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Based on actual lubricating oil production data and the base oil performance indexes of an enterprise, two nonlinear blending schemes corresponding to viscosity and freezing point and four linear blending schemes corresponding to acid value, flash point, oxidation stability, and carbon residue are given in this paper. On the premise that the error of each index is less than 5%, a linear weighted multi-objective optimization model based on integer nonlinear programming considering cost and performance is established, and the lubricating oil blending scheme is obtained. The results show that the blending formula is simple in form and convenient in calculation, and that the overall consistency between the calculated value and the measured value is good. At the same time, the relative error of each performance index, except residual carbon, of the scheme with weight value of (0.5, 0.5) is far less than 5%. Although the performance index is slightly inferior to that of the scheme with a weight value of (0, 1), it is far higher than that of the scheme with a weight value of (1, 0). The linear weighted multi-objective optimization model based on integer nonlinear programming proposed in this paper can well-optimize the blending scheme of industrial lubricating oil, and can re-select different weight combinations according to the actual situation, providing good prospects for application.

In this paper, Fibonacci collocation method is firstly used for approximately solving a class of systems of nonlinear Pantograph differential equations with initial conditions. The problem is firstly reduced into a nonlinear algebraic system via collocation points, later the unknown coefficients of the approximate solution function are calculated. Also, some problems are presented to test the performance of the proposed method by using the absolute error functions. Additionally, the obtained numerical results are compared with exact solutions of the test problems and approximate ones obtained with other methods in the literature.

The paper is devoted to the problem of determining the geoelectric structure of the soil within the procedure of testing the grounding arrangements of existing power plants and substations to the required depth in conditions of dense development. To solve the problem, it was proposed to use the Schlumbergers method , which has a greater sounding depth compared to the Wenner electrode array. The purpose of the work is to develop a mathematical model for interpreting the results of soil sounding by the Schlumberger method in the form of a four-layer geoelectric structure. Methodology. To construct a mathematical model, it is proposed to use the solution of a particular problem about the field of a point current source, which, like the observation point, is located in the first layer of a four-layer soil. Based on this expressions, a system of linear algebraic equations of the 7-th order with respect to the unknown coefficients ai and bi was compiled. On the basis of its analytical solution, an expression for the potential of the electric field was obtained for conducting VES (the point current source and the observation point are located only on the soil surface). Results. Comparison of the results of soil sounding by the Schlumberger installation and the interpretation of its results for the same points shows a sufficient degree of approximation: the maximum relative error does not exceed 9.7 % (for the second point), and the average relative error is 3.6 %. Originality. Based on the obtained expression, a test version of the program was implemented in Visual Basic for Applications to interpret the results of VES by the Schlumberger method. To check the obtained expressions, the interpretation of the VES results was carried out on the territory of a 150 kV substation of one of the mining and processing plants in the city of Kriviy Rih. Practical significance. The developed mathematical model will make it possible to increase the sounding depth, and, consequently, the accuracy of determining the standardized parameters of the grounding arrangements of power stations and substations., Робота присвячена проблематиці визначення геоелектричної структури ґрунту в межах випробування заземлювальних пристроїв діючих електричних станцій та підстанцій на необхідну глибину в умовах щільної забудови. Для вирішення проблеми запропоновано використати установку Шлюмберже, яка має більшу глибину зондування у порівнянні з установкою Веннера. За допомогою методів інтегро-диференційних рівнянь було отримано аналітичні вирази для інтерпретації результатів зондування ґрунту установкою Шлюмберже у випадку чотиришарового ґрунту. Для перевірки отриманих виразів була проведена інтерпретація результатів вертикального електричного зондування на території підстанції 150 кВ одного з гірничо-збагачувальних комбінатів: максимальна відносна похибка не перевищує 9,7 %, а середня – 3,6 %.

Woodchips as a common biomass are widely used in industrial processes and our daily lives. The moisture content in woodchips has a significant effect on the processing and combustion efficiency of woodchips. Therefore, it is necessary to develop a suitable method to measure the moisture content of woodchips. Capacitive sensors are widely used in various fields due to their simple structure, low cost and non-destruction to the samples. Because of the uniform sensitivity distribution compared to the parallel plate sensor design, a helical capacitive sensor is used in this paper to measure the moisture content of woodchips. The structure of the sensor is firstly optimized based on the orthogonal test method using a finite element model. Then, the influence of particle size and packing density of biomass on the capacitance readings is investigated. Finally, the moisture content is predicted through data driven modelling. Woodchip samples with different particle sizes, moisture content and packing densities are used to verify the model. It is found that the relative error between the predicted and reference values is within ±10% over the range of moisture contents from 7% to 49%.

Spectral reconstruction (SR) algorithms attempt to recover hyperspectral information from RGB camera responses. Recently, the most common metric for evaluating the performance of SR algorithms is the Mean Relative Absolute Error (MRAE)—an ℓ1 relative error (also known as percentage error). Unsurprisingly, the leading algorithms based on Deep Neural Networks (DNN) are trained and tested using the MRAE metric. In contrast, the much simpler regression-based methods (which actually can work tolerably well) are trained to optimize a generic Root Mean Square Error (RMSE) and then tested in MRAE. Another issue with the regression methods is—because in SR the linear systems are large and ill-posed—that they are necessarily solved using regularization. However, hitherto the regularization has been applied at a spectrum level, whereas in MRAE the errors are measured per wavelength (i.e., per spectral channel) and then averaged. The two aims of this paper are, first, to reformulate the simple regressions so that they minimize a relative error metric in training—we formulate both ℓ2 and ℓ1 relative error variants where the latter is MRAE—and, second, we adopt a per-channel regularization strategy. Together, our modifications to how the regressions are formulated and solved leads to up to a 14% increment in mean performance and up to 17% in worst-case performance (measured with MRAE). Importantly, our best result narrows the gap between the regression approaches and the leading DNN model to around 8% in mean accuracy.