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EN
The main purpose of the article is to develop a multifactorial model for rapid assessment of the efficiency of biological wastewater treatment reactors. A mathematical model of the process of biological wastewater treatment has been developed based on: changes in the concentration of organic contaminants in the bioreactor over time, taking into account the uneven flow of wastewater to the treatment plant, the process of substrate entering the bioreactor (different amounts may enter at different times). The software implementation of the proposed algorithm for solving the corresponding model problem in Python is carried out. The results of computer experiments on the study of the efficiency of wastewater treatment in biological treatment reactors for different operating conditions of facilities are presented. In particular, such processes were considered with taking into account the unevenness of the load, because the maximum cleaning loads are in the morning and in the evening. The task was solved to simulate a real situation and show how cleaning takes place at the maximum load at a certain time of the day. The results obtained will be useful for calculations in the design of biological treatment facilities or in the reconstruction of existing bioreactors for their prospective operation under new operating conditions.
EN
The article describes the development of a model problem for electrocoagulation treatment of industrial wastewater taking into account changes in voltage and current. The study included computer simulation of the change in the concentration of iron at the output of the electrocoagulator at variable current levels. The laboratory-scale plant was developed for the photocolorimetric analysis of the iron-containing coagulant. It consisted of a flowing opaque cel through which water is pumped with a constant flow and also the block for processing and storage of information. Such structure allows to reduce human participation in the measurement process and to ensure the continuity of measurement without any need for sampling of the tested material, as well as to reduce the measurement cost. During the processing of results, graphical dependences were determined between RGB-components of water colour and the corresponding concentration of total iron and Fe3+ in water.
EN
The paper deals with the issue of production scheduling for various types of employees in a large manufacturing company where the decision-making process was based on a human factor and the foreman’s know-how, which was error-prone. Modern production processes are getting more and more complex. A company that wants to be competitive on the market must consider many factors. Relying only on human factors is not efficient at all. The presented work has the objective of developing a new employee scheduling system that might be considered a particular case of the job shop problem from the set of the employee scheduling problems. The Neuro-Tabu Search algorithm and the data gathered by manufacturing sensors and process controls are used to remotely inspect machine condition and sustainability as well as for preventive maintenance. They were used to build production schedules. The construction of the Neuro-Tabu Search algorithm combines the Tabu Search algorithm, one of the most effective methods of constructing heuristic algorithms for scheduling problems, and a self-organizing neural network that further improves the prohibition mechanism of the Tabu Search algorithm. Additionally, in the paper, sustainability with the use of Industry 4.0 is considered. That would make it possible to minimize the costs of employees’ work and the cost of the overall production process. Solving the optimization problem offered by Neuro-Tabu Search algorithm and real-time data shows a new way of production management.
PL
Wstęp: W artykule przedstawiono koncepcję sterowania systemem produkcyjnym, pozwalającą na zachowanie jego stabilności, a tym samym na realizację założonych planów produkcyjnych. W tym celu zaproponowano połączenia modeli symulacyjnych i modeli sztucznych sieci neuronowych (SSN) systemu produkcyjnego. Połączenie obydwu typów modeli było możliwe dzięki opracowaniu hybrydowego modelu systemu ekspertowego do oceny możliwości realizacji planu produkcji (celu) w zależności od wielkości ryzyka i poziomu stabilności analizowanego systemu produkcyjnego. Analizowany problem - możliwość realizacji planów produkcyjnych w zależności od wielkości ryzyka i poziomu stabilności systemu produkcyjnego - jest trudny do zamodelowania matematycznego. Jednak na podstawie analizy danych, pochodzących z modelu symulacyjnego i modelu ANN, można uzyskać informacje dotyczące zależności odpowiadających sobie wartości wejściowych i wyjściowych. Metody: Na podstawie przedstawionego sposobu zarządzania procesu produkcyjnego z wykorzystaniem modeli komputerowych, przeanalizowano możliwości zastosowania modeli symulacyjnych i modeli ANN w ocenie stabilności i ryzyka systemów produkcyjnych. Dokonano analizy i porównania obydwu typów modeli ze względu na sposób budowy oraz rodzaj danych wejściowych i wyjściowych. Wyniki: Na bezpośrednie połączenie modeli symulacyjnych i modeli SSN nie pozwala ich odmienna budowa, specyfika oraz inne rodzaje danych wejściowych i wyjściowych. Dlatego prezentowana w artykule koncepcja fuzji obydwu typów modeli odbywa się poprzez bazę wiedzy eksperckiej i wnioskowanie rozmyte. Wnioski: Na potrzeby sterowania systemem produkcyjnym, zaproponowano budowę hybrydowego modelu systemu ekspertowego do oceny możliwości realizacji celu w zależności od wielkości ryzyka i poziomu stabilności systemu produkcyjnego.
EN
Background: Control plays the main role in ensuring the stability of production processes, while digital models of processes and methods of artificial intelligence are used more and more commonly in it. Production of highly diversified items in small lots at low inventory levels is characterised by a much lower stability as compared with largelot manufacturing. Additionally, innovations created for items or processes result in disturbances to current work. Although this turbulence is usually momentary, it may lead to a loss of function or manufacturing stability, which in turn translates into financial losses, as well as losing customers. This paper presents the potential of using simulation models and artificial neural network models to assess the stability of a reorganized production system. Methods: The problem analysed in the paper is that of merging a simulation model with an ANN model by designing a hybrid model. A direct connection of both types of models is not possible due to their various structures, specificity, and different purposes, as well as the various types of input and output data. Therefore, the idea of merging these two types of models through an expert knowledge base and fuzzy inference was proposed. The results from the simulation model and the ANN model were used to gather the knowledge on the production system being analysed. It has been proposed that the output from the simulation model provided knowledge of the risk level, while the output from the ANN model provided knowledge of process stability. Results: The paper presents the idea of projecting a hybrid model of the expert system in order to assess the stability of a reorganized production system. A model of a hybrid expert system was developed to assess the potential of executing the assumed production plans. The level of risk and the level of stability determined by the simulation model and the ANN model are entered into the system. The output from the expert model is the value of the variable determining the potential of achieving the goal. In the construction of the model, fuzzy inference was used, which uses linguistic variables and is characterized by a knowledge system in the form of fuzzy rules "if ... then ...". For both the independent variable and for the dependent variable, a set of membership functions representing accepted linguistic variables was proposed, and then decision rules were determined. The idea of merging simulation models with ANN models was tested on a practical example in production system that manufactures products for dishwashers. Conclusions: The potentiality to execute production plans depending on the level of risk and the level of stability of the production system is too complicated to be modelled mathematically, but based on the analysis of data from the simulation and ANN models, it is possible to obtain information concerning the relations between corresponding input and output values.
EN
Mathematical model of the process of water softening using ion exchange pre-treatment of waters to desalination, with a view to removal of scale forming components, such as calcium and magnesium, are formed in the paper. In this process, no additional chemicals, except for brines formed during desalination, are required for regeneration of ion-exchanger in operation cycles. An asymptotic approximation of a solution of a corresponding model problem is constructed. Theoretical description and modelling assumptions included the set of differential equations of mass balance, initial, boundary and operational conditions. The paper deals with the development of a computer model for description and prediction of the performance of ion exchange columns.
PL
W pracy opracowano matematyczny model procesu zmiękczania wody przy użyciu wstępnej obróbki wody poprzez wymianę jonową do odsalania w celu usunięcia składników tworzących kamień, takich jak wapń i magnez. W procesie tym dla regeneracji wymiennika jonowego w cyklach roboczych nie trzeba wykorzystywać dodatkowych chemicznych czynników za wyjątkiem solanek, które powstają podczas odsalania. Opracowano asymptotyczne przybliżenie odpowiedniego rozwiązania z modelem. Opis teoretyczny i założenia modelu obejmują szereg równań różniczkowych bilansu masy, warunków początkowych, granicznych i eksploatacyjnych. Rozpatrzono opracowanie modelu komputerowego dla opisu i prognozowania działania kolumn wymiany jonowej.
EN
A numerical method of quasiconformal mappings for solving the coefficient problems of finding eigenvalues of the conductivity tensor having information about its directions in an anisotropic medium using applied quasipotential tomographic data is generalized. The corresponding algorithm is based on the alternate solving of problems on quasiconformal mappings and parameter identification. The results of numerical experiments of imitative restoration of environment structure are presented.
PL
Opracowano uogólnioną numeryczną metodę mapowania quasi-formalnego w celu rozwiązania zadań znalezienia wartości własnych tensora przewodnictwa posiadając informacje o jego kierunkach w ośrodku anizotropowym z zastosowaniem quasipotencjalnych danych tomograficznych. Podstawą algorytmu jest alternatywne rozwiązanie problemów związanych z mapowaniem quasi-formalnym i identyfikacją parametrów. Przedstawiono wyniki numerycznych symulacji odtworzenia struktury ośrodka.
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