The present paper proposes a model for evaluating geo-ecological protection technologies based on multi-criteria optimization and weighted convolution criteria, on the basis of which the method of calculation is developed, allowing to determine the PQ factor for different objects according to the selected technologies using the Mathlab environment. The work demonstrated the application of the technique in the case of materials made of ash foam concrete with densities and ash content from the incineration of sewage sludge. The determination of the optimum composition of solopenobeton is relevant for the design of noise shields in railway transport. The proposed simulation algorithm in the Matlab environment makes it possible to use the procedure of processing the raw data, using several options of their input: in the form of tables of the format. csv or manual input.
In today’s world, the development of waste-free
and low-waste technologies in industrial sectors and
transport infrastructures against the backdrop of the
crises in economic development is particularly
important: An environmentally and economically
sound approach to the development of new waste
management technologies1. [
Existing methods for the assessment of
geoenvironmental protection technologies [
Therefore, along with the development of new geo-environmental protection technologies, an integrated assessment model based on the full set of existing criteria (environmental, technological and other) is needed to provide an objective assessment of the technology.
A current problem is the creation of recycling
technologies and materials from waste products and
their further use in various industrial and transport
sectors. Waste ash from the incineration of sewage
sludge is one of the types of municipal waste that are
currently under-managed. The ash has an elevated
natural radiation background and is a source of dust
in landfills [
The recycling of such ash is therefore an
important issue in the housing and utilities sectors
and affects the environmental group of criteria for
the use of technologies [
The percentage of sand content substituted by
ash, i.e. the replacement of one material - sand, with
another - with ash, is taken into account in the
assessment of the technology to be developed for the
recycling of ash from the incineration of sewage
sludge. The new material received the name ash
foam concrete [
This produced material (ash foam concrete) is
tested according to different process criteria. [
The present paper proposes a model for evaluating geoecoprotective technologies based on multi-criteria optimization and weighted convolution criteria. On the basis of this model, a calculation methodology has been developed, which makes it possible to determine the PQ factor for different objects according to the selected technologies using the Mathlab environment.
The work demonstrated the application of the
technique in the example of materials made of ash
foam concrete, which are dense and containing ash
from incineration of sludge in an amount of 50% of
sand. The definition of the optimum composition of
ash foam concrete is relevant for the application in
the design of noise shields in railway transport [
The entire chain of technology is suggested as a
sequence of processes: ash recycling, neutralizing its
harmful properties and reducing noise in populated
areas. [
Ws = ws1,...,wsjs – s − я
W = W k
s s=1 of criteria.
the set of Here
is the group of criteria; wsjs − js – й критерий s − й группы. After that, = 1 ,..., m we mark the number of objects to be examined using a group of criteria W . Каждому элементу множества – исследуемому объекту сопоставим матрицу размерности k строк и p столбцов. Здесь p – наибольшее количество критериев по всем k группам ( p = max s ). The 1sk elements of the matrix are the value of the characteristics of the subject of the study according to natural scale criteria. The rows of the matrix are the values of the characteristics of the object on natural scales of groups of criteria.
Show the view shown here d : → Mat(k, p) : d ( j ) = X j = ...
xk1 ... ... ... (1),
... ... xkp where among the elements xil ( j ) occur and zero. This means that there is no feature of the facility in the group of criteria (such element in the matrix е X j is replaced by zero).
Next, each matrix X j compares a matrix Y j , the elements of which are the values of the characteristics of the objects on a single scale for all criteria of the specified groups.
As a single scale set, a segment is selected 0;1 . This set is natural for multi-criteria optimization applications, as the characteristics of the objects are compared with the given values of the criteria, which are numerically given by a point per segment 0;1 .
The objects used are pure ash and molten ash of different densities with 50% ash content from incineration of sewage sludge (instead of sand). Noise-proofing screens along the railways were made of various densities of autoclave ash foam concrete to protect the population from railway noise: 1 – ashes from incineration of sewage sludge; 2 –autoclave ash foam concrete, density of the 3 substance 500 kg m ; 3 –autoclave ash foam concrete, density of the 3 substance 600 kg m ;
3 substance 800 kg m .
4 –autoclave ash foam concrete, density of the Thus, the set of objects being = 1,..., 4 is composed of four elements.
studied model
In the model of assessment of geo-ecological technologies of manufacture autoclave ash foam concreteya distinguish the following groups of criteria:
W – Environmental group;
1 W2 – Technological group;
W3 –Operational group.
Several of the most relevant criteria for decision makers are identified in each group.
For an environmental group, these are: w11 – content of natural radionuclides w12 – dust content
w21 – thermal conductivity w22 – strength w23 – frost resistance w24 – ash content w25 – sound insulating ability For the operating group it is: w31 – noise level in built-up area
Consider the display d : → Mat(k, p) (1) from a set of objects to a set of matrices whose elements set the properties of objects according to criteria scales.
Each object matrix X j with strings and columns (here – number of groups of criteria, – number of criteria per group, p = max s . In the rows 1s3 of the above matrix, the values of the characteristics of the object are arranged according to groups of criteria. In the case , for the set of investigated objects referred to in paragraph 2.1 = 1,..., 4 , we have the following groups of criteria: first group – s1 = 2 criteria; second group – s2 = 5 criteria; third group – s3 = 1 criteria.
Here p = m1sax3 sk = max2,5,1 = 5 .
To harmonize the dimensions, we assume that if one or more criteria are not present in a group, the corresponding matrix elements are replaced by 0.
General type of such matrix for the case: first group – s1 = 2 criteria; second group – s2 = 5 criteria; third group – s3 = 1 criteria; p = m1sax3 sk = 5 has the form: d ( j ) = X j = x21 x31
The numerical values of the characteristics according to the scale of criteria for objects of study - samples from materials 1-4 are given in table 1 below.
Standard methods conforming to the
requirements of the GOST were selected for
qualitative and quantitative analysis of the research
materials [
The data in table 3 are sample averages derived from a series of sample experiments. The statistical processing was done using the Mathlab environment.
All the research was carried out in the centre «Socrates» of the PGUPS; in the test laboratory «Center of testing and certification of SPB»; in the test laboratory of the radiation control of the Test Center «PKTI-Stroistat». All organizations are licensed.
The starting point in the search for an optimum object that satisfies the groups of criteria and the decision on the basis of which it can be used in geoecological protection technologies is the systematization of natural scales.
Natural scales are to be understood as measurements of the characteristics that determine the physical properties of the materials of the tested samples. Table 2 shows the natural scales with measurement units for the criteria variables.
Units of the international SI system and units of measurement according to the GOST test standards were used as units of change.
Table 2 Natural scales of variables describing criteria ) ) ) s t i n u Bq/kg mg/m3 ) ) ) ) ) ) s t i n u W/m2 °C
MPa cycles kg/m3 dB ) ) dB s t i n u
In order to construct a universal scale with an area of variation, the ranges of measurement boundaries for each characteristic were fixed for all criteria.
For all the criteria, the following range boundaries were selected:
1) Natural radionuclides content (NRC) was
reviewed at intervals from 29 Bq/kg (the best value
of the interval is the background value
corresponding to the plaster natural stone as the
cleanest) until 740 Bq/kg (the worst value of the
interval corresponds to the samples allowed for use
in urban construction [
2) The dust content was considered in the range of 0 mg/m3 to 0.3 mg/m3 (norm maximum permissible concentration). The best value (corresponding to the ideal state of the system - total absence of dust)- 0 mg/m3 is assigned a value of 1 in the universal scale, the worst value (0.3 mg/m3) is the value of 0 in the universal scale. The best (0 mg/m3) coincides with the right bound on the universal scale.
3) The thermal conductivity of the samples shall be considered in the range of 0.07 W/m2 °C to 0.20 W/m2 °C. The best value for the heat conductivity criterion (0.07 W/m2 °C) corresponds to the right boundary of the universal scale. 4) The compression strength of the samples shall be considered between 0 MPa and 35 MPa. The best value on the compression strength criterion (35 MPa) corresponds to the right boundary of the universal scale.
5) Frost resistance, the property of the material to damage resistance from the freezing-thaw cycle, is measured in the number of cycles that will withstand the material without damage. The scale of the criterion in natural units of measurement ranges from 5 cycles to 30 cycles. The best value for the cold resistance criterion (30 cycles) corresponds to the left boundary of the universal scale.
6) The ash content of 1 m3 of material is considered in the range of 0 to 500 kg/m3. The best value for the ash content criterion (500 kg/m3) corresponds to the right boundary of the universal scale.
7) The soundproofing capability of sound shields from autoclave ash foam concreteA of different density and thickness is determined by a calculated method. It accepts values on a natural scale from 0 dB to 49 dB. The best value for the soundproofing capacity of the sample (49 dB) corresponds to the right boundary of the universal scale.
8) Noise in populated areas was measured before and after installation of the noise shield. This criterion adopts values on a natural scale ranging from 20 dB to 120 dB. The best value according to the criterion «noise level in populated areas» (20 dB) corresponds to the right border of the universal scale.
Table 3 presents all boundaries with the specified criteria measurement areas .
For each criterion with a natural scale and a range of values of a variable criterion, we construct a display , here – number of groups of criteria, – number of criteria, the field in a universal for all criteria region-segment [0;1].
Said map exhibits the property of strict monotonicity and compares the lowest (highest) value according to the natural scale of the lowest (highest) according to universal: strictly increasing function; strict function.
The type of monotony is determined by the physical characteristics underlying the criteria. – in the case of a – in the case of a
Each object in the set Ѳ is a comparable matrix , whose elements are the values of the variables of all model criteria on a universal scale from a segment [0;1]:
где – a display introduced in 2.3.3, which has the monotonicity pattern property.
Here, the matrix is the variable matrix for the groups of criteria of an object j. .
For sample 1 material, the matrix will be as follows: 0,249 Y1 = 0 0,274 0 0 0 0 0 0 0 0 0 0
0 0
For sample 2 material, the matrix will be as follows: 0,964 1 0 0 0 Y2 = 1 0,356 0,213 0,312 0,936 0,861 0 0 0 0
For sample 3 material, the matrix will be as follows: 0,961 1 0 0 0 Y3 = 0,962 0,520 0,524 0,437 0,944 0,876 0 0 0 0
For sample 4 material, the matrix will be as follows: 0,995 1 0 0 0 Y4 = 0,740 0,842 0,860 0,685 0,956 .
0,891 0 0 0 0
The above matrices show experimental measurement data (table 1) for the subjects of the study, translated into a universal scale. criteria target
The map , built in the preceding paragraphs has a vector character. It compares an object matrix whose elements are characteristic values in natural scales to an object matrix whose elements take values from a segment [0;1] on a universal scale.
the vector objective function whose components are strictly monotone scalar functions. Monotonicity is determined by the property of the natural physical evaluation of the object (sample).
As scalar target functions the continuous bit-linear functions are selected. The choice of this function class is motivated by the fact that the investigated objects are classified into several applications (e.g., materials in construction). The number of sites where these functions are continuously introduced according to the standards of the application areas of the facilities under study.
Based on the above conditions, two types of functions are possible to satisfy scalar target functions.
Type 1: Piece-line, rigidly increasing functions , where – positive real numbers, – range number .
Type 2: Piece-by-piece - linear descending functions , where – positive real numbers, – range number .
Ratios are defined from a system of linear algebraic equations that results from the bilateral continuity of functions at the boundary points of the scale split ranges. Number of equations in the system quantity equal .
The next step in constructing the target function
using the criteria consolidation is to determine the
folding weights [
In each group of criteria, the weight of the criterion is determined taking into account the importance of the criterion in the group.
The relevance of the criterion is determined by the method of peer review, the decision maker based on standards, legislation, worldwide practice and other technical information.
For the weighting coefficients, the natural (additive) normalization condition shall be met: the sum of all weights in a fixed index shall be one: p kl = 1.
l=1
For the four objects considered in the work, for which three groups of criteria are applied, and weights have been determined, the data are listed in table 4.
The result of the weighted collation of criteria in each group is the targeted collation function : , где – weight vector of criteria in k group, аnd – rows of matrix function with bit-linear components.
Each component is defined by linear functions defined on separate ranges of the scales of the corresponding criteria.
The result of applying weighted convolution of criteria to the samples under consideration is given in table 5.
In table 6 the values of the folding functions are specified for k groups of criteria. Because there are large computations with multivariate datasets in work (k groups, criteria in the group, line functions, linear function coefficients), the numerical values of the folding functions were obtained using the Mathlab environment.
Consider the weight vector of the groups of criteria , where weights are derived from the ratio j = ks j s j j=1 where s j - peer review group of criteria number j.
For multiple objects to be considered with three (k=3) the groups of criteria are shown in the table (table 6) weight vector values .
Table 6 shows that when materials are used in geo-ecological protection technologies, the environmental group of criteria has the greatest weight. This should be borne in mind by decision makers. где - weight vector of criteria in group number j.
Calculations with the specified bundles for different objects are carried out in the Mathlab environment using algorithms for processing multivariate data arrays.
These algorithms allow the data to be used
immediately after measurement experiments and to
find target function values for any number of
experimental samples. It saves time and
computational complexity [
On the Figure 1 shows the weighted totals of the criteria groups as a column chart.
The proposed model, based on weighted totals of criteria, makes it possible to compile as a method of calculating the target functions of PQ-factors according to individual optimality criteria. And how to calculate the PQ factors of the group of criteria with the aim of constructing an optimal solution for recommending a decision on the use of materials in the creation of geo-environmental protection.
The final result of the work is an algorithm implemented in the Mathlab environment with processing of multivariate data sets, which can be used for a wide class of tasks of estimation of different technologies under conditions of decisionmaking with full information on different groups of criteria.
The authors express their gratitude to their colleagues at the University of Petersburg for the communication ways of Emperor Alexander I for many years of fruitful cooperation, which led to the emergence of interesting ideas in approaches to solving various applied problems, particularly relevant in today’s environment, such as modelling the reliability and stability of systems/
We also express our gratitude to the departments «Water supply, drainage and hydraulics», «Engineering chemistry and natural history», «Higher mathematics», «Informatics and information security» for the friendly warm atmosphere, Continuous discussion and creative search in solving emerging applications.
We shall mark the high contribution to the organization and holding of the seminar «Models and Methods for Researching Information Systems in Transport» by the employees of the department «Information and computing systems».