Effect of Al addition on microstructure of AZ91D

Casting is a net shape or near net shape forming process so work-hardening will not be applicable for improving properties of magnesium cast alloys. Grain refinement, solid-solution strengthening, precipitation hardening and specially designed heat treatment are the techniques used to enhance the properties of these alloys. This research focusses on grain refinement of magnesium alloy AZ91D, which is a widely used commercial cast alloy. Recently, Al-B based master alloys have shown potential in grain refining AZ91D. A comparative study of the grain refinement of AZ91D by addition of 0.02wt%B, 0.04wt%B, 0.1wt%B, 0.5wt%B and 1.0wt%B of A1-5B master alloy and equivalent amount of solute element aluminium is described in this paper. Hardness profile of AZ91D alloyed with boron and aluminium is compared

A systematic approach to atomicity decomposition in Event-B

Event-B is a state-based formal method that supports a refinement process in which an abstract model is elaborated towards an implementation in a step-wise manner. One weakness of Event-B is that control flow between events is typically modelled implicitly via variables and event guards. While this fits well with Event-B refinement, it can make models involving sequencing of events more difficult to specify and understand than if control flow was explicitly specified. New events may be introduced in Event-B refinement and these are often used to decompose the atomicity of an abstract event into a series of steps. A second weakness of Event-B is that there is no explicit link between such new events that represent a step in the decomposition of atomicity and the abstract event to which they contribute. To address these weaknesses, atomicity decomposition diagrams support the explicit modelling of control flow and refinement relationships for new events. In previous work,the atomicity decomposition approach has been evaluated manually in the development of two large case studies, a multi media protocol and a spacecraft sub-system. The evaluation results helped us to develop a systematic definition of the atomicity decomposition approach, and to develop a tool supporting the approach. In this paper we outline this systematic definition of the approach, the tool that supports it and evaluate the contribution that the tool makes

Applying Atomicity and Model Decomposition to a Space Craft System in Event-B

Event-B is a formal method for modeling and verifying consistency of systems. In formal methods such as Event-B, refinement is the process of enriching or modifying an abstract model in a step-wise manner in order to manage the development of complex and large systems. To further alleviate the complexity of developing large systems, Event-B refinement can be augmented with two techniques, namely atomicity decomposition and model decomposition. Our main objective in this paper is to investigate and evaluate the application of these techniques when used in a refinement based development. These techniques have been applied to the formal development of a space craft system. The outcomes of this experimental work are presented as assessment results. The experience and assessment can form the basis for some guidelines in applying these techniques in future cases

Model based safety analysis for an Unmanned Aerial System

This paper aims at describing safety architectures of autonomous systems by using Event-B formal method. The autonomous systems combine various activities which can be organised in layers. The Event-B formalism well supports the rigorous design of this kind of systems. Its refinement mechanism allows a progressive modelling by checking the correctness and the relevance of the models by discharging proof obligations. The application of the Event-B method within the framework of layered architecture specification enables the emergence of desired global properties with relation to layer interactions. The safety objectives are derived in each layer and they involve static and dynamic properties such as an independence property, a redundant property or a sequential property. The originality of our approach is to consider a refinement process between two layers in which the abstract model is the model of the lower layer. In our modelling, we distinguish nominal behaviour and abnormal behaviour in order to well establish failure propagation in our architecture

A subdivision-based implementation of non-uniform local refinement with THB-splines

Paper accepted for 15th IMA International Conference on Mathematics on Surfaces, 2017. Abstract: Local refinement of spline basis functions is an important process for spline approximation and local feature modelling in computer aided design (CAD). This paper develops an efficient local refinement method for non-uniform and general degree THB-splines(Truncated hierarchical B-splines). A non-uniform subdivision algorithm is improved to efficiently subdivide a single non-uniform B-spline basis function. The subdivision scheme is then applied to locally hierarchically refine non-uniform B-spline basis functions. The refined basis functions are non-uniform and satisfy the properties of linear independence, partition of unity and are locally supported. The refined basis functions are suitable for spline approximation and numerical analysis. The implementation makes it possible for hierarchical approximation to use the same non-uniform B-spline basis functions as existing modelling tools have used. The improved subdivision algorithm is faster than classic knot insertion. The non-uniform THB-spline approximation is shown to be more accurate than uniform low degree hierarchical local refinement when applied to two classical approximation problems

Formal modelling for Ada implementations: tasking Event-B

This paper describes a formal modelling approach, where Ada code is automatically generated from the modelling artefacts. We introduce an implementation-level specification, Tasking Event-B, which is an extension to Event-B. Event-B is a formal method, that can be used to model safety-, and business-critical systems. The work may be of interest to a section of the Ada community who are interested in applying formal modelling techniques in their development process, and automatically generating Ada code from the model. We describe a streamlined process, where the abstract modelling artefacts map easily to Ada language constructs. Initial modelling takes place at a high level of abstraction. We then use refinement, decomposition, and finally implementation-level annotations, to generate Ada code. We provide a brief introduction to Event-B, before illustrating the new approach using small examples taken from a larger case study

Extending Event-B with discrete timing properties

Event-B is a formal language for systems modelling, based on set theory and predicate logic. It has the advantage of mechanized proof, and it is possible to model a system in several levels of abstraction by using refinement. Discrete timing properties are important in many critical systems. However, modelling of timing properties is not directly supported in Event-B. In this work, we identify three main categories of discrete timing properties for trigger response patterns, deadline, delay and expiry. We introduce language constructs for each of these timing properties that augment the Event-B language. We describe how these constructs have been given a semantics in terms of the standard Event-B constructs. To ease the process of using timing properties in a refinement-based development, we introduce patterns for refining the timing constructs that allow timing properties on abstract models to be replaced by timing properties on refined models. The language constructs and refinement patterns are illustrated through some generic examples.We have developed a tool to support our approach. Our tool is a plug-in to the Rodin tool-set for Event-B and automates the translation of timing properties to Event-B as well as the generation of gluing invariants, required to verify the consistency of timing properties refinement. In the end, we demonstrate the practicality of our approach, by going through the modelling and verifying process of two real-time case studies. The main focus will be the usefulness of the timing refinement patterns in a step-wise modelling and verification process of a real-time system

Transforming EVENT B Models into Verified C# Implementations

The refinement-based approach to developing software is based on the correct-by-construction paradigm where software systems are constructed via the step-by-step refinement of an initial high-level specification into a final concrete specification. Proof obligations, generated during this process are discharged to ensure the consistency between refinement levels and hence the system’s overall correctness. Here, we are concerned with the refinement of specifications using the EVENT B modelling language and its associated toolset, the RODIN platform. In particular, we focus on the final steps of the process where the final concrete specification is transformed into an executable algorithm. The transformations involved are (a) the transformation from an EVENT B specification into a concrete recursive algorithm and (b) the transformation from the recursive algorithm into its equivalent iterative version. We prove both transformations correct and verify the correctness of the final code in a static program verification environment for C# programs, namely the Spec# programming syste