scholarly journals Design of a Matlab toolbox and GUI for minimal realizations

2020 ◽  
Vol 17 (2) ◽  
pp. 929
Author(s):  
Karim Cherifi ◽  
Kamel Hariche
Keyword(s):  
Graphical User Interface ◽  
Time Domain ◽  
Space Form ◽  
Memory Storage ◽  
Minimal Realization ◽  
Matlab Toolbox ◽  
Time Domain Data ◽  
Suitable Form ◽  
Minimal Realizations ◽  
The Given

<p>Minimal realization for linear systems has been studied extensively in the literature. Techniques proposed differ in terms of the configuration of the state space form, the time efficiency of the algorithm and the reduction of memory storage. The minimal realization toolbox presented in this paper offers the possibility to test different methods and choose the most suitable form depending on the application. The given system can be represented by a transfer function or by raw (frequency or time domain) data. A graphical user interface (GUI) was implemented in order to ease the use of this toolbox and allow to rapidly test the methods and display the results.</p>

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

Effects of Noise, Time-Domain Damping, Zero-Filling and the FFT Algorithm on the “Exact” Interpolation of Fast Fourier Transform Spectra

1988 ◽  
Vol 42 (5) ◽  
pp. 715-721 ◽  
Author(s):  
Francis R. Verdun ◽  
Carlo Giancaspro ◽  
Alan G. Marshall
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Word Length ◽  
Peak Position ◽  
Double Precision ◽  
Time Domain Data ◽  
Roundoff Errors ◽  
Data Points ◽  
Lorentzian Spectrum

A frequency-domain Lorentzian spectrum can be derived from the Fourier transform of a time-domain exponentially damped sinusoid of infinite duration. Remarkably, it has been shown that even when such a noiseless time-domain signal is truncated to zero amplitude after a finite observation period, one can determine the correct frequency of its corresponding magnitude-mode spectral peak maximum by fitting as few as three spectral data points to a magnitude-mode Lorentzian spectrum. In this paper, we show how the accuracy of such a procedure depends upon the ratio of time-domain acquisition period to exponential damping time constant, number of time-domain data points, computer word length, and number of time-domain zero-fillings. In particular, we show that extended zero-filling (e.g., a “zoom” transform) actually reduces the accuracy with which the spectral peak position can be determined. We also examine the effects of frequency-domain random noise and roundoff errors in the fast Fourier transformation (FFT) of time-domain data of limited discrete data word length (e.g., 20 bit/word at single and double precision). Our main conclusions are: (1) even in the presence of noise, a three-point fit of a magnitude-mode spectrum to a magnitude-mode Lorentzian line shape can offer an accurate estimate of peak position in Fourier transform spectroscopy; (2) the results can be more accurate (by a factor of up to 10) when the FFT processor operates with floating-point (preferably double-precision) rather than fixed-point arithmetic; and (3) FFT roundoff errors can be made negligible by use of sufficiently large (> 16 K) data sets.

scholarly journals A Multimodal Feature Fusion-Based Deep Learning Method for Online Fault Diagnosis of Rotating Machinery

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3521 ◽  
Author(s):  
Funa Zhou ◽  
Po Hu ◽  
Shuai Yang ◽  
Chenglin Wen
Keyword(s):  
Deep Learning ◽  
Fault Diagnosis ◽  
Real Time ◽  
Time Domain ◽  
Feature Fusion ◽  
Rotating Machinery ◽  
Time Domain Data ◽  
Diagnosis Method ◽  
The Time Domain ◽  
Potential Frequency

Rotating machinery usually suffers from a type of fault, where the fault feature extracted in the frequency domain is significant, while the fault feature extracted in the time domain is insignificant. For this type of fault, a deep learning-based fault diagnosis method developed in the frequency domain can reach high accuracy performance without real-time performance, whereas a deep learning-based fault diagnosis method developed in the time domain obtains real-time diagnosis with lower diagnosis accuracy. In this paper, a multimodal feature fusion-based deep learning method for accurate and real-time online diagnosis of rotating machinery is proposed. The proposed method can directly extract the potential frequency of abnormal features involved in the time domain data. Firstly, multimodal features corresponding to the original data, the slope data, and the curvature data are firstly extracted by three separate deep neural networks. Then, a multimodal feature fusion is developed to obtain a new fused feature that can characterize the potential frequency feature involved in the time domain data. Lastly, the fused new feature is used as the input of the Softmax classifier to achieve a real-time online diagnosis result from the frequency-type fault data. A simulation experiment and a case study of the bearing fault diagnosis confirm the high efficiency of the method proposed in this paper.

The Cole‐Cole model in time domain induced polarization

Geophysics ◽  
1981 ◽  
Vol 46 (6) ◽  
pp. 932-933 ◽  
Author(s):  
T. Lee
Keyword(s):  
Equivalent Circuit ◽  
Time Domain ◽  
Induced Polarization ◽  
Relaxation Model ◽  
Trivial Case ◽  
Alternative Expression ◽  
Transient Voltage ◽  
Transient Voltages ◽  
Cole Model ◽  
The Given

Recently Pelton et al. (1978) used a Cole‐Cole relaxation model to simulate the transient voltages that are observed during an induced‐polarization survey. These authors took the impedance of the equivalent circuit Z(ω) to be [Formula: see text]They then gave the expression for the transient voltage [Formula: see text] as [Formula: see text]In equation (2), [Formula: see text] was misprinted as [Formula: see text]. In these equations, [Formula: see text] and [Formula: see text], [Formula: see text] and τ are constants to be determined for the given model. [Formula: see text] is the height of the step current that will flow in the transmitter. A disadvantage of equation (2) is that it is only slowly convergent for large t/τ. Pelton et al. (1978) used a τ which ranged from [Formula: see text] to [Formula: see text]. The purpose of this note is to provide an alternative expression for [Formula: see text] that is valid only at the later stages but which does not have this disadvantage. The trivial case of c = 1.0 is ignored.

scholarly journals Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 136
Author(s):  
Manuel Duarte-Mermoud ◽  
Javier Gallegos ◽  
Norelys Aguila-Camacho ◽  
Rafael Castro-Linares
Keyword(s):  
Fractional Order ◽  
Performance Optimization ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Minimal Realization ◽  
Linear Time Invariant ◽  
Mixed Order ◽  
Linear Time Invariant Systems ◽  
Minimal Realizations ◽  
Time Invariant

Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers.

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