Failure Probability Analysis Research Articles

An optimized method for analysis of existing tunnels undercrossed by new tunnels in rich-water strata

Watery strata and the influence of pore water pressure cannot be ignored when calculating the deformation of existing tunnels induced by the excavation of new undercrossing tunnels. Many parameters can affect the deformation of existing tunnels during the excavation of a new undercrossing tunnel. In this work, an optimized method was developed for calculating the settlement of an existing tunnel undercrossed by a newly excavated tunnel in water-rich strata. This method includes a deterministic calculation model and a probability analysis model. Based on the constitutive behavior of the soil and the poroelasticity theory, the excess pore water pressure at the axis of the existing tunnel was obtained and used in the deterministic calculation model, which computes the deformation of the existing tunnel. In addition, we established a probability model based on Kriging metamodeling, the Latin Hypercube sampling (LHS) and Monte Carlo sampling (MCS) methods, and conducted global sensitivity analysis (GSA) and failure probability analysis. The optimized parameters can be input into the deterministic model to make more accurate predictions. The optimized method was applied in and validated by a metro project in Beijing.

Stability and failure probability analysis of super-large irregularly shaped deep excavation in coastal area considering spatial variability in soil properties

ABSTRACT The objective of this paper is to investigate the effects of spatial variability in coastal silty soil properties on the stability and failure probability of deep excavation. A super-large irregularly shaped deep excavation in the coastal area in Wenzhou, China, is considered. A numerical model is established based on the random field theory, finite difference method and Monte-Carlo simulation method. Focusing on the friction angle and cohesion, the effects of horizontal and vertical correlation distances and variation coefficients on excavation stability are systematically studied. Meanwhile, the reliability evaluation approach is also applied to systematically examine the impact of the correlation distance on the surface settlement and horizontal displacement of pile. The results show that the greater correlation distance leads to a larger dispersion degree of the ground settlement curve and the displacement curve of the diaphragm wall around. The influence of the horizontal correlation distance on land settlement is more significant. The horizontal and vertical displacements of the pile top are less affected by the correlation distance. Compared with the deterministic analysis, the random analysis results considering the soil spatial variability produce larger displacement.

COFUN: A new tool for evaluating containment failure frequency and uncertainty

The feature of the COntainment Failure probability and Uncertainty aNalysis program (COFUN) is the quantification of the containment state. The probability factors used in probabilistic safety assessment (PSA) and the resulting outputs contain probability bands, so it is necessary to present the uncertainty bands as results. The uncertainty analysis process of the level 2 PSA is that a level 1 PSA uncertainty propagates to a level 2 PSA uncertainty. The basic event data including probability distribution were used for the level 1 PSA uncertainty analysis and probability distribution and priority of the fractional branch point were used for uncertainty analysis in a level 2 PSA. Once the input is ready, uncertainty analysis is performed via Monte-Carlo sampling. Finally, the uncertainty analysis can be performed for source term category (STC) and large early release frequency (LERF). One of the outstanding characteristics of the COFUN is to perform level 2 PSA for multi-unit accidents. The one of formats of multi-unit level 2 PSA is the combination of STCs but the combinations could be too many to acquire insight by STC combination itself. The COFUN provides a user-defined combination that makes STC combinations classified and enables the derivation of multi-unit accident LERF result.

Nondeterministic High-Cycle Fatigue Macromodel Updating and Failure Probability Analysis of Welded Joints of Long-Span Structures

Nondeterministic High-Cycle Fatigue Macromodel Updating and Failure Probability Analysis of Welded Joints of Long-Span Structures

Exploring mechanical and fracture properties in geopolymer concrete with ternary precursor waste materials through laboratory investigations and statistical analysis

The prevalent excessive utilization of cement concrete, characterized by energy-intensive processes and notable carbon dioxide emissions, necessitates a shift towards sustainable construction materials. This study addresses the environmental challenges posed by conventional cement concrete by investigating the potential of recycled precursor geopolymer concrete as an environmentally friendly alternative. The research delves into the mechanical and fracture characteristics of ternary blend geopolymer (TBG) concrete incorporating an industrial by-product, red mud (RM), through comprehensive laboratory testing and statistical analysis. The investigation focuses on assessing the impact of varying RM replacement levels (0 %, 8 %, 15 %, 23 %, and 30 %) on mechanical properties and fracture behaviour in both Mode I and Mode II, utilizing semi-circular bend (SCB) specimens for fracture tests. Statistical methodologies, including Weibull fracture failure probability modelling and analysis of variance (ANOVA), were employed to interpret the results derived from 180 SCB test specimens. Furthermore, microstructural analysis through FTIR, SEM, and EDX testing was conducted on the diverse mixes. The outcomes revealed that the incorporation of RM in geopolymer concrete consistently diminished the compressive strength and flexural strength of the geopolymer concrete as the incorporation levels increased. For instance, the compressive strength decreases from approximately 40 MPa in the RM-free sample to about 25 MPa in the sample with 30 % RM. However, statistical analysis revealed that up to 8 % RM inclusion does not significantly affect the compressive strength and, in some cases, may even slightly increase it, highlighting the subtle effect of RM dosage. Additionally, Weibull modelling revealed that the probability of failure for samples with 30 % RM is about five times higher than for samples without RM. The microstructural analysis also depicted that high RM content may lead to decreasing homogeneity and the formation of deep cracks, negatively impacting mechanical properties. Elevated Fe and Al concentrations with higher RM content suggest potential reactions forming stable geopolymer gels and the presence of minerals like katoite.

Spectral Analysis of a Sagged Cable with an Optimal Viscous Inertial Mass Damper under Random Wind in a Generalized State-Space Formulation

In this study, a spectral analysis method is proposed for a sagged cable with an optimal viscous inertial mass damper (VIMD) under random wind loads based on a generalized state-space formulation. The frequency response functions of the cable responses were evaluated for the wind force vector using complex modes orthogonal to the system matrices, from which the power spectral densities of the cable responses were readily obtained for the spectral matrix of the wind force. The accuracy and efficiency of the proposed method were verified by comparing the root mean square responses with those obtained from the time-domain and covariance analyses. The performance of two VIMDs optimized by the fixed-point method and the maximum damping ratio method was investigated for various cases of cable sag and wind properties. Serviceability failure probability analysis was also conducted using the first-passage problem. The results show that the proposed spectral method is computationally more efficient than the other two analysis methods. The VIMDs optimized for the first original cable mode were found to be highly effective in reducing cable vibration and the probability of serviceability failure.

A new approach for effective productivity management of newspaper printing press

Within the modern commercial printing press, a common problem is the ef-ficient management of the maintenance of different machines of newspaper printing press. If Effective Maintenance Management is applied, productivity of the machines can be increased by reducing breakdown time of the ma-chine. Productivity Management is an organizational framework that helps machines to improve productivity. Productivity of a machine is dependent on the failure probability which can be controlled by technical and management actions. The present investigation is established by the analysis of productivi-ty, effectiveness and failure probability on the basis of Pareto Analysis. Pareto chart is also developed to understand the actual scenario where highest prior-ity events are sequentially arranged. It has been observed that the web-offset printing machine has the highest productivity and effectiveness with less failure probability while the exposure unit has the highest failure probability having low productivity and effectiveness. Based on the reduction of proba-bility of failure to meet the acceptable criteria, further maintenance planning can be suggested. This approach confirms that productivity and effectivity of the machines of newspaper printing press can be increased by considering consequences of the machines and their corresponding failure assessments.

MATHEMATICAL MODEL OF RELIABILITY ASSESSMENT FOR DIAGNOSING THE TECHNICAL CONDITION OF ELECTRICAL ENGINEERING COMPLEXES IN DISTRIBUTED WATER SUPPLY SYSTEMS

Distributed water supply systems are high-tech complexes that include a variety of electrical components and control systems. Ensuring their reliable and uninterrupted operation requires continuous monitoring and diagnostics of their technical condition. The diagnosis of distributed water supply systems depends on many factors, which can be both deterministic and random. At present, this is a complex task due to the diversity of processes affecting the parameters of the water supply network's operational state. The non-stationarity of data, caused by cyclic changes in flow rate and pressure over time, also makes their diagnosis challenging. For precise diagnosis of the state of distributed water supply systems, it is necessary to consider not only typical emergency situations but also anomalous water consumption conditions and peculiarities of pressure management system operation. The article proposes a mathematical model for assessing the reliability of electrical engineering complexes in distributed water supply systems for the purpose of their diagnostics. The model is based on the analysis of failure probabilities of various components and subsystems of the complex. The research aims to help identify problematic areas in the water supply system and prevent potential emergency situations. The research results can be used to improve the safety and efficiency of water supply systems, as well as to optimize resource management. The use of the mathematical model in conjunction with modern diagnostic technologies can significantly improve the management of water supply infrastructure and ensure the reliable operation of electrical complexes. A convenient indicator for assessing the diagnosis of the technical condition of electrical engineering complexes in distributed water supply systems is the probability of failure downtime, which reflects both the frequency of failure occurrence and the duration of downtime. For assessing the reliability of the consumer water supply system, it is expedient to use such an indicator: the probability of safe downtime, which takes into account both the frequency of failures and the permissible duration of downtime under safety conditions.

Failure probability analysis of high fill levee considering multiple uncertainties and correlated failure modes

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.

A numerical critical shear crack model and its application to post‐peak behavior assessment of RC and SFRC beams

AbstractIn this paper, a numerical critical shear crack model, in which the shear‐flexural coupling effect is considered and the full process of stress and strain is captured, is proposed to evaluate the post‐peak behavior of reinforced concrete (RC) and steel fiber reinforced concrete (SFRC) beams. The shape of critical shear crack is identified by combining the modified compression field theory considering the bridge effect of steel fibers and the section analysis method. Based on the shape of critical shear crack, the shear capacity of beam members is provided by the shear tension zone and the shear compression zone. The shear capacity of the shear tension zone is calculated by the modified compression field theory and that of the shear compression zone is determined by multiaxial strength criterion of concrete. The vertical displacements caused by the flexure deformation and shear deformation are deduced by the moment area method and integration of shear strain. To verify the proposed numerical approach, a test database of 486 RC beams and 313 SFRC beams was established to predict the shear strength, and the force‐displacement relationships of twelve beam members are used to validate the feasibility for full process analysis. The stochastic analysis of beams with different failure modes is conducted via GF‐discrepancy‐based point selection method and probability density evolution method. The limitation between different failure modes is defined according to the degradation percent of shear capacity and it is taken as threshold value of failure domain, and the failure probability analysis indicates that the designed flexure beam member suffered severe degradation of shear capacity, resulting in a significant decline in safety probability.

Small failure probability analysis of stochastic structures based on a new hybrid approach

The small failure probability problem of stochastic structures is investigated by using two types of surrogate models and the subset simulation method in conjunction with parallel computation. To achieve high computational efficiency, the explicit expression of dynamic responses of stochastic structures is first derived in the form based on the explicit time-domain method. Then, the small failure probability analysis of stochastic structures is efficiently carried out through the Monte Carlo simulation method utilizing explicit expressions. To avoid the repeated calculation for the coefficient matrices or vectors of the explicit expression of stochastic structures, two types of surrogate models, e.g., the backpropagation neural network model and the Kriging model, are introduced to obtain these matrices or vectors for each parameter sample of the stochastic structures. The computational cost is further reduced by using the subset simulation method to generate conditional samples which follow the rule of Metropolis-Hastings. Furthermore, in virtue of the independence of the surrogate models for each time instant and the independence of dynamic analysis for each sample, parallel computation is embedded in the proposed approach, which can fully exploit the characteristics of the proposed approach and further improve the computational efficiency of dynamic reliability analysis. Numerical examples are given to illustrate the validity of the proposed hybrid approach.

Analysis of seepage failure probability for high core rockfill dams during rapid drawdown of reservoir water level

Rapid drawdown (RDD) is an abnormal reservoir flood control operation that may cause seepage failure of high core rockfill dams. In this paper, a novel framework combining Bayesian inference and transient unsaturated seepage simulation is proposed to evaluate the seepage failure probability of the core during RDD. The dynamic hydraulic boundaries utilized in the simulation are first determined by the performance of water release structures. The extreme learning machine (ELM) is then employed as the surrogate model to establish the mapping relationship between material parameters with simulated seepage pressure and hydraulic gradient. The Bayesian inference method is applied to characterize the uncertainty of material parameters based on seepage monitoring data. Finally, the posterior distribution samples of random parameters are utilized to calculate the seepage failure probability of the core. The seepage safety of the core under different drawdown rates is studied with a real 186 m high core rockfill dam. The results reveal that a faster RDD rate can lead to an increased probability of seepage failure. The maximum failure probability is 35.56 % for the four release structures working together (about 0.316 m/h), higher than 23.16 % for the three release structures (about 0.165 m/h). It is also found that the peak of seepage failure probability often occurs in the middle stage of RDD. Therefore, to ensure the safety of the project, it is important to control the RDD rate and carefully monitor the seepage pressure. From the point of view of seepage failure, the proposed method for evaluating the safety of core rockfill dams under RDD is of high guiding significance to the risk assessment of similar projects under extreme conditions.

Bayesian update of fragility curves for equipment failure probability in seismic probabilistic safety assessment in nuclear power plant

The assessment of equipment failure probability during seismic probabilistic safety assessment (PSA) is a crucial and fundamental component in nuclear power plant seismic PSA. A Monte Carlo program must be formulated to compute the equipment failure probability and uncertainty analysis in seismic PSA. A numerical calculation method is employed for the integration calculation to obtain the conditional failure probability and the uncertainty distribution for each equipment. The fragility parameters of the equipment and the hazard data of the plant site serve as the input parameters for the failure probability of equipment in seismic PSA. In this study, the probability of occurrence of the minimal cut set in equipment failure under earthquake conditions is calculated using the Monte Carlo sampling method, and the uncertainty distribution for each peak ground acceleration interval is presented. Furthermore, we have updated the fragility parameters of the equipment through the utilization of the Bayesian approach. Based on the updated fragility curves, we have recalculated the failure probability of the equipment and compared it with the results before the update.

Reliability Evaluation of EB-PVD Thermal Barrier Coatings in High-Speed Rotation and Gas Thermal Shock

The uncertain service life of thermal barrier coatings (TBCs) imposes constraints on their secure application. In addressing this uncertainty, this study employs the Monte Carlo simulation method for reliability evaluation, quantifying the risk of TBC peeling. For reliability evaluation, the failure mode needs to be studied to determine failure criteria. The failure mode of high-speed rotating TBCs under gas thermal shock was studied by combining fluid dynamics simulations and experiments. Based on the main failure mode, the corresponding failure criterion was established using the energy release rate, and its limit state equation was derived. After considering the dispersion of parameters, the reliability of TBCs was quantitatively evaluated using failure probability and sensitivity analysis methods. The results show that the main mode is the fracture of the ceramic layer itself, exhibiting a distinctive top-down “step-like” thinning and peeling morphology. The centrifugal force emerges as the main driving force for this failure mode. The failure probability value on the top side of the blade is higher, signifying that coating failure is more likely at this location, aligning with the experimental findings. The key parameters influencing the reliability of TBCs are rotation speed, temperature, and the thermal expansion coefficient. This study offers a valuable strategy for the secure and reliable application of TBCs on aeroengine turbine blades.

Reliability analysis of parted rope injuries during ship mooring operation under neutrosophic environments

At the national and international levels, many efforts have been made over recent decades to ensure the safety of ships at sea. In marine environments, crews face serious concerns during parted rope injuries during ship mooring operation. This problem can be tackled with the help of failure probability analysis which plays a vital role in detecting and eliminating the aforesaid threats in maritime transportation. Therefore, determining the fundamental causes of parted rope injuries during ship mooring operation is essential for maritime safety researchers. When the failure probability values of basic events are exact, conventional fault tree analysis has previously been successfully applied to determine the cause of failure of the top events. However, sometimes the failure information provided by different analysts for mooring operation may be uncertain and inconsistent. To properly address this important issue, the proposed research reflects a novel approach by extending crisp sets, fuzzy sets, and intuitionistic fuzzy sets into neutrosophic sets. The aforesaid approach is used to compute failure probabilities and reliability intervals for truth-membership, indeterminacy-membership and falsity-membership functions, along with a measure of how much each basic failure event contributes to the failure of the top event. The results obtained by incorporating the proposed approach are compared with those obtained using earlier approaches.

Failure probability analysis of hydrogen doped pipelines based on the Bayesian network

Damage from hydrogen, such as hydrogen embrittlement in natural gas pipelines, is a possibility. There are currently lacking ways for calculating the failure of hydrogen doped pipelines quantitatively; instead, research on the safety of them is mostly concentrated on hydrogen compatibility tests and consequence analysis. A method for quantifying hydrogen doped pipelines losses using Bayesian network-based failure probability analysis is presented. The influence of hydrogen on pipeline failure is introduced using the expert scoring method based on the analysis of historical failure data for gas pipelines. The failure probabilities of various components of hydrogen doped pipelines are then quantified by combining fuzzy mathematical theory and hierarchical analysis, which is subsequently utilized as prior probabilities to input into the Bayesian network for quantitative calculation. The results show that the Bayesian network can more accurately quantify the failure probability of hydrogen doped pipelines. They also show that the Bayesian network can provide a practical approach for quantitative risk assessment and safety evaluation, as well as a decision basis for the prevention of hydrogen doping pipeline failure accidents.

Failure Probability Analysis of Lattice Wind Turbine Towers Under Combined Wind and Earthquake Action

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.

Method study on failure probability and uncertainty analysis of stress corrosion cracking in fixed parts of PWR

To estimate the failure probability of stress corrosion cracking (SCC) in the fixed parts of pressurized water reactors (PWR), an approach based on the Paris model was developed and its uncertainty analysis was performed as well. In the study of SCC failure, the uncertainty of fracture toughness was translated into integral form to improve calculation efficiency. Moreover, uncertainty parameters such as crack size and Paris model coefficients were studied in the uncertainty analysis. On this basis, the thermowell of the pressurizer of PWR as an example was analyzed in this study. The Monte Carlo (MC) method and polynomial chaos expansion (PCE) approach were used to calculate the mean value, relative uncertainty, upper limit of tolerance interval of failure probability, and sensitivity coefficient of input parameter to compare the advantages and disadvantages of these methods. According to the results, compared with the other method, 300 sets of sampling with Latin Hypercube sampling (LHS) and Sobol sequences can converge the mean, and 300 sets of sampling with Halton sequence and Hammersley sequence can converge the relative uncertainty. When LHS with the 4th order Wilks' formula and Halton sequence with the 1st order Wilks' formula to compute the upper limit of tolerance interval, the accuracy and cost of the computation can be balanced. According to the results of the sensitivity analysis, crack aspect ratio is the most sensitive parameter. PCE surrogate model can accurately calculate the mean, relative uncertainty, the upper limit of tolerance interval and sensitivity coefficient, thereby reducing the computational cost.

Deep neural network aided Monte Carlo simulation in solder joint failure probability analysis

In this paper, a novel method based on deep neural networks is proposed to consider the uncertainties of the influential parameters using Monte Carlo simulation. The method reduces the number of sampling by concentrating the sampling range into the state limit function of the power converter of interest. The proposed method is applied to a PV inverter and reduces the calculation time to 25% of the so-called method.

Seismic failure probability analysis of slopes via stochastic material point method

Earthquakes, an important factor in inducing landslides, usually have great randomness. Moreover, landslides are investigated as large deformations, and traditional grid-based methods encounter mesh distortions when dealing with such problems. In this context, the spectral expression method and random functions are introduced to generate stochastic ground motions, and the material point method is adopted to perform probabilistic slope analysis. First, the dry aluminum bar collapse test and the Chiu-fen-erh-shan landslide were simulated to verify the effectiveness of this improved procedure. Then, three typical stochastic ground motions were selected to investigate the effects of material parameters (internal friction angle and cohesion) and slope geometry (slope inclination and height) on the sliding distance of the slope. Finally, the uncertainty of ground motions was taken into account when conducting the probabilistic analysis of earthquake-induced landslides. The results demonstrate that the sliding distance of slopes varies with earthquake action, exhibiting certain randomness, particularly in strong earthquakes. In addition, slope geometry influences sliding distances more than material parameters, and slope geometry should be the prior consideration for slope prevention and mitigation.