Matched Field Processing Research Articles

Passive defect localization on a vibrating plate using Matched-Field Processing

Passive defect localization on a vibrating plate using Matched-Field Processing (MFP). The aim of this study is to investigate the use of MFP for passive localization of a local change in parameter of a vibrating shell in the modal regime. Matched-Field Processing is a beamforming method that uses the correlation between the recorded data and a controllable digital model of wave propagation (replica) to locate a source. Vibration measurements were conducted on an aluminum plate using a laser vibrometer. The plate was tested both with and without damage (added mass) while being excited by a shaker. Replicas were created by performing modal analysis on measurements taken from the undamaged structure. Matched-Field Processing is applied directly to the measured data to locate the active source (shaker) and to the residues (field difference between undamaged and damaged states) to locate a local variation of the parameter (defect). The method's feasibility is also being explored for passive measurements in modal analysis and residue computation.

Source Range Estimation Using Linear Frequency-Difference Matched Field Processing in a Shallow Water Waveguide

Matched field processing (MFP) is an established technique for source localization in known multipath acoustic environments. Unfortunately, in many situations, imperfect knowledge of the actual propagation environment and sidelobes due to modal interference prevent accurate propagation modeling and source localization via MFP. To suppress the sidelobes and improve the method’s robustness, a linear frequency-difference matched field processing (LFDMFP) method for estimating the source range is proposed. A two-neighbor-frequency high-order cross-spectrum between the measurement and the replica of each hydrophone of the vertical line array is first computed. The cost function can then be derived from the dual summation or double integral of the high-order cross-spectrum with respect to the depth of the hydrophones and the candidate sources of the replicas, where the range that corresponds to the minimum is the optimal estimation. Because of the larger modal interference distances, LFDMFP can efficiently provide only one optimal range within the same range search interval rather than some conventional matched field processing. The efficiency of the presented method was verified using simulations and experiments. The LFDMFP unambiguously estimated the source range in two experimental datasets with average relative errors of 2.2 and 1.9%.

Omni-directional wavenumber dictionary modified imaging method for orthotropic composites damage detection using ultrasonic guided waves

The sparse reconstruction imaging method is promising for detecting damage in isotropic and quasi-isotropic materials. However, its effectiveness relies on an accurate dictionary. When applied to orthotropic materials without accounting for wavenumber directionality, the accuracy of the dictionary degrades, leading to inaccurate damage localization. To address this limitation, this paper presents an omnidirectional wavenumber dictionary modified imaging method for orthotropic composites damage detection. The omni-directional wavenumber dispersion curve of ultrasonic guided waves is calculated numerically by converting of elastic stiffness coefficient of orthotropic composites at various propagation angles. A modified propagation model, informed by the omni-directional wavenumber dispersion curve, enhances the precision of the acoustic field dictionary. Utilizing a coherent matched field processor, the method compares the scattered signal's envelope with the acoustic field dictionary's envelope to generate an ambiguity function, which in turn forms a damage image. Simulation and experimental results confirm the method's superiority in resolving damage localization inaccuracies and artifacts typically associated with orthotropic composites. The proposed method exhibits enhanced signal-to-noise ratio and lower positioning error, facilitating precise multi-damage detection in orthotropic composites compared to existing methods.

An Underwater Target Location Algorithm Combined with Schmidt Orthogonalization

Abstract In underwater target localization research, where challenges such as low signal-to-noise ratio and multiple interferences exist in conventional matched field processing, this paper presents a novel approach combining compressed sensing with Schmidt orthogonalization. Initially, an orthogonalization procedure is applied to the observation matrix, yielding a new matrix with reduced column coherence and maximal adherence to the Restricted Isometry Property (RIP) constraint. Subsequently, the Sparse Adaptive Matching Pursuit (SAMP) algorithm from compressed sensing is employed to reconstruct the signal, leading to precise underwater target localization. Simulation experiments substantiate that this combined approach outperforms the conventional matched field algorithm by yielding a higher signal-to-noise ratio for target acoustic source localization and markedly reducing the count of interference virtual sources. Consequently, the performance of localization for targets is substantially enhanced.

Real-time passive underwater localization using a compact acoustic sensor array

This paper proposes an underwater passive localization system that can be installed on remote platforms and can locate in real-time sound sources using a compact 4-element array. The localization system relies on both the Time Difference of Arrival (TDoA) algorithm to localize sources that are impulsive, and a low-complexity implementation of the matched field processing (MFP) algorithm for broadband continuous waves, such as propeller noise. The array is intended to be mounted on small platforms and compact geometries are investigated to optimize the localization accuracy. Figures of merit are defined to assess the accuracy and reliability of the algorithm as a function of the distance between the elements. The proposed algorithm is implemented on a System-on-Chip (SoC) which executes the algorithm on an embedded system for real-time operation. Finally, the performance is assessed in realistic ocean conditions in different environments. It is shown that the MFP provides an excellent angle estimate for broadband continuous sources, but TDoA is more reliable, particularly when the deployment is sensitive to the environment conditions.

Noise source localization using deep learning

Summary Ambient noise source localization is of great significance for estimating seismic noise source distribution, understanding source mechanisms and imaging subsurface structures. The commonly used methods for source localization, such as the matched field processing and the full-waveform inversion, are time-consuming and not applicable for time-lapse monitoring of the noise source distribution. We propose an efficient alternative of using deep learning for noise source localization. In the neural network, the input data are noise cross-correlation functions and the output are matrices containing the information of noise source distribution. It is assumed that the subsurface structure is a horizontally layered earth model and the model parameters are known. A wavefield superposition method is employed to efficiently simulate ambient noise data with quantities of local noise sources labelled as training datasets. We use a weighted binary cross-entropy loss function to address the prediction inaccuracy caused by a sparse label matrix during training. The proposed deep learning framework is validated by synthetic tests and two field data examples. The successful applications to locate an anthropogenic noise source and a carbon dioxide (CO2) degassing area demonstrate the accuracy and efficiency of the proposed deep learning method for noise source localization, which has great potential for monitoring the changes of the noise source distribution in a survey area.

A Deep Learning Localization Method for Acoustic Source via Improved Input Features and Network Structure

Shallow water passive source localization is an essential problem in underwater detection and localization. Traditional matched-field processing (MFP) methods are sensitive to environment mismatches. Many neural network localization methods still have room for improvement in accuracy if they are further adjusted to underwater acoustic characteristics. To address these problems, we propose a deep learning localization method via improved input features and network structure, which can effectively estimate the depth and the closest point of approach (CPA) range of the acoustic source. Firstly, we put forward a feature preprocessing scheme to enhance the localization accuracy and robustness. Secondly, we design a deep learning network structure to improve the localization accuracy further. Finally, we propose a method of visualizing the network to optimize the estimated localization results. Simulations show that the accuracy of the proposed method is better than other compared features and network structures, and the robustness is significantly better than that of the MFP methods. Experimental results further prove the effectiveness of the proposed method.

Mode-informed complex-valued neural processes for matched field processing

Matched field processing (MFP) is a key technique for passive underwater source localization, estimating the source position by matching array measurements with acoustic model replicas. Its effectiveness relies on matching environmental parameters with the actual oceanic environment, but performance declines with environmental mismatches and lower signal-to-noise ratios. This paper proposes a novel approach that integrates neural networks (NNs) and complex Gaussian processes with modal depth functions for acoustic field reconstruction that is more accurate and efficient compared to Gaussian process regression. A meta-learning strategy is used to optimize parameters of the NN. The reconstructed data are denoised and interpolated, generating densely populated acoustic fields at virtual arrays, which are then used as data in MFP. Replicas are also computed at the virtual receivers. This mode-informed complex-valued neural processes enhance MFP performance, particularly in low SNR and mismatched environments. It captures the propagation properties of underwater acoustic fields more comprehensively, showing superior localization performance in both simulated and real-world data from the SWellEx-96 Event S5 environment.

Acoustic source localization on finite structures using remote sensors

Acoustic waves are well-suited for remote sensing applications and structural health monitoring purposes because they convey information about their source and can be measured using non-contacting methods. Source localization is an important structural health monitoring task; however, traditional time-of-flight array signal processing techniques used to localize acoustic sources are ill-suited for many structural engineering applications due to the potential for complicated propagation paths, the dispersive propagation of acoustic waves in structures, and the coupling of the vibrating structure and the surrounding medium. Thus, source localization experiments were conducted using matched field processing (MFP) for a 0.9-m diameter round aluminum plate excited by the impact of a 1.3-cm stainless-steel ball bearing dropped from 7.6-cm. A 14-sensor linear remote acoustic array placed 8.9-cm above the plate measured the sound radiated by the 0.64-cm thick plate. MFP array signal processing localization techniques were used along with a physics-based finite element acoustic model to localize the excitation on the structure. Source localization results in both a quiet environment and environment with additive white Gaussian noise are discussed, and these results are compared to those from an acoustic model where plate edge reflections are neglected. [Work was sponsored by a SMART Scholarship and the NEEC.]

The effects of bathymetry on estimating the depth of a source in range-dependent environments with a single hydrophone

The effects of varying or range-dependent bathymetry, e.g., such as a sloping bottom, on the depth resolution characteristics of single hydrophone matched field processing (MFP), e.g., width of depth main-lobe as a function of source and receiver nominal positions, is not well understood. A major challenge is that in the case of range-dependent environments there are generally no analytical representations for the pressure field, thus requiring numerical methods for their evaluation. To provide some theoretical insights into how the shape of the bathymetry and locations of the source and receiver influences the MFP depth ambiguity function, we study the case of an ideal wedge with perfectly reflective pressure-release boundaries using the analytical solutions of Buckingham [1]. We derive a simple approximation for the depth ambiguity function main lobe width and compare it against the theoretical result for an ideal range-independent environment [2] and then numerically for a penetrable wedge and more realistic shelf-like environments. M.K. Buckingham, “Acoustic propagation in a wedge-shaped ocean with perfectly reflecting boundaries,” NRL report 8793, March 1984. M. Cheney and I.P. Kirsteins, “Resolution of matched field processing for a single hydrophone in a rigid waveguide,” J. Acoust Soc. Am. 151, pp. 3186–3197, 2022.

Passive structural health monitoring of a vibrating shell using data-based matched field processing

This study presents experimental results on passive structural health monitoring of a vibrating elastic structure for defect localization. The approach is based on matched field processing (MFP), which requires a model of the pristine structure. An MFP methodology for localizing a defect in a shell equipped with vibration sensors was developed and numerically demonstrated in [JASA EL 2, 025601 (2022)]. This paper further extends this study to experimental implementation of this MFP methodology without requiring full knowledge of the structure parameters and the boundary conditions of the pristine structure. The method is tested on experimental data for localizing a defect on a rectangular steel plate with non-perfectly, fixed boundary conditions.

Inversion of partially spanning array data for normal mode parameters using seabed impedance constraint

Previous work with fully or nearly spanning vertical line arrays has shown that normal mode shapes can be identified as the eigenvectors of the covariance matrix averaged over lengthy source tracks that served to de-correlate the modes. Recent work with partially spanning arrays has used compressed sensing or super-resolution methods like MUSIC to estimate mode wavenumbers. These methods assume the sound speed profile is available, but not the seabed properties. We will present another alternative for inverting for normal modes under these conditions, including a partially spanning vertical line array, in which sets of candidate modes are restricted to modes that satisfy the same impedance boundary condition at the seabed. Each distinct impedance condition defines a physically consistent set of modes. Thus, our inversion is sparse in impedance conditions. We demonstrate how the normal modes resulting from this process are used to form matched field processing replicas that recover source tracks in range and depth.

A lucky covariance estimator using cumulative coherence

This talk demonstrates a technique to improve covariance estimation using the principles of lucky signal processing and the cumulative coherence. Lucky processing, popularized in astro-photography, is a technique that increases signal quality by selectively keeping only a small fraction from a pool of potential snapshots. Cumulative coherence, a measure of how well a set of vectors is described by its subsets, provides the measure of “data quality” that enables the lucky processing. This approach was applied to covariance estimation on an acoustic array by taking a fixed duration sample of data and creating a dense set of snapshots with higher than usual overlap. From these densely sampled snapshots, the “luckiest” ones were found using cumulative coherence, and the covariance was averaged as normal. It was found that the lucky covariance estimate was successful at adaptive matched field processing and produced a less ambiguous processor output than the conventional estimator. The lucky covariance estimate had a higher estimated signal-to-noise ratio, especially when the source was at longer ranges from the array. [This work is supported by the Office of Naval Research.]

Validity of matched-field source localization in under-ice shallow water

Underwater source localization, such as matched-field processing (MFP), triangulation, and waveguide invariant, have been extensively investigated in temperate oceans. Seasonal or yearlong ice floes or ice cover exist in high-latitude sea regions and the polar ocean. In under-ice shallow water, sound interacts frequently with ice and sea bottom, which results in dramatic reflection, attenuation, and modal dispersion. The boundary effects generate more uncertainties in model-based source localization methods, for example, the MFP method. In this work, we develop the preliminary scheme of the under-ice MFP. The performances of the incoherent Bartlett and minimum variance algorithms are verified by real data collected by a 12-element Vertical line array with a space of 1 m for a source (650–750 Hz) at 2.7-km range and 5-m depth in the northern Yellow Sea in winter. The experimental findings demonstrate that the range error is within 2% and the depth error is within 10%. The error primarily originates from the uncertainty of sea bottom parameters.

Source depth estimation with feature matching using convolutional neural networks in shallow water

A feature matching method based on the convolutional neural network (named FM-CNN), inspired from matched-field processing (MFP), is proposed to estimate source depth in shallow water. The FM-CNN, trained on the acoustic field replicas of a single source generated by an acoustic propagation model in a range-independent environment, is used to estimate single and multiple source depths in range-independent and mildly range-dependent environments. The performance of the FM-CNN is compared to the conventional MFP method. Sensitivity analysis for the two methods is performed to study the impact of different environmental mismatches (i.e., bottom parameters, water column sound speed profile, and topography) on depth estimation performance in the East China Sea environment. Simulation results demonstrate that the FM-CNN is more robust to the environmental mismatch in both single and multiple source depth estimation than the conventional MFP. The proposed FM-CNN is validated by real data collected from four tracks in the East China Sea experiment. Experimental results demonstrate that the FM-CNN is capable of reliably estimating single and multiple source depths in complex environments, while MFP has a large failure probability due to the presence of strong sidelobes and wide mainlobes.

Low frequency inversion method based on multi-layer holizontal variation shallow seafloor model

Sound propagation in shallow water is significantly influenced by geoacoustic properties. Estimating these geoacoustic parameters is essential for sound field analysis and sonar performance assessment. As a common practice, the seafloor is often treated as a single-layer or two-layer range-independent geoacoustic model to reduce the number of involved parameters. However, acoustic parameters inverted through these two geoacoustic models are typically limited in their applicability to a specific frequency range, thus posing challenges when applied across a broader frequency range. A range-dependent multi-layer geoacoustic model based on experimental measurements obtained with a sub-bottom profiler is proposed in this study. The inversion scheme combines three inversion methods to estimate geoacoustic parameters, considering the different sensitivities of geoacoustic parameters to different physical parameters within the acoustic field. Firstly, modal dispersion is used to invert the geoacoustic parameters of each layer, with the dispersion curve obtained through warping transform and the Wigner-Ville distribution. After that, both the localization using matched field processing and the dispersion curve fitting demonstrate the effectiveness of the inversion results for each layer, although the peak of the probability distribution of sound speed in the first layer is broader than in others. Secondly, matched field processing is employed to invert the geoacoustic parameters of the first layer. This method is based on the theory that as frequency increases, the depth of sound rays penetrating the seabed decreases, revealing changes in the first layer's sound speed with the seabed depth. Lastly, bottom attenuation coefficients at different frequencies are inverted by the transmission loss (TL), and a fitting relationship between the attenuation coefficient and the frequency is derived. The inversion results obtained by using the range-dependent multi-layer geoacoustic model are compared with results estimated by the single-layer geoacoustic model. The findings indicate that the transmission loss (TL) error from the range-dependent multi-layer geoacoustic model in this study is smaller than that from the single-layer geoacoustic model, especially in the lower frequency band. The range-dependent multi-layer geoacoustic model proves to be suitable for a broader frequency range, providing better precision in explaining various acoustic phenomena.

Sparse Bayesian learning based on spatio-temporal structure-aware for matched field processing.

In the application of the matched field processing (MFP) algorithm for underwater acoustic source localization, the measurements at each time step are conventionally processed independently. This study incorporates the prior information about the continuous spatial changes of the source over time under realistic conditions, a factor anticipated to improve localization performance. In this paper, a sparse Bayesian learning (SBL) algorithm based on the spatio-temporal structure-aware is described. We exploit a structure prior for sparse coefficients to capture the continuous spatial structure between adjacent time steps. Moreover, the sparse coefficient can automatically select the update method, utilizing the statistical information from adjacent neighbors or updating independently. The hidden variables in the hierarchical Bayesian framework are inferred via variational Bayesian inference (VBI). Additionally, we extend the proposed method to the multi-frequency case. This method inherits the advantages of the SBL and further reduces position estimation errors. Compared to other approaches, the construction of an accurate motion model is not required. The efficacy of the proposed algorithm is demonstrated through simulation examples and an analysis of the SWellEx-96 experimental data.

Experimental Results of Underwater Sound Speed Profile Inversion by Few-Shot Multi-Task Learning

Underwater Sound Speed Profile (SSP) distribution is crucial for the propagation mode of acoustic signals, so fast and accurate estimation of SSP is of great importance in building underwater observation systems. The state-of-the-art SSP inversion methods include frameworks of matched field processing (MFP), compressive sensing (CS), and feed-forward neural networks (FNNs), among which the FNN shows better real-time performance while maintaining the same level of accuracy. However, the training of FNN needs quite a lot historical SSP samples, which is difficult to satisfy in many ocean areas. This situation is called few-shot learning. To tackle this issue, we propose a multi-task learning (MTL) model with partial parameter sharing among different training tasks. By MTL, common features could be extracted, which accelerates the learning process on given tasks, and reduces the demand for reference samples, enhancing the generalization ability in few-shot learning. To verify the feasibility and effectiveness of MTL, a deep-ocean experiment was held in April 2023 in the South China Sea. Results show that MTL outperforms the other mainstream methods in terms of accuracy for SSP inversion, while inheriting the real-time advantage of FNN during the inversion stage.

Rockfall alarm system for railway monitoring: Integrating seismic detection, localization, and characterization

Rockfalls pose a threat to human infrastructure below cliffs. Sensitive and reactive alarm systems are needed for rail traffic safety because small rockfalls ([Formula: see text]) impacting the railroad may cause train derailment. We develop a seismic processing workflow for rockfall early warning, powered by dense arrays deployed along the track. The method is evaluated by dropping rocks from a controlled height and triggering rockfalls on a cliff. We indicate that seismic arrays are highly sensitive to small impacts and are able to detect them, locate them, and estimate their magnitude. The detection can be performed in near real-time with a simple algorithm because small-scale rockfalls produce impulsive waveforms near the impact. Precise localization with matched field processing is able to track the trajectory of a rockfall. Impacts against the steel rails may be recognized by their source signature. The seismic amplitudes are related to the rockfall volume by the Hertz law, which may be used to estimate their volume. These results indicate the potential of seismic-driven near real-time rockfall alarm systems.

Multifrequency matched-field source localization based on Wasserstein metric for probability measures.

Matched-field processing (MFP) for underwater source localization serves as a generalized beamforming approach that assesses the correlation between the received array data and a dictionary of replica vectors. In this study, the processing scheme of MFP is reformulated by computing a statistical metric between two Gaussian probability measures with the cross-spectral density matrices (CSDMs). To achieve this, the Wasserstein metric, a widely used notion of metric in the space of probability measures, is employed for developing the processor to attach the intrinsic properties of CSDMs, expressing the underlying optimal value of the statistic. The Wasserstein processor uses the embedded metric structure to suppress ambiguities, resulting in the ability to distinguish between multiple sources. In this foundation, a multifrequency processor that combines the information at different frequencies is derived, providing improved localization statistics with deficient snapshots. The effectiveness and robustness of the Wasserstein processor are demonstrated using acoustic simulation and the event S5 of the SWellEx-96 experiment data, exhibiting correct localization statistics and a notable reduction in ambiguity. Additionally, this paper presents an approach to derive the averaged Bartlett processor by evaluating the Wasserstein metric between two Dirac measures, providing an innovative perspective for MFP.