Maximal network reliability for a stochastic power transmission network

Many studies regarded a power transmission network as a binary-state network and constructed it with several arcs and vertices to evaluate network reliability. In practice, the power transmission network should be stochastic because each arc (transmission line) combined with several physical lines is multistate. Network reliability is the probability that the network can transmit d units of electric power from a power plant (source) to a high voltage substation at a specific area (sink). This study focuses on searching for the optimal transmission line assignment to the power transmission network such that network reliability is maximized. A genetic algorithm based method integrating the minimal paths and the Recursive Sum of Disjoint Products is developed to solve this assignment problem. A real power transmission network is adopted to demonstrate the computational efficiency of the proposed method while comparing with the random solution generation approach.     

A global procedure for the time-dependent reliability assessment of crane structural members

This paper aims at developing a probabilistic fatigue assessment procedure for crane structural members, using a structural reliability method, namely the stress–strength interference method. A crane member strength law is found by fitting fatigue life distribution parameters using finite element results and experimental data. The stress model is developed by using on-site data to determine probabilistic parametric distributions defining crane member loading. The efficiency of the proposed stress–strength interference method for tower crane member reliability assessment in fatigue is demonstrated on a jib chord member connection.     

Assessment of the efficiency of Kriging surrogate models for structural reliability analysis

This paper presents an assessment of the efficiency of the Kriging interpolation models as surrogate models for structural reliability problems involving time-consuming numerical models such as nonlinear finite element analysis structural models. The efficiency assessment is performed through a systematic comparison of the accuracy of the failure probability predictions based on the first-order reliability method using the most common first- and second-order polynomial regression models and the Kriging interpolation models as surrogates for the true limit state function. An application problem of practical importance in the field of marine structures that requires the evaluation of a nonlinear finite element structural model is adopted as numerical example. The accuracy of the failure probability predictions is characterised as a function of the number of support points, dispersion of the support points in relation to the so-called design point and order of the Kriging basis functions. It is shown with the application problem considered that the Kriging interpolation models are efficient surrogate models for structural reliability problems and can provide significantly more accurate failure probability predictions as compared with the most common polynomial regression models.     

Efficient surrogate models for reliability analysis of systems with multiple failure modes

Despite many advances in the field of computational reliability analysis, the efficient estimation of the reliability of a system with multiple failure modes remains a persistent challenge. Various sampling and analytical methods are available, but they typically require accepting a tradeoff between accuracy and computational efficiency. In this work, a surrogate-based approach is presented that simultaneously addresses the issues of accuracy, efficiency, and unimportant failure modes. The method is based on the creation of Gaussian process surrogate models that are required to be locally accurate only in the regions of the component limit states that contribute to system failure. This approach to constructing surrogate models is demonstrated to be both an efficient and accurate method for system-level reliability analysis.     

A multi-mode failure boundary exploration and exploitation framework using adaptive kriging model for system reliability assessment

Various adaptive reliability analysis methods based on surrogate models have recently been developed. A multi-mode failure boundary exploration and exploitation framework (MFBEEF) was proposed for system reliability assessment using the adaptive kriging model based on sample space partitioning to reduce computational cost and use the characteristics of the failure boundary in multiple failure mode systems. The efficiency of the adaptive construction of kriging model can be improved by using the characteristics of the center sample of the small space to represent the characteristics of all samples in the small space. This method proposes a failure boundary exploration and exploitation strategy and a convergence criterion based on the maximum failure probability error for a system with multiple failure modes to adaptively approximate the failure boundary of a system with multiple failure modes. A multiple-failure-mode learning function was used to identify the optimal training sample to gradually update the kriging model during the failure boundary exploration and exploitation stages. In addition, a complex failure boundary-oriented adaptive hybrid importance sampling method was developed to improve the applicability of the MFBEEF method to small failure probability assessments. Finally, the MFBEEF method was proven to be effective using five system reliability analysis examples: a series system, a parallel system, a series–parallel hybrid system, a multi-dimensional series system with multiple failure modes, and an engineering problem with multiple implicit performance functions.     

Uncertainty analysis of structural output with closed-form expression based on surrogate model

Uncertainty analysis (UA) is the process that quantitatively identifies and characterizes the output uncertainty and has a crucial implication in engineering applications. The research of efficient estimation of structural output moments in probability space plays an important part in the UA and has great engineering significance. Given this point, a new UA method based on the Kriging surrogate model related to closed-form expressions for the perception of the estimation of mean and variance is proposed in this paper. The new proposed method is proven effective because of its direct reflection on the prediction uncertainty of the output moments of metamodel to quantify the accuracy level. The estimation can be completed by directly using the redefined closed-form expressions of the model’s output mean and variance to avoid excess post-processing computational costs and errors. Furthermore, a novel framework of adaptive Kriging estimating mean (AKEM) is demonstrated for more efficiently reducing uncertainty in the estimation of output moment. In the adaptive strategy of AKEM, a new learning function based on the closed-form expression is proposed. Based on the closed-form expression which modifies the computational error caused by the metamodeling uncertainty, the proposed learning function enables the updating of metamodel to reduce prediction uncertainty efficiently and realize the decrease in computational costs. Several applications are introduced to prove the effectiveness and efficiency of the AKEM compared with a universal adaptive Kriging method. Through the good performance of AKEM, its potential in engineering applications can be spotted.     

A Bayesian model averaging method for software reliability modeling and assessment

The software reliability modeling is of great significance in improving software quality and managing the software development process. However, the existing methods are not able to accurately model software reliability improvement behavior because existing single model methods rely on restrictive assumptions and combination models cannot well deal with model uncertainties. In this article, we propose a Bayesian model averaging (BMA) method to model software reliability. First, the existing reliability modeling methods are selected as the candidate models, and the Bayesian theory is used to obtain the posterior probabilities of each reliability model. Then, the posterior probabilities are used as weights to average the candidate models. Both Markov Chain Monte Carlo (MCMC) algorithm and the Expectation–Maximization (EM) algorithm are used to evaluate a candidate model's posterior probability and for comparison purpose. The results show that the BMA method has superior performance in software reliability modeling, and the MCMC algorithm performs better than EM algorithm when they are used to estimate the parameters of BMA method.     

Time-variant reliability global sensitivity analysis with single-loop Kriging model combined with importance sampling

This paper develops a novel failure probability-based global sensitivity index by introducing the Bayes formula into the moment-independent global sensitivity index to approximate the effect of input random variables or stochastic processes on the time-variant reliability. The proposed global sensitivity index can estimate the effect of uncertain inputs on the time-variant reliability by comparing the difference between the unconditional probability density function of input variables and the conditional probability density function in failure state of input variables. Furthermore, a single-loop active learning Kriging method combined with metamodel-based importance sampling is employed to improve the computational efficiency. The accuracy of the results obtained by Kriging model is verified by the reference results provided by the Monte Carlo simulation. Four examples are investigated to demonstrate the significance of the proposed failure probability-based global sensitivity index and the effectiveness of the computational method.     

Unified reliability analysis by active learning Kriging model combining with random‐set based Monte Carlo simulation method

Reliability analysis with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described with random variables, and epistemic uncertainties are tackled with evidence theory. To estimate the bounds of failure probability, several methods have been proposed. However, the existing methods suffer the dimensionality challenge of epistemic variables. To get rid of this challenge, a so‐called random‐set based Monte Carlo simulation (RS‐MCS) method derived from the theory of random sets is offered. Nevertheless, RS‐MCS is also computational expensive. So an active learning Kriging (ALK) model that only rightly predicts the sign of performance function is introduced and closely integrated with RS‐MCS. The proposed method is termed as ALK‐RS‐MCS. ALK‐RS‐MCS accurately predicts the bounds of failure probability using as few function calls as possible. Moreover, in ALK‐RS‐MCS, an optimization method based on Karush–Kuhn–Tucker conditions is proposed to make the estimation of failure probability interval more efficient based on the Kriging model. The efficiency and accuracy of the proposed approach are demonstrated with four examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Reliability assessment for a stochastic manufacturing system with reworking actions

This article evaluates the system reliability of a manufacturing system with reworking actions, where the system reliability is an essential indicator to determine whether the manufacturing system is capable or not. Based on the path concept, we transformed the manufacturing system into a stochastic-flow network in which the capacity of each machine is stochastic (i.e., multistate) due to failure, partial failure, and maintenance. In such a manufacturing network, the input flow (raw materials/WIP; work-in-process) processed by each machine might be defective and thus the output flow (WIP/products) would be less than the input amount. To analyze the different sources processed by the manufacturing network, we decomposed the network into one general processing path and several reworking paths by a graphical technique. Subsequently, an algorithm for the manufacturing network was proposed to generate the lower boundary vector which allows sufficient products to satisfy the demand. In terms of such a vector, the system reliability can be derived easily.     

An uncertain optimization method for overall ballistics based on stochastic programming and a neural network surrogate model

A nonlinear stochastic programming method is proposed in this article to deal with the uncertain optimization problems of overall ballistics. First, a general overall ballistic dynamics model is achieved based on classical interior ballistics, projectile initial disturbance calculation model, exterior ballistics and firing dispersion calculation model. Secondly, the random characteristics of uncertainties are simulated using a hybrid probabilistic and interval model. Then, a nonlinear stochastic programming method is put forward by integrating a back-propagation neural network with the Monte Carlo method. Thus, the uncertain optimization problem is transformed into a deterministic multi-objective optimization problem by employing the mean value, the standard deviation, the probability and the expected loss function, and then the sorting and optimizing of design vectors are realized by the non-dominated sorting genetic algorithm-II. Finally, two numerical examples in practical engineering are presented to demonstrate the effectiveness and robustness of the proposed method.     

An active learning Kriging model combined with directional importance sampling method for efficient reliability analysis

In this paper, the active learning Kriging model (ALK), which has been studied extensively in recent years, has been expanded by combining with the directional importance sampling (DIS) method. The directional sampling method can reduce the dimensionality of the variable space by random sampling or interpolation in the direction of vector diameter, which can improve the efficiency of reliability analysis. It is especially suitable for the surfaces whose limit state is spherical or near-spherical. By introducing the control coefficient and constructing the directional importance sampling density function, the sampling efficiency can be further improved in the design point domain. A novel reliability analysis method called ALK-DIS method is proposed. The greatest advantage of the proposed method is its ability on great computational efficiency and dealing with small failure probability problem In addition, due to the excellent performance of directional sampling method in dealing with multi-failure model reliability problems, the ALK-DIS method has the advantage of being applied to system reliability analysis in this paper successfully. The applicability, feasibility and efficiency of the proposed method are proved on examples which contain linearity equation, non-linear numerical example, non-linear oscillator and system reliability engineering problems.     

Bounds approximation of limit-state surface based on active learning Kriging model with truncated candidate region for random-interval hybrid reliability analysis

This article reports a brand-new methodology based on active learning Kriging model for hybrid reliability analysis (HRA) with both random and interval variables. Unlike probabilistic reliability analysis, the limit state surface (LSS) of HRA is projected into a banded region in the domain of random variables. Only approximating the bounds of the banded region is able to meet the accuracy requirement of HRA. In the proposed methodology, the HRA problem is innovatively transformed into a traditional system reliability analysis (SRA) problem with numerous failure modes. And then a basic idea from the field of SRA is borrowed into HRA, and the so-called truncated candidate region (TCR) for HRA is proposed. In each iteration, the negligible region which probably does not influence the bounds estimation of failure probability is truncated from the original candidate region, and the optimal training point is chosen from the TCR. After several iterations, the TCR will converge to the true ideal candidate region, that is, the candidate region without the inner part of LSS, and the added training points will be driven to the region around the bounds of LSS. The performance of the proposed method is compared with relevant methods by five case studies.     

Photovoltaics in the assessment of wireless sensor network reliability with changing environmental conditions

This paper presents a reliability assessment of a wireless sensor network (WSN) equipped with mini photovoltaic cells (PV‐WSN) under natural environmental conditions while accounting for different types of system failures. In particular, our assessment considers the hardware specifications of the sensors, photovoltaic (PV) specifications, the use of rechargeable batteries, communication protocols, and various elements required for efficient detection of environmental conditions. We accomplished this by developing a simulator that generated data for 2 broad WSN conditions: (1) WSN without PV and (2) WSN with PV. The dynamic source routing protocol was employed for these simulations, and the following variables were assessed for both conditions: WSN reliability, the impact of energy consumption on the network, and the types of failures that lead to sensor unavailability. The following assumptions were made to run the simulation: the distribution of WSN nodes is random, with 1 sink node per rectangular cluster, the sensor nodes are structurally and functionally identical, environmental interference and suboptimal orientation impair PV cell recharge capacity randomly, and no communication loss occurs. Our reliability assessment assumed extreme environmental conditions and further made assessments of component reliability that included the following parameters: sensor and PV cell hardware specifications, the rechargeable nature of PV cell batteries for different sensor activity states, the availability of sunlight for powering PV cells, and the energy efficiency of PV cells. We found that network lifetime was prolonged for the PV‐WSN condition over the WSN without PV condition, introducing a role for PV cells as potential energy sources for WSNs.     

System reliability for a multistate intermodal logistics network with time windows

Network structures have been diffusely adopted in logistics systems, where the most critical target is completing the delivery within the promised timeframe. This paper focuses on a single commodity in a multistate intermodal logistics network (MILN) with transit stations and routes to involve three parameters: a route’s capacity, delivery time and time window. There is a carrier along each route whose number of available containers is multistate because the containers can be occupied by other customers. The delivery time consisting of the service time, travel time and waiting time varies with the number of containers and vehicle type. The arrival time at the transit station should be within the time window, the interval between the earliest and latest acceptable arrival times. This paper evaluates the system reliability, the probability that the MILN can successfully deliver sufficient amount of the commodity to meet market demand via several transit stations under the delivery time threshold and time windows. The system reliability can be treated as a delivery performance index and is evaluated with a proposed algorithm in terms of minimal paths. A practical case of scooter parts distribution between Taiwan and China is presented to emphasise the management implications of system reliability.     

A combined fuzzy DEMATEL and cloud model approach for risk assessment in process industries to improve system reliability

Decision-making trial and evaluation laboratory (DEMATEL) analysis is an effective and comprehensive method for identifying accident factors and converting the relationships among them into a visual structural model. Traditionally, the mean value method is adopted to summarize the initial direct-relation matrix, but it ignores the errors caused by differences in expert knowledge. In addition, a single qualitative risk assessment may not be sufficiently comprehensive and persuasive. The qualitative risk assessment results may not play a complete role in helping industrial plants carry out safety management. Therefore, this study proposes a quantitative risk assessment model based on the cloud model (CM) called the fuzzy DEMATEL-CM. An assessment index model is established by identifying the hazards associated with a converter steelmaking system. Subsequently, fuzzy DEMATEL analysis is applied to determine the relationships among the assessment indices and calculate their weights. Then, the CM is utilized to calculate the risk levels of the assessment indices and determine the comprehensive risk level. Finally, a case study is introduced to verify the practicability and validity of this model, and it is observed that the model has a certain superiority in solving uncertain problems. The quantitative risk assessment results are helpful for preventing accidents to improve the reliability of converter steelmaking plants.     

Dimension reduction model for two-spatial dimensional stochastic wind field: Hybrid approach of spectral decomposition and wavenumber spectral representation

A renewed methodology for simulating two-spatial dimensional stochastic wind field is addressed in the present study. First, the concept of cross wavenumber spectral density (WSD) function is defined on the basis of power spectral density (PSD) function and spatial coherence function to characterize the spatial variability of the stochastic wind field in the two-spatial dimensions. Then, the hybrid approach of spectral representation and wavenumber spectral representation and that of proper orthogonal decomposition and wavenumber spectral representation are respectively derived from the Cholesky decomposition and eigen decomposition of the constructed WSD matrices. Immediately following that, the uniform hybrid expression of spectral decomposition and wavenumber spectral representation is obtained, which integrates the advantages of both the discrete and continuous methods of one-spatial dimensional stochastic field, allowing for reflecting the spatial characteristics of large-scale structures. Moreover, the dimension reduction model for two-spatial dimensional stochastic wind field is established via adopting random functions correlating the high-dimensional orthogonal random variables with merely 3 elementary random variables, such that this explicitly describes the probability information of stochastic wind field in probability density level. Finally, the numerical investigations of the two-spatial dimensional stochastic wind fields respectively acting on a long-span suspension bridge and a super high-rise building are implemented embedded in the FFT algorithm. The validity and engineering applicability of the proposed method are thus fully verified, providing a potentially effective approach for refined wind-resistance dynamic reliability analysis of large-scale complex engineering structures.     

Fuzzy ridgelet neural network prediction model trained by improved particle swarm algorithm for maintenance decision of polypropylene plant

The proper maintenance plan should be made for ensuring the safety and reliability of polypropylene plant and improve economic benefits of petrochemical enterprise. To meet the requirement, a novel maintenance prediction model of polypropylene plant based on fuzzy theory, ridgelet an artificial neural network is constructed. The economy and reliability models of polypropylene plant maintenance are established through comprehensively considering the reliability and economy. The basic structure of fuzzy ridgelet neural network is designed, and the training algorithm is improved through combining the traditional particle swarm algorithm and bacterial foraging algorithm, and the corresponding algorithm flow is confirmed. Finally, prediction simulation analysis is carried out using a polypropylene plant as research object, and analysis results show that the fuzzy ridgelet neural network has best prediction effect, and the optimal maintenance plan can be confirmed to ensure security and reduce maintenance cost of polypropylene plant.     

Reliability assessment for systems suffering common cause failure based on Bayesian networks and proportional hazards model

The Bayesian network (BN) is an efficient tool for probabilistic modeling and causal inference, and it has gained considerable attentions in the field of reliability assessment. The common cause failure (CCF) is simultaneous failure of multiple elements in a system under a common cause, and it is a common phenomenon in engineering systems with dependent elements. Several models and methods have been proposed for modeling and assessment of complex systems with CCF. In this paper, a new reliability assessment method is proposed for the systems suffering from CCF in a dynamic environment. The CCF among components is characterized by a BN, which allows for bidirectional reasoning. A proportional hazards model is applied to capture the dynamic working environment of components and then the reliability function of the system is obtained. The proposed method is validated through an illustrative example, and some comparative studies are also presented.