US 2026/0243558 A1 · DISPLACEMENT INVERSION METHOD FOR DEEPWATER RISER STRUCTURE

Abstract

Disclosed is a displacement inversion method for a deepwater riser structure, including the steps of: performing real-time collection and measurement of sparse discrete curvature data; acquiring continuous curvature data using an interpolation method; generating a continuous curve, and performing real-time partition on this curve to obtain lengths of infinitesimal segments; acquiring relative position information between a riser mid-section and a surface platform, deriving a lower segment's continuous curve equation through recursive progression from a bottom end toward the mid-section, while deriving an upper segment's continuous curve equation through recursive progression from the surface toward the mid-section, integrating the upper and lower segments to obtain a full-length continuous curve equation, and calculating y at any position x. The displacement inversion is achieved by relying on real-time monitored curvature data, demonstrating strong adaptability. Furthermore, an end-error elimination strategy may solve the problem of cumulative error amplification at ends during the recursive progression.

A displacement inversion method for a deepwater riser structure, comprising the steps of

S1, performing real-time collection and measurement of sparse discrete curvature data based on n curvature sensors mounted at a plurality of monitoring points along a deepwater riser structure;
S2, acquiring m pieces of continuous curvature data using an interpolation method;
S3, generating a continuous curve based on the m pieces of continuous curvature data and positional information, and performing real-time partition on the continuous curve to obtain lengths s of m+1 infinitesimal segments;
and
S4, acquiring relative position information between a riser mid-section and a surface platform, deriving a lower segment's continuous curve equation through recursive progression from a bottom end toward the mid-section, while deriving an upper segment's continuous curve equation through recursive progression from the surface toward the mid-section, integrating the upper and lower segments to obtain a full-length continuous curve equation, and calculating y at any position x, with y representing inverted displacement data corresponding to an outer side position of the deepwater riser structure;
and comprising a specific process as follows:
S41, acquiring the relative position information between the riser mid-section and the surface platform, wherein:
based on bottom position beacon information (xbot, ybot) of the deepwater riser, mid-section position beacon information (xmid, ymid) of the riser, and surface offshore platform position global position system (GPS)-derived information (xsur,ysur), a riser mid-section relative position
(
x
mid
*
,
y
mid
*
)
and a surface platform relative position
(
x
sur
*
,
y
sur
*
)
are calculated with a coordinate origin (0,0) at the bottom position of the deepwater riser, where these relative positions satisfy the following relationships:
x
mid
*
=
x
mid
-
x
bot
,
y
mid
*
=
y
mid
-
y
bot
,
x
sur
*
=
x
sur
-
x
bot
,
and
y
sur
*
=
y
sur
-
y
bot
;
S42, deriving the lower segment's continuous curve equation through the recursive progression from the bottom end toward the mid-section, wherein:
a coordinate system is established with the coordinate origin at a riser bottom-end position, with a tangent direction at a starting point defined as an x-axis, and a vertical line at the starting point defined as a y-axis;
and an infinitesimal arc length between two points on the continuous curve is denoted as s, Pi represents an ith interpolation point, Oi and ρi represent a center of an ith infinitesimal arc segment and curvature data (or a curvature radius), and θi represents an included angle between PiOi and a horizontal line;
coordinates of a center O1(O1x,O1y) of a first infinitesimal segment is (0,ρ1), with a continuous curve equation at an arc segment OP1 in a rectangular coordinate system given by:
{
x
=
O
1
⁢
x
+
ρ
1
⁢
cos
⁢
θ
y
=
O
1
⁢
y
+
ρ
1
⁢
sin
⁢
θ
from this, coordinates (P1x, P1y) of a first interpolation point P1 is calculated as:
{
P
1
⁢
x
=
O
1
⁢
x
+
ρ
1
⁢
cos
⁢
θ
1
P
1
⁢
y
=
O
1
⁢
y
+
ρ
1
⁢
sin
⁢
θ
1
due to tangency continuity between adjacent infinitesimal arcs, coordinates (O2x, O2y) of a center O2 of a second infinitesimal arc P1P2, the center O1 of the OP1, and the point of tangency P1 are on a same straight line, further obtaining the following equations:
{
P
1
⁢
x
=
O
2
⁢
x
+
ρ
2
⁢
cos
⁢
θ
1
P
1
⁢
y
=
O
2
⁢
y
+
ρ
2
⁢
sin
⁢
θ
1
the above two equations are combined to obtain the coordinates (O2x, O2y) of the center O2 of the second infinitesimal arc, denoted as:
{
O
2
⁢
x
=
O
1
⁢
x
+
(
ρ
1
-
ρ
2
)
⁢
cos
⁢
θ
1
O
2
⁢
y
=
O
1
⁢
y
+
(
ρ
1
-
ρ
2
)
⁢
sin
⁢
θ
1
a continuous curve equation of the second infinitesimal arc P1P2 is further obtained, denoted as:
{
x
=
O
2
⁢
x
+
ρ
2
⁢
cos
⁢
θ
=
O
1
⁢
x
+
(
ρ
1
-
ρ
2
)
⁢
cos
⁢
θ
1
+
ρ
2
⁢
cos
⁢
θ
y
=
O
2
⁢
y
+
ρ
2
⁢
sin
⁢
θ
=
O
1
⁢
y
+
(
ρ
1
-
ρ
2
)
⁢
sin
⁢
θ
1
+
ρ
2
⁢
sin
⁢
θ
building upon the above procedure, coordinates (O(i−1)x,O(i−1)y) of a center Oi−1 of an i−1th infinitesimal arc, curvature data ρi−1, an included angle θi−1, and ith interpolated curvature data ρi are obtained, with a continuous curve equation for an ith infinitesimal arc ρi−1ρi given by:
{
x
=
O
(
i
-
1
)
⁢
x
+
(
ρ
i
-
1
-
ρ
i
)
⁢
cos
⁢
θ
i
-
1
+
ρ
i
⁢
cos
⁢
θ
y
=
O
(
i
-
1
)
⁢
y
+
(
ρ
i
-
1
-
ρ
i
)
⁢
sin
⁢
θ
i
-
1
+
ρ
i
⁢
sin
⁢
θ
where θi=θi−1+s/ρi;
and
recursion proceeds sequentially until iteration i=n+1, and mid-section position point coordinates
(
x
bot
-
mid
*
,
y
bot
-
mid
*
)
of the continuous curve are derived;
S43, deriving the continuous curve equation for the ith infinitesimal arc Pi−1Pi through a top-down recursive process based on the computational process of S42, with the surface platform position as a starting point:
{
x
=
x
sur
*
+
O
(
i
-
1
)
⁢
x
+
(
ρ
i
-
1
-
ρ
i
)
⁢
cos
⁢
θ
i
-
1
+
ρ
i
⁢
cos
⁢
θ
y
=
y
sur
*
+
O
(
i
-
1
)
⁢
y
+
(
ρ
i
-
1
-
ρ
i
)
⁢
sin
⁢
θ
i
-
1
+
ρ
i
⁢
sin
⁢
θ
proceeding sequentially until reaching i=n+1, and acquiring mid-section position point coordinates
(
x
sur
-
mid
*
,
y
sur
-
mid
*
)
of the continuous curve through the top-down recursive process;
and
S44, integrating the upper and lower segments to obtain the full-length continuous curve equation, wherein:
based on the upper segment's continuous curve equation and the lower segment's continuous curve equation, the full-length continuous curve equation is obtained;
and y is calculated at any position x, where y represents the inverted displacement data corresponding to the outer surface position of the deepwater riser structure.

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Displacement inversion method for deepwater riser structure

Life of this patent

Displacement inversion method for deepwater riser structure

Life of this patent

Abstract

Claims5