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.

A NEURAL NETWORK FOR POSITION INVARIANT PATTERN RECOGNITION COMBINING SPIKING NEURONS WITH THE FOURIER-TRANSFORM

1996 ◽  
Vol 07 (06) ◽  
pp. 727-733 ◽  
Author(s):  
MICHAEL STOECKER ◽  
HERBERT J. REITBOECK
Keyword(s):  
Neural Network ◽  
Fourier Transform ◽  
Time Domain ◽  
Amplitude Spectrum ◽  
Dynamic Network ◽  
Spiking Neurons ◽  
Invariant Representation ◽  
Activity Distribution ◽  
The Fourier Transform ◽  
The Time Domain

We present an approach for position invariant recognition of individual objects in composite scenes, combining neural networks and algorithmic methods. A dynamic network of spiking neurons is used to generate object definition and figure/ground separation via temporal signal correlations. A shift invariant representation of the network spike activity distribution is subsequently realized via the amplitude spectrum of the Fourier-transform. Objects and their transformed representations are therefore linked in the time domain. The model segregates scenes and classifies individual patterns independent of their position in the input scene.

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.

Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. T117-T123 ◽  
Author(s):  
Chunlei Chu ◽  
Paul L. Stoffa
Keyword(s):  
Fourier Transform ◽  
Frequency Response ◽  
Time Domain ◽  
Wave Equations ◽  
Time Integration ◽  
Expansion Method ◽  
Rapid Expansion ◽  
The Fourier Transform ◽  
The Time Domain ◽  
Response Modeling

Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency.

Model Order Reduction and the Heat Transfer Modelling of a Heat Exchanger by Using Artificial Neural Approach

2011 ◽  
Vol 6 (1) ◽  
Author(s):  
Yahya Chetouani
Keyword(s):  
Neural Network ◽  
Experimental Data ◽  
Neural Networks ◽  
Heat Exchanger ◽  
Black Box ◽  
Operating Conditions ◽  
Outlet Temperature ◽  
Input Output ◽  
Reliable Model ◽  
Artificial Neural

The main aim of this paper is to establish a reliable model of a process behavior under the normal operating conditions. The use of this model should reflect the true behavior of the process in the whole way and thus distinguish a normal mode from the abnormal modes. In order to obtain a reliable model for the process dynamics, the black-box identification by means of a NARMAX model has been chosen in this paper. It is based on the neural networks approach. The main advantage of the proposed approach consists in the natural ability of neural networks in modeling non-linear dynamics in a fast and simple way and in the possibility to address the process to be modeled as an input-output black-box, with little or no mathematical information on the system. This paper will show the choice and the performance of the neural network in the training and the test phases. A study is related to the number of inputs, and of hidden neurons used and their influence on the behavior of the neural predictor. Three statistical criterions, Aikeke’s information criterion (AIC), Rissanen’s Minimum Description Length (MDL), and Bayesian information criteria (BIC), are used for the validation of the experimental data. In order to illustrate the ideas proposed concerning the dynamics modelling, a heat exchanger is used. The outlet temperature is modeled according to the inlet temperature. The model is implemented by training a Multilayer Perceptron artificial neural network with input-output experimental data. Satisfactory agreement between identified and experimental data is found and results show that the model successfully predicts the evolution of the outlet temperature of the process.

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.

Calculation of the pulsed electromagnetic field of a plane annular magnetic current

Antennas ◽  
2021 ◽  
Author(s):  
I. P. Kovalyov ◽  
N. I. Kuzikova
Keyword(s):  
Magnetic Field ◽  
Fourier Transform ◽  
Electric Field ◽  
Wave Front ◽  
Time Domain ◽  
Vector Potential ◽  
Magnetic Current ◽  
The Fourier Transform ◽  
The Time Domain ◽  
The Magnetic Field

The work calculates the radiation fields of a plane ring magnetic current in the time domain. Two functions are considered that describe the dependence of the magnetic current on time: the delta function and the unit drop. All calculations are performed in the time domain without using the Fourier transform. First, the time-dependent vector potential is calculated. When writing expressions for the vector potential, the annular magnetic current is represented by the difference between two circular magnetic currents. Then, the magnetic field created by the ring magnetic current is found through the vector potential. Only one φ-th component of the magnetic field is nonzero. Further, from Maxwell's equations through the magnetic field, the components of the electric field of the annular magnetic current are calculated. On the basis of the formulas obtained, various special cases showing the dependence of the emitted field on time and spatial coordinates are considered. The time dependence of the electric field on the ring axis is calculated. It is shown that the Fourier transform of this field leads to a formula known from the literature in the frequency domain for calculating the field on the axis of the ring. The graphs are given showing that near the wave front, the transverse components of the electric and magnetic fields differ only by a factor equal to the wave resistance of the medium (120π for the air medium). The images of the electric field at different times are shown. In the given pictures of the fields, one can observe the movement of the radiation field near the wave front and the formation of a static field in the vicinity of the ring. The analytical expressions obtained in this work can be used to calculate antennas and other structures excited by a coaxial line. They can be used to solve integral equations in the time domain.

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.

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