Decomposition

When decomposing, they are guided by the following rules.

Each partition forms its own level.

The source system is at level zero. After its dismemberment, subsystems of the first level are obtained. The dismemberment of these subsystems or some of them leads to the appearance of subsystems of the second level, etc.

A simplified graphical representation of a decomposed system is called its hierarchical structure .

The hierarchical structure can be depicted as a branching flowchart , similar to that shown in Fig. one.

Here, the initial system C ₁ is located at the zero level, and its subsystems at the next levels (the number of levels and the number of subsystems shown in the figure are chosen arbitrarily). In order to obtain a more complete picture of the system and its connections, the structure includes the super- system and its component parts (zero-level systems, for example, the second C ₂ system).

Graph theory can be used to analyze hierarchical structure. This allows you to move from a graphical model to a mathematical one, in which the description is carried out according to equations similar to Kirchhoff's laws in electrical engineering or equations of hydraulics.

The hierarchical structure is often depicted in the form of a tree, that is, a graph without closed routes, with the arrangement of vertices at certain levels, for example, as shown in Fig. 2. The top of the top level (in the figure - 0) is called the root.

The graph shown in Fig. 2, corresponds to the I-tree : vertices that are located at the same levels are mandatory elements of the above systems.

So, for vertex 0.1, the required elements are 1.1, 1.2, and for vertex 2.2, 3.1, 3.2, and 3.3. For example, a car consists of an engine, and a body, and a chassis.

Along with the I-tree, an OR-tree is used , in which the vertices of the possible elements of structures and their variants are located at the same levels. For example, a car may have an OR engine, OR gas turbine, OR electric.

An AND-OR tree is often used, which connects the levels with the obligatory elements of the structure with the levels of variants of all or part of these elements (Fig. 3). The combination of I and OR levels can be arbitrary and they do not have to alternate.

The system is divided only by one constant for all levels, the attribute

As a sign of decomposition, there may be:

• Functionality of the parts
• constructive device (type of materials, surface shapes, etc.),
• structural features (type of circuit, methods, etc.),
• types of stages and processes (life cycle, physical condition, etc.),
• subject characteristics (economic, informational, technological, etc.),
• other.

So, in the above example, the allocation of a motor, chassis and body in a car was carried out in accordance with a functional feature. When constructing AND-OR trees, a combination of several attributes is possible: one — constant for the AND structure, and one or different at each level — for the OR structure.

Allocated subsystems should fully characterize the system.

But at the same time, the isolated subsystems should mutually exclude each other (especially this concerns OR trees).

For example, if, when listing the parts of a car, we omit, say, a motor, then the functional interaction of the remaining subsystems will not ensure the normal functioning of the entire system (car) as a whole.

In another example, listing the possible types of engines used in a car, it is necessary to cover the entire known area (decomposition - according to the principle of operation). If this is difficult to do, it is allowed to combine the unmentioned (or unknown) elements into one group (subsystem) and name it “others” or “other”, or divide engines, for example, into “thermal” and “non-thermal”.

The use of mutually overlapping subsystems, for example, “electric motors” and “alternating current motors”, can lead to ambiguity, since it is not clear where the asynchronous motor should be related in this case.

For clarity, it is recommended to allocate at each level no more than 7 subsystems. It is unacceptable that one of the subsystems is the system itself.

Decomposition Depth

The degree of detail of the description and the number of levels are determined by the requirements of visibility and ease of perception of the resulting hierarchical structure, its compliance with the levels of knowledge of the specialist working with it.

Usually, as the lower (elementary) level of subsystems, take one on which subsystems are located, the understanding of which device or their description is available to the executor (leader of a group of people or an individual). Thus, the hierarchical structure is always subjectively oriented: for a more qualified specialist, it will be less detailed.

The number of hierarchy levels affects the visibility of the structure: many levels - the task is difficult to see, few levels - the number of subsystems located at the same level increases and it is difficult to establish links between them. Usually, depending on the complexity of the system and the required depth of study, 3 ... 6 levels are distinguished.
For example, when developing a mechanical drive, you can take wheels, shafts, bearings, the engine as a whole as an elementary level. Although the bearings and the motor are complex elements and laborious in design, they appear as elementary parts as ready-made purchased products for the developer. If the engine would have to be developed, then, as a complex system, it would be advisable to decompose.

When constructing a hierarchical structure, its heuristic nature is manifested, first of all, in the choice of the number of levels and the list of their subsystems. The strongest subjectivity in OR-trees, when the form of the system is not yet known and their various representations are possible. For these reasons, the decomposition method is classified as heuristic .

In the design process , decomposition is inextricably linked with the subsequent composition , that is, the assembly and linking of the individual parts (subsystems) into a single system with its verification of realizability as a whole, compatibility (especially subsystems belonging to different branches), and parameter consistency (upstream design). In the matching process, a need may arise for a new, corrective decomposition.

In the general theory of systems it is proved that most systems can be decomposed into basic representations of subsystems. These include: serial (cascading) connection of elements, parallel connection of elements, connection using feedback.

The problem of decomposition is that in complex systems there is no unambiguous correspondence between the law of functioning of subsystems and the algorithm that implements it. Therefore, the formation of several options (or one option, if the system is displayed as a hierarchical structure) decomposition of the system.

• Composition
• Sadt
• IDEF
• THE DRAGON

• Khoroshev A.N. Introduction to the management of the design of mechanical systems: Textbook. - Belgorod, 1999 .-- 372 p. - ISBN 5-217-00016-3 . 2011 electronic version
• Methodical manual for schoolchildren of grades 9-11 "Application of the decomposition method for solving inequalities." - Moscow, 2019. - ^[1]
• Tsurkov V.I. Decomposition in large-scale problems. Ed. G.S. Pospelova . 1981. 352 p.