APPLICATION OF FUZZY MATHEMATICS METHODS TO PROCESSING GEOMETRIC PARAMETERS OF DEGRADATION OF BUILDING STRUCTURES

The aim of research is formalization of the expert experience, which is used in processing geometric parameters of building structure degradation, using fuzzy mathematics. Materials that are used to specify fuzzy models are contained in expert assessments and scientific and technical reports on the technical condition of buildings. The information contained in the reports and assessments


Introduction
Calculation of structures for progressive destruction is one of the requirements for design and provides for local destruction or destruction of individual elements of load-bearing structures within a single floor or parts of floors that do not lead to the destruction of the structure as a whole.In this case, the development of cracks and plastic deformations in individual structural elements and reinforcement is allowed.The choice of the most likely scenarios of emergency destruction is carried out jointly by the designer and the customer, taking into account the factors reducing the bearing capacity of structures [1].
Planning and implementation of construction, repair work and reconstruction of buildings and structures in dense urban development, has a number of features that characterize poorly structured tasks.This class of tasks acquires a mass character and requires the development and implementation of new methods and tools for their solution that will increase the level of automation of the decision-making process in fuzzy conditions in the early stages of ensuring the reliability and safety of construction projects [2,3].Given that the described task is not sufficiently formalized, it is especially relevant in this direction to use expert systems with fuzzy logic.
The main aim of the work is formalization of the expert experience, which is used in the processing of geometric parameters of building structure degradation, using fuzzy mathematics, which will significantly increase the degree of automation of evaluation systems.
To achieve this aim, the following tasks are formulated: -to formalize the geometric parameters of structural degradation, which are characterized by fuzzy information about the position, shape and size of the area of the figure, covering the area of destruction; -to expand the existing knowledge base due to the geometric parameters of degradation, on the basis of which an indistinct conclusion is drawn about the technical state of structures in the systems of fuzzy product rules.

Materials and methods of research
Earlier, the approach based on models and methods of fuzzy mathematics was described in [2][3][4], and examples of formalizing some geometric parameters of cracks and parameters of the influence of the medium on the kinetics of their development are described [4,5].In this paper, the main attention is paid to the processing of information on defects and destruction of load-bearing structures of the building, which are characterized by parameters of the girth area (Fig. 1).Below are examples of the description of the destruction of structures that were discovered during the next visual inspection of the building [6].

Computer Sciences
Facade in axes 1-6 (links to pictures and photos): -destruction of the plaster layer, weathering of the mortar from the seams of the wall masonry in the places of the spillway funnels due to the sedimentation by atmospheric precipitation in the areas of 1 m 2 and 5 m 2 (photos).

Facade in axes AE (links to figures and photos):
-destruction of the plaster layer, weathering and washing out of the mortar from the seams of the brickwork of the wall under the window openings of the second floor on a plot of 1 m 2 (photo).
1st floor (links to layouts and photos): -destruction of the concrete steps of the march on the sections 1100×150 mm, 1700×150 mm, 1800×90 mm (diagram and photo); -detachment of the facing layer of concrete in the walls of the staircase at the site of 2500×2600 mm (diagram and photo).
3rd floor (links to figures and photos): -traces of water saturation, bloom, destruction of the facing layer of concrete on sections of walls with an area of 0.6 m 2 (photo).
4th floor (links to figures and photos): -traces of water saturation, bloom, on sections of walls with an area of 7.0 m 2 (photo).Basement (links to pictures and photos): -traces of water saturation, bloom, fungus, destruction of the facing and plaster layer of concrete on sections of walls with a total area of 30.0 m 2 (photo).
The following is an extract from a typical assessment of the technical condition and operational fitness of the load-bearing structures of the building, which were used to derive fuzzy estimation rules [6].
Extract.When examining the interior, there were signs of destruction of the plaster layer of concrete in the sections of the basement overlap; destruction of concrete steps of the march of the 1st floor; destruction of the plaster layer in the room of the 4th floor in the axes E-F/1-2; traces of water saturation; bloom; fungus; destruction of the facing and plaster layer of concrete on the sections of the walls of the 1st, 3rd and 4th floors with a total area of 30.0 m 2 .According to the results of the assessments, it is established that the structure of the building is in a satisfactory condition, with the exception of the monolithic reinforced concrete floor of the basement.
The fuzzy inference system includes [4]: -set of fuzzy linguistic variables, with the help of which experts describe the type of defects and the state of the structures; -rules on fuzzy variables; -inputs and outputs of the system.

Computer Sciences
Incoming parameters are specified in the form of a vector which coordinates can be, for example, the geometric parameters of defects and fractures.In this paper, it is proposed to extend the vector of initial data due to the geometric parameters of degradation, which are characterized by fuzzy position, shape and size of the area of the figure encompassing the area of destruction.Each incoming parameter corresponds to a linguistic variable, which, in turn, consists of a certain number of terms.Each term is a fuzzy set (Table 1).y i7 -defect position in the object on the facade (f), in the seams between the slabs (sbp); along the armature (aa); in the shelves of plates (sp); on overlapping areas (oa); on sections of walls (w); near supports (in); on sections of the ceiling (directions); on the steps of the flight (sf); above window cuts (wc); under the window slots (ws).
In addition to the descriptions of parameters of structural degradation adopted in the current standards, the specifics of the provision and processing of textual information and software [4,5], which is used to form a system of fuzzy inference, were taken into account.When choosing the terms for the linguistic evaluation of the geometric parameters of degradation, which are characterized by fuzzy information about the figure encompassing the area of destruction, analysis of photos of destruction a (Fig. 1) and method of associations [7][8][9] was used.
The output of a rule is a linguistic variable, which in the given subject area represents the category of a technical state and is characterized by a set of terms normal (N); satisfactory (S); not suitable for normal operation (NS); and emergency (E).
The system of fuzzy rules for evaluating the effect of each defect on the state of constructions consists of formalized expressions that have the form [2,5]: Rule 1: if <defect type -high -area size -minor -triangular shape of the area, and positionon overlapping areas> than <state normal>; Rule 2: if <type of defect -traces of water saturation -the size of the area -significant -the shape of the area is ellipsoid, and the position -on the overlapping areas> than <the state is normal>; Rule 3: if <defect type -high -area size -minor -triangular shape of the area, and positionin overlapping areas> than <state normal>; Rule 4: if <type of defect -destruction of the plaster layer of concrete -the size of the areasignificant -the shape of the area is incorrect, and the position is on the wall sections> than <state is satisfactory>.
The rules are formed on the basis of an expert assessment of the technical condition of the bearing structures of the building, which is carried out in accordance with the qualification criteria of the current regulatory documents [6].
The method of fuzzy inference and the formation of a system of fuzzy inference based on the Sugeno model, as well as an example of the use of fuzzy rules for estimating the degree of suitability for the exploitation of spanning bridge spanning structures, are described in detail in [4].The article [5] formalizes the factors influencing the environment on the rate of destruction of reinforced concrete structures and shows the technology of control of the rules base, by means of which a fuzzy knowledge base is constructed to assess their technical condition.

Fig. 1 .
Fig. 1.Photos -fragments of the basement condition: a, b, c -destruction of the protective layer of concrete overlapping of different sizes and area formations on the sections of the ceiling and the abutment of the ceiling to the wall; d -traces of water saturation, bloom and fungus on sections of the wall with an area of 4 m 2

Table 1
Example of formalization of geometric parameters of structural degradation