Undersampled Signals Research Articles

Blade tip timing signals parameters identification based on Displacement Offset Decreased and Compressed Sensing

High-speed rotating blade vibration monitoring is of great significance for the safe operation of turbomachinery. Blade Tip Timing (BTT) is considered a promising technology in the field of blade vibration monitoring. The BTT signal analysis has the following problem, the displacement offset was caused by speed variation which affected the accuracy of the blade vibration parameter identification. Owing to the under-sampled characteristics of the BTT signals and multiple sensor data are required to identify the parameters. The accurate extraction of blade vibration characteristics is challenging. Thus, a vibration analysis method is proposed based on Displacement Offset Decreased and Compressed Sensing (DOD-CS). Firstly, the BTT signal pairwise is subtracted to reduce the impact of the displacement offset, and based on the subtractive results, a basis function is constructed to rebuild the dictionary matrix of the compressed sensing method. Then, we solved the signal sparse representation equation and obtained the spectrum estimation result, that is, the structure vibration parameters. The analysis of simulation data shows that the parameter identification accuracy of the DOD-CS method is higher than that of the OMP-CS (Orthogonal Matching Pursuit and Compressed Sensing) method, and the identification errors of frequency and amplitude are within 1% and 5%, respectively. The experimental results confirm the feasibility of the proposed method in identifying vibration parameters. Compared with existing methods, the innovation of the proposed method is that it eliminates the influence of displacement offset on the accuracy of parameter identification. For under-sampled signals, only two sensor data information are needed to complete spectrum estimation and parameter identification.

Non-convex sparse regularization via convex optimization for blade tip timing

Blade Tip Timing (BTT), an emerging technology poised to replace strain gauges, enables contactless measurement of rotor blade vibration. However, the blade vibration signals measured by BTT systems often suffer from significant undersampling. Sparse reconstruction methods are instrumental in addressing the challenge of undersampled signal reconstruction. However, traditional approaches grounded in ℓ1 regularization tend to underestimate the amplitude of the true solution. This underestimation is particularly pronounced in the resonance state of the rotor blade, hindering effective prediction of the blade’s operational state. To overcome this limitation, this paper introduces a novel non-convex regularized BTT model, employing a non-convex penalty term with convex-preserving properties to achieve nearly unbiased reconstruction accuracy. Additionally, we propose a new threshold iteration algorithm designed for the swift solution of this model. The accuracy and robustness of the proposed method in identifying the multimodal vibration parameters of rotor blades are validated through simulations and experiments. Comparatively, the proposed method closely aligns with the Orthogonal Matching Pursuit (OMP) method in recognizing blade multimodal vibration amplitude, showcasing significant improvement over the ℓ1 regularization method. Furthermore, it demonstrates lower sensitivity to changes in BTT probe layout when compared to the OMP and ℓ1 regularization methods.

Intelligent condition monitoring with CNN and signal enhancement for undersampled signals

High-frequency signals like vibration and acoustic emission are crucial for condition monitoring, but their high sampling rates challenge data acquisition, especially for online monitoring. Our research developed a novel method for condition identification in undersampled signals using a modified convolutional neural network integrated with a signal enhancement approach. A frequency-domain filtering is applied to suppress similar sidebands and obtain more discriminative features of different conditions, followed by an interpolation-based upsampling in the time domain to restore the signal length and strengthen the low-frequency harmonic information. Enhanced signals are converted into two-dimensional grayscale images for neural network analysis. Tested on bearing datasets and real-world data from regenerative thermal oxidizer lift valve leakage, our method effectively extracts features from low-frequency signals, achieving over 95% fault identification accuracy.

Compressed sensing for rapid tabletop X-ray absorption spectroscopy

X-ray Absorption Fine Structure (XAFS) spectroscopy is an analytical technique of chemical insight. Improvements to this technique are continuously carried out for reduction of the acquisition time and increasing the resolution, especially for studying operando processes. The accurate reconstruction of XAFS signals requires that the collected data are noise-free to extract elemental structure information in post-processing. A novel approach to rapid sampling (encoded measurement) is validated conceptually. The technique relies on sparse signal recovery, i.e. using compressed sensing to reconstruct under-sampled signals. The proof of concept is demonstrated by using a python code to reconstruct under-sampled XAFS spectra. A case study of transition metal samples and their oxides is considered for this purpose. The results demonstrate a robust recovery of chemical information from a 30% sampled signal for the near-edge region analysis and from a 45% sampled signal for extended-edge region analysis. The application of this procedure is important for demonstrating the feasibility of tabletop operation using laboratory X-ray sources which are not continuously tunable.

Deep learning for sub-Nyquist sampling scanning white light interferometry.

This Letter introduces sub-Nyquist sampling vertical scanning white light interferometry (SWLI) using deep learning. The method designs Envelope-Deep Residual Shrinkage Networks with channel-wise thresholds (E-DRSN-cw), a network model extracting oversampling envelopes from undersampled signals. The model improves the training efficiency, accuracy, and robustness by following the soft thresholding nonlinear layer approach, pre-padding undersampled interference signals with zeros, using LayerNorm for augmenting inputs and labels, and predicting regression envelopes. Simulation data train the network, and experiments demonstrate its superior performance over classical methods in the accuracy and the robustness. The E-DRSN-cw provides a swift measurement solution for SWLI, removing the need for prior knowledge.

A wide-beam NCS algorithm for multi-receiver SAS based on azimuth spectrum superposition

The existing multi-receiver synthetic aperture sonar (SAS) imaging algorithms are suitable for narrow-beam width, which will lead to a decrease in imaging quality under wide-beam condition and are not in line with the development needs of SAS. We propose a non-linear chirp scaling algorithm (NCSA) for wide beam multi-receiver SAS. Firstly, the point target reference spectrum (PTRS) of each receiver is obtained by the Lagrange inversion theorem (LIT), and then the under-sampled signal in the azimuth frequency domain is obtained through azimuth spectrum extension; Then, considering the cubic term of range frequency in the PTRS and the linear variation of equivalent frequency modulation slope with range, each receiver is imaged using the NCSA, and coherent superposition is performed in the azimuth frequency domain to eliminate spectrum aliasing caused by azimuth spectrum extension; Finally, the azimuth inverse transform is performed on the superimposed signal to obtain the focusing imaging. Computer simulation experiments and field data verify that this method is superior to the existing SAS imaging algorithm, improving the quality of wide-beam imaging, avoiding the interpolation operation of the traditional range-Doppler algorithm, and saving computation cost.

Parameter identification method of nonuniform and under-sampled blade tip timing based on extended DFT and compressed sensing

Vibration amplitude and frequency are the two most important indicators that characterize the health status of high-speed rotating blades, but the signal obtained by blade tip timing (BTT) technology, one of the best rotating blade vibration monitoring methods, is seriously nonuniform and under-sampled, which makes these two indicators difficult to identify. In view of this problem, the paper proposes a parameter identification method for the nonuniform and under-sampled BTT signal based on extended Discrete Fourier transform and compressed sensing (CS), with the Fourier integral transformation as the goal. It realizes the frequency analysis of nonuniform under-sampled signals by constructing and optimizing the transformation basis function instead of the exponential basis in the traditional FFT transformation in the extended frequency range, and then constructs a CS model through the obtained blade vibration frequency. The complete waveform of the blade vibration is restored by using a small number of under-sampled signals, thus obtaining the blade vibration amplitude and vibration frequency. On the one hand, the method proposed in this paper breaks through the limitation of Nyquist’s sampling theorem, and the number of analytical spectral lines is no longer limited to the number of sampling points, which improves the frequency resolution. On the other hand, only a small number of measurement signals can be reconstructed to achieve a complete vibration signal. The feasibility and reliability of the proposed method are verified by mathematical modeling, simulation analysis, and experimental testing. The results indicate that when the number of sensors is greater than or equal to four, the time domain and frequency domain signals of blade vibration can be accurately analyzed based on the proposed method, the vibration amplitude error is less than 0.01 mm, the frequency error is less than 0.1 Hz, and it has good anti-interference performance.

An undersampling phase measurement algorithm based on parameter estimation for homodyne interferometer

To meet the needs of high speed measurement on hardware, undersampling technique is applied to displacement measurement homodyne interferometer. For orthogonal undersampled signals, the phase to be measured cannot be solved by arctangent function and original unwrapping algorithm. In this paper, a corresponding algorithm is proposed to measure the phases of the undersampled signals in practical conditions. The algorithm is a combination of the original phase solving algorithm and the compensation period. In the algorithm, the phase estimation and the error parameter model based on least square fitting are used to iteratively solve the desired phase. The proposed method is verified by simulations and experiments, and results demonstrate the high feasibility and accuracy of the algorithm.

Federated End-to-End Unrolled Models for Magnetic Resonance Image Reconstruction.

Image reconstruction is the process of recovering an image from raw, under-sampled signal measurements, and is a critical step in diagnostic medical imaging, such as magnetic resonance imaging (MRI). Recently, data-driven methods have led to improved image quality in MRI reconstruction using a limited number of measurements, but these methods typically rely on the existence of a large, centralized database of fully sampled scans for training. In this work, we investigate federated learning for MRI reconstruction using end-to-end unrolled deep learning models as a means of training global models across multiple clients (data sites), while keeping individual scans local. We empirically identify a low-data regime across a large number of heterogeneous scans, where a small number of training samples per client are available and non-collaborative models lead to performance drops. In this regime, we investigate the performance of adaptive federated optimization algorithms as a function of client data distribution and communication budget. Experimental results show that adaptive optimization algorithms are well suited for the federated learning of unrolled models, even in a limited-data regime (50 slices per data site), and that client-sided personalization can improve reconstruction quality for clients that did not participate in training.

The connection between digital-twin model and physical space for rotating blade: an atomic norm-based BTT undersampled signal reconstruction method

The connection between digital-twin model and physical space for rotating blade: an atomic norm-based BTT undersampled signal reconstruction method

A Novel Blade Vibration Monitoring Experimental System Based on Blade Tip Sensing

Due to its non-intrusive manner, blade tip timing (BTT) is considered a potential tool for the condition monitoring of turbomachinery. The challenge of BTT relates to significant under-sampled signal processing, which is induced by a lower number of probes. Signal processing assumes that the ability of the hardware system can meet the requirements of the software algorithm. The abilities of the hardware, including the time resolution of the data acquisition system (DAS) and the dynamic characteristics of rigs, are compromised, particularly when the rotating speed increases. This increase in speed causes two problems for BTT: (1) the rig is less stable, due to the reduction of dynamic stiffness; (2) the time resolution of the DAS can be inadequate for identification. To promote the performance of the hardware system, here a BTT rig was designed with high dynamic performance, including a new DAS with a time resolution of 10 ns. A variety of commonly used BTT signal processing methods are used to analyze the experimental data and verify the good reliability and validity of the experimental platform.

Considerations for Generating Frequency Modulation Waveforms for Fourier Transform-Ion Mobility Experiments.

By casting the information regarding an ion population's mobility in the frequency domain, the coupling of time-dispersive ion mobility techniques is now imminently compatible with slower mass analyzers such as ion traps. Recent reports have detailed the continued progress toward maximizing the efficiency of the Fourier transform ion mobility-mass spectrometry (FT-IM-MS) experiments, but few reports have outlined the intersection between the practical considerations of implementation against the theoretical limits imposed by traditional signal processing techniques. One of the important concerns for Fourier-based multiplexing experiments is avoiding signal aliasing as a product of undersampled signals that may occur during data acquisition. In addition to traditional considerations such as detector sampling frequency, the limitations (i.e., maximum measurable drift time) imposed by experimental mass scan duration and the frequency sweep used for ion gate modulation must also be assessed. This work aims to connect the fundamental underpinnings of FT-IM-MS experiments and the associated experimental parameters that are encountered when coupling the comparatively fast separations in the mobility domain with the slower m/z scanning common for ion-trap mass analyzers. In addition to stating the relevant theory that applies to the FT-IM-MS experiment, this report highlights how aliased signals will manifest post Fourier transform in reconstructed arrival time distributions and calculated mobilities.

A novel method for identification of synchronous resonance frequency of blades based on random arrangement of tip-timing probes

Blade tip-timing (BTT) signal suffers from the undersampling feature, which causes the high-frequency information to be aliased to the low-frequency band, especially the aliasing problem of the synchronous resonance frequency more serious. In order to realize the frequency identification of undersampled signals in synchronous resonance, a novel multiscale cyclic-reverse optimized arrangement (MC-ROA) method based on the random arrangement of tip-timing probes is proposed in this paper. Firstly, a sparse model for frequency recovery is built based on the link between the known undersampled signals and the unknown original signals in the frequency domain, and the subspace pursuit (SP) algorithm of compressive sensing (CS) is used for frequency recovery. Then, under the random arrangement of probes, the number of ideal probes is adjusted at multiple scales and the datum probes are selected cyclically to obtain multiple sets of solutions. Finally, the target frequency weights are used to overcome the limitations of the restricted isometry property (RIP) of the parameterized compression matrix to determine the optimal recovery frequency. The BTT experiments are given to verify the effectiveness of the proposed method.

Characteristics analysis of blade tip timing signals in synchronous resonance and frequency recovery based on subspace pursuit algorithm

Long-term high cycle fatigue vibration will lead to the reduction of life of the blade. Blade Tip Timing (BTT) technology is a research hotspot in the non-contact measurement of blades. Due to the limitation of the number of sensors, BTT signals present serious undersampled conditions. Identifying the frequency of blade vibration through the analysis of undersampled signals is the key problem of the current BTT technology. A sub-Nyquist technique, called multi-coset sampling (MCS), which is suitable for the BTT sampling model can be applied. In this paper, the characteristics of BTT signals under blade synchronous resonance are described and the deficiency of this feature in the recovery process using the orthogonal matching pursuit (OMP) algorithm is found. Based on the problem, the subspace pursuit (SP) algorithm adapted to this feature is proposed. The validity of the algorithm is verified by the blade rotation experiment. The advantage of this algorithm is that the synchronous resonance frequency of the blades can be recovered with a higher probability, which provides a new idea for the development of BTT technology.

A Time–Frequency Representation Approach of Undersampled Signals With Multiple Periodic FM Components

Periodic frequency-modulated (FM) interference signals, commonly employed by jammers and radars, may lead to the performance degradation or even failure of global navigation satellite systems and wireless communications. Time–frequency (TF) representations play an essential role in FM signal analysis and instantaneous frequency (IF) estimation, which is the basis of many nonstationary interference suppression algorithms. This article provides a TF representation approach for signals with multiple periodic FM components in the presence of sample loss. The proposed approach utilizes the periodicity and the sparsity of signal components in the TF domain to suppress cross-terms and artifacts. We reconstruct TF distributions of each component by time-averaging Wigner–Ville distribution. Then, the residual artifacts are eliminated by a low-complexity sparse-based adaptive directional TF filtering method. Simulation results confirm that the proposed approach provides an outstanding suppression of cross-terms and artifacts. The proposed TF representation approach can effectively improve the accuracy of the IF estimation of each signal component.

Vehicle axle detection from under-sampled signal through compressed-sensing-based signal recovery

In traffic data collection, sampling design should satisfy the requirements of identifying prominent pulses corresponding to vehicle axle passage. Insufficient measurement leads to signal distortion and attenuation, reducing the quality of signal pulses. This study exploits the value of under-sampled data by applying compressed sensing (CS) methods to recover signal components that are critical for vehicle axle detection. Two CS methods are investigated in this study to recover the strain signal pulses from inside-pavement instrumented sensors at high-speed traversals. The CS methods successfully recovered the signal pulses from all axles of the truck used for testing. A comparison of the measured axle distances with the reference measurements validated the effectiveness of signal recovery methods. Therefore, the CS methods have the potential of reducing the cost, energy consumption, and data storage space, and improving the data transmission efficiency in practical implementations by enabling sampling devices designed for static measurements to achieve dynamic measurements.

Sub-Nyquist optical pulse sampling for photonic blind source separation.

We propose and experimentally demonstrate an optical pulse sampling method for photonic blind source separation. The photonic system processes and separates wideband signals based on the statistical information of the mixed signals, and thus the sampling frequency can be orders of magnitude lower than the bandwidth of the signals. The ultra-fast optical pulses collect samples of the signals at very low sampling rates, and each sample is short enough to maintain the statistical properties of the signals. The low sampling frequency reduces the workloads of the analog to digital conversion and digital signal processing systems. In the meantime, the short pulse sampling maintains the accuracy of the sampled signals, so the statistical properties of the under-sampled signals are the same as the statistical properties of the original signals. The linear power range measurement shows that the sampling system with ultra-narrow optical pulse achieves a 30dB power dynamic range.

Optimization and assessment of blade tip timing probe layout with concrete autoencoder and reconstruction error

Blade tip timing (BTT) is a promising non-contact measurement method for blade vibration monitoring. The limited number of probes leads to the inherent under-sampled problem of BTT signal. The quality of the analysis result of under-sampled signal depends on the probe layout. However, the application of existing probe layout optimization methods requires domain knowledge about blade vibration. Additionally, the lack of comparisons of probe layouts generated by different probe layout optimization methods makes it difficult to evaluate the performance of different methods. In this paper, we proposed a new probe layout optimization method based on a concrete autoencoder to reduce the reliance on the domain knowledge. The probe layouts were compared using an independently trained reconstructor in the time domain. And the spectral distance was defined to evaluate the performance of different probe layouts in the frequency domain. The validation results showed that the proposed method has superior time domain reconstruction performance and decent frequency domain reconstruction performance compared to other methods. The most informative and representative probe layout can be effectively selected by the proposed method.

Time-Frequency Sparse Reconstruction of Non-Uniform Sampling for Non-Stationary Signal

We address the problem of the reconstruction of time-frequency characteristics of sparse multi-band signals by using the discrete multi-coset sampling (DMCS) model. In this article, the signal is characterized by complicated time-variable components. According to the feature of the short-time Fourier transform (STFT) analysis method, we obtain the rewritten matrix form of the discrete STFT. Then, an analysis method of the multi-coset sliding window (MCSW) is proposed, and the discrete multi-coset sampling sequence is locally windowed. The sparse signal reconstruction algorithm is used to obtain the optimal time-frequency reconstruction value of the original signal. Numerical simulations show the feasibility of this method. We simulate the effects of measurement noise, sampling rate, and time-frequency analysis parameters on the reconstruction accuracy. Our method can carry out time-frequency reconstruction for undersampled signals obtained from multi-coset sampling to ensure the time-varying feature of the original signals, which can well highlight the characteristics of signals. The method is of great significance to the research and development of the sub-Nyquist sampling technique.

Optimization of Nonuniform Sensor Placement for Blade Tip Timing Based on Equiangular Tight Frame Theory

Abstract Blade tip timing (BTT) data are usually an under-sampled signal and are vulnerable to noise and sensor failures. In this paper, based on an arbitrary-angle compressed-sensing method and equiangular tight frame theory, combined with a niching microgenetic algorithm, a method for placing BTT sensors is proposed to ensure higher reconstruction accuracy and reliability. If the dimensions of the sensing matrix are moderate, the index range of arrangements with excellent performance in multifrequency signal reconstruction is determined by enumerating all the uniform-distribution extraction placements. A two-parameter search method is then proposed. Reconstruction of a mixed-signal is carried out to verify the asynchronous signal-reconstruction performance. Thus, to achieve a larger frequency multiplication recognition range and probe-installation flexibility, a method for optimizing the BTT sensor placement is proposed. Finally, a finite-element simulation of the signal from an aero-engine fan blade is used to verify the reconstruction ability of the proposed method. The results show that the placement determined by the optimization algorithm can achieve similar or even better performance than the optimal placement under uniform distribution extraction. The proposed sensor-placement optimization method has a high reconstruction success rate and the BTT system is robust. This approach has significant value for engineering applications.