Towards a theory of granular plasticity

A theory of granular plasticity based on the time-averaged rigid-plastic flow equations is presented. Slow granular flows in hoppers are often modeled as rigid-plastic flows with frictional yield conditions. However, such constitutive relations lead to systems of partial differential equations that are ill-posed: they possess instabilities in the short-wavelength limit. In addition, features of these flows clearly depend on microstructure in a way not modeled by such continuum models. Here an attempt is made to address both short-comings by splitting variables into ‘fluctuating’ plus ‘average’ parts and time-averaging the rigid-plastic flow equations to produce effective equations which depend on the ‘average’ variables and variances of the ‘fluctuating’ variables. Microstructural physics can be introduced by appealing to the kinetic theory of inelastic hard-spheres to develop a constitutive relation for the new ‘fluctuating’ variables. The equations can then be closed by a suitable consitutive equation, requiring that this system of equations be stable in the short-wavelength limit. In this way a granular length-scale is introduced to the rigid-plastic flow equations.     

A logic flowgraph-based concept for decision support and management of nuclear plant operation

The architecture of au automated decision support system for nuclear plant operators is presented and discussed. The system is based on the use of ‘logic flowgraph’ process models and is designed in a hierarchical fashion. Its functionality spans from ‘function oriented’ plant status and alternative success path information displayed to the plant operators at its higher access levels to ‘process oriented’ diagnostic and recovery information deduced and displayed at its lowest. The design basis for this architecture is the ‘defense in depth’ plant safety concept. The decision support system goal is to provide plant operators, in the presence of an unforeseen transient, with the best and safest alternative between plant stabilization after shutdown and recovery of normal operation based on early diagnosis. Examples of the system capability to interpret and diagnose abnormal plant conditions and of the information that it can supply to the operators at its three access levels are presented and discussed.     

Crystallographic features of phase transformations in solids

The paper reviews the current knowledge and understanding of the crystallographic features of phase transformations in solid materials – metals, ceramics and alloys. It covers both of the broad classes of phase transformations in crystalline solids – martensitic or ‘displacive’ and ‘diffusional’ or ‘reconstructive’. The factors that govern the crystallographic features of these two classes of transformations are compared and contrasted. This provides an appropriate basis for examining the ‘diffusional–displacive’ transformations that appear to exhibit the characteristics of both classes. After a brief summary of the considerable body of experimental data available on the crystallographic characteristics of these various types of phase transformation, the different models/theories advanced to account for these observations are discussed. The main emphasis is on those models/theories that are capable of predicting, rather than just rationalising or explaining, these crystallographic features. The review purposely adopts a unifying approach and attempts to reconcile the controversy that has on occasions existed between the ‘displacive’ group and the ‘diffusional’ group – particularly in respect of the ‘diffusional–displacive’ transformation. Developing a comprehensive understanding of the crystallographic features of all classes of phase transformations is obviously the ultimate goal. The review concludes by assessing how close we are to this final achievement, identifies the gaps in current knowledge and suggests future work.     

Models and model uncertainty in the context of risk analysis

This paper addresses the concept of model uncertainty within the context of risk analysis. Though model uncertainty is a topic widely discussed in the risk analysis literature, no consensus seems to exist on its meaning, how it should be measured, or its impact on the application of analysis results in decision processes. The purpose of this paper is to contribute to clarification. The first parts of the paper look into the contents of the two terms ‘model’ and ‘uncertainty’. On this platform it is discussed how focus on model uncertainty merely leads to muddling up the message of the analysis, if risk is interpreted as a true, inherent property of the system, to be estimated in the risk analysis. An alternative approach is to see the models as means for expressing uncertainty regarding the system performance. In this case, it is argued, the term ‘model uncertainty’ loses its meaning.     

Generalized renewal process for repairable systems based on finite Weibull mixture

Repairable systems can be brought to one of possible states following a repair. These states are: ‘as good as new’, ‘as bad as old’ and ‘better than old but worse than new’. The probabilistic models traditionally used to estimate the expected number of failures account for the first two states, but they do not properly apply to the last one, which is more realistic in practice. In this paper, a probabilistic model that is applicable to all of the three after-repair states, called generalized renewal process (GRP), is applied. Simplistically, GRP addresses the repair assumption by introducing the concept of virtual age into the stochastic point processes to enable them to represent the full spectrum of repair assumptions. The shape of measured or design life distributions of systems can vary considerably, and therefore frequently cannot be approximated by simple distribution functions. The scope of the paper is to prove that a finite Weibull mixture, with positive component weights only, can be used as underlying distribution of the time to first failure (TTFF) of the GRP model, on condition that the unknown parameters can be estimated. To support the main idea, three examples are presented. In order to estimate the unknown parameters of the GRP model with m-fold Weibull mixture, the EM algorithm is applied. The GRP model with m mixture components distributions is compared to the standard GRP model based on two-parameter Weibull distribution by calculating the expected number of failures. It can be concluded that the suggested GRP model with Weibull mixture with an arbitrary but finite number of components is suitable for predicting failures based on the past performance of the system.     

Automated fault tree synthesis by semantic network modeling, rulebased development and recursive 3-value procedure

A concept of flow is introduced to represent any material, information, energy, activity, or phenomenon which can move or propagate along flow paths to cause events specific to the system to be analyzed. A graphical equipment library is given to represent typical types of ‘generation rate’ and ‘aperture’ controllers. The system is modeled by a semantic network with labeled arrows showing effect to cause (backward) relationships between flow and equipment nodes. A correspondence between the equipment library and the system components is established, and the semantic network is constructed by integrating network fragments in the library. Fixed and/or free boundary conditions can be specified explicitly for flow or equipment nodes. Forward-chaining event development rules locally trace the labeled arrows, while a 3-value procedure guides the FT generation by recursive rule applications. The rules are obtained from tables and equipment definitions. The 3-value logic is used to truncate FTs according to the boundary conditions. Different FTs are generated for different top events and boundary conditions, given a semantic network model. FT modules and their hierarchies can be identified by examining network theoretic properties of flow nodes. The proposed approach is demonstrated for a relay system, a hypothetical swimming pool reactor and a chemical reactor.     

Modifications to the ‘directional simulation in the load space’ approach to structural reliability analysis

‘Directional simulation in the load space (DS-LS)’ is a simulation-based technique used to perform reliability analysis of structures subjected to time-invariant or time-variant random loads. To perform DS-LS a location must first be chosen for an ‘origin of simulation’. The origin may be positioned in either the safe or failure region of the load space, and its precise location (with respect to these regions) influences the DS-LS formulation needed to evaluate reliability correctly. The current formulation requires the origin to be positioned in the safe region. However, even for simple structures, the ‘exact’ location of the safe and failure region is not always known explicitly ‘a priori’. Modifications to allow for the possibility of positioning the origin not only in the ‘safe’ region but in the ‘failure’ region are proposed in this paper. Some numerical examples involving one or more stationary continuous Gaussian loads and the simulation of directions by ‘Monte Carlo’ and ‘the hyperspace division method’ are presented to demonstrate the validity of the proposed formulations. Some comments on convergence are made.     

A general discrete-time dynamic programming model for the opportunistic replacement policy and its application to ball-bearing systems

A general discrete-time, stochastic, dynamic-programming model of opportunistic corrective and preventive replacement policy is presented for multi-component systems with a different life distribution for each component. An approach to optimize the corrective and preventive maintenance policy is proposed, which is based on the introduction of the ‘oldest age’ concept and an ‘array dimensionality reduction technique’. The application of this policy to ball-bearing systems has resulted in considerable savings, as this paper demonstrates.     

Analogical reasoning for reliability analysis based on generic data

The paper suggests using the systemic concept ‘analogy’ for the foundation of an approach to analyze system reliability on the basis of generic data, describing the method of structuring the set that defines analogical models, an approach of transition from the analogical model to a reliability model and a way of obtaining reliability intervals of analogous objects.     

Risk tolerance and safety management

The recent introduction of the concept of risk tolerability is discussed in relation to the management of risk in high-technology industries. Differences between ‘acceptable’ and ‘tolerable’ risk are described and a model of those factors which constitute risk tolerability is presented. The recent approach of the UK Health and Safety Executive to the problem of risk tolerance is assessed and found to be wanting in two key areas. On the one hand there is a need for greater emphasis on the ‘safety net’ arrangements necessary to tackle residual risks and beyond design basis accidents. On the other hand, a greater emphasis is needed on the significant role which the communication of risks makes to the public tolerability of high technology.     

Geotechnical system reliability of slopes

In slope stability analysis it is customary to search for the critical slip surface considering the conventional factor of safety as an index of stability. With the development of reliability analysis approaches within a probabilistic framework, alternative definitions of the critical slip surface can be adopted. Thus one may define a critical slip surface as one with the lowest reliability index or one with the highest probability of failure. However, it is important to consider the slope stability problem in terms of a system of many potential slip surfaces. For such a system, the calculation of system reliability is appropriate and desirable. In this paper, system reliability bounds are calculated within a probabilistic framework. The ‘system reliability’ or the ‘system probability of failure’ must be estimated for comparison with the corresponding reliability or probability of failure with respect to a ‘critical’ slip surface. The general slope stability problem involving non-zero internal friction angle involves a non-linear performance function. Moreover, the expression for factor of safety is usually inexplicit except for the ordinary method of slices which is not accurate except when ‘ø = 0’. This paper addresses the system reliability for inexplicit and non-linear performance functions as well as for linear and explicit ones. Any version of the method of slices may be used although the proposed approach is presented on the basis of the Bishop simplified method. It is shown that the upper bound system failure probability is higher than the failure probability associated with a critical slip surface. The difference increases as the coefficient of variation of the shear strength parameters increases.     

Considerations on the elements of quantifying human reliability

This paper attempts to provide a contribution for the discussion of what the term ‘data’ means and how the qualitative perspective can be linked with the quantitative one. It will argue that the terms ‘quantitative data’ and ‘qualitative data’ are not distinct but a continuum that spans over the entire spectrum of the expertise that has to be involved in the HRA process. It elaborates the rational behind any human reliability quantification figure and suggests a scientific way forward to better data for human reliability assessment.     

Generalized renewal process for analysis of repairable systems with limited failure experience

Repairable systems can be brought to one of possible states following a repair. These states are: ‘as good as new’, ‘as bad as old’, ‘better than old but worse than new’, ‘better than new’, and ‘worse than old’. The probabilistic models traditionally used to estimate the expected number of failures account for the first two states, but they do not properly apply to the last three, which are more realistic in practice. In this paper, a robust solution to a probabilistic model that is applicable to all of the five after repair states, called generalized renewal process (GRP), is presented. This research demonstrates that the GRP offers a general approach to modeling repairable systems and discusses application of the classical maximum likelihood and Bayesian approaches to estimation of the GRP parameters. This paper also presents a review of the traditional approaches to the analysis of repairable systems as well as some applications of the GRP and shows that they are subsets of the GRP approach. It is shown that the proposed GRP solution accurately describes the failure data, even when a small amount of failure data is available.Recent emphasis in the use of performance-based analysis in operation and regulation of complex engineering systems (such as those in space and process industries) require use of sound models for predicting failures based on the past performance of the systems. The GRP solution in this paper is a promising and efficient approach for such performance-based applications.     

Strength prediction of sheet to tube single sided resistance spot welding

Single-Sided Spot Welding (SSSW) procedure is considered as a feasible method to join hydroformed or closed section parts to others in vehicle productions. A ‘doughnut’ shaped or ring nugget can be formed between the two workpieces during this process. The strengths of conventional button spot welds can be determined by the attributes of weldments and many functions that link weld diameter, sheet thickness and material properties to weld strength have been established. For welds of sheet to tube joining, the strength prediction model is greatly different from that of conventional welds for the completely different nugget form. In this study, computer experiments were conduced using the concept of design of experiments (DOE) and the method of finite element used to simulate the tensile-shear tests. The stress and strain distribution contour clouds during tensile-shear process were analyzed and quantitative relationship models were established to link a weld’s geometric and material properties to its tensile-shear strength. The results can give a simple judgment whether a ring spot weld was good only by its appearance.     

Searching the Patent Space

The Patent Space is a model to explain different kinds of patent searches in an illustrative and comprehensible way to laymen in the field of patents and patent searches, e.g. to customers like R + D staff or members of the Board. The most important kinds of patent searches are shown as examples of the applications of the ‘Patent Space’ concept.     

Technology of the new society

To seriously speculate about the rôle of technology in a society of the future it is necessary to carefully distinguish between quantitative and qualitative aspects of life. Thus ‘progress’ and ‘improvement’, as well as ‘surviving’ and ‘living’, are pairs of notions inspected in this Paper as to their relative importance for society.

Résumé

To seriously speculate about the rôle of technology in a society of the future it is necessary to carefully distinguish between quantitative and qualitative aspects of life. Thus ‘progress’ and ‘improvement’, as well as ‘surviving’ and ‘living’, are pairs of notions inspected in this Paper as to their relative importance for society.     

The use of technical planes in structuring the classification

In a previous article, the idea of technical ‘planes’ into which the collective field of disclosure naturally divides, was discussed. The ideas of ‘function’ and ‘application’ were related to this more general concept. The present article demonstrates, with examples, some of the practical effects of the idea of planes on the design and development of the Classification.     

Optimal structural design under stochastic uncertainty by stochastic linear programming methods

In the optimal plastic design of mechanical structures one has to minimize a certain cost function under the equilibrium equation, the yield condition and some additional simple constraints, like box constraints. A basic problem is that the model parameters and the external loads are random variables with a certain probability distribution. In order to get reliable/robust optimal designs with respect to random parameter variations, by using stochastic optimization methods, the original random structural optimization problem must be replaced by an appropriate deterministic substitute problem. Starting from the equilibrium equation and the yield condition, the problem can be described in the framework of stochastic (linear) programming problems with ‘complete fixed recourse’. The main properties of this class of substitute problems are discussed, especially the ‘dual decomposition’ data structure which enables the use of very efficient special purpose LP-solvers.     

Bayesian estimation of unavailability

This paper gives two Bayesian methods for estimating test-and-maintenance unavailability. Both unplanned and periodic maintenance are considered. One estimation method uses ‘detailed data,’ the individual outage times. The other method uses ‘summary data,’ totals of outage time and exposure time in various time periods such as calendar months. Either method can use either a noninformative or an informative prior distribution. Both methods are illustrated with an example data set, and the results are compared.