In this letter, we present a deep learning algorithm for channel estimation in communication systems. We consider the time-frequency response of a fast fading communication channel as a 2D image. The ...aim is to find the unknown values of the channel response using some known values at the pilot locations. To this end, a general pipeline using deep image processing techniques, image super-resolution (SR), and image restoration (IR) is proposed. This scheme considers the pilot values, altogether, as a low-resolution image and uses an SR network cascaded with a denoising IR network to estimate the channel. Moreover, the implementation of the proposed pipeline is presented. The estimation error shows that the presented algorithm is comparable to the minimum mean square error (MMSE) with full knowledge of the channel statistics, and it is better than an approximation to linear MMSE. The results confirm that this pipeline can be used efficiently in channel estimation.
Recurrent sequence-to-sequence models using encoder-decoder architecture have made great progress in speech recognition task. However, they suffer from the drawback of slow training speed because the ...internal recurrence limits the training parallelization. In this paper, we present the Speech-Transformer, a no-recurrence sequence-to-sequence model entirely relies on attention mechanisms to learn the positional dependencies, which can be trained faster with more efficiency. We also propose a 2D-Attention mechanism, which can jointly attend to the time and frequency axes of the 2-dimensional speech inputs, thus providing more expressive representations for the Speech-Transformer. Evaluated on the Wall Street Journal (WSJ) speech recognition dataset, our best model achieves competitive word error rate (WER) of 10.9%, while the whole training process only takes 1.2 days on 1 GPU, significantly faster than the published results of recurrent sequence-to-sequence models.
Time‐frequency analysis based on Wigner‐Ville distribution (WVD) plays a significant role in analysing non‐stationary signals, but it is susceptible to interference from cross‐terms (CTs) for ...multi‐component signals. To address this issue, a novel WVD enhancement method based on generative adversarial networks (namely WVD‐GAN) is proposed, to achieve highly‐concentrated time‐frequency (TF) representation. Specifically, a deep feature extraction module is designed with multiple residual connections in the generator of WVD‐GAN to leverage the latent information encoded in the shallow representations. Meanwhile, a simple and effective attention module is introduced to enhance auto‐term features. Moreover, a multi‐scale discriminator is proposed based on dilated convolutions to guide the generator to reconstruct high‐resolution TF images by discriminating CT. Finally, a comparative analysis is provided to demonstrate the effectiveness and robustness of the proposed method on different simulated and real‐life datasets. Extensive experiments demonstrate that the proposed method outperforms several state‐of‐the‐art methods.
A novel approach is presented for Wigner‐Ville distribution enhancement based on generative adversarial networks to achieve high‐resolution time‐frequency representation. The authors’ method utilises the Wigner‐Ville distribution method to generate time‐frequency images of non‐stationary signals. Then a Wigner‐Ville distribution enhancement model based generative adversarial networks is proposed to construct highly‐concentrated time‐frequency representations. Extensive experiments demonstrate that the proposed method achieves high‐resolution time‐frequency images and can effectively restore the instantaneous frequency trajectory of non‐stationary signals, while maintaining energy concentration.
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In this paper, we introduce a new time-frequency (TF) analysis (TFA) method to study the trend and instantaneous frequency (IF) of nonlinear and nonstationary data. Our proposed method is termed the ...synchroextracting transform (SET), which belongs to a postprocessing procedure of the short-time Fourier transform (STFT). Compared with classical TFA methods, the proposed method can generate a more energy concentrated TF representation and allow for signal reconstruction. The proposed SET method is inspired by the recently proposed synchrosqueezing transform (SST) and the theory of the ideal TFA. To analyze a signal, it is important to obtain the time-varying information, such as the IF and instantaneous amplitude. The SST is to squeeze all TF coefficients into the IF trajectory. Differ from the squeezing manner of SST, the main idea of SET is to only retain the TF information of STFT results most related to time-varying features of the signal and to remove most smeared TF energy, such that the energy concentration of the novel TF representation can be enhanced greatly. Numerical and real-world signals are employed to validate the effectiveness of the SET method.
Data-driven time–frequency analysis Hou, Thomas Y.; Shi, Zuoqiang
Applied and computational harmonic analysis,
September 2013, 2013-09-00, 20130901, Volume:
35, Issue:
2
Journal Article
Peer reviewed
Open access
In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and nonstationary data. This method is inspired by the Empirical Mode ...Decomposition method (EMD) and the recently developed compressed (compressive) sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form {a(t)cos(θ(t))}, where a∈V(θ), V(θ) consists of the functions smoother than cos(θ(t)) and θ′⩾0. This problem can be formulated as a nonlinear l0 optimization problem. In order to solve this optimization problem, we propose a nonlinear matching pursuit method by generalizing the classical matching pursuit for the l0 optimization problem. One important advantage of this nonlinear matching pursuit method is it can be implemented very efficiently and is very stable to noise. Further, we provide an error analysis of our nonlinear matching pursuit method under certain scale separation assumptions. Extensive numerical examples will be given to demonstrate the robustness of our method and comparison will be made with the state-of-the-art methods. We also apply our method to study data without scale separation, and data with incomplete or under-sampled data.
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As a typical nonstationary signal, rolling bearing fault signals exhibit dynamic characteristics and low signal-to-noise ratio, which lead to fuzzy spectrograms from traditional time-frequency ...analysis (TFA) methods. It is a challenging task to accurately represent its instantaneous frequency (IF) trajectory. To solve this problem, this article proposes a TFA method which is called match-extracting chirplet transform for analyzing multicomponent dynamic signals. It generates a time-frequency (TF) representation of high energy concentration by constructing a basis function that matches the chirp rate with the original signal at any TF point. A matching extraction operator is built to extract the best matching ridges on the IF trajectory to further improve the quality of the spectrum. The proposed method can effectively characterize the dynamic characteristics of multicomponent signals and reduce the energy divergence. Meanwhile the algorithm retains signal reconstruction and can be used to recover significant components by adaptively searching modal ridges. Numerical verification shows that this method has a better performance in TF location and noise robustness. Finally, the validity of this method in mechanical fault diagnosis is verified by applying it to actual bearing signals.
The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part II. Because there is virtually no application of the NNMs to large-scale engineering structures, ...these papers are an attempt to highlight several aspects that might drive their development in the future. Specifically, we support that (i) numerical methods for the continuation of periodic solutions pave the way for an effective and practical computation of NNMs, and (ii) time–frequency analysis is particularly suitable for the analysis of the resulting dynamics. Another objective of the present paper is to describe, in simple terms, and to illustrate the fundamental properties of NNMs. This is achieved to convince the structural dynamicist not necessarily acquainted with them that they are a useful framework for the analysis of nonlinear vibrating structures.
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Low and medium speed magnetic levitation traffic with short power supply distance and complex grounding network structure, prone to power supply rail grounding faults. However, the existing fault ...location methods do not accurately locate the fault point, making it difficult for the protective device to act to cut off the fault. To address the above problems, this paper builds a dynamic simulation model of the low and medium speed magnetic levitation power supply rails to study the distribution characteristics of the fault traveling waves after a ground fault occurs in the power supply rails, and analyses the generation mechanism of the traveling wave spectrum through formula calculation. First, the difference in current between the positive and negative bus bars is analyzed to determine whether a ground fault has occurred. Second, the direction of the current difference between stations is compared to locate the faulty section. Finally, the fault distance is calculated from the frequency difference of the fault voltage at the double‐ended station. Through simulation, the method is validated to be unaffected by fault location, fault transition resistance, noise interference, and is applicable to short circuit faults caused by lightning strikes, and the ranging error always remains within 20 m. The method has strong robustness, can effectively solve the problem of protection misoperation and accurately locate the fault point. It is suitable for low and medium speed magnetic levitation transportation power supply rail ground fault.
A dynamic simulation model of the low and medium speed magnetic levitation power supply rails is built to study the distribution characteristics of the fault traveling waves after an earth fault occurs on the power supply rails, and the generation mechanism of the traveling wave spectrum is analysed by means of equation calculations.
The difference between the positive and negative bus currents is analysed to locate the fault section, and the fault distance is calculated from the frequency difference of the fault voltage at the double‐ended station.
The article method is not affected by fault location, fault transition resistance, noise interference and is applicable to short circuit faults caused by lightning strikes.
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This paper presents a novel approach for detecting cracked or broken reciprocating compressor valves under varying load conditions. The main idea is that the time frequency representation of ...vibration measurement data will show typical patterns depending on the fault state. The problem is to detect these patterns reliably. For the detection task, we make a detour via the two dimensional autocorrelation. The autocorrelation emphasizes the patterns and reduces noise effects. This makes it easier to define appropriate features. After feature extraction, classification is done using logistic regression and support vector machines. The method׳s performance is validated by analyzing real world measurement data. The results will show a very high detection accuracy while keeping the false alarm rates at a very low level for different compressor loads, thus achieving a load-independent method. The proposed approach is, to our best knowledge, the first automated method for reciprocating compressor valve fault detection that can handle varying load conditions.
•Load changes and valve faults show different patterns in the spectrogram.•Autocorrelation of the spectrogram difference emphasizes these patterns.•Distinctive features can be extracted from autocorrelation representation.•Classification works well for arbitrary load levels of the compressor.
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The vibration signal of planetary gearboxes exhibits the characteristics of both amplitude modulation (AM) and frequency modulation (FM), and thus has a complex sideband structure. Time-varying speed ...and/or load will result in time variant characteristic frequency components. Since the modulating frequency is related to the gear fault characteristic frequency, the AM and FM parts each alone contains the information of the gear fault. We propose a time–frequency amplitude and frequency demodulation analysis metbhod to avoid the complex time-variant sideband analysis, and thereby identify the time-variant gear fault characteristic frequency. We enhance the time–frequency analysis via iterative generalized demodulation (IGD). The time-varying amplitude and frequency demodulated spectra have fine time–frequency resolution and are free of cross term interferences. They do not involve complex time-variant sidebands, thus considerably facilitating fault diagnosis of planetary gearboxes under nonstationary conditions. The method is validated using both numerically simulated data and experimental signals.
•The proposed method has fine time–frequency resolution and is free from cross term interferences.•It avoids the complex time-varying sidebands analysis of planetary gearbox signals.•It is effective in extracting the time-varying gear fault characteristic frequencies.•It is effective in diagnosing both the local and distributed gear faults.
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