Narrow Results

Disasters such as ice and wind can pose a serious threat to the normal operation of power transmission lines. Wind-induced fatigue damage can further reduce the load-carrying capacity of transmission towers, increasing their fragility to ice and wind disasters. To assess the comprehensive capability of transmission towers to resist extreme ice and wind disasters, this paper proposes a failure probability evaluation framework for transmission towers considering wind-induced fatigue damage under the coupled effect of ice and wind. Taking a certain transmission line in Hunan as an example, the failure probability caused by ice and wind disasters is calculated for different years of service. First, based on the historical meteorological data in three cities in Hunan, a joint probability model of wind speed and wind direction considering their correlation is established using the copula function. Then, based on this probability model, the wind-induced fatigue damage of transmission towers is calculated using the Miner linear damage theory and the S-N curve. Subsequently, the fragility of the tower under the coupled load of ice and wind is calculated for different years of service. Finally, by combining the structural fragility function with the joint probability distribution model of ice thickness and wind speed, the collapse probability of the transmission tower under the action of ice and wind disasters is calculated. The results indicate that the influence of wind-induced fatigue damage cannot be ignored when transmission towers encounter ice and wind disasters. With increasing service time, the ability of transmission towers to resist ice and wind disasters gradually decreases, and the failure probability also increases under extreme ice and wind conditions.

Since multiple-failure event can destroy the safety policy of redundancy, accurate prediction of multiple-failure probability is of great importance. However, the statistical dependence between component failures might lead to unrealistic estimation of the conventional system failure probability model since it is valid only in the situation of independent component failures. On the other hand, the lack of multiple-failure event data makes the statistical estimation of multiple-failure probability suffer serious uncertainty. General failure event data experienced by other systems might be the only data available to estimate the system under study. In order to evaluate the target system in such a situation, an appropriate approach is highly required by which the right information can be mined from the operating experience of reference systems.

Based on the multiple-failure information contained in load-strength interference relationship, this paper presents an approach to estimate multiple-failure probability of dependent k-out-of-n system according to failure event data available. The data may come from the operating experience of the system to be evaluated or reference systems with similar load-strength interference relationships. As examples, the failure probabilities of emergency diesel generator groups are estimated according to the multiple-failure event data of reference groups of different sizes. The estimation results are consistent well with the operating records.

A stochastic optimization which makes use of a reliability constraint, expressing a performance requirement, is proposed for linear elastic systems subject to random dynamic loads. The criterion selected for the optimum design is the minimization of a deterministic measure, whereas the constraint condition requires that system failure probability must be smaller than a given allowable level, where failure is associated to the first exceeding of system response from a safe domain. The proposed method is then developed for the optimum design of a Tuned Mass Damper, utilized for reducing undesirable vibrations originated in structures by random loads.

Unlike conventional TMD designs based on minimizing the mean-square response, a reliability-based performance measure is then considered in the proposed design, which properly accounts for uncertainties in loads. A sensitivity analysis is carried out and results are shown in a useful manner for TMD design decision support.

The intrinsic relationship between deterministic system and stochastic system is profoundly revealed by the probability density evolution method (PDEM) with introduction of physical law into the stochastic system. On this basis, stochastic dynamic stability analysis of single-layer dome structures under stochastic seismic excitation is firstly studied via incorporating an energetic physical criterion for identification of dynamic instability of dome structures into PDEM, which yields to sample stability (stable reliability). However, dynamic instability is not identical to structural failure definitely, where strength failure can be experienced not only in the stable structure but also when the structure is out of dynamic stability. It is practically feasible to decouple the stochastic dynamic response of dome structures to be a stable one and an unstable one according to the generalized density evolution equation (GDEE). Consequently, the global failure probability can be investigated separately based on the corresponding independent stochastic response. For unstable failure probability assessment, the failure probability is the unstable probability if the dome's failure is attributed to instability, whereas inverse absorbing is firstly implemented to get rid of the stochastic response before instability and a complementary process is filled in the safe domain immediately to finally assess the probability of strength failure after dynamic instability.

Extreme actions, such as impact loads, contain many uncertainties and hence, may not be analyzed by a deterministic approach. In this paper, an effective framework for performance evaluation of reinforced concrete (RC) beams subjected to impact loadings is proposed. For this purpose, a simple yet effective model considering the shear-flexural interaction is developed based on available impact test results. By incorporating the shear effect, both the maximum displacement and impact force are well predicted, by which the proposed model for the impact analysis of RC beams is validated. The joint probability density function (PDF) of two damage indexes, i.e. local drift ratio and overall support rotation, is used to represent the local shear damage degree and the overall flexural damage degree. Taking advantage of the probabilistic framework and the effective model, reliability analysis of the RC beams under different impact scenarios is performed. The damage, described in this study by the joint PDF, is highly affected by the combination of impact mass and velocity. Thus, the mass–velocity ($m$–$v)$ diagrams for various performance levels are generated for the damage assessment of the RC beams. Furthermore, the contribution of the local and global responses to the failure probability is quantified using the proposed probabilistic framework.

Currently, there is no unified criterion to evaluate the failure of single-layer latticed domes, and an accurate nonlinear time-history analysis (NTHA) is generally required; however, this does not consider the uncertainties found in practice. The seismic instability of domes subjected to earthquake ground motions has not been thoroughly investigated. In this paper, a new approach is developed to automatically capture the instability points in the incremental dynamic analysis (IDA) of single-layer lattice domes by integrating different efficient and robust methods. First, a seismic fragility analysis with instability parameters is performed using the bootstrap calibration method for the perfect dome. Second, based on the Sobol sequence, the quasi-Monte Carlo (QMC) sampling method is used to efficiently calculate the failure probability of the dome with uncertain parameters, in which the truncated distributions of random parameters are considered. Third, the maximum entropy principle (MEP) method is used to improve the computational efficiency in the analyses of structures with uncertainties. Last, the uncertain interval of the domes is determined based on the IDA method. The proposed method has been used to investigate the instability of single-layer lattice domes with uncertain parameters. The results show that it can determine the probability of structural failure with high efficiency and reliability. Additionally, the limitations of the proposed method for parallel computation are discussed.

With wind farms expanding into seismically active areas, wind turbines face the combined hazard of wind and earthquakes. Strong winds often accompany strong earthquakes, posing a significant threat to wind turbine safety. When subjected to multihazard loads, ignoring the correlation between loads could underestimate the risk to the structure. However, there is limited research on wind turbines under the combined effect of wind and earthquakes. In this paper, based on historical data considering the correlation between wind and earthquakes, a failure probability analysis method for wind turbine towers under the joint action of wind and earthquakes is presented. To accurately simulate the mechanical behavior of lattice-type wind turbine towers, the bolt slippage effect is taken into account. A finite element model of a lattice wind turbine tower is established, and the failure probability of the tower under the joint action of wind and earthquakes is calculated. The study also analyzes the influence of the bolt slippage effect and load correlation on the reliability of lattice-type wind turbine towers. The results indicate that ignoring load correlation can underestimate the failure probability of the structure, thus decreasing its safety. Similarly, ignoring the bolt slippage effect can also underestimate the failure probability of the structure and seriously threaten the safety of wind turbines.

Instability is one of the major failure modes of long span arch bridges, and its possibility of occurrence will be increased as triggered by earthquake excitations. However, the randomness of each ground motion causes the difficulty in achieving a reliable assessment of the safety of the bridges in regard to its stability issue based on certain time history analysis. Therefore, a failure probability-based instability evaluation method and corresponding instability damage index are proposed in this study to solve this problem, converting the deterministic analysis of a ground motion into a probability analysis of a group of random ground motions. The results find that the input direction, the velocity pulse and the pulse period of the ground motion have a significant impact on the stability of the bridge, while seismic moment and PGV/PGA ratio do not. The fragility curves show that the bridge has more than 60% probability of slight instability when input PGA reaches 0.2 g, 50% probability of moderate instability when input PGA reaches 0.6 g, and 20% probability of collapse when input PGA reaches 1.0 g. Moreover, when the PGA approaches 1.0 g, it is discovered that the velocity pulse and the pulse period can increase the chance of the occurrence of bridge instability by 20%–30%.

Reducing the failure probability is an important task in the design of engineering structures. In this paper, a reliability sensitivity analysis technique, called failure probability ratio function, is firstly developed for providing the analysts quantitative information on failure probability reduction while one or a set of distribution parameters of model inputs are changed. Then, based on the failure probability ratio function, a global sensitivity analysis technique, called R-index, is proposed for measuring the average contribution of the distribution parameters to the failure probability while they vary in intervals. The proposed failure probability ratio function and R-index can be especially useful for failure probability reduction, reliability-based optimization and reduction of the epistemic uncertainty of parameters. The Monte Carlo simulation (MCS), Importance Sampling (IS) and Truncated Importance Sampling (TIS) procedures, which need only a set of samples for implementing them, are introduced for efficiently computing the proposed sensitivity indices. A numerical example is introduced for illustrating the engineering significance of the proposed sensitivity indices and verifying the efficiency and accuracy of the MCS, IS and TIS procedures. At last, the proposed sensitivity techniques are applied to a planar 10-bar structure for achieving a targeted 80% reduction of the failure probability.

Failures of flood defenses have been one of the major reasons in the past leading to flooding of the hinterland behind flood defenses along rivers and at the sea. It is therefore inevitable to investigate the reliability of such defenses for extreme events as have occurred in the past and are discussed to happen more frequently in the future and due to climate changes. The first subproject in XtremRisK (SP 1) and the related papers in this issue [Gönnert, G. and Gerkensmeier, B. [2015] "A multi-method approach to develop extreme storm surge events to strengthen the resilience of highly vulnerable coastal areas," Coast. Eng. J., this special issue; Wahl, T. et al. [2015] "Statistical assessment of storm surge scenarios within integrated risk analyses," Coast. Eng. J., this special issue; Tayel, M. and Oumeraci, H. [2015] "A hybrid approach using hydrodynamic modelling and artificial neural networks for extreme storm surge prediction, Coast. Eng. J., this special issue] have investigated the components of storm surges and their statistical occurrence, also in relation to the wave parameters. These results can now be used as input for investigating the reliability of flood defenses and provide an overall failure probability for different types of defenses and different failure modes. This paper therefore summarizes the key findings of the "risk pathway" analysis of XtremRisK Subproject 2 (SP 2) which comprise a reliability analysis and breach modeling of coastal and estuarine flood defenses using storm surge scenarios and sea states, including their occurrence probabilities provided by XtremRisK SP 1. The paper discusses the key results, the progress, and challenges in reliability analysis and breach modeling of flood defenses. The developed and advanced methods were applied to pilot sites in Hamburg (Elbe Estuary) and the Island of Sylt (North Sea). These pilot sites are mainly protected by linear flood defenses such as sea dikes, estuarine dikes, coastal dunes, and flood defense walls. Results have shown that under extreme conditions many dikes may fail simply from wave overtopping and even overflow but also from dike breaching due to the severe loading of the dike slopes when heavy overtopping and overflow occurs. The inflowing water volumes were calculated based on time-dependent water levels and then used for inundation modeling of the hinterland in Subproject 3 (SP 3) of XtremRisK. Furthermore, the limit state equations for wave overtopping and overflow had been adapted to time-dependent simulations. An importance factor was introduced for the probability of breaching of sea dikes leading to significantly different failure probabilities. The length effect considering the different homogeneous segments in the dike ring of Hamburg-Wilhelmsburg was estimated using an upper and lower bound approach showing the importance of the segmentation of the dike ring.

Crown heights of seawalls should be designed to suppress overtopping discharge to a permissible level. The permissible level is determined from viewpoints of the structure types of coastal seawalls and hinterland use. It is usually difficult to design the crown heights of seawalls, especially in the present time where climate change due to global warming is expected. This study analyzes climate change effects such as sea level rise (SLR) and increase of waves and surges on the failure probability of seawalls under various conditions of crown height, toe depth and slope by using a Level III reliability analysis. It was found that the difference of SLR trends (fast, medium or low) has less impact on overtopping rates than the differences in wave height change for a seawall at a target location.

This paper presents a methodology/model for elastro-plastic analysis of the wire bonding packages. The methodology is based on finite element method for rate sensitive materials and applicable to very large deformation processes. Ultrasonic power is simulated as displacement boundary condition. Stress induced by the mismatch of the coefficient of thermal expansion (CTE) in the system because of temperature increase due to application of the ultrasonic or the reflow process is considered. The effect of temperature increase on material property is also accounted for. Nonlinear spring elements are adopted to simulate the gradual formation of intermetallic bonding layer between the ball and the electric pad. With these spring elements, the effect of stress and strain relaxation of the ball in the subsequent procedures such as reflow process is taken into account. The mechanical behavior of the silicon chip during the wire bonding with the ultrasonic irradiation and reflow process is thus revealed. Failure probability with reference to the stress distribution is discussed. The developed FE methodology is simple but effective to evaluate the failure probability of wire-bonding packages.

In structural engineering earthquakes are often represented as random phenomena. Frequently, filtered white noise stochastic processes are adopted to properly model their frequency content. In order to model the time variation of earthquake intensity, these processes are assumed nonstationary, and time modulation functions (MFs) are used. For these, different shapes and formulas have been proposed in literature till now, but only few works have dealt with their comparison in terms of structural response. This paper focuses on this topic: at this aim, a simple linear single degree of freedom (SDoF) system, which represents a structure vibrating in its fundamental mode, is considered subject to a time modulated filtered stochastic process. Different shapes of the MF are considered and the influence on two structural response indices, i.e. the maximum displacement standard deviation and the failure probability, is investigated. A sensitivity analysis is finally performed by varying peak ground acceleration (PGA), Arias intensity and structural period.

This study evaluates the risk of failure for an endodontically treated premolar with mesio-occlosal (MO) preparation and four different computer-aided design/manufacturing (CAD/CAM) ceramic restoration configurations. Four three-dimensional finite element (FE) models designed with CAD/CAM ceramic inlay, endoinlay, endocrown, and classical crown restorations were constructed to perform simulations. The Weibull function was incorporated with an FE analysis to calculate the long-term failure probability relative to different load conditions. The results indicated that the stress values on the enamel, dentin, and luting cement for endocrown restoration were the lowest values relative to the other three restorations. According to the Weibull analysis, overall failure probabilities were found at 100, 100, 1 and 1% for the inlay, endoinlay, endocrown, and classical crown restorations, respectively in the normal biting. The corresponding values for clenching were over 100% for inlay and endoinlay restorations and about 87 and 70% for endocrown and classical crown, respectively. This numerical investigation suggests that endocrown and classical crown restorations for endodontically treated premolars with MO preparation present similar longevity.

In this paper, reliability assessment of sealing ring in hydraulic systems is carried out based on the Back Propagation (BP) neural networks. An O-ring Finite Element Model (FEM) is established based on ANSYS software, by which the calculated maximum contact stress is taken as failure criteria. The diameter, oil pressure, the amount of compression, and modulus of elasticity are treated as random variables to take into account the parameters variations for studying the effect of parameter uncertainty on the sealing performance. Simulation data that generated from the FEM model is trained by using the artificial neural network toolbox to fit the relationship between the input data and output response. The trained neural network model is finally combined with the importance sampling method, to study the effect of the parameter variations on the reliability of the seal.