Underwater Pipeline Survey
With a Towed
Underwater Pipeline
Tracking
2.1
Introduction
Submarine infrastructures of off-shore industries require periodic in-spections to maintain the proper safety level and avoid environmen-tal risks. Underwater pipeline and cable survey is a time-consuming, expensive and demanding task. Nowadays commercial companies perform the task with a Remotely Operated Vehicle (ROV), linked to a surface ship through an umbilical cable, and carrying some payload sensors as the inspection task may require (e.g., camera, imaging sonar, magnetometer, etc.). The ROVs are generally driven by a two people team, one to keep the vehicle along the pipeline track, the other to monitor the payload sensor data. The task is very demanding for the team members and so a team shift is needed after no more than four hours, because the usual lack of variability
in the inspection data (sonar/video images etc.) makes it difficult to maintain the proper concentration and level of attention, expos-ing the task itself to human errors. Given the reasons above, there is a considerable effort in oceanic engineering toward the investiga-tion of devices and techniques that may lead to a partial or possibly complete automation of the survey task.
Several approaches have been explored, from the ambitious goal of employing Autonomous Underwater Vehicles (AUVs) for detecting and following the pipeline, in a totally autonomous mode, [5] and [6], to the use of visual feedback to enhance the ROV steering and mitigate the potential damage due to decrease of attention of the pilots [7] and [8].
This chapter reports the developing efforts and the results of a project directed toward the realization of a towed vehicle able to maintain itself centred over the pipeline at a specified altitude, while the towing ship follows the nominal pipeline route. The towed ve-hicle is equipped with navigation sensors (inclinometer, compass), pipeline following sensors (two magnetometers installed in differ-ential configuration) and both depth (pressure) and altitude (echo sounder) sensors. Autonomous vehicle steering is accomplished through control surfaces and rudder orientation. The availability of such a system will eliminate the need of steering, allowing the operator team to concentrate on the inspection data only. Moreover, a towed sys-tem allows to increase the velocity of the surface ship with respect to ROV inspection, contributing to the reduction of the overall survey time. Additional requirements for such a system are ease of trans-portation and operation, to allow it to be installed also on small work boat, and low cost.
The project is a joint effort between the Dept. of Mechanical Engineering of the University of Genova – DIMEC – and ISME, the Italian Interuniversity Ctr. of Integrated Systems for the Marine Environment. In particular, DIMEC has the responsibility of the mechanical and hydrodynamic design, while ISME is in charge of the tracking and control system.
Towed underwater systems with autonomous or semi-autonomous navigation capabilities are not common, either as commercial prod-ucts or research prototypes. One notable exception is the Triaxus system, [9], which however has been designed as a general-purpose payload carrier for oceanographic measurements in the water col-umn. The different application field has led to a very different sys-tem with respect to the one investigated in this work, with conse-quent differences in the dynamic and control issues addressed. The dynamic behaviour of towed underwater bodies has quite peculiar characteristics and it has been studied in detail for passive systems (see [10] and references therein) or with the goal of positioning the towed system with respect to the towing ship [4].
This chapter reports, in section 2.2, a general description of the system and its main features. In section 2.3 the non linear dynamic model of the vehicle has been developed following the standard treat-ment described - for instance - in [11], while the towing cable has been modelled by the spatial discretiziation of the cable into finite linear segments, using the lumped mass approach [3]. In section 2.4 the pipeline detection method based on the differential measurement of the geomagnetic field around an iron pipeline – or a conductor ca-ble – is reported together with the results of tests carried out to evaluate the performance of the pipeline sensing apparatus. On the
basis of both, the previous numerical models and the results of the tests, an automatic guidance system has been developed using, in the feedback loop, the measurements coming from the differential magnetometers. The automatic control system is described in sec-tion 2.5, while in secsec-tions 2.6 simulasec-tions in synthetic environment are reported and, in section 2.7 the results of experimental tests at the INSEAN towing tank are reported and analyzed.
2.2
The automatic system for pipeline
inspection
In its final design the towed vehicle has a modular architecture and presents a torpedo-shaped body with six fins (see figure 2.2). The vehicle consists of three main modules: the payload module at the centre, and two steering modules, one at bow and the others at stern. The bow steering module has three fins, which are independently ac-tuated by the three motors placed inside the module itself, while, the two horizontal fins of the stern module are jointly actuated. As a result, the towed system controls five degrees of freedom. The vehi-cle has an approximate length of 1.4 m, and an internal diameter of 0.25 m, it has a large space, in the central module, for custom pay-loads, plus a suite of internal sensors for navigation: inclinometer, compass, echosounder and depth sensors. Transversal to the system bow (dark in Figure 2.2) is a cylinder cap on which two magne-tometers are installed, to provide data on the pipeline position with respect to the surge axis of the vehicle. A similar cylinder is placed at the stern of system, to provide additional information on the pipe
line position. The differential magnetometers measurement of the magnetic field is proportional to the point wise asymmetry due to the misalignment between the pipeline and the sensor. Having two such systems at the bow and stern of the vehicle, assuming a flat seabed, with stable pitch and roll, it is possible to derive the error in vehicle orientation with respect to the pipeline and the error in the surge-sway plane between the vehicle centre of mass and the pipeline position. Maintaining to zero both errors allows the payload to be always positioned vertically above the pipelines. Of course, being it a towed system, the control objective can be met only if the towing ship has approximately the same route of the pipeline, above the pipeline. The underwater vehicle has no thrusters, the propulsion is accomplished through the towing cable. The DC power (+35V) is provided to the towfish through a suitable power line included in the cable. The cable also has two serial lines to transmit the data to and from the towed vehicle in order to allow the towing ship to main-tain the desired route. A serial communication RS485, at a speed of 38400 bit per second, is used to monitor the data measured by the navigation sensors, while a second serial line can be used to transmit the data measured by the payload. A user-friendly software interface is used, on board of the towing ship, to display the measured data in order to allow the ship master to correct the gross deviation from the desired route. The on board software application can also be used to set-up the parameters of the mission (e.g. the altitude set point) or manually drive the towed vehicle in case of malfunctioning or other needs.
The guidance system, based on PID controllers, has the goal of keeping the vehicle centred over the inspected pipeline, at a fixed
Figure 2.1: CAD drawing of the designed vehicle (courtesy of DIMEC), The dark cylinders, one in front and one at the rear of the vehicle, are the differential magnetometers employed for pipeline tracking.
Figure 2.2: The prototype of the underwater towed vehicle during the engineering tests at the INSEAN towing tank in Rome.
altitude, maintaining the vehicle surge axis parallel to the pipeline on the basis of the measurement provided by the two gradiometer.
Both the depth and the steering controllers have been synthe-sized separately considering the motion on the vertical plane and on the horizontal plane respectively, as usually made in AUV control systems [1], and tuned in order to allow the vehicle to translate, in line with the pipeline axis, by small pitch and yaw angles. The mag-netic sensors provide the feedback signal for the steering controller and allow tracking even if the pipeline is partially buried.
So the control system is intended to compensate for small devi-ations (up to some meters), from the equilibrium position.
The control system, whose architecture is reported in figure 2.3, consist of five components: the main unit is the on-board computer, based on the standard PC104 with a CPU at 400 MHz and Linux Embedded as operating system. The on-board PC communicates with the other components through the I/O board directly connected to the internal bus. The payload sensors unit provides an hardware interface for customizable payloads. The attitude and position unit includes the mission sensors which provide the state of the vehi-cle (angles of attitude and position with respect to the inspected pipeline) and some additional information such as the internal tem-perature and humidity of both the bow and the stern watertight steering modules. The actuator unit includes five motors (MOOG BN 23-13), used to move the fins, each motors has a power of 80W, an optical encoder, and is controlled through HARMonica drivers linked to the on-board PC through a CAN bus. The drivers directly control the position of the fins on the basis of the data coming from the optical encoders of the motors, and provides this information to
the main controller. This solution allows to reduce the number of inputs in the I/O board and the computational power of the CPU, since there is no need to manage low level controls such as the an-gular positions of the controlled surfaces. Further advantage is the reduced complexity of the system due to the low number of internal cables. The value of all the sensors is acquired at a sampling fre-quency of 2 Hz and transmitted through the towing cable using the RS485 serial port of the communication module. The communica-tion module also provides a wireless LAN conneccommunica-tion which can be used during the setting of the vehicle.
2.3
Dynamic system modelling
The dynamic model of the system has been developed by separately modelling the towed vehicle, the towing cable and the towing ship and then joining the three models. As for the cable, a lumped pa-rameters dynamic model has been developed following the approach proposed by [3], [12], [13]; the standard treatment for autonomous underwater vehicle ([11] and [1]) has been considered to model the towed vehicle; as far as the towing ship is concerned, a simple kine-matic model has been considered.
2.3.1
Cable model
The motion of the underwater cable is described by a nonlinear and nonstationary system of differential equations. The values of both the acceleration and the velocity along the cable are required in order to compute the total force action on the cable; moreover geometric
I/O Board
CPU
PC I/O
Devices
Compass Inclinometer Altimeter Depthmeter Magnetometer Temperature Humidity Actuators Motors Encoders Wireless Ethernet RS-485 Flash Disk INTERNAL BUS CAN BUS Remote Control Interfaceconstraints must be considered. A finite-difference method could solve the nonlinear system of equation, however, the computational effort would be large because the solution involves an iterative in-tegration in time and space. An approximate solution is obtain for the motion of the towing cable considering a finite elements model (FEM). The model of the towing described in [3] has been adopted and, for completeness, reported in the following.
The cable is divided into n equal length elements and the motion of each element is described by a simple equation on the basis of Newton’s Second Law. The motion of the cable is described with respect to a body reference system (Xb, Yb,Zb), placed on the surface
vessel, being Xb the ship surge direction; it is assumed that the ship
is moving at constant velocity vb, directed along Xb. Through this
assumption, the ship reference system is an inertial reference system, and the velocity vb becomes a parameter of the model. The cable is
divided into n equal length elastic elements, and the mass of each element is lumped at the nodes at both ends of the element. Internal and external forces are applied to every node except the top one, whose motion is prescribed by the towing ship. The motion of each node can be evaluated separately, on the basis of the lumped mass approximation; while the elastic internal force allows to satisfy the geometric compatibility equations by constraining this motion. Each cable element of the cable has a body frame p1, p2, and, q linked to it, where p1 is normal, p2 is bi-normal and q is tangent to the cable element.
Kinematic model
The orientation of each discretized cable element is represented using a Z-Y-X (ψi, θi, φi) Euler angle set [14]. The torsion of the cable
is not considered in the model, and, as a result, only two of the three Euler angles are required to specify the orientation of each cable element. The orthogonal rotation matrix, Ri
IB describes the
mapping from the local, body-fixed frame of the i-th cable element to the inertial frame. Applying the specified Euler angle set, the rotation matrix from the body fixed frame of the i-th cable element to the inertial frame becomes:
RiIB = ⎡ ⎢ ⎣
cos θi sin θisin φi sin θicos φi
0 cos φi − sin φi
− sin θi cos θisin φi cos θicos φi
⎤ ⎥
⎦ (2.1)
The Euler angles can be calculated at any instant provided that the endpoints of the cable element are known. Consider the i-th ele-ment of the cable, shown on the left in 2.4, that is bounded by nodes
i-1 and i. When expressed in terms of the body fixed frame, the only
non-zero component of the vector li (the length of the element) is in
the tangential direction. Therefore we obtain:
RIBi . ⎡ ⎢ ⎣ 0 0 li ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ rXib − riX−1 b ri Yb− r i−1 Yb ri Zb− r i−1 Zb ⎤ ⎥ ⎦ (2.2)
where li is the length of the i-th element, at any instant in time
li = ri Xb− r i−1 Xb 2 +ri Yb − r i−1 Yb 2 +ri Zb− r i−1 Zb 2 (2.3) and ri is the position vector, with components ri
Xb, r
i Yb, r
i Zb,
de-scribing the location of the i-th node in the inertial frame. Substitu-tion of 2.1 into 2.2 results in the following set of non-linear equaSubstitu-tions:
lisin θicos φi = rXib − r i−1 Xb (2.4) −lisin φi = rYib − r i−1 Yb (2.5) licos θicos φi = riZb − r i−1 Zb (2.6)
The solution of the kinematic problem is obtained by combining 2.4 and 2.6: θi = arctan rXi b− r i−1 Xb , r i Zb − r i−1 Zb (2.7) A numerically stable solution for the φiangle is obtained applying
the following rules:
if cos θi > sin θi φi = tan−1 −rYi b − r i−1 Yb , ri Zb− r i−1 Zb cos θi (2.8) if cos θi < sin θi φi = tan−1 −rYi b − r i−1 Yb , ri Xb− r i−1 Xb sin θi (2.9)
Internal forces
Internal forces are generated by the cables elastic behaviour. The methodology for calculating these forces in three dimensional ca-ble modelling applications has been presented by [15]. With this approach, the tension within the cable element, Ti, acts in the
tan-gential direction q of the element, and is modeled by a linear function of the strain within and the axial stiffness of the discrete cable ele-ments: Ti = Ki (2.10) i = li− lui lu i (2.11) where lu
i is the unstretched length of the i-th cable element, K
is the axial elastic constant of the cable element, and i is the strain
experienced within the i-th element. The friction between the braids of the cable, along with the polymer coatings that protect the con-ductors contained in the cable core, create a damping effect. This effect is assumed to be linear with the following relationship between tangential strain rate and damping force. The axial force in the i-th element generated by damping is:
Pi = Cv
viq− vqi−1 (2.12)
where viq is the component of the i-th node velocity in the tan-gential direction q, and Cv is an internal viscous damping coefficient for the i-th element.
External forces
The external forces acting on a cable element are those generated by the surrounding environment. These include hydrodynamic drag, weight, and buoyancy. The drag forces on the i-th cable element can be calculated according to:
Dpi1 =−1 2ρwCddcl i ufp vi 2 vpi1 (vp1)2+ (vp2)2 (2.13) Dpi2 =−1 2ρwCddcl i ufp vi 2 vpi2 (vp1)2+ (vp2)2 (2.14) Diq =−sgnvqi 1 2ρwCddcl i ufp vi 2 (2.15)
where Dpi1, Dip2, and Dqi are the components of the hydrodynamic drag when represented in the body-fixed frame; ρw is the density of
the water; dc is the cable diameter; Cdis the normal drag coefficient
of the cable; and vi is the velocity of the geometric center of the i-th cable element with respect to the surrounding fluid, with components
vpi1, vpi2, and viq. The drag coefficient is modified by loading functions
fp and fq, which are functions of, η, the relative angle between the
i-th cable element and the incident fluid flow. The loading functions
account for the non-linear breakup of drag between the normal and tangential directions as discussed in [16].
fp(η) = 0.5− 0.1 cos η + 0.1 sin η − 0.4 cos 2η − 0.11 sin 2η
fq(η) =
0.012.008− 0.3858η + 1.9159η2− 4.1615η3+ 3.5064η4− 1.1873η5 (2.16) The relative velocity of the flow over a particular cable element is found by using the equations of relative motion between points on the elements and the end nodes to interpolate the velocity of the geometric center of the element. Once the drag for i-th and and (i + 1)-st element are calculated, half of each value is applied to the
i-th node that joins the two elements.
The mass and buoyancy of the i-th cable element are given by,
Wi= ⎡ ⎢ ⎣ 0 0 gρcVci ⎤ ⎥ ⎦ (2.17) Bi = ⎡ ⎢ ⎣ 0 0 gρwVci ⎤ ⎥ ⎦ (2.18)
where ρc is density of the cable, g is the acceleration due to gravity,
and Vi
c is the volume of the i-th cable element. The effects of added
mass are accounted for in the cable element mass matrix.
Dynamic model
Applying Newton’s Second Law for the i-th node of the cable we obtain:
1 i q v -i q v 1 i -i v C K i l i W i B i D i T 1 i T -1 i -i 1 q 1 1 p 1 2 p 3 q 3 1 p 3 2 p 2 q 2 1 p 2 2 p b X b Y b Z 1 r 2 r 3 r qi fi
Figure 2.4: On the left: the finite elements model of the cable where the body-fixed reference frame of each element are highlighted in color and the inertial reference frame (fixed on the boat) are reported in black. On the right: the model of each cable element and both the internal (on the top) and external (on the bottom) forces acting on it.
¨ ri = Mi−1 (Ti+1+ Pi+1)− (Ti+ Pi) + 12(Di+ Di+1+ Wi+ Wi+1) −1 2(Bi+ Bi+1) (2.19) where Ti is the internal force generated by the cable’s elastic
behaviour of the i-th element, Pi is the internal damping in the
element i, Di is the drag force acting on the element i while Bi and
Wi are the buoyancy and the weight of the element respectively. Mi
is the inertial matrix and ri the position of the i-th node. All the
previous quantities are referred to the inertial reference frame. This method allows to easily join the models of the towing ship, the cable and the towed vehicle simply defining the motion at the ends of the cable by the dynamics of the two vehicles.
2.3.2
Vehicle model
The model of the towed vehicle is synthesized by modelling it as an autonomous vehicle, in [1] the three-dimensional equations of mo-tion for an hydrodynamic torpedo-shaped underwater vehicle have been described using a suitable body fixed coordinate frame, located at the centre of buoyancy of the vehicle itself. The motion of the body-fixed frame of reference is described relative to an inertial refer-ence frame. The body fixed frame has six velocity components, v =
u v w p q r
, while the six components of position, in the global reference frame, are η =
η1 η2 = x y z φ θ ψ . Control inputs are related to the orientation of the control surfaces, no thrusters are present, being the propulsion accomplished through the towing cable, so the inputs vector is u =
δr δs δb δbs δbp
in which the first two components correspond to the rudder and stern plane deflection, and the last three correspond to the rudder, port and starboard bow plane.
Figure 2.5: On the left: the three systems of reference and the model of the finite elements model of the cable. On the right: towfish-fixed and Inertial coordinate systems.
The generalized torque acting on the vehicle, in the body fixed reference frame is τ = τv + τc, where τc is the towing force provided
through the cable, while τv =
X Y Z K M N
includes coriolis, gravitational and centrifugal terms, hydrostatic and hydro-dynamics forces and moment.
The motion of the towed vehicle is described by a system of non-linear equations as a function of the vehicle generalized coordinates
η:
Mv(η)¨η + Bv(η, ˙η) + Dv(η, ˙η) + Gv(η) = τv + τc (2.20)
hy-drodynamic added masses. Starting from the previous equation and following the method proposed by [1], two simplified linear models are derived, in order to synthesize the control system, as described in section 2.5.
2.4
Pipelines and cables detection method
A critical point in the system, in order to properly track the pipeline, is the method employed to detect and follow the pipeline itself. In subsection 2.4.1 a detection method, based on the measuring of the geomagnetic gradient around an iron pipeline is reported. In subsec-tion 2.4.3 the theoretical results are compared to the magnetic field measured over a buried sewage pipeline and the performance of the pipeline sensing system is investigated considering the interference of the towfish motors.
2.4.1
Pipeline detection
Let us consider the presence of a magnetic induction field B in a region of empty space. If a permeable magnetic body is placed in the region, the intensity of the magnetic induction is modified and the field lines tend to become normal to the surface of the body. Let us consider an infinitely long cylindrical pipeline with internal radius
a and external radius b and magnetic permeability µ.
Let us consider the problem of finding the fields H end B in a region of space where a constant magnetic induction field is applied to an infinitely long cylinder with internal radius a and external radius b and magnetic permeability µ. Let us suppose the external
field directed along the y axis: normal to the cylinder axis (see fig 2.6).
Figure 2.6: Magnetostatic problem: Constant magnetic field applied to an infinitely long cylinder.
In static condition, and in absence of currents, the magnetic field
H is derivable from a scalar potential−→H =−∇Φ (r, θ) and, from the
equation of the divergence, the potential Φ has to satisfy the Laplace equation ∇2Φ = 0 everywhere: outside and inside the pipeline and at the pipeline itself.
Considering the Laplace’s equation in cylindrical coordinates, with no x-dependence: ∂2 ∂r2Φ (r, θ) + 1 r ∂ ∂rΦ (r, θ) + 1 r2 ∂2 ∂θ2Φ (r, θ) = 0 (2.21)
by applying the separation of variables method the solution is written as a product of functions:
where Θ (θ) is a function of the θ only and satisfies the following ordinary differential equation (ODE):
Θ(θ) + λΘ (θ) = 0 (2.23)
whose eigefunctions are Θ (θ) = A sin θ√λ + B cos θ√λ , where, considering θ as periodic of period 2π, we obtain λ = n2 and
n ∈. While in eq. 10 R (r) is a function of the r only and satisfies
the following ODE:
r2R (r)+ rR (r) − n2R (r) = 0 (2.24) whose solutions are
R (r) = C + D ln (r) n = 0 R (r) = Enrn+ Fnr−n n = 0
(2.25) Therefore, the general solution for the magnetic potential Φ is:
Φ (r, θ) = D ln (r) + ∞ n=1 Enrn+ Fnr−n (Ansin (nθ) + Bncos (nθ)) (2.26) Since that solution must be finite as r → 0, and outside the pipeline the solution must give the applied field as r → ∞, and considering the external field directed along y and the symmetry of the problem, we obtain the follow expression for the magnetic potential in the different region: inside the pipeline, outside the pipeline and at the pipeline itself.
Φint(r, θ) = ∞
n=1
Φext(r, θ) = − B0 µ0 cos θ + ∞ n=1 r−nDncos (nθ) (2.28) Φpipe(r, θ) = ∞ n=1 r−n+ βnrn Fncos (nθ) (2.29) . Where Bn = BnEn, Dn = BnFn, Fn = BnFn, βn = En/Fn
and B0 is the value of the external field. At each boundary the normal component of the magnetic induction B, and the tangential component of the magnetic field H are continuous. Applying the boundary condition, from the equations 14 we obtain:
• Boundary condition at the interface r = b:
−B0cos θ− µ0 ∞ n=1 nb−n−1Dncos (nθ) = = µ ∞ n=1 −nb−n−1+ nβ nbn−1 Fncos (nθ) B0 µ0b sin θ− ∞ n=1 nb−nDnsin (nθ) =− ∞ n=1 nb−n+ βnbn Fnsin (nθ)
• Boundary condition at the interface r = a:
µ0 ∞ n=1 nan−1Bncos (nθ) = µ ∞ n=1 −na−n−1+ nβ nan−1 Fncos (nθ) −∞ n=1 nanBnsin (nθ) =− ∞ n=1 na−n+ βnan Fnsin (nθ) .
The external field imposes that n = 1, so posing n = 1 we obtain a four equations linear system which provides the values of the four unknowns Bn, Dn, Fn, βn: B1 = 4µB0b2 a2(µ−µ0)2−b2(µ+µ0)2 β1 = a −2 µ+µ0 µ−µ0 D1 = (a2− b2)B0 µ0 b2(µ2−µ20) a2(µ−µ0)2−b2(µ+µ0)2 F1 = 2B0a2b2(µ−µ0) a2(µ−µ0)2−b2(µ+µ0)2 (2.30) and so the expression of the scalar potential Φ in all the regions:
Φint(r, θ) = 4µB0b2 a2(µ− µ0)2− b2(µ + µ0)2r cos θ (2.31) Φext(r, θ) = B0 µ0 (a2− b2) r b2(µ2− µ20) a2(µ− µ0)2− b2(µ + µ0)2 − r cos θ (2.32) Φpipe(r, θ) = = B0 (µ− µ0) r + (µ + µ0) r a2 2a2b2 a2(µ− µ0)2− b2(µ + µ0)2 cos θ (2.33) Appling the relation−→H =−∇Φ (r, θ) we obtain the components
of the magnetic field H in cylindrical coordinates.
We are interested in the expression of the magnetic field H, out-side the pipeline. By solving the Laplace equation, in cylindrical coordinate, we obtain the expression of the potential Φ
Φext(r, θ) = B0 µ0 K r − r cos θ K = b 2(µ2− µ2 0) (a2 − b2) a2(µ− µ0)2− b2(µ + µ0)2 (2.34)
where K is a function of the pipeline’s geometrical properties and of the material of which the pipeline is made, µ0 is the magnetic permeability of the vacuum.
2.4.2
Cable detection
The pipeline detection method described in the section above can be usefully employed for tracking and inspections of underwater electric cables. Let us consider the well known equation of Biot-Savart in Cartesian reference frame:
B(P ) = µ0i
2π
x ˆy− y ˆx
x2+ y2 (2.35)
where the conductor cable is placed at the origin, directed along
z axis, i is the current and notation (ˆ. refers to unit versor.
Let us consider the gradient of the magnetic induction field B:
∇B = −µ0i
2π ·√(x2x+y2)3 , −
µ0i
2π · √(x2y+y2)3
Considering the vertical coordinate y as a constant (the towed vehicle works at constant depth or altitude), the magnetic induction field reaches its maximum over the cable (x = 0), as in the case of the pipeline. Measuring the horizontal gradient of the magnetic field, it is possible to know the position of the towed vehicle with respect to the cable, so the differential measurement of the magnetic
induction field is used in the automatic steering controller as in the case of the pipeline inspection.
2.4.3
Analysis of the gradiometer performance
Outdoor test: detection of a buried sewage pipeline
To confirm the theoretical results and verify the functioning of the sensors, a field test has been performed on land over a known buried sewage pipeline of dimensions similar to those expected by pipelines at sea, but with thinner walls. In particular, the land test pipeline has a diameter of 0.8 m and a thickness of 0.003 m, buried at a depth of 0.7 m in clayey soil. The pipeline material has a relative magnetic permeability estimated above 4000. The intensity of the magnetic field has been measured sampling the magnetic field on a vertical section normal to the pipeline axis, with extension of 6 m in the horizontal direction and 1.6 m in the vertical direction re-spectively. The horizontal sampling distance has been of 0.2 m, and 0.4 m the vertical one. In figure 2.7 the resulting magnetic field intensity (reconstructed from the samples with multiquadrics inter-polation) is shown (on the top) and compared to the theoretical one (on the bottom) obtained from the eq. 2.34 by using the parameters of the testing pipeline. It is worthwhile to note that, from the avail-able data, it can be seen that the local maximum intensity of the magnetic induction field is not in correspondence of the vertical over the pipeline, but it depends on the mutual orientation of the local geomagnetic field with respect to the pipeline. This is accounted for using the International Geomagnetic Reference Field [17] together with the eq. 2.34: in particular, the vertical component of the
ge-omagnetic field can have an inclination between 45° and 60° with respect to the Earth surface, in the Mediterranean sea, so that, the maximum deviation from the normal to the pipeline axis is about 30° - 45°. This kind of behaviour has been taken in to account to synthesize the system of guidance.
Indoor test: electromagnetic interference evaluation
A second indoor test has been performed in order to assess the in-fluence of the motors on the differential magnetometers. The dif-ferential system has been placed at an horizontal distance varying from 0.2 to 1.4 m from a brushless motor of nominal power of 12 W (12 V, 1 A). The two magnetometers are symmetrically placed with respect to the motor, as in the vehicle design.
The power to the motor has been varied during the test, in order to simulate transients behaviour. Irrespectively from the distance, the perturbation of the motor to the single magnetic field measure-ment can be quantized in an offset of approximately 1300 nT. As far as the differential measurement is concerned, however, the measured gradient average is not affected – what is affected is the standard deviation of the measurement. In particular, in the case of 0.2 m dis-tance (the worst case, and also the effective case for the stern unit), the gradient standard deviation with the motor off is 20 nT/m, while with motor on is 130 nT/m - one order of magnitude more.
Such a high standard deviation in the measurements cannot be tolerated, since it would completely mask the measurement in op-erational conditions. For this reason, filtering of the measurement signal has been investigated, and it turns out that a simple
mov-Figure 2.7: On the top: theoretical magnetic field induction con-sidering the parameters of the testing pipeline and external vertical field of 44µT. On the bottom: experimentally measured magnetic field intensity over a sewage pipeline (bottom of the figure). The drawing is in scale with the pipeline photograph.
ing average algorithm can greatly reduce the measurement standard deviation and improve the signal to noise ratio (SNR). In the imple-mentation of the moving average filter, the magnetometers have been sampled at 15 Hz sampling frequency, and a window of 10 samples has been considered for the average.
The standard deviation measured with motor on after application of the moving average filter is 34 nT/m, with a SNR improvement estimated in 23 dB. Longer windows can further increase the SNR and reduce the measurement standard deviation. It has to be taken into account, however, that the moving average filter on the output measurement implies a low pass filter in the overall control loop: this means that it slows down the transient response of the controlled system, the more so the longer the averaging window. A compromise between SNR in the measurement and requirements on the transient behaviour of the controlled system will be determined at the stage of synthesizing and implementing the control law.
Sensor performance
The most critical factors, in order to correctly detect a pipeline or a cable, are both the sensitivity of the magnetic sensors and the electromagnetic disturbances due to the electronics and electrical components of the towed vehicle. The gradient of the magnetic field around a cable or a pipeline decreases as a function of the distance, so it is fundamental the definition of the maximum working altitude for the vehicle. The sensitivity region of the sensor has been computed considering an horizontal detection threshold of 67nT/m, ten times less than the actual sensitivity of the sensor in order to take in to
0 100 200 300 400 500 600 700 800 900 49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 Time [s] Magnetic Field [ µT] DC Motor Interference 50cm 70cm 90cm 110cm 130cm 150cm NoMotor
account the noise due to the motors. In Figure 2.9 the sensitivity regions of the sensor are reported in both cases: considering the pipeline or the conductor cable.
The sensor sensitivity region around the cable is different with respect to the one related to the pipeline, but, near the cable and the pipeline, the two regions have the same shape. Moreover, as it is shown on the bottom in figure 2.9, in the case of the cable, the sensitivity region depends on the current intensity. In order to simulate the presence of a pipeline like those used in the outdoor tests of the gradiometers, a current of 10A is required.
As outlined in the figure, the useful region can be approximated by rectangle with an height of 8m and a width of 10m, centred over the pipeline.
2.5
Control System
The control system is based on two PID controllers, one for the ver-tical plain is meant to maintain the vehicle at a specified depth (or altitude with respect to the sea-bottom) and the other to track the pipeline on the basis of the measurements coming from the differen-tial magnetometers.
The vehicle altitude and pitch are controlled trough the horizon-tal surfaces placed at stern and bow. Even though the two bow surfaces are independent, they are jointly controlled, and the con-trol action is opposite to the one applied at the stern surface. A simple inner-and-outer (pitch-and-depth) loop PID depth controller is tuned on the basis of a decoupled linearized model, obtained from
Figure 2.9: On the top: magnetic field around a conductor cable, and sensor sensitivity region as a function of the current. On the bottom: magnetic field around an iron pipeline and sensor sensitivity region. The outer white bold line is related to a current of 10A, the inner line is related to a current of 5A.
equation 2.20, considering the steady state condition (nominal surge velocity of 2 knots and values of the attitude angles equal to zero). As shown in figure 2.10, the pitch angle, in the inner loop, is con-trolled through a PID, while in the outer loop, the depth controller has the proportional term only.
Pitch ÷÷ø ö ççè æ + + -s s P i d t t q 1 1 ÷÷ø ö ççè æ + + -s s P i d t t y 1 1 + + m P Z P r b d d s d bp bs d d q e y e d q d y q y + ez B D Filter Depth Z DepthRef Heading Pipeline position Gradient dr ds dbs dbp db ds
Figure 2.10: Control system: in red the depth-and-pitch control system; in yellow the heading-and-position control system.
The control law for the inner loop can be expressed as:
δs(s) eθ(s) =−Pθ 1 + τds + 1 τis (2.36) where eθ = θd−θ is the difference between the desired pitch angle
and the actual pitch of the vehicle, Pθis the proportional gain and
τd, τi the derivative and the integral time constants respectively.
The control law for the outer loop can be expressed as:
θ (s) ez(s)
Parameter Value Pθ 2.3
τd 0.3
τi 1.75
Pz 2
Table 2.1: Parameters of the pitch-depth controller
where ez = zd−z is the difference between the desired depth and
the actual depth of the towfish, and Pz is the proportional gain.
A second order response has been assumed for the system and the controller parameters tuned in order to have a settling time of 10s and maximum overshoot of 5%. The values of the parameters are reported in table 2.1
As for the steering controller, an analogue procedure has been followed. The vehicle yaw and horizontal position with respect to the pipeline are controlled through the joined action of the two vertical rudders, placed underneath the vehicle at bow and stern. A PD controller is used in the inner loop to control the yaw angle, while, in the outer loop, a term proportional to the gradient of the magnet induction field provides the yaw reference to the inner loop.
The control law for the steering control can be expressed as:
δr(s)
eψ(s)
=−Pψ(1 + Tds) (2.38)
where eψ = ψd−ψ is the difference between the desired yaw angle
and the actual yaw angle of the towfish, Pψ is the proportional gain
and Td the derivative time constant.
Parameter Value Pψ 20
Td 0.5
Pm 12000
Table 2.2: Parameters of the steering controller
ψ = Pm(∆B− Γ) (2.39)
where Pm is the proportional gain, Γ is a correction term which
takes in to account the relative orientation between the pipeline axis and the vertical direction of the geomagnetic field, as discussed in subsection 2.4.2, while
∆B =|Blef t| − |Bright| (2.40)
is the difference between the magnitude of the magnetic induction field measured by the left magnetometer and the right one respec-tively.
The steering controller has been tuned in order to have a settling time of 10s and a damping factor of 0.95; the values of the parameters are reported in 2.4.
Note that the minus sign applied to the proportional gain of the pitch and yaw control laws is due to the difference in sign conven-tions between the stern plane angle and vehicle pitch angle, and between the rudder angle and vehicle yaw angle. A positive stern angle will force the vehicle to pitch down, generating a negative mo-ment around the y-axis.
The wide range of manoeuvre around the steady state position allows to compute the length of the cable deployed as a function of both the speed of the towing ship and the pipeline depth, without considering it as a control variable.
2.6
Synthetic environment simulation
A synthetic environment simulation tool has been used to visual-ize the motion of the towed vehicle during the automatic docking manoeuvre (figure 2.11).
The synthetic environment allows to better analyze how the con-trol system moves the concon-trolled surfaces as a function of both the position and the attitude of the towed vehicle. In the simulation an underwater pipeline, placed at 148m depth, having the same properties of the one described in section 2.4, has been considered. The towing ship, perfectly aligned to the pipeline axis, has a con-stant surge velocity of 1.8 m/s. The towfish, initially aligned to the pipeline, starts from the steady state condition (142 m depth): pre-viously reached with a 300 meters long towing cable ( the simulation parameters of the towing cable are reported in table 2.3). During the first part of the simulation the vehicle is manually driven by the operator in order to acquire a raw measurement of the magnetic field around the pipeline, while the depth controller has to keep the vehicle at constant depth. The path followed by the vehicle is shown on the top in figure 2.12: while, on the bottom, the noisy measure-ments of the gradient, acquired during the mission, are reported in violet, and the filtered values in black. A noise having a standard
Figure 2.11: Synthetic environment simulation: a synthetic environ-ment has been design in order to preliminary evaluate the motion of the vehicle during the automatic docking manoeuvre.
Parameter Value
Number of elements 6
Element length 50 m
Cable elastic constant 107N m
Internal viscous damping coefficient 3000 N s/m
Water density 1028 kg/m3
Cable density 3100 kg/m3
Cable diameter 0.0332 m
Drag coefficient 2.054
Table 2.3: Parameters of the towing cable considered in the synthetic environment simulations.
deviation of 130nT/m has been considered. The gradient sign indi-cates whether the towfish is on the left side (negative gradient) or the right side (positive gradient) with respect to the pipeline. Once a preliminary measure of the magnetic field is available, the vehi-cle is brought into the applicability region of the sensor (2.4.3 and figure 2.9) and the steering control system is activated (at the time
t = 60) allowing the towfish to autonomously follow the pipeline.
During the automatic approaching manoeuvre the vehicle has been requested to reach a new depth reference of 145 m. The orientation of the control surfaces is shown in figure 2.13. As reported in figures 2.13 and 2.12, during the docking manoeuvre, the vehicle attitude angles are, in general, less than 10° and the towfish correctly reaches the pipeline moving in line with its axis.
Figure 2.12: Pipeline docking manoeuvre simulation: On the
top: position of the towfish with respect to the pipeline axis
dur-ing the dockdur-ing manoeuvre, in the first part of the simulation (light yellow) the vehicle is manually driven while the depth controller maintains constant depth. On the bottom: measurements of the gra-dient of the magnetic field close to the pipeline (raw measurements in violet, filtered data in black)
Figure 2.13: Pipeline docking manoeuvre simulation: On the
top: attitude angles of the towfish. The attitude angles are in general
less than 10°. On the bottom: deflection angles of the control surfaces (δr and δs).
2.7
Towing tank test field
The prototype of the towed vehicle has been tested at the towing tank of the INSEAN (Istituto Nazionale di Studi ed Esperienze per l’Architettura Navale) in Rome (see figure 2.18). Controlled con-ditions have been preferred to at sea tests to allow verifications of the vehicle performance and the experiments results. The tests have been performed in a towing tank with a length of 250m, a width of 9m and a depth of 3,5m, and it is served by a carriage that can reach a speed of 10m/s. In order to test the automatic guidance system, based on the differential measurement of the magnetic field, the effect of an underwater pipeline on the magnetic field has been reproduced by a conductor cable placed on the bottom of the tow-ing tank ustow-ing a current of 10A. The gradient of the magnetic field around the cable has the same shape of the one related to an iron pipeline, as described in section 2.4.2. During the tests, the pro-totype has been towed with a 6m cable at a speed of 2 knots and an altitude of 2m: with this set-up the horizontal manoeuvrability range is larger than 4m, while the vertical range is about 2m, to avoid impacts against the bottom of the towing tank. All the tests have been performed at the nominal speed of 2 knots, and the results are reported and analyzed, in particular with respect to the vehicle control and pipeline tracking capabilities.
Parameter Value Pθ 1.0 τd 0.1 τi 8.0 Pz 1.0 Pψ 2 Td 0.1 Pm 10000
Table 2.4: arameters of the control system tuned on the basis of the tests in the towing tank
2.7.1
Test of the attitude and depth control
sys-tem
Preliminary tests, aimed to evaluate the performances of both the depth and attitude control systems (in particular, as far as the pitch angle is concerned), have been performed before using the automatic guidance system based on the magnetic sensors, for the tracking of the conductor cable.
The prototype has been requested to maintain the depth of 2m and the North direction (having the towing tank a North-South ori-entation). The values of both the attitude angles and the depth are reported in figure 2.14.
During the test the depth control system correctly maintains the vehicle at constant depth, while the attitude angles are lower than 10 degrees. It is important to remark that there is no roll controller but pitch and heading only, the vehicle has been designed in order
to have intrinsic roll stability.
A second test to evaluate the performance of the depth controller has been performed by asking the prototype to change its depth of about 70cm: from 1.7m to 2.4m, compatibly with the length of the cable. The maneuver has been completed in about 15s, during this period the pitch angle reaches quite high peak values, but the control system is able to stabilize the pitch motion in about 20s. Depth and pitch of the prototype are shown in figure 2.15.
2.7.2
Test of the automatic guidance system:
cable docking
Once the preliminary tests have been completed and the parameters of the control system set up, the automatic guidance system for pipeline/cable tracking has been tested. A conductor cable has been placed on the bottom of the towing tank, using a DC current of 10A. The automatic guidance system is meant to maintain the towed vehicle centered over the cable, where the gradient of the magnetic field tends to zero. The conductor cable has been correctly tracked by the vehicle: the control system leads the prototype over the cable, in a region where the gradient of the magnetic field is close to zero or, however, lower than the sensitivity of the sensors. During the automatic docking maneuver the values of the attitude angles are bounded, though a negligible pitch oscillation has been measured during the turning maneuvers; this oscillation has no influence on the depth control.
The raw measurements of the magnetic field are shown in figure 2.16: during the first part of the experiment (in light green), the
0 50 100 150 200 250 −20
−10 0 10
20 Towfish Attitude and Depth
Roll [°] 0 50 100 150 200 250 −20 −10 0 10 20 Pitch [°] 0 50 100 150 200 250 −20 −10 0 10 20 Heading [°] 0 50 100 150 200 250 0 1 2 3 Depth [m] Time [s]
Figure 2.14: Attitude angles and depth position of the towed vehicle during the first test. The vehicle has been requested to maintain constant attitude and depth. (It is important to remember that the roll motion is not controlled).
0 20 40 60 80 100 120 1.6 1.8 2 2.2 2.4 2.6 Depth [m] 0 20 40 60 80 100 120 −30 −20 −10 0 10 20 30 Pitch [°] Time [s]
Figure 2.15: Depth and pitch of the vehicle during the test of depth changing.
Figure 2.16: Raw measurement of the gradient of the magnetic field around the conductor cable during the automatic docking maneuver. In the first part of the experiment, highlighted in light green, the vehicle was manually driven in order to obtain a preliminary map of the magnetic field. In the second part, at the time t = 50, the automatic steering system has been activated and the cable correctly docked.
prototype is manually driven by the operator, while in the second part (at the time t=50) the automatic steering system is activated. In figures 2.16 and 2.17 it is possible to note how the value of both the gradient and the heading tend to zero simultaneously. This means that the prototype correctly reaches the equilibrium point. Some oscillations around the conductor cable are present: this kind of behavior is related to both the presence of a moving average filter in the control loop, used to reduce the disturbances of the motors on the magnetic sensors, and the dead-zone of the magnetic sensors, highlighted in grey in figure 2.16.
2.8
Conclusions
An automatic system for underwater pipeline (or cable) inspection has been presented. In particular the underwater towed vehicle and its main features have been described, focusing on the mechanical and hydrodynamical design and the implementation of the control system. The pipeline sensing system, based on small and low cost magnetometers, has been analyzed, simulative results have been val-idated through indoor tests (to evaluate the electromagnetic distur-bances induced by a brushless motor) and outdoor tests (to evaluate the detection capabilities of the system).
Experiments have been carried out at the INSEAN towing tank, with the objective of evaluating the performance of the system. The results of the tests have been reported and analyzed, in particular with respect to the vehicle control and pipeline tracking capabilities: the simulative expectations have been confirmed, in fact the vehicle
Figure 2.17: Attitude angles and depth of the towed vehicle during the docking maneuver. The prototype correctly maintains the depth of 2m and reaches the equilibrium point (gradient and heading tends to zero simultaneously).
showed a good tracking behaviour in operative conditions up to a towing speed of 2 knots.
From the analysis of the performance of the magnetic sensors and the maneuverability of the towed vehicle, it has been observed that the sensitivity of the pipeline detection sensors is the current limit of the system. Even though the detection altitude depends on the physical properties of the pipeline (or the current in the cable), in most practical cases, it must be lower than 8m.
The prototype has been tested for more than 16 hours without any malfunctioning or failures.
2.9
Acknowledgement
I wish to express my grateful thanks to all the members of the PipeTracking-research group. The personnel and staff of INSEAN, for their supportive and cooperative help during the tank tests. DIMEC, University of Genova, developed the mechanical and actu-ation part of the prototype. The work has been partially supported by Parco Scientifico e Tecnologico della Liguria.
Figure 2.18: On the left: towing tank of the INSEAN institute: test field of the underwater pipeline tracking vehicle. On the right: The crane used to tow the underwater vehicle.
