Using minimal cuts to evaluate the system reliability of a stochastic-flow network with failures at nodes and arcs

This paper deals with a stochastic-flow network in which each node and arc has a designated capacity, which will have different lower levels due to various partial and complete failures. We try to evaluate the system reliability that the maximum flow of the network is not less than a demand (d+1). A simple algorithm in terms of minimal cuts is first proposed to generate all upper boundary points for d, and then the system reliability can be calculated in terms of such points. The upper boundary point for d is a maximal vector, which represents the capacity of each component (arc or node), such that the maximum flow of the network is d. A computer example is shown to illustrate the solution procedure.     

A simple algorithm to generate all (d,B)-MCs of a multicommodity stochastic-flow network

Both minimal paths and minimal cuts are important media to evaluate the performance indexes, the system reliability or unreliability, for a single-commodity stochastic-flow network. This paper concentrates on a multicommodity stochastic-flow network in which each arc has both the capacity and cost attributes. Different from the single-commodity case, the system capacity is a pattern for multicommodity case. Since the traditional performance indexes are not suitable for multicommodity case, we propose a new performance index, the probability that the system capacity is less than or equal to a given pattern under the budget constraint. A simple algorithm based on minimal cuts is presented to generate all (d,B)-MCs that are the maximal capacity vectors meeting the demand d and budget B. The proposed performance index can be evaluated in terms of (d,B)-MCs.     

A simple approach to search for all d-MCs of a limited-flow network

Many real-world systems are multistate systems composed of multistate components in which the reliability can be computed in terms of the lower bound points of level d, called d-MCs. Such systems (electric power, transportation, etc.) may be regarded as flow networks whose arcs have independent, discrete, limited and multivalued random capacities. In this study, all MCs are assumed to be known in advance and we focused on how to find the entire d-MCs before calculating the reliability value of a network. Just based on the definition of d-MC, we develop an intuitive algorithm which is better than the best-known existing method. Analysis of our algorithm and comparison to existing algorithms shows that our proposed method is easier to understand and implement. Finally, the computational complexity of the proposed algorithm is analysed and compared with the existing methods.     

A simple MC-based algorithm for evaluating reliability of stochastic-flow network with unreliable nodes

A MP/minimal cutset (MC) is a path/cut set such that if any edge is removed from this path/cut set, then the remaining set is no longer a path/cut set. An intuitive method is proposed to evaluate the reliability in terms of MCs in a stochastic-flow network subject to both edge and node failures under the condition that all of the MCs are given in advance. This is an extension of the best of known algorithms for solving the d-MC (a special MC but formatted in a system-state vector, where d is the lower bound points of the system capacity level) problem from the stochastic-flow network without unreliable nodes to with unreliable nodes by introducing some simple concepts. These concepts were first developed in the literature to implement the proposed algorithm to reduce the number of d-MC candidates. This method is more efficient than the best of known existing algorithms regardless if the network has or does not have unreliable nodes. Two examples are illustrated to show how the reliability is determined using the proposed algorithm in the network with or without unreliable nodes. The computational complexity of the proposed algorithm is analyzed and compared with the existing methods.     

A neural network for predicting normal boiling point of pure refrigerants using molecular groups and a topological index

An artificial neuron network based on genetic algorithm is presented to predict the normal boiling point (T_b) of refrigerants from 16 molecular groups and a topological index. The 16 molecular groups used in this paper can cover most refrigerants or working fluids in refrigeration, heat pump and organic Rankine cycle; the chosen topological index is able to distinguish all the refrigerant isomers. A total of 334 data points from previous experiments are used to create this network. The calculated results, which are based on a developed numerical method, show a good agreement with experimental data; the average absolute deviations for training, validation and test sets are 1.83%, 1.77%, 2.13%, respectively. A performance comparison between the developed numerical model and the other two existing models, namely QSPR approach and UNIFAC group contribution method, shows that the proposed model can predict T_b of refrigerants in a better accord with experimental data.     

Evaluation of the reliability of transport networks based on the stochastic flow of moving objects

In transport networks, human beings are moving objects whose moving direction is stochastic in emergency situations. Based on this idea, a new model—stochastic moving network (SMN) is proposed. It is different from binary-state networks and stochastic-flow networks. The flow of SMNs has multiple-saturated states, that correspond to different flow values in each arc. In this paper, we try to evaluate the system reliability, defined as the probability that the saturated flow of the network is not less than a given demand d. Based on this new model, we obtain the flow probability distribution of every arc by simulation. An algorithm based on the blocking cutset of the SMN is proposed to evaluate the network reliability. An example is used to show how to calculate the corresponding reliabilities for different given demands of the SMN. Simulation experiments of different size were made and the system reliability precision was calculated. The precision of simulation results also discussed.     

Reliability of a Multi‐State Computer Network Through k Minimal Paths Within Tolerable Error Rate and Time Threshold

A computer system is usually modeled as a network topology where each branch denotes a transmission medium and each vertex represents a station of servers. Each branch has multiple capacities/states due to failure, partial failure, and maintenance. Such a network is named a multi‐state computer network (MSCN). From the viewpoint of quality management, transmission error rate and transmission time are both critical performance indicators to assess Internet quality for system managers and customers. Within both tolerable error rate and time threshold, the addressed problem is concentrated on an MSCN for computing the probability that d units of data can be sent through multiple minimal paths simultaneously. Such a probability is named system reliability. A solution procedure including an efficient algorithm based on MPs is proposed to derive the lower boundary vectors (LBVs) meeting the requirements. Then system reliability, which is represented as the probability of union of subsets, can be subsequently evaluated by the LBVs. Copyright © 2015 John Wiley & Sons, Ltd.     

Reliability of a computer network in case capacity weight varying with arcs, nodes and types of commodity

The computer network can be modeled as a capacitated-flow network. This paper concentrates on a two-commodity capacitated-flow network with three characters: (1) nodes as well as arcs have multiple possible capacities and may fail, (2) each component (arc/node) has both capacity and cost attributes; and (3) the capacity weight varies with arcs, nodes and types of commodity (or named file). We study the possibility that a given quantity of two types of files can be transmitted through this network simultaneously under the budget constraint. Such a possibility is named the system reliability which is a performance index to measure the quality level of supply demand systems such as computer, telecommunication, electric-power transmission and transportation systems. The approach of minimal paths is applied to describe the relationship among flow assignments and capacity vectors. A simple algorithm in terms of minimal paths is proposed to evaluate the system reliability.     

Probabilistic learning on manifolds (PLoM) with partition

The probabilistic learning on manifolds (PLoM) introduced in 2016 has solved difficult supervised problems for the “small data” limit where the number N of points in the training set is small. Many extensions have since been proposed, making it possible to deal with increasingly complex cases. However, the performance limit has been observed and explained for applications for which N is very small and for which the dimension of the diffusion-map basis is close to N. For these cases, we propose a novel extension based on the introduction of a partition in independent random vectors. We take advantage of this development to present improvements of the PLoM such as a simplified algorithm for constructing the diffusion-map basis and a new mathematical result for quantifying the concentration of the probability measure in terms of a probability upper bound. The analysis of the efficiency of this extension is presented through two applications.     

Confidence bounds for the reliability of binary capacitated two-terminal networks

Binary capacitated two-terminal reliability at demand level d (2TR_d) is defined as the probability that network capacity, generated by binary capacitated components, between specified source and sink nodes is greater than or equal to a demand of d units. For the components that comprise these networks, reliability estimates are usually obtained from some source of testing. For these estimates and depending on the type of testing, there is an associated uncertainty that can significantly affect the overall estimation of 2TR_d. That is, an accurate estimate of 2TR_d is highly dependent on the uncertainty associated to the reliability of the network components. Current methods for the estimation of network reliability and associated uncertainty are restricted to the case where the network follows a series-parallel architecture and the components are binary and non-capacitated. For different capacitated network designs, an estimate on 2TR_d can only be approximated for specific scenarios. This paper presents a bounding approach for 2TR_d by explaining how component reliability and associated uncertainty impact estimates at the network level. The proposed method is based on a structured approach that generates a α-level confidence interval (CI) for binary capacitated two-terminal network reliability. Simulation results on different test networks show that the proposed methods can be used to develop very accurate bounds of two-terminal network reliability.     

Generation of Low-Delay and High-Stability Multicast Tree

Delay and stability are two key factors that affect the performance of multicast data transmission in a network. However, current algorithms of tree generation hardly meet the requirements of low delay and high stability simultaneously. Given a general network, the generation algorithm of a multicast tree with minimum delay and maximum stability is an NP-hard problem, without a precise and efficient algorithm. To address these challenges, this paper studies the generation of low-delay and high-stability multicast trees under the model of spanning tree based on stability probability, degree-constrained, edge-weighted for multicast (T-SDE). A class of algorithms was proposed which creates the multicast tree greedy on the ratio of fan-out to delay (RFD) and probability of stability of terminal to obtain a high performance in multicast. The proposed algorithms greedily select terminals with a large RFD and a high probability of stability as forwarding nodes in the generation of the multicast tree, where the larger RFD and higher stability of upstream nodes are beneficial to achieve a low transmission delay and high stability in multicast. The proposed RFD can be compatible with the original model, which can take advantage of network connectivity during the generation of a multicast tree. This paper carries out simulation experiments on Matlab R2016b to measure the performance of the proposed algorithm. Experimental results show that the proposed algorithm can provide a smaller height, higher stability, and a lower transmission delay of the resulting multicast tree than other solutions. The spanning tree of the proposed algorithms can support low transmission delay and high stability in multicast transmission.     

Thermodynamic analysis of the tetragonal to monoclinic transformation in a constrained zirconia microcrystal

A thermodynamic analysis was made of a simple model comprising a transforming t-ZrO₂ microcrystal of sized constrained in a matrix subjected to a hydrostatic tensile stress field. The field generated a critical size range such that a t-particle transformed ifd _cl<d <d _cu. The lower limitd _cl exists because at this point the maximum energy (supplied by the applied stress) which can be taken up by the crystal is insufficient to drive the transformation. The upper limitd _cu is a consequence of the microcrystal being so large that it transforms spontaneously when the material is cooled to room temperature. Using the thermodynamic (Griffith) approach and assuming that transformation toughening is due to the dilational strain energy, this mechanism accounted for about one-third of the total observed effective surface energy in a peak-aged Ca-PSZ alloy.     

The effect of visual perception on the required performance of imaging systems

Abstract

Current performance measures for infrared imagers are applicable to linear mechanically scanned systems but not to those with focal plane arrays of detector elements, because these are nonlinear due to aliasing. The performance of an imager affects the ability of an observer to perform perception tasks using it. Psychophysical trials have been undertaken in an attempt to identify more appropriate performance measures. Simple shapes degraded by various degrees of Gaussian blurring and pixelation were selected at random and displayed on a computer monitor. A correlation has been found between the probability of recognition of an image and a quantity called ‘recognition contrast’ (C _R). This is related to the shape observed and a template of the equivalently degraded alternative shape most similar to it. This quantity C _R was refined following trials in which spatial noise was added to Gaussian blurred images. C _R is calculated from information about each of the two images and is directly proportional to the sensitivity index d' obtained from probability measurements. The results described are believed to have a wide range of applications such as in defining image quality and performance measures for imaging equipment.     

Assessing the lifetime performance index for Kumaraswamy distribution under first-failure progressive censoring scheme for ball bearing revolutions

First-failure progressive censoring schemes have potential usefulness in practice where budget constraints in place or there is a necessary for speedy test. To test the process capability, the lifetime performance index C_L is widely recommended for evaluating the performance of the products lifetime. This paper is devoted to construct the maximum likelihood estimator of the lifetime performance index C_L and the hypothesis testing technique for implementing C_L under first-failure progressive censoring sample from Kumaraswamy population. Finally, to illustrate the potentiality of the proposed procedure, two real engineering applications and a simulated example are given.     

Improving efficiency of solving d-MC problem in stochastic-flow network

Solving d-MC problem is often a tedious process. Three ways are suggested to improve the efficiency of solving d-MC problem. The first way is to make the best use of some special properties of network. A property of Network with Joint Parallel Part, which is more common than series–parallel network, is illustrated. The second way is to reduce the number of d-MC candidates and then to reduce the cost of testing. Two theorems on how to find the d-MCs with only one element unsaturated and on how to set the Lower Capacity Limits (LCLs) of elements to some values higher than zero are proved. These two theorems will be helpful to reduce d-MC candidates without any loss of real d-MC. The third way is to efficiently remove the duplicated d-MCs. A theorem, elucidating which Minimal Cuts (MCs) the duplicated d-MCs will be generated from, is proved. Finally, an algorithm is proposed by adding a pre-numerating step to the algorithm presented in Yeh [A new approach to the d-MC problem. Reliab Eng Syst Safety 2002;77(2):201–6], and two examples are employed to illustrate the proposed algorithm, especially the pre-numerating step.     

Networks originating from the multiple cracking of different scales in rocks and swelling soils

The objective of this work is not a fracture prediction or prevention. We are interested in modeling the crack network geometry in rocks and swelling soils and in the application of the model to rock volume fragmentation or preferential flow in swelling soils. Natural and explosion-induced rock fragmentation is important in geophysics and mining. Preferential flow in swelling soils is important in agricultural and environmental engineering. The presentation gives a brief review of the authors' work in this area. A concentration criterion of crack connection and effective independency of cracks in the case of multiple cracking are a basis for the modeling of a crack network. This basis enables one to introduce a condition of fragment formation at crack connection and a number of relevant concepts (an average cracking – an average crack number of x dimension in volume; crack connection probability of x dimension; fragment formation probability; average and maximum fragment dimensions; crack connectedness – a ratio connected to the total number of cracks; and crack network tortuosity), as well as to suggest quantitative relations between the concepts. In the frame of an application, the average fragment dimension and crack connectedness (or the maximum fragment dimension and fragment formation probability) can depend on the spatial coordinates and parameters specific for the application. The simplest application relates to the block-dimension distribution of a rock mass for statistically homogeneous conditions. The second application relates to the granulometric composition of a blasted rock mass in quarries. In this case the specific parameters are the preliminary rock disturbance (including natural cracking), charge construction, blasting scheme and others. The third application relates to the shrinkage crack network geometry in swelling clay soils, the spatial coordinate being the soil depth. The specific parameters are an upper layer thickness (of a few tens of centimeters) of intensive cracking and the maximum crack depth (its boundary being the depth of the water table level). Crack width, depth, spacing, volume, and tortuosity of the crack network are estimated by using the shrinkage curve of the soil and a water content profile. The fourth application relates to the hydraulic properties of capillary crack networks in swelling soils as compared to those of the soil matrix. For all the applications considered, comparison between the model prediction and available data shows good agreement.     

Improved Bounds for Quaternary Linear Codes of Dimension 6

In this paper, twenty new codes of dimension 6 are presented which give improved bounds on the maximum possible minimum distance of quaternary linear codes. These codes belong to the class of quasi-twisted (QT) codes, and have been constructed using a stochastic optimization algorithm, tabu search. A table of upper and lower bounds for d ⁴(n,6) is presented for n≤ 200. Received: 20 December 1996 / Accepted: 13 May 1997     

Stochastic user equilibrium model with a tradable credit scheme and application in maximizing network reserve capacity

The tradable credit scheme (TCS) outperforms congestion pricing in terms of social equity and revenue neutrality, apart from the same perfect performance on congestion mitigation. This article investigates the effectiveness and efficiency of TCS on enhancing transportation network capacity in a stochastic user equilibrium (SUE) modelling framework. First, the SUE and credit market equilibrium conditions are presented; then an equivalent general SUE model with TCS is established by virtue of two constructed functions, which can be further simplified under a specific probability distribution. To enhance the network capacity by utilizing TCS, a bi-level mathematical programming model is established for the optimal TCS design problem, with the upper level optimization objective maximizing network reserve capacity and lower level being the proposed SUE model. The heuristic sensitivity analysis-based algorithm is developed to solve the bi-level model. Three numerical examples are provided to illustrate the improvement effect of TCS on the network in different scenarios.     

UO2芯块运输容器核临界安全分析

目的 在开展二氧化铀（UO₂）芯块运输容器设计时,应进行临界安全分析,优化容器设计,并通过得出的临界安全指数（CSI）限定可运输货包的数量,确保在任何可信的运输情景下的核临界安全。方法 文中采用蒙特卡罗软件SuperMC对符合要求的国际临界安全手册中6类49个基准实验案例进行建模计算,获得本案例的次临界上限值,再基于运输容器经受正常运输条件与运输事故条件试验的结果,计算得出正常运输条件与运输事故条件下的单货包与货包阵列的最大中子增殖系数keff值。结果 该案例的次临界限值（USL）为0.91974;UO₂芯块运输容器在正常运输条件与运输事故条件下单货包的最大keff值分别为0.286 08,无限阵列货包的最大keff值为0.798 34。结论 UO₂芯块运输容器在正常运输条件与运输事故条件下的最大keff值均小于0.919 74,临界安全指数为0,容器设计临界安全性能可确保可运输安全。