C9 - Modelling of bulk and guided waves in the Non-Destructive Evaluation of structures; software and implementation by industry
Submitting InstitutionImperial College London
Unit of AssessmentMathematical Sciences
Summary Impact TypeTechnological
Research Subject Area(s)
Mathematical Sciences: Numerical and Computational Mathematics, Statistics
Information and Computing Sciences: Computation Theory and Mathematics
Summary of the impact
The waves group in the Mathematics Department at Imperial College London
has developed methodology in several areas, including novel absorbing
layer techniques and Hybrid methods (with Rolls Royce and CEA) for Finite
Element software, and efficient techniques for finding the properties of
waves in curved plates, bars and pipes. The impact is facilitated by a
long-standing research collaboration with the Non-destructive Evaluation
group in the Mechanical Engineering department, incorporated with
industrial partners through the UK Research Centre in Non- Destructive
Our work has been directly implemented in DISPERSE — the world leading
software modelling tool for guided stress waves (licensed by Imperial
Consultants) — and by Rolls-Royce. [text removed for publication].
Rolls-Royce use the models for improved inspection techniques, resulting
in reduced man hour costs and multiple £50Ks of equipment savings.
The initial collaboration between the Non-destructive Evaluation (NDE)
group (Mechanical Engineering) and Mathematics involved studying
dispersion curves which are vital in the interpretation and understanding
of guided elastic waves [G1]. A technical, but practically important,
issue is the efficient and accurate evaluation of such curves for
waveguide structures (such as pipelines) that is guaranteed not to miss
any curves and which remains reliable and stable for the industrial user.
The theory created in [1,2] does precisely this for the important class of
circumferential guided waves in pipelines and is incorporated in the
DISPERSE releases from 2002-present. DISPERSE is the world's leading
modelling tool for guided stress waves, developed in Imperial College and
licensed by Imperial Consultants. A further industry requirement is for
dispersion curves for porous elastic media, anisotropy for
fibre-reinforced composite pipelines, inhomogeneous media and buried
pipelines. Again, progress in the theory  has been made and, for porous
media, this has actively been taken up by the geophysics and petroleum
In practical terms, ultrasonic modelling in industry is dominated by ray
modelling (the world leading code is CIVA, http://www-civa.cea.fr/en/,
developed by the Commissariat à l'énergie atomique et aux énergies
alternatives, CEA, in France) but this is not good for scattering for
which finite element (FE) models are strongest; commercial FE codes such
as ABAQUS are widely-available and well established. When modelling
scattering by defects in practical structures of large size, the greatest
limitation in numerical modelling is unwanted reflections from model
boundaries that are manifest as additional reverberations in the
ultrasonic signal that contaminate and poison the results. Arbitrarily
extending the domain size to large extents requires high-cost computing
and long-time solutions, and indeed is unfeasible for all but the simplest
cases. The removal of unwanted reflections is a challenging practical
problem, and a research area in its own right, but a key issue ignored by
the academic literature is that implementation in industry must use finite
element codes that are professionally accredited and meet industry
standards. Contributions from Mathematics were to identify how perfectly
matched layers (PMLs) can be used to address elastic waveguide modes that
have negative group velocity , a technical point that destroyed
applications of bespoke FE codes to ultrasonics in waveguides, and then
use this knowledge to tackle the industry bottleneck. The primarily
academic work then grew into an investigation of absorbing layers versus
PMLs with the emphasis on how to actually implement these research ideas
into the codes (ABAQUS) that Rolls-Royce [G2] and many others in industry
actually use. We were successful in this, as described in , and our
techniques are now implemented by Rolls- Royce.
In practice, scattering from defects may occur in large complex
structures (rail tracks, components in nuclear plants etc, [G3]) with
considerable separation between excitation transducer, defect and receiver
and the subsequent numerical modelling can lead to vast memory
requirements, particularly in 3D. This industry bottleneck motivated the
group to develop hybrid methods whereby only the source, receiver and
scatterer are modelled numerically and these small "boxes" then
communicate mathematically with each other as described and implemented
for commercial FE in . These advances enable large scale realistic
simulations, even in 3D, to be practical in CIVA and this is key to
applications of modern ultrasonics. This success led to the invitation by
CEA to join a consortium developing CIVA which is used by industry
- Professor R Craster, Head of Department of Mathematics, Imperial
College, Oct 1998-present
- Professor M Lowe, Professor in Mechanical Engineering, Imperial
- Dr E Skelton, RA, Department of Mathematics, Imperial College,
References to the research
(* References that best indicate quality of underpinning research)
 J. Fong, M.J.S. Lowe, D. Gridin and R.V.
Craster, "Fast techniques for calculating dispersion relations of
circumferential waves in annular structures'', Review of Progress in
Quantitative NDE (American Institute of Physics conference proceedings),
22, 213-220 (2002). DOI.
 *D. Gridin, R.V. Craster, J. Fong, M.J.S.
Lowe and M. Beard, "The high frequency asymptotic
analysis of guided waves in a circular elastic annulus'', Wave
Motion, 38, 67-90 (2003). DOI.
 A.T.I. Adamou and R.V. Craster, "Spectral methods
for modelling guided waves in elastic media'', J. Acoust. Soc. Am.
116, 1524-1535 (2004). DOI.
 *E.A. Skelton, S.D.M. Adams, and R.V. Craster,
"Guided Elastic Waves and perfectly matched layers", Wave Motion,
44, 573-592 (2007). DOI.
 P. Rajagopal, M. Drozdz, E. Skelton, M.J.S.
Lowe and R.V. Craster, "On the use of absorbing layers to
simulate the propagation of elastic waves in unbounded media using
commercially available Finite Element packages", NDT & E
International, 51, 30-40 (2012). DOI.
 *P. Rajagopal, E.A. Skelton, M.J.S. Lowe and R.V.
Craster, "A generic hybrid model for bulk elastodynamics, with
application to ultrasonic Non-Destructive Evaluation", IEEE Trans.
Ultrasonics, Ferroelectrics and Frequency Control, 59, 1239-252 (2012). DOI.
Relevant Research Grants:
[G1] EPSRC, GR/R32031,
"Distorted Elastic Waveguides: Theory and Application", PI: R.
Craster, Co-Is: P. Cawley, M. Lowe, 01/10/01-30/09/04, £236,682
[G2] Rolls-Royce and MoD direct funding of research programme in Mech Eng
(PIs: P Cawley, M Lowe), to develop ultrasonic inspection methods for
nuclear plant components. Total >£3M over period 2004-2013
[G3] EPSRC, EP/I018948/1,
"Modelling of ultrasonic response from rough cracks", PI: M. Lowe,
Co-I: R Craster, 1/1/11-31/12/13, £292,750 + £90K Industrial from project
partners (EDF- Energy, Rolls Royce Naval Marine), 01/01/11-31/12/13
Details of the impact
The theory work of [1,2] is incorporated into the commercial package
DISPERSE [A] v2 which was released in 2002 and continues to be updated and
developed by Imperial College, led by Prof M Lowe, Mechanical Engineering.
DISPERSE was first released to external users in 1991 [text removed for
publication] [C]. DISPERSE is an interactive Windows program designed to
calculate dispersion curves for multi-layered flat or cylindrical
structures. The facility to model accurately circumferential modes (added
in 2002) is an attractive addition to the original code and has helped it
to maintain its pre-eminent position in this area. [text removed for
publication]. The spectral approach to generating dispersion curves
accurately, developed in paper  drove the development of a porous
elastic version by Karpfinger and colleagues at Schlumberger Oilfield
Services and Shell International. This allowed real time completion
modelling in deepwater oil wells with the technique now widely utilised in
those applications. An article in The Leading Edge, a magazine reporting
new geophysical advances to the Society of Exploration Geophysicists,
acknowledges the contribution of the spectral theory based on  to both
experiments and the development of real-time completion modelling for oil
Since 2004 Rolls-Royce has been working in collaboration with Imperial's
departments of Mathematics and Mechanical Engineering on the development
of the Finite Element Method (FEM) for the modelling of ultrasonic wave
propagation and defect interaction [G2]. The aim of the work was to model
capably the interaction of ultrasonic waves with small and geometrically
complex flaws typical of the types found in nuclear plants due to
manufacturing and service induced mechanisms. The limitations of existing
models placed unnecessary cost on the company due to "extended
inspection durations and test piece trials" [E]. An aim of the
collaboration with Imperial was to "provide a generic modelling
capability to reduce inspection development costs through a greater
emphasis on modelling rather than test piece trials" [E]. The
absorbing boundaries work [4,5] proved "invaluable for the overall aims
of Rolls-Royce as it allowed small regions of a component to be modelled
using the FEM without wasting computing resources on unnecessarily large
models" [E]. These developments have "delivered significant
reductions in the model sizes required of typical inspection scenarios"
[E]. Financial impact to Rolls-Royce can be summarised in two ways:
- The modelling improvements described above "will significantly
reduce the number of ultrasonic test pieces required during inspection
development" where a typical test piece adds in the region of
£50,000-100,000 to inspection costs;
- The "production of component safety justifications requires
thousands of man hours that represents millions of pounds of cost"
and a small benefit provided to this effort removes "significant cost
from the submarine enterprise" [E].
The projects that the Imperial group delivered "provided Rolls-Royce
with a significant improvement in modelling capability" and have led
to two sponsored EngD projects to further refine the ideas and transfer
the technology into Rolls-Royce. Additionally, one of the collaborators
for this work, M. Drozdz, is now a fulltime employee at Rolls-Royce.
The hybrid technique  has similarly been implemented in code by
Rolls-Royce and this successful implementation has created momentum with
the impact on-going and developing internationally. For instance, it led
CEA (the developers of CIVA, the pre-eminent ray code used in ultrasonics)
to invite Imperial College to join the EU project `Simulation Platform for
Non Destructive Evaluation of Structures and Materials' (SIMPOSIUM)
that it project manages [F]. SIMPOSIUM started in September 2011 and will
develop over a period of 3 years. The cost of Project is €5.99m and
involves Volkswagen, European Aeronautic Defense and Space Company (EADS),
SKF and Serco amongst others as industrial partners [D]. The key objective
of the SIMPOSIUM project is to "build interoperable tools based on
hybrid modelling, for ultrasonic and electromagnetic NDE, in order to
solve very complex industrial cases from different fields (steel
nuclear, energy, aeronautics), software solution providers, and academic
teams" [F]. The "expertise, skills and know-how concerning both
NDE and mathematics from Imperial College" is leading the
developments based on hybrid modelling for ultrasonic simulation, for
which it is "necessary to combine mathematical and physics knowledge to
develop efficient hybrid and coupling formulations" [F]. The core of
the work being delivered by Imperial College relates to "a hybrid code
dedicated to ultrasonic simulation, based on the CIVA beam module
(prediction of the incident ultrasonic beam) and a "scattering box",
based on the well-known ABAQUS software, which contains a complex flaw"
The advantage of the absorbing boundaries work combined with the hybrid
work is profound. For the first time, industrial companies such as
Rolls-Royce are able to perform realistic simulations of the scattering of
ultrasound from defects, using FE codes that are accepted in the industry.
The realism includes thick and complex-shaped components, containing
complex-shaped defects, including fatigue cracks with rough surfaces
(collaborative research is on-going on this aspect too). This means that
they can make cases to justify proposed inspection of safety-critical
components at much-reduced expense. The cost reductions include the
reduced need to make experimental test (justification) samples, and the
possibility to replace radiographical inspections with ultrasound
inspections, avoiding the need to evacuate personnel during inspection and
the attendant health and safety issues.
Sources to corroborate the impact
[A] DISPERSE software website — An Interactive Program for Generating
Dispersion Curves http://www3.imperial.ac.uk/nde/products%20and%20services/disperse
(archived at https://www.imperial.ac.uk/ref/webarchive/g9f
[B] A. Bakulin, F. Karpfinger and B. Gurevich, `Understanding the
acoustic response of deepwater completions', The Leading Edge:
special section on permanent monitoring, smart oil fields and reservoir
surveillance, December 2008, 1646-1653. DOI.
[N.B. Reference to Craster in the acknowledgments]
[C] Letter from Imperial Consultants (ICON), June 2013. [text removed for
publication] (available from Imperial on request).
[D] Simposium project, partners webpage, http://www.simposium.eu/imperial-college
(archived at https://www.imperial.ac.uk/ref/webarchive/fpf
[E] Letter from NDE Development Engineer, Rolls-Royce Submarines, May
2013 (available from Imperial on request)
[F] Letter from NDE Senior Expert and Coordinator of the SIMPOSIUM
project, CEA, 17/7/13 (available from Imperial on request)