Beam Domain Research Articles

Performance of CUF Approach to Analyze the Structural Behavior of Slender Bodies

This paper deals with the accurate evaluation of complete three-dimensional (3D) stress fields in beam structures with compact and bridge-like sections. A refined beam finite-element (FE) formulation is employed, which permits any-order expansions for the three displacement components over the section domain by means of the Carrera Unified Formulation (CUF). Classical (Euler-Bernoulli and Timoshenko) beam theories are considered as particular cases. Comparisons with 3D solid FE analyses are provided. End effects caused by the boundary conditions are investigated. Bending and torsional loadings are considered. The proposed formulation has shown its capability of leading to quasi-3D stress fields over the beam domain. Higher-order beam theories are necessary for the case of bridge-like sections. Various theories are also compared in terms of shear correction factors on the basis of definitions found in the open literature. It has been confirmed that different theories could lead to very different values of shear correction factors, the accuracy of which is subordinate to a great extent to the section geometries and loading conditions. However, an accurate evaluation of shear correction factors is obtained by means of the present higher-order theories.

Inverse planning for IMRT with nonuniform beam profiles using total‐variation regularization (TVR)

Radiation therapy with high dose rate and flattening filter-free (FFF) beams has the potential advantage of greatly reduced treatment time and out-of-field dose. Current inverse planning algorithms are, however, not customized for beams with nonuniform incident profiles and the resultant IMRT plans are often inefficient in delivery. The authors propose a total-variation regularization (TVR)-based formalism by taking the inherent shapes of incident beam profiles into account. A novel TVR-based inverse planning formalism is established for IMRT with nonuniform beam profiles. The authors introduce a TVR term into the objective function, which encourages piecewise constant fluence in the nonuniform FFF fluence domain. The proposed algorithm is applied to lung and prostate and head and neck cases and its performance is evaluated by comparing the resulting plans to those obtained using a conventional beamlet-based optimization (BBO). For the prostate case, the authors' algorithm produces acceptable dose distributions with only 21 segments, while the conventional BBO requires 114 segments. For the lung case and the head and neck case, the proposed method generates similar coverage of target volume and sparing of the organs-at-risk as compared to BBO, but with a markedly reduced segment number. TVR-based optimization in nonflat beam domain provides an effective way to maximally leverage the technical capacity of radiation therapy with FFF fields. The technique can generate effective IMRT plans with improved dose delivery efficiency without significant deterioration of the dose distribution.

Method and apparatus for acoustic source tracking using a horizontal line array

An apparatus for processing passive acoustic signals received on a horizontal line array that were either emitted from an underwater object or echo returned from an object, is proposed to track the motion (bearing change and range change) of an object (target) relative to the receiver horizontal line array. Adaptive array processing for a moving object is biased for a moving source when the number of data samples is limited by the stationariness condition. Motion compensation can be carried out in the beam domain by beam shifting for a bearing changing object and frequency shifting for a range changing object. The method includes receiving acoustic signals from the target, determining the beam covariance matrices, determining the target bearing rate and range rate, processing the beam covariance matrices by compensating for the target motion, and producing a beam power plot versus time. Interference signal is suppressed when the interference source does not have the same motion (bearing and range rate) as the target. The method does not need detailed environmental acoustic information of the sound channel normally required to model the sound propagation.

Forward modeling requirement for short-range geoacoustic inversion on a towed array

For geoacoustic inversion using the tow-ship noise received on a towed horizontal line array (HLA), one of the issues is speed and accuracy of the forward model. Is the normal mode good enough or is ray propagation adequate for modeling short-range forward propagation? Earlier work [Kuperman et al., IEEE J. Oceanic Eng. 10 (1985)] showed that the continuum contribution arrives at beams far away from the forward directions. For practical applications, such contributions are often neglected to minimize interference from undesired sources. We examine in this paper the same issue (the importance of high angle arrivals at short range) in both the time and beam domain in the context of several bottom models (templates). Note that the high angle arrival contributions depend on the bottom type, the source–receiver range, the towed array aperture/spacing and the acoustic frequencies. The results of this analysis will shed light on the requirement of forward models at short ranges on a HLA. [Work supported by ONR.]

Motion compensation for adaptive horizontal line array processing: A beam domain approach

Large aperture horizontal line arrays have small resolution cells and can be used to separate a target signal from an interference signal by array beamforming. High-resolution adaptive array processing can be used to place a null at the interference signal. But these features are significantly degraded by the source motion, which reduces the time period under which the environment can be considered stationary. For adaptive array processing, a large number of data samples are generally required to minimize the variance of the cross-spectral density between the array elements. The penalty of integrating over a large number of samples, when the source and/or interference moves, is the spread of signal and interference energy to many eigenvalues and consequently, the ability to suppress the interference suffers. We adapt a beam domain approach to compensate for the source motion allowing the beam covariance matrix of the signal to be integrated over a large number of data samples without signal energy loss. We employ an equivalent of a rotating coordinate frame to track the signal bearing-change and use the waveguide invariant theory to compensate the signal range-change by frequency shifting. [Work supported by ONR.]

Temporal coherence of matched-field, matched-mode, and matched-beam correlation as a function of frequency and range in the Sicily Strait

Ocean medium fluctuations reduce the temporal coherence of acoustic signals. Temporal coherence limits the time duration a replica field can be used for matched-field, matched-mode, and matched-beam source localization in a random ocean. During the Advent 99 experiment, which took place in the Sicily Strait in May 1999, narrow-band signals (12 tones in the band 200–1500 Hz) were transmitted from a bottom-mounted tower and received on a 64-phone line array covering the water column; the water depth was 80 m. The data were collected at three ranges: 2, 5, and 10 km. Using a reference signal as the replica, temporal coherence was measured for the vertical array in the phone domain (matched-field correlation), mode domain (matched-mode correlation), and in the beam domain (matched-beam correlation). For the latter two cases, coherence is a function of the modes and beams used. This paper presents the preliminary results of the data analysis and comparison with acoustic simulations based on an internal wave model. Implications for signal processing will be discussed. [Work was supported by ONR and SACLANTCEN.]

Adaptive matched beam processing for source localization

Matched beam processing (MBP) has been previously applied to a horizontal line array for localizing a moving source in bearing and range, and for differentiating a submerged target from a surface clutter [T. C. Yang and T. Yates, J. Acoust. Soc. Am. 104 (1998)]. MBP is matched field processing in the beam domain. Using the Bartlett processor, bearing and depth resolutions are often inadequate for rejecting surface clutter and other noise sources. High-resolution processors may be required. We note that in situations where many clutters exist, adaptive (plane-wave) beamforming has effectively rejected clutter by either high-angular resolution or by steering a null to the interference source. Motivated by this approach, an adaptive MBP will be investigated in this paper. The new processor will apply adaptive beamforming to the data and replica fields such that interference has already been removed before the matched field correlation. This approach differs from the adaptive matched field processing where interference remains in the data field. The latter approach is known to be sensitive to environmental mismatch, as a result the correlation between the replica and the interference fields may be present as substantial clutter. Initial numerical results will be presented using simulated data with interference sources. [Work supported by the Office of Naval Research.]

Improved vertical array performance in shallow water with a directional noise field

The detection and localization performance of a vertical array against a submerged target in shallow water can be significantly improved if the noise field is directional and the signal arrives in the null (notch) of the noise field. This often happens in a summer environment with a downward refractive sound speed profile in which the surface generated noise field exhibits a notch in the noise vertical directionality distribution at mid (e.g., 500 Hz) frequencies. Using conventional beamforming, by steering the beams to the shallow arrival angle of the target signal, the (undesired) noise which arrives at steep angles can be suppressed. However, conventional beamforming often suffers from significant signal gain degradation due to multipaths in the shallow water environment. Matched-field processing yields a theoretical signal gain by coherently processing the signal, but its ability to reject the directional noise is limited. Matched-beam processing, which is matched-field processing in the beam domain, incorporates the advantages of matched-field processing for coherent signal integration, and conventional beamforming for noise rejection. For the summer environment studied, matched-beam processing yields the highest array gain, almost a twice longer detection range, and a superior capability in detecting a deep target compared with the other two processors. This is demonstrated using simulated signal and noise fields with a full water column vertical array.

Matched-beam processing: Range tracking with vertical arrays in mismatched environments

This paper addresses the problem of range tracking using one or more vertical arrays in certain mismatched shallow-water environments. The objective is to obtain continuous tracking of a target thereby allowing the target to be distinguished from false alarms. It is shown that bottom mismatch can cause large range errors at discrete source ranges as observed in previous experiments. Also, significant range errors (offsets) can result from unknown array tilt. Discrete range errors impede the ability to detect a target by integrating along the target track (track-before-detect) or by a probability based target detection and tracking algorithm. Large range errors impede the ability to localize and track the target from multiple vertical arrays. These problems are addressed using matched-beam processing whereby certain bottom mismatch is minimized by a beam filter and unknown array tilt is estimated by matching the measured beam pattern against the calculated one. Beam filtering and beam matching are simple and convenient methods to implement in practical systems. Comments are also given on other applications using beam domain processing.

Matched-beam processing: Application to a horizontal line array in shallow water

Matched-beam processing of a horizontal line array in a multipath shallow-water environment is presented. With conventional beamforming, the signal is split into several beams when the target is away from the broadside direction. This can result in signal gain degradation and severe bearing bias. Matched-beam processing is matched-field processing applied in the beam domain. It offers an efficient and robust approach for correcting bearing errors and signal gain degradation of horizontal line arrays in shallow water. It is based on conventional beams but extends conventional processing to incorporate full-field processing. It is applicable to existing systems where the conventional beam outputs are the only data readily available. Many of the signal processing algorithms for horizontal arrays, such as adaptive beamforming for nulling strong interferences, can be incorporated directly into matched-beam processing. Target bearing tracking and depth discrimination are illustrated using matched-beam processing for a horizontal line array.

Vertical array performance in shallow water with a directional noise field

The performance of a vertical array for source localization and for target detection (array gain) is studied in shallow water under a directional noise field. The acoustic environment consists of a downward refractive sound-speed profile. At mid (e.g., 500 Hz) frequencies the vertical directionality of the surface generated noise exhibits a notch near the signal arrival direction, i.e., which is close to horizontal for a submerged source. The ability of the beam filter in rejecting directional noise has been previously demonstrated using conventional beamforming. The same capability is carried over into full field processing by using matched-beam processing which is an equivalent of matched-field processing conducted in the beam domain. It is shown with simulated data that matched-beam processing incorporating a beam filter of 10 deg enhances the array output signal-to-noise ratio (array gain) by more than 5 dB compared with conventional beamforming and matched-field processing. For white noise, matched-field processing yields a higher peak-to-sidelobe ratio than matched-beam processing with a beam filter. For directional noise, matched-beam processing with a beam filter yields better results than matched beam processing using a minimum variance correlator. The noise field in the background ambiguity surface (the sidelobes) has been suppressed by the beam filter.

Matched-beam processing: A synthesis of conventional beamforming and matched-field processing

Conventional beamforming, based on the concept of delay and sum of plane-wave signals, has been the cornerstone for radar and underwater acoustic array processing for many years. Matched-field processing, which has received much attention in recent years, represents a departure from conventional beamforming in that the signal propagation is an integral part of the processor. In this paper a framework is presented (i.e., matched beam processing) in which conventional beamforming and matched-field processing can be unified and treated on an equal footing. Matched-beam processing is matched-field processing in the beam domain. The resulting benefits are (1) the extension of full field processing to conventional beams, (2) the ability to do spatial filtering based on the angle of arrival, and (3) the ease of integration of the (matched-beam) processor into existing systems. For a horizontal array in shallow water, conventional beamforming would be the processor to use, but it suffers from signal gain degradation and bearing bias when the signal energy is split over many beams. Matched-field processing can be used to estimate the bearing accurately, but it must simultaneously estimate the target range, depth, and bearing. Using matched-beam processing, bearing can be estimated accurately while maintaining some tolerance to environmental mismatch.

Acoustic inversion of bottom reflectivity and bottom sound‐speed profile in shallow water.

This paper presents a full field technique to invert bottom sound profile and bottom reflectivity from acoustic data collected in shallow water. Bottom sound‐speed profile and bottom reflectivity have been traditionally estimated using seismic reflection/refraction when acoustic ray paths and travel time can be identified and measured from the data. Due to the shallow depth in shallow water, the many multipaths due to bottom reflection/refraction make such identification and measurement rather difficult. A full field inversion technique is presented which uses a broadband source and an easily deployable array for bottom sound speed and reflectivity inversion. The technique is a modified matched‐field inversion technique referred to as matched beam processing. Matched beam processing uses conventional beamforming processing to transform the field data into the beam domain and correlate that with the replica field also in the beam domain. This allows the analysis to track the acoustic field as a function of incidence/reflected angle and minimize contamination or mismatch due to sidelobe leakage. This technique is illustrated with simulated data for a vertical array and can be generalized to other array configurations, such as a towed array.

Acoustic inversion of bottom reflectivity and bottom sound-speed profile

This paper applies a full-field technique to invert bottom sound profile and bottom reflectivity from simulated acoustic data in a shallow water environment. Bottom sound-speed profile and bottom reflectivity have been traditionally estimated using seismic reflection/refraction techniques when acoustic ray paths and travel time can be identified and measured from the data. However, in shallow water, the many multipaths due to bottom reflection/refraction make such identification and measurement rather difficult. A full-field inversion technique is presented here that uses a broad-band source and a vertical array for bottom sound-speed and reflectivity inversion. The technique is a modified matched field inversion technique referred to as matched beam processing. Matched beam processing uses conventional beamforming processing to transform the field data into the beam domain and correlate that with the replica field also in the beam domain. This allows the analysis to track the acoustic field as a function of incident/reflected angle and minimize contamination or mismatch due to sidelobe leakage.

Whistler emissions produced by modulated electron beams injected into the ionosphere

The electric and magnetic fields emitted by semi‐infinite, modulated electron beams artificially injected into the Earth ionosphere are calculated. For whistler mode waves recorded by a remote VLF receiver the spectrum of the signal depends crucially on the time from the beginning of the injection. The amplitude of a transient signal from the beam front is controlled by the difference between the modulation frequency and the frequency determined from the stationary phase point in the corresponding integral (the latter varies with time due to the beam front motion). Far from the beam front, only the forced oscillations due to the modulation of the beam density will be registered. The intrinsic frequency width of the whistler signal δf connected with the ray representation of a wave field determines the optimal frequency bandwidth of the receiver in use. The value of δf ∼ (1/R)1/2 (R is the transverse distance between the beam axis and the receiver) also determines the beam domain, ∼ R1/2 along its axis which gives the main contribution to the registered signal (Fresnel zone). The interference of waves emitted by electrons with different parallel velocities u can reduce the amplitude of the registered wave field significantly. This problem is discussed in connection with the existence of a stationary phase point (SPP) over u. It is shown that this SPP condition can be satisfied only for the wave packets emitted in the near zone of the electron gun. The amplitudes of the coherent and incoherent beam emissions are compared. In the case of a dense plasma (where the plasma frequency ωp is much greater than the electron gyrofrequency ωc) the main results are obtained analytically.

A new passive synthetic aperture technique for towed arrays

An algorithm that synthesizes apertures in the beam domain using FFT transformations and performs coherent processing of subaperture signals at successive time intervals is presented. Experimental tests of the algorithm show that for ocean environments with spatial coherence longer than the synthetic aperture length and for signals with temporal coherence longer than the required acquisition time, a synthetic array gain is achieved which roughly corresponds to the length of an equivalent fully populated array. In the experiments, transducer generated CW with phase stability and pseudorandom signals were used. Limitations on the spatial and temporal coherence were introduced only by the medium, the temporal coherence of the pseudorandom signal, and the shape and stability of the line array used. >

An improved finite difference analysis of uncoupled vibrations of cantilevered beams

Natural frequencies and mode shapes of uniform cantilever beams are obtained with use of the first and second order central difference schemes. It is observed that the improved finite difference scheme with second order central differences produces the natural frequencies and characteristic functions with a rapid convergence as compared to the conventional approach of using the first order central differences. Further, the present approach facilitates a direct determination of the dynamic characteristics of beams without any necessity of extrapolations of the results or application of iterative procedures for improving the accuracy. Satisfaction of the boundary conditions and elimination of the fictitious stations lying outside the beam domain has been a serious problem in the previous investigations in which higher order central differences have been used. In the present study some recursive relations have been implemented which can be derived by using the first order central differences and application of these simple and elegant relations to higher order difference schemes has been demonstrated to improve the accuracy over conventional approaches.