Quantifying coal rib stability and support requirements using bonded block modeling and reliability analysis based on the random set theory

Rock slope reliability analysis based on distinct element method and random set theory

Uncertainty assessment of flow and contaminant transport in the vadose zone entails probability density functions (PDFs) of soil hydraulic parameters. An unconventional maximum likelihood (ML) approach was used in this study to estimate the PDFs of water retention parameters (e.g., van Genuchten α and m) for a situation common in field‐scale modeling where core samples are sparse and prior PDFs of the parameters are unknown. In this situation, the unconventional ML approach approximates the PDFs as multivariate Gaussian. This study developed a method of estimating the mean and covariance of the multivariate Gaussian PDF based on the results of least square methods that can be easily obtained in practice. The developed method was applied to and evaluated through numerical simulation of unsaturated flow and tracer transport at the proposed Yucca Mountain geologic repository. Another focus of this study was to investigate the effect of uncertainty in the water retention parameters on predictive uncertainty. By comparing the predictive uncertainty before and after incorporating random water retention parameters, it was found that the random water retention parameters had limited effects on the mean predictions of the state variables including percolation flux and tracer travel time from the potential repository to the water table. Incorporating the uncertainty in the water retention parameters, however, significantly increased the magnitude and spatial extent of predictive uncertainty of the state variables. In particular, incorporating the random water retention parameters significantly changed the 5th and 95th percentiles of the tracer travel time by tens of thousands of years.

Uncertainty, Sensitivity and Geostatistical Studies of Flow and Contaminant Transport in Heterogeneous Unsaturated Zone by Feng Pan Dr. Zhongbo Yu, Examination Committee Chair Associate Professor of Hydrology University of Nevada Las Vegas Dr. Jianting Zhu, Examination Committee Co-Chair Associate Professor of Hydrologic Science Desert Research Institute The objectives of this study are: (1) to develop a methodology of estimating probability density functions (PDFs) of unsaturated hydraulic parameters when field samples are sparse, (2) to evaluate the predictive uncertainties in flow and contaminant transport due to parameter uncertainties in the layerand local-scale heterogeneities of hydraulic parameters in unsaturated zone (UZ), (3) to investigate the contributions of the parameter uncertainties to the flow and transport uncertainties, and (4) to estimate the spatial correlation structures of hydraulic parameters by incorporating prior information and site measurements. At layer scale, the uncertainty assessment of flow and contaminant transport in UZ entails PDFs of the hydraulic parameters. A non-conventional maximum likelihood (ML) approach is used in this study to estimate the PDFs of water retention parameters (e.g., van Genuchten a and ri) for situations common in field scale applications where core samples are sparse and prior PDFs of the parameters are unknown. This study also investigates the effects of the uncertainties in the water retention parameters on the predictive uncertainties in flow and transport in UZ. By comparing the predictive uncertainties with and without incorporating the random water retention parameters, it is found that the random water retention parameters have limited effects on the mean predictions of the state variables including percolation flux, normalized cumulative mass arrival, and contaminant travel time. However, incorporating the uncertainties in the water retention parameters significantly increases the magnitude and spatial extent of predictive uncertainties of the state variables. The layer-scale uncertainty is specific to hydrogeologic layers, while the localscale heterogeneity refers to the spatial variation of hydraulic properties within a layer. The local-scale heterogeneity is important in predicting flow path, velocity, and travel time of contaminants, but it is often neglected in modeling practices. This study incorporates the local-scale heterogeneity and examines its relative effects to the layerscale uncertainty on flow and transport uncertainties in UZ. Results illustrate that localscale heterogeneity significantly increases predictive uncertainties in the percolation fluxes and contaminant plumes, whereas the mean predictions are only slightly affected by the local-scale heterogeneity. Layer-scale uncertainty is more important than localscale heterogeneity for simulating overall contaminant travel time, suggesting that it would be more cost-effective to reduce the layer-scale parameter uncertainty in order to reduce predictive uncertainty in contaminant transport.

This study presents a procedure applied to design problems for lateral loaded piles. Calculations for a rigid concrete pile in non-cohesive soil are conducted with the aim of estimating the allowable horizontal force using the methods of Broms and Petrasovit. Random sets are applied to represent the uncertainties of soil parameters, including the internal friction angle and unit weight. Random variables are described using log-normal and beta distributions. Random set theory is utilised to represent variability in the form of probability boxes, possibility distributions, cumulative distribution functions, or intervals. Based on the assumed distributions of the subsoil, the lower and upper bounds for the precise probability of fulfilment of the limit state function of a laterally loaded pile are estimated. The reliability calculation procedure is implemented using the R package (R Studio v2024.12.1+563), and the limit forces and reliability indicators calculated using the two considered methods are compared. The presented procedure serves as an example of the use of a probabilistic approach for the assessment of the capacity of a laterally loaded pile, using a setup for the task involving set-based data and discrete probability distributions.

Modular multi‐level converter (MMC) with press‐packing IGBT devices is the popular and key equipment of VSC‐HVDC system, its reliability is directly related to the equipment safe operation. However, it is difficult to analyse the reliability using the failure statistical approach due to less fault data. In order to improve the reliability analyses accuracy, it is necessary to use the physical failure method by considering the main components fatigue failure mode. The reliability analysis models are presented for the MMC sub‐module with the press‐packing IGBT device and metallised film capacitors. First, based on the MMC‐HVDC simulation model, the losses and the junction temperatures of the IGBT devices were derived by the temperature field model, which the failure rates can be calculated. Furthermore, based the corrosion failure mode, the failure rate calculation of the metallised film capacitor was investigated using the voltage stress and thermal stress, the reliability calculation of the MMC sub‐module was presented by combining the main components failure rates. Finally, the reliability of the VSC‐HVDC based MMC was also presented with the different operation mode. The achievement is helpful to assess and improve the reliability of the VSC‐HVDC.

Engineering fuzzy heat conduction problem with subjective uncertainties in input parameters constitutes a significant challenge. Based on fuzzy and interval theory, this paper presents novel numerical methods to efficiently identify the effect of fuzzy uncertainty on the system reliability analysis and optimization design. Firstly using the interval ranking strategy, the interval safety possibility in the transition state can be precisely quantified, and the eventual fuzzy safety possibility is calculated by integral operation. Then a fuzzy reliability-based optimization model is established with considerable computational cost caused by the two-layer nested loop. In order to improve the computational efficiency, a subinterval perturbation method based on the first-order Taylor series is presented to replace the inner loop. Comparing numerical results with traditional reliability model, two numerical examples are provided to evidence the superiority of proposed model and method for fuzzy reliability analysis and optimization in practical engineering.

Traditional reliability analysis generally uses probability approach to quantify the uncertainty, while it needs a great amount of information to construct precise distributions of the uncertain parameters. In this paper, a new reliability analysis technique is developed based on a hybrid uncertain model, which can deal with problems with limited information. All uncertain parameters are treated as random variables, while some of their distribution parameters are not given precise values but variation intervals. Due to the existence of the interval parameters, a limit-state strip enclosed by two bounding hyper-surfaces will be resulted in the transformed normal space, instead of a single hyper-surface as we usually obtain in conventional reliability analysis. All the limit-state strips are then summarized into two different classes and corresponding reliability analysis models are proposed for them. A monotonicity analysis is carried out for probability transformations of the random variables, through which effects of the interval distribution parameters on the limit state can be well revealed. Based on the monotonicity analysis, two algorithms are then formulated to solve the proposed hybrid reliability models. Three numerical examples are investigated to demonstrate the effectiveness of the present method.

During the service of the missile suspension structure, the unexpected fatigue failure is emerged because of the dimension dispersibility resulting from machining deviation and design tolerance. In order to get the main factor of failure, based on the moment method of structural reliability assessment and PCL (Patran Command Language) redevelopment technology of finite element parameter analysis, an effective method is proposed to perform the missile suspension structure fatigue life reliability and parameter sensitivity analysis. Using proposed method, the result of reliability and parameter sensitivity analysis can be got readily with only 81 samples of finite element analysis. Compared with Monte-Carlo, proposed method in this paper is more effective with deducing the number of samples, especially fit for some structural reliability and parameter sensitivity analysis under implicit limit state equation.

At the present stage of excavation design,the embedded depth of braced structure should meet the requirement of circular sliding stability when the bottom is soft soil. By increasing the embedded depth of support structure, the requirements of stability could be meet. In the normal design, the support structure must penetrate the soft soil layer when the bottom exist soft soil. While when the excavation is narrow and long, because of the obviously spatial effect, there is no need to determine the embedded depth based on the general circular sliding stability. In this paper, based on one the project example, calculate and analyze the similar stability using strength reduction method through the finite element software Plaxis and Midas.

With regard to the fuzziness of limit state in the deep sliding stability of gravity dams, the fuzzy response surface method is put forward to analyze the reliability, including algorithm of fuzzy response surface method and determination of membership function. The concept of primary limit state and subordinate limit state is proposed for the fuzzy response surface method. The safety factor is endowed with general meaning, and the limit state equation is established with the combination of safety factor method and reliability theory. Both the traditional reliability index and fuzzy reliability index are calculated based on strength reduction method. The results show that the reliability indices and safety factor meet the design specifications, but the fuzzy reliability index is smaller than traditional reliability index. It's proved that the results from reliability theory and strength reduction method are consistent with each other, and can make up the shortcomings for each other. It's recommended that the safety level should be raised to take account of the fuzziness of limit state when strength reduction method is used to analyze the deep sliding stability of gravity dams.

Dynamic reliability analysis using the extended support vector regression (X-SVR)

Reliability analysis of Multi-State Systems using random set theory

As the core foundation of reliability engineering and one of the most crucial aspects of general quality, reliability has been attracting increasing attention from industry and academia. Numerous publications on reliability analysis (RA) have appeared in academic journals, conference proceedings, and technical reports. However, there has not been a systematic summary that covers RA data, models, methods, indicators, and software comprehensively. To fill this gap, this paper analyzed the challenges and the state of the art, as well as determined the future prospects for research on RA. This paper introduces the features of modern complex electromechanical systems (CES), then summarizes the current challenges to the RA of CES. Next, it reviews the latest developments, such as reliability theories, models, methods, and software, then summarizes and compares their advantages and limitations. Finally, it discusses future prospects from the perspectives of reliability data, modeling, decoupling, evaluation indicators, and timely prediction. It is expected that this paper would serve as an introduction to RA for researchers new to this field and as a summary of the current frontiers of RA for experienced researchers.

To effectively perform the reliability analysis of the flap deflection angle, the reliability analysis framework is developed by introducing fault logic and a data-driven model. Herein, the fault logic analysis is used to study the fault mechanism and filter out the characteristic fault parameters that can be used to collect input data for data-driven modelling; the data-driven modelling is employed to establish a reliability analysis model with a small amount of input data. Under this proposed framework, the improved dung beetle optimization algorithm for back propagation (IDBO-BP) method is developed to perform the reliability modelling of the flap deflection angle. To validate the effectiveness of the proposed framework, we study the fault logic of flap symmetry and establish a surrogate model of flap deflection based on the fault parameters and the IDBO-BP algorithm. According to the predicted results of the flap deflection angle, the reliability model based on the fault mechanism can reflect the actual flap motion. At the same time, the proposed IDBO-BP algorithm has excellent modelling and simulation property by comparing with other optimization algorithms. Thus, the efforts of this study provide a new solution to the problem of reliable analysis with uncertain fault parameters. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

Slope instability, driven by factors such as rainfall, seismic activity, and human influence, presents a pervasive hazard worldwide. Timely assessment of slope stability and accurate identification of its most critical slip surface are important for slope safety early warning and management. Currently, for the slope reliability analysis by the strength reduction method (SRM), the critical failure path is approximately determined through visualization techniques, which is not sufficiently precise. Therefore, this study proposes a critical failure search method based on SRM for slope reliability analysis, aiming to accurately identify the critical slip surface. The critical failure path is considered as the path with the maximum plastic dissipative energy density (PDED) and is searched in the constructed weighted graph based on the dissipated energy of the slope. This proposed method is further applied with an engineering slope to find the critical failure path and assess its reliability during and after construction. The searched critical failure path lies within the approximate range obtained through conventional visualization methods. Finally, a reliability prediction model consisting of time, rainfall, and deformation component is further constructed, which allows rapid estimation of the slope reliability through available monitor data. The results of reliability analysis indicate that construction disturbances have a significant impact on slope stability, along with other factors such as rainfall and creep.