Modeling and optimization of the consumer properties of mobile energy units in the agricultural industry

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Introduction

Agricultural industry development requires innovative production equipment and technology that ensure high performance of agricultural operations. Among those equipment and technology widely used in the agricultural industry are mobile power units (MPUs). They couple with various agricultural implements both hauled and mounted. According to Resolution No. 740 of the Russian Federation On Determining Functional Performance (Consumer Properties) and Performance of Agricultural Machinery and Equipment, agriculture requires machinery and equipment with high functional performance, including MPUs (tractors). State-of-the-art agricultural MPUs used in agriculture are sophisticated devices consisting of many parts and assemblies and performing various crop production, livestock farming, gardening, and other operations. They have multiple performance, technology, and environmental properties. At the stage of MPU design and operation, functional performance specifications of consumer properties require optimization. Such specifications are numerous and the optimization problem has multiple criteria.

Materials and methods

Collection and analysis of scientific works, research papers, and other references on the R&Ds of intelligent vehicles and machinery; key indicators of consumer properties of agricultural MPUs, and improvement of guidelines and software for multi-criteria optimization calculations of MPU performance. Methods of scientific generalization and statistical processing of available information and analytical Russian and foreign references were used to solve the problem.

Results and discussion

We analyzed consumer properties of agricultural MPUs and built a classification of specifications, i.e. quality criteria of MPUs (Fig. 1).

 

Fig. 1. Classification of properties that are quality criteria of a mobile energy unit.

Рис. 1. Классификация характеристик — критериев качества МЭС.

 

When solving problems with a single-criterion statement, a single vector and a single objective function are usually produced. Depending on the problem statement, by minimizing or maximizing the objective function data, we find the best value of a specific objective function. However, due to certain limitations of single-criteria optimization methods, recent years have seen a trend toward development and design of multi-criteria optimization (MCO) methods and tools. MCO is typically reduced to the search for Pareto–optimal sets of quality criteria that characterize the optimized object. Pareto–optimal sets are points (object variants) with values that cannot be improved simultaneously without degradation of at least one of them in the totality of all criteria [1–3].

Based on the analysis of the classification of functional, operational, and economic performance specifications of MPUs (consumer properties) and their expert review, we developed a multi-criteria problem of substantiating the performance of MPUs. As a result, the MCO problem statement includes the following 5 quality criteria: soil pressure (q^кₘₐₓ) productivity (W), total repair and maintenance costs (З_pᵢ), energy rate based on the relative reduction of the total specific fuel and energy costs of the MPUs(Э_wⁿ), and energy efficiency (E_c). The problem is stated as follows:

$\left(\begin{array}{l}{q}_{\text{max}}^{к}=F_1\left(x_1,x_2,\dots ,x_n\right)\\ W=F_2\left(x_1,x_2,\dots ,x_j\right)\\ {Э}_w^{п}=F_3\left(x_1,x_2,\dots ,x_i\right)\\ {З}_{p_i}=F_4\left(x_1,x_2,\dots ,x_k\right)\\ E_c=F_5\left(x_1,x_2,\dots ,x_m\right)\end{array}\right)\Rightarrow \mathrm{opt}.\text{(Pareto set)}$                                                                    (1)

where F₁–F₅ are quality criteria; x₁, x₂,..., x_n, x_i, x_j, x_k, x_m are variable parameters.

Mathematical models of the above criteria include numerous variable parameters related to the operational features of the MPUs, i.e. drawbar force, implement effective width, operational speed, shift time, specific fuel consumption of the MPU, etc.

Procedural flow chart of the algorithm used to solve the MCO problem of MPU specifications is shown in Fig. 2.

 

Fig. 2. The block diagram of the multi-criteria optimization of the properties of a mobile energy unit.

Рис. 2. Блок-схема алгоритма многокритериальной оптимизации (МКО) характеристик мобильных энергосредств (МЭС).

 

In addition, when building and finding the optimal set for the problem, the following tasks were solved: preparation of initial data, preparation of the algorithm, calculation of the quality criteria value, charting of the tests table, introduction of criteria and functional restrictions, development of admissible sets, and obtaining Pareto sets.

Selection of admissible solutions with the introduced criteria restrictions is shown in Fig. 3.

 

Fig. 3. Selection of the set of acceptable solutions.

Рис. 3. Иллюстрация выбора множества допустимых решений.

 

Thus, the analytical decision maker dialog system allows us, with 1,000–1,500 points at the initial stage, to eventually obtain one or two Pareto points that are not inferior to each other in terms of the criteria set.

 

Table 1. Initial data of the variables for a mobile energy unit of the drawbar category 1.4 (basic tractor is the MTZ-82.1, the alternative tractor is the Belarus-1025)*

Таблица 1. Исходные данные варьируемых параметров по МЭС тягового класса 1,4 (базовый трактор- МТЗ-82.1, аналог «Беларус-1025»)*

Variable parameters	Plowing	Sowing	Chemicalization (pesticides application)
Bp— Implement effective width, m	1,05–1,4	2,1–5,4	10,08–24
β — Effective width utilization ratio	0,8–1,0	0,8–0,95	0,8–0,95
Vp — Implement operational speed, km/h	8–10	10–15	6–12
Tсм — Standard shift hours, h	8	8	8
τ — Shift hours utilization ratio	0,8–0,85	0,7–0,8	0,7–0,8
Э — Tractor energy consumption, mJ/h	110–140	107–140	110–130
Э — Energy consumption of fuel for the base-case scenario and ratios,* mJ/h	880–910	880–1000	850–950
а is the ratio of structural masses of a new and base-case tractors	0,8–0,9	0,8–0,9	0,8–0,9
b is the ratio of the new specific fuel consumption to the base-case MPU	0,75–0,9	0,71–0,8	0,75–0,85
с is the ratio of the replacement new and base-case MPU productivity based on the range of operations	1,2–1,28	1,1–1,27	1,2–1,28
nм is the number of machines or implements mounted on the MPU (supplied with the device), pcs	1	1	1
Бмⱼ is the price of j-th device (excl. VAT), RUB	2 500 000–3 500 000	2 700 000–3 600 000	2 750 000–3 800 000
μдв is the engine efficiency	0,38–0,4	0,38–0,4	0,38–0,4
Pдв is the engine power, kW	50–75	50–75	50–75
μкпд.тр is the tractor propulsion efficiency	0,65–0,75	0,65–0,75	0,65–0,75
W is the productivity rate, ha/h	0,54–1,12	1,01–2,84	2,90–8,52
m is the MPU weight (for drawbar category 1.4), kg	4000–4200	4700–5000	4100–4600

*The data are sourced from the Concept System of Machines and Technology for Comprehensive Motorization and Automation of Agricultural Industry up to 2020 developed by the Federal Scientific Agroengineering Center VIM of the RUSSIAN AGRICULTURAL ACADEMY (Volume 1, Plant Growing. Moscow, 2012). When compiling the initial data, it was assumed that the following machine sets would be used: plows PLN-3-35, PLN-4-35U; seeders SZ-3,6A, SZP-3,6A, SZT-3,6A, and sprayers OSH-3000, OPSH-15-03, OP-2000-01.

 

Similar problems for tractors of drawbar category 1.4 were solved for 3 specific processes (plowing, sowing, chemicalization), where multi-criteria optimization was used to substantiate the effective consumer properties of mobile power units. A similar algorithm may be applied both at the stage of design, development, and production of the MPUs and at the stage of MPU operation during creation of the vehicle and tractor fleet. Interviews with existing authors and analysis of the references allowed us to conclude that we can use up to five quality criteria. According to the mathematical models of the quality criteria used, the initial data for the MPUs of drawbar category 1.4 were generated for all 3 processes (Table 1) [1–7].

Optimization calculations are shown in the summary tables of Pareto–optimal points for MPUs when performing Plowing, Sowing, and Chemicalization processes shown in Table 2 [1–7].

 

Table 2. Summary table of values of the Pareto-optimal points for a mobile energy unit of the drawbar category 1.4 at selected technological operations

Таблица 2. Сводная таблица значений Парето-оптимальных точек для МЭС тягового класса 1,4 на выбранных технологических операциях

Quality criteria	Plowing		Sowing		Chemicalization
	Point	Criterion value	Point	Criterion value	Point	Criterion value
F1 — Soil pressure, kPa	69 245 363 387 599	163,639 139,924 145,012 151,082 127,984	15 39 51	149,327 165,623 152,707	11 129 287	162,877 177,513 122,941
F2 — Productivity rate, ha/h	69 245 363 387 599	0,633 1,214 1,171 1,571 1,588	15 39 51	2,872 3,391 2,966	11 129 287	3,463 3,541 3,689
F3 — Energy rate based  on the relative  reduction of the total specific MPU costs, %	69 245 363 387 599	25,094 28,381 35,036 25,098 33,693	15 39 51	35,342 22,051 30,203	11 129 287	21,962 22,806 19,552
F4 — Total repair and maintenance  costs, ’000 RUB	69 245 363 387 599	149,331 149,743 149,216 179,461 224,861	15 39 51	178,386 188,332 202,011	11 129 287	207,562 124,408 125,089
F5 — Energy efficiency,  kWh/ha	69 245 363 387 599	42,788 23,867 19,713 17,084 15,296	15 39 51	24,173 18,510 12,706	11 129 287	37,195 32,101 29,637

* Сorresponding author / Автор, ответственный за переписку

 

Thus, according to the decision maker and based on resulting calculations, the below points have been selected as the most preferable among the obtained Pareto points when operating a category 1.4 tractor:

1. Plowing: productivity rate is 1.17 ha/h; soil pressure: 145 kPa; total costs: RUB 149,200; energy rate: 35.0%, energy efficiency: 19.7 kW*ha/h.
2. Sowing: productivity rate is 2.87 ha/h; soil pressure: 149.3 kPa; total costs: RUB 178,390; energy rate: 35.3%, energy efficiency: 24.17 kW*ha/h.
3. Chemicalization: productivity rate is 3.541 ha/h; soil pressure: 177.513 kPa; total costs: RUB 124,408; energy rate: 22.8%, energy efficiency: 32.10 kW*ha/h.

Conclusion

Today, due to the fact that the diversity of operational, functional, and production performance specifications of equipment has greatly increased, it has become necessary to solve optimization problems of MPU consumer properties using a multi-criteria statement at the stage of the MPU design and operation.

To simulate and optimize consumer properties of the MPU, the agricultural sector has developed a software package to solve the MCO problem allowing to solve problems with more than 50 variable parameters and 20 quality criteria.

The analysis of the classification of functional, operational and economic performance specifications of the MPU (consumer properties) and their expert review resulted in identifying 5 main quality criteria, including soil pressure (q^кₘₐₓ), productivity rate (W), total repair and maintenance costs(З_pᵢ), energy rate based on the relative reduction of the total specific fuel and energy costs of the MPU (Э_wⁿ), and energy efficiency (E_c).

Thus, for complete understanding of the optimal operational consumer properties of mobile power units, we selected MPUs of drawbar category 1.4 and the three most important operations (plowing, sowing, and chemicalization).

This method allows argumentation at the stage of approval and setting the optimal functional MPU parameters and at the design stage; at the stage of the equipment operation, it is possible to select machines with the specifications selected by the decision maker, including for selecting the coupling capability of implements or when creating a vehicle and tractor fleet as a whole.

ADDITIONAL INFORMATION

Author contributions. T.Z. Godzhaev — development of the mathematical models of economic quality criteria of mobile energy units, optimization models and building of the block diagram of the algorithm; V.A. Zubina — problem statement, development of the mathematical models of functional properties of mobile energy units, formation of a list of variables, preparation of the introduction and conclusions; conducting optimization calculations. All authors made a substantial contribution to the conception of the work, acquisition, analysis, interpretation of data for the work, drafting and revising the work, final approval of the version to be published and agree to be accountable for all aspects of the work.

Disclosure of interests. The authors declare the absence of obvious and potential conflicts of interest.

Funding sources. This study was not supported by any external sources of funding.

ДОПОЛНИТЕЛЬНАЯ ИНФОРМАЦИЯ

Вклад авторов. Т.З. Годжаев — разработка математических моделей экономических критериев качества МЭС, оптимизационных моделей и построение блок-схемы алгоритма; В.А Зубина — постановка задачи, разработка математических моделей функциональных характеристик МЭС, формирование перечня варьируемых параметров, подготовка введения и выводов; а также проведение оптимизационных расчётов. Авторы подтверждают соответствие своего авторства международным критериям ICMJE (авторы внесли существенный вклад в разработку концепции, проведение исследования и подготовку статьи, прочли и одобрили финальную версию перед публикацией).

Раскрытие интересов. Авторы декларируют отсутствие явных и потенциальных конфликтов интересов, связанных с публикацией настоящей статьи.

Источники финансирования. Авторы заявляют об отсутствии внешнего финансирования при проведении исследования.

About the authors

Teymur Z. Godzhaev

Federal Scientific Agroengineering Center VIM

Author for correspondence.
Email: tgodzhaev95@yandex.ru
ORCID iD: 0000-0002-4496-0711
SPIN-code: 1892-8405
Scopus Author ID: 57216628693

Head of the Modeling and Optimization of MEUs Sector

Russian Federation, 5, 1st Institutsky dr, Moscow, 109428

Valeria A. Zubina

Federal Scientific Agroengineering Center VIM

Email: lera_zubina@mail.ru
ORCID iD: 0000-0002-6657-1899
SPIN-code: 3410-5062
Scopus Author ID: 57201638381

Cand. Sci. (Engineering), Senior Researcher of the Laboratory of Moving Energy Units

Russian Federation, 5, 1st Institutsky dr, Moscow, 109428

References

Supplementary files