Optimization of wide-band linear arrays

An optimization method is proposed for linear arrays to be used in ultrasound systems under wide-band operation. A fast algorithm, the threshold accepting, has been utilized to determine the element positions and weight coefficients of a linear array that generates a desired beam pattern. To reduce the computational burden in the optimization procedure, an efficient numerical routine for the beam pattern evaluation has been implemented. We address the optimization problem of both dense and sparse wideband arrays. In the first case, the goal is to minimize the side-lobe energy by varying the element weights; we compare the optimized beam pattern with that obtained with classical shading functions, showing that better results can be achieved with a wide-band optimization. We also consider the optimization of the layout (positions and weights) of a sparse linear array to achieve a desired beam pattern with a fixed or minimum number of array elements. The comparison of the proposed method with a narrow-band optimization algorithm is presented, showing that better performances (about -7 dB further reduction of the side-lobe level) can be achieved with a wide-band sparse array optimization. Further numerical simulations are given, showing that the proposed method yields better results than wideband sparse random arrays and periodic arrays with the same aperture width     

Sparse 2-D arrays for 3-D phased array imaging--design methods

One of the most promising techniques for limiting complexity for real-time 3-D ultrasound systems is to use sparse 2-D layouts. For a given number of channels, optimization of performance is desirable to ensure high quality volume images. To find optimal layouts, several approaches have been followed with varying success. The most promising designs proposed are Vernier arrays, but also these suffer from high peaks in the sidelobe region compared with a dense array. In this work, we propose new methods based on the principles of suppression of grating lobes to form symmetric and non-symmetric regular sparse periodic and radially periodic designs. The proposed methods extend the concept of sparse periodic layouts by exploiting either an increased number of symmetry axes or radial symmetry. We also introduce two new strategies to form designs with nonoverlapping elements. The performance of the new layouts range from the performance of Vernier arrays to almost that of dense arrays. Our designs have simplicity in construction, flexibility in the number of active elements, and the possibility of trade off sidelobe peaks against sidelobe energy.     

基于凸优化方法的期望主瓣幅度响应波束图设计

将发射阵的期望主瓣幅度响应波束设计转化为凸优化问题,并利用cvx工具箱求解最优加权。首先,根据期望波束的主瓣范围,将空间区域分为主瓣区域和旁瓣区域,再在主瓣区域内将设计波束和期望波束之差的2-范数最小化,并将设计波束图旁瓣级控制在期望值之下。最后,利用cvx工具箱对该凸优化问题进行求解,获得满足要求的设计波束图。通过计算机仿真对所提波束图设计方法的有效性进行了验证。     

Shape optimization in three-dimensional linear elasticity by the boundary contour method

A variant of the usual boundary element method (BEM), called the boundary contour method (BCM), has been presented in the literature in recent years. In the BCM in three dimensions, surface integrals on boundary elements of the usual BEM are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. The BCM employs global shape functions with the weights, in the linear combinations of these shape functions, being defined piecewise on boundary elements. A very useful consequence of this approach is that stresses, at suitable points on the boundary of a body, can be easily obtained from a post-processing step of the standard BCM. The subject of this paper is shape optimization in three-dimensional (3D) linear elasticity by the BCM. This is achieved by coupling a 3D BCM code with a mathematical programming code based on the successive quadratic programming (SQP) algorithm. Numerical results are presented for several interesting illustrative examples.     

Sparse-periodic hybrid array beamformer

A novel approach to the design of spatial arrays is presented. The hybrid array beamformer consists of a sparse array in which some of the elements are arranged periodically, thus creating a periodic sub-array. The outputs of the sparse and periodic arrays are then fused to create a beampattern with good resolution and low peak sidelobe levels. This approach is seen as matching the performance of standard periodic arrays but with a significant saving in terms of the required number of elements. Applications include sonar, radar and ultrasonic systems     

基于二阶锥规划的稳健低旁瓣自适应波束形成

针对水下成像时圆弧阵常规波束旁瓣级较高,当存在强干扰时容易带来较多虚警的缺点,提出一种基于二阶锥规划的稳健低旁瓣自适应波束形成方法。该方法通过对波束旁瓣进行优化设计,可以将波束旁瓣级进行严格控制,并进一步结合协方差矩阵重构法,使波束形成器的稳健性得到提高,最后将该波束优化问题转化为二阶锥规划问题进行求解。计算机仿真结果表明,相较于其他算法来说,文中算法在波束旁瓣级得到严格控制的同时,可以在存在各类失配的情况下获得更高的输出信干噪比,稳健性更高。水池实验进一步验证了该方法的有效性,该研究成果可以在声呐成像领域应用。     

一种旁瓣级可控的MVDR波束形成算法

针对传统的最小方差无畸变响应（Minimum Variance Distortionless Response,MVDR）波束形成方法存在的旁瓣较高且抑制干扰性能不稳健的情况,提出一种旁瓣级可控的自适应波束形成算法。该算法在MVDR基础上进行峰值搜索,将获得的峰值点从大到小进行排序,取次大值作为最高旁瓣的值,将得到的最高旁瓣值与期望旁瓣值比较,在其方位添加虚拟干扰加以抑制,从而得到新的波束图。再对新的波束图进行峰值搜索,不断重复上述过程,经过有限次迭代以达到期望旁瓣值。计算机仿真结果表明在均匀线阵基础上该算法能够将旁瓣控制到期望旁瓣级以下且比较稳健。     

Element size effect on phase aberration correction

The distortion effect of tissue on ultrasonic beamforming is simplified as a 2-D time-shifting screen placed against the array surface. The ideal correction of such distortion requires a 2-D array with infinitesimally small elements. However, elements of finite sizes must be utilized in practice, causing the so-called residual phase error (RPE). As element size is reduced, the magnitude of the RPE is reduced, and its spatial feature becomes finer. Analyses have been performed to reveal that the magnitude of the RPE is proportional to the imaging frequency, the rms magnitude of the original time-delay error, and the diagonal size of individual rectangular elements, and is inversely proportional to the correlation length of the original time-delay error. Simulations have been performed to study the peak sidelobe level caused by the RPE as the element sizes are reduced. The sidelobe is defined here as the difference between the ideal beam (with no phase error) and the beam obtained in the presence of the RPE. For a multi-row array in which a conventional 1-D array is divided into N rows of independent elements in the elevation direction, the peak sidelobe level is found to vary approximately as N/sup -1/ instead of the anticipated N/sup -2/. The reduction is caused by the reduced magnitude of the RPE, and the finer spatial feature of the RPE, although apparent in the reduced spatial correlation length, does not result in additional reduction of the sidelobe level. The reason for this has been analyzed. The results of this study provide guidance for designing multi-row arrays suitable for phase aberration correction.     

A point-matching method for array pattern synthesis

In this paper, a newly developed point-matching method is presented to obtain a set of excitation coefficients of a linear array that generates a desired radiation pattern with arbitrarily suppressed sidelobe levels. This method can be used for linear arrays with nonuniform spacing and nonisotropic elements. The design examples presented show that the point-matching method is both effective and efficient     

Investigation of hybrid elliptical antenna arrays

Novel types of antenna arrays constructed from combination of linear and elliptical antenna arrays are presented. These types are called elliptical, concentric elliptical, elliptical cylindrical and elliptical coaxial cylindrical arrays where only the array factors are considered. The effect of the element factor can be considered separately and combined to the array factor. The expression for the array factor of elliptical array has been obtained. Then, array factors of other three types are derived by the combination of linear and elliptical array properties. Their directivities and sidelobe levels are simulated in various current distributions. The effect of ellipse eccentricity, element spacing and number of elements are calculated and compared with those parameters.     

The cross algorithm for phase-aberration correction in medical ultrasound images formed with two-dimensional arrays

Common-midpoint signals in the near-field signal-redundancy (NFSR) algorithm for one-dimensional arrays are acquired using three consecutive transducer elements. An all-row-plus-two-column algorithm has been proposed to implement the one-dimensional NFSR algorithm on two dimensional arrays. The disadvantage of this method is that its ambiguity profile is not linear and a timeconsuming iterative method has to be used to linearize the ambiguity profile. An all-row-plus-two-column-and-a-diagonal algorithm has also been proposed. Its ambiguity profile is linear, but it is very sensitive to noise and cannot be used. In this paper, a novel cross algorithm is proposed to implement the NFSR algorithm on two-dimensional arrays. In this algorithm, common-midpoint signals are acquired using four adjacent transducer elements, which is not available in one-dimensional arrays. Its advantage includes a linear ambiguity profile and a higher measurement signal-to-noise ratio. The performance of the cross algorithm is evaluated theoretically. The region of redundancy is analyzed. The procedure for deriving the phaseaberration profile from peak positions of cross-correlation functions between common-midpoint signals is discussed. This algorithm is tested with a simulated data set acquired with a two-dimensional array, and the result shows that the cross algorithm performs better than the all-row plus-twocolumn NFSR algorithm.     

Reconstructing design parameters of a rectangular resonator via peak signal-to-noise ratio and global optimization algorithms

This article proposes an approach for reconstructing physical parameters of a sample in a rectangular resonator during microwave radiation, knowing a priori, its electric field distribution. The inverse problem was solved using two global optimization algorithms and the peak signal-to-noise ratio (PSNR) criterion. First, the Self-regulated Fretwidth Harmony Search algorithm (SFHS) identified suitable resonant frequencies for a given configuration. Next, the unified Particle Swarm Optimization (UPSO) optimized said configuration. Together, they became a maximization strategy of the PSNR through a dual optimization process. Results showed the ability of the approach for estimating the height of each sample block and the resonating frequency of the cavity. This process takes longer to finish as a higher PSNR is demanded (mainly due to the aforementioned dual optimization). Even so, it allows for more similar electric field distributions between both, the direct and inverse problems.     

Chemical Composition Design of Superalloys for Maximum Stress, Temperature, and Time-to-Rupture Using Self-Adapting Response Surface Optimization

We have adapted an advanced semistochastic evolutionary algorithm for constrained multiobjective optimization and combined it with experimental testing and verification to determine optimum concentrations of alloying elements in heat-resistant austenitic stainless steel alloys and superalloys that will simultaneously maximize a number of the alloy's mechanical properties. The optimization algorithm allows for a finite number of ingredients in the alloy to be optimized so that a finite number of physical properties of the alloy are either minimized or maximized, while satisfying a finite number of equality and inequality constraints. Alternatively, an inverse design method was developed, which uses the same optimization algorithm to determine chemical compositions of alloys that will be able to sustain a specified level of stress at a given temperature for a specified length of time. The main benefits of the self-adapting response surface optimization algorithm are its outstanding reliability in avoiding local minimums, its computational speed, ability to work with realistic nonsmooth variations of experimentally obtained data and for accurate interpolation of such data, and a significantly reduced number of required experimentally evaluated alloy samples compared with more traditional gradient-based and genetic optimization algorithms. Experimentally preparing samples of the optimized alloys and testing them have verified the superior performance of alloy compositions determined by this multiobjective optimization.     

Implementation of broadband low-sidelobe beamforming in time domain

In modern active and passive sonar systems, broadband beamforming for acoustic arrays is widely used to suppress unwanted interference and to detect target signals of interest. A broadband low sidelobe beamforming scheme in time domain is proposed in this paper. The first step of this scheme is to delay the outputs of each element in the acoustic array by a tapped-delay-line (TDL) to accomplish the integer part of the time delay need to form a beam. Then, finite impulse response (FIR) digital filters are used to implement the fractional part of the time delay. The weighting coefficients for all array elements at different frequencies to realize the low sidelobe beams are also implemented with the FIR digital filters. Finally, the outputs of the digital filters are summed up to yield the time domain beam output. The design of low sidelobe beam pattern and that of the FIR digital filters are two crucial technical issues in this beamforming procedure. The low sidelobe beams of each sub-band are designed using the optimized beam synthesis approach based on the principle of MVDR beamforming. An improved adaptive approach are used for the design of FIR digital filters, and the design requirements of these filters were specified by the weights of low sidelobe beams of each sub-band over the broad frequency band. Results of computer simulation for a twelve-element arc array show that the beamforming scheme is very effective in forming low sidelobe broadband beam.     

Wavefront amplitude distortion and image sidelobe levels. I. Theory and computer simulations

The quality of an imaging system is degraded by propagation anomalies that distort wavefronts propagating through the medium. Adaptive phase-deaberration algorithms compensate for phase errors in the wavefront. The algorithms suffer, however, when the wavefront is also significantly distorted. A theory which shows that the rise of image background level, which is the average sidelobe floor (ASF), in a single point-like source image is proportional to the amplitude distortion of the wavefront and inversely proportional to the effective number of array elements is derived. From the theory, the tolerance to the amplitude distortion, after the phasefront has been corrected by a deaberration algorithm, can be calculated based on the design requirement of the sidelobe floor for a given array. Computer simulations show good agreement with the theory.     

Code optimization for direct sequence spread spectrum and SAW-matched filter implementation

This paper introduces a new optimization algorithm for the minimization of the time sidelobes of the correlation function of a pseudonoise (PN) sequence by applying dynamic weighting to the sequence. The resulting optimized time sidelobe level sequences are to be used in direct sequence spread spectrum (DS-SS) systems with digital modulations such as BPSK, DPSK, QPSK, etc. The new optimization algorithm starts with a PN sequence. It first optimizes the correlation time sidelobes for the case where the consecutive data bits are identical (11 or 00). It then optimizes the correlation time sidelobes for the case of alternating consecutive data bits (10 or 01). The suppressed time sidelobe level sequences are derived by iterating these algorithms alternately starting from the initial PN sequence. The derived suppressed time sidelobe sequences show excellent correlation characteristics when compared to conventional PN sequences such as maximal length sequences, Gold sequences and Barker codes. Surface acoustic wave (SAW) devices were used to implement the optimized time sidelobe level sequences in a matched filter pair. The design of the apodized SAW-matched filters and their predicted second order effects are presented. The experimental results for the SAW-matched filters for the optimized time sidelobe level sequences derived from a Barker code were found to be in good agreement with the theoretical predictions from this new algorithm.     

Ultrasparse, ultrawideband arrays

This paper investigates the properties of highly thinned ultrawideband (UWB) arrays. The design aim is high resolution and very low side radiation levels (SL). One- and two-dimensional ultrasparse UWB arrays can be designed to achieve both. The minimum available pulse-echo SL is shown to approach N(-4) where N is the number of elements in the transmit and receive arrays. Periodic thinning is shown to be superior to random thinning, and amplitude taper is shown to raise the SL. Two-dimensional curvilinear deployment of elements are shown to outperform rectilinear designs, and different transmit and receive arrays in pulse-echo systems are shown to outperform systems that use the same array for transmit and receive. Very low SL is achievable in an ultrasparse UWB system with so few elements that echo signal-to-noise ratio (SNR) rather than SL becomes the constraint on the minimum number of elements required by the system for the array to be useful for imaging. For example, in ultrasonic pulse-echo breast imaging, SL approximately -70 dB is desired to distinguish small cysts from tumors. A 2-D randomly thinned array requires about 10,000 elements. A 2-D ultrasparse UWB periodic array requires less than 100 to satisfy SL, a reduction of 100:1, but provides insufficient SNR. A 500-element, 7.5 MHz array operating with 4 cm penetration depth satisfies both. Experimental results demonstrate the theory.     

任意结构基阵波束优化的稳健性分析

分析了任意结构基阵波束优化的稳健性。首先从理论上推导了阵列误差、权向量误差和权向量范数等因素与波束旁瓣畸变之间的关系,并利用优化波束的白噪声增益和权向量范数之间的关系,提出了任意结构基阵波束优化时权向量范数约束上限的选取方法。针对圆阵进行了大量的计算机仿真,分析了不同权向量范数约束条件下获得的优化波束的稳健性,证明了理论推导的正确性。     

Broad-bandwidth radiation patterns of sparse two-dimensionalvernier arrays

The fabrication of a dense (one-half wavelength element spacing) two-dimensional (2D) transducer array suitable for medical ultrasound imaging is unrealistic using existing technology. Consequently, there is interest in developing sparse 2D transducer arrays. In this paper, we present the results of a study looking at the broad-bandwidth radiation patterns of 72 different sparse 2D vernier arrays. Suppression of grating lobes is achieved by choosing a different arrangement of transmit and receive elements using an analogy with a vernier scale. The broad-bandwidth radiation patterns were investigated by simulating volumetric sector scan of a point target. We summarize these results by deriving a set of design curves that predicts the minimum number of elements, element spacing, and apodization required for a desired beam width and maximum secondary lobe. The results show that a sparse vernier array can be designed with significantly lower average and peak secondary lobes compared with a sparse random array with the same number of elements and aperture size     

Thinning and weighting of large planar arrays by simulated annealing

Two-dimensional arrays offer the potential for producing three-dimensional acoustic imaging. The major problem is the complexity arising from the large number of elements in such arrays. In this paper, a synthesis method is proposed that is aimed at designing an aperiodic sparse two-dimensional array to be used with a conventional beam-former. The stochastic algorithm of simulated annealing has been utilized to minimize the number of elements necessary to produce a spatial response that meets given requirements. The proposed method is highly innovative, as it can design very large arrays, optimize both positions and weight coefficients, synthesize asymmetric arrays, and generate array configurations that are valid for every steering direction. Several results are presented, showing notable improvements in the array characteristics and performances over those reported in the literature.