Conventional Cross-correlation Method Research Articles

Deep learning for particle image velocimetry with attentional transformer and cross-correlation embedded

Deep learning-powered methodologies have realized remarkable advancements in the fluid mechanics community, including applications in the particle image velocimetry (PIV) task. However, previous deep learning-based methods still lack robustness and generalization in the real flow scenarios. To solve this problem, we put forward a deep learning architecture called DeepST-CC for PIV estimation, which embeds an attentional transformer and cross-correlation strategy. Specifically, we introduce the Swin Transformer into the optical flow model Recurrent All-pairs Field Transforms (RAFT) to enhance the features of flow images. Then, the global matching between features is efficiently computed by applying a 4D correlation volume. Afterwards, the conventional cross-correlation method derives the initial velocity field from a coarse correlation, which is fed to the GRU-based flow update module. This approach enhances the robustness of the proposed model by incorporating coarse velocity information. Finally, a supervised learning strategy is performed to guide the model training on the synthetic dataset. Extensive experimental are conducted to demonstrate that our proposed approach delivers exceptional performance on the public dataset. In addition, DeepST-CC exhibits good generalization ability towards complex experimental PIV images.

Lamb-Waves-Based Sparse Distributed Penetrating Communication via Phase-Position Modulation for Enclosed Metal Structures

Sensor nodes have been widely used for mechanical equipment condition monitoring, especially for enclosed metal structures. In these cases, it is important to achieve communication between the sensor nodes inside the enclosed metal structures and the outside receiver node. Conventional wired communication using cables will affect the structural integrity, and wireless communication using electromagnetic waves will be shielded by metal structures, so neither is desirable. Motivated by these issues, this study proposes a Lamb waves-based sparse distributed penetrating communication (SDPC) system using the propagation characteristics of Lamb waves considered harmful in previous studies to accomplish wireless simultaneous data communication. Combining phase shift keying and pulse position modulation mechanisms, a phase-position modulation (P-PM) technology is proposed to improve the communication rate. To overcome the intersymbol interference (ISI) problem caused by the propagation characteristics of Lamb waves, a phase-position sparse reconstruction (P-PSR) strategy is proposed for demodulation, which is more convenient and accurate compared with the conventional cross-correlation method. It should be noted that the maximum bit rate without bit error reaches 830.48 kbps via P-PM parameter optimization, which is 8.3 times higher than that of on-off keying modulation approach under the same experimental conditions. Finally, distributed communication experiments and simulations further verify the high accuracy, efficiency and strong robustness of the proposed SDPC system, which can meet the communication requirements of enclosed metal structures.

Research and Application of Microseismic First Arrival Picking Method Based on Geophone Spacing Constraint

Picking the first arrival of microseismic events has been widely recognized as an essential step for data processing of microseismic monitoring. In this paper, we have provided a practical method, which was developed by introducing geophone spacing constraint to original cross-correlation functions for further optimization of seismic arrival picking. First, all valuable traces are processed by a cross-correlation algorithm and time difference correction. Then, based on distance constraints between geophones, local cross-correlation is applied to manipulate those acquired records for further time difference correction and multi-trace records after the second time difference correction are superimposed to form stacking traces, followed by picking the arrivals of microseismic events using the STA/LTA method. Finally, by combining the stacking of first arrival information and the relative correction of time difference, the first arrival time of microseismic events can be obtained. The actual data processing results show that, compared with the conventional multi-trace cross-correlation method, our proposed method reasonably avoids the influence of the offset on the first arrival time, thus effectively improving the accuracy of the first arrival picking of microseismic events.

Time-Delay Estimation of Microseismic DAS Data Using Band-Limited Phase-Only Correlation

Time-delay estimation is a critical step in many geophysical applications. Conventional approaches are mainly based on the cross correlation of waveforms in time domain but show strong distortions with multiple oscillations and side lobes. We propose a band-limited phase-only correlation (POC) algorithm for time-delay estimation. The algorithm involves the following key steps: 1) transforming 1-D waveform into 2-D time–frequency spectra using S-transform; 2) calculating the band-limited POC function of the transformed spectra; and 3) measuring time delays by analyzing POC coefficient. We demonstrate the effectiveness of the proposed algorithm using synthetic and real microseismic fiber-optic distributed acoustic sensing (DAS) datasets. Results show that POC can effectively and accurately estimate the time delays of waveforms. Compared with the performance of the conventional cross correlation method in time domain, the proposed method has three main advantages: 1) better identification of event and noise waveforms; 2) lower uncertainty of narrow correlation peaks; and 3) weaker distortions with small oscillations and side lobes.

Kinematic training of convolutional neural networks for particle image velocimetry

Convolutional neural networks (CNNs) offer an alternative to the image cross-correlation methods used in particle image velocimetry (PIV) to reconstruct the fluid velocity field from the experimental recording. Despite the flexibility of CNNs, the accuracy and robustness of the standard image processing remains unsurpassed for general PIV data. As CNNs are non-linear and typically entail up to millions of trainable parameters, they require large and carefully designed training datasets to avoid over-fitting and to obtain results that are accurate for a wide range of flow conditions and length scales. Most training datasets consist of PIV-like data that are generated from displacement fields resulting from numerical flow simulations, which, in addition of being computationally expensive, may be able to inform the network only about relatively few classes of flow problems. To overcome this issue and improve the accuracy of the velocity reconstructed by CNNs, we propose to train the networks with synthetic PIV-like data generated from random displacement fields. The underlying idea is that the training dataset simply needs to teach the network about the kinematic relationship between position and velocity. These kinematic training datasets are computationally inexpensive and may allow a much richer variability in terms of length scales by varying the generation parameters. By training a state-of-the-art CNN, we investigate the accuracy of the reconstructed displacement and velocity with synthetic and experimental test cases, such as a sinusoidal flow and wind-tunnel data from a turbulent-boundary-layer and a cylinder-wake experiment. We demonstrate that kinematic training can drastically improve the accuracy of the CNN and allows the network to outperform conventional cross-correlation methods, being more robust with respect to data noise and providing reconstructed velocity fields that have considerably higher spatial resolution (at pixel level).

A new method to estimate the total magnetization direction from the magnetic anomaly: Multiple correlation

Natural remanent magnetization diverts the direction of the total magnetization vector from the earth’s magnetic field direction. It is important to determine the magnetization direction because the processing and inversion of magnetic usually need the magnetization direction as a priori information. The conventional strategy for estimating the magnetization direction is to compute the crosscorrelation between the reduced-to-the-pole (RTP) field and one magnetic magnitude transform, which is insensitive to the magnetization direction. A new theory and method are proposed that the total magnetization direction is determined by computing the multiple correlation coefficients between the RTP field and the multiple direction-insensitive magnitudes transforms, such as the total magnitude anomaly and the normalized source strength. The linear regression between the RTP field and the direction-insensitive magnitude transforms is established. Then, the correlation is computed by the RTP field and the constructed regressor. The proposed method is tested on synthetic of single and complex models, respectively. Then, the method is applied to the field data of the Yeshan region (eastern China) and the Black Hill Norite (southern Australia). The proposed multiple correlation is an extension of the conventional crosscorrelation method that provides an accurate and robust way to estimate the magnetization direction from the total field anomaly.

A New Adaptive GCC Method and Its Application to Slug Flow Velocity Measurement in Small Channels.

In this work, an adaptive generalized cross-correlation (AGCC) method is proposed that focuses on the problem of the conventional cross-correlation method not effectively realizing the time delay estimation of signals with strong periodicity. With the proposed method, the periodicity of signals is judged and the center frequencies of the strongly periodical components are determined through the spectral analysis of the input signals. Band-stop filters that are used to suppress the strongly periodical components are designed and the mutual power spectral density of the input signals that is processed by the band-stop filters is calculated. Then, the cross-correlation function that is processed is the inverse Fourier transform of the mutual power spectral density. Finally, the time delay is estimated by seeking the peak position of the processed cross-correlation function. Simulation experiments and practical velocity measurement experiments were carried out to verify the effectiveness of the proposed AGCC method. The experimental results showed that the new AGCC method could effectively realize the time delay estimation of signals with strong periodicity. In the simulation experiments, the new method could realize the effective time delay estimation of signals with strong periodicity when the energy ratio of the strongly periodical component to the aperiodic component was under 150. Meanwhile, the cross-correlation method and other generalized cross-correlation methods fail in time delay estimation when the energy ratio is higher than 30. In the practical experiments, the velocity measurement of slug flow with strong periodicity was implemented in small channels with inner diameters of 2.0 mm, 2.5 mm and 3.0 mm. With the proposed method, the relative errors of the velocity measurement were less than 4.50%.

High Precision Phase-OFDR Scheme Based on Fading Noise Suppression

In recent years, Optical Frequency Domain Reflectometry (OFDR) has been able to realize strain measurement with high sensitivity and high spatial resolution (SR) along the sensing fiber. Compared with the conventional cross-correlation method, OFDR based on phase-measuring method has the potential to obtain strain information with better SR. However, the accuracy of this method is severely affected by coherent fading. In this paper, a method combining multi-frequency detection and nearest neighbor analysis is proposed to solve this problem. By comparing the sub-phase curves in different wavelength regions, we successfully eliminate the interference of fading noise and obtain the undistorted phase signal. Finally, in the case of an effective wavelength scanning range of 3.6 nm (corresponding to the ranging SR of 0.22 mm), we realized the deformation measurement with standard deviation of 0.015 μm and SR of 1.1 mm, as well as the strain measurement with standard deviation of 0.55 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μϵ</i> and SR of 5.6 cm. The experimental results also show that compared with the conventional multi-frequency average method, the proposed scheme can achieve similar phase measurement accuracy under less frequency division, so as to obtain better SR in the same scanning range.

Experimental velocity data estimation for imperfect particle images using machine learning

We propose a method using supervised machine learning to estimate velocity fields from particle images having missing regions due to experimental limitations. As a first example, a velocity field around a square cylinder at the Reynolds number of ReD=300 is considered. To train machine learning models, we utilize artificial particle images (APIs) as the input data, which mimic the images of the particle image velocimetry (PIV). The output data are the velocity fields, and the correct answers for them are given by a direct numerical simulation (DNS). We examine two types of the input data: APIs without missing regions (i.e., full APIs) and APIs with missing regions (lacked APIs). The missing regions in the lacked APIs are assumed following the exact experimental situation in our wind tunnel setup. The velocity fields estimated from both full and lacked APIs are in great agreement with the reference DNS data in terms of various statistical assessments. We further apply these machine learned models trained with the DNS data to experimental particle images so that their applicability to the exact experimental situation can be investigated. The velocity fields estimated by the machine learned models contain approximately 40 fold denser data than that with the conventional cross-correlation method. This finding suggests that we may be able to obtain finer and hidden structures of the flow field, which cannot be resolved with the conventional cross-correlation method. We also find that even the complex flow structures are hidden due to the alignment of two square cylinders, the machine learned model is able to estimate the field in the missing region reasonably well. The present results indicate a great potential of the proposed machine learning-based method as a new data reconstruction method for PIV.

Estimation of the size and structure of the broad line region using Bayesian approach

ABSTRACT Understanding the geometry and kinematics of the broad line region (BLR) of active galactic nuclei (AGN) is important to estimate black hole masses in AGN and study the accretion process. The technique of reverberation mapping (RM) has provided estimates of BLR size for more than 100 AGN now; however, the structure of the BLR has been studied for only a handful number of objects. Towards this, we investigated the geometry of the BLR for a large sample of 57 AGN using archival RM data. We performed systematic modelling of the continuum and emission line light curves using a Markov chain Monte Carlo method based on Bayesian statistics implemented in PBMAP (Parallel Bayesian code for reverberation−MAPping data) code to constrain BLR geometrical parameters and recover velocity integrated transfer function. We found that the recovered transfer functions have various shapes such as single-peaked, double-peaked, and top-hat suggesting that AGN have very different BLR geometries. Our model lags are in general consistent with that estimated using the conventional cross-correlation methods. The BLR sizes obtained from our modelling approach is related to the luminosity with a slope of 0.583 ± 0.026 and 0.471 ± 0.084 based on H β and H α lines, respectively. We found a non-linear response of emission line fluxes to the ionizing optical continuum for 93 ${{\ \rm per\ cent}}$ objects. The estimated virial factors for the AGN studied in this work range from 0.79 to 4.94 having a mean at 1.78 ± 1.77 consistent with the values found in the literature.

Optical-Flow Algorithm for Near-Wake Analysis of Axisymmetric Blunt-Based Body at Low-Speed Conditions

Abstract In this study, ability of an optical-flow algorithm in extracting wake structure of axisymmetric model was investigated. The initial data for optical-flow processing were obtained in low-speed conditions by particle image velocimetry method. The Reynolds number based on the model diameter was around ReD = 1.97 × 104 in this study. Both the time-averaged and transient flow characteristics of near-wake flow were illustrated and examined by the optical-flow analysis method proposed. The processing results of optical-flow method showed good agreement with conventional cross-correlation methods. The ability of optical-flow method to extract flow fields was, thereby, confirmed for blunt-based flow at low-speed conditions. This study showed that the antisymmetric flow behavior of the near wake is the dominant type at low-speed conditions. Differing to traditional methods and cross-correlation results, the optical-flow results showed a frequency at around StD = 0.015 of the near wake for the first time, which is connected to vortex shedding behavior of the wake flow.

MCNP-polimi simulation for the compressed-sensing based reconstruction in a coded-aperture imaging CAI extended to partially-coded field-of-view

This paper deals with accurate image reconstruction of gamma camera using a coded-aperture mask based on pixel-type CsI(Tl) scintillator coupled with silicon photomultipliers (SiPMs) array. Coded-aperture imaging (CAI) system typically has a smaller effective viewing angle than Compton camera. Thus, if the position of the gamma source to be searched is out of the fully-coded field-of-view (FCFOV) region of the CAI system, artifacts can be generated when the image is reconstructed by using the conventional cross-correlation (CC) method. In this work, we propose an effective method for more accurate reconstruction in CAI considering the source distribution of partially-coded field-of-view (PCFOV) in the reconstruction in attempt to overcome this drawback. We employed an iterative algorithm based on compressed-sensing (CS) and compared the reconstruction quality with that of the CC algorithm. Both algorithms were implemented and performed a systematic Monte Carlo simulation to demonstrate the possiblilty of the proposed method. The reconstructed image qualities were quantitatively evaluated in sense of the root mean square error (RMSE) and the peak signal-to-noise ratio (PSNR). Our simulation results indicate that the proposed method provides more accurate location information of the simulated gamma source than the CC-based method.

Particle volume flow rate measurement by combination of dual electrical capacitance tomography sensor and plug flow shape model

Particle volume flow rate QPLUG· in plug flow through a cross section of horizontal pipe has been accurately measured by a combination of dual electrical capacitance tomography sensor and plug flow shape model (dECT-PFSM). The plug flow shape model divides the trapezoidal shape of the plug flow into three flow regions which are Tip, Filling, and Tail regions. The plug flow volume VPLUG is estimated by velocity and length which are measured in each region by the normalized permittivity signal changes obtained from the dECT images under the plug flow in the trapezoidal shape. The path time difference of the plug flow ΔtPLUG is also measured. The total volume flow rate of the plug flow is subsequently obtained from the sum of the plug flow volume of the three regions divided by ΔtPLUG. Consequently, the volume flow rate of the plug flow obtained by dECT-PFSM QECT, PFSM· is compared with that of high-speed camera (HSC) as reference and conventional cross-correlation (CC) method. The absolute error Eabs of the proposed method is less than that of the CC method. The dECT-PFSM method is, therefore an affordable noninvasive technique for accurate determination of the volume flow rate of the plug flow.

Use of PVDF Wire Sensors for Leakage Localization in a Fluid-Filled Pipe.

The detection and location of pipeline leakage can be deduced from the time difference between the arrival leak signals measured by sensors placed at the pipe access points on either side of a suspected leak. Progress has been made in this area to offer a potential improvement over the conventional cross-correlation method for time delay estimation. This paper is concerned with identifying suitable sensors that can be easily deployed to monitor the pipe vibration due to the propagation of leak noise along the pipeline. In response to this, based on the low-frequency propagation characteristics of leak noise in our previous study, polyvinylidene fluoride (PVDF) wire sensors are proposed as a potential solution to detect the pipeline leak signals. Experimental investigations were carried out at a leak detection pipe rig built in the Chinese Academy of Sciences. Their performances for leak detection were shown in comparison with hydrophones. It is suggested that with special considerations given to aspects pertaining to non-intrusive deployment and low cost, the PVDF wire sensors are of particular interest and may lead to a promising replacement for commercial leak noise transducers.

A discrete time domain approach on time delay estimation

A time delay estimation method based on the discrete time domain approach is introduced here. In this dual-channel time delay estimation model, the criterion function compares the time differences of time sequences between channels, not the magnitude values of time functions as in the conventional cross-correlation method. An estimation task is formulated as an extreme value problem in discrete index space. Using the index delay giving extreme value to the criterion function, it is possible to find the best estimate for time delay distribution in the meaning of that criterion. Using this method, the estimated delay distribution and criterion function are clearly separated. Thus, there are no theoretical problems in the determination of the average time delay or velocity in the non-constant or changing time delay case as long as a sufficient statistical similarity (correlation) exists between channel signals. &lt;p class="Abstract"&gt;The theoretical values of several criterion functions and the probability of occurrence of an anomalous estimate with the cross-covariance criterion function are derived. A basic performance analysis of the estimation method is presented. Some potential real-time supervision methods based on the use of criterion functions in the detection of the possible unreliability of the time delay estimate are outlined.&lt;/p&gt;

Bender element measurement of small strain shear modulus of cement-treated marine clay – Effect of test setup and methodology

This paper examines the effect of experimental methodology on the measurement of small strain shear modulus of cement-treated marine clay using bender element. The specimens tested have cement content ranging from 20% to 50%, this being the typical range of cement content used for ground improvement in relation to underground construction. The experimental aspects studied include specimen set-up, travel time identification, excitation frequency and specimen size effects. The results indicate that, where a pre-made slot is used for the bender element, infilling the slot with an appropriate material will help to enhance probe-soil contact, reduce the sensitivity of the measurements to slot size accuracy and ensure consistency in received signal. Both the first arrival and first peak approaches for travel time determination are found to be sensitive to the system. The conventional cross-correlation method was also found to give erroneous measurements when the second peak is higher than the first. A modified cross-correlation method with window control is proposed which works well with both bender element systems studied. The source frequency used should also be higher than 3 kHz and the wave path length to wave length ratio should be larger than about 0.73. Finally aspect ratio of much higher 2 may also lead to erroneous measurements and should be avoided.

Optical-flow-based background-oriented schlieren technique for measuring a laser-induced underwater shock wave

The background-oriented schlieren (BOS) technique with the physics-based optical flow method (OF-BOS) is developed for measuring the pressure field of a laser-induced underwater shock wave. Compared to BOS with the conventional cross-correlation method in PIV (called PIV-BOS), by using the OF-BOS, the displacement field generated by the small density gradient in water can be obtained at the spatial resolution of one vector per pixel. The corresponding density and pressure fields can be further extracted. It is particularly demonstrated that the sufficiently high spatial resolution of the extracted displacement vector field is required in the tomographic reconstruction to correctly infer the pressure field of the spherical underwater shock wave. The capability of the OF-BOS is critically evaluated based on synchronized hydrophone measurements. Special emphasis is placed on direct comparison between the OF-BOS with the PIV-BOS.

Passive-source multitaper-spectral method based low-frequency data reconstruction for active seismic sources

Passive seismic data contain large amounts of low-frequency information. To effectively extract and compensate active seismic data that lack low frequencies, we propose a multitaper spectral reconstruction method based on multiple sinusoidal tapers and derive equations for multisource and multitrace conditions. Compared to conventional cross correlation and deconvolution reconstruction methods, the proposed method can more accurately reconstruct the relative amplitude of recordings. Multidomain iterative denoising improves the SNR of retrieved data. By analyzing the spectral characteristics of passive data before and after reconstruction, we found that the data are expressed more clearly after reconstruction and denoising. To compensate for the low-frequency information in active data using passive seismic data, we match the power spectrum, supplement it, and then smooth it in the frequency domain. Finally, we use numerical simulation to verify the proposed method and conduct prestack depth migration using data after low-frequency compensation. The proposed power-matching method adds the losing low frequency information in the active seismic data using the low-frequency information of passivesource seismic data. The imaging of compensated data gives a more detailed information of deep structures.

Phase-shift correlation method for accurate phase difference estimation in range finder.

High-precision phase-difference measurement is a key technology for a phase-shift laser range finder. In order to improve the estimation accuracy of phase difference between two sinusoidal signals with identical frequency, the phase-shift correlation method is described. Theoretical analysis shows that the conventional cross-correlation method will bring notable deviations when the true phase difference is close to 0° or 180° in the presence of noise. For reducing the influence of noise, two step calculations--phase-shift autocorrelation and phase-shift cross correlation--are used in the phase-shift correlation method. The estimation bias is eliminated by phase-shift autocorrelation in which the autocorrelation is calculated between the 2π phase-shifted signal and the original signal, and the periodic errors are eliminated by phase-shift cross correlation in which the phase difference is estimated when the true phase difference is near 90° or 270°. The effect of frequency drift on the phase difference is also discussed. The experiment results show that the maximum error of the conventional method is about 0.15°, while the estimation error of our proposed method is much less than 0.01° under the same conditions.

A Cross-Correlation Method in Wavelet Domain for Demodulation of FBG-FP Static-Strain Sensors

Static-strain can be detected by measuring a cross-correlation of two FBG-based Fabry-Perot interferometers (FBG-FPs). This letter addresses applying the wavelet transform to cross-correlation processing in noise-contaminated FBG-FP reflection spectrums for crust deformation measurement. Since the wavelet transform has a unique feature of varying time-frequency resolution, cross-correlation processing in the wavelet domain is more robust with correlated noise and window size and is less sensitive to nonstationary data. We discuss the experimental results in respect of the factors that could influence the sensor resolution. In addition, a staticstrain resolution of 1.3 n\(\varepsilon \) , higher than conventional cross-correlation method is obtained in the laboratory test by using this technique.