Qualitative Modeling of Trees Cultivated with Processed Wastewater
Cultivation of forest trees with processed wastewater is an effective method to reduce the release of harmful substances. For this purpose, the detailed experiments shall be carried out to investigate the ability of trees to absorb chemical elements under increased concentrations in wastewater. The...
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nasplib_isofts_kiev_ua-123456789-1336352025-02-09T14:14:09Z Qualitative Modeling of Trees Cultivated with Processed Wastewater Vissikirsky, V. Cultivation of forest trees with processed wastewater is an effective method to reduce the release of harmful substances. For this purpose, the detailed experiments shall be carried out to investigate the ability of trees to absorb chemical elements under increased concentrations in wastewater. The paper considers the development of qualitative modeling tools to support the investigation process. A qualitative inference system shall provide the investigator with qualitative tools showing the complex interactions in a transparent way. Культивация лесных деревьев обработанными сточными водами является эффективным методом уменьшения выбросов вредных веществ. Для этого проводятся детальные эксперименты по изучению способности деревьев поглощать химические элементы при повышенных концентрациях в сточных водах. В работе рассматривается разработка качественных инструментов моделирования для поддержки этого процесса изучения. Система качественного вывода обеспечивает исследователя качественными инструментами, показывая сложные взаимодействия прозрачно. Культивація лісових дерев обробленими стічними водами є ефективним методом зменшення викидів шкідливих речовин. Для цього проводяться детальні експерименти з вивчення здатності дерев поглинати хімічні елементи при підвищених концентраціях у стічних водах. В роботі розглядається розробка якісних інструментів моделювання для підтримки цього процесу вивчення. Система якісного виведення забезпечує дослідника якісними інструментами, показуючи складні взаємодії прозоро. 2017 Article Qualitative Modeling of Trees Cultivated with Processed Wastewater / V. Vissikirsky // Індуктивне моделювання складних систем: Зб. наук. пр. — К.: МННЦ ІТС НАН та МОН України, 2017. — Вип. 9. — С. 5-11. — Бібліогр.: 7 назв. — англ. XXXX-0044 https://nasplib.isofts.kiev.ua/handle/123456789/133635 004.048 en Індуктивне моделювання складних систем application/pdf Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
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Cultivation of forest trees with processed wastewater is an effective method to reduce the release of harmful substances. For this purpose, the detailed experiments shall be carried out to investigate the ability of trees to absorb chemical elements under increased concentrations in wastewater. The paper considers the development of qualitative modeling tools to support the investigation process. A qualitative inference system shall provide the investigator with qualitative tools showing the complex interactions in a transparent way. |
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Vissikirsky, V. |
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Vissikirsky, V. Qualitative Modeling of Trees Cultivated with Processed Wastewater Індуктивне моделювання складних систем |
| author_facet |
Vissikirsky, V. |
| author_sort |
Vissikirsky, V. |
| title |
Qualitative Modeling of Trees Cultivated with Processed Wastewater |
| title_short |
Qualitative Modeling of Trees Cultivated with Processed Wastewater |
| title_full |
Qualitative Modeling of Trees Cultivated with Processed Wastewater |
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Qualitative Modeling of Trees Cultivated with Processed Wastewater |
| title_full_unstemmed |
Qualitative Modeling of Trees Cultivated with Processed Wastewater |
| title_sort |
qualitative modeling of trees cultivated with processed wastewater |
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Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
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2017 |
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| citation_txt |
Qualitative Modeling of Trees Cultivated with Processed Wastewater / V. Vissikirsky // Індуктивне моделювання складних систем: Зб. наук. пр. — К.: МННЦ ІТС НАН та МОН України, 2017. — Вип. 9. — С. 5-11. — Бібліогр.: 7 назв. — англ. |
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Індуктивне моделювання складних систем |
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AT vissikirskyv qualitativemodelingoftreescultivatedwithprocessedwastewater |
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2025-11-26T16:36:17Z |
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2025-11-26T16:36:17Z |
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1849871544883347456 |
| fulltext |
V. Vissikirsky
5
Індуктивне моделювання складних систем, випуск 9, 2017
УДК 004.048
QUALITATIVE MODELING OF TREES CULTIVATED
WITH PROCESSED WASTEWATER
V. Vissikirsky
International Research and Training Centre for Information Technologies and
Systems of the NAS and MES of Ukraine, Akademik Glushkov Prospect 40,
03680 Kyiv, Ukraine
vlanvis@gmail.com
Культивація лісових дерев обробленими стічними водами є
ефективним методом зменшення викидів шкідливих речовин. Для цього
проводяться детальні експерименти з вивчення здатності дерев поглинати
хімічні елементи при підвищених концентраціях у стічних водах. В роботі
розглядається розробка якісних інструментів моделювання для підтримки
цього процесу вивчення. Система якісного виведення забезпечує дослідника
якісними інструментами, показуючи складні взаємодії прозоро.
Ключові слова: лісові дерева, екологічні мережі, якісне моделювання.
Cultivation of forest trees with processed wastewater is an effective method
to reduce the release of harmful substances. For this purpose, the detailed
experiments shall be carried out to investigate the ability of trees to absorb
chemical elements under increased concentrations in wastewater. The paper
considers the development of qualitative modeling tools to support the
investigation process. A qualitative inference system shall provide the investigator
with qualitative tools showing the complex interactions in a transparent way.
Key words: forest trees, ecological networks, qualitative modeling.
Культивация лесных деревьев обработанными сточными водами
является эффективным методом уменьшения выбросов вредных веществ.
Для этого проводятся детальные эксперименты по изучению способности
деревьев поглощать химические элементы при повышенных концентрациях
в сточных водах. В работе рассматривается разработка качественных
инструментов моделирования для поддержки этого процесса изучения.
Система качественного вывода обеспечивает исследователя качественными
инструментами, показывая сложные взаимодействия прозрачно.
Ключевые слова: лесные деревья, экологические сети, качественное
моделирования.
Introduction
Wide utilization of wastewater and sludge for agricultural purposes requires
a thorough investigation of the behavior of various trees in biological, chemical,
https://mail.ukr.net/classic#sendmsg,to=0WHM9_FLJNC_9u1L9AiT9hN
Qualitative modeling of trees cultivated with processed wastewater
6
Індуктивне моделювання складних систем, випуск 9, 2017
and physical aspects under different wastewater supply conditions. The problem
involves many factors and parameters, such as the impacts of treatments on soil
and flora, survival and mortality rates of trees, their growth, silvicultural issues
(roots and crown development, competition), wood properties, assimilation
behavior for different chemical elements, etc. [1, 2, 3].
The investigation problem of cultivating the trees under wastewater supply
has the following features:
- experiments shall be conducted under a long-term program with the
extension of number of investigated trees in different areas;
- behavior and properties of the trees grown under wastewater supply
conditions are the result of various cause-effect dynamical interactions in
ecological networks, for which mathematical models of underlying processes are
unknown [4];
- criteria of a “good” solution, which would clearly identify all aspects of
the problem, are ill-defined, often contradictory, and cannot be formally stated;
- search within some model for a “good” solution is being carried out in
multidimensional solution space under uncertainty conditions.
In this paper, a solution is proposed to the development of computer-based
tools intended for the empirical modeling of trees behavior and qualitative
reasoning [5] with imprecise information about this behavior.
Model analysis
As an example, let the concentrations of chemical elements in the leaves of
different forest trees were measured during their cultivation with processed waste
and irrigation water. Also, four water supply cases were applied for three tree
species (combinations of processed wastewater, irrigation water, and sludge).
Measured concentrations were averaged for every group of trees and their
parts (leaves, roots), and represented in the form of plots as functions f
i i
W
i
M
:C C
for heavy metal ei {Cu
++
, Mn
++
, Zn
++
,...}, C
W
and C
M
- concentrations in water
and in parts of trees respectively. Below the following notations will be used: W -
set of water supply cases; S - set of trees; M - set of measured parts of trees; E - set
of heavy metals (in general, chemical elements); C - vector (in general, ordered
set) of real values of measured concentrations.
As an example, for a given set of experiments we have:
- W={w1,w2,w3}, where w1 is processed wastewater; w2 - irrigation water; w3
- irrigation water with added heavy metals;
- S={s1,s2,s3} - set of trees;
- M={m1,m2}, m1 - leaves; m2 - roots;
- E={e1,e2,e3}, e1 - Cu; e2 - Mn; e3 - Zn.
The relationships between interacting objects can be represented as the
following chain:
V. Vissikirsky
7
Індуктивне моделювання складних систем, випуск 9, 2017
)()( ESE
SW
CC . (1)
The task is to determine the reaction of trees by estimating C
S
and by
matching the pair (C
W
, C
S
). The estimation of C
S
consists in the determination of
whether the values of concentrations hold within admissible limits, how high/low
is the concentration and its rate of change in whole within some range of values.
When matching (C
W
, C
S
), the main focus is made on how significantly they differ
from each other by values and rates of change.
The ecological chain of cause-effect interactions can be represented as
follows:
).()( EMSEW
MW
CC (2)
This chain allows the investigator to provide more detailed analysis of trees
behavior due to more detailed structure as to compare with relationships (1). Thus,
analysis of the concentrations in roots and leaves and their matching gives
additional information about peculiarities of biological processes inherent in
different trees. Because the objective within the chain of relationships (2) is to
estimate and analyze the functional relationship between C
W
and C
M
, relationships
(2) can be represented in the following form:
)()(
,,
EE
MMSWW
CC , (3)
where sets W, S, and M are the sets of cases for which the function is
estimated.
During long-term investigations of complex ecological interaction
networks, the model gradually extends and becomes more detailed, and one of the
reasons of such extension is an attempt to explain unclear points in a trees‟
behavior. Unpredictable behavior arises due to lack of knowledge within some
model, or if the model itself is not sufficiently adequate to take into account some
important factors influencing on the behavior.
At the same time, as the chain extends, its analysis becomes more
complicated. Let, for example, the measurements of concentrations of heavy
metals in soil G under the trees be included in the model:
).()()( EMSEGEW
MGW
CCC (4)
Now, the concentrations E in water W may be considered as factors that
make an influence on S through the soil characteristics and thus, ensure mode deep
and adequate view on the processes developed around investigated objects S.
Qualitative modeling of trees cultivated with processed wastewater
8
Індуктивне моделювання складних систем, випуск 9, 2017
Ecological chain as a chain of binary mappings
The relationships (1)-(4) of ecological chains can be considered as models
that reflect an understanding of the problem at some stage of investigation and are
a priory knowledge before a series of experiments starts. Further, the experiments
are directed toward the estimation of unknown functional relationships within a
given structure of the model, and the interpretation of obtained results.
The ecological chain (2) may be represented as a chain of binary mappings
between each pair of its adjacent sets (Figure 1). One way from an object of the
initial set W to an object of the end set E represents a minimal “cut” of functional
relationship with single objects from W, E, S, M, and may be represented by the
plot (C
W
, C
M
). In ultimate case, all possible ways after their empirical estimation
cover a solution space within a given structure of the model. In principle, it would
be enough to make some “good” clusterization of such a space to estimate a
distribution of the ways on C
M
for the function (3). In practice, however, the
investigator iteratively makes cuts with different capacities by fixating subsets of
the objects of interest, i.e., by selecting subsets of ways in the chain of binary
mappings.
Let us consider the examples of such selection taken from the conclusions
derived on the basis of experiments for the chain (2).
Example 1: Under wastewater (w1), the concentrations of all metals (E) in
leaves (m1) and roots (m2) slightly increase (for all trees).
Without an assessment of “slightly increase”, the relevant variant of the
chain (2) has the following form:
,}{ 1 EMSEw (5)
where subset of mappings is obtained by reducing W to single object w1.
Fig. 1 Binary mappings for the chain (2)
Zn
Cu
Mn
Heavy
Metals(E)
Wastewater
(w1)
Water(W)
Irrigation
Water(w2)
Irrigation
Water
+Added
Metals(w3)
s2
Trees (S)
s1
s3
Zn
Cu
Mn
Heavy
Metals(E)
Leaves
(m1)
Roots
(m2)
Measured
Parts (M)
V. Vissikirsky
9
Індуктивне моделювання складних систем, випуск 9, 2017
Example 2: Irrigation with high concentrations (w3) of Cu
++
, Mn
++
, and
Zn
++
(E) resulted to significantly higher concentrations of the metals in the roots
(m2) than in leaves (m1):
],}{}[{]}{}[{ 2313 EmSEwEmSEw
or more briefly:
,}][{}{ 213 EmmSEw (6)
where the sign denotes matching two cases.
Example 3: Under irrigation with high concentrations (w3), for trees (S)
except (s3), there is a tolerance in leaves (m1) for all heavy metals (E):
.}{}]{},[{}{ 13213 EmsssEw (7)
Example 4: Under increased concentrations of heavy metals in irrigation
water (w3), (s2) absorbs Cu
++
and Zn
++
in the leaves (m1) at much higher quantities
than the other trees:
}.,{}{}],{}[{},{}{ 13123 ZnCumsssZnCuw (8)
Example 5: For the increased concentrations of metals (E) in irrigation
water (w3), the roots (m2) absorb high concentrations in all trees (S):
.}{}{ 23 EmSEw (9)
Example 6: In case of w3, the concentration of Cu
++
in the roots (m2) of (s2),
when the highest concentration of Cu
++
was applied in w3, increased dramatically
in relation to the other trees {s1,s3}:
}.{}{}],{}[{}{}{ 23123 CumsssCuw (10)
These examples show that the investigator should have the possibility to
control the mappings by reducing the number of objects and factors under
consideration, i.e., selecting a subset of possible ways in the interaction network.
Thus, in the example 3 above, the analysis of the function f
W M
:C C is reduced
to the cases w3 and m1, and attention is focused on the objects from S, namely, how
the trees behave and differ from each other by concentrations in leaves under the
irrigation water with increased concentrations:
.}{}{ 13
?
EmSEw (11)
Analysis of qualitative reasoning about function obtained from empirical
results.
Qualitative modeling of trees cultivated with processed wastewater
10
Індуктивне моделювання складних систем, випуск 9, 2017
Qualitative knowledge derived from empirical data is virtually a description
of solution space with substantially reduced dimensionality. Qualitative
knowledge plays role of a skeleton to provide integral picture of multifactor
environment at any investigation step, and to concentrate other information for the
regions of space of special interest.
Recall that for the chain (2) there is an interest to estimate the function (3)
between the concentrations of heavy metals in supplied water and in the parts of
trees. Here, for each element from E, there is a real-value line C on which discrete
values of concentrations are empirically obtained. Then each measurement made
for the estimation of function f
W M
:C C can be represented as a way between
two real-value lines C
W
and C
M
through the sets W, S, and M involved in the chain.
In Figure 2, an example is shown of empirical estimation for one heavy metal. One
way reflects one measured point on the plot (C
W
, C
M
) for given objects from W, S,
and M. The plot in whole is a subset of ways selected under the conditions that
measured points on C
W
are ordered within a given range. As can be seen from
Figure 2, output concentrations C
M
have different distributions depending of
mapping cases, (m1 m2) or m1, with their own qualitative estimations.
Figure 2. Estimation of f:C
W
C
M
by mappings through W, S, M.
All the above examples of conclusions include such characteristics as
“high”, “higher”, “highest”, “increase”, “slight increase”, “dramatically
increased”, and others, by means of which the investigator qualitatively estimate
the function f
W M
:C C . Therefore, it is reasonable to use the concept of
qualitative sets
12
and assign to C
W
and C
M
some qualitative variables Qx={q
(x)
i},
i=1,...,n1, and Qy={q
(y)
j}, j=1,...,n2. Here, q
(x)
i and q
(y)
j are qualitative values with
overlapping membership functions that reflect some qualitative ranges of real
values of concentrations, for example, {Zero, Low, Medium, High, Very High,
Highest}.
Conclusions
In a whole, the tools to support the investigation shall include:
- a model description of causal relationships between objects of interaction
network;
w3
C
W
s1 m2
C
M
(m1 m2)
w1
w2
s2
s3
m1
C
M
(m1)
V. Vissikirsky
11
Індуктивне моделювання складних систем, випуск 9, 2017
- GMDH [6, 7] or neural network modules that approximate and
qualitatively estimate direct functional relationships between objects of the model;
- a qualitative inference system that provides the investigator with
qualitative reasoning about functional relationships of the model;
- a control system, which, under the investigator‟s request, filters out a
required subset of mappings in the model, supplies neural network modules and
qualitative inference system with required information, and supervises their
operation.
References
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“Reliability and Exploitation of Waste-Water Treatment Plants Using Diagnostic
Methods” Intern. J. Environmental Studies , Vol.40, 267-280, (1992).
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and Desert Areas using the „Kallidendron Technology”, Food Flavors:
Generation, Analysis and Process Influence, Elsevier Science, 1947-2023, (1995).
3. Drakatos P., Fanariotu I., Kalavrouziotis I., Kallistratos G., Skuras D.,
and Stoyianni M., “Concentration of Heavy Metals and Nutrients in the Leafs of
Certain Forest Trees Irrigated by Treated Wastewater”, Food Flavors: Generation,
Analysis and Process Influence, Elsevier Science, 1881-1894, (1995).
4. Vissikirsky V., Stepashko V., Kalavrouziotis I., and Varnavas S., “The
Road Pollution Impact on Zea mays: Inductive Modeling and Qualitative
Assessment”, Water, Air & Soil Pollution, 195, 301-310 (2008).
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Knowledge Proceed from Computer Simulation Results”, Proceedings of ASME
International - Greek Section, First Nat. Conf. on Recent Advances in Mech. Eng.,
September 17-20, 2001, Patras, Greece.
6. Kalavrouziotis I., Stepashko V., Vissikirsky V., and Drakatos P. “Group
Method of Data Handling (GMDH) application for modelling of mechanical
properties of trees irrigated with wastewater”, International Journal of
Environment and Pollution 18(6): 589-601, (2002).
7. Vissikirsky V., Stepashko V., Kalavrouziotis I., and Drakatos P.
“Growth Dynamics of trees Irrigated with wastewater: GMDH Modeling,
Assessment and Control Issues”, Instrumentation Science and Technology, pp.
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