Neural network model of investment process of biogas production

The paper forms a neural network model of the investment process of biogas production, which allows increasing the efficiency of the management decision-making process on the feasibility of investing in biogas plants. Biogas plants are becoming widespread in the world, although natural climatic conditions are not favorable for biogas production. But modern technological solutions for insulation of bioreactors, their automation and thermal stabilization, allow obtaining biogas in different latitudes. The construction of biogas plants requires significant capital investment. Therefore, these investments require a detailed feasibility study, including consideration of both technical and economic aspects of biogas production. The authors propose to use the mathematical apparatus of shallow neural networks and create a ten-neuron shallow neural mathematical model with the MATLAB mathematical package, which can serve as a tool to support investment decisions in the implementation of the biogas plant project. The proposed model, in contrast to existing approaches, allows us to take into account both quantitative and qualitative factors, which are obtained analytically, expertly and experimentally. In addition, the proposed model allows combining both economic and technical criteria that affect the decision-making process for investing in the process of biogas production. The calculation of investment attractiveness of introduction of biogas utilization unit for the researched enterprise is given. According to the simulation results, it is determined that the investment attractiveness of the introduction of a biogas plant for the given set of input factors indicates the feasibility of implementing a biogas plant.


Introduction
In today's world of economics, humanity faces several important issues related to sustainable development, among which the important goals are to increase the production of energy from renewable sources around the world and ecological production.Permanent increase in energy prices causes a constant increase in production costs and reduces profits.One of the ways to ensure energy saving measures is to use biogas as an alternative energy source.This issue is especially relevant for agricultural producers and the food industry, as they regularly receive a significant amount of organic waste, which should be transformed into biogas.The use of biogas as a way to overcome the energy crisis in developing countries is considered [1].Yu et al [2] analyzed the complex productivity of single-phase and two-phase anaerobic digestion using a hybrid method and determined that the decisive factors are the yield of biogas, electricity consumption and biofertilizers.
The results of research by Nwokolo et al [3] allow us to conclude that the use of biogas plants provides benefits such as reducing greenhouse gas emissions into the environment and improving energy security.In addition, the use of produced biogas leads to a reduction in 1254 (2023) 012103 IOP Publishing doi:10.1088/1755-1315/1254/1/012103 2 purchased energy and waste disposal in the biogas plant based on the system of sewage sludge treatment at treatment plants.
In Europe, biogas is produced in a large number of countries, including Poland [4], Finland [5], Germany [6], Hungary [7].In particular, more than 1,000 biogas plants were built in Germany from 2000 to 2014 [8].Some questions connected with the state of biofuel in Ukraine are considered by Stanytsina et al [9], Bogoslavska et al [10].
The construction of biogas plants requires significant capital investment.Therefore, these investments require a detailed feasibility study, including consideration of both technical and economic aspects of biogas production.Nurgaliev et al [11] proposed to assess the efficiency of investing in biogas plants by calculating the classic performance indicators of investment projects with and without discounting, given the rapid change in variables.
Taking into account quantitative and qualitative factors, which are obtained analytically, expertly and experimentally, requires a specialized mathematical apparatus.The best mathematical apparatus, in our opinion, is either the theory of fuzzy logic and linguistic variables or the theory of neural networks.
The aim of the work is to form a neural network model of the investment process of biogas production, which allows us to increase the efficiency of the management decision-making process on the feasibility of investing in biogas plants.
Fuzzy logic theory uses a limited information base, within which fuzzy logical equations are formed and the result is calculated [12][13][14][15].Fuzzy logic theory works in a closed information environment, which is limited by knowledge bases.Neural networks are used for processing large data sets, universal approximation and further training of mathematical models.The neural network is a universal approximator, which is an example of artificial intelligence and allows you to support decision-making based on the results of processing large arrays of quantitative and qualitative information.It is proposed to use the mathematical apparatus of shallow neural networks and create a ten-neural shallow neural mathematical model with the MATLAB mathematical package, which can serve as a tool to support investment decisions in the implementation of the biogas plant project.

Results and discussion
The production of agricultural products is accompanied by the constant accumulation of organic waste from animal life, crop products, wood processing, etc. Ukraine produces more than 57,000 tons of organic waste annually [16], the vast majority of which simply pollutes the environment.All these wastes require proper and safe disposal, preferably with the simultaneous production of products necessary for agriculture.One of such directions of ecologically safe utilization of organic waste is biogas production.The process of anaerobic fermentation in bioreactors allows you not only to dispose of environmentally hazardous waste, but also to process it into biogas and valuable organic fertilizer.
Biogas plants are becoming widespread in the world, although natural climatic conditions are not favorable for biogas production.But modern technological solutions for insulation of bioreactors, their automation and thermal stabilization, allow us to obtain biogas in different latitudes.A biogas plant is a complex set of interconnected technological elements of the process of utilization of organic waste with their processing into biogas and biofertilizers.The central element of the biogas plant is a bioreactor, that is an insulated tank with a heating element, stirrer, devices for loading the substrate and removing it, gasholder, process control devices.The process of anaerobic fermentation takes place in a bioreactor, but before the raw material enters the reactor, it must go a long way of collection and preparation.First of all, organic waste must be delivered to the site, then crushed and mixed with water, fed at a certain temperature to the reactor.The output of biogas from different types of organic waste is also different (table 1).
The process of anaerobic fermentation is also significantly influenced by the temperature of the fermentation regime, thermal stabilization in the volume of the bioreactor, the fineness of raw materials, etc.In addition to complex technical requirements for the implementation of the waste processing process, the investment process of such a decision is subject to significant restrictions on financial, economic and operational requirements.
Biogas can be burned directly, but taking into account the large number of impurities (about 40% CO 2 + other gases 1..3%), it is better to clean it first.From 1 m 3 of biogas with a methane content of 60%, you can get about 2.5 kWh of electricity, or 2.6 kWh of heat.
The process of implementation of the investment decision on the implementation of the disposal plant requires the assessment of many factors of influence, which have both quantitative and qualitative characteristics.Biogas plants require significant capital investment, stable supply of the reactor with heat and electricity, continuous supply of raw materials, maintenance of temperature in the fermentation environment, etc.The decision to implement a biogas plant at the enterprise must be made comprehensively using modern advances in science and technology.In our opinion, in this case, the optimal method of intellectual decision support is the theory of neural networks [17,18].This theory allows us to combine into a single mathematical model quantitative and qualitative factors of the technological process of fermentation, as well as financial, economic and operational components of the process of disposal of organic waste as an investment object.The decision to implement a biogas plant must be made taking into account a large number of influencing factors.Significant cost of installations requires careful analysis of all risks and features of the technological process.In addition to the complex technological requirements for the process of anaerobic fermentation related to the quality of raw materials, temperature and humidity of the substrate, there are a number of human factors related to qualifications, motivation and other factors.In general, we propose to determine the degree of feasibility of implementing a biogas plant by the values of investment attractiveness.For this indicator D, we have proposed ranges of values of factors in which it acquires a certain content saturation.If D belongs to the range of values [0…2], then the implementation of the project for the construction of a biogas plant is impractical.In the range [2…4] the investment attractiveness of the construction process biogas plant is below average, in the range (4…6) it is average, in the range (6…8) it is above average; in the range [8…10] it is the maximum investment attractiveness The investment attractiveness of the introduction of biogas disposal plant can be considered in the form of the ratio: where X is a set of financial and economic factors; Y is a set of technical factors; Z is a set of operational factors.
In turn, the above sets of factors can be deployed in the following dependences: Detailed characteristics of factors influencing the investment process, their universal set of variations and linguistic terms for evaluation are given in table 2.
Group of financial and economic factors: • Factor x 1 -linguistic variable (LV) "Qualification level of personnel" characterizes the level of qualification of personnel that will service the biogas plant.Linguistically, we decided to evaluate this factor in terms of "insignificant, medium, high".It is clear that the higher the qualification level of staff is, the more attractive the process of implementing this decision is.• Factor x 2 -LV "Dependence on external financing entities" characterizes the degree of borrowed capital in total investment capital and the cost of borrowed capital.The higher the share of borrowing is and the higher the cost of such capital is, the less attractive the investment is.• Factor x 3 -LV "Level of raw material costs" characterizes the level of raw material costs for a biogas plant.Raw materials can be provided free of charge; raw materials utilization can be paid for or they have to be bought.Purchasing raw materials for biogas production is the least advantageous option when considering alternatives.• Factor x 4 -LV "Level of capital costs" characterizes the amount of capital investment for the construction of a biogas plant in terms of 1 kWh of electricity produced from biogas.According to research results, depending on the type of raw material and temperature regime, this factor may be in the range of 2…10 thousand euros/kWh.It is clear that the higher the level of capital expenditures is, the riskier the investment is.• The last factor from the financial and economic block is x 5 -LV "Complexity of logistics" characterizes the complexity of delivery of raw materials for the operation of biogas plants and transportation and storage of fermentation products -biogas and biofertilizers to consumers.The volume of processed biomass is slightly different from the input volume of raw materials, and it can be applied to the fields only in spring or autumn.Therefore, the rest of the time the processed biomass must be stored somewhere.Most of the above factors are estimated in conditional points expertly as it is almost impossible to quantify them.

Group of technical factors:
• Factor y 1 -"Type of raw material".Raw materials play an important role in the process of biogas production.The best raw material is sugar pulp or waste, which contains a large proportion of fat.Potato tops, corn stalks, cattle and pig waste are more difficult to decompose in the bioreactor.The "worst" ones are silage and sawdust.(points) Z 3 -LV "Level of automation of the U(z 3 ) = 10�90 low, medium, high production process" (percent) Z 4 -LV "Degree of reduction of U(z 4 ) = 10�90 low, medium, high harmful emissions into the environment" (percent) • Equally important is the crushing of raw materials, which is described visually by experts in the range of {1…10} points -factor y 2 .The intensity of the anaerobic fermentation process is directly dependent on the ambient temperature.• There are three main temperature regimes: "cryophilic" (T opt = 20 • C); "mesophilic" (T opt = 3242 • C); "thermophilic" (T opt = 4851 • C).Factor y 3 -LV "Temperature mode" characterizes the temperature regime in the reactor in the range 20…55 • C. The temperature in the environment should be uniform.This is quite difficult to achieve, given the large volumes of the reactor, the presence of stagnant zones under the heating elements, the technological limitations of the mixing speed of the substrate.Thermal stabilization of the fermentation process is estimated by the value of the temperature difference between the hottest and the coldest zone of the reactor volume.It is generally accepted that the temperature difference in the reactor zone should not exceed 3 • C.
Main operational factors: • The technical complexity of the operational process is assessed by experts and is in the range from [10…90]%.• The level of purification of biogas from impurities is estimated in the range [0… 99]% and is determined by technological calculations.• The level of automation of the production process and the degree of reduction of harmful emissions into the environment are estimated in the same range.
To develop a mathematical model of intellectual support of decision-making to assess the investment attractiveness of a biogas plant project, there is a need to form a knowledge matrixconcentrated coded information determined by technological calculations, expert evaluations, analytical calculations.The knowledge matrix is a table where the numerical value shows the results of various types of research.The fragment of the knowledge matrix is given in table 3. The sample size for building the model was more than 200 data rows.Table 3.The fragment of the knowledge matrix.To build a neural network that would solve the problem with some accuracy, we propose to use a shallow neural network, the block diagram of which is shown in figure 1.A two-layer network of direct feed with hidden sigmoid neurons and neurons of linear output can quite successfully solve the problem without excessive accuracy and complexity of calculations (figure 2).This network can also be called a Multilayer Perceptron (MLP) as it is a two-layer neural network with a nonlinear hidden layer that can be used for classification and regression tasks.The network will be studied according to the Levenberg-Marquardt backpropagation algorithm.The Levenberg-Marquardt algorithm is an optimization method used for adjusting  the weights of a neural network during training.This algorithm is an iterative method based on gradient descent and is designed to solve optimization problems with nonlinear constraints.After loading the data into the MATLAB mathematical package, we performed calculations and determined the calculation errors (figure 3), as well as made a regression graph and determined the coefficient of determination, which in our case was R = 0.91, indicating a high connection density.
For practical use of the proposed model, it is best to create a Simulink model in the MATLAB package.This model has only three blocks: the constant block, where the input values are entered in the form of a vector; the block of the neural network and the visualization block.
In our case -the monitor, where the simulation result is shown as a number (figure 4).The decision-making on the feasibility of investing in the construction of a biogas plant is as follows: analytically, expertly or experimentally, the input values are entered into the table .Then their values are loaded into the vector column of the program.
After the calculation, the program displays on the block the value of the investment attractiveness of the introduction of biogas disposal plant (table 4).
According to the simulation results, it is determined that the investment attractiveness of the introduction of a biogas plant with a given set of input factors is D = 7.54, which corresponds to the range "above average", i.e. the plant can be implemented.

Conclusions
Thus, the paper proposes a neural network model of the investment process of biogas production.
Taking into account quantitative and qualitative factors, which are obtained analytically, expertly and experimentally, requires a specialized mathematical apparatus.The best mathematical apparatus, in our opinion, is either the theory of fuzzy logic and linguistic variables or the theory of neural networks.
It is proposed to use the mathematical apparatus of shallow neural networks and create a ten-neuron shallow neural mathematical model with the MATLAB mathematical package, which can serve as a tool to support investment decisions in the implementation of the biogas plant project.The proposed model, in contrast to existing approaches, allows us to take into account both quantitative and qualitative factors, which are obtained analytically, expertly and experimentally.In addition, the proposed model allows us to combine both economic and technical criteria that affect the decision-making process for investing in the process of biogas production.The calculation of investment attractiveness of introduction of biogas utilization unit for the researched enterprise is given.
According to the simulation results, it is determined that the investment attractiveness of the introduction of a biogas plant for the given set of input factors indicates the feasibility of implementing a biogas plant.

Figure 1 .
Figure 1.Block diagram of a two-layer neural shallow network.

Figure 3 .
Figure 3. Regression and value of the coefficient of determination.

Figure 4 .
Figure 4. Fragment of the window of the Simulink package of the MATLAB program with the program of neural network modeling.

Table 1 .
[3]gas yield and methane content when using different types of waste[3].

Table 2 .
Influencing factors as linguistic variables.

Table 4 .
Values of input and output variables.