Conventional Cross-correlation Research Articles

Single shot interferenceless coded aperture correlation holography via a learnable Wiener deconvolution network

One of the challenges in interferenceless coded aperture correlation holography (I-COACH) is high-quality single-shot reconstruction, as conventional cross-correlation reconstruction algorithm requires recording multiple holograms and complex reconstruction operations, resulting in serious background noise. Here, we present a deep learning based single-shot reconstruction by introducing a learnable Wiener deconvolution network in I-COACH. By feeding the point spread hologram (PSH) of I-COACH system and object hologram (OH) into Wiener deconvolution, a mapping relationship between Wiener deconvolution result and ground truth is generated. A Res-UNet is trained to learn optimal filter and noise regularization parameters, thereby achieving high quality reconstruction. Moreover, the training dataset used in our network are simulated using PSH that is obtained through only one experiment acquisition in advance, greatly simplifying experimental OH dataset acquisition. Compared to the conventional correlation reconstruction methods, the proposed Wiener deconvolution network can conveniently realize high-quality single-shot reconstruction in I-COACH, and the axial sensitivity in 3D reconstruction can be demonstrated by varying scattering degree of coded phase mask. Importantly, this Wiener deconvolution solution will provide an enlightening reference for dynamic imaging in I-COACH.

Comparative evaluation of electrical resistance tomography, positron emission particle tracking and high-speed imaging for analysing horizontal particle-liquid flow in a pipe

We evaluate three experimental techniques - electrical resistance tomography (ERT), positron emission particle tracking (PEPT) and high-speed imaging (HSI) – for analysing the local particle velocity field and spatial distribution in a horizontal particle-liquid pipe flow under varying conditions of solid concentration. A new ERT methodology is devised for estimating particle velocity, circumventing the limitations of the conventional cross-correlation technique. Furthermore, an enhanced HSI approach is introduced and systematically compared with PEPT and ERT. Results show that, under all conditions, PEPT provides the most accurate particle velocity field followed by HSI, whilst ERT yields the most accurate concentration field, followed by HSI. The enhanced HSI emerges as a simple cost-effective option compared to PEPT and ERT. A combined measurement approach using PEPT for local particle velocity and ERT for local concentration, however, delivers the best comprehensive two-phase flow characterization, highlighting potential synergies between these methods for complex flow studies.

Probing Tissue Viscoelasticity With STL Ultrasound Shearwave Spectroscopy Using Cole-Cole Diagrams.

Viscoelasticity is mapped by dispersion in shearwave elastography. Incomplete spectral information of shearwaves is therefore used to estimate mechanical stiffness. We propose capturing the "full-waveform-information" of the shear wave spectra to better resolve complex shear modulus μ* (ω). Approach is validated on phantom models, animal tissues, and feasibility demonstrated on human post-delivery placenta. We captured robust estimates of μ* in ex-vivo livers subjected to water bath ablation, glutaraldehyde exposure and in the placenta. Complex modulus at 200 Hz is more reflective of tissue stiffness than cross-correlation estimate. Bias increased in phantoms with higher gelatin (G) (0.65: 6% G) and oil (O) (0.58: 6% G and 40% O) concentration, compared to elastic phantoms with low stiffness (0.33: 3% G). Actual tissues also reported higher bias in cross-correlation estimate (rabbit liver: 0.61, porcine liver: 2.20, and human placenta: 0.63). Stiffness is sensitive to ablation temperature, where the overall modulus changed from 3.02 KPa at 16 °C to 2.75 KPa at 56 °C in water bath. With exposure to Glutaraldehyde, the overall modulus increased from 2.37 to 9.03 KPa. Reconstruction errors in the loss modulus decreased by 68% with the power law compared to a Maxwell model in porcine livers with Cole-Cole inverse fitting. Omitting Shear wave attenuation leads to bias. Reconstruction of rheological response with a model is sensitive to its architecture and also the framework. We use "full spectral information" in ultrasound shear wave elastography to better map μ*(ω) changes in viscoelastic tissues.

Consistency of the inverse scattering imaging condition, the energy norm imaging condition and the impedance kernel in acoustic and elastic reverse-time migration

Abstract In this work, we draw connections between the imaging conditions using the impedance kernel, the inverse scattering imaging condition, and the energy norm imaging condition in acoustic and elastic reverse-time migration (RTM). Traditional RTM often introduces large low-wavenumber artifacts that degrade image quality in intricate geological structures with large velocity variations. In practice, the Laplacian filter is commonly used to remove these low-wavenumber artifacts, but it changes the image wavenumber spectrum. The advanced imaging conditions of the inverse scattering, the energy norm, and the impedance kernel can effectively remove the low-wavenumber artifacts while not changing the wavenumber spectrum. This study aims to build a connection between these three types of imaging conditions by conducting detailed analysis in the wavenumber domain for acoustic and elastic RTMs. We find that they are exactly the same except for the varying weights of the source-receiver wavefield cross-correlation. All three imaging conditions can generate clear RTM images that are not affected by low-wavenumber artifacts. Numerical examples for a simple model, Sigsbee 2a, and BP models verify the consistency of these three imaging conditions and show their advantage over conventional simple zero-lag cross-correlation imaging conditions. This is important for improving the quality and reliability of seismic imaging technology.

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.

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.

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.

A D-norm cross-correlation method for particle velocity measurement through electrostatic sensing

The cross-correlation (CC) method is conventionally used for measuring the velocity of gas–solid flows using electrostatic sensors, wherein velocity measurement is transformed into a time-delay estimation problem. However, owing to the intricacies of signals in gas–solid flows, the cross-correlation function may exhibit multiple peaks, resulting in peak misjudgment and time-delay estimation bias. To address these issues, this paper proposes a D-norm cross-correlation (DCC) velocity measurement method and applies it to flow velocity measurements in pneumatic conveying. Such a technique leverages the sensitivity of D-norm to pulses, highlighting the pulse characteristics of measurement signals. This approach increases the accuracy of time-delay estimation for upstream and downstream signals, mitigating the issues caused by multi-peaks and fake peaks in the cross-correlation function. Compared to conventional CC, the DCC can eliminate the problem of multiple and fake peaks in cross-correlation functions more effectively, thereby increasing the reliability of velocity measurements.

A model for multiphase flow velocity calculation in pipelines based on ultrasonic sensors

In the petroleum and natural gas industry, a wide variety of multiphase fluids are prevalent, and precise measurement of their flow velocity in pipelines holds significant importance for different stages of well drilling and construction. However, due to the presence of large solid particles and the corrosive nature of the liquid phase in multiphase fluids within the petroleum industry, invasive measurement methods struggle to maintain long-term acceptable detection accuracy. Therefore, the non-contact fluid flow velocity measurement method based on ultrasonic sensors exhibits substantial research value. Nonetheless, when employing this approach for pipeline multiphase fluid flow velocity measurement, the abundance of background interference noise at the site poses challenges in Doppler echo signal reconstruction and results in lower precision for frequency shift extraction, leading to considerable errors in flow velocity calculation results. To address this issue, the present study utilizes a transmit-receive separated continuous wave ultrasonic sensor. First, a mathematical model is developed for the superimposed signal of ultrasonic Doppler echoes within the pipeline. Next, a novel signal reconstruction method is proposed by employing Chebyshev polynomials for interpolation computation of the sampled discrete signals. Subsequently, a Doppler shift model is introduced, leading to the formulation of a new model for multiphase flow velocity calculation in pipelines based on ultrasonic sensors. Finally, a comparison experiment for full-pipe multiphase flow velocity detection is conducted to validate the computational performance of the new model. The experimental results show that, compared with the FFT model and the conventional cross correlation model, the comprehensive meter factor of the ultrasonic flow measurement system with the new model is reduced by 0.024 445, the accuracy is reduced by 2.98%, the nonlinear error is reduced by 2.4405%, the average relative error is reduced by 0.646%, the standard deviation is reduced by 0.045 175, and the root mean squared error is reduced by 0.029 615.

Displacement extraction of background-oriented schlieren images using Swin Transformer.

Displacement extraction of background-oriented schlieren (BOS) is an essential step in BOS reconstruction, which directly determines the accuracy of the results. Typically, the displacement is calculated from the background images with and without inhomogeneous flow using the cross-correlation (CC) or optical flow (OF) method. This paper discusses the disadvantages of the CC and OF methods, and an end-to-end deep neural network was designed to estimate the BOS displacement. The proposed network is based on a Swin Transformer, which can build long-range correlations. A synthetic dataset used for training was generated using the simulated flow field by computational fluid dynamics. After training, the displacement can be obtained using the BOS image pair without additional parameters. Finally, the effectiveness of the proposed network was verified through experiments. The experiments illustrate that the proposed method performs stably on synthetic and real experimental images and outperforms conventional CC or OF methods and classic convolutional neural networks for OF tasks.

Click chemistry, FRET-FCS, and expansion microscopy reveal that Na, K-ATPase forms complexes in the plasma membrane

In order to study the spatial distribution of Na, K-ATPase alpha and beta subunits in the plasma membrane of epithelial cells we have developed sample preparation protocols based on genetic code expansion, click chemistry and expansion microscopy. HEK 293T cells were transiently transfected with constructs containing the coding sequence for Na, K-ATPase subunits (alpha1 and beta1) carrying a premature amber or ochre stop codon. Two bioorthogonal tRNA and tRNA synthetase pairs were also transfected for stop codon suppression and site-specific insertion of two unnatural amino acids. The unnatural amino acids were then labelled with small organic dyes using CuAAC and SPIEDAC click reactions. Care was taken to keep the transfection and expression levels low.In living cells, we used Fluorescence Correlation Spectroscopy (FCS) and FRET to assess the density of click-labeled and endogenous [SE1] Na, K-ATPase in the plasma membrane. The dyes Alexa488 and Alexa647 were used as a FRET sensor for homo- and heterodimer analysis and, using FRET-FCS, we could detect the oligomerization of alpha and beta in a complex containing two alpha and two beta subunits in a heterodimer.FCS measurements in cells where both the alpha and beta subunits were labeled was used to calculate the absolute density of endogenous and exogenous Na, K-ATPase in the plasma membrane. To detect oligomerization, we used cells where the beta subunit was labeled with a 50/50 mix of Alexa488 and Alexa647. We successfully detected FRET signals and an analysis of the FRET-FCS data revealed a high density of oligomers. FRET-FCS is, compared to conventional cross-correlation FCCS, one to two orders of magnitude more sensitive for the detection of oligomers. FRET-FCS is also inherently insensitive to heterogenous labeling efficiencies, which is a great advantage during live cell measurementsExpansion microscopy was performed using a modified MAP protocol, reaching an isotropic expansion of approximately 4.5-fold. Confocal airyscan microscopy of the expanded cells with <50nm resolution revealed local variations in Na, K-ATPase density and enabled detailed cluster analysis.In conclusion we demonstrate that the density of Na, K-ATPase has large local variations and that the Na, K-ATPase oligomerizes in the plasma membrane. We propose that this oligomerization can have a regulatory function for the net efficiency of Na, K-ATPase in the cell. VR 2020-05347, VR 2019-00217 (Swedish Research Council) This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

A lightweight convolutional neural network to reconstruct deformation in BOS recordings

We introduce a Convolutional Neural Network (CNN) that is specifically designed and trained to post-process recordings obtained by Background Oriented Schlieren (BOS), a popular technique to visualize compressible and convective flows. To reconstruct BOS image deformation, we devised a lightweight network (LIMA) that has comparatively fewer parameters to train than the CNNs that have been previously proposed for optical flow. To train LIMA, we introduce a novel strategy based on the generation of synthetic images from random-irrotational deformation fields, which are intended to mimic those provided by real BOS recordings. This allows us to generate a large number of training examples at minimal computational cost. To assess the accuracy of the reconstructed displacements, we consider test cases consisting of synthetic images with sinusoidal displacement as well as images obtained in the experimental studies of a hot plume in air and a flow past and inside a heated hollow hemisphere. By comparing the reconstructed deformation fields using the LIMA or conventional post-processing techniques used in Direct Image Correlation (DIC) or conventional image cross-correlation, we show that LIMA is more accurate and robust in the synthetic test case. When applied to experimental BOS recordings, all methods provide similar and consistent deformation fields. As LIMA is capable of achieving a comparable or better accuracy at a fraction of the computational costs, it represents a valuable alternative to conventional post-processing techniques for BOS experiments.

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.

On the estimation of reflectivity in reverse time migration: Implementational forms of the inverse-scattering imaging condition

The inverse-scattering imaging condition (ISIC) for reverse time migration (RTM) aims at recovering amplitudes proportional to seismic reflectivity. It has been derived as the high-frequency asymptotic inverse of Born modeling, which justifies its being called a true-amplitude imaging condition. It involves the temporal and spatial derivatives of the up- and downgoing wavefields, in this way generalizing the conventional crosscorrelation imaging condition. The temporal derivations can be redistributed between different wavefield contributions, in this way deriving a set of different implementational forms of the ISIC. By making use of the wave equation for the up- and downgoing wavefields, one can substitute the time derivatives by the Laplacian operator. This provides a theoretical foundation for a popular filter for reducing the backscattering artifacts in RTM. Using Born data from a simple three-layer model and the Marmousi II model as well as the Sigsbee2b data, we have determined that the theoretical equivalence of the equations leads to similar but not identical images. Our numerical tests indicate that the ISIC versions using spatial derivatives are the most economical approach, and that the images obtained with the second time derivative of the source wavefield indicate slightly improved resolution over the other implementations, making the combination of these two characteristics the best choice.

Progress towards a Miniaturised PIV System.

Particle image velocimetry is an important optical flow diagnostic tool due to its capacity for investigating a whole flow field without introducing disturbances. However, a significant drawback of PIV methods is their requirement for optical access, making capturing data in closed cavities and confined spaces extremely challenging. A potential approach to overcome this difficulty is miniaturising the system and placing the optical components inside the model. Conventional cross-correlation PIV methods do not allow this due to the size of current PIV cameras. In this study, a miniaturised autocorrelation-based stereo PIV system, which is volumetrically 1.2% of the conventional PIV cameras, was developed and tested. The miniature system is compared with a conventional stereo PIV in wind tunnel experiments up to 16 m/s free stream velocity and a 1.6% velocity difference is observed in the boundary layer flow. Despite a comparatively slow measurement rate of 4.5 Hz, the miniature PIV system demonstrates the ability to measure inside confined spaces and cavities and the ability to be mounted on board models and vehicles. However, limitations remain around conducting measurements with large velocity ranges and with regions of reversed flow due to the challenge of resolving a velocity of 0 m/s.

Simultaneous measurement of microscale fluid viscosity, temperature, and velocity fields by tracking Janus particle on microparticle image velocimetry

Multifunctional sensing capability enables a comprehensive understanding of the unknown target to be measured. Given that fluid viscosity, temperature, and velocity fields are usually coupled parameters in a system, simultaneous measurement of the three environmental factors can prevent cross-talk and improve reliability. However, the task is apparently challenging because of the microscale targets. A technique combining microparticle image velocimetry and Janus particles was developed in this study to address such demand. With the rotational diffusivity and particle trajectories measured by the proposed technique and an empirical water-based viscosity-temperature relationship, the three unknown variables in a microfluidic environment were solved. The blinking frequency was derived using the Hilbert Huang Transform. Compared with those in a static and uniform temperature field, the measured data had good agreement with the predicted values. However, the agreement was impaired when the heating rate exceeded 0.34 °C/s. The optimal temperature range was found between 10 °C and 40 °C in the water-based solution. For a steady-state and nonuniform temperature field, two-dimensional (2D) numerical simulations of three linear temperature gradients were also studied. Results showed that the deviation increased as the temperature gradient increased or was near the low-temperature region. The same procedure was eventually applied to a real thermophoretic flow induced by an IR laser in a microchip. The 2D fluid viscosity, temperature, and velocity fields in the microchip were successfully obtained by tracking 10 particles. The potential of the approach provides insight into understanding some microfluidic applications with mild changes in temperature or creeping flow. This study combined µPIV with Janus particles to achieve simultaneous measurement of 2D microscale fluid viscosity, temperature, and velocity fields. By simply tracking the particles, particle trajectories and blinking signal were obtained. Both parameters provided sophisticated information of particle velocity and rotational diffusivity. With the information, the viscosity and temperature were hence derived from the empirical viscosity–temperature relationship and the Stokes-Einstein-Debye relation. The velocity was derived alone based on the conventional cross-correlation algorithm. • Using Janus particles as tracers to provide dynamic information of blinking signal and trajectories. • Simultaneous measurement of whole field fluid viscosity, temperature, and velocity at the microscale. • Extraction of the frequency spectrum out of blinking signal by Hilbert Huang Transform. • A measurable temperature range between 10 °C and 40 °C.

An Envelope Travel-Time Objective Function for Reducing Source–Velocity Trade-Offs in Wave-Equation Tomography

In conventional cross-correlation (CC)-based wave-equation travel-time tomography, wrong source wavelets can result in inaccurate velocity inversion results, which is known as the source–velocity trade-off. In this study, an envelope travel-time objective function is developed for wave-equation tomography to alleviate the non-uniqueness and uncertainty due to wrong source wavelets. The envelope of a seismic signal helps reduce the waveform fluctuations/distortions caused by variations of the source time function. We show that for two seismic signals generated with different source wavelets, the travel-time shift calculated by cross-correlation of their envelopes is more accurate compared to that obtained by directly cross-correlating their waveforms. Then, the CC-based envelope travel-time (ET) objective function is introduced for wave-equation tomography. A new adjoint source has also been derived to calculate the sensitivity kernels. In the numerical inversion experiments, a synthetic example with cross-well survey is first given to show that compared to the traditional CC travel-time objective function, the ET objective function is relatively insensitive to source wavelet variations and can reconstruct the elastic velocity structures more reliably. Finally, the effectiveness and advantages of our method are verified by inversion of early arrivals in a practical seismic survey for recovering near-surface velocity structures.

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%.