target echo strength software benchmarking · 2017-10-31 · target echo strength software...

Target Echo Strength Software Benchmarking Tasks 1 and 2 Under Canada-Netherlands-Sweden Project Arrangement on Target Echo Strength

Layton Gilroy DRDC – Atlantic Research Centre

llkka Karasalo, FOI, Swedish Defence Research Agency

Defence Research and Development Canada

Scientific Report

DRDC-RDDC-2017-R091

August 2017

Template in use: (2010) SR Advanced Template_EN (051115).dotm

© Her Majesty the Queen in Right of Canada, as represented by the Minister of National Defence, 2017

© Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de la Défense nationale,

2017

DRDC-RDDC-2017-R091 i

Abstract

As part of the Canada-Netherlands-Sweden Project Arrangement on Target Echo Strength (TES),

Canada and Sweden agreed to benchmark their software tools for predicting TES using relatively

simple geometric models. This was the first of two steps, the second being the comparison of

these software tools against experimental submarine data. In this study, Defence Research and

Development Canada (DRDC) and Swedish Defence Research Agency (FOI, Totalförsvarets

forskningsinstitut) used their boundary element, Kirchhoff approximation, and ray tracing codes

to evaluate a rotationally symmetric ellipsoid, a cylinder with one hemispherical and one flat

endcap, and an airfoil—all sized similar to their related submarine structures. In general, for each

technique, results from the various implementations agreed fairly well. Both DRDC and FOI

showed results from boundary element codes, Kirchhoff approximation codes, and ray tracers,

while DRDC also added results from the analytically-based BASIS code. As expected due to their

formulation, the DRDC Kirchhoff and ray tracing codes do not accurately predict forward scatter

when performing bistatic predictions. Even excluding this forward scatter, the FOI Kirchhoff

codes (two versions) generally performed slightly better than the DRDC version, although

differences were small. Both boundary element codes agreed quite well, but were limited to about

3 kHz (for this size model) by computer memory limitations. Again, excluding forward scatter,

the two ray tracers performed similarly, with the FOI version seeming more computationally

efficient. Results for the DRDC ray tracer would improve with more rays, but this was not

feasible within the time frame of the project. In the few cases where applicable, the BASIS code

gave reasonable results with significantly lower computational times. Overall, either country’s

versions will give comparable results when used within their capabilities. The DRDC ray tracer

requires upgrades to optimize its performance and allow for larger numbers of rays. As well,

recent efforts to migrate boundary element codes to large CPU clusters may allow for some

expansion of their frequency ranges. The results of this study indicate that the various tools

should give comparable results when examining more realistic naval platform models.

Significance to Defence and Security

Comparison of the DRDC target echo strength software tools to those of Sweden allows for

confidence in the reliability and areas of applicability which is not available from comparisons to

limited theoretical values. This ensures that the software available to the participants’ navies can

be used with confidence and can then be assessed against more realistic targets such as

submarines and other naval platforms.

ii DRDC-RDDC-2017-R091

Résumé

Dans le cadre de l’accord de projet Canada-Pays-Bas-Suède sur l’intensité des échos de cible

(TES), le Canada et la Suède ont convenu d’évaluer les performances de leurs outils logiciels

visant à prédire la TES au moyen de modèles géométriques relativement simples. Cette

évaluation constitue la première de deux étapes, la seconde étant la comparaison des outils

logiciels par rapport aux données expérimentales des sous-marins. Dans cette étude, Recherche et

développement pour la défense Canada (RDDC) et l’Agence suédoise de recherche pour la

défense (FOI, Totalförsvarets forskningsinstitut) ont utilisé leurs codes de calcul basés sur les

techniques d’élément de frontière, d’approximation de Kirchhoff et du lancer de rayon pour

évaluer un ellipsoïde à rotation symétrique, un cylindre muni d’un embout hémisphérique et d’un

embout plat, ainsi qu’un profil aérodynamique : soit des structures ayant des dimensions

similaires à celles des structures correspondantes sur les sous-marins. En général, pour chacune

des techniques, les résultats des différentes implémentations concordent assez bien. RDDC et FOI

ont présenté des résultats de codes de l’élément de frontière, d’approximation de Kirchhoff et de

lancer de rayon, tandis que RDDC a ajouté ceux du code BASIS, un outil basé sur une méthode

analytique. Comme le prévoit leur formulation, les codes de Kirchhoff et de lancer de rayon de

RDDC ne prédisent pas avec précision la diffusion vers l’avant lorsqu’ils effectuent des

prédictions bistatiques. Même en excluant cette diffusion vers l’avant, les codes de Kirchhoff de

FOI (deux versions) donnent en général des résultats légèrement plus précis que celle de RDDC,

mais les différences sont petites. Les codes de l’élément de frontière concordent assez bien, mais

sont limités à environ 3 kHz (pour un modèle de cette taille) en raison des limites de mémoire des

ordinateurs. Encore une fois, en excluant la diffusion vers l’avant, les deux lanceurs de rayon ont

fonctionné de façon similaire, et la version de FOI semble plus efficace sur le plan informatique.

Les résultats pour le lanceur de rayon de RDDC s’amélioreraient s’il y avait plus de rayons, mais

ceci est impossible en raison de l’échéancier du projet. Dans les rares cas où le code BASIS a été

utilisé, ce dernier a donné des résultats raisonnables tout en nécessitant des temps de calcul

beaucoup plus courts. Dans l’ensemble, les versions des deux pays donnent des résultats

comparables lorsqu’elles ne dépassent pas leurs capacités. Le lanceur de rayon de RDDC doit être

perfectionné pour optimiser ses performances et permettre un nombre plus élevé de rayons. Par

ailleurs, des efforts récents visant à migrer les codes de l’élément de frontière vers de grandes

grappes d’unités centrales pourraient permettre une certaine augmentation de leurs gammes de

fréquences. Selon les résultats de l’étude, divers outils devraient donner des résultats comparables

lorsque des modèles de plateforme navale plus réalistes sont examinés.

Importance pour la défense et la sécurité

La comparaison des outils logiciels pour l’intensité des échos de cible de RDDC par rapport à

ceux de la Suède favorise la confiance envers la fiabilité et les domaines d’application qui ne sont

pas disponibles aux fins de comparaison avec le nombre restreint de valeurs théoriques. Elle

permet de s’assurer que le logiciel disponible aux forces navales des pays participants peut être

utilisé en toute confiance, puis être évalué par rapport à des cibles plus réalistes, comme des

sous-marins et d’autres plateformes navales.

DRDC-RDDC-2017-R091 iii

Table of Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Significance to Defence and Security . . . . . . . . . . . . . . . . . . . . . . i

Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Importance pour la défense et la sécurité . . . . . . . . . . . . . . . . . . . . ii

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Basic Formulae . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Sweden (FOI) . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2.1 Boundary Integral Equation Method (BIEM) . . . . . . . . . . . . 3

2.2.2 Kirchhoff Approximation Methods . . . . . . . . . . . . . . . 4

2.2.3 Eigenray Method . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Canada (DRDC) . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 BASIS . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.2 Boundary Integral Equation Method (BIEM) . . . . . . . . . . . . 7

2.3.3 Kirchhoff Approximation Method . . . . . . . . . . . . . . . . 7

2.3.4 Ray Tracing Method . . . . . . . . . . . . . . . . . . . . . 8

3 Geometric Models . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1 Ellipsoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2 Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3 Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Numerical Models . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.1 Ellipsoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.2 Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3 Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.1 Ellipsoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.2 Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.3 Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Annex A Ellipse Results . . . . . . . . . . . . . . . . . . . . . . . . . 23

Annex B Cylinder Results . . . . . . . . . . . . . . . . . . . . . . . . 31

Annex C Airfoil Results . . . . . . . . . . . . . . . . . . . . . . . . . 39

iv DRDC-RDDC-2017-R091

List of Figures

Figure 1: BASIS-TS submarine shape model. . . . . . . . . . . . . . . . . . . 6

Figure 2: AVAST ray-tracing algorithm. . . . . . . . . . . . . . . . . . . . . 9

Figure 3: Ellipsoid geometric model. . . . . . . . . . . . . . . . . . . . . . 10

Figure 4: Cylinder geometric model. . . . . . . . . . . . . . . . . . . . . . 11

Figure 5: Airfoil geometric model. . . . . . . . . . . . . . . . . . . . . . . 12

Figure A.1: Ellipse, monostatic, 200 m, 1 kHz. . . . . . . . . . . . . . . . . . . 23






Figure A.7: Ellipse, monostatic, 2000 m, 10 kHz. . . . . . . . . . . . . . . . . . 26

Figure A.8: Ellipse, monostatic, 2000 m, 30 kHz. . . . . . . . . . . . . . . . . . 26

Figure A.9: Ellipse, bistatic, 200 m, 1 kHz. . . . . . . . . . . . . . . . . . . . . 27

Figure A.10: Ellipse, bistatic, 200 m, 3 kHz. . . . . . . . . . . . . . . . . . . . . 27

Figure A.11: Ellipse, bistatic, 200 m, 10 kHz. . . . . . . . . . . . . . . . . . . . 28






Figure B.1: Cylinder, monostatic, 200 m, 1 kHz. . . . . . . . . . . . . . . . . . 31






Figure B.7: Cylinder, monostatic, 2000 m, 10 kHz. . . . . . . . . . . . . . . . . 34

Figure B.8: Cylinder, monostatic, 2000 m, 30 kHz. . . . . . . . . . . . . . . . . 34

Figure B.9: Cylinder, bistatic, 200 m, 1 kHz. . . . . . . . . . . . . . . . . . . . 35

DRDC-RDDC-2017-R091 v

Figure B.10: Cylinder, bistatic, 200 m, 3 kHz. . . . . . . . . . . . . . . . . . . . 35

Figure B.11: Cylinder, bistatic, 200 m, 10 kHz. . . . . . . . . . . . . . . . . . . 36






Figure C.1: Airfoil, monostatic, 200 m, 1 kHz. . . . . . . . . . . . . . . . . . . 39






Figure C.7: Airfoil, monostatic, 2000 m, 10 kHz. . . . . . . . . . . . . . . . . . 42

Figure C.8: Airfoil, monostatic, 2000 m, 30 kHz. . . . . . . . . . . . . . . . . . 42

Figure C.9: Airfoil, bistatic, 200 m, 1 kHz. . . . . . . . . . . . . . . . . . . . . 43

Figure C.10: Airfoil, bistatic, 200 m, 3 kHz. . . . . . . . . . . . . . . . . . . . . 43

Figure C.11: Airfoil, bistatic, 200 m, 10 kHz. . . . . . . . . . . . . . . . . . . . 44






vi DRDC-RDDC-2017-R091

List of Tables

Table 1: NACA coefficients for airfoil. . . . . . . . . . . . . . . . . . . . . 12

Table 2: Graph legends. . . . . . . . . . . . . . . . . . . . . . . . . . . 15

DRDC-RDDC-2017-R091 1

1 Introduction

In 2014, Canada (CAN), The Netherlands, (NLD) and Sweden (SWE) established a Project

Arrangement (PA) under the CAN/NLD/SWE Cooperative Science and Technology

Memorandum of Understanding (2003) [1]. This PA was focused on Target Echo Strength (TES)

and one of the primary objectives was to improve the participants’ collective understanding of the

performance and validity of their TES prediction software through collaboration and coordination

of national projects.

Under this PA, Tasks 1 and 2 were focused using the participants’ (in this case, Canada and

Sweden) existing numerical tools to predict the TES of relatively simple geometric shapes over a

broad range of frequencies. The intent was to compare the resulting predictions for these “simple”

shapes to evaluate the relative performance of the tools and to determine the appropriate tools for

each frequency range of interest. Subsequent tasks would evaluate the tools when used against a

more realistic complete submarine model. Under these tasks, existing methods for predicting the

TES of submarines were evaluated to investigate specific issues with how the methods work,

including accuracy, computation time and robustness. Work in Canada was conducted by

Defence Research and Development Canada (DRDC) – Atlantic Research Centre and that in

Sweden by FOI (Totalförsvarets forskningsinstitut) Defence Research Agency.

Two test cases were considered. The first involved a smooth body which allowed computing the

full field solution accurately (monostatic and bistatic), likely using a Boundary Integral Equation

Method (BIEM) or its equivalent. This case would then be used as a reference when investigating

the validity of fast approximate methods (e.g., the Kirchhoff approximation on bodies represented

by triangular facets and ray-tracing or geometrical optics on bodies with a smooth surface). The

second test case was a cylinder with one flat end and one hemispherical end. While maintaining

simplicity, this was a more realistic test case of the shapes in which the participants are most

interested and was used to explore higher frequencies not addressable with the BIEM. The

cylinder was sized to simulate a submarine. To further investigate submarine-related geometries,

predictions were also made of an airfoil of 10 m length and 5 m height which is approximately

the appropriate size for the cylinder described above to simulate a submarine sail structure. Of

particular interest for all test cases was the examination of both monostatic and bistatic TES to

explore the limitations of the various methods.

All TES predictions were made at two particular distances: a short range prediction (200 m)

which simulates typical full-scale measurement distances, and 2000 m which simulates a more

realistic tactical distance. Frequencies were selected to be operationally relevant and to match

those used in recent BeTSSi [2] workshops:

1 kHz – Low Frequency Active Sonar (LFAS)

3 kHz – Sonobuoys

10 kHz – Hull Mounted Sonar (HMS), dipping sonar

30 kHz – Weapons (torpedoes)

2 DRDC-RDDC-2017-R091

The following sections will outline the numerical tools used for the predictions by the

participants, the geometric and numerical models created, the results of the predictions, and some

general conclusions and observations.

Follow-on tasks under the PA include the comparison of numerical predictions and experimental

measurements made of a retired Dutch Zwaardvis/Tijgerhaai-class submarine which will be

reported in a separate document.


2 Numerical Methods

This section will outline the basic methods used by the participants along with some limited

theoretical development.

2.1 Basic Formulae

The complex acoustic pressure p(s) at any point s outside a three-dimensional body (the target) is

given by the Kirchhoff-Helmholtz (KH) representation integral. For an acoustically rigid body,

the KH integral has the form

𝑝�𝒔 = 𝑝𝑖�𝒔 − 𝑝�𝒓 𝜕𝑔�𝒓, 𝒔

𝜕𝑛 𝑑𝑆(𝒓)

(1)

where S denotes the surface of the body, pi(s) is the incident field, the complex acoustic pressure

that would be excited by the source (the active sonar) if the target were absent, and g(r,s) is the

Green's function of the underwater medium with no target present. For a homogeneous water

space the Green's function is

𝑔�𝒓, 𝒔 = −1

4𝜋

𝑒−𝑖𝑘𝒓−𝒔

𝒓 − 𝒔

(2)

where is the wave number with f and c denoting frequency and sound speed.

For points s on the surface S the acoustic pressure p(s) can be shown to satisfy the boundary

integral equation

1

2𝑝�𝒔 + 𝑝�𝒓

𝜕𝑔�𝒓, 𝒔

𝜕𝑛 𝑑𝑆�𝒓 = 𝑝𝑖�𝒔 𝒔𝑆

(3)

2.2 Sweden (FOI)

Four target strength prediction methods, denoted BIE, KIR, KIT and RAY, were used in this

work. The methods compute the acoustic field reflected by the target using, respectively,

boundary integral equations (BIE), Kirchhoff’s approximation (KIR, KIT), and ray theory (RAY).


2.2.1 Boundary Integral Equation Method (BIEM)

In the FOI boundary integral equation method (BIE) the surface of the scatterer is defined by a

function

𝒓 = 𝑹�∅, 𝜃 0 ≤ ∅ ≤ 2𝜋, 0 ≤ 𝜃 ≤ 2𝜋 (4)

represented by B-spline expansions fitted to data on the scatterer shape by interpolation and/or

smoothing. Thus R(Ø,θ) is a smooth function, i.e., the surface S of the scatterer is free from edges

and corners.

The boundary integral equation (3) is discretized by point collocation using B-spline basis

functions and high order numerical quadrature formulated in rotated spherical coordinates

(spherical coordinates (∅′ ,𝜃′) on a rotated unit sphere with ∅′ = 0 at the collocation point). The

discretized boundary integral equation (3) is a linear system of equations

�1

2𝑰 + 𝑲 𝜸 = 𝜸𝒊

(5)

where and are vectors of the coefficients of the B-spline expansions of the unknown and the

incident complex pressure, respectively, on the surface S. I and K are matrices mapping the

coefficients of a B-spline expansion to the values of the two terms on the left side of equation (3)

at the collocation points. More details can be found in the References [3–8].

The discretized boundary integral equation system (5) is assembled in parallel on a multi-core

system running under MPI and maintained in distributed form at the slave processes. The system

(5) is solved iteratively by the GMRES method [7] combined with preconditioning. A useful

preconditioner for the test cases considered was obtained by reducing the coefficient matrix in (5)

to block circulant structure by averaging over the azimuthal B-spline index and then transforming

the matrix to block diagonal form by Fast Fourier Transform (FFT) [7, 8].

The computational requirements of the BIE method are dominated by the workload and storage

space needed for assembling and solving the equation system (5), which limits the applicability of

the BIE method to low and medium frequencies such that the size of all scatterers is small to

moderate in number of wavelengths. The actual frequency range for applicability of the BIE

method is of course highly dependent on the available computational resources.

2.2.2 Kirchhoff Approximation Methods

In the KIR and KIT methods, the value of the complex pressure p(s) in the HK integral (1) is set

to the Kirchhoff approximation

𝑝�𝒔 = 2𝑝𝑖�𝒔 (6)


on insonified parts of S and

𝑝�𝒔 = 0 (7)

on shaded parts of S. This eliminates the work and storage space required for assembling and

solving the boundary integral equation (3) and thus extends the range of manageable frequencies

beyond that of the BIE method.

The KIR and KIT methods [9] use different techniques for modelling of the surface and

computing the integral (1). In the KIR method, these techniques are identical to those used by the

BIE method. S is the smooth surface defined by (4) and the integral (1) is computed by high-order

global quadrature over the unit sphere.

In the KIT method, the surface S is represented by triangular facets and the integral (1) is

computed as a sum of contributions from the triangles. The contribution from each triangle is

computed with a formula that is exact for integrands of the form

𝐹�𝒓 = 𝑒𝑖𝒌∙𝒓 𝐺(𝒓) (8)

where k is a constant vector and the function G(r) is linear. For accuracy the triangulation must be

such that (i) F(r) is a good approximation of the integrand in (1) on each insonified triangle and

(ii) the shape of the scatterer is sufficiently resolved. Thus, in particular, the triangulation need

not be refined as frequency increases.

2.2.3 Eigenray Method

As in the BIE and KIR methods, S is the smooth surface defined by (4). Denoting the position of

the source with 𝒓𝟎 , the scattered complex pressure at a point 𝒓𝟏 outside S is computed in two

steps.

First, the reflection point on S of the source → scatterer → receiver eigenray is found, according

to Fermat’s principle, by minimizing the travel time along the ray

𝑇�∅,𝜃 = � 𝒓𝟎 −𝑹�∅, 𝜃 + 𝒓𝟏 − 𝑹�∅,𝜃 /𝑐 (9)

over �∅, 𝜃 where 𝑹�∅, 𝜃 is the function in equation (4). The solution of this non-linear

optimization problem is computed by a robust and rapidly converging trust-region method [10].

The amplitude of the transfer function of the complex pressure as a function of arc length s along

the eigenray is then given by the ray tube cross sectional area factor

𝐴0�𝑠 = 1

4𝜋

cos𝜃0

𝐽(𝑠) 1/2

(10)


see [11, Sec. 3.3.3 equation 3.56]. J(s) is the determinant of the 3×3 Jacobian matrix of the partial

derivatives of the ray path function 𝒓�𝑠, 𝜃0,∅0 where s, 𝜃0 , and ∅0 are the arc length along the

ray and the vertical and horizontal launch angle, respectively [11, Sec. 3.3.3 equation 3.45].

2.3 Canada (DRDC)

The primary software used by DRDC is AVAST [12, 13] which has been developed under

contract to Lloyd’s Register Applied Technology Group (formerly Martec Ltd.). The AVAST

software suite comprises many separate capabilities including a Boundary Integral Equation

Method (BIEM), a first-order Kirchhoff approximation, and a high frequency ray tracing method,

all of which were used in this project arrangement. Upon request of the participants, DRDC also

included some results using the BASIS software. These methods will be described below.

2.3.1 BASIS

BASIS (Bistatic Acoustic Simple Integrated Structure) was developed in cooperation with the US

Naval Research Laboratory (NRL) and was based on work by Drumheller et al. [14]. The

software, programmed in Matlab [15], uses a physical optics integral methodology to determine

approximate formulae for simple shapes such as plates, cylinders, spheres, etc. The resulting

complex formulae for the shapes are then analytically solved and coherently added to provide a

simple physically-based target strength model. The coherent addition is critical to correctly

obtaining the full effect of secondary scatterers and it should also be noted that this type of model

is inherently sensitive to the relative positions of the individual shapes. The target in question is

modelled using the available set of shapes which includes cylinders (horizontal and vertical,

circular and elliptical), ellipsoids, spheres, plates, truncated cones, and airfoils.

Figure 1 shows a combination of shapes implemented in BASIS. Tail fins and the back of the sail

are modelled by two flat plates set at an angle to the centreline of the main hull cylinder. The

origin of all objects is the centre of mass of the main hull cylinder. The bow of the target

consists of a half-sphere and a short half-cylinder that combine to make half of a vertical,

hemispherically-capped cylinder. A bow ellipsoid as well as an airfoil sail may also be used

instead. This version of BASIS is essentially two-dimensional—only allowing for predictions in

the horizontal plane. BASIS is expected to perform best in the medium-frequency range (from

about 1 kHz to at most 7 kHz). It is an approximate method most useful for the ease of modelling

and rapid solution times.


Figure 1: BASIS-TS submarine shape model.

2.3.2 Boundary Integral Equation Method (BIEM)

The boundary integral equation method (BIEM), as noted above, is one of the available

techniques for determining the target strength of submerged structures. In a similar fashion to the

FOI method, AVAST employs a boundary element formulation based upon the classical

Helmholtz integral equation. Standard numerical techniques are used to solve this integral

formulation and include the discretization of the wet surface of the body, or structure, into a

collection of boundary element panels (either three- or four-noded), followed by the numerical

integration of the Helmholtz integral equation over the surface of the body (represented by these

panels). This leads to a system of algebraic equations relating the acoustic pressure on the surface

of the body to the incident pressure field and surface normal velocities, which is then solved for

the surface acoustic pressures. Finally, the surface acoustic pressures are used to predict the field

pressures at points in the fluid domain and, from these, estimates of the body’s target strength can

be generated using the definition of TES. Care should be taken to ensure that the degree of mesh

refinement is sufficient to capture the distribution of the acoustic pressure at the prescribed

frequency. AVAST analyses have indicated that on the order of 10–12 boundary element panels

per acoustic wavelength are required.

The underlying boundary element based algorithms employed by the AVAST solver are best

suited for low frequencies (typically up to 2 kHz for a submarine-sized target). Attempts to model

the acoustic response at higher frequencies can quickly overwhelm the memory/disk-space

resources of most computers.

2.3.3 Kirchhoff Approximation Method

The Kirchhoff approximation developed for AVAST was based on the work published by

Schneider, et al. [16, 17]. The basic Kirchhoff formulation has been implemented in the AVAST

code, for both the bistatic and monostatic cases. Discretization of the model into panels is still

required, but the memory requirements for this method are much reduced compared to the BIEM.

One trade-off is in accuracy as, unfortunately, the Kirchhoff approximation does not model

forward scatter correctly and, as a result, is limited in its bistatic predictions over a range of

bistatic angles (typically ±60º from the source location). The Kirchhoff approximation also does

not deal well with complex (particularly concave) objects unless multiple reflections are


specifically managed and calculated within the software which has not been incorporated in the

AVAST version. These types of targets are not an issue with the BIEM. In general, the AVAST

Kirchhoff approximation provides a fast solution for full three-dimensional structures with

relatively complex shapes and can address frequencies well above those available to the BIEM.

While these formulations within AVAST have been successfully validated, practical limitations

have restricted the usable frequency range. The model must still be discretized subject to the

desired frequency. Testing has shown that, even with the Kirchhoff method, approximately

2 panels per wavelength are necessary for the predicted TES to converge. For example, for a

frequency of 20 kHz, this typically results in submarine models with about 2 million panels.

While not necessarily a computational difficulty, it becomes extremely difficult to generate,

visualize, and modify these models. A submarine model valid for 30 kHz might result in a file

size of several hundred GB.

2.3.4 Ray Tracing Method

To address the high frequency regime, the ray-tracing method was developed. The concept behind

ray-tracing is relatively simple [18]. At high frequencies, the sound power generated by a sound

source can be represented by a collection of rays. These rays travel through the acoustical domain

and are reflected by the scattering body. During that time, the energy in the rays decreases as a

consequence of the sound absorption in the fluid domain and with scattering/transmission

interactions with the body. When the rays cross predefined volumes (receivers) the energy

associated with each ray is combined to approximate the sound intensity at that location. Once

this value is known then the TES can be computed using the standard formulation.

From a numerical modelling perspective, and given the above description of the ray tracing

method, the implementation of a ray tracing algorithm into AVAST was relatively straight

forward. The main deficiency was a set of tools capable of performing the geometric operations,

i.e., computing the intersections between straight lines (representing the acoustic rays) and the

target body. This was addressed by the acquisition of a set of advanced non-uniform rational basis

spline (NURBS) based geometry libraries. These libraries encompass extensive definition and

manipulation of NURBS curves and surfaces, including the ability to compute intersections

between lines and complex geometric bodies. This use of NURBS-based models allows for the

analysis of complex geometric targets without the need of creating an approximate faceted

representation of the surface as is done in the BIEM and Kirchhoff methods. Ship hulls, created in

third-party modelling tools, could be imported directly into AVAST as Initial Graphics Exchange

Specification (IGES) files without the need for any additional geometric manipulation.

The basic algorithm designed and implemented in AVAST is outlined below in Figure 2. Once

model data has been entered, a series of rays representing the incident acoustic field are then

generated and passed through the acoustic domain. Intersections between these incident field rays

and a target receiver positioned at the centre of the acoustic target are used to compute the

incident acoustic field at the centre of the acoustic target (the sum of the energy associated with

the individual rays intersecting the volume of the receiver positioned at the acoustic centre is used

to compute the approximate incident acoustic at the centre of the target).

At this stage the scattered field is computed by inserting the target into the acoustic domain. Rays

are then permitted to scatter or reflect off the target’s surface. Each time a ray collides with the


target, a portion of the ray’s energy will potentially be lost. Eventually, if a sufficiently large

number of collisions occur, the energy associated with the ray will drop below a predefined

threshold and the ray will cease travelling through the acoustic domain. Once all the reflections

have been computed, the scattered rays are then processed to establish intersections with the

receivers. The energy associated with the scattered rays impinging upon each individual receiver

are then summed up and used to represent the scattered field at that receiver.

While this method is useful for predicting the monostatic TES, as rays cannot penetrate the target,

nor creep around the target, this method will not any predict forward scattering, thus limiting its

use for bistatic TES predictions. However, it can produce realistic bistatic results over a

reasonable arc in the backscatter direction.

Figure 2: AVAST ray-tracing algorithm.


3 Geometric Models

As described in the Project Arrangement, the initial stage of the software comparison consisted of

using the various codes to predict the TES of a variety of relatively simple geometric shapes

reminiscent of submarine geometries. The shapes chosen include a rotationally symmetric

ellipsoid, a right cylinder with different endcaps, and a large NACA-section airfoil, all with

dimensions appropriate to a full-scale diesel-electric submarine. From these geometric models,

numerical models were then constructed.

3.1 Ellipsoid

The criteria for the first test case included having a body with a surface which was smooth

everywhere, e.g., an ellipsoid or super-ellipsoid, to avoid edge effects and ensure convenient

convergence of the full-field solver. This would allow computing the full field solution accurately

(monostatic and bistatic) using a full Boundary Integral Equation Method (BIEM) or its

equivalent. This was then used as a reference when checking the validity of the fast approximate

methods (e.g., Kirchhoff). An ellipse with simple dimensions was chosen and the model was thus

a rotated ellipse with a major axis of 35 m and a minor axis of 3.5 m (to roughly match submarine

dimensions) as seen in Figure 3.

Figure 3: Ellipsoid geometric model.

3.2 Cylinder

As a complement to the first test case, the second test case was a simple cylinder with one flat end

and one hemispherical end. While maintaining simplicity, this is a more realistic test case of the

shapes in which the participants are most interested (submarine pressure hulls). The cylinder was

sized to simulate a submarine with a diameter of 7 m and an overall length (including the

hemispherical endcap) of 70 m as shown in Figure 4.


Figure 4: Cylinder geometric model.

3.3 Airfoil

To further investigate submarine-related geometries, predictions were also made of an airfoil of

10 m length and 5 m height which is approximately the correct size for the cylinder described

above to simulate a submarine sail structure. The airfoil was based on a symmetric 4-digit NACA

profile as described in [18]. The particular airfoil selection was somewhat arbitrary, largely an

aesthetic choice. The particular airfoil selected was a NACA 0017 which is based on the

following equation:

𝑧𝑛 = 5𝑡�𝑎0𝑥𝑛0.5 − 𝑎1𝑥𝑛 + 𝑎2𝑥𝑛

2 − 𝑎3𝑥𝑛3 + 𝑎4𝑥𝑛

4 (11)

where zn is the airfoil thickness at point n, is the length to point n from the leading edge of the

airfoil (running from 0 to 1), t defines the ratio of width to length (set to 0.17 for this airfoil) and

the coefficients a0 to a4 are defined in [19] and are shown in Table 1 below. The resulting curve

was then scaled to a length of 10 m, assigned a height of 5 m, and then a top and bottom plate

were added to complete the geometric object, shown in Figure 5.


Figure 5: Airfoil geometric model.

Table 1: NACA coefficients for airfoil.

NACA Coefficient Value

0 0.2969

1 0.1260

2 0.3516

3 0.2843

4 0.1015


4 Numerical Models

Using the basic geometries as described above, IGES geometric files were created for each object

and distributed to the participants for their own use. These data files are typically quite small in

size (less than 1 MB) and, hence, easily transportable. For the BIEM and Kirchhoff methods, a

panelized representation of the model is required with the number of panels correlated to the

desired analysis frequency. For the DRDC ray-tracing method, the IGES file is used directly,

while the BASIS model is constructed using the geometric parameters as input for the various

elemental component modules.

4.1 Ellipsoid

For AVAST, BIEM and Kirchhoff files were created with panel sizes of 250 mm to 12.5 mm,

resulting in panel numbers of 18,000 to 7.8 million respectively. Based on the panels/wavelength

criterion discussed above, these panel sizes cover frequencies of 600 Hz (BIEM) to 60 kHz

(Kirchhoff) while noting that the largest model (smallest panel size) resulted in a file size of more

than 1 GB, which was extremely difficult to manually edit (as is often required). The IGES file,

used for the ray tracing analysis, was only 380 KB in size.

For the BASIS model, the “bow elliptical cylinder” primitive was used. This primitive was

selected as the closest match from the available set and used a vertical cylinder with an elliptical

cross-section (rather than circular) with dimensions matching the ellipsoid axes. The height was

selected to roughly coincide with the submarine parameters. As could be expected, the vertical

cylinder walls do not provide a good match for the actual rotationally symmetric ellipsoid.

In the FOI methods BIE, KIR and RAY, no panelling is used; instead the analytical formula of

the ellipsoid is used directly to describe the shape of the scatterer. In the KIT method, the shape is

discretized into planar or quadratically-curved triangular elements. The triangles must be

sufficiently small so that (i) the shape of the scatterer is resolved and (ii) a plane wave with

linearly varying amplitude is a good approximation of the Kirchhoff integrand on each triangle,

see equation (3) of Section 2.2. In particular, the triangle sizes need not be restricted to a fraction

of the wavelength. For the ellipsoid, convergence of the TES curve at range 200 m and frequency

10 kHz is obtained for approximately 500,000 triangles (average difference from previous curve

of less than 0.1 dB), resulting in a maximum triangle side/wavelength ratio of 1.47.

4.2 Cylinder

Similarly, for the cylinder, AVAST files (BIEM and Kirchhoff) with panel sizes of 250 mm to

37.5 mm (26,000 to 1.2 million panels) were created, covering the same frequency range as the

ellipsoid. Due to the separate endcaps, the IGES file was slightly larger, about 860 KB.

For this BASIS model, the hull cylinder, bow spherical cap, and tail plate primitives were used

which should provide an excellent representation of the actual model.


In the FOI methods BIE, KIR and RAY, again no panelling is used, instead the shape of the

cylinder is described by a smooth map of the unit sphere. The map is represented by a B-spline

expansion which interpolates to the cylinder surface on a uniform latitude/longitude grid on a unit

sphere. In the KIT method, the shape of the map-described cylinder is discretized into planar or

quadratically curved triangular elements, with triangle size restricted by the conditions stated

above for the ellipsoid. For the cylinder, visual convergence of the TES curve at range 200 m and

frequency 10 kHz is obtained for approximately 720,000 triangles, a maximum triangle

side/wavelength ratio of 1.67.

4.3 Airfoil

Using equation (11), and adding a top and bottom plate, an IGES model was created for the

airfoil. As above, this was discretized for the AVAST BIEM and Kirchhoff models, creating files

with panel sizes of 12.5 mm and 37.5 mm (730,000 and 81,000 panels) to match 30 kHz and

10 kHz (Kirchhoff only). During the initial evaluation, discrepancies in the results led to a further

examination of the model, resulting in the creation of a highly detailed panel mesh using 5 mm

panels (resulting in 4.6M panels and a file size of 630 MB). From this, errors in the original

geometry were found and corrected. The final IGES file was only 200 MB in size.

As an airfoil primitive exists within BASIS, this was used as a precise representation of the actual

airfoil model.

Once again, for the FOI methods BIE, KIR and RAY no panelling is used, instead the shape of

the airfoil is described by a smooth map of the unit sphere. The map is represented by a B-spline

expansion which interpolates to the airfoil surface on a uniform latitude/longitude grid on a unit

sphere. In the KIT method, the shape of the map-described airfoil is again discretized into planar

or quadratically curved triangular elements, with triangle size restricted by the conditions stated

above for the ellipsoid. For the airfoil, visual convergence of the TES curve at range 200 m and

frequency 10 kHz is obtained for approximately 320,000 triangles, a maximum triangle

side/wavelength ratio of 0.665.


5 Results

In general, each geometric model was examined at four frequencies (1, 3, 10, and 30 kHz) and

two distances (200 m and 2000 m) as outlined in the original Project Arrangement. As well as

monostatic target strength, a single bistatic target strength was also calculated using a source

located at 45º from the “bow” of the notional submarine with receivers covering the full 360º

circle around the object. In all cases, the TES was only examined in the horizontal plane running

through the geometric centre of the models.

In all results in this report, 0º is located at the “bow” (the hemispherical end for the cylinder

model and the leading edge of the airfoil), 180º is the stern and 90º is the port side. All results are

contained in the annexes at the end of the report. Graph legends are summarized in Table 2. If the

method was not used for a particular case, the legend entry was removed from the plot.

Table 2: Graph legends.

Graph Legend Meaning

DRDC B DRDC BIEM results

DRDC K DRDC Kirchhoff results

DRDC RT DRDC ray tracing results

FOI B FOI BIEM results

FOI KT FOI KIT method results

FOI KR FOI KIR method results

FOI RT FOI eigenray results

BASIS DRDC BASIS results

Due to symmetry, monostatic TES results are only shown for 0º–180º for the cylinder and airfoil

and for 0º–90º for the ellipse. Bistatic results are shown for the full 360º circle.

Note that not all methods were used in every case. Typically this was due to frequency limits

inherent to the method. For example, the BIEM results are typically limited to 3 kHz due to

computer memory limitations, while the DRDC ray-tracing method is frequency independent and

only considered applicable at high frequencies (the 10 and 30 kHz cases in this instance). The

BASIS model is intended as a far field model and was not used for predictions at the 200 m


distance. BASIS was also only used for monostatic predictions. At other times, the lack of results

may be due to issues related to that particular test case and those will be discussed in the

following section.

Overall, the various models show the expected trends. Reflected peaks tend to be much broader at

close range, getting narrower at longer ranges. For the bistatic cases, specular reflections appear

at 135º and the main forward scatter lobe appears at 225º. Main lobes and side lobes tend to get

sharper with frequency. Note that this is sometimes not easily seen due to the 1º increments used.

A 0.1º increment tends to show this a little better, particularly at the higher frequencies. The

DRDC RT will sometimes not show any reflections due to the range or geometry and these show

as gaps in the plot. The DRDC RT method also has a finite lower bound for each case which can

be decreased by increasing the number of rays. A sufficient number of rays was not always

possible due to computer memory limitations. Note though, that these gaps exist in areas of very

low target strength (the reason why they exist) and thus, as such, have lesser operational

significance.

5.1 Ellipsoid

The ellipsoid model was intended to allow the most exact computations and comparisons due to

its symmetry and simplicity. These same characteristics also allowed for very simple modelling

either for the facetted models or the more geometric based models. Complete results for the

monostatic and bistatic calculations are shown in Annex A.

The monostatic nearfield results (Figures A.1–A.4) show generally good agreement with the

DRDC RT showing small differences. There appears to be a slight overprediction at 0º, crossing

to an underprediction at about 10º, followed by general agreement after 60º. At 30 kHz, the

DRDC plots compare well, but show some differences with respect to the FOI results. The FOI

results show excellent agreement overall. The lack of smoothness in the DRDC K trace at 30 kHz

is likely due to insufficient elements at such a high frequency.

Agreement was quite good at the longer ranges (Figures A.5–A.8) except for the BASIS results

which do not agree well with the FOI results. This is likely due to the choice of primitives within

BASIS which was the best match possible, but still a relatively poor match. In this case the

selected primitive was a vertical-walled elliptical cylinder which presents straight sides to the

source. This results in a significant overprediction. A better match could be achieved by selecting

a cylinder height different from the ellipsoid height, but there is no physical basis for the choice

of height. Due to the “perfection” of the rounded geometric shape, the DRDC RT software does

not produce many reflections back to the receiver at such long ranges unless significantly more

rays are used (not possible with the version available). This can be remedied by incorporating

some non-specular reflection in the model—a capability which exists in AVAST—but this was

not done in this analysis. The FOI B results (only available at 1 kHz) also show variability rather

than the smooth results of the other methods. The DRDC K (first two frequencies), FOI RT, KR,

and KT all agree well. DRDC B was not run for this model.

For the nearfield bistatic results (Figures A.9–A.12), there is more variation in the methods. It is

already known that the DRDC K and DRDC RT methods do not predict accurately in the forward

scatter direction (225º in this case). This is also the case for the FOI RT method. At 1 kHz, there


is quite good agreement elsewhere between all methods (even the RT ones). The primary source

is located at 45º, so a specular reflection is expected at 135º, with a forward scatter peak at 225º.

As can be seen at 3 kHz, similar results appear, but the DRDC B method is showing instabilities

due to a lack of elements (no increase was possible due to memory limitations). At 10 kHz,

results are again similar but at 30 kHz there is no DRDC K available. While the FOI KR and KT

results show very good agreement everywhere, the two ray tracers do show good agreement

outside of 170º–300º.

At the longer range (Figures A.13–A.16), the DRDC methods again had issues. DRDC B and

DRDC K were not run at the lower frequencies, due to capacity issues. In this case, it was

possible to get results from the DRDC RT method which shows some agreement with the FOI

methods (again, very few reflections are coming back). The FOI methods show good agreement

with similar caveats to the nearfield in the forward scatter direction.

5.2 Cylinder

The cylinder model was intended to continue the symmetry of the ellipsoid while introducing a

geometry more comparable to actual submarines. Note that rotational symmetry (about the long

axis) is broken by the differing hemispherical and flat endcaps located at 0º and 180º,

respectively. Complete results for the monostatic and bistatic calculations are shown in Annex B.

The monostatic results only span 180º due to the bilateral symmetry.

Overall, the monostatic nearfield results (Figures B.1–B.4) show generally good agreement. Both

RT methods show some variations, but generally follow the overall trend. The boundary element

and Kirchhoff methods show strong lobes after 120º at 1 kHz, which disappear as the frequency

increases. There appears to be a small negative bias in the DRDC RT and FOI KT before 90º.

This disappears for the FOI KT model at higher frequencies; however the method appears to

break down at cylinder broadside as frequency increases (while maintaining reasonable “average”

values). At 3 kHz and 10 kHz, DRDC K is showing much larger nulls after about 100º (it is not

clear why) and the DRDC RT shows a broader peak at the spherical end at 10 kHz and 30 kHz.

For this case, the FOI KR and FOI RT seem to be most consistent.

For the long range monostatic predictions (Figures B.5–B.8), the overall agreement is quite good.

The BASIS results are surprisingly good at 1 kHz, but seem to have issues with flat end cap at

higher frequencies. DRDC RT appears to overpredict by about 5 dB; this would likely decrease

with more rays (the crenelated appearance is an indication of insufficient rays). As with the

nearfield, DRDC K appears to show lower response for the flat end. For this case, all the FOI

models show excellent at all frequencies.

For the nearfield bistatic results (Figures B.9–B.12), there is quite good agreement at the first

three frequencies except in the forward scatter direction (about 180º to 270º) where it is known

that DRDC K and DRDC RT do not predict well. The large deviations seen with DRDC K at

30 kHz indicate the panel size is too small and more refinement is necessary. This same effect is

visible with FOI KT to a lesser extent.

Similar results to the short range are seen at the longer range (Figures B.13–B.16). Both RT

methods show narrower peaks at the lower frequencies; however they agree better at the higher


frequencies. The overall agreement is quite good, except for DRDC K at 30 kHz where there are

likely not enough panels.

5.3 Airfoil

The final model used was the airfoil, meant to mimic the submarine sail. Again this is

symmetrical about the long axis, so the monostatic results are shown for only 0º to 180º.

Complete results for the monostatic and bistatic calculations are shown in Annex C.

Overall, the monostatic nearfield results (Figures C.1–C.4) show generally good agreement. Both

RT methods show differences at lower frequencies where they are typically less accurate, but

generally follow the overall trend. DRDC K and FOI KT start to show some differences at the

higher frequencies, but are still quite reasonable. In many of the models, an instability seems to

arise around the 45º mark. This is particularly apparent at 30 kHz, but appears at all frequencies

for the FOI RT model. This was the location of the geometric error noted in Section 4.3. It may

indicate a very small geometric error which would only affect the highest frequencies or some ray

tracing methods. Note that DRDC RT does not show the effect. Note also the boundary element

methods (DRDC B and FOI B) show stronger lobe structures at 1 kHz than the Kirchhoff

methods. At this frequency, the boundary element solution is generally considered “correct.”

Results are similar for the long range monostatic predictions (Figures C.5–C.8), although the ray

tracing predictions are much further off, only becoming acceptable (within 5 dB) at 30 kHz. It is

not clear why this occurs for this shape only in this study. The other methods show quite good

agreement.

For the nearfield bistatic results (Figures C.9–C.12), a similar trend is seen with the ongoing

caveat that the DRDC K and RT methods are poor in the forward scatter. Here the ray tracing

methods are poor at 1 kHz, but quite good at the other frequencies, and the boundary element and

Kirchhoff models generally agree quite well. Note that this is a physically smaller shape, so it is

easier to compute enough panels to accommodate the 30 kHz test case for the Kirchhoff models.

A similar comparison to the monostatic case is seen at the longer range (Figures C.13–C.16) for

the bistatic case. The ray tracing methods are poor at low frequencies, becoming much better as

frequency increases. There is also generally good agreement for the Kirchhoff methods (except in

forward scatter).


6 Conclusions

As part of the Canada-Netherlands-Sweden Project Arrangement on Target Echo Strength,

Canada and Sweden agreed to compare their various tools for predicting TES using relatively

simple geometric models. This was the first of two steps, the second being the comparison of

these software tools against experimental submarine data which will be documented separately. In

this study, DRDC and FOI used their boundary element, Kirchhoff approximation, and ray

tracing models to evaluate a rotationally symmetric ellipsoid, a cylinder with one hemispherical

and one flat endcap, and an airfoil—all sized similar to their related submarine structures.

In many cases, the various methods (Kirchhoff, etc.) agreed fairly well with each other, but in

others the agreement was poor. Both DRDC and FOI provided results from boundary element

codes, Kirchhoff approximations, and ray tracers, while DRDC also added the analytically-based

BASIS code as well. As expected due to their formulation, the DRDC Kirchhoff and ray tracing

codes do not accurately predict forward scatter when performing bistatic predictions. A reminder

that the boundary element codes are limited by memory to the lower two frequency ranges, the

Kirchhoff codes are intended for above 1 kHz, and the ray tracers are only valid at the highest

frequencies (30 kHz and possibly 10 kHz).

Even excluding the forward scatter direction, the FOI Kirchhoff codes generally performed

slightly better than the DRDC versions, although differences were small. Both boundary element

codes agreed quite well, but are limited to about 3 kHz (for this size model) by computer memory

limitations. Again, excluding forward scatter, the two ray tracers performed similarly, with the

FOI version seeming more computationally efficient. Results for the DRDC ray tracer would

improve with more rays, but this was not feasible within the time frame. Note In the few cases

where applicable, the BASIS code gave reasonable results (and is significantly faster than any of

the others).

The “simple” ellipsoid showed unexpected difficulties due to the smooth geometric shape. At

longer ranges, the DRDC RT code did not produce any reflections back to the receiver due to the

smoothness of the geometry. Either extremely large number of rays or the addition of a roughness

factor (no-specular scattering) would be required to overcome this. Both the cylinder and the

airfoil showed more consistent results for all methods.

Overall, either country’s methods will give comparable results when used within their

capabilities. The DRDC ray tracer requires upgrades to optimize its performance and allow for

larger numbers of rays. As well, recent efforts to migrate boundary element codes to large CPU

clusters may allow for some expansion of their frequency ranges. The results of this study

indicate that the various tools should give comparable results when examining more realistic

naval platform models.


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References

[1] Project Arrangement Number 2014-01 To The CAN/NLD/SWE Cooperative Science and

Technology Memorandum of Understanding Dated 23 May 2003 Concerning Target Echo

Strength, September 2014.

[2] J. Ehrlich, L. Fillinger, L. Gilroy, M. Nijhof, and I. Schäfer, “BeTSSi IIB Benchmark Target

Strength Simulation,” Workshop Planning Document, July 2016.

[3] I. Karasalo, J. Mattsson, “Numerical modelling of acoustic scattering by smooth inclusions in

a layered fluid-solid medium, High Frequency Acoustics in Shallow Water,” SACLANT

Conference Proceedings Series CP-45, pp. 283–290, 1997.

[4] I. Karasalo, “Acoustic scattering from a generic submarine,” Proc. Fourth UK Conference on

Boundary Integral Methods, Salford University, pp. 205–213, September 2003.

[5] I. Karasalo, Modelling of target strength measurement in shallow water, FOI-R-3031-SE,

Swedish Defence Agency FOI – Totalförsvarets forskningsinstitut, 2010.

[6] I. Karasalo and J. Hovem, “Transient bistatic scattering from buried objects.” In Experimental

Acoustic Inversion Methods for Exploration of the Shallow Water Environment, A. Caiti,

J.-P. Hermand, S.M. Jesus, and M.B. Porter, eds. Kluwer Academic Publishers, pp. 161–176,

Carvoeiro, Portugal, 2000.

[7] I. Karasalo, “BIE and hybrid -BIE-FEM methods for acoustic scattering from structured

elastic objects.” Theoretical and Computational Acoustics, M. Taroudakis and P. Papadakis,

eds. ISBN 978-960-89758-4-2, Heraklion, Crete, Greece, 2007.

[8] I. Karasalo, “On evaluation of hypersingular integrals over smooth surfaces,” Computational

Mechanics, vol. 40, pp. 617–625, 2007.

[9] I. Karasalo, “Transient acoustic scattering from a small underwater vehicle in shallow water,”

Report FOI-R--1713--SE, Swedish Defence Research Agency, September 2005.

[10] R. Fletcher, Practical Methods of Optimization. Wiley, New York, 1988.

[11] F. Jensen, W. Kuperman, M. Porter, and H. Schmidt, Computational Ocean Acoustics.

Second edition, DOI 10.1007/978-1-4419-8678-8, Springer-Verlag New York, 2011.

[12] L.E. Gilroy and D.P. Brennan, “Predicting Acoustic Target Strength with AVAST,”

DREA TM 2000-071, Defence Research Establishment Atlantic, 2000.

[13] L.E. Gilroy, “Numerically Predicted Aspects of Submarine Target Strength,”

DREA TM 2000-089, Defence Research Establishment Atlantic, 2000.

[14] D.M. Drumheller, M.G. Hazen, and L.E. Gilroy, “The Bistatic Acoustic Simple Integrated

Structure (BASIS) Target Strength Model,” NRL/FR-MM/&140-02-10019, April 2002.


[15] MATLAB 6.1, The MathWorks Inc., Natick, MA, 2000.

[16] H.G. Schneider, C. Fiedler, R. Berg, L.E. Gilroy, I. Karasalo, I. MacGillivray,

M. Ter-Morshuizen, and A. Volker, “Benchmark Target Strength Simulation Workshop,”

Proceedings of UDT Europe 2003, Malmo, Sweden, 24–26 June 2003.

[17] H.G. Schneider, C. Fiedler, R. Berg, L.E. Gilroy, I. Karasalo, I. MacGillivray,

M. Ter-Morshuizen, and A. Volker, “Acoustic Scattering by a Submarine: Results from a

Benchmark Target Strength Simulation Workshop,” 10th International Congress on Sound

and Vibration, Stockholm, Sweden, 7–10 July 2003.

[18] D.O. Elorza, “Room Acoustics, Modeling Using the Ray Tracing Method: Implementation

and Evaluation,” Licentiate Thesis, University of Turku Department of Physics, 2005.

[19] I.H. Abbott and A.E. Von Doenhoff, Theory of Wing Sections, Including a Summary of

Airfoil Data, Dover Publications, 1959.


Annex A Ellipse Results

Figure A.1: Ellipse, monostatic, 200 m, 1 kHz.



Figure A.9: Ellipse, bistatic, 200 m, 1 kHz.



Annex B Cylinder Results

Figure B.1: Cylinder, monostatic, 200 m, 1 kHz.



Figure B.9: Cylinder, bistatic, 200 m, 1 kHz.



Annex C Airfoil Results

Figure C.1: Airfoil, monostatic, 200 m, 1 kHz.



Figure C.9: Airfoil, bistatic, 200 m, 1 kHz.


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DRDC – Atlantic Research CentreDefence Research and Development Canada9 Grove StreetP.O. Box 1012Dartmouth, Nova Scotia B2Y 3Z7Canada

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Target Echo Strength Software Benchmarking: Tasks 1 and 2 Under Canada-Netherlands-Sweden Project Arrangement on Target Echo Strength

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Gilroy, L.; Karasalo, I.

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August 2017

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including Annexes, Appendices,

etc.)

52

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(Total cited in document.)

19

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e.g., interim, progress, summary, annual or final. Give the inclusive dates when a specific reporting period is covered.)

Scientific Report

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DRDC – Atlantic Research CentreDefence Research and Development Canada9 Grove StreetP.O. Box 1012Dartmouth, Nova Scotia B2Y 3Z7Canada

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and development project or grant number under which the document

was written. Please specify whether project or grant.)

01ec

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which the document was written.)

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number by which the document is identified by the originating

activity. This number must be unique to this document.)

DRDC-RDDC-2017-R091

10b. OTHER DOCUMENT NO(s). (Any other numbers which may be

assigned this document either by the originator or by the sponsor.)

11. DOCUMENT AVAILABILITY (Any limitations on further dissemination of the document, other than those imposed by security classification.)

Unlimited

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Document Availability (11). However, where further distribution (beyond the audience specified in (11) is possible, a wider announcement

audience may be selected.))

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13. ABSTRACT (A brief and factual summary of the document. It may also appear elsewhere in the body of the document itself. It is highly desirable that

the abstract of classified documents be unclassified. Each paragraph of the abstract shall begin with an indication of the security classification of the

information in the paragraph (unless the document itself is unclassified) represented as (S), (C), (R), or (U). It is not necessary to include here abstracts in

both official languages unless the text is bilingual.)

As part of the Canada-Netherlands-Sweden Project Arrangement on Target Echo Strength

(TES), Canada and Sweden agreed to benchmark their software tools for predicting TES using

relatively simple geometric models. This was the first of two steps, the second being the

comparison of these software tools against experimental submarine data. In this study, Defence

Research and Development Canada (DRDC) and Swedish Defence Research Agency (FOI,

Totalförsvarets forskningsinstitut) used their boundary element, Kirchhoff approximation, and

ray tracing codes to evaluate a rotationally symmetric ellipsoid, a cylinder with one

hemispherical and one flat endcap, and an airfoil—all sized similar to their related submarine

structures. In general, for each technique, results from the various implementations agreed fairly

well. Both DRDC and FOI showed results from boundary element codes, Kirchhoff

approximation codes, and ray tracers, while DRDC also added results from the

analytically-based BASIS code. As expected due to their formulation, the DRDC Kirchhoff and

ray tracing codes do not accurately predict forward scatter when performing bistatic predictions.

Even excluding this forward scatter, the FOI Kirchhoff codes (two versions) generally

performed slightly better than the DRDC version, although differences were small. Both

boundary element codes agreed quite well, but were limited to about 3 kHz (for this size model)

by computer memory limitations. Again, excluding forward scatter, the two ray tracers

performed similarly, with the FOI version seeming more computationally efficient. Results for

the DRDC ray tracer would improve with more rays, but this was not feasible within the time

frame of the project. In the few cases where applicable, the BASIS code gave reasonable results

with significantly lower computational times. Overall, either country’s versions will give

comparable results when used within their capabilities. The DRDC ray tracer requires upgrades

to optimize its performance and allow for larger numbers of rays. As well, recent efforts to

migrate boundary element codes to large CPU clusters may allow for some expansion of their

frequency ranges. The results of this study indicate that the various tools should give

comparable results when examining more realistic naval platform models.

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Dans le cadre de l’accord de projet Canada-Pays-Bas-Suède sur l’intensité des échos de cible

(TES), le Canada et la Suède ont convenu d’évaluer les performances de leurs outils logiciels

visant à prédire la TES au moyen de modèles géométriques relativement simples. Cette

évaluation constitue la première de deux étapes, la seconde étant la comparaison des outils

logiciels par rapport aux données expérimentales des sous-marins. Dans cette étude, Recherche

et développement pour la défense Canada (RDDC) et l’Agence suédoise de recherche pour la

défense (FOI, Totalförsvarets forskningsinstitut) ont utilisé leurs codes de calcul basés sur les

techniques d’élément de frontière, d’approximation de Kirchhoff et du lancer de rayon pour

évaluer un ellipsoïde à rotation symétrique, un cylindre muni d’un embout hémisphérique et

d’un embout plat, ainsi qu’un profil aérodynamique : soit des structures ayant des dimensions

similaires à celles des structures correspondantes sur les sous-marins. En général, pour chacune

des techniques, les résultats des différentes implémentations concordent assez bien. RDDC et

FOI ont présenté des résultats de codes de l’élément de frontière, d’approximation de Kirchhoff

et de lancer de rayon, tandis que RDDC a ajouté ceux du code BASIS, un outil basé sur une

méthode analytique. Comme le prévoit leur formulation, les codes de Kirchhoff et de lancer de

rayon de RDDC ne prédisent pas avec précision la diffusion vers l’avant lorsqu’ils effectuent

des prédictions bistatiques. Même en excluant cette diffusion vers l’avant, les codes de

Kirchhoff de FOI (deux versions) donnent en général des résultats légèrement plus précis que

celle de RDDC, mais les différences sont petites. Les codes de l’élément de frontière concordent

assez bien, mais sont limités à environ 3 kHz (pour un modèle de cette taille) en raison des

limites de mémoire des ordinateurs. Encore une fois, en excluant la diffusion vers l’avant, les

deux lanceurs de rayon ont fonctionné de façon similaire, et la version de FOI semble plus

efficace sur le plan informatique. Les résultats pour le lanceur de rayon de RDDC

s’amélioreraient s’il y avait plus de rayons, mais ceci est impossible en raison de l’échéancier du

projet. Dans les rares cas où le code BASIS a été utilisé, ce dernier a donné des résultats

raisonnables tout en nécessitant des temps de calcul beaucoup plus courts. Dans l’ensemble, les

versions des deux pays donnent des résultats comparables lorsqu’elles ne dépassent pas leurs

capacités. Le lanceur de rayon de RDDC doit être perfectionné pour optimiser ses performances

et permettre un nombre plus élevé de rayons. Par ailleurs, des efforts récents visant à migrer les

codes de l’élément de frontière vers de grandes grappes d’unités centrales pourraient permettre

une certaine augmentation de leurs gammes de fréquences. Selon les résultats de l’étude, divers

outils devraient donner des résultats comparables lorsque des modèles de plateforme navale plus

réalistes sont examinés. 14. KEYWORDS, DESCRIPTORS or IDENTIFIERS (Technically meaningful terms or short phrases that characterize a document and could be helpful

in cataloguing the document. They should be selected so that no security classification is required. Identifiers, such as equipment model designation,

trade name, military project code name, geographic location may also be included. If possible keywords should be selected from a published thesaurus,

e.g., Thesaurus of Engineering and Scientific Terms (TEST) and that thesaurus identified. If it is not possible to select indexing terms which are

Unclassified, the classification of each should be indicated as with the title.)

target echo strength; cylinder; airfoil; ellipse; benchmark

target echo strength software benchmarking · 2017-10-31 · target echo strength software...

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