A method for evaluating geo-environmental technologies based on a weighted convolution of partial performance criteria in the Mathlab environment. Ekaterina V. Rusanova,a, Evgeniy V. Runeva a Emperor Alexander I St. Petersburg State Transport University, 9 Moskovsky pr., Saint Petersburg, 190031, Russia Abstract 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. Keywords multi-criteria optimization, collation of criteria, Matlab, geo-ecoprotective technologies, PQ index proposed and often address only one group of 1. Introduction criteria. This approach does not provide an objective assessment of all possible groups of criteria to be taken into account by decision makers when using In today’s world, the development of waste-free the technology. and low-waste technologies in industrial sectors and Therefore, along with the development of new transport infrastructures against the backdrop of the geo-environmental protection technologies, an crises in economic development is particularly integrated assessment model based on the full set of important: An environmentally and economically existing criteria (environmental, technological and sound approach to the development of new waste other) is needed to provide an objective assessment management technologies1. [1], [2]. Methodologies of the technology. for assessing such waste management technologies A current problem is the creation of recycling are also necessary [3], [4]. technologies and materials from waste products and Existing methods for the assessment of geo- their further use in various industrial and transport environmental protection technologies [5], [6] do not sectors. Waste ash from the incineration of sewage provide a complete picture of the technologies sludge is one of the types of municipal waste that are currently under-managed. The ash has an elevated Models and Methods for Researching Information Systems natural radiation background and is a source of dust in Transport , December 11–12, 2020, Saint-Petersburg, Russia in landfills [4], [7]. EMAIL: rusanovaev@mail.ru (E.V.Rusanova); The recycling of such ash is therefore an jr_2010@mail.ru (E.V. Runev); ORCID: 0000-0002-3108-947X (E.V.Rusanova); important issue in the housing and utilities sectors 0000-0001-6707-888X(E.V. Runev) and affects the environmental group of criteria for ©️ 2020 Copyright for this paper by its authors. Use permitted under Creative the use of technologies [8]. Commons License Attribution 4.0 International (CC BY 4.0). The percentage of sand content substituted by CEUR Workshop Proceedings (CEUR-WS.org) ash, i.e. the replacement of one material - sand, with 92 another - with ash, is taken into account in the  x11 x12 ... ... x1 p    assessment of the technology to be developed for the recycling of ash from the incineration of sewage ( ) d  j = X j =  ... ... ... ... ...  (1), sludge. The new material received the name ash    x k1 x k 2 ... ... xkp  foam concrete [9], [10], [11], [12]. This produced material (ash foam concrete) is where among the elements xil  j ( ) occur and zero. tested according to different process criteria. [13], This means that there is no feature of the facility in [14]. The use of recyclable material (ash) in the next the group of criteria (such element in the matrix е production cycle is also taken into account. The use is to protect the public from noise in the railway X j is replaced by zero). industry [15]. The present paper proposes a model for Next, each matrix X j compares a matrix Y j , the evaluating geoecoprotective technologies based on elements of which are the values of the multi-criteria optimization and weighted convolution characteristics of the objects on a single scale for all criteria. On the basis of this model, a calculation criteria of the specified groups. methodology has been developed, which makes it possible to determine the PQ factor for different As a single scale set, a segment is selected 0;1 . objects according to the selected technologies using This set is natural for multi-criteria optimization the Mathlab environment. applications, as the characteristics of the objects are The work demonstrated the application of the compared with the given values of the criteria, which technique in the example of materials made of ash are numerically given by a point per segment 0;1 . 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 2.1. Set of model objects ash foam concrete is relevant for the application in the design of noise shields in railway transport [4]. The objects used are pure ash and molten ash of The entire chain of technology is suggested as a different densities with 50% ash content from sequence of processes: ash recycling, neutralizing its incineration of sewage sludge (instead of sand). harmful properties and reducing noise in populated Noise-proofing screens along the railways were areas. [19]. made of various densities of autoclave ash foam concrete to protect the population from railway noise: 2. Problem statement 1 – ashes from incineration of sewage sludge;  2 –autoclave ash foam concrete, density of the  k Let’s define by W = Ws s =1 the set of substance 500 kg m ; 3 possible groups of criteria. Here is  3 –autoclave ash foam concrete, density of the   Ws = ws1 ,...,wsjs – s − я the group of criteria; 3 substance 600 kg m ; wsjs − js – й критерий s − й группы. After that,  4 –autoclave ash foam concrete, density of the  = 1 ,..., m  we mark the number of objects to be 3 substance 800 kg m . examined using a group of criteria W . Каждому Thus, the set of objects being studied элементу множества  – исследуемому объекту  = 1 ,..., 4  is composed of four elements. сопоставим матрицу размерности k строк и p столбцов. Здесь p – наибольшее количество 2.2. Groups of criteria and model критериев по всем k группам ( p = max s ). The 1 s k criteria elements of the matrix are the value of the characteristics of the subject of the study according In the model of assessment of geo-ecological to natural scale criteria. The rows of the matrix are technologies of manufacture autoclave ash foam the values of the characteristics of the object on concreteya distinguish the following groups of natural scales of groups of criteria. criteria: Show the view shown here d :  → Mat (k , p ) : W1 – Environmental group; W2 – Technological group; 93 W3 –Operational group. и - it is the lower and upper Several of the most relevant criteria for decision limits of the range of the relevant criterion scale. makers are identified in each group. 2.3.1. The numerical values of criteria For an environmental group, these are: characteristics w11 – content of natural radionuclides w12 – dust content The numerical values of the characteristics For the technology group, this is: according to the scale of criteria for objects of study w 21 – thermal conductivity - samples from materials 1-4 are given in table 1 w 22 – strength below. w 23 – frost resistance Table 1 Experimentally measured w 24 – ash content w 25 – sound insulating ability For the operating group it is: w31 – noise level in built-up area Samples of materials 2.3. Scale of criteria Consider the display d :  → Mat (k , p ) (1) from W/m2 °C. kg/m3 cycles mg/m3 Bq/kg MPa dB a set of objects to a set of matrices whose elements dB set the properties of objects according to criteria scales. Each object matrix X j with strings and ash 615 3,51 0 0 0 0 0 0 columns (here – number of groups of criteria, – D500 96 0 12 16,5 15 80 38 65 number of criteria per group, p = max s . In the rows 1 s 3 D600 100 0 14 20 15 115 41 57 of the above matrix, the values of the characteristics D800 107 0 17 25 15 205 43 50 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  , Standard methods conforming to the we have the following groups of criteria: requirements of the GOST were selected for first group – s1 = 2 criteria; qualitative and quantitative analysis of the research materials [9], [10]. second group – s 2 = 5 criteria; The data in table 3 are sample averages derived third group – s 3 = 1 criteria. from a series of sample experiments. The statistical Here p = max sk = max2,5,1 = 5 . processing was done using the Mathlab environment. 1 s 3 All the research was carried out in the centre To harmonize the dimensions, we assume that if «Socrates» of the PGUPS; in the test laboratory one or more criteria are not present in a group, the «Center of testing and certification of SPB»; in the corresponding matrix elements are replaced by 0. test laboratory of the radiation control of the Test General type of such matrix for the case: Center «PKTI-Stroistat». All organizations are first group – s1 = 2 criteria; second group – s 2 = 5 licensed. criteria; third group – s 3 = 1 criteria; p = max sk = 5 1 s 3 has the form: 2.3.2. Natural scale of objects  x11 x12 0 0 0  according to criteria   ( ) d  j = X j =  x21 x22 x23 x24 x25  , x 0  The starting point in the search for an optimum  31 0 0 0 object that satisfies the groups of criteria and the . decision on the basis of which it can be used in geo- ecological protection technologies is the systematization of natural scales. 94 Natural scales are to be understood as 4) The compression strength of the samples measurements of the characteristics that determine shall be considered between 0 MPa and 35 MPa. The the physical properties of the materials of the tested best value on the compression strength criterion (35 samples. Table 2 shows the natural scales with MPa) corresponds to the right boundary of the measurement units for the criteria variables. universal scale. Units of the international SI system and units of 5) Frost resistance, the property of the material measurement according to the GOST test standards to damage resistance from the freezing-thaw cycle, is were used as units of change. measured in the number of cycles that will withstand Table 2 Natural scales of variables describing the material without damage. The scale of the criteria 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 units ) ) ) units units the left boundary of the universal scale. ) Bq/kg ) W/m2 °C ) dB 6) The ash content of 1 m3 of material is considered in the range of 0 to 500 kg/m3. The best ) mg/m3 ) MPa value for the ash content criterion (500 kg/m3) corresponds to the right boundary of the universal ) cycles scale. ) kg/m3 7) The soundproofing capability of sound shields from autoclave ash foam concreteA of ) dB different density and thickness is determined by a calculated method. It accepts values on a natural 2.3.3. Limit values of the measurement scale from 0 dB to 49 dB. The best value for the soundproofing capacity of the sample (49 dB) scales corresponds to the right boundary of the universal scale. In order to construct a universal scale with an 8) Noise in populated areas was measured area of variation, the ranges of measurement before and after installation of the noise shield. This boundaries for each characteristic were fixed for all criterion adopts values on a natural scale ranging criteria. from 20 dB to 120 dB. The best value according to For all the criteria, the following range the criterion «noise level in populated areas» (20 dB) boundaries were selected: corresponds to the right border of the universal scale. 1) Natural radionuclides content (NRC) was Table 3 presents all boundaries with the specified reviewed at intervals from 29 Bq/kg (the best value criteria measurement areas . of the interval is the background value corresponding to the plaster natural stone as the Table 3 Areas and boundaries of variable changes cleanest) until 740 Bq/kg (the worst value of the criterion units interval corresponds to the samples allowed for use in urban construction [9]). Best natural radionuclide ): content criterion (29 Bq/kg) coincides with the right ) Bq/kg [29;740] limit of the universal scale, i.е. 1. ) mg/m3 [0;0,3] ): 2) The dust content was considered in the range of 0 mg/m3 to 0.3 mg/m3 (norm maximum ) W/m2·°C [0,07;0,20] ) MPa [0;35] permissible concentration). The best value ) cycles [5;30] (corresponding to the ideal state of the system - total ) kg/m3 [0;500] absence of dust)- 0 mg/m3 is assigned a value of 1 in ) dB [0;49] the universal scale, the worst value (0.3 mg/m3) is ): the value of 0 in the universal scale. The best (0 ) dB [20;120] mg/m3) coincides with the right bound on the universal scale. 3) The thermal conductivity of the samples For each criterion with a natural scale and a range shall be considered in the range of 0.07 W/m2 °C to of values of a variable criterion, we construct a 0.20 W/m2 °C. The best value for the heat display , here – number of groups of criteria, conductivity criterion (0.07 W/m2 °C) corresponds – number of criteria, the field in a universal for all to the right boundary of the universal scale. criteria region-segment [0;1]. 95 Said map exhibits the property of strict 2.5. Design of criteria target monotonicity and compares the lowest (highest) value according to the natural scale of the lowest functions (highest) according to universal: – in the case of a The map , built strictly increasing function; in the preceding paragraphs has a vector character. It – in the case of a compares an object matrix whose elements are strict function. characteristic values in natural scales to an object The type of monotony is determined by the matrix whose elements take values from a segment physical characteristics underlying the criteria. [0;1] on a universal scale. the vector objective function whose components are strictly monotone scalar functions. 2.4. Matrix shapes Monotonicity is determined by the property of the natural physical evaluation of the object (sample). Each object in the set Ѳ is a comparable matrix As scalar target functions the continuous , whose elements are the values of the variables of bit-linear functions are selected. The choice of this all model criteria on a universal scale from a function class is motivated by the fact that the segment [0;1]: investigated objects are classified into several applications (e.g., materials in construction). The где – a display introduced in 2.3.3, number of sites where these functions are which has the monotonicity pattern property. continuously introduced according to the standards Here, the matrix is the variable of the application areas of the facilities under study. matrix for the groups of criteria of an object j. Based on the above conditions, two types of functions are possible to satisfy scalar target . functions. For sample 1 material, the matrix will be as Type 1: Piece-line, rigidly increasing functions follows: ,  0,249 0 0 0 0  where – positive real numbers, –   Y1 =  0 0 0 0 0  range number .  0,274  Type 2: Piece-by-piece - linear descending  0 0 0 0  functions For sample 2 material, the matrix will be as , follows: where – positive real numbers, –  0,964 1 0 0 0  range number .   Y2 =  1 0,356 0,213 0,312 0,936  Ratios are defined from a system  0,861 0  of linear algebraic equations that results from the  0 0 0 bilateral continuity of functions at the For sample 3 material, the matrix will be as boundary points of the scale split ranges. Number of follows: equations in the system quantity equal .  0,961 1 0 0 0    Y3 =  0,962 0,520 0,524 0,437 0,944  2.6. Weighted consolidation of  0,876 0   0 0 0 criteria For sample 4 material, the matrix will be as follows: The next step in constructing the target function  0,995 1 0 0 0  using the criteria consolidation is to determine the   folding weights [17],[18],[19]. Y4 =  0,740 0,842 0,860 0,685 0,956  .  0,891 0  In each group of criteria, the weight of the  0 0 0 criterion is determined taking into account the The above matrices show experimental importance of the criterion in the group. measurement data (table 1) for the subjects of the The relevance of the criterion is determined by study, translated into a universal scale. the method of peer review, the decision maker based on standards, legislation, worldwide practice and other technical information. 96 For the weighting coefficients, the natural Table 5 Grouping of criteria (additive) normalization condition shall be met: Environmenta the sum of all weights in a fixed index shall l Criteria ash D500 D600 D800 Group be one: 0,249 0,968 0,965 0,963 p  kl = 1 . Group of Technology ash D500 D600 D800 l =1 Criteria For the four objects considered in the work, for 0 0,535 0,646 0,828 which three groups of criteria are applied, and Performance ash D500 D600 D800 weights have been determined, the data are listed in Criteria Group 0,244 0,868 0,876 0,891 table 4. Table 4 Weight matrix of private criteria 2.7. Weighted grouping of criteria Environmental Criteria Group of Technology Performance Criteria Consider the weight vector of the groups of criteria , where weights are Criteria Group derived from the ratio Group s j = k j , sj j =1 content of thermal noise in where s j - peer review group of criteria number j. natural 0,90 conductivity 0,20 settlements 1,00 radionuclides For multiple objects to be considered with three (k=3) the groups of criteria are shown in the table dust content 0,10 strength 0,13 0 (table 6) weight vector values . Table 6 shows that when materials are used in frost geo-ecological protection technologies, the 0 resistance 0,15 0 environmental group of criteria has the greatest weight. This should be borne in mind by decision ash content makers. 0 0,35 0 sound Table 6 Weights of groups of criteria insulating 0 0,35 0 Group of ability Environmental Performance Group of Technology Criteria Group Criteria criteria Criteria Group The result of the weighted collation of criteria in 0,4 0,3 0,3 each group is the targeted collation function : , The target function of a weighted group bundle где – weight vector of criteria generally has the form [20],[21],[22]: in k group, аnd – rows of matrix G (t ) =   j G j (t ) =   j  j , F j (t ) = k k function with bit-linear components. j =1 j =1 Each component is defined by linear =    j   jl F jl (t ) k p functions defined on separate ranges of the scales of the corresponding criteria. j =1l =1 The result of applying weighted convolution of The intended function in the particular case under criteria to the samples under consideration is given consideration is for k=3: in table 5. In table 6 the values of the folding functions are , specified for k groups of criteria. Because где - weight vector of criteria in there are large computations with multivariate group number j. datasets in work (k groups, criteria in the group, Calculations with the specified bundles for line functions, linear function coefficients), different objects are carried out in the Mathlab the numerical values of the folding functions were environment using algorithms for processing obtained using the Mathlab environment. multivariate data arrays. 97 These algorithms allow the data to be used many years of fruitful cooperation, which led to the immediately after measurement experiments and to emergence of interesting ideas in approaches to find target function values for any number of solving various applied problems, particularly experimental samples. It saves time and relevant in today’s environment, such as modelling computational complexity [23]. the reliability and stability of systems/ We also express our gratitude to the departments 2.8. Optimal solution «Water supply, drainage and hydraulics», «Engineering chemistry and natural history», «Higher mathematics», «Informatics and On the Figure 1 shows the weighted totals of the information security» for the friendly warm criteria groups as a column chart. 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». References [1] Svatovskaya L.B., Makarova E.I., Shershnyeva Figure 1: Weighted folding totals of criteria M.V and other. «New eco-protection groups technologies on railway transport». 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