Model Based Systems Engineering

Fundamentals and Methods

Patrice Micouin

• Publisher: Wiley-ISTE
• Year: 2014
• ISBN:
  9781118579596
• Edition: 1
• Topic: Technologie et ingénierie
• Subtopic: Ingénierie de l'électricité et des télécommunications

This book is a contribution to the definition of a model based system engineering (MBSE) approach, designed to meet the objectives laid out by the INCOSE. After pointing out the complexity that jeopardizes a lot of system developments, the book examines fundamental aspects of systems under consideration. It goes on to address methodological issues and proposes a methodic approach of MBSE that provides, unlike current practices, systematic and integrated model-based engineering processes. An annex describes relevant features of the VHDL-AMS language supporting the methodological issues described in the book.

PART 1

Fundamentals

1

General Systems Theory

1.1. Introduction

What do a nerve cell, the mathematical field of complex numbers and the Rosetta stone have in common? Nothing much, apparently. However, all three are systems, each in its own way. To grasp the unity behind this diversity of appearances, we must resort to general systems theory (GST), a theory that does not concern a specific type of systems in particular, but instead what makes a system a system. In the following, we will refer to GST, developed by Mario A. Bunge, in particular in volume 4 of his Treatise on Basic Philosophy [BUN 79]. We consider that Bunge’s theory develops that of L. von Bertalanffy [BER 69], as well as renews it.

In this chapter, we define a system as a composite object characterized by (1) its composition, (2) its environment and (3) its structure. We will differentiate two types of systems: abstract or concrete depending on whether the objects composing the system are abstract or concrete. We will examine the relationships between the components and the environment according to whether the systems are abstract or concrete. We will also introduce the concepts of a subsystem and a level. More detailed analysis of the objects and properties will be done depending on whether the objects are material or abstract. We will introduce different classifications of properties: accidental and essential properties with the related concept of a type, structural and behavioral properties with the related concept of a dispositional property and, finally for systems, the resulting and emerging properties. We will also define the concepts of state, event, process, behavior and fact. The chapter will conclude with the three types of systems of interest for systems engineering: technological systems, systems of knowledge and systems of signs (or semiotic systems).

1.2. What is a system?

Following on from Bunge, a system Σ is an object composed of several parts (its components). These components have relationships between each other. We call endo-structure S_int of a system the network of these relationships between components, whereas the system components may have relationships with objects that do not form part of the system and what we call the environment E. The network of relationships between system components and the environment is called the exo-structure S_ext of this system. The structure S of a system is, therefore, the union of both its endo-structure and exo-structure: S = S_int ∪ S_ext.

In summary, a system Σ is an object denoted by a triplet (C, E and S) such that:

– card(C) > 1, which expresses the fact that Σ is composed of several parts (composite object);

– S = S_int ∪S_ext with S_int ≠ ∅, which expresses the fact that the endo-structure of Σ is not empty.

Figure 1.1. System composition, structure and environment

When E is empty, we say that the system Σ is a closed system. In the opposite case, we would say that this is an open system.

When its endo-structure S_int is empty, the object Σ is not a system; this is the case for fictitious stellar objects such as constellations. Ursa Major, unlike the galaxy M31 or the galaxy of Andromeda, is not a stellar system, whereas the stars that form it are themselves systems.

The definition of a system that we state deviates from the one proposed by von Bertalanffy and by many authors later on, beginning with the definition given in [SEB 13], namely “a system is a set of elements in interaction”. In fact, in the case of the definition by Bunge, a system is an object whereas in the second case, it is a set. This may appear to be a negligible difference, two slightly different ways of designing the same reality. However, we claim at the opposite that the definition by Bunge provides us with a particularly fruitful characterization of a system, whereas its definition as a set prevents this characterization. In fact, a set is a particular type of object, i.e. an abstraction, resulting from a movement of mind, which allows different individual elements to be taken as a whole, whatever they are, (Ursa Major, for example). If all systems (concrete or abstract) are considered as sets (i.e. are mathematical beings), they are fictions resulting from movements of mind (brain processes), then systems could not exist independent of human beings who think of them. This is exactly the point of view held by constructivists¹.

Bunge provides an opposing realist vision to these constructivist theories: the objects exist according to two very different modalities: only concrete objects really exist objectively, whereas abstract objects only exist as fictions (which we will discuss later on in Chapter 3). So, a system may be either a concrete object (i.e. a material object) or an abstract object (i.e. a fiction) with all components of a material system being material objects, whereas in an abstract system it is only composed of abstract parts.

Figure 1.2. Concrete and abstract systems composition

The following are examples of concrete (material) systems: the solar system, a macromolecule, the central nervous system of Homo sapiens, a family unit. Similarly, a project team, a book, a hospital, a factory and an airplane are also concrete systems, as well as a country’s airspace, an energy production and distribution system at a continental scale. We are able to talk about the latter as systems of systems [LUZ 10]. To conclude with Bunge on this point, we hold the view that “the world is a world of systems” and that any concrete object is a system, a part of a system or both.

The following are examples of abstract systems: the mathematical theory of complex numbers field, the analytical mechanics of J.L. Lagrange, and the system of gods and goddesses of Olympus.

If, by definition, a concrete system is composed of concrete objects, however, it may have abstract systems in its environment; in this case, the concrete system is said to be capable of designating objects of abstract systems using concrete objects. Just as an example, languages, such as English and French (which are concrete systems), allow us to designate the same abstract concept of “system” in GST (which is an abstract system, more specifically a theory) using the different concrete words: “system” in English, “systeme” in French, “CHcreMa” in Russian, and so on’.

Similarly, if an abstract system is inevitably composed of abstract objects it may, however, have concrete systems in its environment; in this case, the abstract system is said to be capable of representing objects of concrete systems using abstract objects. Therefore, a theory such as GST (which is an abstract system) allows us to represent any type of concrete or abstract system and to point out the essential characteristics.

Figure 1.3. Concrete and abstract systems environment

The type of relationships, among the components of a system (endo-structure), on the one hand, and those connecting components with the elements in the environment (exo-structure), on the other hand, depends on the nature of the systems considered.

For the endo-structure, (1) with concrete systems, the relationships are material binding relationships (links) or non-binding material relationships; whereas with abstract systems, the relationships are formal relationships. We are concerned with links between concrete components when a change of state in some induces a change in state of others; this is typical in a mechanical system whose degrees of freedom are reduced by the links between parts. However, the links in question are not limited to mechanical links; they may be multiphysical (electrical, magnetic, nuclear etc.), chemical, biological or psychosocial. In addition to these links, the endo-structure may include non-binding material links such as topological, metric and temporal relationships. For example, “to be before, after, above, below, aligned with, centered, previous to, simultaneous, subsequent” are non binding relationships. (2) For abstract systems, the relationships forming their endo-structure are formal relationships including logical operators (e.g. negation, conjunction and disjunction), relational operators (e.g. equality, comparisons, belonging and inclusion), as well as assessment functions (e.g. “being well formed”, “having the following meaning” and “being approximately true”).

For the exo-structure, we find the same type of relationships as for the endo-structure; to these we must add relationships including those between concrete and abstract objects such as representation and designation relationships that will be discussed in Chapters 3 and 4.

Table 1.1. Endo and exo-structure for concrete and abstract systems

1.3. Systems, subsystems and levels

The fact that a system is a composite object makes it possible for the components of a system to be considered separately. We can then ask the question: can the parts of a system be considered as systems for themselves?

We have an immediate answer to this question if we consider, for example, an atom of helium. This is definitely a system, composed of two electrons and a nucleus whose cohesion is assured by electromagnetic bonds (photons). Electrons are not systems since they belong to the set of elementary particles. The helium nucleus is also a system composed of two protons and two neutrons whose confinement is assured by strong nuclear bonds (gluons). However, neutrons and protons are not considered as systems.

A system can therefore be composed of objects that are themselves systems. We can say that any systems composing a system Σ are subsystems of Σ.

If σ

(c, e, s) is a subsystem of Σ

(C, E, S), we obtain c ⊂ C, E ⊂ e and s ⊂ S, which means that components of σ are components of Σ, the environment of Σ is included in that of σ and the structure of σ is included in that of Σ.

This possibility for a system to be composed of subsystems can obviously be repeated and this allows us to understand a system as being a hierarchy of subsystems with successive levels with the required decomposition depth.

For example, Dillinger [DIL 90] described a language as a system of signs (concrete system) that is composed of sentences, which are subsystems composed of clauses. These clauses are, in turn, subsystems composed of phrases. Phrases are subsystems composed of words, which are composed of morphemes, which, to finish, are systems of phonemes.

In other words, Dillinger provides us with a language description (true or not, this is another topic) as a system hierarchically organized into six levels (true or not, this is another topic):

1) sentences;

2) clauses;

3) phrases;

4) words;

5) morphemes;

6) phonemes.

1.4. Concrete and abstract objects

Starting from Aristotle’s statement, from his Metaphysics, being (ousia) is a compound of matter and form (hylomorphism)². It follows two complimentary ontological clauses: the world is exclusively made of concrete objects, and a concrete object is made of matter with material properties.

For example, according to the standard model of elementary particles, an electron is an elementary particle, characterized particularly by the following properties: a mass of 9.109 × 10^-31 kg, an electric charge of –1.602 × 10^-19 C, a radius less than 10^-22 m and a spin of 1/2. Moreover, a photon is a stable particle with a spin of 1, and its electric charge and mass are zero. Assumed by G. Stoney, its existence was then proved by J. Thomson.

For Bunge, the hallmark of material objects would be to have energy [BUN 10]. In other words, energy would be a universal property of matter, whereas this would be lacking in immaterial objects, which is quite understandable given the incongruity of a phrase such as “the internal energy of the number π”. As a corollary, the hallmark of concrete objects would be their aptitude for change, that is to say, they are capable of moving in a space of states. Briefly told, an object is concrete or material if and only if it possesses an energy or iff it is capable of being changed. Therefore, material objects have a real mode of existence, and according to both Bunge and Heraclitus “to be is to become”.

According to this ontological assumption, concrete systems have energy and are able to change. This means that the composition C (t), environment E (t) and structure S (t) a specific system may change during the lifecycle of the system. Denotation of a concrete system Å (t) ) by the triplet (C (t), E (t), S (t)) allows us to highlight its evolution over time.

On the contrary, an abstract object lacks energy and is immutable. It only exists as a fiction produced and reproduced by those who know it. The modes of existence of immaterial and material objects are, therefore, distinct. The transcendental number π, like a unicorn or a chimera, is an “eternal” object whose mode of being is that of fiction imagined by those who invented it or have knowledge of it, whereas the mode of being of the sun, galaxies and elements composing it down to the elementary particles is that of material reality, independently of any informed or non-informed individual.

Figure 1.4. Representation of fictions (Arezzo Chimera and pi number)

1.5. Properties

1.5.1. Material and formal properties

Just like the modes of existence of immaterial and material objects differ, their properties are also distinct. The properties of concrete objects are material or factual properties such as “having a position”, “having a speed”, “having an energy”, etc. Properties would be considered as absurd if we tried to associate them with a concept or a proposition.

Figure 1.5. Concrete and abstract objects

Just like material objects, abstractions, such as a concept or a proposition, have properties called abstract or formal properties. Properties of abstract objects include the meaning of a concept or the truth of a proposition. Meaning and truth are properties associated with abstract objects, and it would be equally absurd if we want to relate them to concrete objects such as a stone or an airplane (signs, despite the fact that they are concrete objects, have a particular status).

1.5.2 Accidental and essential properties, laws and types

In this section, we are going to describe briefly the main assumptions and results from the theory of properties [BUN 77a, BUN 77b] designed by Bunge. Our theory of property-based requirements (PBRs) is based on these results, which will be discussed in Chapters 6, 7, 9 and 10.

When we consider objects and properties, there are two possible entries: an entry by the properties and an entry by the objects.

Using the first entry, the following definition is proposed: for a property P, the set of individual objects owning this property makes up the class C(P) of P. The class C(P) defines the extension of property P. For example, property E: “having an energy” for class C(E) represents the collection of material objects.

Bunge defines a precedence relation “≤” between the properties P and Q of material ob...

Table of contents

• Cover
• Contents
• Title Page
• Copyright
• List of Figures and Tables
• Acknowledgements
• Foreword
• Introduction: Goals of Property-Model Methodology
• PART 1: Fundamentals
• PART 2: Methods
• Appendix
• Bibliography
• Index