Rare Failure Events Research Articles

A physics-informed neural network enhanced importance sampling (PINN-IS) for data-free reliability analysis

Reliability analysis of highly sensitive structures is crucial to prevent catastrophic failures and ensure safety. Therefore, these safety-critical systems are to be designed for extremely rare failure events. Accurate statistical quantification of these events associated with a very low probability of occurrence requires millions of evaluations of the limit state function (LSF) involving computationally expensive numerical simulations. Variance reduction techniques like importance sampling (IS) reduce such repetitions to a few thousand. The use of a data-centric metamodel can further cut it down to a few hundred. In data-centric metamodeling approaches, the actual complex numerical analysis is performed at a few points to train the metamodel for approximating the structural response. On the other hand, a physics-informed neural network (PINN) can predict the structural response based on the governing differential equation describing the physics of the problem, without a single evaluation of the complex numerical solver, i.e., data-free. However, the existing PINN models for reliability analysis have been effective only in estimating a large range of failure probabilities (10-1∼10-3). To address this issue, the present study develops a PINN-based data-free reliability analysis for low failure probabilities (<10-5). In doing so, a two-stage PINN integrated with IS (PINN-IS) is proposed. The first stage is employed to approximate the most probable failure point (MPP) appropriately while the second stage enhances the accuracy of LSF predictions at the IS population centred on the approximated MPP. The effectiveness of the proposed approach is numerically illustrated by three structural reliability analysis examples.

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.

Interpretable machine learning models for failure cause prediction in imbalanced oil pipeline data

Pipelines are critical arteries in the oil and gas industry and require massive capital investment to safely construct networks that transport hydrocarbons across diverse environments. However, these pipeline systems are prone to integrity failure, which results in significant economic losses and environmental damage. Accurate prediction of pipeline failure events using historical oil pipeline accident data enables asset managers to plan sufficient maintenance, rehabilitation, and repair activities to prevent catastrophic failures. However, learning the complex interdependencies between pipeline attributes and rare failure events presents several analytical challenges. This study proposes a novel machine learning (ML) framework to accurately predict pipeline failure causes on highly class-imbalanced data compiled by the United States Pipeline and Hazardous Materials Safety Administration. Natural language processing techniques were leveraged to extract informative features from unstructured text data. Furthermore, class imbalance in the dataset was addressed via oversampling and intrinsic cost-sensitive learning (CSL) strategies adapted for the multi-class case. Nine machine and deep learning architectures were benchmarked, with LightGBM demonstrating superior performance. The integration of CSL yielded an 86% F1 score and a 0.82 Cohen kappa score, significantly advancing prior research. This study leveraged a comprehensive Shapley Additive explanation analysis to interpret the predictions from the LightGBM algorithm, revealing the key factors driving failure probabilities. Leveraging sentiment analysis allowed the models to capture a richer, more multifaceted representation of the textual data. This study developed a novel CSL approach that integrates domain knowledge regarding the varying cost impacts of misclassifying different failure types into ML models. This research demonstrated an effective fusion of text insights from inspection reports with structured pipeline data that enhances model interpretability. The resulting AI modeling framework generated data-driven predictions of the causes of failure that could enable transportation agencies with actionable insights. These insights enable tailored preventative maintenance decisions to proactively mitigate emerging pipeline failures.

Parallel adaptive ensemble of metamodels combined with hypersphere sampling for rare failure events

In practical engineering, especially in aeronautical engineering, the failure probability is extremely rare due to the incorporation of safety factors in the mechanical design phase. Consequently, a significant challenge is to assess the reliability of mechanical products with implicit functions and rare failure events. To address this issue, this work presents a parallel adaptive ensemble of metamodels (EM) coupled with hypersphere sampling strategy to improve the accuracy and efficiency of reliability analysis. The proposed method consists of three main features. First, a new heuristic ensemble strategy is proposed to provide a powerful and robust metamodel. Second, a n-dimensional uniform sampling technique with better space-filling ability is taken to improve efficiency, which leads to a decrease in the extensive sample size required to capture rare failure events. Third, an effective parallel enrichment strategy is developed by the proposed pseudo-improved U learning function. When parallel computation is possible, the proposed method can select a batch of informative updated points simultaneously to update the EM. Three numerical examples and a planar ten-bar structure are presented to demonstrate the accuracy and efficiency of the proposed method. This method is also applied to the reliability assessment of the aircraft lock mechanism.

Importance sampling enhanced by adaptive two-stage Kriging model and active subspace for analyzing rare probability with high dimensional input vector

For the high dimensional and small failure probability events widely existing in engineering, structural reliability analysis method still faces challenges at present. Since active subspace (AS) method can effectively reduce the dimension of input vector space, and metamodel-based importance sampling (IS) can efficiently estimate small failure probability, this paper combines AS with IS to propose an adaptive two-stage Kriging model method (AS-IS-AK2) for rare failure event with high dimensional problem. The proposed AS-IS-AK2 includes two stages. In the first stage, a new learning function is proposed to construct the Kriging model for roughly estimating the performance function values of all IS samples, and the gradient information is provided as a by-product for AS. In the second stage, an adaptive Kriging method is constructed in the reduced dimension space to accurately judge the states of all IS samples. Since AS reduces the dimension of input vector space, and IS reduces the required size of candidate sample pool for obtaining the convergent failure probability estimation, the computational complexity is reduced in reconstructing the Kriging model to judge the states of IS samples. The results of three examples verify the advantage of the proposed method for high dimensional problem with small failure probability.

Shadow loans and regulatory arbitrage: Evidence from China

This paper examines how Chinese banks used on-balance sheet shadow loans for regulatory arbitrage and whether the financial market priced in the banks’ use of shadow loans and the resulting vulnerabilities in 2014–2022. It finds that banks chose to window dress their regulatory capital ratio by using shadow loans when their capital adequacy ratio was close to the regulatory minimum. It also shows that banks with a higher shadow loan ratio or a lower breakeven non-performing loan ratio obtained from reverse stress testing faced higher wholesale funding costs. Finally, after the announcement of a rare bank failure event, more vulnerable banks witnessed lower cumulative stock and bond returns.

A Coupled Adaptive Kriging Model and Generalized Subset Simulation Hybrid Reliability Analysis Method for Rare Failure Events

A Coupled Adaptive Kriging Model and Generalized Subset Simulation Hybrid Reliability Analysis Method for Rare Failure Events

RBIK-SS: A parallel adaptive structural reliability analysis method for rare failure events

RBIK-SS: A parallel adaptive structural reliability analysis method for rare failure events

Dynamic civil facility degradation prediction for rare defects under imperfect maintenance

PurposeThis paper aims to develop a dynamic civil facility degradation prediction model to forecast the reliability performance tendency and remaining useful life under imperfect maintenance based on the inspection records and the maintenance actions.Design/methodology/approachA real-time hidden Markov chain (HMM) model is proposed in this paper to predict the reliability performance tendency and remaining useful life under imperfect maintenance based on rare failure events. The model assumes a Poisson arrival pattern for facility failure events occurrence. HMM is further adopted to establish the transmission probabilities among stages. Finally, the simulation inference is conducted using Particle filter (PF) to estimate the most probable model parameters. Water seals at the spillway hydraulic gate in a Taiwan's reservoir are used to examine the appropriateness of the approach.FindingsThe results of defect probabilities tendency from the real-time HMM model are highly consistent with the real defect trend pattern of civil facilities. The proposed facility degradation prediction model can provide the maintenance division with early warning of potential failure to establish a proper proactive maintenance plan, even under the condition of rare defects.Originality/valueThis model is a new method of civil facility degradation prediction under imperfect maintenance, even with rare failure events. It overcomes several limitations of classical failure pattern prediction approaches and can reliably simulate the occurrence of rare defects under imperfect maintenance and the effect of inspection reliability caused by human error. Based on the degradation trend pattern prediction, effective maintenance management plans can be practically implemented to minimize the frequency of the occurrence and the consequence of civil facility failures.

Sequential Sampling-Based Asymptotic Probability Estimation of High-Dimensional Rare Events

Abstract Accurate analysis of rare failure events with an affordable computational cost is often challenging in many engineering applications, particularly for problems with high-dimensional system inputs. The extremely low probabilities of occurrence often lead to large probability estimation errors and low computational efficiency. Thus, it is vital to develop advanced probability analysis methods that are capable of providing robust estimations of rare event probabilities with narrow confidence bounds. The general method of determining confidence intervals of an estimator using the central limit theorem faces the critical obstacle of low computational efficiency. This is a side effect of the widely used Monte Carlo method, which often requires a large number of simulation samples to derive a reasonably narrow confidence interval. In this paper, a new probability analysis approach is developed which can be used to derive the estimates of rare event probabilities efficiently with narrow estimation bounds simultaneously for high-dimensional problems and complex engineering systems. The asymptotic behavior of the developed estimator is proven theoretically without imposing strong assumptions. An asymptotic confidence interval is established for the developed estimator. The presented study offers important insights into the robust estimations of the probability of occurrences for rare events. The accuracy and computational efficiency of the developed technique are assessed with numerical and engineering case studies. Case study results have demonstrated that narrow bounds can be obtained efficiently using the developed approach with the true values consistently located within the estimation bounds.

Bayesian updating of reliability by cross entropy-based importance sampling

Bayesian analysis enables a consistent updating of the failure probability of engineering systems when new data is available. To this end, we introduce an adaptive importance sampling (IS) method based on the principle of cross entropy (CE) minimization. The key contribution is a novel IS density associated with the posterior probability density function (PDF) of the uncertain parameters, that facilitates efficient sampling from the important region of the failure domain, especially when the failure event is rare. The IS density is designed via a two-step procedure. The first step involves construction of a sample-based approximation of the posterior, which we build using the CE method. Here the aim is to determine the parameters of a chosen parametric distribution family that minimize its Kullback–Leibler divergence from the posterior PDF. The second step of the proposed method constructs the desired IS density for sampling the failure domain through a second round of CE minimization, starting from the approximate posterior obtained in the first step. An adaptive, multi-level approach is employed to solve the two CE optimization problems. The IS densities deduced in the two steps are then applied to construct an efficient estimator for the posterior probability of failure. Through numerical studies, we investigate and demonstrate the efficacy of the method in accurately estimating the reliability of engineering systems with rare failure events.

Parallel adaptive Bayesian quadrature for rare event estimation

Various numerical methods have been extensively studied and used for reliability analysis over the past several decades. However, how to understand the effect of numerical uncertainty (i.e., numerical error due to the discretization of the performance function) on the failure probability is still a challenging issue. The active learning probabilistic integration (ALPI) method offers a principled approach to quantify, propagate and reduce the numerical uncertainty via computation within a Bayesian framework, which has not been fully investigated in context of probabilistic reliability analysis. In this study, a novel method termed ‘Parallel Adaptive Bayesian Quadrature’ (PABQ) is proposed on the theoretical basis of ALPI, and is aimed at broadening its scope of application. First, the Monte Carlo method used in ALPI is replaced with an importance ball sampling technique so as to reduce the sample size that is needed for rare failure event estimation. Second, a multi-point selection criterion is proposed to enable parallel distributed processing. Four numerical examples are studied to demonstrate the effectiveness and efficiency of the proposed method. It is shown that PABQ can effectively assess small failure probabilities (e.g., as low as 10−7) with a minimum number of iterations by taking advantage of parallel computing.

Rare event estimation using stochastic spectral embedding

Estimating the probability of rare failure events is an essential step in the reliability assessment of engineering systems. Computing this failure probability for complex non-linear systems is challenging, and has recently spurred the development of active-learning reliability methods. These methods approximate the limit-state function (LSF) using surrogate models trained with a sequentially enriched set of model evaluations. A recently proposed method called stochastic spectral embedding (SSE) aims to improve the local approximation accuracy of global, spectral surrogate modelling techniques by sequentially embedding local residual expansions in subdomains of the input space. In this work we apply SSE to the LSF, giving rise to a stochastic spectral embedding-based reliability (SSER) method. The resulting partition of the input space decomposes the failure probability into a set of easy-to-compute conditional failure probabilities. We propose a set of modifications that tailor the algorithm to efficiently solve rare event estimation problems. These modifications include specialized refinement domain selection, partitioning and enrichment strategies. We showcase the algorithm performance on four benchmark problems of various dimensionality and complexity in the LSF.

Efficient subset simulation for rare-event integrating point-evolution kernel density and adaptive polynomial chaos kriging

Rare-event probability estimation has a wide range of applications, including the design and manufacture of precision equipment, aerospace systems, and critical industrial and civil structures. However, traditional simulation-based reliability calculation methods, such as brute Monte Carlo simulation (MCS) and subset simulation (SS), face challenges in efficiently evaluating small-failure probabilities due to the need for a large number of simulations, especially for non-linear and complex scenarios. Thus, to efficiently assess the probability of rare failure events in structural engineering, this paper develops a novel method for assessing the small-failure probability by integrating the point-evolution kernel density (PKDE), SS, and polynomial chaos kriging (PCK). The proposed PKDE-Adaptive PCK-based SS (PAPS) method aims to reduce the implementation of the original performance function by PCK and enrich the training set using an adaptive strategy. Moreover, the initial cumulative distribution function (CDF) of the performance function estimated by PKDE is modified gradually to facilitate the estimation of small-failure probability. Four numerical examples of small-failure probability estimation involving classical analytical cases, time-variant cases, and non-linear stochastic structures are used to illustrate the accuracy and efficiency of the proposed method. The computational results show that the proposed method can provide accurate computational results with a smaller computational burden than traditional methods (e.g., MCS, SS, LHS-PCK-SS).

Endurance of 2 Mbit Based BEOL Integrated ReRAM

In this work, we experimentally characterize the endurance of 2 Mbit resistive switching random access memories (ReRAMs) from a 16 MBit test-chip. Here, very rare failure events where the memory cells become stuck in the low-resistive state (LRS) are observed. As this failure mechanism is the limiting one concerning the endurance of this ReRAM implementation, extensive investigations are conducted and presented. The experimental findings are detailed via a voltage divider model, illustrating why memory cells can become stuck in the LRS. It is proposed, that an insufficient voltage dropping over the cell due to an unfavorable combination of cell- and transistor resistances is responsible for stuck-at-LRS bits. Furthermore, we give predictions for the origin of these suboptimal combinations. Additionally, a one-dimensional Kinetic Monte Carlo (KMC) model that allows a statistical investigation of large numbers of cells with regard to rare random events has been developed. Here, we fortify our proposed explanation for the observed failure mechanism by the simulation and evaluation of the switching process of the memory. All simulations are in very good agreement with the experimental data. Finally, based on our findings, we give suggestions for the improvement of switching algorithms.

AKSE: A novel adaptive Kriging method combining sampling region scheme and error-based stopping criterion for structural reliability analysis

The reliability analysis of complex structures usually involves implicit performance function and expensive-to-evaluate computational models, which pose a great challenge for the estimation of failure probability. In this paper, an adaptive Kriging-based method is proposed for the efficient estimation of failure probability with high accuracy. Starting from a small set of initial design of experiments (DoE), a Kriging model is constructed and iteratively refined by adding judiciously selected sample points to the DoE. To effectively select more sample points for updating the Kriging model, a new learning function is proposed for the selection of representative samples following the idea of the penalty function method in optimization. Besides, the inclusion of the term that measures the distance between the candidate samples and those in DoE controls the density of samples, and thus enables efficient exploration of the regions of interest. To improve the efficiency of the algorithm, this learning function is integrated with a sampling region scheme to filter out sample points in regions with rather low probability density from the candidate sampling pool. Moreover, a convergence criterion based on the error-based stopping criterion is developed to terminate the learning process at an appropriate stage. Hence, the proposed method is referred to as the Adaptive Kriging method combining Sampling region scheme and Error-based stopping criterion (AKSE). To further explore the possible schemes for the improvement of the proposed method, the combinations of AKSE with a dynamic Kriging method and the bootstrap variance are also investigated. For rare failure events, the Monte Carlo simulation (MCS) in AKSE is replaced by the importance sampling (IS) to establish an improved version of AKSE, namely the AKSE-IS. The performance of the proposed algorithm is evaluated through five numerical examples and the results demonstrate the superior performance of the proposed method both in terms of accuracy and efficiency.

Dynamic Write VMIN and Yield Estimation for Nanoscale SRAMs

The dynamic write-access operation in an SRAM has a long-tailed distribution that sets the threshold for write-access failures. The distribution takes a long time to evaluate since rare failure events lie in its long and heavily skewed tail. Moreover, advanced FinFET technologies are becoming increasingly reliant on assist techniques to resolve these rare failures in the tail for improved dynamic performance and stability. In this work, we present various analytical approaches that work well in both super-threshold and subthreshold regions of operation to quickly determine the write-access failure probability. For FinFET based SRAMs, we present a modified sensitivity analysis-based method to evaluate the write-access operation distribution and discuss the evaluation of contention-limited write-access failures. The impact of various write-assist techniques on the performance and stability of FinFET SRAMs is also discussed. All simulations are performed using commercial 65nm bulk planar and 12nm FinFET technologies.

A recursive dimension-reduction method for high-dimensional reliability analysis with rare failure event

A new dimension-reduction method (DRM), called ’subset active subspace method (SASM)’, is proposed to compute small failure probabilities encountered in high-dimensional reliability analysis of engineering systems. The basic idea is to introduce a recursive procedure to improve the efficiency, accuracy and applicability of the conventional active subspace method (ASM). For the reliability problems with a rare event, SASM firstly transfers the original high-dimensional reliability problem into a low-dimensional reliability problem in a proper failure domain. Then, a simplified low-dimensional surrogate model is built in order to improve the result of reliability analysis by increasing significantly the samples with a minimum additional computational effort. The proposed method is verified by three nonlinear numerical examples, including theoretical and industrial, explicit and implicit performance functions. Besides, some other existing methods are also investigated and compared to the proposed method. It is found that the proposed method can keep the trade-off between accuracy and efficiency.

An efficient method by nesting adaptive Kriging into Importance Sampling for failure-probability-based global sensitivity analysis

Failure-probability-based global sensitivity (FP-GS) analysis can measure the effect of the input uncertainty on the failure probability. The state-of-the-art for estimating the FP-GS are less efficient for the rare failure event and the implicit performance function case. Thus, an adaptive Kriging nested Importance Sampling (AK-IS) method is proposed in this work to efficiently estimate the FP-GS. For eliminating the dimensionality dependence in the calculation, an equivalent form of the FP-GS transformed by the Bayes’ formula is employed by the proposed method. Then the AK model is nested into IS for recognizing the failure samples. After all the failure samples are correctly identified from the IS sample pool, the failure samples are transformed into those subjected to the original conditional probability density function (PDF) on the failure domain by the Metropolis–Hastings algorithm, on which the conditional PDF of the input on the failure domain can be estimated for the FP-GS finally. The proposed method highly improves the efficiency of estimating the FP-GS comparing with the state-of-the-art, which is illustrated by the results of several examples in this paper.

Cross-Entropy-Based Composite System Reliability Evaluation Using Subset Simulation and Minimum Computational Burden Criterion

The cross-entropy (CE) method can accelerate power system reliability evaluation effectively. An importance sampling (IS) based iterative parameter updating algorithm is usually used in CE optimization. However, the efficiency in capturing the concerned samples for parameter updating may be unsatisfactory, especially for a system with intrinsic nature of rare failure events. Besides, the stopping criterion of this iterative algorithm is usually determined subjectively, incurring insufficient or excessive parameter updating and a resultant higher computational burden of the entire simulation. To address the above two problems, a CE method based on subset simulation and minimum computational burden criterion is proposed. In CE optimization, the subset simulation combined with M-H sampling is adopted as an alternative to IS to effectively improve the efficiency of capturing desired samples for parameter updating at each iteration. Moreover, a novel quantitative stopping criterion is presented in such a way that the computational burden for the entire simulation is estimated and compared after each parameter updating iteration, and the optimal parameters corresponding to the minimum computational burden can be determined. The computational performance of the proposed method is validated by comparing the proposed approach with existing methods under several numerical tests including a realistic power system.