scholarly journals COHEN’S CLASS TIME-FREQUENCY DISTRIBUTIONS FOR MEASUREMENT SIGNALS AS A MEANS OF MONITORING TECHNOLOGICAL PROCESSES

2019 ◽  
Vol 62 (4) ◽  
pp. 324-329
Author(s):  
D. B. Fedosenkov ◽  
A. A. Simikova ◽  
S. M. Kulakov ◽  
B. A. Fedosenkov
Keyword(s):  
Wigner Distribution ◽  
Bulk Material ◽  
Mathematical Tool ◽  
Distribution Map ◽  
Frequency Distributions ◽  
One Dimensional ◽  
Time Frequency ◽  
Technological Processes ◽  
Class Time ◽  
Cohen's Class

The article presents and describes Cohen’s class time-frequency distributions which are expedient to use as a mathematical tool that allows to create a convenient – in terms of information content and semantic clarity – visual-graphical representation of the opera ting modes of various technological processes including processes of ferrous metallurgy. It was noted that a controlling process is usually implemented without simultaneous visual monitoring of each scalar (one-dimensional) coordinate that is under control, but the presence of such monitoring is an important condition for the computer-aided controlling of the dynamics of non-stationary technological processes. To eliminate this drawback, it was proposed to perform synchronous monitoring using the multidimensional Cohen’s class time-frequency distributions, when each measurement scalar signal is specifically represented through one of these distributions, for example, the Wigner-Ville distribution. An expression is given for the generalized distribution of Cohen’s class with a distribution kernel and an ambiguity function. This function allows receiving distributions of various types from the maternal function. The most typical representatives of time-frequency distributions forming this class are given with their available  kernels. The possibility of appearance of interference elements, which make it difficult to identify the controlled modes, on a signal distribution map is proved. Case of the formation of virtual elements within the Wigner-Ville distribution representing a two-component one-dimensional signal is considered. Te conditions are explained for the emergence of parasitic elements on the distribution map, obtained, for example, during realizing the process of multi-component feeding the bulk blast furnace charge materials in the production of sintering mixture. An analytical expression is obtained for the Wigner distribution, which displays a multi-component scalar signal and contains the information (useful) and virtual (parasitic) parts of the time-frequency distribution. A link between the number of bulk material feeders available in the feeding devices unit and the number of parasitic (virtual) elements in the Wigner distribution was determined. Using the dosing process as an example, the effect of the noise components propagation in the Wigner distribution is demonstrated. An example is given to illustrate the penetration of noise into the Wigner distribution and appearance of the virtual concentration in it when displaying a signal waveform with a noisy pause and two sections with different frequencies. An expression for the Wigner distribution in the form of a comb function is obtained. The conclusion was made about the parameters of the distribution periodicity and the required sampling frequency of measurement signals.

scholarly journals Cohen’s Class Time-Frequency Distributions for Measurement Signals as a Means of Monitoring Technological Processes

2019 ◽  
Vol 49 (4) ◽  
pp. 252-256
Author(s):  
D. B. Fedosenkov ◽  
A. A. Simikova ◽  
S. M. Kulakov ◽  
B. A. Fedosenkov
Keyword(s):  
Frequency Distributions ◽  
Time Frequency ◽  
Technological Processes ◽  
Class Time ◽  
Cohen's Class

scholarly journals MULTIDIMENSIONAL REPRESENTATION OF AUTOMATIC DOSING DEVICE SIGNALS

2018 ◽  
pp. 26-32
Author(s):  
Denis Borisovich Fedosenkov ◽  
Anna Alekseevna Simikova ◽  
Boris Andreevich Fedosenkov ◽  
Stanislav Matveevich Kulakov
Keyword(s):  
Fourier Transform ◽  
Wigner Distribution ◽  
Low Frequency ◽  
Stationary Flow ◽  
Complex Model ◽  
Signal Spectrum ◽  
One Dimensional ◽  
Time Frequency ◽  
Cohen's Class ◽  
Discrete Values

The article describes the development of a special approach based on using multidimensional wavelet distributions principle to monitor and control the feed dozing processes in the mix preparation unit. As a key component, this approach uses the multidimensional time-frequency Wigner-Ville distribution, which is the part of Cohen's class distributions. The research focuses on signals characterizing mass transfer processes in the form of material flow measuring signals in relevant points of the unit. Wigner-Ville distribution has been shown in time terms as Fourier transform of products of multiplied parts of the signal under consideration for past and future time moments; corresponding distribution for the frequency spectrum is shown as Fourier transform of the products of signal parts for high-frequency and low-frequency fragments of the signal spectrum. It has been noted that when using a complex model of a dozing signal, discrete values (samples) of the latter are considered as its real values. The description of the signal parameters (amplitude, phase, frequency) has been carried out with the help of Hilbert transform. In Cohen's class distributions which represent one-dimensional non-stationary flow signals, the concept of ‘instantaneous frequency’ has been introduced. A graphical explanation for the transformation of a process flow signal from a one-dimensional time domain to a time-frequency 2 D/ 3 D -space is presented. The technology of developing a multidimensional image in the form of Wigner distribution for one-dimensional signals of continuous spiral or screw-type feeders has been examined in detail. There have been considered the features to support Wigner distribution, which allow to guess the presence or absence of time-frequency distribution elements in the interval of signal recording. There has been demonstrated how Wigner distribution can be obtained for a continuous-intermittent feeding signal. It has been concluded that for a certain types of the signal for zero fragments of the latter, non-zero time-frequency elements (i.e. virtual, anomalous ones) appear on the distribution. In addition to Wigner distribution, two other distributions - of Rihachek and Page - are considered. They display the same signal and also contain virtual elements, but in different domains of the time-frequency space. A generalized multidimensional compound signal distribution with a so-called distribution kernel available in it is presented, which includes a correction parameter that allows controlling the intensity of the virtual signal energy.

APPLICATION OF COHEN'S CLASS TIME-FREQUENCY DISTRIBUTIONS IN THE BELOUSOV–ZHABOTINSKY REACTION ANALYSIS

2004 ◽  
Vol 14 (10) ◽  
pp. 3679-3688 ◽  
Author(s):  
K. DAROWICKI ◽  
W. FELISIAK
Keyword(s):  
Batch Reactor ◽  
Three Dimensional ◽  
Power Spectra ◽  
Kernel Functions ◽  
Function Parameter ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Class Time ◽  
Cohen's Class ◽  
Belousov Zhabotinsky Reaction

The systematic study of application of Cohen's class time-frequency representations in the analysis of periodic BZ oscillations generated in batch reactor has been presented. Several distributions belonging to Cohen's class have been applied in the analysis of selected signal being the register of bromide selective electrode. Among them were Wigner–Ville, Choi–Williams and cone-shaped distributions. The application of mentioned methods allow instantaneous power spectra to be obtained and simultaneously give the possibility of observing evolution of frequency composition of investigated oscillations. The systematic filtering of signal, using so-called kernel functions, allows to eliminate undesirable cross terms and finally leads to the selection of a suitable method for chemical oscillations decomposition. The results presented in the form of three-dimensional pictures, illustrate the decrease in frequency of oscillations of exponential character. On the basis of the obtained results the cone-shaped distribution for kernel function parameter α=1 has been selected as the best method for Belousov–Zhabotinsky oscillations analysis in joint time-frequency domain.

scholarly journals The wavelet transforms technique in the computer-aided system for controlling the quarry unmanned vehicles

2021 ◽  
Vol 315 ◽  
pp. 03022
Author(s):  
Ivan Chicherin ◽  
Boris Fedosenkov ◽  
Dmitriy Dubinkin ◽  
Wang Zhenbo
Keyword(s):  
Wavelet Transforms ◽  
Matching Pursuit ◽  
Effective Means ◽  
Unmanned Vehicles ◽  
Open Pit ◽  
Open Pit Mining ◽  
Frequency Distributions ◽  
One Dimensional ◽  
Time Frequency ◽  
Computer Aided

Introduction. Purpose of the work. Within the framework of the computer-aided system, a technology has been formed for the method of controlling the current trajectories (CTs) of unmanned vehicles (UMVs) when they move along routes in a quarry in open pit mining. The purpose of the presented studies is to analyze the application of a wavelet transforms technique to the problem of routing unmanned vehicles when they move along routes within open pit roads. Methodology. The results of modeling certain one-dimensional signals corresponding to the UMV current trajectories when they deviate to the left / right from a nominal axial trajectory (NAT), as well as their time-frequency representations in a wavelet medium are presented. An algorithm of the procedure for displaying scalar UMV CT control signals in a complex medium of time-frequency wavelet transforms has been developed and described. Such a transformation allows for a functionally transparent and information-capacious monitoring of the UMV movement and efficiently manage the processes of trajectory routing dump trucks in an open pit. Research results, analysis. The processes of modifying the UMV movement current trajectories under the control of the computer-aided system are generated using wavelet transforms methods. They are based on algorithms for projecting the trajectory signals with a time-dependent frequency (chirp signals) onto a set of wavelet functions as part of a wavelet thesaurus (wavelet dictionary), executing certain wavelet matching pursuit procedures, and displaying the CT scalar signals in a specific multidimensional medium of Cohen’s class time-frequency distributions. The simulation results in the form of the current trajectory (CT-) signals waveforms and their three-dimensional time-frequency representations as Wigner maps showing the UMV movement in a start-stop mode, as well as the signals of formed continuous deviation trajectories when they leave to the left and to the right from the NAT, are presented. An algorithm for the formation of 3D-representations of UMV current trajectory one-dimensional signals is presented. Conclusion. The conclusion is made that the mathematical technique of wavelet transforms is the most expedient and effective means for computer-aided monitoring and controlling the dynamics of UMV movement along routes within open pit roads.

scholarly journals The technique of wavelet transforms in the computer-aided system for controlling the unmanned dump trucks movement

2021 ◽  
Vol 1 (3) ◽  
pp. 106-114
Author(s):  
Ivan V. Chicherin
Keyword(s):  
Wavelet Transforms ◽  
Matching Pursuit ◽  
Unmanned Vehicles ◽  
Open Pit ◽  
Open Pit Mining ◽  
Frequency Distributions ◽  
One Dimensional ◽  
Time Frequency ◽  
Computer Aided ◽  
Dump Trucks

Introduction, purpose of the work. Within the framework of the computer-aided system, the technology of a method is formed to control the current trajectories (CT) of unmanned vehicles (UMV) when they move along quarry routes in open-pit mining. The purpose of the presented research is to analyze the application of the wavelet transforms technique to the problem of routing unmanned vehicles when they move along quarry routes. Methodology. The results of modeling one-dimensional signals corresponding to the UMV current trajectories are presented, when the latters deviate to the left / right from the nominal axial trajectory (NAT), as well as their time-frequency distributions in the wavelet medium. The algorithm of the procedure for displaying scalar signals is developed and described to control UMV CT in a complex medium of time-frequency wavelet transforms. This transformation allows you to monitor the movement of UMV in a functionally transparent and informative way and effectively manage the processes of trajectory routing of dump trucks in the quarry. The analysis of research results. The processes of modifying the current trajectories of the UMV movement under the control of the computer-aided system are generated using the methods of wavelet transforms. They are based on algorithms for projecting trajectory signals with a time-dependent frequency (chirp signals) onto a set of wavelet functions within a wavelet thesaurus (wavelet dictionary), wavelet matching pursuit procedures, and representing scalar signals in a specific multidimensional medium of Cohen’s class time-frequency distributions. Simulation results in the form of waveform trajectory (CT-) signals and their three-dimensional Wigner time-frequency maps representing the movement of UMV in a start-stop mode, and the signals of formed continuous deviation trajectories while they deflect to the left and right of NAT. The algorithm for generating a 3D-image of a UMV current trajectory one-dimensional signal is presented. Conclusion. It is concluded that the mathematical technique of wavelet transforms is the most appropriate and effective one for computer-aided monitoring and controlling the dynamics of UMV moving along opencast mine routes.

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