U.S. patent application number 14/265257 was filed with the patent office on 2015-10-29 for system and method for monitoring drilling systems.
This patent application is currently assigned to Sinopec Tech Houston, LLC.. The applicant listed for this patent is China Petroleum & Chemical Corporation, Sinopec Tech Houston, LLC.. Invention is credited to Weiping XU, Sheng ZHAN, Jinhai ZHAO, Herong ZHENG.
Application Number | 20150308191 14/265257 |
Document ID | / |
Family ID | 54334271 |
Filed Date | 2015-10-29 |
United States Patent
Application |
20150308191 |
Kind Code |
A1 |
ZHAN; Sheng ; et
al. |
October 29, 2015 |
SYSTEM AND METHOD FOR MONITORING DRILLING SYSTEMS
Abstract
The present disclosure provides methods and systems for
monitoring a drilling system, including methods and systems for
estimating the life consumption of downhole drilling tools. The
system employs a plurality of sensors that provide sensor signals
related to the status of components in the drilling system. The
sensor signals are analyzed using Functional Principal Component
Analysis (FPCA) to give estimations for one or more performance
metrics, including the life consumption of downhole drilling
tools.
Inventors: |
ZHAN; Sheng; (Houston,
TX) ; ZHAO; Jinhai; (Houston, TX) ; ZHENG;
Herong; (Houston, TX) ; XU; Weiping; (Houston,
TX) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
China Petroleum & Chemical Corporation
Sinopec Tech Houston, LLC. |
Beijing
Houston |
TX |
CN
US |
|
|
Assignee: |
Sinopec Tech Houston, LLC.
Houston
TX
China Petroleum & Chemical Corporation
Beijing
|
Family ID: |
54334271 |
Appl. No.: |
14/265257 |
Filed: |
April 29, 2014 |
Current U.S.
Class: |
703/2 |
Current CPC
Class: |
G06F 17/18 20130101;
G06F 2119/04 20200101; E21B 44/00 20130101; E21B 12/02
20130101 |
International
Class: |
E21B 7/00 20060101
E21B007/00 |
Claims
1. A method for monitoring a drilling system, comprising:
collecting a first set of sensor signals; constructing a model
using Functional Principal Component Analysis (FPGA) based on the
first set of sensor signals, wherein the model is used to estimate
one or more performance metrics of a component in the downhole
drilling tool; collecting a second set of sensor signals; revising
the model based on the second set of sensor signals; and estimating
the one or more performance metrics of the component in the
downhole drilling tool using the revised model, wherein the sensor
signals reflect one or more conditions of the component in the
downhole drilling tool.
2. The method of claim 1, wherein the component in the drilling
system is chosen from a drill bit, a drill string, a downhole
motor, a MWD/LWD instrument, a drilling pipe, a drilling collar, a
battery, a sensor, or an alternator, a bearing, and a pump.
3. The method of claim 2, wherein the condition of the component in
the drilling system is chosen from a temperature, a pressure, a
vibration, a weight on bit, a noise level, or an RPM.
4. The method of claim 1, wherein the component in the drilling
system is a printed circuit board assembly (PCBA).
5. The method of claim 1, wherein the performance metric is chosen
from a failure probability, a life consumption, or a remaining
useful life.
6. The method of claim 1, wherein the model comprises a plurality
of model parameters, including a grand mean function, a plurality
of eigenfunctions, and a plurality of FPCA function scores.
7. The method of claim 1, wherein the first set of sensor signals
is used as a training dataset to construct the model.
8. The method of claim 1, wherein the second set of sensor signals
comprises a test dataset.
9. The method of claim 7, wherein the first set of sensor signals
comprises signal readings from the component in the downhole
drilling tool from inception of an operation to failure of the
component.
10. The method of claim 8, the first set of sensor signals
comprises signal readings from the same component from more than
one operations.
11. A system for monitoring a downhole drilling tool, comprising: a
drilling assembly; a plurality of sensors disposed about the
drilling assembly, wherein the sensors provide sensor signals
associated with the drilling assembly; a processor; a
non-transitory machine readable medium communicably coupled to the
processor; a set of processor-executable instructions embodied in
the non-transitory machine readable medium, the instructions being
configured to implement a method, the method comprising: collecting
a first set of sensor signals; constructing a model using
Functional Principal Component Analysis (FPGA) based on the first
set of sensor signals, wherein the model estimates a performance
metric of a component in the downhole drilling assembly; collecting
a second set of sensor signals; revising the model based on the
second set of sensor signals; and estimating the performance metric
of the component in the downhole drilling assembly using the
revised model, wherein the sensor signals reflect at least one
condition of the component in the downhole drilling assembly.
12. The system of claim 11, wherein the drilling assembly comprises
a drill bit, a drilling collar, and a MWD/LWD instrument.
13. A drilling system, comprising: a downhole drilling tool; a
plurality of sensors disposed about the downhole drilling tool,
wherein the plurality of sensors traverse a underground formation
with the downhole drilling tool and generate sensor signals that
reflect a condition of one or more components of the downhole
drilling tool; a computer configured to implement a method, the
method comprising: collecting a first set of sensor signals;
constructing a model using Functional Principal Component Analysis
(FPGA) based on the first set of sensor signals, wherein the model
estimates a performance metrics of a component in the downhole
drilling tool; collecting a second set of sensor signals; revising
the model based on the second set of sensor signals; and estimating
the performance metrics of the component in the downhole drilling
tool using the revised model.
14. The drilling system of claim 13, wherein the component in the
downhole drilling tool is chosen from a drill bit, a drill string,
a downhole motor, a MWD/LWD instrument, a drilling pipe, a drilling
collar, a battery, a sensor, or an alternator.
15. The drilling system of claim 14, wherein the condition of the
component in the downhole drilling tool is chosen from a
temperature, a pressure, a vibration, an a weight on bit (WOB), or
an RPM.
16. The drilling system of claim 13, wherein the component in the
downhole drilling tool is a printed circuit board assembly
(PCBA).
17. The method of claim 13, wherein the performance metric is
chosen from a failure probability, a life consumption, or a
remaining useful life.
Description
TECHNICAL FIELD
[0001] The present disclosure relates to systems and methods for
monitoring drilling systems for oil and gas exploration,
particularly systems and methods for real-time estimation of life
consumption and life span of downhole drilling tools.
BACKGROUND
[0002] The drilling system used in the modern petroleum and gas
explorations complex electro-mechanical systems. It includes both
surface equipment as well as downhole drilling tools. A drilling
assembly is a downhole drilling tool that breaks and traverses the
earth formation. A drilling assembly includes a drill bit and a
drill collar. It may also include a downhole motor, a rotary
steerable system, telemetry transmitters, as well as
measurement-while-drilling (MWD) and logging-while-drilling (LWD)
instruments. Although MWD refers to the measurement of the movement
and location of the drilling assembly while the drilling continues
and LWD focuses more on the measurement of formation properties,
they are used interchangeably in this disclosure.
[0003] Properties of the earth formation measured in the drilling
process typically include resistivity, density, porosity,
permeability, acoustic properties, nuclear-magnetic resonance
properties, corrosive properties of the fluids or formation, and
salt or saline contents. Parameters of the drilling assembly
measured typically include velocity, vibration, bending moment,
etc. Downhole vibrations can be further categorized into axial
vibration (e.g., bit bounce), which is along the drill string axis;
lateral vibration (e.g., whirl), which is transverse to the drill
string axis; and torsional vibration (e.g., stick slip), which is
in rotary path about the drill string axis. The MWD/LWD instruments
also monitor drilling operating parameters including weight-on-bit
(WOB), drilling fluid flow rate, pressure, temperature, rate of
penetration, azimuth, tool face, drill bit rotation, etc.
[0004] Alternative to or complimentary to the MWD/LWD instruments,
wireline logging may be used to examine the earth formation.
Typically, after the drill string is removed from the borehole, a
sonde is lowered to the bottom of the region of interest and
subsequently pulled upward. On the upward trip, the sonde measures
the properties of the formation along its path.
[0005] Sensors are employed to obtain measurements in both the
MWD/LWD instruments and the wireline logging approach. Other
electronic components include active components, such as printed
circuit board assemblies (PCBA) and transistors, or passive
components, such as resistors and capacitors. PCBAs are used
throughout a drilling assembly. For example, a PCBA can be used in
the operation of the power supply, temperature sensors, pressure
transducers, the battery, etc. The master memory board, the read
out board, the transmitter or a receiver board, and the
accelerometer board are among PCBAs commonly used in a downhole
environment.
[0006] A PCBA can be coupled to various sensors in a drilling
assembly by any known methods. In some embodiments, sensors may be
integrated in the PCBA, e.g., on a master memory board. Sensors can
be measurement sensors that monitor real-time conditions during a
drilling process. In other embodiments, sensors may be prognostic
sensors. Prognostic sensors are subject to more severe conditions
than in a typical drilling operation (e.g., higher temperature or
pressure) so that they fail at an accelerated rate. They could be
used to estimate the time of failure of another component.
[0007] Other than monitoring the condition of a PCBA, sensors can
be mounted on any other suitable components in a drilling assembly.
For example, they can be attached to a drill bit to monitor its
movement or temperature. Sensors can also be mounted along the
borehole, for example, to monitor the pressure or flow rate of the
drilling mud along the path. Sensors (e.g., RFID) can even be put
into the fluid in the drilling system and be dispersed into the
earth formation.
[0008] A processor usually is a part of the PCBA. It is configured
to receive, store, or execute data such as computer codes or sensor
signals. For example, a processor can be coupled to a program
module which supplies executable instructions and a recording
medium that stores various results of calculations performed by the
processor. Sensor signals are the input to the processor.
[0009] In addition to the drilling assembly, a drilling system also
includes downhole drilling tools such as drill pipes, casing, and
packers that divide the borehole into different sections. The
drilling system further includes surface equipment or subsystems a
drilling mud circulation system (mud pumps, flow meters, etc.), a
drilling platform and its associated hardware (valves, manifolds,
generators, pumps, etc.), as well as additional monitoring and
control systems on the surface.
[0010] Any downtime in a drilling system for repair and maintenance
can be costly. Modern oil and gas explorations in deeper wells and
harder to reach locations further increase the failure rate as well
as the overall cost of the drilling operation. For example,
directional drilling systems face considerably severe operating
environments, with bottom hole temperatures in excess of
200.degree. C., high lateral and axial vibrations of 15 g_RMS (Root
Mean Square), and pressures exceeding 250000 PSI while drilling
profiles requiring up to 15/100 ft. Therefore, it becomes more
desirable to implement cost-effective maintenance strategies, for
example, longer on-stream time, less frequent equipment
replacements, and smaller inventory of replacement parts. To
achieve these goals would require closer monitoring of the status
of downhole drilling tools and better understanding of the
environment in which they operate. The present disclosure provides
methods and apparatus for monitoring a drilling system, including
methods and apparatus for predicting the degradation trend and the
useful lifetime of downhole drilling tools.
SUMMARY
[0011] The present disclosure provides a method for monitoring a
drilling system. The method comprises a step of collecting a first
set of sensor signals. The sensor signals are from sensors deployed
throughout the drilling system, including downhole drilling tools,
which includes mechanical and electronic parts. Sensor signals
reflect one or more conditions of the component in the downhole
drilling tool, such as temperature, pressure, and vibrations. The
method also involves a step of constructing a model using
Functional Principal Component Analysis (FPCA) based on the first
set of sensor signals. The sensor signals are used to determine
model parameters.
[0012] Furthermore, after collecting a second set of sensor
signals, the model is updated using the second set of sensor
signals by adjusting the model parameters. The model is used in
estimating one or more performance metrics of the components in the
drilling system, including life consumption and remaining useful
life. Accordingly, the operator can obtain real time estimates of
the life consumption of the drilling tools.
[0013] The present disclosure also provides a system for monitoring
a downhole drilling tool. The system comprises a drilling assembly
and a plurality of sensors disposed about the drilling assembly,
wherein the sensors provide sensor signals associated with the
drilling assembly. The system also includes one or more computers
which has a processor, a non-transitory machine readable medium
communicably coupled to the processor, and a set of
processor-executable instructions embodied in the non-transitory
machine readable medium. The instructions are configured to
implement a method for monitoring a downhole drilling tool
described herein.
[0014] The present disclosure further provides a drilling system.
The drilling system includes a downhole drilling tool and a
plurality of sensors disposed about the downhole drilling tool,
wherein the plurality of sensors traverse a underground formation
with the downhole drilling tool and generate sensor signals that
reflect a condition of one or more components of the downhole
drilling tool. The drilling system also includes a computer
configured to implement a method for monitoring a downhole drilling
tool described herein.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] The teachings of the present invention can be readily
understood by considering the following detailed description in
conjunction with the accompanying drawings.
[0016] FIG. 1 shows a test data set used in validating the FPCA
model of the current disclosure.
[0017] FIG. 2 illustrates Fraction of Variance Exampled (FVE) in
response to the number of principal components selected.
[0018] FIG. 3 shows the life consumption estimation in comparison
with the true life consumption.
[0019] FIG. 4 illustrates a method of the current disclosure.
DETAILED DESCRIPTION
[0020] Reference will now be made in detail to embodiments of the
present disclosure, examples of which are illustrated in the
accompanying drawings. It is noted that wherever practicable,
similar or like reference numbers may be used in the drawings and
may indicate similar or like elements.
[0021] The drawings depict embodiments of the present disclosure
for purposes of illustration only. One skilled in the art would
readily recognize from the following description that alternative
embodiments exist without departing from the general principles of
the present disclosure.
[0022] According to one aspect of the current disclosure, sensors
are deployed throughout a drilling system including downhole
drilling tools, which further comprises a drilling assembly, drill
pipes, casing, and packers. The sensors can be attached to the
surface of or reside inside the body of parts such as the drill
bit, the drill string, the downhole motor, a drilling pipe, the
drilling collar, the downhole battery, and the downhole alternator.
They are also employed in electronic components such the MWD/LWD
instruments.
[0023] According to another aspect of the current disclosure, the
sensors measure one or more performance metrics of the downhole
drilling tool, such as vibration, pressure, temperature, the weight
on bit (WOB), RPM, and transmit the sensor signals to a computer
system for storage and analysis. The measurement sensor signals
report the status of a downhole component. The prognostic sensor
signals may not directly reflect the status (e.g., temperature,
vibration) of a downhole component but may be correlated to the
status of a component that the sensor is not directly associated
with. For example, a prognostic sensor may be used to predict the
life time of a PCBA board. To do so, a correlation can be first
made in a controlled environment (e.g., a lab) wherein the sensor
is subject to a temperature higher (e.g., 20.degree. C. higher)
than the PCBA is subject to. The prognostic sensor may fail at an
accelerated rate than the PCBA, from which an accelerated factor
can be obtained. With this correlation of life span, in a downhole
environment, the status of a prognostic sensor can be used to
estimate the status of another component, such as a PCBA.
[0024] According to a further aspect of the current disclosure,
sensors are installed on the components of a drilling system that
are on the surface. For example, in a managed pressure drilling
system, the rotating control device (RCD) is a subsystem that
employs high pressure seals, bearings, manifolds, and pumps.
Sensors are deployed on the RCD to monitor the vibration or the
noise level of the bearings and high pressure seals. Flow meters,
pressure sensors, vibration detectors, temperature sensors are
installed on the mud circulation pumps.
[0025] According to a further aspect of the current disclosure, the
sensor signals are used to predict or estimate a performance metric
of the downhole drilling tool or surface equipment or subsystems.
The metrics may include failure probability, life consumption, and
remaining useful life. The sensor signals can be used in performing
cumulative damage analysis, degradation analysis, and life cycle
management. The information obtained from the sensors can be used
to optimize the drilling and exploration performance, to avoid
Non-Productive Time (NPT) on the rig site, and to reduce the repair
and maintenance expense.
[0026] According to still one aspect of the current disclosure,
Functional Data Analysis (FDA) is used to estimate the performance
metrics, e.g., life consumption, of a drilling tool. The Functional
Principal Component Analysis (FPCA) models is constructed for
sensor signals and provides a collection of computational tools to
handle the collected degradation trends from different failure
components of the same type. The resulting unit-specific FPC scores
capture pattern changes in the sensor signal on an individual unit,
and these scores can be adjusted when new sensor signals are
collected. In this case, a sensor signal associated with a drilling
tool that fails over time is also referred to as a degradation
signal as it reflects the trend of degradation of the drilling
tool.
[0027] The first step in conducting a FDA analysis is to build a
FPCA model. In this regard, a degradation signal can be described
by a smooth curve contaminated by random errors. Consider one
signal first. Let x.sub.j(t.sub.ij) be the ith measurement of
signal on unit j at time t, with the end of the time interval
T:
X.sub.j(t.sub.ij)=R.sub.j(t.sub.ij)+.epsilon..sub.ij, i=1,2, . . .
, n.sub.j, 0.ltoreq.t.sub.ij.ltoreq.T, (1)
[0028] wherein R.sub.j(t.sub.ij) is the uncontaminated signal and
.epsilon..sub.ij is an independent identically distributed (i.i.d.)
random error following the normal distribution N(0,.sigma..sup.2).
According to Karhunen-Loeve theorem, a stochastic process can be
represented by an infinite linear combination of orthogonal
functions:
R j ( t ij ) = M X ( t ij ) + s = 1 .infin. .theta. js .xi. s ( t
ij ) .apprxeq. M X ( t ij ) + s = 1 N X .theta. js .xi. s ( t ij )
, ( 2 ) ##EQU00001##
[0029] where M.sub.X(t.sub.ij) is the grand mean curve of the
signal across all units, .xi..sub.s(t.sub.ij) is the value of the
sth eigenfunction at t.sub.ij, the number of eigenvalues N.sub.X,
to be included can be determined based on the explained proportion
of functional variation, and .theta..sub.js are the unit-specific
FPCA scores. The set of orthonormal eigenfunctions .xi..sub.s(t)
account for the basic functions about the expansion of the signal
which approximates the signal as closely as possible. Particularly,
these functions need to satisfy:
.intg..sub.0.sup.T.xi..sub.s.sub.1.sup.2(t)dt=1,
.intg..sub.0.sup.T.xi..sub.s.sub.2.sup.2(t)dt=1,
.intg..sub.0.sup.T.xi..sub.s.sub.1(t).xi..sub.s.sub.2(t)dt=0.
(3)
[0030] These eigenfunctions can be estimated in a non-parametrical
manner. R.sub.j(t) is one of its independent realizations of the
stochastic signal R(t). The relationship of eigenvalues and
eigenfunctions can be found via the Fredholin integral
eigenequation on the covariance C.sub.R(u,v) of R(t):
.intg..sub.0.sup.TC.sub.R(u,v).xi..sub.s(v)dv=.lamda..sub.s.xi..sub.s(u)-
, 0.ltoreq.u.ltoreq.T. (4)
[0031] Then, the orthogonal expression of C.sub.R(u,v) in terms of
the resulting eigenfunctions and eigenvalues is:
C R ( u , v ) = s = 1 .infin. .lamda. s .xi. s ( u ) .xi. s ( v )
.apprxeq. s = 1 N X .lamda. s .xi. s ( u ) .xi. s ( v ) , 0
.ltoreq. u , v .ltoreq. T , ( 5 ) ##EQU00002##
[0032] The functional scores .theta..sub.js of unit j can be
calculated by:
.theta..sub.js=.intg..sub.0.sup.T[R.sub.j(t)-M.sub.X(t)].xi..sub.s(t)dt.
(6)
[0033] Considering other model parameters, Eq. (1) becomes:
X j ( t ij ) .apprxeq. M X ( t ij ) + s = 1 N X .theta. js .xi. s (
t ij ) + ij , i = 1 , 2 , , n j . ( 7 ) ##EQU00003##
[0034] Once the model is constructed, parameters in the model are
estimated, including the grand mean function, the FPCA function
scores, etc.
Estimation of Grand Mean Function M.sub.x(t.sub.ij)
[0035] The grand mean smoother across all available training
degradation signals X=[X.sub.1(t.sub.11), . . . ,
X.sub.m(t.sub.n.sub.m.sub.m)].sup.T can be captured by Locally
Weighted Scatterplot Smoothing (LOWESS) technique. The prominent
advantage of LOWESS is to model a process without relying on
physical knowledge about the process. Gaussian kernel has been
widely used to compromise the performance and computational cost.
The local approximation can be fitted by the local linear kernel
regression with the coefficients [a.sub.0,a.sub.1] estimated
by:
min { j = 1 m i = 1 n j W ( t - t ij h c ) [ X j ( t ij ) - ( a 0 +
a 1 t ) ] 2 } , ( 8 ) ##EQU00004##
[0036] where
W ( ( t - t ij ) h c ) , { W ( x ) = 1 2 .pi. x 2 2 }
##EQU00005##
is the Gaussian kernel function, and the bandwidth h.sub.c can be
determined by the cross-validation. The estimated coefficients
depending on time t are:
[a.sub.0,a.sub.1].sup.T=(T.sup.TWT).sup.-1T.sup.TWX, (9)
[0037] wherein
T = ( 1 1 1 t 11 t n j j t n m m ) T , and ##EQU00006## W = diag (
W ( t - t 11 h c ) , , W ( t - t n m m h c ) ) . ##EQU00006.2##
[0038] Estimation of Functional Scores
[0039] To explain the major variation of a sensor signal, the
significant eigenvalues can be found based on the covariance of the
signals. Let K.sub.X(u,v)=cov(X(u),X(v)) be the covariance of the
collected stochastic signals. The coefficients [B.sub.0, B.sub.11,
B.sub.12] depending on the query moments [u, v] can be solved
through the optimization:
min j = 1 m i = 1 z = 1 i .noteq. z n j W ( t ij - u h u , t zj - v
h v ) [ K ^ X j ( t ij , t zj ) - ( B 0 + B 11 u + B 12 v ) ) ] 2 ,
( 10 ) ##EQU00007##
[0040] where h.sub.u and h.sub.v are respective bandwidths, and
{circumflex over (K)}.sub.X.sub.j(t.sub.ij,t.sub.zj) is the raw
covariance estimated by:
{circumflex over
(K)}.sub.X.sub.j(t.sub.ij,t.sub.zj)=(X.sub.j(t.sub.ij)-{circumflex
over (M)}.sub.X(t.sub.ij))(X.sub.j(t.sub.zj)-{circumflex over
(M)}.sub.X(t.sub.zj)). (11)
[0041] Since K.sub.X(u,v)=C.sub.R(u,v)+.sigma..sup.2I.sub.(u=v), in
which I.sub.(u=v)={1 when u=v; 0 otherwise}. In case of the intense
signal data, each eigenvalue .lamda..sub.s can be estimated by
performing numerical integration:
{circumflex over
(.lamda.)}.sub.s=.intg..sub.0.sup.T.intg..sub.0.sup.T{circumflex
over (.xi.)}.sub.s(u)C.sub.R(u,v){circumflex over
(.xi.)}.sub.s(v)dudv. (12)
[0042] The FPCA scores for each unit j can be calculated by:
.theta. ^ js = i = 1 n j [ X j ( t ij ) - M ^ X ( t ij ) ] .xi. ^ s
( t ij ) ( t ij - t i - 1 j ) . ( 13 ) ##EQU00008##
[0043] The FPCA scores estimated from Eq. (13) would be biased for
sparse signal readings contaminated by measurement errors. An
effective alternative method to correct this problem is called
Principal Analysis by Conditional Expectation (PACE). Let
{circumflex over (.theta.)}.sub.js be the sth FPCA score of unit j
given n.sub.j observations X.sub.j=[X.sub.j(t.sub.1j), . . . ,
X.sub.j(t.sub.n.sub.j.sub.j)].sup.T collected so far. The
conditional expectation of {circumflex over (.theta.)}.sub.js
is:
{circumflex over (.theta.)}.sub.js*=E[{circumflex over
(.theta.)}.sub.js|X.sub.j]={circumflex over
(.lamda.)}.sub.S{circumflex over
(.xi.)}.sub.js.sup.T.SIGMA..sub.j.sup.-1(X.sub.j-{circumflex over
(M)}.sub.X), (14)
[0044] wherein the functional scores {circumflex over
(.xi.)}.sub.js=[{circumflex over (.xi.)}.sub.s(t.sub.1j), . . . ,
{circumflex over (.xi.)}.sub.s(t.sub.n.sub.j.sub.j)].sup.T and
smoothing functions {circumflex over (M)}.sub.X=[{circumflex over
(M)}.sub.X(t.sub.1j), . . . , {circumflex over
(M)}.sub.X(t.sub.n.sub.j.sub.j)].sup.T are evaluated at all
collected measured moments n.sub.j. .SIGMA..sub.j.sup.-1 is the
n.sub.j.times.n.sub.j covariance matrix estimated at all entries of
C.sub.R(t.sub.ij,t.sub.i'j)+{circumflex over
(.sigma.)}.sup.2I.sub.(t.sub.ij.sub.=t.sub.i'j.sub.). The
covariance matrix of FPCA scores {circumflex over
(.theta.)}.sub.j=[{circumflex over (.theta.)}.sub.j1, . . . ,
{circumflex over (.theta.)}.sub.js, . . . , {circumflex over
(.theta.)}.sub.jN.sub.X].sup.T can be expressed as:
cov({circumflex over (.theta.)}.sub.jX.sub.j)={circumflex over
(X)}{circumflex over (.SIGMA.)}.sub.j.sup.-1H.sup.T, (15)
[0045] where H=cov({circumflex over
(.theta.)}.sub.j,X.sub.j)=[{circumflex over
(.lamda.)}.sub.1{circumflex over (.xi.)}.sub.j1, . . . ,
{circumflex over (.lamda.)}.sub.s{circumflex over (.xi.)}.sub.js, .
. . , {circumflex over (.lamda.)}.sub.N.sub.X{circumflex over
(.xi.)}.sub.jN.sub.X].sup.T.
[0046] Given estimation of all the model parameters, the sensor
signal X.sub.j(t.sub.kj) at time t.sub.kj(k>i) can be predicted
by:
E [ X ^ j ( t kj ) ] = M ^ X ( t kj ) + s = 1 N x .theta. ^ js *
.xi. ^ s ( t kj ) . ( 16 ) ##EQU00009##
[0047] Moreover, it is proved that the asymptotic point-wise
Standard Deviation (STD) of {circumflex over (X)}.sub.j(t.sub.kj)
is:
STD({circumflex over (X)}.sub.j(t.sub.kj))= {square root over
({circumflex over (.xi.)}.sup.T(t.sub.kj){circumflex over
(.OMEGA.)}.sub.j{circumflex over (.xi.)}(t.sub.kj)+{circumflex over
(.sigma.)}.sup.2)}, (17)
[0048] where {circumflex over (.xi.)}(t.sub.kj)=[{circumflex over
(.xi.)}.sub.1(t.sub.kj), {circumflex over (.xi.)}.sub.2(t.sub.kj),
. . . , {circumflex over (.xi.)}.sub.N.sub.X(t.sub.kj)].sup.T,
and
{circumflex over (.OMEGA.)}.sub.j=diag({circumflex over
(.lamda.)}.sub.1,{circumflex over (.lamda.)}.sub.2, . . . ,
{circumflex over (.lamda.)}.sub.N.sub.X)-cov({circumflex over
(.theta.)}.sub.j|X.sub.j).
[0049] The confidence interval of X.sub.j(t.sub.kj) can be known at
desired significant level a as:
[E[{circumflex over
(X)}.sub.j(t.sub.kj)]-z.sub.1-.alpha./2STD({circumflex over
(X)}.sub.j(t.sub.kj)), E[{circumflex over
(X)}.sub.j(t.sub.kj)]+z.sub.1-.alpha./2STD({circumflex over
(X)}.sub.j(t.sub.kj))]. (18)
[0050] where z.sub.1-.alpha./2 is the 1-.alpha./2 percentile of the
standard normal distribution.
[0051] The FPCA model has been validated. In one example,
degradation profiles of turbofan engines of the same type due to
wear and tear were simulated based on the usage patterns (four
different combinations of operational conditions and fault modes).
The damage degree of these turbine engines may vary from one
another as different engines often undergo different operating
conditions. Fifteen engines under the same combination of
operational condition (Sea Level) and fault mode (HPC degradation)
were selected. For each engine, sensor readings were collected from
26 sensor channels and the sensor measuring the Low
Pressure-Turbine (LPT) outlet temperature was utilized to indicate
degradation process. The training dataset include LPT readings from
ten engines from inception of their operations to the moment that
they failed. The data from the other five engines is treated as the
test dataset.
[0052] Note that the same validation can be applied to a component
in a downhole drilling tool, e.g., a drill bit. For example, sensor
signals associated with multiple drill bits in their respective
operations can be used as the training dataset to construct a FPCA
model. The model thus constructed can be used in predicting the
performance metric of a drill bit in operation using sensor signals
as the test dataset. The test dataset in turn can be used to update
the training dataset so that the model estimation becomes more
accurate as more and more sensor signals become available.
[0053] As shown in FIG. 1, in the test dataset, different
proportions of available measurements were use, i.e., 50%, 60%, 70%
and 80% of the complete set of data from the start of the operation
to the failure of the components. Estimations were made regarding
the life consumption or remaining useful life after each available
proportion of signals passes. The moment at which the degradation
trend reaches the preset failure threshold (1430 unit temperature
in this case) was recorded as the predicted failure time. Estimated
life consumption from the time of analysis was performed were
calculated to provide an estimated failure time.
[0054] In applying the FPCA model to predict failure moment, a
traditional way is to use time information as the predictor and
amplitude information as the response variable. That is to say,
given a known response value (fixed amplitude threshold), the
predictor value (time) will be derived reversely from the model.
Alternatively, amplitude can be used as the predictor and time
information as the response variable. This transformed axis
facilitates the mathematical calculation since it is convenient to
fit the model given the fixed amplitude threshold value as
predictor.
[0055] The FPCA model includes a grand mean function, several
eigenfunctions, and Functional scores. In this example, the
bandwidth chosen for the mean function is 5.9474, and the bandwidth
values for the covariance function are (1.4795, 1.4795). From the
training dataset, the first three eigenvalues are: {circumflex over
(.rho.)}.sub.1=78601, {circumflex over (.SIGMA.)}.sub.2=4327 and
{circumflex over (.rho.)}.sub.3=3046, which account for 98.33% of
Functional Variation Explained (FVE).
[0056] Assuming 95% of FVE, the FPCA model for the LPT signal based
on a transformed axis can be expressed as:
t j ( X ij ) .apprxeq. M t ( X ij ) + s = 1 3 .theta. js .xi. s ( X
ij ) + ij . ( 19 ) ##EQU00010##
[0057] The FPCA model obtained from the training dataset was used
to predict the failure moments for each test units given the
different available proportions of LPT signal readings which are
used to obtain the unit-specific FPCA scores as addressed in Eq.
(14). In the second stage, the failure moment at fixed LPT
temperature amplitude threshold was predicted with 100(1-.alpha.)%
confidence interval using Eqs. (16) and (18). The reliability
metric applied here is called Life Consumption (LC):
Life Consumption = T ( Query ) T ( Failure ) . ( 35 )
##EQU00011##
[0058] where T(Query) stands for current query moment, and
T(Failure) means the real or predicted failure time.
[0059] Another similar metric is remaining useful life, which
is:
Remaining Useful Life=T(Failure)-T(Query). (36)
[0060] Accordingly, compared with the true life consumption
(True_LC) at query moment, the estimation error of the Estimated_LC
is calculated using the following equation:
L C Estimation Error = abs ( True_LC - Estimated_LC True_LC ) * 100
% . ( 37 ) ##EQU00012##
[0061] The predicted life consumption errors are listed in Table 1
to demonstrate the performance of the FPCA model. Table 1 shows
estimation errors using different amount of data, i.e., 50%, 60%,
70%, and 80% of the total signal readings through the whole life
span of a monitored component. In other words, 50% means data from
the beginning of the operation up to half of the life time of the
drilling tool is used in the model. As shown, when the estimation
is based on a larger set of data, the estimation error becomes
smaller. When 80% of data was used, the estimation error is less
than 5%. Confidence interval of LC estimation when 80% signal
readings are collected is also shown on FIG. 3.
TABLE-US-00001 TABLE 1 Life Consumption Estimation Performance
Percentage of Signal Readings Used 50% 60% 70% 80% Test unit 1
30.82% 14.37% 4.76% 0.01% Test unit 2 24.72% 16.63% 11.84% 4.09%
Test unit 3 37.77% 19.18% 3.26% 1.63% Test unit 4 38.71% 8.50% 6.6%
2.27% Test unit 5 36.27% 17.40% 3.79% 5.09%
[0062] The FPCA model disclosed herein performs better in
comparison with others, such as the Path Classification and
Estimation Model (PCE), which combines the linear regression and
kernel weighted average. Table 2 summarizes the percentage of
estimation errors of the FPCA model and the PCE model. As shown,
the FPCA model offered much higher estimation accuracy for all the
five test components from 50% available signal proportion up to
80%.
TABLE-US-00002 TABLE 2 Life Consumption Estimation Error Comparison
Percentage Signal Readings Used 50% 60% 70% 80% PCE FPCA PCE FPCA
PCE FPCA PCE FPCA Test 1 71.54% 30.82% 73.8% 14.37% 57.23% 4.76%
15.79% 0.01% Test 2 70.13% 24.12% 67.97% 16.63% 56.64% 11.84%
44.18% 4.09% Test 3 45.77% 35.77% 43.71% 19.18% 41.66% 3.26% 43.97%
1.63% Test 4 71.52% 38.71% 57.3% 8.5% 35.65% 6.6% 35.15% 2.27% Test
5 1.93% 36.27% 9.37% 17.4% 11.41% 3.79% 11.65% 5.09%
[0063] Therefore, as shown in FIG. 4, the current disclosure method
comprises the steps of collecting a first set of sensor signals
(e.g., the training dataset) and constructing a model using
Functional Principal Component Analysis (FPCA) based on the first
set of sensor signals, wherein the model is used to estimate one or
more performance metrics of a component in the downhole drilling
tool. The method also comprises steps of collecting a second set of
sensor signals (e.g., the test dataset) and revising the model
based on the second set of sensor signals. The revised FPCA model
is used to estimate one or more performance metrics of the
component (e.g., failure probability, life consumption, etc.).
[0064] The systems and methods provided in this disclosure have
many variations. For example, sensor signals from different
components in the drilling tool can be weighted and then combined
to predict the life consumption of the drilling tool overall. The
method is employed for optimizing the drilling & exploration
performance, avoiding Non-Productive Time (NPT) on the rig site,
and reducing the repair and maintenance expense.
[0065] Embodiments of the present disclosure have been described in
detail. Other embodiments will become apparent to those skilled in
the art from consideration and practice of the present disclosure.
Accordingly, it is intended that the specification and the drawings
be considered as exemplary and explanatory only, with the true
scope of the present disclosure being set forth in the following
claims.
* * * * *