding to the target TDFP. Finally, a sampling-based method combined with a double-loop Kriging model is proposed to efficiently estimate the quantile, and it is embedded into QSORA to improve the efficiency of safety life analysis. Two learning functions are adopted to ensure the accuracy of double-loop Kriging model. Numerical and engineering examples verify the efficiency and accuracy of the proposed method for safety life analysis.

Safety Lifetime Analysis Using Two-Phase Subset Simulation Combined with Kriging Model

The safety lifetime analysis under the required time-dependent failure probability (R-FP) constraint is essential to ensure structure service safety, but existing methods are unaffordable for solving the safety lifetime under a small R-FP constraint. For this issue, a novel method is proposed by combining a two-phase subset simulation with an adaptive kriging model (TP-SS-AK). The innovations of the TP-SS-AK include three aspects. First, it creatively transforms the safety lifetime under a small R-FP constraint into that under a large conditional R-FP constraint by subset simulation, which can greatly improve efficiency because the large conditional R-FP constraint only needs a small candidate sample pool for searching the safety lifetime. Second, by deducing the misclassification probability of the time-dependent structure state in the first phase, the first new learning strategy is established to train the kriging model of the time-dependent performance function and further determine a reasonable lifetime search interval efficiently. Third, by deriving the misclassification probability of the first failure instant, the second new learning strategy is constructed to efficiently update the kriging model in the second phase and further search the safety lifetime. Because the proposed TP-SS-AK combines the advantages of the two-phase subset simulation and two new learning strategies, it is superior to the existing methods in efficiency, and its superiority is verified by the examples.

A Reliability-Based Framework for Damage Accumulation Due to Multiple Earthquakes: A Case Study on Bridges

Damage accumulation due to multiple seismic impacts over time has a significant effect on the residual service life of the bridge. A reliability-based framework was developed to make decisions in bridge maintenance activities. The feature of the framework enables quantifying the time-dependent probability of failure of bridges due to the impact of multiple earthquakes and progressive deterioration. To estimate the reliability of the bridge systems, the probability of failure of the bridge was used. Two case studies were utilised to demonstrate how the method can be applied to the real world. Results show that the accumulated damage caused by multiple earthquakes and progressive deterioration significantly impact the remaining useful life of the bridge. Furthermore, the soil conditions predominantly influence the progressive deterioration and reduce the service life of the bridge. Overall, the proposed framework enables the sustainable decision-making process for bridge maintenance activities. The results reveal the necessity of including the combined impact in the bridge maintenance system and that there is a more than 40% increase in the probability of failure, due to the combined effect of progressive deterioration and earthquake impacts, compared to the impact only due to seismic loads for the considered case study bridge.

Time-dependent reliability analysis under random and interval uncertainties based on Kriging modeling and saddlepoint approximation

Time-dependent reliability analysis is capable of evaluating the reliability of the system over its full life cycle, which is of highly concerned for designers. In practice, some uncertainties cannot be simply described by a deterministic distribution due to lack of knowledge or information, and generally, their upper and lower bounds can be obtained. Thus, this paper develops a novel computational method for time-dependent reliability under random and interval uncertainties. The first step of the proposed method is to construct the Kriging surrogating model of the most probable point trajectory, with which the bound of the limit-state function can be efficiently recast as an equivalent Gaussian process. In this case, the computation of the bound of time-dependent failure probability (TDFP) is converted to a high-dimensional Gaussian integral problem. To solve this problem, the expansion optimal linear estimation, sparse-grid Gaussian quadrature technique and saddlepoint approximation method are integrated so that the above integral can be efficiently computed. Finally, four engineering examples are studied to demonstrate the effectiveness of the proposed method by comparison with previous methods. The results show this novel method can provide accurate and efficient time-dependent reliability analysis in terms of random and interval uncertainties.

The effect of long-term spaceflight on drug potency and the risk of medication failure

Pharmaceuticals selected for exploration space missions must remain stable and effective throughout mission timeframes. Although there have been six spaceflight drug stability studies, there has not been a comprehensive analytical analysis of these data. We sought to use these studies to quantify the rate of spaceflight drug degradation and the time-dependent probability of drug failure resulting from the loss of active pharmaceutical ingredient (API). Additionally, existing spaceflight drug stability studies were reviewed to identify research gaps to be addressed prior to exploration missions. Data were extracted from the six spaceflight studies to quantify API loss for 36 drug products with long-duration exposure to spaceflight. Medications stored for up to 2.4 years in low Earth orbit (LEO) exhibit a small increase in the rate of API loss with a corresponding increase in risk of product failure. Overall, the potency for all spaceflight-exposed medications remains within 10% of terrestrial lot-matched control with a ~1.5 increase in degradation rate. All existing studies of spaceflight drug stability have focused primarily on repackaged solid oral medications, which is important because non-protective repackaging is a well-established factor contributing to loss of drug potency. The factor most detrimental to drug stability appears to be nonprotective drug repackaging, based on premature failure of drug products in the terrestrial control group. The result of this study supports a critical need to evaluate the effects of current repackaging processes on drug shelf life, and to develop and validate suitable protective repackaging strategies that help assure the stability of medications throughout the full duration of exploration space missions.

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.

A novel single-loop meta-model importance sampling with adaptive Kriging for time-dependent failure probability function

A novel single-loop meta-model importance sampling with adaptive Kriging for time-dependent failure probability function

A new acquisition function combined with subset simulation for active learning of small and time-dependent failure probability

A new acquisition function combined with subset simulation for active learning of small and time-dependent failure probability

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.

Proof testing to improve the reliability and lifetime of ceramic dental prostheses.

Ceramic dental prostheses exhibit increasing failure rates with service time. In particular, veneered crowns and bridges are susceptible to chipping and other fracture modes of failure. The purpose of this manuscript is to introduce a computational methodology and associated software that can predict the time-dependent probability of failure for ceramic prostheses and subsequently design proof test protocols to significantly enhance their reliabilities and lifetimes. Transient reliability and corresponding proof testing theories are introduced. These theories are coded in the Ceramic Analysis and Reliability Evaluation of Structures (CARES/Life) code. This software will be used to demonstrate the predictive capability of the theory as well as its use in designing proof test protocols to significantly improve the reliability (survival probability) and lifetime for dental prostheses. A three-unit fixed dental prosthesis (FDP) with zirconia core (ZirCAD) and veneering ceramic (ZirPress) are used to compare the predicted probabilities of failure to general clinical results. In addition, the capability to use proof testing to significantly improve the performance (reliability and lifetime) for this restoration is demonstrated. The probability of failure, Pf, after five years without proof testing is predicted to be 0.337. This compares to clinical studies showing the failure rate to be between 0.2 and 0.23 after 5 years. After 10 years, reference 18 found the clinical failure rate for similar bridges (but not the same) to be up to 0.28 compared to the predicted Pf of 0.38. The difference may be due to the analysis applying the load at an inclination of 75° which is more critical than vertical loading. In addition, clinical studies often report a simple survival rate instead of using Kaplan-Meier analysis to properly account for late enrollees. Therefore, true clinical failure rates may be higher than reported and may more closely match the predictions of this manuscript. The effectiveness of proof testing increases with selecting materials less susceptible to slow crack growth (higher SCG exponent, N). For example, proof testing the ZirPress glass-veneered bridges with N=43.4 analyzed in this manuscript at 400N bite force for 1s which induces a failure rate during proof testing of 0.31, reduces the Pf of bridges not proof tested from 0.45 to an attenuated-proof-tested probability of failure Pfa of 0.21 after 20 years of usage. If another material is selected with improved resistance to SCG of N=60 and the same loading conditions, the failure rate for the proof tested bridges after 20 years of service drops to 2 in 10,000 from 2.4 in 100 had they been not proof tested. The failure rate during proof testing for this material would be 5.1 in 100. Proof testing a material with absolutely no susceptibility to SCG at the same service load (in this case 285N, not even the 400N load used above) results in 0 % failure rate and is of course independent of time. The transient reliability and proof test theory presented in this paper and associated computational software CARES/Life were successful in predicting the performance of ceramic dental restorations when compared to clinical data. Well-designed proof test protocols combined with proper material selection can significantly enhance the reliabilities and lifetimes of ceramic prostheses. This proof test capability can be a translational technology if properly applied to dental restorations.

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

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

On the use of time-dependent success criteria within risk-informed analyses. Application to LONF-ATWS sequences in PWR reactors

The classical Probabilistic Safety Analysis (PSA) does not include any time dependence explicitly. However, the success criteria (SC) could evolve during the cycle for some initiating events. In that sense, there is a type of sequence in which this time-dependency is quite important, the family of Anticipated Transient without Scram (ATWS) sequences in Pressurized Water Reactors. Therefore, a new risk-informed approach is proposed in this paper, which makes it possible to obtain the time-dependent SC evolution of the safety functions affected by the Moderator Temperature Coefficient (MTC) value. Then, the evolution of the ATWS conditional core damage probability (CCDP) could be obtained using a PSA model. To quantify the CCDP, the average values of the time-dependent failure probabilities must be computed. Finally, the comparison between the CCDP obtained through the application of the classical PSA approach and the new one makes it possible to quantify the impact of time-dependence on the SC of the headers that this new risk-informed ATWS approach can provide.

Prognostic modeling of predictive maintenance with survival analysis for mobile work equipment

In recent years there is a data surge of industrial and business data. This posses opportunities and challenges at the same time because the wealth of information is usually buried in complex and frequently disconnected data sets. Predictive maintenance utilizes such data for developing prognostic and diagnostic models that allow the optimization of the life cycle of machine components. In this paper, we address the modeling of the prognostics of machine components from mobile work equipment. Specifically, we are estimating survival curves and hazard rates using parametric and non-parametric models to characterize time dependent failure probabilities of machine components. As a result, we find the presence of different types of censoring masking the presence of different populations that can cause severe problems for statistical estimators and the interpretations of results. Furthermore, we show that the obtained hazard functions for different machine components are complex and versatile and are best modeled via non-parametric estimators. However, notable exceptions for individual machine components can be found amenable for a Generalized-gamma and Weibull model.