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The present work is devoted to the analysis of the most important reliability indicators of components of electrical devices of mining dump trucks, and analytical methods of their evaluation are proposed. A mathematical model for calculating the reliability of electrical devices integrated into the electrical systems of quarry dump trucks is presented. The model takes into account various loads arising in the process of operation and their influence on reliability reduction. Optimisation of maintenance and repair schedules of electrical equipment has revealed problems for research. One of them is the classification of electrical equipment by similar residual life, which allows the formation of effective repair and maintenance cycles. The analysis of statistical data on damages revealed the regularities of their occurrence, which is an important factor in assessing the reliability of electrical equipment in mining production. For quantitative assessment of reliability, it is proposed to use the parameter of the average expected operating time per failure. This parameter characterises the relative reliability of electrical equipment and is a determining factor of its reliability. The developed mathematical model of equipment failures with differentiation of maintained equipment by repeated service life allows flexible schedules of maintenance and repair to be created. The realisation of such cycles makes it possible to move from planned repairs to the system of repair according to the actual resource of the equipment.

Sea level rise (SLR), a well-documented and urgent aspect of anthropogenic global warming, threatens population and assets located in low-lying coastal regions all around the world. Common flood hazard assessment practices typically account for one driver at a time (e.g., either fluvial flooding only or ocean flooding only), whereas coastal cities vulnerable to SLR are at risk for flooding from multiple drivers (e.g., extreme coastal high tide, storm surge, and river flow). Here, we propose a bivariate flood hazard assessment approach that accounts for compound flooding from river flow and coastal water level, and we show that a univariate approach may not appropriately characterize the flood hazard if there are compounding effects. Using copulas and bivariate dependence analysis, we also quantify the increases in failure probabilities for 2030 and 2050 caused by SLR under representative concentration pathways 4.5 and 8.5. Additionally, the increase in failure probability is shown to be strongly affected by compounding effects. The proposed failure probability method offers an innovative tool for assessing compounding flood hazards in a warming climate.

This paper proposes an efficient Kriging-based subset simulation (KSS) method for hybrid reliability analysis under random and interval variables (HRA-RI) with small failure probability. In this method, Kriging metamodel is employed to replace the true performance function, and it is smartly updated based on the samples in the first and last levels of subset simulation (SS). To achieve the smart update, a new update strategy is developed to search out samples located around the projection outlines on the limit-state surface. Meanwhile, the number of samples in each level of SS is adaptively adjusted according to the coefficients of variation of estimated failure probabilities. Besides, to quantify the Kriging metamodel uncertainty in the estimation of the upper and lower bounds of the small failure probability, two uncertainty functions are defined and the corresponding termination conditions are developed to control Kriging update. The performance of KSS is tested by four examples. Results indicate that KSS is accurate and efficient for HRA-RI with small failure probability.

Previous empirical studies find that lottery-like stocks significantly underperform their non-lottery-like counterparts. Using five different measures of the lottery features in the literature, we document that the anomalies associated with these measures are state dependent: the evidence supporting these anomalies is strong and robust among stocks where investors have lost money, whereas among stocks where investors have gained profits, the evidence is either weak or even reversed. Several potential explanations for such empirical findings are examined, and we document support for the explanation based on reference-dependent preferences. Our results provide a unified framework to understand the lottery-related anomalies in the literature. This paper was accepted by Tyler Shumway, finance.

It is widely recognized that the active learning kriging (AK) combined with Monte Carlo simulation (AK-MCS) is a very efficient strategy for failure probability estimation. However, for the rare failure event, the AK-MCS would be time-consuming due to the large size of the sample pool. Therefore, an efficient method coupling the subset simulation (SS) with AK is proposed to overcome the time-consuming character of AK-MCS in case of estimating the small failure probability. The SS strategy is firstly employed by the proposed method to transform the small failure probability into the product of a series of larger conditional failure probabilities of the introduced intermediate failure events. Then, a kriging model is iteratively updated for each intermediate failure event until all the conditional failure probabilities are obtained by the well-trained kriging model, on which the failure probability will be estimated by the product of these conditional failure probabilities. The proposed method significantly reduces the number of evaluating the actual complicated limit state function compared with AK-MCS, and it overcomes the time-consuming character of AK-MCS since the sample pool size of SS is significantly smaller than that of MCS. The presented examples demonstrate the efficiency and accuracy of the proposed method.

Active-learning surrogate model–based reliability analysis is widely employed in engineering structural reliability analysis to alleviate the computational burden of the Monte Carlo method. To date, most of these methods are built based on the single-fidelity surrogate model, such as the Kriging model. However, the computational burden of constructing a fine Kriging model may be still expensive if the high-fidelity (HF) simulation is extremely time-consuming. To solve this problem, an active-learning method based on the multi-fidelity (MF) Kriging model for structural reliability analysis (abbreviated as AMK-MCS+AEFF), which is an online data-driven method fusing information from different fidelities, is proposed in this paper. First, an augmented expected feasibility function (AEFF) is defined by considering the cross-correlation, the sampling density, and the cost query between HF and low-fidelity (LF) models. During the active-learning process of AMK-MCS+AEFF, both the location and fidelity level of the updated sample can be determined objectively and adaptively by maximizing the AEFF. Second, a new stopping criterion that associates with the estimated relative error is proposed to ensure that the iterative process terminates in a proper iteration. The proposed method is compared with several state-of-the-art methods through three numerical examples and an engineering case. Results show that the proposed method can provide an accurate failure probability estimation with a less computational cost.

For the multi-failure-mode system with multi-dimensional distribution parameter, estimating system failure probability function (SFPF) is essential to grasp the influence of the distribution parameter on system failure probability and decouple the reliability-based design optimization model constrained by system failure probability. However, there is still a significant challenge in efficiently estimating the SFPF at present. Therefore, an efficient and universal algorithm is proposed in this paper for estimating the SFPF. In the proposed algorithm, a unified sampling probability density function, which is independent with the distribution parameter, is originally constructed by the integration operation over the concerned design domain of the distribution parameter, on which a single-loop numerical simulation can be formulated to simultaneously estimate the SFPF at arbitrary realization of multi-dimensional distribution parameter. Since the single-loop method is used to replace the direct double-loop one in the proposed algorithm, the computational efficiency is greatly improved in estimating the SFPF. Additionally, the proposed algorithm has no restriction on the dimensionality and the concerned design domain of the distribution parameter, and an adaptive Kriging model of the system performance function is embedded to help the proposed algorithm further improve the computational efficiency. A new adaptive learning strategy, which considers the possible correlations among the multi-failure-mode Kriging models, is presented using the probability of the multi-failure-mode Kriging model misjudging the candidate sample state. The superiority of the proposed algorithm in terms of single-loop numerical simulation and the new learning strategy over the existing methods is fully demonstrated by numerical and engineering examples.

Nacre, the iridescent material of the shells of pearl oysters and abalone, consists mostly of aragonite (a form of CaCO₃), a brittle constituent of relatively low strength (≈10 MPa). Yet it has astonishing mean tensile strength (≈150 MPa) and fracture energy (≈350 to 1,240 J/m²). The reasons have recently become well understood: (i) the nanoscale thickness (≈300 nm) of nacre’s building blocks, the aragonite lamellae (or platelets), and (ii) the imbricated, or staggered, arrangement of these lamellea, bound by biopolymer layers only ≈25 nm thick, occupying <5% of volume. These properties inspire manmade biomimetic materials. For engineering applications, however, the failure probability of ≤10−6 is generally required. To guarantee it, the type of probability density function (pdf) of strength, including its tail, must be determined. This objective, not pursued previously, is hardly achievable by experiments alone, since >10⁸ tests of specimens would be needed. Here we outline a statistical model of strength that resembles a fishnet pulled diagonally, captures the tail of pdf of strength and, importantly, allows analytical safety assessments of nacreous materials. The analysis shows that, in terms of safety, the imbricated lamellar structure provides a major additional advantage—∼10% strength increase at tail failure probability 10−6 and a 1 to 2 orders of magnitude tail probability decrease at fixed stress. Another advantage is that a high scatter of microstructure properties diminishes the strength difference between the mean and the probability tail, compared with the weakest link model. These advantages of nacre-like materials are here justified analytically and supported by millions of Monte Carlo simulations.

Such complex causative factors in current failure probability models are represented by simply random uncertainty and completely independent or correlation of failure modes, which can often limit the model utility. In this study, we developed a methodology to construct failure probability models for high fill levees, incorporating the identification of uncertainties and an analysis of failure modes. Based on quantification of stochastic-grey-fuzzy uncertainties, probability analysis involved with overtopping, instability and seepage failure modes was implemented combined with probability and non-probability methods. Given that the interaction among failure modes typically exhibits nonlinear behavior, rather than linear correlation or complete independence, a simple methodology for the binary Copula function was established and implemented in MATLAB. This methodology was applied to the high fill segments of a long-distance water transfer project characterized by high population density. It shows that the failure probability of a single failure mode is overestimated when uncertainties are not considered, because of the randomness and fuzziness of some parameters and the greyness of information. Meanwhile, it is found that the magnitude of failure probability related to levee breach is overestimated without respect to failure modes correlation, especially when the probabilities of seepage and instability are both significant and closely aligned.

To learn the effect of interested distribution parameter, also the design variable of random input vector, on time-dependent failure probability, and to decouple time-dependent reliability-based design optimization (T-RBDO), estimating time-dependent failure probability function (T-FPF), a relation of time-dependent failure probability varying with the distribution parameter in interested design region, is necessary. However, estimating T-FPF is time-consuming and a challenge at present. Thus, this paper proposes a novel single-loop meta-model importance sampling with adaptive Kriging model (SL-Meta-IS-AK) to estimate T-FPF efficiently. In SL-Meta-IS-AK, for estimating the T-FPF by single-loop simulation, an optimal importance sampling probability density function (IS-PDF), which can envelope the interested distribution parameter region and be free of the distribution parameter, is constructed by an integral operation. After the Kriging model is adaptively constructed for time-dependent performance function to approach optimal IS-PDF for T-FPF by quasi-optimal one, a simple sampling strategy is designed to extract the samples of quasi-optimal IS-PDF, and a time-dependent misclassification probability function is derived to update the Kriging model adaptively until it can accurately recognize the states of all extracted samples, on which the T-FPF at the whole interested distribution parameter region can be estimated as a byproduct. Due to the single-loop simulation aided by the IS-PDF covering the interested distribution parameter region but free of the distribution parameter, the efficiency of estimating T-FPF is improved by the proposed SL-Meta-IS-AK, which is verified by presented numerical and aviation engineering examples including a wing structure and a turbine shaft structure.