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ТЕХНОЛОГИЯ И ОРГАНИЗАЦИЯ СТРОИТЕЛЬСТВА. ЭКОНОМИКА И УПРАВЛЕНИЕ В СТРОИТЕЛЬСТВЕ
НАУЧНАЯ СТАТЬЯ I RESEARCH PAPER UDC 331.103.3:004
DOI: 10.22227I1997-0935.2023.4.638-650
Regression rationing of labour costs based on the estimation of their actual values by neural network modelling
Khoshnaw Y.B. Hussein1, Sergey A. Bolotin1, Nadim Q.R. Huraini1, Haitham Boxan1, 2
1 Saint Petersburg State University of Architecture and Civil Engineering (SPbGASU); Saint Petersburg, Russian Federation; 2 Thi-Qar University; Republic of Iraq
ABSTRACT
Introduction. Labour rationing is an integral part of effective management of construction production. It is proved by the experience of economically developed countries, where labour rationing is connected with all spheres of enterprises: industrial, technical, organizational, financial, economic and social. Modern methods of labour rationing were created by specialists from economically developed countries. The purpose of this article is to improve the efficiency of the construction industry in the Republic of Iraq by adapting modern labour cost standards to the construction industry. Materials and methods. The method of neural network modelling was used in the work. (3 (3 Results. The networks under consideration were tested to obtain labour costs based on the implementation of production
O O standards, which are known to be the inverse of labour costs. As a result of the experiment, instead of actual labour costs
, , the actual output was introduced, and the inverse value was calculated using the output standards obtained from the neural
^ ^ network modelling.
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0 ¡J Conclusions. The presented excursus on the labour rationing methods used makes it clear that the creation of appropriate
j? $ databases requires significant costs and time. Therefore, another alternative to this approach is to use already developed
3 ~ regulatory databases that can be adapted to the construction industry in the Republic of Iraq. In order to implement such
AO W an approach, it is necessary to analyze the existing databases and establish such an up-to-date database that would have
to g the greatest correspondence with the actual labour costs specific to the construction industry of the Republic of Iraq. As
£ a generalized conclusion about the practical result of the presented development, a stepwise regression methodology for
2 3 the formation of labour costs for a selected type of work is presented.
* I
• ' KEYWORDS: labour cost, labour regulation, neural network, statistics, construction management, regression analysis, <u <u construction industry, approximating, neural network modelling, linear models, nonlinear models, measurement, database — -3
O (¿ FOR CITATION: Hussein Kh.Y.B., Bolotin S.A., Huraini N.Q.R., Boxan H. Regression rationing of labour costs based
on the estimation of their actual values by neural network modelling. Vestnik MGSU [Monthly Journal on Construction and Architecture]. 2023; 18(4):638-650. DOI: 10.22227/1997-0935.2023.4.638-650 (rus.).
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Corresponding author: Khoshnaw Y.B. Hussein, yousif.babakr@gmail.com.
Регрессионное нормирование трудозатрат на основе оценки £ <3 их фактических значений методом нейросетевого моделирования
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§ | Хошнав Юсиф Бабакр Хуссейн1, Сергей Алексеевич Болотин1,
со ° Надим К.Р. Хурейни1, Хайтам Бохан1, 2
1 Санкт-Петербургский государственный архитектурно-строительный университет
<л g (СПбГАСУ); г. Санкт-Петербург, Россия;
— 2 2 Университет Ди-Кар; Республика Ирак
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ю АННОТАЦИЯ
Е Введение. Органической частью эффективного управления строительным производством служит нормирование
5 £ труда. На это указывает опыт экономически развитых стран, где с нормированием труда связаны все сферы дея-
■Е £ тельности предприятий: производственная, техническая, организационная, финансово-экономическая и социаль-
О (П ная. Современные методы нормирования труда были созданы специалистами экономически развитых стран. Цель
ВО > исследования — повысить эффективность строительной отрасли в Республике Ирак на основе адаптации современных стандартов затрат на рабочую силу к строительной отрасли.
© Х.Ю.Б. Хуссейн, С.А. Болотин, Н.К.Р. Хурейни, Х. Бохан, 2023 Распространяется на основании Creative Commons Attribution Non-Commercial (CC BY-NC)
Материалы и методы. Использовался метод нейросетевого моделирования.
Результаты. Рассматриваемые сети протестированы на получение трудозатрат по результатам внедрения производственных стандартов, которые, как известно, являются обратной величиной трудозатрат. В результате эксперимента вместо фактических трудозатрат введены фактические выработки, а обратная величина рассчитана с помощью нормы выработки, полученной в итоге нейросетевого моделирования.
Выводы. Представленный экскурс по применяемым методам нормирования труда позволяет понять, что для создания соответствующих баз данных (БД) требуются существенные затраты и время. Поэтому другая альтернатива указанного подхода — использование уже разработанных нормативных БД, которые можно адаптировать к строительной отрасли Республики Ирак. Для того чтобы внедрить этот подход, необходимо проанализировать имеющиеся БД и установить такую актуальную БД, которая обладала бы наибольшим соответствием фактических трудовых затрат, характерных для строительной отрасли Республики Ирак. В качестве обобщенного вывода о практическом результате данной разработки представлена пошаговая регрессионная методология формирования трудозатрат для выбранного вида работ.
КЛЮЧЕВЫЕ СЛОВА: затраты на рабочую силу, регулирование труда, нейронная сеть, статистика, управление строительством, регрессионный анализ, строительная отрасль, аппроксимация, нейросетевое моделирование, линейные модели, нелинейные модели, измерение, база данных
ДЛЯ ЦИТИРОВАНИЯ: ХуссейнХ.Ю.Б., Болотин С.А., ХурейниН.К.Р., БоханХ. Regression rationing of labour costs based on the estimation of their actual values by neural network modeling // Вестник МГСУ. 2023. Т. 18. Вып. 4. С. 638-650. DOI: 10.22227/1997-0935.2023.4.638-650
Автор, ответственный за переписку: Хошнав Юсиф Бабакр Хуссейн, yousif.babakr@gmail.com.
INTRODUCTION
The aim of this paper, to enhance the efficiency of the construction industry in the Republic of Iraq based on the adaptation of modern standards of labour costs to the construction industry.
Own regulatory framework should be created, and for its creation it is necessary to form an appropriate rational approach. An organic part of effective construction management is labour regulation. This is indicated by the experience of economically developed countries, where all areas of activity of enterprises are associated with labour standards: production, technical, organizational, financial, economic and social. Modern methods of labour regulation were created by specialists of economically developed countries. In order to enhance the efficiency of the functioning of the construction industry in the Republic of Iraq, its own regulatory framework must be created, and for its creation it is necessary to formulate an appropriate rational approach.
As one of the options, you can consider creating your own regulatory framework based on the use of classical timing methods. In its essence, the timing approach involves the physical measurement of the duration of construction processes, and various software tools are used to process the measurement results. For example, the Canadian company Quetech Ltd developed the WorkStudy + program, whose users include such well-known corporations as General Motors, Boeing, Deloitte & Touch.
Another timing method is the method of moment observations, which consists in the statistical processing of the results of observations carried out over a certain time period for individual groups of workers and mechanisms. Using this method, the observer systematically or at random points in time notes which actions are carried out by an employee or a group of employees at the time of observation.
A productive approach is implemented in the so-called physiological method, which provides extremely high accuracy and objectivity of measurement results, which is uncharacteristic of most other methods. The essence of this method is that labour standards are
determined on the basis of measurements of the en- e J
ergy costs of the employee obtained from the follow- n H
ing characteristics: oxygen consumed by the employee, k U
heart rate, pulmonary ventilation, body temperature and 3 ^
lactic acid concentration in the blood. The physiologi- S r
cal method has established itself as the most accurate in D y
rationing physical labour [1, 2]. o S
The presented excursion on the methods used to § œ
standardize labour makes it possible to understand that § 1
significant costs and time are required to create appro- o 7
priate databases. Therefore, another alternative to this 3 9
approach is the use of already developed regulatory da- ? 5
tabases that can be adapted to the construction industry C >
of the Republic of Iraq. In order to implement such an ° )
approach, it is necessary to analyze the available da- o S
tabases and establish such an up-to-date database that a N
would have the greatest correspondence to the actual § 3
labour costs characteristic of the construction industry d g
in the Republic of Iraq. > §
Consider the general features of building a base of i §
labour costs based on the analysis of the following sci- C o
entific publications [3-6]. In any country that has devel- > o
oped a database of labour costs, there are corresponding . •
organizations that produce collections of standards with ° t
different intervals. In the UK, these are BCIS (Build- c g
ing Cost Information Service) and Davis Langdon, an D £
AECOM Company (Spon's Price Books); in the USA, £ ^
Compass International (Global Construction Costs Year- z
book, etc.) and RSMeans (Building Construction Cost w y
Data Book, etc.); in France — Groupe Moniteur (col- <d k
lection of Le coùt des travaux de bâtiment, etc.), etc. In D d
the USSR, all norms were drafted on the basis of data 0 0 obtained by regulatory research stations, which were subsequently directed by the state into the construction
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industry. In the Russian Federation, which is the successor of the USSR, norms are also introduced by the state, but in many cases they are advisory in nature.
In most countries, the development of cost indicators and indicators of labour costs-is a separate type of commercial activity, and the price collections produced by them are applied on a voluntary basis. For example, RSMeans is a large commercial organization in the United States specializing in the development and production of a collection of construction cost indicators: single, elemental, and enlarged. The RSMeans compilation is published under the name Building Construction Cost Data and is annually released. It contains information about the unit performing the work, the output per 1 shift per 8 hours, labour costs in man-hours per unit of output, direct costs for materials, workers' wages, costs for machinery and equipment, and other indicators. The main purpose of the RSMeans collection is to form the cost of construction, and information on labour costs by type of work is informational. A distinctive feature of RSMeans collections is the lack of a technical part and a description of the quality requirements for the final product [7].
The French group of companies Groupe Moniteur publishes the collection Le cout des travaux de batiment (Cost of construction work). It is intended, first of all, to determine the cost of the project at the first stage of the investment process and is a set of aggregated prices. The collection includes 2 volumes — new construction and reconstruction. It is annually produced and it lists prices for each elementary type of work, indicators of labour costs, as well as cost indicators for expenditure items (auxiliary materials, devices, tools, etc.). A factor that distinguishes the French collection from the American collection is the presence of a brief technical part that describes the specific features of production processes.
The Finnish association "Construction Industry" created RATU standards, which are a card index of the standardization system for construction production, and they are made in the form of technological maps for construction work with a detailed description of the operations, and these standards contain enlarged and operational information on labour costs, the recommended composition of the link, the necessary documents and plans, the required materials, machines and equipment, safety measures, quality assurance measures, as well as special instructions and instructions. RATU cards are industrial and technological in nature, and data have been collected for them since the 70s by specialists of several major construction companies in Finland. With the development of engineering and technology, the file cabinet is being improved, and outdated standards are being replaced by new ones, but without a predetermined frequency1. Several dozen construction compa-
1 Porshneva L.G. Finnish experience: cadres decide everything. Bulletin of the National Association of Builders. 2011; 8(15):57-133. URL: http://sroamur.rf/doc/nostroy_bull/15.pdf (rus.).
nies and construction sites are constantly involved in collecting and replenishing the source data. The companies and construction sites participating in the study are located in various regions of Finland. Each rate is calculated based on data obtained from at least 10 objects. Moreover, its error does not exceed 10 %.
In Russia, the norms of labour costs are also production and are called "Unified Norms and Prices" which was later updated to be "State elemental estimated norms for the construction work" (SEENCW). All norms included in the SEENCW and RATU are determined by the normal conditions of work that do not take into account possible random fluctuations. Table 1 presents a comparison of regulatory documents that determine the norms of labour costs.
As a result of the presented analysis, it can be argued that the creation of a database of labour costs requires quite large resource costs. Therefore, for the Republic of Iraq, a less resource-intensive method can be recommended, namely, a regression method of creating a database, which is based on taking into account the actual labour costs of construction organizations.
Implementation of the proposed method can be carried out based on the usage of statistics on projects built in the republic, the information on which is reflected in the relevant executive documentation and supplemented by expert assessments of the conditions under which actual labour costs were received. From the point of view of the methodological implementation of the regression method, it is necessary to justify the regression procedure used in it. As the main alternatives, we consider the usage of traditional regression analysis and a more modern method based on the neural networks modeling.
MATERIALS AND METHODS
The problem of approximating the limited data obtained in solving complex problems can be solved both with the help of regression analysis and neural network modelling, built on the concepts presented in the monograph [8-13]. It is known that initially the multiple regression analysis method was focused on the description of linear models. To solve similar nonlinear models, the corresponding nonlinear form must be known and then individual models can be artificially reduced to a linear form, or a specific nonlinear regression algorithm should be developed for them [14]. Thus, to solve nonlinear problems by means of classical regression analysis, preliminary information on the form of the nonlinear connection of the desired function and its arguments is required.
In the general case, neural network modelling is used for a wide variety of applied [15]. In [16] and in the source2, the author asks the question: "What is the difference between neural networks and statistics?".
2 What is the difference between neural networks and statis-
tics? URL: https://helpiks.org/3-10999.html
Table 1. Comparison of normative documents defining labour standards during construction work
Name of characteristic SEENCW RATU RSMeans
Country Russia Finland USA
Type of organization issuing the norm State State Commercial
CHARACTER of the document Production standards Technological standards Estimated Norms
Main purpose Establishment of normative production of workers Guide for the production of works Pricing
Update Frequency The latest database update dates back to 2022 Supplement occur as develop or improve technologies Annually
Described Parameters 1. Scope of work. 2. The composition of the link. 3. Product meter. 4. Technical parameters of products. 5. The rate of time. 6. Rates (for workers) 1. Communication with other works. 2. Scope of work. 3. The indicators of labour costs enlarged and operational. 4. The composition of the link. 5. Required documents and plans. 6. The influence of variable factors on labour costs. 7. Consumption of materials. 8. Technology (operational with illustrations). 9. Required materials, machinery and equipment. 10. Safety. 11. Quality. Assurance Activities. 12. Special instructions 1. Type of work. 2. Technical parameters of products. 3. Product meter. 4. The composition of the link. 5. Daily output. 6. Labour costs. 7. Direct costs (materials, labour, equipment). 8. Cost taking into account overhead costs and profits (for subcontractor). 9. The coefficient on the general conditions of the work. 10. Overhead (for general contractor). 11. Profit (for general contractor)
Technical part There is There is There is not
Product quality requirements There is There is There is not
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His answer boils down to the following conclusion: "When describing their methods, statistics appeal to formulas and equations, and neuro computing to a graphical description of neural architectures". As a result, in the statistical approach, the main time for solving the problem is mainly spent on the analysis of pair correlations, while in neural network modelling, the main time is spent on training the networks.
It is believed that linear regression is useful for some tasks, but in many situations it is not effective, and polynomial regression is completely replaced by networks of high-order neurons. At the same time, many neural paradigms, such as Kohonen networks or the Boltzmann machine, have no direct analogues among statistical methods.
In the source3, James McCaffrey defines the goal of a regression problem — to predict the value of a numerical variable based on the values of one or more independent variables, called predictors, which can be either numerical or categorical. He identifies the fol-
3 McCaffrey J. Test run — neural network regression. Test Run — Neural Network Regression. URL: https://learn.mi-crosoft.com/en-us/archive/msdn-magazine/2016/march/test-run-neural-network-regression
lowing most common types of regression: polynomial regression, general linear model regression and neural network regression (NNR), and considers the latter type of regression to be the most powerful form.
In source4, the use of neural network technologies for processing the climate data table is described. For processing, we took the database on climate and vegetation of the Forest Institute of the Siberian Branch of the Russian Academy of Sciences in Krasnoyarsk, built on the mean long-term values of the climate characteristics measured at 170 weather stations. For 121 weather stations, there were values of six climatic parameters, the rest in different combinations did not have values of one to three parameters. The aim of the work was to predict the missing values, which shows such an important additional possibility of using neural networks in the face of insufficient data.
Another positive feature of the usage of neural networks is the rejection of a specific approximating expression, since neural networks can approximate the desired response surfaces by any continuous func-
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4 Application of neural network technologies for processing the climate data table. URL: https://studfile.net/preview/ 475257/page:23 (rus.).
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tions. In [17, 18], a generalized approximation theorem was proved, according to which, using linear operations and cascading neurons, it is possible to obtain a device from an arbitrary nonlinear element that calculates any continuous function with some predetermined accuracy.
We show examples of the unambiguous and ambiguous choice of an approximating expression based on traditional regression analysis. It is good when the form of the model is logically predetermined by the correct statement of the problem. For example, in [19], a methodology was described for assessing the conformity of real indicators of the dynamics of wear of structures and the corresponding standard values. The form of the logistic curve was taken as the basis, and the assessment was carried out by calculating the deviation of the average relative error of the survey data from the calculated values obtained from the technical wear standards of residential buildings adopted in the Russian Federation. This example shows the adequate applicability of classical regression analysis, but there are other examples.
In [20], to show the decrease in shift production — y from the number of workers — x, a regression dependence of the formy = a + b/x was used, in which a and b are the parameters of the desired regression (see Fig. 1).
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However, the presented dependence can equally well be replaced by an exponential form, which is the result of integrating a differential equation that takes into account a linear decrease in productivity from the number of workers.
Let us present another example showing the almost complete absence of physical meaning in the regression model. In [21], an equation is presented that determines the level of thermal protection of a blind section of the external walls when installing non-ventilated facade systems — K. It is also believed that the desired level of thermal protection is determined by the following regression expression and depends on 7 factors that measure the defective performance of work (from Xx to X7):
K=0.66843-0.08368Xj -0.01626X2 --0.17707X3 + 0.0287X4 -0.07676X5 -
-0.1673X6 + 0.0829X7 + 0.04412X,X3 -
6 7 1 3 (1) -0.02661XjX5 -0.04712XjX6 + 0.0165X1 X7 +
+0.01603X3X4 -0.0324X3X5 -0.06979X3X6 +
+0.0503X3X7 -0.0334X4X5 + 0.02285X4X6,
where X1 — gap at the junction of the insulation boards; X2 — the gap at the junction of the bracket with a heater plate; X3 — peeling of insulation boards from the base; X4 — deviation from the design value of the thickness of the base; X5 — deviation from the design value of the coefficient thermal conductivity of the base material; X6 — deviation from the design value of the thickness of the insulating layer; X7 — deviation from the design value of the coefficient thermal conductivity of the material of the insulating layer.
The inclusion in the regression formula (1) of the terms that determine the pairwise influence of certain factors on the final value of the thermal protection of the structure leads to inexplicable results. For example, an increase in the gap at the junction of the X1 boards and the detachment of the X3 insulation from the base reduce thermal protection, and the product of the same factors, on the contrary, increases thermal protection. Such physical inconsistencies are obtained with the purely formal application of such universal programs as the (STATISTICA).
As noted above, to describe the conditions for obtaining the values of actual labour costs, it is necessary to assess the compliance of the completed labour processes with their normative values. To do this, select the following parameters.
X1 — assessment of the conformity of the numerical and qualification composition of labour resources to their normative values; X2 — conformity assessment of labour supply with machinery and equipment; X3 — assessment of the security of the labour process with structures, materials, products, etc.
The characteristics presented fully comply with the accounting of production conditions laid down in the most technologically sound standards, such as the Russian (SEENCW) and Finnish RATU. However, in a number of Russian regions, due to their harsh climate, various correction factors are additionally introduced [22], which can also be considered part of the regulatory framework for labour costs adopted in the Russian Federation. Therefore, given the influence of climatic factors on labour productivity in construction, it is advisable for the Republic of Iraq to introduce an additional factor — X4, which shows the degree of neutralization of weather conditions during the production process.
We draw attention to the fact that the presented estimated characteristics can only be quantified based on the application of expert methods. It is also necessary to take into account that in the problem under
consideration, there is no theoretical relationship between the norms of labour costs and the security parameters for their implementation. The difference between the neural network modelling method and the classical regression analysis lies precisely in the fact that it does not need to establish a priori any dependence, since this method latently takes into account any nonlinearity. However, for the correct implementation of the neural network modelling method, the construction of an adequate neural network architecture is required.
Artificial neural networks are built on the principle of the organization and functioning of biological neural networks. They are a system of connected and interacting simple processors, defined as artificial neurons. At the same time, the processors themselves are quite simple, but being connected to a large network are capable of performing very complex tasks. Carrying out the training procedure for neural networks makes it possible to get the right result even on the basis of data that were not in the training set.
Basically, neural networks are based on the image of a formal neuron, the scheme of which is shown in Fig. 2. A formal neuron has a group of so-called synapses that connect this neuron to the outputs of other neurons through unidirectional input connections, the signals from which are designated as x..
Fig. 3, a shows the threshold activation function that generates a single signal at the output when a certain threshold at the input is indicated by the letter T. Fig. 3, b shows a linear activation function that generates a signal proportional to the signal at the axon input. Fig. 3, c shows the activation function that generates an output signal determined by the hyperbolic tangent. Fig. 3, d shows the logistic activation function calculated by the equation:
Y = -
1
l+Exp(-NET)
(3)
In the modern design of neural networks, other activation functions are also used, the features of the practical application of which can be found in the sources5, 6 and in [23-26]. The monograph [27] noted that the logistic activation function is the most popular, and therefore it can be used to solve our regression problem.
Using the logistic activation function, you can build the simplest network consisting of one neuron. The signals x. is applied to the inputs of the formal neuron, which are summed with the corresponding weights in the NET operator, which integrates the weighted signals according to formula (2), and the activation function chosen by us follows the adder. As a result of using the single-neural model, the functional relationship between the output and the inputs will have a non-linear representation, determined by the following formula:
Y
1
Fig. 2. Formal neuron
Each synapse is characterized by the value of the synoptic connection or its weight wi. As a result, the general state of each neuron is determined by the weighted sum of its inputs:
NET = Ywx. (2)
A neuron has an axon that determines the output signal of a given neuron, which enters the synapses of the following neurons. The output of a neuron is a function of its state, which is called an activation function. Artificial neurons use various activation functions. Fig. 3 shows the main types of activation functions.
1 + Exp (-w1 x1 - w2x2 - w3 x3 - w4x4)
(4)
The solution to the problem of finding the set of weights wi occurs in the training mode on a priori set sample size. In this case, the initial values of unknown weights are calculated using random numbers evenly distributed in the range from -0.5 to +0.5. This is followed by an iterative procedure, which is based on the determination of the output error, and then, based on the obtained output error, the weights are adjusted using the inverse error distribution algorithm. The iterative procedure ends when a certain result is determined by the network designer, for example, when a certain number of steps are exhausted, a given error is achieved, etc.
However, if we use the simplest one-neural network and the linear activation function for the solution, then the problem of finding unknown weights can be solved in a more efficient way using the least squares method. When using the activation function of the logistic type, it is also possible to reduce the problem to the least squares method by linearizing the problem
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5 Deep learning. URL: https://www.deeplearningbook.org/
6 CS-231N winter 2016 (Convolutional Neural Networks for visual recognition). CS231n-Andrej_Karpathy_Stanford. URL: http://cs231n.stanford.edu/2016/
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by applying the following change of the desired variable Y:
Z = ln-
1 - Y
(5)
Then, in this case, the solution of the problem will be reduced to a similar nonlinear approximation problem using a priori given form of equation (4).
The most used family in direct distribution networks are multilayer perceptrons, in which layered neurons have unidirectional connections between layers. Fig. 4 shows a two-layer perceptron, which we used as one of the networks, in which signals simulating independent variables are supplied to the neuron inputs, and a signal is removed from the output neuron that provides an approximation of the functional connection of type Y X2, Xy X).
Since neural networks work with numerical data lying in different ranges, normalization is carried out for all variables, which brings all the inputs and outputs to a single range from 0 to 1. If we denote the normalized parameter of the input value by L, then its value will be calculated according to the formula:
L =-
X,. - minX,. maxX,. - minX,.
(6)
RESULTS OF THE RESEARCH
The input and output data are normalized over the entire training array, an example of which is presented in Table 2.
The first four rows of Table 2 show the results of entering 10 data options on the conditions of security
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Wm 2.474 W2 1 1 0.832
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W1,1,3 2.834 0.957 K 7 W 2 1 3 0.678 0.908
-0.642 0.984 \\/1 W 2,1,4 -2.621 0.914
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W1,2,1 3.299 W -0.833 W1
W1,2,2 -3.134 2,2,1 W 2,2,2 -1.430 -1.108 Y
W 1,2,3 5.112 0.990 W -0.306 0.078 W2 1.000
W 1,2,4 -0.707 0.998 \S\fL 2.2.3 W 2.2.4 2.250 0.073 1.173 Y2
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W 2,3,1 0.361 / -1.281 A = Y- Y2
W 2,3,2 1.798 X2 3 / - W4 0.858
W 0.518 0.930 2.657 0.138
2.3.3 W 2.3.4 -2.599 0.934
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W1,4,1 2.439 X14 W 2,4,2 -1.248 X2 4
W1,4,2 W -5.841 0.011 W -0.342 0.117
1.4.3 W 1.4.4 0.965 0.002 2.4.3 W 2.4.4 4.640 0.109
Fig. 4. Two-layer perceptron approximator Y (X, X, X3, X4) Table 2. Example training array consisting of 10 data options
Option number 1 2 3 4 5 6 7 8 9 10
Workers Xp % 60 50 50 60 60 70 70 75 75 80
Machines X2, % 75 50 60 60 65 70 70 70 80 80
Materials X3, % 55 50 60 60 60 60 65 70 70 80
WeatherX4, % 65 50 70 70 75 75 80 80 80 80
Standardization Х1 0.33 0.00 0.00 0.33 0.33 0.67 0.67 0.83 0.83 1.00
Standardization Х2 0.83 0.00 0.33 0.33 0.50 0.67 0.67 0.67 1.00 1.00
Standardization Х3 0.17 0.00 0.33 0.33 0.33 0.33 0.50 0.67 0.67 1.00
Standardization Х4 0.50 0.00 0.67 0.67 0.83 0.83 1.00 1.00 1.00 1.00
Y, person cm/m3 0.75 0.72 0.705 0.69 0.68 0.66 0.645 0.63 0.615 0.6
Standardization Y 1.00 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00
Yield calculation — Y1 0.93 0.85 0.72 0.43 0.57 0.42 0.25 0.13 0.20 0.09
Yield calculation — Y2 0.93 0.81 0.68 0.35 0.56 0.40 0.23 0.16 0.19 0.14
Yield calculation — Y3 0.90 0.80 0.68 0.43 0.55 0.32 0.35 0.13 0.14 0.12
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of actual labour costs (ALC). The next four rows of Table 2 show the results of calculating the normalized values of the data on the security of regulatory conditions leading to the receipt of ALC. The question of how many observations you need to have to train the network is often difficult. In the general survey on neural networks presented in the source7, the following heuristic rule is given: the number of observations should be ten times the number of connections in the network. For our purposes, in view of the informational complexity of the primary problem, solved on the basis of collecting a large number of statistical data, the training array is determined by 10 options. This number of options satisfies the lower boundary of the representativeness of the data obtained in the process of creating the Finnish labour standards RATU.
After the normalized values that determine the conditions for the process, Table 2 presents a line that directly shows the values of the ALC determined by the letter — Y, and the next line presents its normalized values, which are calculated by a formula similar to formula (6). In the future, the actual data on labour costs will play the role of a "teacher", with the help of which weight factors are selected for all neurons of the adopted network.
As noted earlier, the ability to learn is a fundamental property of the neural network, and the learning process itself can be considered as setting up the network architecture and connection weights for the effective implementation of the regression task. There are different models that define the learning algorithm. In the case of training: "with a teachef', the neural network has the correct answers, that is, the known network outputs (ALC) for each variant of the input data. It has been empirically established for networks working with a "teachef' that the optimal number of hidden neurons is much smaller than when using training without a "teacher" [28].
In Fig. 4 all calculated weighting factors are represented by three indices, the first index determines the number of the network layer, the second—the number of the neuron in the layer, the third — the serial number of the input of a particular neuron. In the output layer, consisting of a single neuron, the corresponding weights are determined by a single index. In Fig. 4 the network output is represented by a set of normalized values obtained on the basis of the calculated values of the network output and their differences, by which all weighting factors are adjusted. When modifying the scales, the principle of error correction is used, which provides a gradual reduction in error.
As the error function, the sum of the squared errors is most often taken, i.e. when all errors of the output elements for all observations are squared and then summed. The best-known version of the neural net-
work learning algorithm is called the back propagation algorithm. In this algorithm, the error surface gradient vector is calculated, which indicates the direction of the shortest descent along the surface from a given point, and when moving along it, the error decreases.
A certain difficulty is the question of how to take the length of the calculation step, which determines its speed. To find the right speed in complex (from a computational point of view) networks, adaptive algorithms for dynamic speed control are used [29-31]. For example, with a long stride length, convergence will be faster, but there is a danger of jumping over the solution or (if the error surface has a particularly elaborate shape) to go in the wrong direction. It is believed that the right choice of learning speed depends on a specific task and is usually carried out empirically. For problems solved on the basis of statistics on labour costs, response surfaces can be quite complex, but without the presence of various kinds of singularities. Guided by the analysis made, we can conclude that the step length should be determined empirically, based on an acceptable training time. The entire learning process stops either when a certain number of steps are taken, or when the error reaches a certain level of smallness, or when the error stops decreasing.
Thus, the user can choose the desired stopping condition.
In the monograph [27], a recommendation is made regarding the equality of the number of neurons in the input layer to the number of input parameters. The following is a recommendation regarding the adequacy of the three hidden layers with a sequential decrease in the number of neurons in the layer as they move away from the entrance. However, another observation is also given: "Sometimes the best results are obtained if the number of parameters in all hidden layers is the same, but not reduced". There is one more rule of thumb: "The smaller the network, the fewer local minima in it, and in a large network of local minima there can be many".
We proceed to show the specific results of using a multilayer perceptron, the scheme and parameters of which are based on the scientific and practical recommendations considered above. The initial data presented in Table 2 were introduced into three types of neural networks: a single-layer, two-layer, and three-layer networks, which are marked in Table 3 by the corresponding indices.
Table 3. The results of the calculation of labour costs
Number of layers Y P Z P
1 0.540 0.96 0.556 0.96
2 0.554 0.94 0.556 0.96
3 0.556 0.97 0.557 0.97
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The results of calculating labour costs for different networks turned out to be fairly close, and their relative error did not exceed 1 %. Together, the calcula-
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tion showed that the coefficient of pair correlation of the results of a three-layer network with actual data was the highest value p = 0.97. Thus, based on the Table 3 and other similar experimental data, a three-layer network can be recommended for use.
The networks under consideration were tested for obtaining labour costs based on the results of introducing production standards, which, as you know, are the inverse of labour costs. As a result of the experiment, the actual workings were introduced instead of the actual labour costs, and the inverse value was calculated using the norm of the workings obtained as a result of neural network modelling. An example of the final discrepancy is presented in Table 3 in the column under the letter Z. As can be seen from the data in Table 3, the results of calculating direct and inverse values practically coincide, and the corresponding pair correlation coefficients have values close to maximum. Thus, the "universality" of the use of neural network regression to nonlinear dependence is "experimentally" confirmed.
Common characteristics for modelling networks are: the volume of the training sample, consisting of 10 options, the iteration step, which determines the calculation time and is assumed to be 0.2 and the total number of iterations is 10,000. At the same time, the calculation time carried out in the macro program and implemented in the environment Excel spreadsheet processor, less than one second.
The presented characteristics and the experiments associated with them allow us to adjust the parameters that determine the estimated time, that is, the speed and volume of iterations. Table 4 shows the network testing data associated with the estimation of the reproducibility error of the calculation results.
~ Table 4. Network test data for reproducibility of results
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Y2 551 546 550 550 551 549 551 551 548
Y3 559 567 556 568 564 562 556 565 569
N 10 11 12 13 14 15 16 17 18
Y1 543 543 542 542 542 540 542 541 543
Y2 547 551 551 553 554 548 539 554 551
Y3 566 557 571 555 567 552 553 560 569
CONCLUSION AND DISCUSSION
In the general case, to build an adequate neural network, it is necessary to use many neurons that form such a property of the network as its multilayer. By definition, an artificial neural network layer is a set of neurons that simultaneously receive signals from other neurons in a given network at each time step. As a result of the functioning of the multilayer network, the interaction of neurons occurs in layers. The choice of artificial
neural network architecture is determined by a specific task. Moreover, the architecture of the neural network can be considered as a directed graph having weighted connections between nodes, which are used as artificial neurons, shown in Fig. 2. According to the connection architecture, neural networks are divided into direct distribution networks in which graphs do not have loops, and recurrent networks which include feedbacks. Recursive networks are dynamic, since, due to feedbacks, the inputs of neurons are modified in them, which leads to a change in the state of the network. Direct distribution networks are static in the sense that for a given vector of input values they produce one set of output values that are not dependent on the previous state of the network. It follows that to solve the problem posed by us, a direct distribution network is applicable.
Based on the processing of the data presented, the value of the coefficient of variation was less than 2 %, and this is quite enough to determine the standard of labour costs. As mentioned above, the margin of error established by the developers of the Finnish labour standards RATU is limited to 10 %. A much larger error in the result of the regression determination of labour costs is introduced by the error in determining percent compliance with the regulatory conditions for the implementation of the labour process. For example, if we reduce all the initial data for assessing the percent of compliance with regulatory conditions by 10 %, then the calculated standard of labour costs will decrease by about the same amount. It follows that in order to obtain more relevant results when using the proposed method, it is necessary to combine it with effective methods of expert assessments, one of the variants based on the processing of the data presented, the value of the coefficient of variation was less than 2 %, and this is quite enough to determine the standard of labour costs. As mentioned above, the margin of error established by the developers of the Finnish labour standards RATU is limited to 10 %. A much larger error in the result of the regression determination of labour costs is introduced by the error in determining percent compliance with the regulatory conditions for the implementation of the labour process. For example, if we reduce all the initial data for assessing the percent of compliance with regulatory conditions by 10 %, then the calculated standard of labour costs will decrease by about the same amount. It follows that in order to obtain more relevant results when using the proposed method, it is necessary to combine it with effective methods of expert assessments, one of the variants of which is the method of stochastic qualimetry [32, 33].
As a preamble, we conclude with a quote from the monograph [27]. "The price that you have to pay for wider (non-linear) modelling capabilities using neural networks is that, by adjusting the network to minimize errors, we can never be sure that it's impossible to make even less mistake". This warning in no way
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reduces the efficiency of using neural networks, since there are sufficiently proven algorithms for verifying approximated data.
As a generalized conclusion on the practical result of the presented development, we can present a step-by-step methodology for the regression of the formation of labour costs for the selected type of work, which reduces to the following elementary procedures.
• A lot of construction objects are determined, on which there is executive documentation for the chosen type of work.
• According to the executive documentation for the selected type of work, labour costs are determined associated with a unit volume of work performed, which corresponds to the values of actual labour costs.
• According to the adopted scale, which should be uniform for the entire set of objects, the security of the actual conditions of work is assessed.
• Taking into account the normalization defined by formula (6), a training array of normalized data is formed.
• Next, the training array is processed in a neural network formed taking into account the characteristics described above, and as a result, data are obtained on approximating the dependence of labour costs on the conditions for their receipt.
• The final part of the regression reproduction of the norm of labour costs is based on the extrapolation procedure, which takes into account the full (100 %) security of meeting the conditions for the organization of the labour process.
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ReceivedAugust 16, 2022.
Adopted in revised form on March 10, 2023.
Approved for publication on March 23, 2023.
Bionotes: Khoshnaw Y.B. Hussein — postgraduate student; Saint Petersburg State University of Architecture and Civil Engineering (SPbGASU); 4 Vtoraya Krasnoarmeiskaya st., Saint Petersburg, 190005, Russian Federation; yousif.babakr@gmail.com;
Sergey A. Bolotin — Doctor of Technical Sciences, Professor; Saint Petersburg State University of Architecture and Civil Engineering (SPbGASU); 4 Vtoraya Krasnoarmeiskaya st., Saint Petersburg, 190005, Russian Federation; ID RSCI: 247664; sbolotin@mail.ru;
Nadim Q.R. Huraini — postgraduate student; Saint Petersburg State University of Architecture and Civil Engineering (SPbGASU); 4 Vtoraya Krasnoarmeiskaya st., Saint Petersburg, 190005, Russian Federation; ID RSCI: 1143546; nadimhuraini@gmail.com;
Haitham Boxan — postgraduate student; Saint Petersburg State University of Architecture and Civil Engineering (SPbGASU); 4 Vtoraya Krasnoarmeiskaya st., Saint Petersburg, 190005, Russian Federation; lecturer; Thi-Qar University; Republic of Iraq; haitham_kh9@yahoo.com.
Contribution of the authors: all authors have made an equivalent contribution to the preparation of the publication. The authors declare that there is no conflict of interest.
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Поступила в редакцию 16 августа 2022 г.
Принята в доработанном виде 10 марта 2023 г.
Одобрена для публикации 23 марта 2023 г.
Об авторах: Хошнав Юсиф Бабакр Хуссейн — аспирант; Санкт-Петербургский государственный архитектурно-строительный университет (СПбГАСУ); 190005, г. Санкт-Петербург, 2-я Красноармейская ул., д. 4; yousif.babakr@gmail.com;
Сергей Алексеевич Болотин — доктор технических наук, профессор; Санкт-Петербургский государственный архитектурно-строительный университет (СПбГАСУ); 190005, г. Санкт-Петербург, 2-я Красноармейская ул., д. 4; РИНЦ ID: 247664; sbolotin@mail.ru;
Надим К.Р. Хурейни — аспирант; Санкт-Петербургский государственный архитектурно-строительный университет (СПбГАСУ); 190005, г. Санкт-Петербург, 2-я Красноармейская ул., д. 4; РИНЦ ID: 1143546; nadimhuraini@gmail.com;
Хайтам Бохан — аспирант; Санкт-Петербургский государственный архитектурно-строительный университет (СПбГАСУ); 190005, г. Санкт-Петербург, 2-я Красноармейская ул., д. 4; преподаватель; Университет Ди-Кар; Республика Ирак; haitham_kh9@yahoo.
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Вклад авторов: все авторы сделали эквивалентный вклад в подготовку публикации. Авторы заявляют об отсутствии конфликта интересов.
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