Vol 28, No 2 (2020)

The paper proposes a method for constructing digital filters for solving inverse problems of recovering signals, time series, and images using an approximation approach. The considered inverse problems belong to the class of incorrectly posed ones and require the use of certain regularizing procedures to synthesize optimal reconstruction algorithms and solve computational problems associated with this.

In this regard, a method is proposed for constructing an approximation model of the weight function of the inverse (reconstruction) filter, based on the criterion of the minimum quadratic error of the mismatch of the distorted signal model obtained after the direct (distorting) filter processes the reconstructed (unknown) signal and the existing distorted signal. The weight function of the direct filter is assumed to be known.

The statement of the problem of reconstructing signals, time series, and images in the case of a one-dimensional point scattering function is formulated. An algorithm is presented that allows one to reduce the amount of computation when finding the values ​​of the weight function of the inverse filter.

The algorithms were tested on model examples when processing real images obtained by remote sensing of the Earth, as well as on specially formed contrast images. To quantify the quality of reconstruction, a relative mean-square measure of the difference between the reference and reconstructed signals (images) was used. The results of testing show that using this approach allows to reduce the error of recovery, which gives an advantage in solving problems of approximation and data recovery.

The formulation and method of solution of the problem of time-optimal control of induction heating process of an unlimited plate with two control actions on the value of internal heat sources with technological constraint in relation to a one-dimensional model of the temperature field are proposed. The problem is solved under the conditions of a given accuracy of uniform approximation of the final temperature distribution over the thickness of the plate to the required. The method of finite integral transformations is used to search for the input-output characteristics of an object with distributed parameters with two control actions. The preliminary parameterization of control actions based on analytical optimality conditions in the form of the Pontryagin maximum principle is used. At the next stage reduction is performed to the problem of semi-infinite optimization, the solution of which is found using the alternance method. The alternance properties of the final resulting temperature state at the end of the optimal process lead to a basic system of relations, which, if there is additional information about the shape of the temperature distribution curve, is reduced to a system of equations that can be solved. An example of solving the problem of time-optimal control of temperature field of an unlimited plate with two offices is carried out in two stages. At first stage the case of induction heating without maximum temperature constraints is considered, at the second stage is carried out on the basis of the results of the first stage to obtain the solution subject to the limitation on the maximum temperature of the heated billet.

Aspects of gas permeability measurement on samples of terrigenic and carbonate rocks of oil and gas collectors, as well as artificial samples on the domestic Darsimeter plant are considered. The following types of reservoir rocks were used for the study: pore, fractured, cavernous. The scope of application of the Darcy Law for pore-type rocks was clarified, which is limited to small pore pressures. Permeability coefficients were determined taking into account the gas slip-law effect of Klinkenberg on regression equations. Apparent permeability at low pressure drops was determined. For a number of samples with low permeability, the pore size was calculated to relate to the apparent permeability value. The calculation was carried out on the basis of the obtained values of structural coefficients of rocks by the method of electrical resistivity and on the basis of porosity values determined using the Preobrazhenskiy method.For a number of crack and capillary samples, the relationship between the pressure gradient and the filtration rate became nonlinear, and types of filtration laws were determined. Establishing the applicability of Darcy 's law or nonlinear law was controlled by constructing indicator curves and calculating the Reynolds number. For terrigenic rocks of high permeability, errors of measurement of gas permeability coefficients at different pressure drop intervals were determined: dispersion and coefficient of variation showing low values were calculated.

This publication discusses the task of developing an induction heating system for billets made of aluminum alloy with a given limit on the permissible temperature deviation. The purpose of the work is to determine the parameters of the inductor sections and the settings of the control system to achieve a given distribution of the billet before being fed under the press. The complexity of the problem is associated with the presence of several heater sections that differ in length from the workpieces, which leads to an additional factor leading to an increase in the unevenness in the distribution of temperature in the load. The model of the electromagnetic process is built taking into account the change in resistivity in the workpieces. When searching for a more efficient calculation algorithm, a joint solution to the thermal and electromagnetic problems is considered, which allows to simplify the procedure for exchanging data between applications. This approach is very convenient for solving problems that are not connected with harsh conditions with the achievement of the final state. When modeling thermal processes, the formulation of the problem takes into account all the features associated with radiant heat transfer between extended surfaces having different temperatures, temperature dependences of the workpiece parameters, a varying heat release region due to displacement. As options for a heating system, software control and a multichannel system with control correction for temperature control at one point are considered. When simulating a multi-channel heating control system, built-in software functions were used that made it possible to form control actions for each channel and recommend the location of temperature sensors providing high-quality control of heating.