scholarly journals Frequency Domain System Identification With Instrumental Variable Based Subspace Algorithm

1997 ◽  
Author(s):  
Tomas McKelvey
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Instrumental Variable ◽  
Theoretical Discussion ◽  
Subspace Algorithm ◽  
Input And Output ◽  
Rank Constraint ◽  
The Fourier Transform ◽  
The Time Domain

Abstract In this paper we discuss how the time domain subspace based identification algorithms can be modified in order to be applicable when the primary measurements are given as samples of the Fourier transform of the input and output signals or alternatively samples of the transfer function. An instrumental variable (IV) based subspace algorithm is presented. We show that this method is consistent if a certain rank constraint is satisfied and the frequency domain noise is zero mean with bounded covariances. An example is presented which illuminates the theoretical discussion.

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.

A Multiple Harmonic Open-Loop Controller for Hydro/Aerodynamic Force Measurements in Rotating Machinery Using Magnetic Bearings

2002 ◽  
Vol 124 (4) ◽  
pp. 827-834 ◽  
Author(s):  
D. O. Baun ◽  
E. H. Maslen ◽  
C. R. Knospe ◽  
R. D. Flack
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Open Loop ◽  
Rotating Machinery ◽  
Operating Conditions ◽  
Rotor Vibration ◽  
Aerodynamic Forces ◽  
Analog Input ◽  
Input And Output ◽  
The Time Domain

Inherent in the construction of many experimental apparatus designed to measure the hydro/aerodynamic forces of rotating machinery are features that contribute undesirable parasitic forces to the measured or test forces. Typically, these parasitic forces are due to seals, drive couplings, and hydraulic and/or inertial unbalance. To obtain accurate and sensitive measurement of the hydro/aerodynamic forces in these situations, it is necessary to subtract the parasitic forces from the test forces. In general, both the test forces and the parasitic forces will be dependent on the system operating conditions including the specific motion of the rotor. Therefore, to properly remove the parasitic forces the vibration orbits and operating conditions must be the same in tests for determining the hydro/aerodynamic forces and tests for determining the parasitic forces. This, in turn, necessitates a means by which the test rotor’s motion can be accurately controlled to an arbitrarily defined trajectory. Here in, an interrupt-driven multiple harmonic open-loop controller was developed and implemented on a laboratory centrifugal pump rotor supported in magnetic bearings (active load cells) for this purpose. This allowed the simultaneous control of subharmonic, synchronous, and superharmonic rotor vibration frequencies with each frequency independently forced to some user defined orbital path. The open-loop controller was implemented on a standard PC using commercially available analog input and output cards. All analog input and output functions, transformation of the position signals from the time domain to the frequency domain, and transformation of the open-loop control signals from the frequency domain to the time domain were performed in an interrupt service routine. Rotor vibration was attenuated to the noise floor, vibration amplitude ≈0.2 μm, or forced to a user specified orbital trajectory. Between the whirl frequencies of 14 and 2 times running speed, the orbit semi-major and semi-minor axis magnitudes were controlled to within 0.5% of the requested axis magnitudes. The ellipse angles and amplitude phase angles of the imposed orbits were within 0.3 deg and 1.0 deg, respectively, of their requested counterparts.

IDENTIFICATION OF INTERHARMONICS BASED ON WAVELET PACKET TRANSFORM

2021 ◽  
Vol 3 (1) ◽  
pp. 031-036
Author(s):  
S. A. GOROVOY ◽  
◽  
V. I. SKOROKHODOV ◽  
D. I. PLOTNIKOV ◽  
◽  
...  
Keyword(s):  
Fourier Transform ◽  
Simulation Model ◽  
Frequency Domain ◽  
Time Domain ◽  
Wavelet Packet ◽  
High Accuracy ◽  
Wavelet Packet Transform ◽  
Mathematical Apparatus ◽  
Nonlinear Load ◽  
The Time Domain

This paper deals with the analysis of interharmonics, which are due to the presence of a nonlinear load. The tool for the analysis was a mathematical apparatus - wavelet packet transform. Which has a number of advantages over the traditional Fourier transform. A simulation model was developed in Simulink to simulate a non-stationary non-sinusoidal mode. The use of the wavelet packet transform will allow to determine the mode parameters with high accuracy from the obtained wavelet coefficients. It also makes it possible to obtain information, both in the frequency domain of the signal and in the time domain.

A Deep Neural Network Model for Learning Runtime Frequency Response Function Using Sensor Measurements

2021 ◽  
Author(s):  
Yongzhi Qu ◽  
Gregory W. Vogl ◽  
Zechao Wang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fourier Transform ◽  
Time Domain ◽  
Frequency Response Function ◽  
Frequency Component ◽  
Operating Conditions ◽  
Input Output ◽  
The Fourier Transform ◽  
The Time Domain

Abstract The frequency response function (FRF), defined as the ratio between the Fourier transform of the time-domain output and the Fourier transform of the time-domain input, is a common tool to analyze the relationships between inputs and outputs of a mechanical system. Learning the FRF for mechanical systems can facilitate system identification, condition-based health monitoring, and improve performance metrics, by providing an input-output model that describes the system dynamics. Existing FRF identification assumes there is a one-to-one mapping between each input frequency component and output frequency component. However, during dynamic operations, the FRF can present complex dependencies with frequency cross-correlations due to modulation effects, nonlinearities, and mechanical noise. Furthermore, existing FRFs assume linearity between input-output spectrums with varying mechanical loads, while in practice FRFs can depend on the operating conditions and show high nonlinearities. Outputs of existing neural networks are typically low-dimensional labels rather than real-time high-dimensional measurements. This paper proposes a vector regression method based on deep neural networks for the learning of runtime FRFs from measurement data under different operating conditions. More specifically, a neural network based on an encoder-decoder with a symmetric compression structure is proposed. The deep encoder-decoder network features simultaneous learning of the regression relationship between input and output embeddings, as well as a discriminative model for output spectrum classification under different operating conditions. The learning model is validated using experimental data from a high-pressure hydraulic test rig. The results show that the proposed model can learn the FRF between sensor measurements under different operating conditions with high accuracy and denoising capability. The learned FRF model provides an estimation for sensor measurements when a physical sensor is not feasible and can be used for operating condition recognition.

scholarly journals Radiofrequency Microwave Double Resonance Experiments in Fourier Transform Technique

1988 ◽  
Vol 43 (3) ◽  
pp. 280-282 ◽  
Author(s):  
N. Heineking ◽  
W. Stahl ◽  
H. Dreizler
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Double Resonance ◽  
Fourier Transform Spectroscopy ◽  
Microwave Spectroscopy ◽  
Valuable Method ◽  
The Time Domain

Abstract Radiofrequency microwave double resonance has proved as a valuable method in microwave spectroscopy in the frequency domain. We present comparable experiments in the time domain Fourier transform spectroscopy.

scholarly journals The Comparison of the Effect of Haimming Window and Blackman Window in the Time-Scaling and Pitch-Shifting Algorithms

2011 ◽  
Vol 1 ◽  
pp. 221-225
Author(s):  
Zhi Wei Lin ◽  
Li Da ◽  
Hao Wang ◽  
Wei Han ◽  
Fan Lin
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Domain Method ◽  
Domain Type ◽  
Domain Method ◽  
Time Scaling ◽  
Window Functions ◽  
Inherent Frequency ◽  
The Time Domain

The real-time pitch shifting process is widely used in various types of music production. The pitch shifting technology can be divided into two major types, the time domain type and the frequency domain type. Compared with the time domain method, the frequency domain method has the advantage of large shifting scale, low total cost of computing and the more flexibility of the algorithm. However, the use of Fourier Transform in frequency domain processing leads to the inevitable inherent frequency leakage effects which decrease the accuracy of the pitch shifting effect. In order to restrain the side effect of Fourier Transform, window functions are used to fall down the spectrum-aliasing. In practical processing, Haimming Window and Blackman Window are frequently used. In this paper, we compare both the effect of the two window functions in the restraint of frequency leakage and the performance and accuracy in subjective based on the traditional phase vocoder[1]. Experiment shows that Haimming Window is generally better than Blackman Window in pitch shifting process.

scholarly journals Study of Blockage Diagnosis for Hydrocyclone Using Vibration-Based Technique Based on Wavelet Denoising and Discrete-Time Fourier Transform Method

Processes ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 440 ◽  
Author(s):  
Guanghui Wang ◽  
Qun Liu ◽  
Chuanzhen Wang ◽  
Lulu Dong ◽  
Dan Dai ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Standard Deviation ◽  
Frequency Domain ◽  
Discrete Time ◽  
Time Domain ◽  
Wavelet Denoising ◽  
Transform Method ◽  
Fourier Transform Method ◽  
The Time Domain ◽  
Separation Devices

Hydrocyclones are extensively known as important separation devices which are used in many industrial fields. However, the general method to estimate device performance is time-consuming and has a high cost. The aim of this paper was to investigate the blockage diagnosis for a lab-scale hydrocyclone using a vibration-based technique based on wavelet denoising and the discrete-time Fourier transform method. The results indicate that the farther away the installation location from feed inlet the more regular the frequency is, which reveals that the installation plane near to the spigot generated the regular frequency distribution. Furthermore, the acceleration amplitude under blockage degrees 0%, 50% and 100% fluctuates as a sine shape with increasing time, meanwhile the vibration frequency of the hydrocyclone rises with increasing throughput. Moreover, the distribution of four dimensional and five non-dimensional parameters for the time domain shows that the standard deviation, compared to the others, reduced gradually with increases in blockage degree. Thus, the standard deviation was used to evaluate the online diagnosis of the blockage. The frequency domain distribution under different throughput reveals that the characteristic peaks consisting of the faulty frequency and multiple frequency were produced by the faulty blockage and the feed pump, respectively. Hence, the faulty peak of 16–17 Hz was adopted to judge the real-time blockage of the hydrocyclone, i.e., the presence of the characteristic peak marks the blockage, and its value is proportional to the blockage degree. The application of the online monitoring system demonstrates that the combination of the time domain and the frequency domain could admirably detect the running state and rapidly recognize blockage faults.

Research and analysis of the wheeled vehicle load spectrum editing method based on short-time Fourier transform

2019 ◽  
Vol 233 (14) ◽  
pp. 3671-3683
Author(s):  
Zongkai Liu ◽  
Chuan Peng ◽  
Xiaoqiang Yang
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Fatigue Damage ◽  
Time Domain ◽  
Short Time Fourier Transform ◽  
Load Spectrum ◽  
Statistical Parameters ◽  
Original Spectrum ◽  
The Time Domain ◽  
Short Time

The measured uniaxial-head load spectrum in the road simulation test has a large number of useless small loads. When applying the measured load spectrum directly, it will take a lot of time. This paper designs a comprehensive road spectrum measurement system to collect data and proposes a method for editing the uniaxial-head acceleration load spectrum using short-time Fourier transform to speed up the reliability test process and reduce time costs. In this method, the time domain and frequency domain information of the signal is obtained by short-time Fourier transform. The concept of accumulated power spectral density is proposed to identify the reduced load data, and the relative fatigue damage is used as the pass criterion. The length of the edited spectrum is only 66% of the original spectrum through the above-mentioned editing method and retains the relative damage amount of 91%. Finally, through the analysis of time domain, frequency domain, and fatigue statistical parameters, it demonstrates that the short-time Fourier transform–based acceleration load spectrum edition method could achieve a similar fatigue damage to the original spectrum in a shorter time.

Discrete Time, Discrete Frequency

2021 ◽  
pp. 106-155
Author(s):  
Victor Lazzarini
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Discrete Time ◽  
Time Domain ◽  
Continuous Time ◽  
Time Varying ◽  
Discrete Frequency ◽  
The Fourier Transform ◽  
Definition Of ◽  
The Time Domain

This chapter is dedicated to exploring a form of the Fourier transform that can be applied to digital waveforms, the discrete Fourier transform (DFT). The theory is introduced and discussed as a modification to the continuous-time transform, alongside the concept of windowing in the time domain. The fast Fourier transform is explored as an efficient algorithm for the computation of the DFT. The operation of discrete-time convolution is presented as a straight application of the DFT in musical signal processing. The chapter closes with a detailed look at time-varying convolution, which extends the principles developed earlier. The conclusion expands the definition of spectrum once more.

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