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Morphological analysis and synthesis. Algorithm of morphological synthesis.

Lecture



So, let us assume that there is a universal knowledge representation tool. Consider the question - how to automate the design. One of the approaches known for a long time is morphological analysis and synthesis.

The morphological machine was known in antiquity and was a set of concentric circles of increasing diameter, mounted on one axis, and painted with words around the circle. By rotating the circles, it was possible to invent anything by combinations of words.

A systematic description of this method was carried out by F. Zwicky in the 30s of the XX century. The method consists of a tool - a morphological machine, criteria for the selection of options, an operation algorithm.



Morphological analysis and synthesis

Groups of signs
one Type of movement rotational, translational, fixed, constant, oscillatory, uniform, ...
2 Nature of movement continuous, impulsive, ...
3 The nature of the energy supply point, linear, surface, field, ...
four Type of energy used thermal, electrical, chemical, mechanical, ...
five Physico-chemical effect diffusion, erosion, water hammer, electrolysis, ...
6 View state of aggregation solid, liquid, gaseous, plasma, melt, ...
7 Spatial relationship above, below, above, inside, ...
eight Connection electrostatic coupling, hinge, wire, ...
9 Geometric shape paraboloid, square, ball, spiral, ...
ten Material transparent, conductive, non-thermal, ...
... and so on ...

The idea of ​​the method is as follows. For signs, specific values ​​are chosen and, thus, a product (project) is obtained. Further, it is evaluated by criteria. Generate new. And again evaluated. You can generate a huge number of products. Repeat this procedure until an optimal solution is found.

Consider an example.

Heating element (E 2 )
Heat release and heating of water in the tank until boiling 		Refractory (E 5 )
Heating element support 		Capacity (E 31 )
Increasing the amount of heat transferred from the heating element of the fluid container 		Capacity (E 32 )
Reducing heat loss to the environment
spiral heat-insulating refractory material curved mirror reflecting the heat flux to the bottom of the tank materials with low thermal conductivity and bulk density for thermal insulation of tiles and its external elements
high resistive metal plate lightweight refractory grid of insulating material Insulated heating element from which heat is transferred to the vessel walls through a material with high thermal conductivity a mirror in the form of a light cylindrical vertical casing around the tank and a tile for reflecting thermal radiation
inert gas coil spiral in rigid tubes of insulating material heat pipes between the heating element and the bottom of the tank the same with a lid above the container

From the above morphological table, you can generate 3 * 3 * 3 * 3 = 81 variant.

Clearly, the options are represented by a morphological tree:

Morphological analysis and synthesis. Algorithm of morphological synthesis.
fig.7.1

In this AND-OR-tree, the black circles denote the AND nodes, the white ones - OR.

After creating a morphological table, in order to find the optimal solution, it is required to generate a list of requirements consisting of mandatory requirements (restrictions) and additional requirements (criteria).

The next stage is the folding of indicators. Only "AND" requirements are subject to collapse. You can roll in various ways:

Morphological analysis and synthesis. Algorithm of morphological synthesis. The amount (for example, the mass of the product - the sum of all its elements).
Morphological analysis and synthesis. Algorithm of morphological synthesis. Minimax (for example, performance is calculated at a minimum from the performance maxima of parts of the product).
Morphological analysis and synthesis. Algorithm of morphological synthesis. Weighted average (the time of heating water in the kettle is 0.3 * the time of heating the tank + 0.7 * the time of heating the water).
Morphological analysis and synthesis. Algorithm of morphological synthesis. Classification - returns 0 or 1, depending on the requirement. For example, the shape must be elliptical (either yes or no).



Algorithm of morphological synthesis

1) Narrowing the scope of the search due to dissatisfaction requirements
1) Selects the requirements for which the convolution type is the same in all vertices
2) Check the vertices selected in the first step for compliance. If requirements are not met, the vertex is marked as deleted.
3) Enumerating all the vertices from the leaves to the root and checking the two rules: if we have the vertex "I", and one of the receivers is marked as deleted, then it is marked as remote; if the vertex is "OR" and all receivers are remote, then the vertex is marked as remote
2) Enumerate options and compare indicators
1) Calculate one of the subtrees
2) Is among the generated subtrees such which will have the best set of criteria

For the use of morphological synthesis, much preparatory work must be carried out. In addition, busting a tree may not lead to a result or give an obvious solution. The advantage of the method is its high automatization.

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