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• GROUPING PREDICTORS IN COMBINED PIECEWISE LINEAR REGRESSION

  S.I. Noskov , S.V. Belyaev

  120-127

  2025-10-01

  Abstract ▼

  The article provides a brief overview of publications on the application of combined structures containing known model forms as constituent elements in mathematical modeling of complex systems. In particular, the following are considered: an algorithm for estimating parameters for creating mathematical models of dynamic systems; structured mathematical models of an oxygen electrode and biological wastewater treatment; a combined model including ion exchange between calcium and copper; a combination of non-standard finite-difference schemes and the Richardson extrapolation method to obtain numerical solutions of two models of biological systems; a mathematical formulation of the problem and a heuristic approach to optimal planning of delivery routes in a multimodal system; a mathematical model for optimizing strategic and tactical decisions in all types of biomass-based supply chains; a method for developing models of various types for elements of chemical-engineering systems taking into account various types of available information and combining these models into a single complex. Two variants of the problem statement for calculating the estimates of the parameters of a combined piecewise linear regression are formulated: with a non-empty and empty intersection of the index sets that define the composition of the independent variables in the linear and piecewise linear components of the model. It is shown that in both cases, when the sum of absolute deviations of approximation errors is selected as the loss function, both variants are reduced to linear-Boolean programming problems. Two versions of a combined piecewise linear regression model of revenue of the mining and metallurgical company Severstal are constructed. The following production volumes are used as independent variables of the model: hot-rolled, cold-rolled and galvanized sheet, sheet with another metal coating, sheet with a polymer coating, rolled products, hardware products.

• RANDOM ERROR OF PULSE DURATION MEASUREMENT WITH OSCILLATIONS AT THE TOP BY MULTI-THRESHOLD DURATION METERS

  D.V. Belyaev, D.E. Gubarev, К. Е. Rumyantsev

  2021-12-24

  Abstract ▼

  In systems for automatic measurement of the duration of video pulses, various devices for amplifying
  and shaping pulses of a normalized level are used, the duration of which is equal to the duration
  of the input signals. A rough measurement of the duration of video pulses can be made with onethreshold
  meters. More accurate are multi-threshold and floating-threshold meters. Pulse duration
  meters have found wide application in electronic warfare equipment, in measuring technology. The
  variation in the shape of electrical signals does not allow the use of a single measurement method,
  which is the best for all shapes, therefore, the search for technical solutions that satisfy the conflicting
  requirements continues: a wide range of durations and duty cycles. The aim of this work is to
  carry out a mathematical analysis of the random error in measuring the pulse duration with oscillations
  at the top by multi-threshold duration meters. In the course of the work, the results of a numerical
  experiment were obtained to measure the duration of a pulse with oscillations at the top using
  multi-threshold duration meters. And also a comparison was made of four multi-threshold duration
  meters for the investigated pulse shape. The calculation results are presented for a signal dynamic
  range of 60 dB and an amplitude quantization step of 3dB and 12 dB.

• CONTROL SIGNAL GENERATOR OF A NEW GENERATION

  D.V. Belyaev, А.B. Rempe, А. N. Zikiy

  2023-08-14

  Abstract ▼

  Control signal generators (SCS) allow for the rapid assessment of the condition of radio receiving
  equipment during its operation, therefore, much attention is paid to their research and
  development. Very often, noise generators or generators on Gann diodes with low frequency stability
  are used as control signal generators. Due to the appearance of available frequency synthesizer
  chips with a built-in voltage-controlled generator, an attempt has been made to use a frequency
  synthesizer as a master generator in a control signal generator. The use of a frequency
  synthesizer chip with sequential loading of control codes led to the need to use a microcontroller.
  An experimental study of a two-frequency control signal generator has been carried out. The functional
  scheme of the GCS is presented. A brief description of the element base is given. A twofrequency
  synthesizer Si4133GT was used as a master generator. As the results of the study are
  presented: – output signal spectrum; – waveforms of the output signal; – dependence of the output power on the frequency for three instances of the cell; – dependence of the output power on the
  attenuator control code. The following results have been achieved: – operating frequencies 450
  and 1200 MHz; – the output power of each channel is at least 100 MW; – relative instability of
  the carrier frequency 10-5; – the attenuation range of the step attenuator is not less than 20 dB;
  – pulse modulation depth of at least 30 dB; – duration range of modulating pulses from 10 to
  100 microseconds; – the range of variation of the repetition period from 300 to 1000 microseconds;
  – it is possible to enter an external control signal. By most parameters, the developed GCS
  exceeds the parameters of the GCS previously developed at the enterprise. GCS is supposed to be
  used as part of a multi-channel receiver.