Failure Probability Distribution Research Articles

Research on Fault Diagnosis Algorithm of Power Cable Based on Deep Learning

The self-learning method is used to realize the online monitoring of optical cable after the fault occurs. According to the fuzzy characteristic of cable fault, a fuzzy basis function network is constructed which is similar to nonlinear function. Thus, the dynamic characteristics of the cable system are obtained. Then, this paper iterates each additional sample to realize the learning of the center point and radial of the network. A normal multivariable fuzzy distribution is used to determine the expected output of the new sample, and recursive operations are performed on the matrix and covariance matrix of the original sample. In this way, all failure probability distributions at the sampling points are obtained. Finally, the hardware module of the system is designed from two aspects: the distributed short-circuit fault collecting and processing equipment and the on-line temperature measuring equipment for grounding fault. In this way, the functions of software module reset, storage and communication are realized.

Alarm rationalization and dynamic risk analyses for rare abnormal events

In this paper, improved alarm rationalization strategies are introduced to evaluate the quality of the multivariate alarm systems developed in previous work – with the alarm thresholds and response actions modified appropriately, based on key statistical metrics. For an exothermic CSTR, our strategies resulted in a significant reduction in the number of nuisance alarms, focusing on only quality alarms, which, if ignored, are more likely to result in an abnormal shift in operation to the undesirable regions. Next, their real-time performance is evaluated using dynamic risk analysis (DRAn), in which, the associated risk is analyzed by estimating the failure probabilities of the multivariate alarm systems using Bayesian statistics, based on multiple dynamic simulations for the process, inclusive of control, alarms and response actions. As expected, the failure probability distribution developed for the exothermic CSTR has a much lower variance as compared to one developed using a flat prior distribution.

Failure distribution and reliable analysis of ferroelectric ceramics under pulsed electric field

Dielectric breakdown at high electric field plays an important role in the application of ferroelectric ceramics. In this paper, the failure probability versus electric shock time of ferroelectric ceramics under positive pulse electric field is analyzed statistically. The failure probability distribution of ceramics after 10 electric shocks is studied. Piezoelectric constant, <i>P-E</i> loop of ferroelectric ceramics after 10 thousand electric shocks are measured and the breakdown mechanism is discussed. The results indicate that the relation between failure probability and electric shock number of ferroelectric ceramics is shown by a bath-tube curve and the failure probability of samples after 10 electric shocks decreases by 4 orders of magnitudes compared with that of origin sample. According to the results of piezoelectric constant and <i>P-E</i> loop, the samples subjected to positive pulse electric field many times do not show obvious fatigue or aging effect. So pulse electric field loading at 4.5 kV/mm is close to non-destructive condition. Considering the spread speed of cracks, it can be found that the rupture of ferroelectric ceramics under pulsed electric field roots from extension and connection of multi-cracks from multi-defects.

Systematic framework for handling uncertainty in probabilistic failure analysis of corroded concretes

Due to ambiguous correlations between input random variables and multi-source uncertainties from the electrochemical model, significant differences between deterministic corrosion prediction models and actual measurements are often observed. A systematic framework of quantification of uncertainties is developed for structures with correlated random variables originated from multiple sources, which allows efficiently estimating the failure probability distribution of the steel corrosion over time considering the randomness of the cover depth, the surface chloride concentration, and the chloride diffusion coefficient. After partitioning correlated random variables into different groups based on their uncertain sources, the Morris one-step-at-a-time and Sobol model is established to rank with respect to the importance of each correlated random variable. Based on polynomial chaos expansions and genetic programming methods, a more condensed set of random variables is created to propagate parametric problems. The unknown probability distribution of the input random variables is formulated by the Markov chain Monte Carlo to realize rigorous uncertainty quantification of the structural reliability. The application of the systematic framework to a set of numerical examples of steel corrosion includes experimental validation and uncertainty quantification and propagation of environmental, material and geometric properties. The results show that the framework can be integrated with parametric electrochemical models to allow robustness and reliability of corrosion prediction.

Multi-dimensional T-S dynamic fault tree analysis method involving failure correlation

The lack of effective failure correlation analysis is one main reason for the gap between the reliability models and the actual complex systems with mixed static and dynamic characteristics. Takagi and Sugeno (T-S) dynamic fault tree is one powerful tool to analyze the static and dynamic failure logic relationship but it assumes the failure probability of the event is independent. Therefore, this paper proposes a multi-dimensional T-S dynamic fault tree analysis method involving failure correlation. The method integrates the failure probability distribution function of basic events with multi-factors and the multi-dimensional copula function, and the important measure of this method is also deduced. The reliability model expression for systems with failure correlations, both in series and in parallel, is discussed and verified. Compare the proposed method with the assumption that the probability of a failure event is independent. This method solves the problem of a large error when ignoring the failure correlation between parts and the degree of the correlation between variables can be characterized. The reliability analysis can be conducted on complex systems affected both by multi-factors and failure correlations. The proposed method is applied to the reliability analysis of a hydraulic height adjustment system and the correctness and superiority of the method are verified.

Influence of heterogeneity due to toughness variations on weakest-link modeling for brittle failure

The effect of heterogeneous microstructures on the macroscopic probability of failure is studied by use of weakest-link modeling. Heterogeneity is here associated with a local variation of toughness, where a size scale characteristic of this variation defines a length parameter. The ratio between this length parameter and the size of the active fracture process zone, defined as the heterogeneity ratio, is key to evaluating the impact of a heterogeneous microstructure. Two extremes are identified; small-scale heterogeneity (SSH) and large-scale heterogeneity (LSH). For these cases, it is possible to formulate analytical expressions based on the weakest-link concept, and references are made to existing models in the literature. Typically, heterogeneity along the crack front, where gradients of the mechanical fields are small, falls under the category of SSH. On the other hand, the effect of heterogeneity in a plane perpendicular to the crack front depends strongly on the heterogeneity ratio. Cases that can neither be identified with SSH nor LSH must be addressed with care. How this can be done is discussed, and examples are given for four different microstructure configurations of interest. The investigation is carried out by numerical analysis of a modified boundary layer model. The cumulative probability of failure by cleavage fracture is evaluated in a post-processing step, where two different statistical models are examined; the Beremin model and the Kroon–Faleskog model. Both models render the same conclusion about the alteration of the overall failure probability distributions caused by heterogeneity.

Probabilistic-based investigation on tensile behavior of engineered cementitious composites (ECC): A macro-scale stochastic model

Micromechanics-based models are extensively used to simulate the tensile behavior of engineered cementitious composites (ECC). However, obtaining the micromechanical parameters in these models requires complicated experiments. This study proposes a macro-scale stochastic model to straightforwardly simulate the tensile behavior of ECC based on the strength criterion of strain-hardening. Specifically, the model simulates the multiple cracking of ECC as a stochastic process, in which the strength criterion is used to determine the formation of a crack. The failure probability distribution of the cracks is calculated by using statistical parameters of cracking strength and fiber bridging strength. Afterward, the crack number and tensile strain capacity of ECC are derived from the expectation of the failure probability distribution. Results show that the model predicts the crack number and tensile strain capacity of ECC with errors lower than 9.4% and 14.9%, respectively. Parametric analysis reveals that the crack number increases with the increasing difference value between cracking strength and fiber bridging strength. The stochastic model provides a comprehensive understanding on the multiple cracking of strain-hardening materials.

Pipelines reliability assessment considering corrosion-related failure modes and probability distributions characteristic using subset simulation

A methodology using the subset simulation and the modified Metropolis-Hastings algorithm with delayed rejection (SS-MMHDR) is developed to evaluate the time-dependent reliability of corroded pipelines under multiple failure modes. This methodology considers the competition between the small leak and burst failures and the correlated non-normal distribution of the defect variables, and characterizes the defect geometric probability distribution from extensive inspection data. Results demonstrate that SS-MMHDR has high accuracy and low variability in evaluating the pipeline failures, outperforming the SS-MMH and Monte Carlo simulation algorithms, especially under low probability levels, but with slightly increased computation time. The Generalized Extreme Value Type II (GEVII) distribution is the optimal distribution for internal corrosion defect lengths from the Kolmogorov-Smirnov test. Lognormal, Weibull and Normal distributions provide more conservative estimates on burst and composite failure probabilities and limiting maintenance times than GEVII. Effects of operating pressure and its variability, corrosion rate on failure probability, and pipeline limiting maintenance time are also revealed through numerical cases.

Calculation of Instantaneous Reliability of Grain Structure Under Small Samples

Under the condition of small sample, the performance parameters’ interval quantization and instantaneous reliability calculation of solid rocket motor grain structure are researched. Two important mechanical properties of material: Relaxation modulus and Poisson’s ratio are obtained by experiments of grain material. Since the data of parameters obtained are a small sample, the method of gray theory is used to mine the experimental data. It realizes the uncertainty quantitative analysis of grain material performance parameters and obtains the quantitative interval of performance parameters. Considering that the evidence theory can directly attribute probabilistic mass to the set or interval, the instantaneous reliability of grain structure is analyzed based on the evidence theory. By establishing the relationship between failure surface and the frame of discernment, and using the belief function and plausibility function to obtain the upper and lower bound probability distribution of structural reliability and failure probability, the instantaneous reliability probability interval of structure is obtained.

Quantification of model uncertainty and variability for landslide displacement prediction based on Monte Carlo simulation

Reliable and accurate prediction of landslide displacement is essential for early warning systems, as well as for disaster prevention and mitigation. Machine learning and deep learning algorithms are capable of modeling the relationship between step-like deformation and causal factors for displacement prediction. The ratio of the training set to the testing and the randomness of model parameters affect the assessment of model prediction capacity, which has been neglected in the literature. To take a more integrated view of the displacement prediction model and results, this study develops a hybrid approach that combines random training set length, Monte Carlo simulation, and performance function to evaluate the prediction model. The proposed approach is applied to a typical step-like case of the Jiuxianping landslide in the Three Gorges reservoir area. The uncertainty and variability of two extensively explored neural network models in the prediction of Jiuxianping landslide are systematically explored. The results showed that the probability of failure (and coefficient of variation (COV)) values for the LSTM and RNN models were 16.20% (COV = 0.19%) and 17.12% (COV = 0.42%), respectively. The LSTM model outperformed the RNN model in terms of failure probability, COV, and error distribution. The proposed scheme is worthy of reference and allows for a comprehensive evaluation of the prediction model and results.

A fatigue reliability assessment approach for wind turbine blades based on continuous time Bayesian network and FEA

AbstractWind turbine blades made by composite materials (CWTBs), encounter fatigue failures, such as cracks, fractures, delamination, etc. Finite Element Analysis (FEA) is applied for fatigue performance simulations of CWTBs as the full‐scale testing is costly. To consider correlated failures and uncertainties in load and material parameters, this paper proposes a fatigue reliability assessment method based on continuous time Bayesian network and FEA. Specifically, the dangerous regions of each component of CWTBs are determined by finite element fatigue simulation. The failure probability distributions of components are then computed by quantifying the uncertainties of several factors including the load and material parameters. A continuous time Bayesian network model is constructed for the fatigue reliability of CWTBs. The performance of the proposed method is verified by a comprehensive analysis with the results of discrete time Bayesian networks.

Reliability and lifetime estimation of bioregenerative life support system based on 370-day closed human experiment of lunar palace 1 and Monte Carlo simulation

It is extremely important to accurately estimate reliability and lifetime of Bioregenerative Life Support System (BLSS) for its proper design, building and operation. However, this problem remains unsolved due to data deficiency of long-period prototype experiments. In this paper, the first ground-based experimental prototype of BLSS in China, Lunar Palace 1 (LP1), was selected as representative to estimate the reliability and lifetime of BLSS, because the number and time of each unit failure of LP1 was accurately recorded during the 370-day closed human experiment of LP1. Based on these time-series data, failure number probability distribution function of each unit and overall LP1 were formulated through parameter estimation and composite probability distribution function derived from units’ series and parallel connection. Then, the influence of each unit failure on overall BLSS reliability and lifetime was determined correspondingly through sensitivity analysis and Monte Carlo simulations. Finally, the numerous pseudo-random numbers obeying the overall failure probability distribution function of LP1 were generated to estimate the reliability and lifetime of BLSS through maximum likelihood estimation and Monte Carlo simulations. The results demonstrate that the failure possibility of five units, water treatment unit, mineral element supply unit, LED light source unit, atmosphere management unit and temperature and humidity control unit have greater impact on reliability and lifetime of BLSS, and the mean lifetime of BLSS was 19112.37 days (about 52.4 years) with 95% confidence interval of [17367.11, 20672.68] days (about [47.58, 56.64] years) under normal operation and maintenance of BLSS. This research can lay a theoretical foundation for design, building and operation of BLSS with high reliability and long lifetime in the future.

Reliability Analysis of a Helicopter Utility Hydraulic System Using Reliability-centered Maintenance and Bayesian Network

Purpose: Reliability-centered maintenance (RCM) provides a standardized procedure for maintenance decision-making. The Bayesian network (BN) is a powerful tool for estimating the posterior probability based on the likelihood and prior probability distribution of failures. This study demonstrates reliability analysis and maintenance decision-making using RCM and BN.BRMethods: Maintenance decisions are made following the RCM framework for the failure of the utility hydraulic system. Bayesian updating and reliability analysis can be performed using the BN model. Real cases of field failure and the survival data of AH-64E were used for this study. The common cause failure (CCF) mode was incorporated into the BN to consider aircraft battle damages.BRResults: Failure diagnostic ability was demonstrated, and the life of the system was obtained. The most effective maintenance action was suggested based on reliability calculation. In addition, the results offered support that CCF should be considered for reliability calculation.BRConclusion: Reliability analysis conducted using RCM and BN can prove beneficial for system-level maintenance decision-making. The BN with CCF revealed unforeseen risks of aircraft battle damage.

Reliability and maintainability optimization of load haul dump machines using genetic algorithm and particle swarm optimization

PurposeReliability and maintainability estimation of any system depends on the identification of the best-fitted probability distribution of failure and repair rates. The parameters of the best-fitted probability distribution are also contributing significantly to reliability estimation. In this work, a case study of load haul dump (LHD) machines is illustrated that consider the optimization of failure and repair rate parameters using two well established metaheuristic approaches, namely, genetic algorithm (GA) and particle swarm optimization (PSO). This paper aims to analyze the aforementioned points.Design/methodology/approachThe data on time between failures (TBF) and time to repairs (TTR) are collected for a LHD machine. The descriptive statistical analysis of TBF & TTR data is performed, trend and serial correlation tested and using Anderson–Darling (AD) value best-fitted distributions are identified for repair and failure times of various subsystems. The traditional methods of estimation like maximum likelihood estimation, method of moments, least-square estimation method help only in finding the local solution. Here, for finding the global solution two well-known metaheuristic approaches are applied.FindingsThe reliability of the LHD machine after 60 days on the real data set is 28.55%, using GA on 250 generations is 17.64%, and using PSO on 100 generations and 100 iterations is 30.25%. The PSO technique gives the global best value of reliability.Practical implicationsThe present work will be very convenient for reliability engineers, researchers and maintenance managers to understand the failure and repair pattern of LHD machines. The same methodology can be applied in other process industries also.Originality/valueIn this case study, initially likelihood function of the best-fitted distribution is optimized by GA and PSO. Reliability and maintainability of LHD machines evaluated by the traditional approach, GA and PSO are compared. These results will be very helpful for maintenance engineers to plan new maintenance strategies for better functioning of LHD machines.

Topology optimization of adhesively bonded double lap joints

Current studies show great, but unutilized potential for mechanical optimization of adhesively bonded joints. There are different approaches, e. g. mixed adhesive joints; tapered adherends or joints with spew fillets, all of which try to redistribute the stress peaks, occurring at the ends of adhesive layer overlap, in favor to the load capacity. However, these investigations fail to take a general approach to find optimal geometric solutions to the problem of joining two materials by means of adhesive bonding. Instead the geometry is changed by predefined parameters such as tapering angles, spew fillet radii or the number of adhesives in mixed adhesive joints. To allow a non-parametric optimization, this paper proposes and investigates an extended bi-directional evolutionary structural optimization methodology based on a failure criterion to account for othotropic materials, which are often used in the context of bonding. The optimized joint geometry, generated by the proposed algorithm, resulted in a fairly constant distribution of elemental failure probability compared to the non-optimized state, thus eliminating underutilized spots of material and increasing the efficiency of the connection. Furthermore the influence of different parameters such as the overlap-length to adherend thickness ratio; the stiffness between adherend and adhesive as well as the adherend degree of orthotropy were investigated for optimal joint geometry.

Efficient method for fully quantifying the uncertainty of failure probability

It has been recognized that the uncertainty of distribution parameters has a significant effect on the outcome of structural reliability analysis. In this study, an efficient and accurate method is proposed to fully quantify failure probability, considering the uncertainty of the distribution parameters. This method obtains predictive failure probability by integrating the probability space of the conditional reliability index instead of directly utilizing the point-estimate method on the conditional failure probability as in previous studies. In the proposed method, a three-parameter lognormal distribution is suggested to approach the distribution of the conditional reliability index. The first three central moments of the conditional reliability index are estimated utilizing the point-estimate method combined with the bivariate dimension-reduction method. Based on this, the analytical solutions for the quantiles and probability distribution of the conditional failure probability can be readily derived without redundant calculations. Four illustrative examples were investigated to verify the efficiency and accuracy of the proposed method. The results show that the proposed method produces sufficiently accurate results in an efficient and simple way. It also presents a complete picture of the structural reliability evaluation results considering distribution parameter uncertainty in a wide range of applications.

Structural reliability analysis: A Bayesian perspective

Numerical methods play a dominant role in structural reliability analysis, and the goal has long been to produce a failure probability estimate with a desired level of accuracy using a minimum number of performance function evaluations. In the present study, we attempt to offer a Bayesian perspective on the failure probability integral estimation, as opposed to the classical frequentist perspective. For this purpose, a principled Bayesian Failure Probability Inference (BFPI) framework is first developed, which allows to quantify, propagate and reduce numerical uncertainty behind the failure probability due to discretization error. Especially, the posterior variance of the failure probability is derived in a semi-analytical form, and the Gaussianity of the posterior failure probability distribution is investigated numerically. Then, a Parallel Adaptive-Bayesian Failure Probability Learning (PA-BFPL) method is proposed within the Bayesian framework. In the PA-BFPL method, a variance-amplified importance sampling technique is presented to evaluate the posterior mean and variance of the failure probability, and an adaptive parallel active learning strategy is proposed to identify multiple updating points at each iteration. Thus, a novel advantage of PA-BFPL is that both prior knowledge and parallel computing can be used to make inference about the failure probability. Four numerical examples are investigated, indicating the potential benefits by advocating a Bayesian approach to failure probability estimation.

Integrated Planning of Cyber-Physical Active Distribution System Considering Multidimensional Uncertainties

The integration of cyber technologies is transforming the power distribution network into a cyber-physical active distribution system (CPADS), and brings more flexibility to its operation. However, various uncertainties from the cyber space and physical space are emerging and coupled with each other, which results in significant challenges for the distribution network planning and operation. Thus, a bilevel integrated planning model accounting for multidimensional uncertainties from both the cyber space and physical space is proposed for the CPADS in this paper. With the goal of minimizing the annual investment and operation costs, the model comprehensively considers the location and selection of active-management elements (e.g., electrical storage systems, capacitor banks, and switches), investment constraints, power flow constraints, and operation constraints for all the active-management elements, etc. Moreover, based on the typical cyber system failure scenario represented by information link failure (ILF), a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N-k</i> uncertainty set considering the failure probability distribution is proposed, while the uncertainties of renewable energy and load demand are characterized by box-like uncertainty sets. Finally, the proposed planning model is recast into a multi-stage robust optimization model which can be divided into a master problem and two-step subproblems (SP-1 and SP-2) to be solved by the column and constraint generation (CCG) algorithm. Case studies and comparative analysis on the PG 69 distribution system are performed to verify the effectiveness of the proposed method.

A Machine Learning-Based Reliability Evaluation Model for Integrated Power-Gas Systems

This paper proposes a machine learning method for the reliability evaluation of integrated power-gas systems (IPGS) under the uncertain component failure probability distributions. The Random Forest (RF) method is designed to select important features to solve the insufficient quantity of data and the curse of dimensionality problems. The Extreme Gradient Boosting (XGBoost) regression algorithm is developed to quantify the relationship between the uncertain parameters and reliability metrics. Moreover, a ten-fold cross-validation method is employed to further improve the accuracy of the regression model. Simulation results on three test systems show that the proposed method can achieve high accuracy for the reliability evaluation.

Probabilistic failure assessment of oil pipelines due to internal corrosion

AbstractOil and gas pipelines play a key role in the safe and efficient delivery of energy resources around the world. Crude oil by itself is not corrosive, but oil extracted from geological reservoirs is accompanied by varying amounts of water and acidic gases such as carbon dioxide (CO2), which can form a corrosive combination. Estimating the corrosion rate and depth in pipelines is essential for predicting their failure probability. In the present study, a Bayesian network has been developed for predicting the distribution of corrosion rate in oil pipelines given the point estimates generated using an empirical corrosion simulation model. For this purpose, the simulation model considers corrosion parameters such as pipe diameter, flow temperature, flow velocity, and CO2 partial pressure, among others. With the corrosion rate distribution predicted by the Bayesian network, corrosion depth–rate relationships have been employed to convert the corrosion rate distribution into failure probability distribution.