A response-modeling alternative to surrogate models for support in computational analyses

Often, the objectives in a computational analysis involve characterization of system performance based on some function of the computed response. In general, this characterization includes (at least) an estimate or prediction for some performance measure and an estimate of the associated uncertainty. Surrogate models can be used to approximate the response in regions where simulations were not performed. For most surrogate modeling approaches, however, (1) estimates are based on smoothing of available data and (2) uncertainty in the response is specified in a point-wise (in the input space) fashion. These aspects of the surrogate model construction might limit their capabilities.One alternative is to construct a probability measure, G(r), for the computer response, r, based on available data. This “response-modeling” approach will permit probability estimation for an arbitrary event, E(r), based on the computer response. In this general setting, event probabilities can be computed: prob(E)=∫_rI(E(r))dG(r) where I is the indicator function. Furthermore, one can use G(r) to calculate an induced distribution on a performance measure, pm. For prediction problems where the performance measure is a scalar, its distribution F_pm is determined by: F_pm(z)=∫_rI(pm(r)z)dG(r). We introduce response models for scalar computer output and then generalize the approach to more complicated responses that utilize multiple response models.     

STEINER PROBLEMS IN GRAPHS: ALGORITHMS AND APPLICATIONS

Consider an undirected graph G = (V, E) with positive edge weights and a nonempty set S ? V, where Vand E are the sets of vertices and edges of G respectively. The Steiner problem in graphs is that of finding a subgraph of G which spans S and is of minimum total edge weight. In this paper we survey solution procedures for this problem. As the associated decision problem is NP-Complete we place special emphasis on heuristic methods of solution. We also examine special cases, related problems, and applications. The paper concludes with ideas for the development of new, efficient heuristics.     

A simple algorithm for evaluating the k-out-of-n network reliability

Evaluating the network reliability is an important topic in the planning, designing, and control of systems. The minimal cut set (MC, an edge set) is one of the major and fundamental tools for evaluating network reliability. A k-out-of-n MC is a special MC in a k-out-of-n network in which some nodes must receive at least k flows from their n input edges, where k is an integer number between 1 and n. In this study, an alternative method is given first to define a MC using a node set (called MCN) in k-out-of-n networks. A very simple algorithm based on some intuitive theorems that characterize the structure of the MCN and the relationship between MC and MCN is developed to solve the k-out-of-n network reliability by finding the k-out-of-n MCs between two special nodes. The proposed algorithm is not only easier to understand and implement, but is also better than the existing algorithm. The correctness of the proposed algorithm will be analyzed and proven. Two examples are illustrated to show how all k-out-of-n MCs are generated and verified in a k-out-of-n network using the proposed algorithm. The reliability of one example is then computing using one example.     

A path-based algorithm for evaluating the k-out-of-n flow network reliability

Evaluating the network reliability is an important topic in the planning, designing and control of systems. The minimal path (MP, an edge set) set is one of the major, fundamental tools for evaluating network reliability. A k-out-of-n MP is a union of some MPs in a k-out-of-n flow network in which some nodes must receive flows from their k input distinctive edges (each input edge has one flow) to generate one flow, where k is an integer number between 2 and n. In this study, a very simple a-lgorithm based on some intuitive theorems that characterize the k-out-of-n MP structure and the relationship between k-out-of-n MPs and k-out-of-n MP candidates is developed to solve the k-out-of-n flow network reliability by finding the k-out-of-n MPs between two special nodes. The proposed algorithm is easier to understand and implement. The correctness of the proposed algorithm will be analyzed and proven. One example is illustrated to show how all k-out-of-n MPs are generated and verified in a k-out-of-n flow network using the proposed algorithm. The reliability of one example is then computing using the same example.     

Pointwise recurrent one-dimensional flows

Let (G,?X) be a flow, where X is a graph and G is a finitely generated group. In this article, it is shown that (G,?X) is a pointwise recurrent flow if and only if one of the following two statements holds:

(1)?X?=?𝕊¹, and (G,?𝕊¹) is a minimal flow conjugate to an isometric flow, or to a finite cover of a proximal flow;

(2)?G is finite.     

Network reliability assessment using a cellular automata approach

Two cellular automata (CA) models that evaluate the s–t connectedness and shortest path in a network are presented. CA based algorithms enhance the performance of classical algorithms, since they allow a more reliable and straightforward parallel implementation resulting in a dynamic network evaluation, where changes in the connectivity and/or link costs can readily be incorporated avoiding recalculation from scratch. The paper also demonstrates how these algorithms can be applied for network reliability evaluation (based on Monte-Carlo approach) and for finding s–t path with maximal reliability.     

Looking for errors of omission and commission or The Hunting of the Snark revisited

Since the early 1990s, considerable effort has been spent to understand what is meant by an “error of commission” (EOC), to complement the traditional notion of an “error of omission” (EOO). This paper argues that the EOO–EOC dyad, as an artefact of the PSA event tree, is insufficient for human reliability analysis (HRA) for several reasons: (1) EOO–EOC fail to distinguish between manifestation and cause; (2) EOO–EOC refer to classes of incorrect actions rather than to specific instances; (3) there is no unique way of classifying an event using EOO–EOC; (4) the set of error modes that cannot reasonably be classified as EOO is too diverse to fit into any single category of its own. Since the use of EOO–EOC leads to serious problems for HRA, an alternative is required. This can be found in the concept of error modes, which has a long history in risk analysis. A specific system for error mode prediction was tested in a simulator experiment. The analysis of the results showed that error modes could be qualitatively predicted with sufficient accuracy (68% correct) to propose this method as a way to determine how operator actions can fail in PSA-cum-HRA. Although this still leaves the thorny issue of quantification, a consistent prediction of error modes provides a better starting point for determining probabilities than the EOO–EOC dyad. It also opens a possibility for quantification methods where the influence of the common performance conditions is prior to and more important than individual failure rates.     

A new algorithm for generating minimal cut sets in k-out-of-n networks

Evaluating the network reliability is an important topic in the planning, designing, and control of systems. A k-out-of-n network is a special network in that some nodes must receive at least k (>1) flows from all of their input edges (n). In real-life cases, many networks such as computer and telecommunications include k-out-of-n nodes for redundancy. The minimal-cut-node-set (MCN) is the major and fundamental tools for evaluating the k-out-of-n network reliability. In this study, a very simple algorithm based on some intuitive theorems that characterize the structure of the MCN is developed to solve the k-out-of-n network reliability. Compared to the existing algorithms, the proposed algorithm generates all k-out-of-n MCs without duplication based on fewer MCNs and fewer (k-out-of-n MC) candidates. The proposed algorithm is not only easier to understand and implement, but is also better than the existing algorithms. The correctness of the proposed algorithm will be analyzed and proven. One example is illustrated to show how all k-out-of-n MCs are generated, verified, and implemented to evaluate the k-out-of-n network reliability using the proposed algorithm.     

A semi-Markovian model allowing for inhomogenities with respect to process time

A non-homogeneous semi-Markov process is considered as an approach to model reliability characteristics of components or small systems with complex test resp. maintenance strategies. This approach generalizes previous results achieved for ordinary inhomogeneous Markov processes. This paper focuses on the following topics to make the application of semi-Markovian models feasible: rather than transition probabilities Q_ij(t), which are used in normal mathematical text books to define semi-Markov processes, transition rates λ_ij( ) are used, as is usual for ordinary Markov processes. These transition rates may depend on two types of time in general: on process time and on sojourn time in state i. Such transition rates can be followed from failure and repair rates of the underlying technical components, in much the same way, as this is known for ordinary Markov processes. Rather than immediately starting to solve the Kolmogorov equations, which would result in N² integral equations, a system of N integral equations for frequency densities of reaching states is considered. Once this system is solved, the initial value problem for state probabilities can be solved by straightforward integration. An example involving 14 states has been solved as an illustration using the approach.     

Computation of the relaxation and creep functions of elastomers from harmonic shear modulus

The purpose of this paper is to compute the relaxation and creep functions from the data of shear complex modulus, G ^∗(iν). The experimental data are available in the frequency window ν∈[ν_min,ν_max] in terms of the storage G′(ν) and loss G″(ν) moduli. The loss factor h( n) = \fracG"( n)G￠(n)\eta( \nu) = \frac{G'( \nu )}{G'(\nu )} is asymmetrical function. Therefore, a five-parameter fractional derivative model is used to predict the complex shear modulus, G ^∗(iν). The corresponding relaxation spectrum is evaluated numerically because the analytical solution does not exist. Thereby, the fractional model is approximated by a generalized Maxwell model and its rheological parameters (G _k ,τ _k ,N) are determined leading to the discrete relaxation spectrum G(t) valid in time interval corresponding to the frequency window of the input experimental data. Based on the deterministic approach, the creep compliance J(t) is computed on inversing the relaxation function G(t).     

Minimal cut sets of s–t networks with k-out-of-n nodes

In this paper, we extend traditional directed s–t network by letting nodes have k-out-of-n property: To generate output flows, a node must receive at least k flows from its n input links, where k is an integer assigned for the node and its value can be any number from 1 to n. To evaluate the system reliability, minimal cut sets for the extended network are defined for nodes. Under this definition, an extended network and its sink node have the same minimal cut sets. A new algorithm is designed to generate minimal cut sets for all nodes, starting with the source node and ending with the sink node. With different initializations, the algorithm can be applied for extended s–t networks with or without node failures.     

Predicting fatigue transverse crack growth in cross-ply carbon–epoxy laminates from quasi static strength tests by using iso-damage curves

Cross-ply laminates made of carbon/epoxy IM7/977-2 system are investigated. The fatigue study is confined to ambient temperature conditions and zero loading ratio. Damage is characterized by the transverse crack density ρ in the central 90°-layer. The family of experimental fatigue cracking curves (ρ versus N, where N is the number of cycles, for each tensile test maximum stress amplitude) can be replaced with a set of “iso-damage curves”, i.e. contour curves of constant ρ in the σ–log (N) plane. The iso-damage curves approximately constitute a fan of straight lines that intersect at a common point (σ_e, log (N_s)), where N_s is a very large number of cycles beyond which no more crack appears, and σ_e is some fatigue limit.Our aim is to propose a simple method to predict fatigue cracking at an arbitrary maximum stress level loading by using data stemming from a constant strain rate test. This method essentially rests upon the construction of the above “iso-damage” curves, using very simple assumptions.     

Mode III interlaminar fracture of carbon/epoxy laminates using a four-point bending plate test

A new four-point bending plate (4PBP) test was used for characterising the mode III interlaminar fracture of carbon/epoxy laminates. The specimen has a cross-ply lay-up and two edge delaminations whose propagation becomes visible at the edges. Although the test setup is very simple, determination of the mode III critical strain energy release rate G_IIIc requires finite element analyses (FEA). The virtual crack closure technique with an assumed initiation region was first proposed for computing G_IIIc. This scheme was subsequently validated by crack growth simulations with a cohesive zone model. The results showed an average G_IIIc = 1550 J/m², which is significantly higher than the G_IIIc = 850–1100 J/m² and G_IIc = 800 J/m² measured in previous studies.     

A non-parametric monotone maximum likelihood estimator of time trend for repairable system data

The trend-renewal process (TRP) is defined to be a time-transformed renewal process, where the time transformation is given by a trend function λ(·) which is similar to the intensity of a non-homogeneous Poisson process (NHPP). A non-parametric maximum likelihood estimator of the trend function of a TRP is obtained under the often natural condition that λ(·) is monotone. An algorithm for computing the estimate is suggested and examined in detail in the case where the renewal distribution of the TRP is a Weibull distribution. The case where one has data from several systems is also briefly studied.     

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.     

Communication Reliability Analysis of Wireless Sensor Networks Using Phased‐Mission Model

Communication reliability of wireless sensor networks (WSNs) is essential to ensure the correct and reliable operation of the network. Two distinct communication paradigms exist in WSNs: infrastructure communication and application communication, and a practical communication task typically involves both types of communications. To the best of our knowledge, no reliability studies on WSNs have been dedicated to combining the two communication paradigms. In this paper, we advance the state‐of‐the‐art by proposing a phased‐mission framework to analyze the communication reliability of WSNs considering both infrastructure communication and application communication, as well as K‐coverage requirements. WSNs containing two types of sensor nodes (energy harvesting sensor nodes and battery‐powered sensor nodes) are modeled. Corresponding to the two types of sensor nodes, two different link reliability models are first presented. Binary decision diagram (BDD) based algorithms are then developed for the phased‐mission communication reliability analysis of WSNs. Case studies are given to illustrate the application of the proposed algorithms. Copyright © 2016 John Wiley & Sons, Ltd.     

Analysis of OREDA data for maintenance optimisation

This paper provides estimates for the average rate of occurrence of failures, ROCOF (“failure rate”), for critical failures when also degraded failures are present. The estimation approach is exemplified with a data set from the offshore equipment reliability database “OREDA”. The suggested modelling provides a means of predicting how maintenance tasks will affect the rate of critical failures.     

A Parallel Strategy for the Logical‐probabilistic Calculus‐based Method to Calculate Two‐terminal Reliability

The theory of network reliability has been applied to many complicated network structures, such as computer and communication networks, piping systems, electricity networks, and traffic networks. The theory is used to evaluate the operational performance of networks that can be modeled by probabilistic graphs. Although evaluating network reliability is an Non‐deterministic Polynomial‐time hard problem, numerous solutions have been proposed. However, most of them are based on sequential computing, which under‐utilizes the benefits of multi‐core processor architectures. This paper addresses this limitation by proposing an efficient strategy for calculating the two‐terminal (terminal‐pair) reliability of a binary‐state network that uses parallel computing. Existing methods are analyzed. Then, an efficient method for calculating terminal‐pair reliability based on logical‐probabilistic calculus is proposed. Finally, a parallel version of the proposed algorithm is developed. This is the first study to implement an algorithm for estimating terminal‐pair reliability in parallel on multi‐core processor architectures. The experimental results show that the proposed algorithm and its parallel version outperform an existing sequential algorithm in terms of execution time. Copyright © 2015 John Wiley & Sons, Ltd.     

Hierarchical parameter estimation of GRN based on topological analysis

Reverse engineering of gene regulatory network (GRN) is an important and challenging task in systems biology. Existing parameter estimation approaches that compute model parameters with the same importance are usually computationally expensive or infeasible, especially in dealing with complex biological networks.In order to improve the efficiency of computational modeling, the paper applies a hierarchical estimation methodology in computational modeling of GRN based on topological analysis. This paper divides nodes in a network into various priority levels using the graph‐based measure and genetic algorithm. The nodes in the first level, that correspond to root strongly connected components(SCC) in the digraph of GRN, are given top priority in parameter estimation. The estimated parameters of vertices in the previous priority level ARE used to infer the parameters for nodes in the next priority level. The proposed hierarchical estimation methodology obtains lower error indexes while consuming less computational resources compared with single estimation methodology. Experimental outcomes with insilico networks and a realistic network show that gene networks are decomposed into no more than four levels, which is consistent with the properties of inherent modularity for GRN. In addition, the proposed hierarchical parameter estimation achieves a balance between computational efficiency and accuracy.Inspec keywords: biology computing, network theory (graphs), reverse engineering, graph theory, genetics, genetic algorithms, directed graphs, parameter estimationOther keywords: hierarchical parameter estimation, GRN, topological analysis, gene regulatory network, important task, computational systems biology, compute model parameters, complex biological networks, efficient information, model quality, parameter reliability, computational modelling, study divides nodes, priority levels, graph‐based measure, previous priority level, hierarchical estimation methodology obtains, computational resources, single time estimation, insilico network, realistic network show, computational efficiency     

1/f noise of electrolytic capacitors as a reliability indicator

The electrical noise of capacitors and the relationship between typical imperfections in capacitors and their excess noise are described. It was assumed that a noisy capacitor is a poor-quality one. Investigations were aimed at the determination of a correlation between the inherent noise of capacitors and their reliability (time to failure) and also at the determination of an indicator to predict reliability. Investigations (noise measurements and reliability tests) were carried out on two samples of aluminium electrolytic capacitors. The method of reliability prediction for electrolytic capacitors based on their low-frequency noise is described. For reliability prediction the noise intensity G at a frequency of 2 Hz was used as a reliability indicator. It was found that the evaluated correlation coefficients between the noise parameter G and the time to failure, t, are statistically significant. It is concluded that it is possible to predict the lifetime of aluminium electrolytic capacitors on the basis of their 1/f noise. © 1998 John Wiley & Sons, Ltd.