A New Interval Pattern Analysis Method of Array Antennas Based on Taylor Expansion

Hu, Naigang; Duan, Baoyan; Xu, Wanye; Zhou, Jinzhu

doi:10.1109/tap.2017.2754458

Cited by 30 publications

(22 citation statements)

References 20 publications

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“…In particular, the first two elements of the Taylor expansion are used as a linearization of a function behaviour at the given point and its surroundings [20]. The Taylor expansion is used in solutions of partial differential equations (PDE) [1,7,17], ordinary differential equations (ODE) [2,6,21] , integral equations (IE) integro-differential equations (IDE) [1,11], approximation of inverse functions (AIF) [8], control theory [4], fluid flow visualization of 3D flow using radial basis functions [12,13,15], computer vision [5,18], in statistical mechanics [10], antenna design [6,9], operator theory [3], etc.…”

Section: Introductionmentioning

confidence: 99%

Efficient Taylor expansion computation of multidimensional vector functions on GPU

Skala¹

2021

AMI

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The Taylor expansion [19] is used in many applications for a value estimation of scalar functions of one or two variables in the neighbour point. Usually, only the first two elements of the Taylor expansion are used, i.e. a value in the given point and derivatives estimation. The Taylor expansion can be also used for vector functions, too. The usual formulae are well known, but if the second element of the expansion, i.e. with the second derivatives are to be used, mathematical formulations are getting too complex for efficient programming, as it leads to the use of multi-dimensional matrices.This contribution describes a new form of the Taylor expansion for multidimensional vector functions. The proposed approach uses "standard" formalism of linear algebra, i.e. using vectors and matrices, which is simple, easy to implement. It leads to efficient computation on the GPU in the three dimensional case, as the GPU offers fast vector-vector computation and many parts can be done in parallel.

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Section: Introductionmentioning

confidence: 99%

Efficient Taylor expansion computation of multidimensional vector functions on GPU

Skala¹

2021

AMI

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“…The effect of array factor tolerance on its power pattern has been analysed in several studies. A tolerance analysis method for the effect of array factor errors (excitation amplitude or phase) of a linear antenna array on the radiation pattern has been proposed via interval analysis (IA) [3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…Neither analytic [16,17] (e.g., statistics and probability) nor numerical methods (e.g., FEM, FDTD, and MoM) are suitable for addressing the tolerance issue because a large amount of statistical data, complex probability distribution functions, or significant computing resources are required. However, the interval arithmetic method can sufficiently address the problem of the interval parameter (i.e., tolerance); this method has been adapted for tolerance analysis of reflector antennas [18][19][20], arrays [3][4][5][6][7], reflector arrays [12], radomes [21,22], and CLAS [23]. Both the dimensions [12] and material errors [21] of an antenna resulting from the fabrication process are modelled as interval variables, and their effects on the radiation pattern are analysed; however, no studies regarding tolerance analysis of an antenna array's element factor (pattern) currently exist.…”

Section: Introductionmentioning

confidence: 99%

Taylor Expansion and Matrix-Based Interval Analysis of Linear Arrays With Patch Element Pattern Tolerance

Wang

Song

2021

IEEE Access

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In this study, a novel interval analysis (IA) approach for linear arrays with element pattern tolerance is proposed. This study differentiates itself from the classic interval analysis (CIA) method because it focuses on the effects of the array element (e.g., patch) pattern tolerance on the antenna array pattern; the tolerance may be caused by fabrication errors in the element. The closed-form pattern expressions of the element (e.g., patch) and array are deduced by the interval arithmetic method. To mitigate the interval extension (also referred to as the overestimation problem) caused by the dependency problem, Taylor expansion and matrix-based interval analysis (TMIA) methods are proposed and implemented in this study. A set of numerical examples is reported and analysed to indicate the effectiveness of the proposed TMIA approach with the results of Monte Carlo (MC) and CIA methods, as well as to indicate its potential capabilities and advantages in the actual application of industrial antenna arrays.INDEX TERMS Antenna array, element pattern, interval analysis (IA), overestimation, patch, tolerance analysis.

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“…[17][18][19] The IA-based analysis for a microstrip reflect array has been already presented in literatures. 20,21 To minimize the over-estimation problem of the conventional interval-based method, the Minkowski sum 22 and Taylor expansion 23 methods are proposed, and they have achieved good results. They analyzed and compared the difference between the upper and lower boundaries of three interval algorithms to calculate the power pattern of an array antenna.…”

Section: Introductionmentioning

confidence: 99%

Tolerance analysis of 3D printed patch antennas based on interval arithmetic

Wang

et al. 2020

Micro & Optical Tech Letters

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A tolerance analysis approach based on interval arithmetic (IA) is proposed for heterogeneous three-dimensional (3D) printed patch antennas. Four key parameters-patch length, width, substrate thickness, and material properties-are considered that can introduce errors in the analysis results. Investigating the comprehensive effect of these parameters on resonant frequency and the E/H pattern of the patch is difficult and time-consuming when classical numerical simulations are employed. Thus, in this work, the four parameters are modeled as interval variables, and the equations between error and resonant frequency and the E/H pattern are derived using IA. Then, for the given tolerances (error intervals), the corresponding resonant frequency interval and E/H pattern interval are calculated using the proposed approach and compared with HFSS simulation results. Some samples of the patch antenna are fabricated via a self-developed heterogeneous 3D printer, which employs ink injection and laser sintering to fabricate the patch and the microstrip; furthermore, ultraviolet (UV) resin injection and curing are used to fabricate the substrate. The transmission performance of the samples is evaluated by comparing simulation and measurement results to verify the effectiveness of the proposed IA-based approach.

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A New Interval Pattern Analysis Method of Array Antennas Based on Taylor Expansion

Cited by 30 publications

References 20 publications

Efficient Taylor expansion computation of multidimensional vector functions on GPU

Efficient Taylor expansion computation of multidimensional vector functions on GPU

Taylor Expansion and Matrix-Based Interval Analysis of Linear Arrays With Patch Element Pattern Tolerance

Tolerance analysis of 3D printed patch antennas based on interval arithmetic

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