=Paper=
{{Paper
|id=Vol-1901/paper42
|storemode=property
|title=Complex matrix model for data and knowledge representation for road-climatic zoning of the territories and the results of its approbation
|pdfUrl=https://ceur-ws.org/Vol-1901/paper42.pdf
|volume=Vol-1901
|authors=Anna Yankovskaya,Alexey Sukhorukov
}}
==Complex matrix model for data and knowledge representation for road-climatic zoning of the territories and the results of its approbation ==
https://ceur-ws.org/Vol-1901/paper42.pdf
Complex Matrix Model for Data and Knowledge Representation for
Road-Climatic Zoning of the Territories and the Results of Its Approbation
A. Yankovskaya1,2,3,4, A. Sukhorukov2
1
Tomsk State University of Architecture and Building, 634003, Tomsk, Russia
2
National Research Tomsk State University, 634050, Tomsk, Russia
3
National Research Tomsk Polytechnic University, 634050, Tomsk, Russia
4
Tomsk State University of Control Systems and Radioelectronics, 634050, Tomsk, Russia
Abstract
Complex matrix model of data and knowledge representation is proposed for solution of a road-climatic zoning of the territories problem using
an intelligent system. This model consists of: 1) an extended matrix model, which includes extended description and distinguishing matrices
(the extension is realized by the way of including of additional columns into the description matrix) for the territories under investigation,
2) description and distinguishing matrices of highly qualified experts’ knowledge and 3) a partial matrix model, consisting of an extended
description matrix of the territories under investigation (recognition). For the first time original approbation results of intelligent data and
knowledge analysis on the base of intelligent instrumental software IMSLOG are given. The system is designed and developed in intelligent
systems laboratory of the Tomsk State University of Architecture and Building to solve the problem of road-climatic zoning.
Keywords: complex matrix model; intelligent data analysis; approbation results; geocomplex, road-climatic zoning
1. Introduction
An urgent need in intelligent systems (IS) application for a number of problem areas is not in doubt. Among the basic IS
applications are those given in the monograph [1]: medicine, engineering, transport system and others. Among the fundamental
IS components we distinguish the data and knowledge base. In this paper we will concentrate our efforts on the base
construction.
When developing the design standards for the highways we should take into account the regional features of the geographic
territories. It is performed through the method of road-climatic zoning. The method serves as a basis for the development of
building regulations, directives and guidelines valid in Russia [2,3], China [4,5], USA [6], Germany [7], Great Britain,
Sweden [8] and in other countries, including such neighboring countries as Kazakhstan [9], Belorussia [10], Kyrgyzstan [11].
According to the building regulations [2,3] the Russian Federation territory is zone differentiated and divided into 5 road-
climatic zones, which are differing sufficiently in terms of the complexes of nature-climatic and geoengineering conditions. In
their turn, the zones are divided into 9 subzones due to the road industry standards [9] and into 13 subzones due to the set of
rules [3]. Depending on the position of the road section under design in one or another zone and subzone the road designers
make technical decisions, providing safe and convenient traffic according to the requirement stated in [2,3].
A number of researchers in their papers [12–15] point out that the existing special position of the zones and subzones
boundaries does not allow to provide the level of operational reliability of the highways due to the operability criterion since the
position of the zones and subzones are not substantiated sufficiently. This situation is especially inherent to Western Siberia and
Far East. That leads to an increase in financial and labor resources for maintaining and restoring the required technical condition
of highways. Thus the research of the new approaches to the road-climatic zoning design is rather actually. The specificity of
data and knowledge to solve the problem of the road-climatic zoning requires the new methods of the data and knowledge
representation. Taking into consideration is proposed to choose intelligent instrumental software IMSLOG (IIS IMSLOG)
[16,17] for IS construction of road-climatic zoning of territories (IS RCZT).
Hereafter we give a description of a complex matrix model for the data and knowledge representation for the IS RCZT. The
IS RCZT is based on test methods of pattern recognition and cognitive graphics tools.
2. Complex Matrix Model for Data and Knowledge Representation
For the first time we suggest to represent the complex model by 3 types of the following matrix models of data and
knowledge representation [18,19]:
1. An extended matrix model including an extended matrix of descriptions and a matrix of distinguishing. The extension is
performed due to additional columns introduction to the matrix of descriptions [19]. The matrix of descriptions sets the objects
description within the space of characteristic features. The additional columns correspond to compulsory features: zones,
subzones, road districts, supporting point of the investigated territories. The present paper deals with the research results on
Western Siberia territory. The columns of the extended matrix of descriptions correspond to characteristic features, represented
by the 3 groups of factors. Those factors constitute the geographical complex of the territory: zonal, intrazonal and regional
factors. The columns of the matrix of distinguishing correspond to the zones, subzones and road districts. We use integer
features in the model.
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2. A matrix of expert knowledge description without compulsory features and a matrix of distinguishing. The columns of the
matrix of distinguishing, as well as those of the matrix of distinguishing of the extended matrix model, correspond to the zones,
subzones and road districts. Here we also use integer features.
3. A partial matrix model, consisting only of the extended matrix of description of the investigated territories under
recognition.
Now we concentrate on the elements description of the matrices under consideration. The integer values of the characteristic
features including grouped ones and the compulsory features are the elements of the extended matrix of objects’ description
(Qe). The group characteristic features are split into the features of the integer values, which correspond to a certain partition
intervals of the feature under study. A column of the matrix Q e corresponds to each characteristic features. A row of the matrix
Qe corresponds to the stronghold for which the values of characteristic features are determined. Thus, the element of the matrix
Qe is the value of the integer characteristic features, including compulsory one. This feature correspond to a certain supporting
point [18]. Note that the compulsory features are not used in regulations revealing. They are implemented only for the mapping
of the zones, subzones and road districts.
Integer values of the classification features of three types are the elements of the matrix of distinguishing (R e). We restrict our
study to the diagnostic matrix of distinguishing. For the matrix under study each subsequent column splits the previous one into
the classes of equivalency. Due to the methodology given in [20,21], we will use the three classification features of diagnostic
type. The 1st feature corresponds to the zones, the 2nd one – to the subzones, the 3rd one – to the road districts.
We note that we need the 2nd matrix model due to the incomplete information on the zones, subzones and road districts. Such
information is contained in the 1st matrix model. The rows of the matrix of description and the matrix of distinguishing are
fulfilled by the highly qualified experts in the problem area. Matrix fulfillment with data is performed by the colleagues of the
Automobile roads building department of the Tomsk State University of Architecture and Building.
The learning sample is represented by the extended matrix model. In the learning sample some combinations of the
classification features could not be represented. Therefore, the dimensions of the matrix of description and the matrix of
distinguishing could exceeded sufficiently the dimensions of the matrix of the extended matrix model, fulfilled beforehand. This
is due to the absence of a number of combinations of the classification features values in the learning sample.
The extended matrix of description of the territories under recognition for the partial matrix model is fulfilled by the highly
qualified experts. They use the reference data and the data acquired during field and/or laboratory research. The research results
could be transmitted both to the system’s users and to the enterprises, interested in the road-climatic zoning research results.
The decision making about the supporting point correspondence to a certain zone, subzone and road district we perform using
the two aforementioned matrix representations (extended matrix and the one based on the expert knowledge) based on the rules
of the total decision making with use of IS RCZT. The architecture IS RCZT is presented in the publication [22].
3. Data and knowledge structuring. Bases of a database and knowledge construction
The basis of the information technology of road-climatic zoning of territories is IS RCZT. To create the IS we united our
efforts with our colleagues. Together with specialists in the cognitive science and experts in road-climatic zoning we have
structured the data and knowledge on road-climatic zoning. The structuring has been performed based on the complex matrix
model of data and knowledge representation, described in section 2.
A list of characteristic features with indicating their values for the matrices of description is given in Table 1. The
characteristic features are grouped ones beginning with characteristic features z 10. Symbolic characteristic features, intervals of
the integer characteristic features partitions as well as the real characteristic features are coded by numbers. The number 20
(limiter) is used only for the sake of size reduction of the data and knowledge matrix representation. In table 1, the value of an
integer feature is not greater than 8.
Table 1. A list of characteristic features excluding compulsory ones.
Characteristic feature Code Intervals of values
Vegetation type z1 1 – tundra vegetation; 2 – forest-tundra vegetation; 3 – forest vegetation (northern taiga, with
propagation of permafrost soils); 4 – forest vegetation (middle taiga); 5 – forest vegetation (southern
taiga); 6 – forest-steppe vegetation; 7 – steppe vegetation; 8 – desert and desert steppe vegetation
Terrain relief z2 1 – flat terrain with a relative elevation of the relief (RER) up to 25 m; 2 – hilly with RER from 25 m
up to 200 m; 3 – mountainous (low mountains terrain) with RER from 200 m up to 500 m, and with a
prevailing slope gradient (PSG) from 5° up to 10°; 4 – mountainous (mid-mountain terrain) with RER
from 500 m up to 1000 m, PSG from 10° up to 25°, and elevation above sea level of about 1000–2000
m; 5 – mountainous (highland terrain) with RER from 1000 m, PSG more than 25°, and elevation
above the sea level more than 2000 m
Calculated soil z3 1 – low soil moisture with CSM up to 0.4; 2 – normal soil moisture with CSM from 0.4, up to 0.6; 3 –
moisture (CSM), p.u. increased soil moisture with CSM from 0.6, up to 0.8; 4 – waterlogged soil with CSM from 0.8, up to 1
Evaporation from the z4 1 – extremely low, from 100 mm up to 150 mm (arctic deserts); 2 –very low, from150 mm up to 200
land surface, mm/year mm (Siberian tundra provinces); 3 – low, from 200 mm up to 400 mm; 4 – average, from 400 mm up to
600 mm (taiga, central and central black earth regions of Russia, Krasnodar region); 5 – increased, from
600 mm up to 700 mm (mixed forests); 6 – high evaporation, from 700 mm up to 800 mm; 7 – very
high evaporation, from 800 mm up to 900 mm (steppers); 8 – extremely high, from 900 mm up to1000
mm (semi-deserts and deserts)
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Continuation table 1.
Characteristic feature Code Intervals of values
Syelyaninov’s z5 1 – redundant moistening of the soil with SHC from 1,4 to 5; 2 – significant moistening of the soil in
hydrothermic particular years with SHC from 1 to 1,4; 3 – insufficient moistening of the soil with SHC from 0,5 to 1;
coefficient 4 – dry regions with SHC up to 0.5
A number of days with z6 1 – low from 141 to 198; 2 – medium from 199 to 246; 3 – high from 247 to 315
negative air
temperature
Snow cover height z7 1 – snowless regions with SCH up to 300; 2 – little snow cover regions with SCH from 300 to 500; 3 –
(SCH), mm medium snow cover regions with SCH from 500 to 700; 4 – high snow cover regions with SCH from
700 to 1000; 5 – exclusive high snow cover regions with SCH from 1000 to 2900
Soil frost depth (SFD), z8 1 – small frost depth with SFD from 50 to 180; 2- medium frost depth with SFD from 180 to 220; 3 –
cm high frost depth with SFD from 220 to 260; 4 – very high frost depth with SFD from 260 to 300;
excessive frost depth with SFD from 300 to 600
Soil type according to z9 1 – continuous distribution of the frozen soils for many years; 2 – continuous in general of the frozen
natural condition I zone soils for many years; 3 – predominately island distribution of the frozen soils for many years
Average air z10 1 – extremely low temperature with AAT from –15.5 to –10.0; 2 – very low temperature with AAT
temperature for many from –10.0 to –6.0; 3 – low temperature with AAT from –6.0 to –2.0; 4 – medium temperature with
years, ºC AAT from –2.0 to 2.0; 5 – high temperature with AAT from 2.0 to 6.0; 6 – very high temperature with
AAT from 6.0 to 10.0; 7 – extremely high temperature with AAT from 10.0 to 14.2
Average minimum air z11 1 – extremely low temperature less than –40.0; 2 – very low temperature from –39.9 to –32.0; 3 – low
temperature, ºC temperature from –31.9 to –24.0; 4 – medium temperature from –23.9 to –16.0; 5 – high temperature
from –15.9 to –8.0; 6 – very high temperature from –7.9 to 0.0; 7 – extremely high temperature above 0.0
Average annual z12 1 – extremely low temperature from 0 to 4; 2 – very low temperature from 4 to 7; 3 – low temperature
maximum air from 8 to 11; 4 – medium temperature from 12 to 15; 5 – high temperature from –16 to 19; 6 – very
temperature, ºC high temperature from 20 to 23; 7 – extremely high temperature above 24
Annual precipitation, z13 1 – low less than 250; 2 – medium from 251 to 500; 3 – high from 501 to 1000; 4 – very high above
mm 1000
Annual precipitation z14 1 – low less than 60; 2 – medium from 61 to 150; 3 – high from 151 to 405; 4 – very high above 405
for the cold season, mm
Annual precipitation z15 1 – low less than 190; 2 – medium from 191 to 340; 3 – high from 341 to 600; 4 – very high above 600
for the warm season,
mm
Soil humidity on the z16 1 – low from 0.29 to 0.33; 2 – medium from 0.34 to 0.38; 3 – high from 0.39 to 0.43
liquid limit, p.u.
Soil humidity on the z17 1 – low from 0.20 to 0.23; 2 – medium from 0.24 to 0.26; 3 – high from 0.27 to 0.30
plastic limit, p.u.
Plasticity index, % z18 1 – non-cohesive soil (sand, etc.) from 0 to 1; 2 – clay sand from 1 to 7; 3 – light clay loam from 7 to
12; 4 – heavy clay loam from 12 to 17; 5 – light clay from 17 to 27; 6 – heavy clay from 27 and above
Grain-size composition z19 1 – clay sand above 50; 2 – pulverescent clay sand less than 50
of the clay sands, sand
grain content, mass %
Grain-size composition z20 1 – low from 70.540 to 73.279; 2 – medium from 73.280 to 76.019; 3 – high from 76.020 to 78.76
of the clay sands, sand
grain content, mass %
Grain-size composition z21 1 – low from 7.120 to 9.150; 2 – medium from 8.160 to 11.199; 3 – high from 11.200 to 13.240
of the clay sands, clay
grain content, mass %
Grain-size composition z22 1 – sandy clay loam over 40; 2 – pulverescent clay loam less than 50
of the clay loams, sand
grain content, mass%
Grain-size composition z23 1 – low from 72.310 to 75.589; 2 – medium from 77.489 to 75.590; 3 – high from 77.490 to 77.540
of the clay loams,
pulverescent grains
content, mass %
Grain-size composition z24 1 – low from 18.400 to 18.455; 2 – medium from 18.456 to 20.510; 3 – high from 20.511 to 23.870
of the clay loams, clay
grains content, mass %
Grain-size composition z25 1 – sandy clay over 40; 2 – pulverescent clay, less than 50
of the clays, sand grain
content, mass %
z26 1 – low from 68.954 to 70.080; 2 – medium from 70.081 to 71.205; 3 – high from 71.343 to 72.329
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Continuation table 1.
Characteristic feature Code Intervals of values
Grain-size composition z27 1 – low from 23.871 to 24.895; 2 – medium from 25.896 to 27.920; 3 – high from 27.921 to 29.945
of the clays,
pulverescent grain
content, mass %
To the above mentioned characteristic features we add 4 compulsory features (zone, subzone, road district, supporting point).
The compulsory features are applied to 3 zones only, since Western Siberian territory has been investigated partly. We pointed
out 1 subzone and 1 road district in the 1st zone, 2 subzones and 7 road districts – in the 2nd zone and 2 subzones and 3 road
districts – in the 3rd zone.
Illustrating example of matrices Qe, Re and R' descriptions is given in Fig. 1. The matrices correspond to partial knowledge
description. We use only a part of the characteristic features space and its values.
𝑧1 𝑧2 𝑧3 𝑧4 𝑧5 𝑧6 𝑧7 𝑧8 𝑧9 𝑘1 𝑘2 𝑘3
1 5 1 3 3 3 3 4 4 2 1 1 1 1
1 4 1 4 3 3 3 4 4 2 1 1 1 2
1 4 1 4 3 3 3 4 4 2 1 1 1 3
1 4 1 3 3 3 3 5 4 2 1 2 2 4
2 4 1 3 3 2 3 5 4 2 1 2 2 5
1 4 1 3 3 2 3 5 4 2 1 2 2 6
1 4 1 3 3 3 3 5 4 2 1 2 2 7
1 4 1 4 3 3 3 5 4 2 1 2 2 8
2 4 1 3 3 3 3 5 4 2 1 2 2 9
e 2 4 1 3 3 3 3 5 4
e 2 1 2
'
2 10
Q ... ... ... ... ... ... ... ... ... R ... ... ... R ... ...
3 4 1 3 3 3 3 5 3 3 1 3 8 24
2 4 1 3 3 2 3 5 4 2 3 2 9 25
2 4 1 4 3 3 3 5 3 2 3 2 9 26
4 4 1 3 2 2 2 5 0 2 3 2 9 27
3 4 2 3 2 2 3 5 3 2 3 2 9 28
2 4 2 3 3 3 3 5 0 2 2 2 10 29
4 4 2 3 3 2 3 5 3 3 2 1 11 30
4 4 2 3 2 2 3 5 3 3 2 1 11 31
4 4 2 0 3 3 3 5 0 3 2 1 11 32
2 4 2 3 3 3 3 5 2 2 2 1 12 33
Fig. 1. Fragments of the extended matrices of description and distinguishing.
For the matrix model, filled in by the experts, the expert knowledge on the four zones, all the subzones and all the road
districts are included. The fragments of description and distinguishing the matrices are represented in Fig. 2.
There are examples of usage of some visualization tools including cognitive graphics tools. The free-distributed open-street
maps (OSM) [23] with information layer overlay for the presentation of common information are proposed. Information layer
presents road regions with borders and some information about its. This information is a number of zone and subzone which are
determined for road region. The proposed visualization tool is presented on Fig. 3.
In doing so note that for the mapping of decision-making results with usage of cognitive graphics tools we use 3-simplex for
the zones representation and 2-simplex for subzones representation in case when the number of subzones equals 3 [24].
The information layer is denoted by number 1. It is a transparent layer over the map. The thin black lines separate the
different road regions. The different color tones are used for labeling the different zones (red color tone is used for zone 2, blue
color tone is used for zone 3). Each color of the road region in every zone is unique color gradation from zone base color given
from color transformation in the hue-saturation-bright palette (HSB palette). The wide black lines are used to separate the
different zones. Hatching over road region shows subzone type. Only 3 hatching types are used and only 2 types from them
presented on Fig. 3. Description for all used colors and hatching is presented in the legend (see Fig. 3) and it is denoted by
number 2. There is a list of all used hatchings and presented subzones in the upper part of the legend. The list of all used zones
and correlated road regions is in the bottom part of the legend.
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The information window for a road region is shown after click on a road region presentation. This window contains full
information about a region. This information contains the road region name, 3-simplex and 2-simplex as information about
proximity to specific zone (left 3-simplex) and subzone (right 2-simplex). The OUI (road region) is displayed as the circle with a
big radius. Objects of learning sample are displayed as circles with smaller radiuses. The distance from the object OUI to an
edge is directly-proportional to proximity of the object to the pattern corresponding to the edge. Distances of an OUI to edges are
displayed as color lines. Color of an OUI (or objects from a learning sample) is mapped to the pattern which belongs to the
concrete object. Mathematical foundations of the visualization of these objects with use of n-simplex are given in [25,26].
𝑧1 𝑧2 𝑧3 𝑧4 𝑧5 𝑧6 𝑧7 𝑧8 𝑧9 𝑘1 𝑘2 𝑘3
2 4 2 4 3 3 2 5 4 2 1 1 1 1
2 4 2 4 3 3 2 5 4 2 1 1 1 2
2 4 2 4 3 3 2 5 4 2 1 1 1 3
2 4 2 4 3 3 2 5 4 2 1 2 2 4
2 4 2 4 3 3 2 5 4 2 1 2 2 5
2 4 2 4 3 3 2 5 4 2 1 2 2 6
2 4 2 4 3 3 2 5 4
2 1 2
2 7
2 4 2 4 3 3 2 5 4 2 1 2 2 8
1 4 1 0 3 3 3 4 5 2 1 2 2 9
1 4 1 0 3 3 3 4 5
e
2 1 2
'
2 10
Q ... ... ... ... ... ... ... ...
... R ... ...
... R ... ...
4 4 4 2 2 2 2 6 2 3 1 3 8 207
4 4 4 2 2 2 2 6 2 2 3 2 9 208
4 4 4 2 2 2 2 6 2 2 3 2 9 209
4 4 4 2 2 2 2 6 2 2 3 2 9 210
4 4 4 2 2 2 2 6 2 2 3 2 9 211
4 4 4 2 2 2 2 6 2 2 2 2 10 212
4 4 4 2 2 2 2 6 2 3 2 1 11 213
4 4 4 2 2 2 2 6 2 3 2 1 11 214
4 4 4 2 2 2 2 6 2 3 2 1 11 215
4 4 4 2 2 2 2 6 2 2 2 1 12 216
Fig. 2. Fragments of the matrices of description and distinguishing, filled in by highly qualified experts.
Fig. 3. Visualization tool for representation of the map with zoning results.
We revealed the different types of regularities on the basis of algorithms proposed by A. Yankovskaya and realized in IS
RCZT. The revealed regularities allowed to reduce the features space from 27 to 11. That, in turn, has led to reduction of
quantity of revealed feature values on 59 %.
We also verified the decisions-making using the generated supporting point descriptions proposed by A. Yankovskaya. The
research results showed the IS RCZT development will lead to reduce significantly the expenditure and the cost of field and
laboratory works on the territories under investigation. That, in its turn, will essentially reduce time expenses the specialists of
road branch for the identification of zone, subzone and road district of the territory under investigation.
The proposed approach on road-climatic zoning of territories will allow to provide the required level of operational reliability
of the highways.
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4. Conclusion
The analysis of domestic and foreign standards of designing and building of highways is given. The advisability of creation
intelligent systems road-climatic zoning of territories is substantiated.
For the first time we proposed the complex matrix model of data and knowledge representation for road-climatic zoning. It
has allowed to carry out structurization of the data and knowledge on the road-climatic zoning. Complex matrix model is
represented by the 3 matrix models: the extended matrix model that includes the extended matrix of description and the matrix of
distinguishing; the matrix of knowledge description and the matrix of distinguishing filled with highly qualified experts; the
partial matrix model consisting of the extended matrix of description of the territories under study.
It is created a prototype of the intelligent system of road-climatic zoning. On the basis of extended matrix representation it is
created data and knowledge base using the research results on natural and climatic conditions of Western Siberian regions. The
base of date and knowledge was created highly qualified experts.
For the 1st and the 2nd matrix representations of data and knowledge are revealed and is eliminated at a finding of intersections
of objects descriptions from different patterns.
Results of a research prototype approbation of road-climatic zoning of the territories intelligent system have shown as
follows: reduction on 59 % of necessary number of characteristic features for decision-making on reference of territory part
under study to this or that zone, a subzone and road district. Application IS RCZT will decrease significantly the expenditure and
cost on the field and laboratory research of the territories under study. That will also save the reduce time expenses of the road
branch specialists.
The proposed approach on road-climatic zoning of the territories will allow to provide demanded level of operational
reliability of again under construction and reconstructed highways and first of all in regions with the poorly developed network
of highways.
Acknowledgements
The research was funded by RFBR grant (project No. 14-07-00673a and No. 16-07-0859a). The authors are grateful to V.
Efimenko, Doctor of Science; S. Efimenko, Doctor of Science; M. Badina, Candidate of Science for the information on road-
climatic zoning of West Siberian regions; to V. Churilin, senior lecturer for the data and knowledge base fulfilling; to R.
Ametov, Deputy director of the Information Technologies Center of the Tomsk State University of Architecture and Building
and A. Yamshanov, Junior research fellow, assistant of the Tomsk State University of Control Systems and Radioelectronics for
the IIS IMSLOG development and for revealing the regularities within the developed data and knowledge base on road climatic
zoning; to S. Kitler, the executor of the project No 16-07-00859a for experiments conducting.
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