U.S. patent application number 12/363801 was filed with the patent office on 2009-08-06 for order tracking method and system.
Invention is credited to Karl Hans Bert Janssens, Herman Van Der Auweraer, Pieter Frans Van Vlierberghe.
Application Number | 20090193900 12/363801 |
Document ID | / |
Family ID | 39591617 |
Filed Date | 2009-08-06 |
United States Patent
Application |
20090193900 |
Kind Code |
A1 |
Janssens; Karl Hans Bert ;
et al. |
August 6, 2009 |
ORDER TRACKING METHOD AND SYSTEM
Abstract
The present invention describes an order tracking system (200)
and method (100) for tracking at least one order from mechanical
and/or acoustic vibrations generated by a periodic excitation
process of a physical system. The order tracking system (200)
comprises a means for obtaining (212) a mechanical and/or acoustic
vibration data of a physical system and a means for obtaining (214)
system reference data. It further comprises a means for combining
(224) the mechanical and/or acoustic vibration data with the system
reference data and a means for applying (226) a digital FIR filter
to at least the mechanical and/or acoustic vibration data for
deriving based thereon at least one order.
Inventors: |
Janssens; Karl Hans Bert;
(Kessel-lo, BE) ; Van Vlierberghe; Pieter Frans;
(Kessel-lo, BE) ; Van Der Auweraer; Herman;
(Lubbeek-Linden, BE) |
Correspondence
Address: |
BACON & THOMAS, PLLC
625 SLATERS LANE, FOURTH FLOOR
ALEXANDRIA
VA
22314-1176
US
|
Family ID: |
39591617 |
Appl. No.: |
12/363801 |
Filed: |
February 2, 2009 |
Current U.S.
Class: |
73/649 |
Current CPC
Class: |
G01H 1/003 20130101 |
Class at
Publication: |
73/649 |
International
Class: |
G01H 11/00 20060101
G01H011/00 |
Foreign Application Data
Date |
Code |
Application Number |
Feb 2, 2008 |
EP |
EP 08150992.9 |
Claims
1. An order tracking system (200) for tracking at least one order
from mechanical and/or acoustic vibrations generated by a periodic
excitation process of a physical system, the order tracking system
(200) comprising means (212) for obtaining mechanical and/or
acoustic vibration data of a physical system and a means (214) for
obtaining system reference data characterizing the angular speed of
the excitation process, means (224) for demodulating the mechanical
and/or acoustic vibration data by multiplying it with the order
carrier wave(s) of which the frequency evolution is a multiple or
fraction of the angular speed of the periodic excitation process,
and means (226) for applying a digital FIR filter to the
demodulated mechanical and/or acoustic vibration data for deriving
based thereon at least one order.
2. An order tracking system (200) according to claim 1, wherein the
system reference data is an angular speed of the periodic
excitation process, a multiple or fraction of it, a corresponding
oscillator, a tacho pulse train, or any variable derived
therefrom.
3. An order tracking system (200) according to claim 1, wherein the
order tracking system (200) operates in the angle-domain and/or
wherein the order tracking system (200) is adapted to operate an
adaptive FIR filter in the time-domain.
4. An order tracking system (200) according to claim 1, wherein the
means (226) for applying a digital FIR filter is adapted for
applying a digital low pass FIR filter to the combined mechanical
and/or acoustic vibration data and the system reference data.
5. An order tracking system (200) according to claim 1, wherein the
means (212) for obtaining mechanical and/or acoustic vibration data
is adapted for obtaining a sampled mechanical and/or acoustic
vibration data in different finite observation frames wherein the
data is periodic and wherein the means for combining (224) is
adapted for performing said combining once per corresponding
observation interval using the data in this observation interval,
or wherein the means for obtaining (212) mechanical and/or acoustic
vibration data is adapted for obtaining sampled mechanical and/or
acoustic vibration data in different finite observation frames and
wherein the means for applying (226) the digital FIR filter is
adapted for applying the digital FIR filter once per observation
frame.
6. An order tracking system (200) according to claim 1, wherein the
means for applying (226) a digital FIR filter is a means for
applying a digital FIR filter having a cut-off frequency which is
smaller than half an order resolution of the order of interest.
7. An order tracking system (200) according to claim 1, wherein the
system (200) furthermore comprises a means for detecting the
mechanical and/or acoustic vibrations from the physical system and
converting it in mechanical and/or acoustic vibration data.
8. An order tracking system (200) according to claim 1, wherein an
order sampling rate is selectable by the user.
9. An order tracking system (200) according to claim 1, the order
tracking system (200) furthermore comprising an output means (240)
for putting out order information.
10. An order tracking system (200) according to claim 1, wherein a
Fourier Transform based computation scheme is adopted.
11. An order tracking system (200) according to claim 11, wherein
the means for combining (224) and means for applying (226) comprise
means for obtaining a Fourier Transform of the mechanical and/or
acoustic vibration data, a means for obtaining a Fourier Transform
of a bandpass FIR filter and a means for combining the Fourier
Transform of the mechanical and/or acoustic vibration data and the
Fourier Transform of the bandpass FIR filter.
12. An entity comprising a physical system and an order tracking
system (200) according to claim 1, wherein the order tracking
system (200) is adapted to provide information to the physical
system regarding its mechanical and/or acoustic vibration frequency
spectrum.
13. An entity comprising a simulation system and an order tracking
system (200) according to claim 1, the simulation system being
adapted to provide simulation of a mechanical and/or acoustical
vibration signal(s) using order information generated with said
order tracking system (200).
14. A method (100) for tracking at least one order from mechanical
and/or acoustic vibrations generated by a periodic excitation
process of a physical system, the method comprising obtaining (110)
mechanical and/or acoustic vibration data of a physical system,
obtaining (120) system reference data characterising the angular
speed of the excitation process, demodulating the mechanical and/or
acoustic vibration data by multiplying it with the order carrier
wave(s) of which the frequency evolution is a multiple or fraction
of the angular speed of the periodic excitation process and
applying (150) a digital FIR filter to the demodulated mechanical
and/or acoustic vibration data for deriving based thereon at least
one order.
15. A method (100) according to claim 14, wherein the tracking of
at least one order operates in the angle-domain.
16. A method (100) according to claim 14, wherein applying (150) a
FIR filter comprises applying an adaptive FIR filter in the
time-domain.
17. A method (100) according to claim 14, wherein applying (150) a
digital FIR filter comprises applying a digital low pass FIR filter
to the combined mechanical and/or acoustic vibration data and the
system reference data.
18. A method (100) according to claim 14, wherein obtaining (110)
mechanical and/or acoustic vibration data comprises obtaining
mechanical and/or acoustic vibration data in different observation
frames and wherein the combining (140) is performed once per
observation interval.
19. A method (100) according to claim 14, wherein combining (140)
and applying (150) comprise obtaining a Fourier Transform of the
mechanical and/or acoustic vibration data, obtaining a Fourier
Transform of a bandpass FIR filter, and combining the Fourier
Transform of the mechanical and/or acoustic vibration data and the
Fourier Transform of the bandpass FIR filter.
20. A method (100) according to claim 14, obtaining (110)
mechanical and/or acoustic vibration data comprises obtaining
mechanical and/or acoustic vibration data in different observation
frames and wherein applying a digital FIR filter comprises applying
a digital FIR filter once per observation frame.
21. A method (100) according to claim 14, the method (100)
comprising controlling a physical system as function of said
derived order information or comprising simulating a mechanical
and/or acoustic vibration using said derived order information.
22. A computer program product for executing the method as claimed
in claim 14.
23. A machine-readable data storage device storing the computer
program product of claim 22.
24. Transmission of the computer program product of claim 22 over a
local or wide area telecommunications network.
Description
TECHNICAL FIELD OF THE INVENTION
[0001] The present invention relates to methods and systems for
studying vibrational and/or acoustic phenomena. More particularly,
the present invention relates to methods and systems for tracking
orders in the study or analysis of mechanical vibrations and/or
noise of physical systems as well as to the application
thereof.
BACKGROUND OF THE INVENTION
[0002] Sound and vibration phenomena often are analysed in order to
optimise them, e.g. to reduce the amount of disturbance that is
generated for a user or the environment, to make a product
compliant with specifications or with regulations set or to
identify sources of disturbance, to control a system, etc. A known
way for sound and vibration analysis is making use of order
tracking. Order tracking typically is applied to variable-speed
systems generating sound or another mechanical vibration.
[0003] Order tracking concerns the extraction of the complex
envelope of order components from measured mechanical and/or
acoustic vibrations. Orders are harmonic components of which the
kernel frequency is a multiple or fraction of the angular speed of
the periodic excitation.
[0004] The oldest order tracking technique is based on performing
Fourier Transforms on time domain data. Fourier Transforms with
constant kernel frequencies are used. The transformed data is
displayed in either a waterfall or color map format. Orders of
interest are then estimated through determining the average
frequency of each order over which the Fourier Transforms were
performed and extracting the corresponding frequency lines. The
limitations of these techniques are many and can be significant.
The two largest limitations are limited order resolution at lower
rotational speeds and slow sweep rates.
[0005] Considerable improvements in order tracking were achieved
since the late eighties. DC-estimation techniques were developed in
which the Fourier Transform kernels explicitly take account of the
changes in rotational speed. Two variants of DC-estimation methods
exist, i.e. DC estimation in the angle-domain and DC estimation in
the time-domain. The angle-domain variant, also referred to as
resampling-based order tracking, is for example known from U.S.
Pat. No. 6,351,714. The method is based on a limited observation
interval of the angle-sampled signal x(.alpha.), during which the
complex order component envelopes X.sub.k(.rho.(.alpha.)), being a
function of the rotational speed .rho. which is a function of the
angle .alpha., are assumed to be constant. An interval
[.theta.-.DELTA..alpha., .theta.+.DELTA..alpha.] is picked wherein
x(.alpha.) is periodic with period Q and wherein the variation of
the angle .DELTA..alpha.=Q.sub.TT. 1/Q is also known as the order
resolution. The order is then estimated as follows:
X ^ k ( .rho. ( .theta. ) ) = .intg. .theta. - .DELTA..alpha.
.theta. + .DELTA. .alpha. C w W ( .alpha. ) x ( .alpha. ) j k
.alpha. Q .alpha. [ 1 ] ##EQU00001##
wherein W(.alpha.) is a windowing function to avoid leakage and
C.sub.w is a window correction factor. By moving the independent
variable to the time-domain, we obtain the time-domain variant,
which is mathematically equivalent and often referred to as
time-variant DFT. The time-variant DFT formulation is as
follows:
X ^ k ( .rho. ( T ) ) = .intg. T 0 T 1 C w W ( .alpha. ( t ) ) x (
t ) j k .alpha. ( t ) Q .alpha. t t [ 2 ] ##EQU00002##
where:
.alpha.(T)=0
(T.sub.0)=.theta.-.DELTA..alpha.
.alpha.(T.sub.1)=.theta.+.DELTA..alpha.
[0006] The weakness of the DC-estimation approach is the assumption
that the order X.sub.k(.rho.(.alpha.)) must be constant over the
observation interval. It assumes a zero angle-domain order
bandwidth, i.e. B.sup..alpha..sub.k (1/rad)=0. However, this
assumption is only true at constant rotational speed. When the
rotational speed .rho. changes in the observation interval, which
is obviously the case in run-up and coast-down measurements,
B.sup..alpha..sub.k is not longer zero and the DC-estimation method
starts suffering from order crosstalk. Orders then leak into
adjacent ones and cannot be longer separated. The cross-talk and
resulting DC-estimation errors increase with (i) decreasing order
spacing 1/Q, (ii) decreasing rotational speed .rho., (iii)
increasing angular acceleration d.rho./dt and (iv) increasing order
bandwidth B.sup..rho..sub.k (s/rad) in the rotational speed domain.
Here, B.sup..rho..sub.k characterizes the order envelope variations
with rotational speed. B.sup..rho..sub.k is a system characteristic
which depends on the system transfer function characteristics.
[0007] Another known and widely-used type of order tracking
technique is referred to as a Vold-Kalman order tracking approach
for rotating machinery. This time-domain method centres the order
of interest about DC and applies a particular type of low-pass
filter to the phasor-shifted data. The Vold-Kalman order tracking
filter acts as an autoregressive, IIR type of filter with a limited
number of poles. The tracking characteristics of the filter are
determined by the HCF (Harmonic Confidence Factor) weighting
parameter. Undesired phase distortions on the order estimates are
minimized by adopting a total Least Squares solution algorithm.
This algorithm estimates the full order envelope at once from the
complete data signal. However, this makes the Vold-Kalman approach
computationally very heavy and explains its off-line character and
use.
[0008] There is a further need for good methods and systems for
order tracking, being accurate and at the same time computational
efficient.
SUMMARY OF THE INVENTION
[0009] It is an object of embodiments of the present invention to
provide good apparatus or methods for order tracking in the study
of a noise and/or mechanical vibration of a physical system and
methods and systems using them. It is an advantage of embodiments
according to the present invention that an accurate order tracking
technique is obtained. It is furthermore an advantage according to
embodiments according to the present invention that a computational
efficient order tracking technique is obtained. It is an advantage
of embodiments according to the present invention that the
technique is user friendly and can be tailored depending on the
user's needs. The above objective is accomplished by a method and
device according to the present invention.
[0010] The present invention relates to an order tracking system
for tracking at least one order from mechanical and/or acoustic
vibrations generated by a periodic excitation process of a physical
system, the order tracking system comprising a means for obtaining
mechanical and/or acoustic vibration data of a physical system, a
means for obtaining system reference data characterizing the
angular speed of the excitation process, a means for combining the
mechanical and/or acoustic vibration data with the system reference
data, and a means for applying a digital FIR filter to at least the
mechanical and/or acoustic vibration data for deriving based
thereon at least one order. The excitation process may be a
stationary or variable speed excitation process. It is an advantage
of embodiments according to the present invention that a high
accuracy can be obtained. It is an advantage of embodiments
according to the present invention that an efficient computational
technique is obtained.
[0011] It is an advantage of embodiments according to the present
invention that the FIR low-pass filter can be a sharp filter. It is
an advantage of embodiments according to the present invention that
the user only needs to specify the order resolution and attenuation
of the filter. In other words, it is an advantage of embodiments
according to the present invention that it provides a user-friendly
technique for performing order tracking. It is an advantage of
embodiments according to the present invention that, in contrast to
the hard-to-understand parameters used in the Vold-Kalman approach,
such as e.g. the HCF weighing factor, the resolution and
attenuation parameters of the FIR filter are understandable and
have a clear influence on the result.
[0012] The system reference data may be an angular speed of the
periodic excitation process, a multiple or fraction of it, a
corresponding oscillator, a tacho pulse train, or any variable
derived there from.
[0013] The order tracking system may operate in the
angle-domain.
[0014] The order tracking system may be adapted to operate an
adaptive FIR filter in the time-domain.
[0015] It is an advantage of embodiments according to the present
invention that the order tracking method and system can be based
both on an angle-domain formulation of the order tracking technique
and/or on a time-domain formulation of the order technique.
[0016] The means for applying a digital FIR filter may be adapted
for applying a digital low pass FIR filter to the combined
mechanical and/or acoustic vibration data and the system reference
data.
[0017] The means for combining the mechanical and/or acoustic
vibration data and the system reference data may be a means for
multiplying the mechanical and/or acoustic vibration data with an
order carrier wave of which the frequency evolution is a multiple
or fraction of an angular speed of the periodic excitation
process.
[0018] The means for obtaining mechanical and/or acoustic vibration
data may be adapted for obtaining a sampled mechanical and/or
acoustic vibration data in different finite observation frames
wherein the data may be periodic. The multiplying may be performed
once per corresponding observation interval using the data in this
observation interval.
[0019] The means for obtaining mechanical and/or acoustic vibration
data may be adapted for obtaining sampled mechanical and/or
acoustic vibration data in different finite observation frames and
the means for applying the digital FIR filter may be adapted for
performing the FIR filter once per observation frame.
[0020] The means for applying a digital FIR filter may be a means
for applying a digital FIR filter having a cut-off frequency which
is smaller than half an order resolution of the order of interest.
It is an advantage of embodiments according to the present
invention that the system allows good distinction between the
different orders in the order tracking technique.
[0021] A FIR filter design of the FIR filter may be a trade off
between the amount of data needed to run the filters, the
computation effort required and the accuracy of the filter.
[0022] The system furthermore may comprise a means for detecting
the mechanical and/or acoustic vibrations from the physical system
and converting it in mechanical and/or acoustic vibration data.
[0023] The system reference data may be indicative of a periodic
process. The system reference data may be constant. The system
reference data may be non-stationary.
[0024] It is an advantage of embodiments according to the present
invention that the complex order envelopes X.sub.k(.rho.(.alpha.))
can vary in the observation period. As long as the order bandwidth
is limited, e.g. the order bandwidth B.sup..alpha..sub.k<0.5/Q,
an order component can be very well separated from the adjacent
ones. The latter allows an improved technique for order tracking,
resulting in a better resolving of the different orders.
Embodiments according to the present invention thus result in an
analysis technique whereby a good accuracy can be obtained.
[0025] The order sampling rate may be selectable by the user.
[0026] The order tracking system furthermore may comprise an output
means for putting out order information.
[0027] A Fourier Transform based computation scheme may be adopted.
It is an advantage of embodiments according to the present
invention that such a Fourier Transform based computation may be
applied for both the angle and time domain variants. It is an
advantage of embodiments according to the present invention that
such a Fourier Transform based computation may yield the same
results, but may have better performance for high channel
count/orders.
[0028] The means for combining and means for applying may comprise
means for obtaining a Fourier Transform of the mechanical and/or
acoustic vibration data, means for obtaining a Fourier Transform of
a band-pass FIR filter and means for combining the Fourier
Transform of the mechanical and/or acoustic vibration data and the
Fourier Transform of the band-pass FIR filter.
[0029] The present invention also relates to an entity comprising a
physical system and an order tracking system as described above,
wherein the order tracking system is adapted to provide information
to the physical system regarding its mechanical vibration frequency
spectrum.
[0030] The present invention furthermore relates to an entity
comprising a simulation system and an order tracking system as
described above, the simulation system being adapted to provide
simulation of a mechanical vibration signal(s) using order
information generated with said order tracking system.
[0031] The present invention also relates to a method for tracking
at least one order from mechanical and/or acoustic vibrations
generated by a periodic excitation process of a physical system,
the method comprising obtaining mechanical and/or acoustic
vibration data of a physical system, obtaining system reference
data characterising the angular speed of the excitation process,
combining the mechanical and/or acoustic vibration data and the
system reference data and applying a digital FIR filter to at least
the mechanical and/or acoustic vibration data.
[0032] The method for tracking of at least one order may be
operated in the angle-domain.
[0033] Applying a FIR filter may comprise applying an adaptive FIR
filter in the time-domain.
[0034] Applying a digital FIR filter may comprise applying a
digital low pass FIR filter to the combined mechanical and/or
acoustic vibration data and the system reference data.
[0035] Combining the mechanical and/or acoustic vibration data and
the system reference data may comprise multiplying the mechanical
vibration frequency data and an order carrier wave of which the
frequency evolution is a multiple or fraction of an angular speed
of the periodic excitation process.
[0036] Obtaining a mechanical and/or acoustic vibration data may
comprise obtaining a mechanical and/or acoustic vibration data in
different observation frames and combining may be performed once
per observation interval.
[0037] Combining and applying may comprise obtaining a Fourier
Transform of the mechanical and/or acoustic vibration data,
obtaining a Fourier Transform of a band-pass FIR filter, and
combining the Fourier Transform of the mechanical and/or acoustic
vibration data and the Fourier Transform of the band-pass FIR
filter.
[0038] Obtaining a mechanical and/or acoustic vibration data may
comprise obtaining a mechanical and/or acoustic vibration data in
different observation frames and applying a digital FIR filter may
comprise applying a digital FIR filter once per observation
frame.
[0039] The method may comprise controlling a physical system as
function of said derived order information.
[0040] The method may comprise simulating a mechanical and/or
acoustic vibration using said derived order information.
[0041] The present invention also relates to a computer program
product for executing the method as described above and below.
[0042] The present invention furthermore relates to a
machine-readable data storage device storing such a computer
program product and/or the transmission of such a computer program
product over a local or wide area telecommunications network.
[0043] It is an advantage of embodiments according to the present
invention that a high performance level for the analysis, more
particularly for the order tracking process, can be obtained.
[0044] It is an advantage of embodiments according to the present
invention that systems and methods are provided that allow to deal
with mechanical vibration signals or corresponding data having a
rapidly varying order content, such as for example mechanical
vibration signals or corresponding data stemming from rotating
machinery having a fast run-up and/or coast down.
[0045] It is an advantage of embodiments according to the present
invention that the systems and methods for order tracking can be
applied in real-time, allowing a more efficient study e.g.
analysis, evaluation, control and/or simulation.
[0046] It is an advantage of embodiments according to the present
invention that computation for the order tracking technique can
start as soon as a data frame with the length of the filter window
for the FIR filter is available. It is an advantage of embodiments
according to the present invention that the filter does not require
future data. The latter results in the advantage that the order
tracking methods and systems according to embodiments of the
present invention can be applied in an on-line fashion, i.e. in
real time. It is an advantage of embodiments according to the
present invention that the methods and systems do not require the
measurement of the complete signals or corresponding data before
the order envelope can be computed, in contrast to e.g. the
Vold-Kalman approach.
[0047] It is an advantage of embodiments according to the present
invention that the computational effort required to perform the
order tracking technique is limited. This is a result of at least
the fact that the order envelope is not to be computed sample by
sample. Applying the filter multiplication only once per
observation frame may be sufficient to obtain an appropriate
result. The order tracking technique therefore may be down
deciminated, depending on the required accuracy. It thus is an
advantage of embodiments according to the present invention that
the filter is not auto-regressive.
[0048] It is an advantage of embodiments according to the present
invention that the filter can produce a sharp cut-off, while
remaining computationally efficient.
[0049] Particular and preferred aspects of the invention are set
out in the accompanying independent and dependent claims. Features
from the dependent claims may be combined with features of the
independent claims and with features of other dependent claims as
appropriate and not merely as explicitly set out in the claims.
[0050] The teachings of the present invention permit the design of
improved methods and apparatus for studying, evaluating, optimising
and/or simulating mechanical vibration or noise in physical
systems.
[0051] The above and other characteristics, features and advantages
of the present invention will become apparent from the following
detailed description, taken in conjunction with the accompanying
drawings, which illustrate, by way of example, the principles of
the invention. This description is given for the sake of example
only, without limiting the scope of the invention. The reference
figures quoted below refer to the attached drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0052] FIG. 1 is a schematic diagram of different standard and
optional steps in a method for order tracking according to an
embodiment of the first aspect of the present invention.
[0053] FIG. 2 is an example of a waterfall spectrum of a run-up
vibration signal or corresponding data, illustrating the presence
and evolution of different order components with rotational speed,
as can be obtained using embodiments according to the present
invention.
[0054] FIG. 3 is an illustration of the first order amplitude
profile as function of the rotational speed as identified from the
signal or data shown in FIG. 2.
[0055] FIG. 4 is a diagrammatic representation of standard and
optional components of an order tracking system according to an
embodiment of the present invention.
[0056] FIG. 5 is a schematic view of a computer system that may be
used to implement a method and/or system according to an embodiment
of the present invention.
[0057] FIG. 6 shows a performance analysis of a method for order
tracking according to an embodiment of the present invention in
comparison to the known DC-estimation approach applying a uniform
window or a Hanning window.
[0058] FIG. 7 shows an example of an order 2 profile for an
acoustic response point inside the passenger compartment of a
vehicle as can be studied using a method for tracking according to
an embodiment of the present invention.
[0059] FIG. 8 shows an example of the rotational speed as function
of the angle for a linear run-up in speed from 1000 RPM to 6000 RPM
in 30 seconds, as can, for example, be used as reference signal or
corresponding reference data in a method for order tracking
according to an embodiment of the present invention.
DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS
[0060] The present invention will be described with respect to
particular embodiments and with reference to certain drawings but
the invention is not limited thereto but only by the claims. The
drawings described are only schematic and are non-limiting. In the
drawings, the size of some of the elements may be exaggerated and
not drawn on scale for illustrative purposes. The dimensions and
the relative dimensions do not correspond to actual reductions to
practice of the invention.
[0061] Furthermore, the terms first, second, third and the like in
the description and in the claims, are used for distinguishing
between similar elements and not necessarily for describing a
sequence, either temporally, spatially, in ranking or in any other
manner. It is to be understood that the terms so used are
interchangeable under appropriate circumstances and that the
embodiments of the invention described herein are capable of
operation in other sequences than described or illustrated
herein.
[0062] It is to be noticed that the term "comprising", used in the
claims, should not be interpreted as being restricted to the means
listed thereafter; it does not exclude other elements or steps. It
is thus to be interpreted as specifying the presence of the stated
features, integers, steps or components as referred to, but does
not preclude the presence or addition of one or more other
features, integers, steps or components, or groups thereof. Thus,
the scope of the expression "a device comprising means A and B"
should not be limited to devices consisting only of components A
and B. It means that with respect to the present invention, the
only relevant components of the device are A and B.
[0063] Reference throughout this specification to "one embodiment"
or "an embodiment" means that a particular feature, structure or
characteristic described in connection with the embodiment is
included in at least one embodiment of the present invention. Thus,
appearances of the phrases "in one embodiment" or "in an
embodiment" in various places throughout this specification are not
necessarily all referring to the same embodiment, but may.
Furthermore, the particular features, structures or characteristics
may be combined in any suitable manner, as would be apparent to one
of ordinary skill in the art from this disclosure, in one or more
embodiments.
[0064] Similarly it should be appreciated that in the description
of exemplary embodiments of the invention, various features of the
invention are sometimes grouped together in a single embodiment,
figure, or description thereof for the purpose of streamlining the
disclosure and aiding in the understanding of one or more of the
various inventive aspects. This method of disclosure, however, is
not to be interpreted as reflecting an intention that the claimed
invention requires more features than are expressly recited in each
claim. Rather, as the following claims reflect, inventive aspects
lie in less than all features of a single foregoing disclosed
embodiment. Thus, the claims following the detailed description are
hereby expressly incorporated into this detailed description, with
each claim standing on its own as a separate embodiment of this
invention.
[0065] Furthermore, while some embodiments described herein include
some but not other features included in other embodiments,
combinations of features of different embodiments are meant to be
within the scope of the invention, and form different embodiments,
as would be understood by those in the art. For example, in the
following claims, any of the claimed embodiments can be used in any
combination.
[0066] Furthermore, some of the embodiments are described herein as
a method or combination of elements of a method that can be
implemented by a processor of a computer system or by other means
of carrying out the function. Thus, a processor with the necessary
instructions for carrying out such a method or element of a method
forms a means for carrying out the method or element of a method.
Furthermore, an element described herein of an apparatus embodiment
is an example of a means for carrying out the function performed by
the element for the purpose of carrying out the invention.
[0067] In the description provided herein, numerous specific
details are set forth. However, it is understood that embodiments
of the invention may be practiced without these specific details.
In other instances, well-known methods, structures and techniques
have not been shown in detail in order not to obscure an
understanding of this description.
[0068] The following terms are provided solely to aid in the
understanding of the invention. The term "order" relates to
frequencies in the vibration frequency spectrum that are related to
a system reference parameter, such as for example a rotation speed
of a component of the physical system. The term "order" can be seen
as a harmonic of a given baseline signal or corresponding data
generated by a periodic process in the physical system under study.
Such a related frequency may correspond with a fraction or a
multiple of a variation frequency of a system reference parameter.
Orders in the vibration frequency spectrum may have a significant
larger amplitude in the vibration frequency spectrum than the
remaining part of the vibration frequency spectrum.
[0069] With "Finite Impulse Response filter" or "FIR filter" a
category of digital filters is envisaged. The FIR filter is
characterized in that the impulse response of the filter, i.e. the
filter's response to a Kronecker delta input, is `finite` because
it settles to zero in a finite number of sample intervals. An Nth
order FIR filter has a response to an impulse that is N+1 samples
in duration. The filters have the advantage that they are
inherently stable due to the fact that all poles are located at the
origin. The filters require no feedback and have only very limited
phase distortion.
[0070] The invention will now be described by a detailed
description of several embodiments of the invention. It is clear
that other embodiments of the invention can be configured according
to the knowledge of persons skilled in the art without departing
from the true spirit or technical teaching of the invention, the
invention being limited only by the terms of the appended
claims.
[0071] In a first aspect, the present invention relates to a method
for tracking an order in mechanical and/or acoustic vibration
signals or corresponding data. Such mechanical and/or acoustic
vibration signals may for example be caused by a periodic process
in the physical system to be measured. This may be a rotating
component in the physical system, an electrical ignition, etc. The
order tracking method comprises obtaining mechanical vibration data
of a physical system and obtaining system reference data. Such
system reference data thus may be representative for a phenomenon
inducing a baseline frequency signal or corresponding data and thus
may influence the mechanical and/or acoustic vibration signals and
corresponding data generated and consequently also the orders
present in the mechanical and/or acoustic vibration signals or
corresponding data generated by the physical system. It may be an
angular speed, a rotational speed, a tacho pulse train, an order
oscillator, etc. The method further comprises combining the
mechanical vibration data with the system reference data and
applying a digital Finite Impulse Response (FIR) filter to the
data. Combining the mechanical and/or acoustic vibration data and
the system reference data may be combination of the mechanical
and/or acoustic vibration data with a rotational speed RPM, with a
tacho pulse train, with an order oscillator, with an order carrier
wave, etc. Such combining may be demodulating the mechanical and/or
acoustic vibration data. In one example, combining the data may
comprise multiplying the mechanical and/or acoustic vibration data
with the order carrier wave, of which the kernel frequency is a
multiple or fraction of the reference angular speed, where after a
digital Finite Impulse Response (FIR) low-pass filter is applied to
the combined data. In another example, a Fourier Transform is
applied to a band-pass FIR filter and to the mechanical and/or
acoustic vibration data which then are combined, e.g. by
multiplying the spectral lines. Combination of the mechanical
and/or acoustic vibration data and the system reference data and
applying a digital FIR filter then is performed indirectly by
generating a band-pass FIR filter, which implies centering of a FIR
filter around the carrier frequency of the order whereby the system
reference data is used for determining the carrier frequency order,
and by combining the Fourier Transform of the digital FIR filter
with the Fourier Transform of the mechanical vibration data.
Application of the FIR filter according to embodiments of the
present invention results in good accuracy, a user-friendly system
and a computational efficient system. Based on the filtered
results, at least one order can be identified, and thus tracked. In
embodiments of the present invention order information such as for
example the amplitude and/or phase profile of an order thus may be
tracked using a combination of the mechanical and/or acoustic
vibration data per observation interval with the order carrier
wave, and using a sharp FIR filter, with limited phase distortion
on it. The methods and systems according to the present invention
may be suitable for studying, analysing, evaluating, controlling,
adjusting or simulating physical systems based on mechanical
vibrations. Such mechanical vibrations may for example be noise,
strain, a vibration, etc. The mechanical vibrations under study
thereby may be induced by a periodic process influenced or
determined by a system reference parameter. The periodic process
may be a repetitive process. Such a periodic process may for
example be rotation of a component of a system, e.g. in rotational
machinery, electric ignition in a motor, etc.
[0072] By way of illustration, the present invention not being
limited thereto, an exemplary method according to an embodiment of
the present invention will be described with reference to FIG. 1,
indicating standard and optional steps of such a method.
[0073] The method 100 for order tracking may be performed on a
mechanical and/or acoustic vibration data of a physical system in
operation, e.g. standard operation, predetermined test conditions
etc. The mechanical and/or acoustic vibrations may be any type of
mechanical and/or acoustic vibration, such as for example, but not
limited to, a noise. The mechanical and/or acoustic vibrations may
be caused by any type of system, e.g. a physical system. Such
physical systems may for example be engines, gear boxes, exhaust
systems, electrical generators, pumps, etc. It may be caused by one
or more pieces of rotating machinery. It may for example be caused
by rotating physical elements, such as for example rotating shaft.
The latter may be running at constant speed or at non-stationary
speed. Such a method may be used for analysing a system, for
evaluating it, for optimising the physical system with respect to
the mechanical vibration, e.g. for reducing the mechanical
vibration or reducing certain components of the mechanical
vibration, as input for simulating a mechanical vibration, etc. The
physical system may be operated in standard operating conditions.
The physical system may be operated according to a ramp up or coast
down experiment. For example, when using rotating machinery, the
experiment may comprise a ramp up or coast down of the rotation
speed. The method thus may comprise a step of operating 105 the
physical system according to predetermined system reference data.
The reference data preferably is varied over the experiment. Such
variation thus may be an increase, decrease or a combination
thereof. Other physical phenomena generating a mechanical vibration
also may be studied.
[0074] The method of order tracking 100 comprises obtaining 110
data for a mechanical and/or acoustic vibration data from a
physical system. A dedicated detection of data for the mechanical
and/or acoustic vibration signal or corresponding data from the
physical system may be performed. Such detection may be performed
using a dedicated detector, such as for example an accelerometer
for detection of mechanical vibrations, a microphone for detecting
acoustic pressure variations, a strain sensor to measure strains, a
P-U Microflown probe to measure acoustic particle velocity and
intensity, etc. Alternatively, or in addition thereto, obtaining
data for a mechanical and/or acoustic vibration data may comprise
receiving data regarding a mechanical and/or acoustic vibration
signal detected from the physical system, e.g. a pre-stored signal,
a realtime recorded signal, etc.
[0075] The method of order tracking 100 furthermore comprises
obtaining 120 data of a system reference signal, i.e. also referred
to as system reference data or system reference parameter values.
Such a system reference signal characterizes the periodic
excitation process, being either stationary or varying in speed.
For a rotating system, this may for example be the angular speed or
rotational speed of one of the rotating shafts, or a multiple or
fraction of it, a corresponding oscillator, a tacho pulse train or
an order carrier wave, the invention not being limited thereto. The
system reference data may be recorded using a suitable detection
technique. Alternatively or in addition thereto, obtaining data of
a system reference data may comprise receiving data regarding a
system reference signal, e.g. pre-stored data, real-time recorded
data, etc.
[0076] It is to be noticed that the steps for obtaining information
may be interchanged, i.e. obtaining of the system reference data
and obtaining the mechanical and/or acoustic vibration data may be
done one after the other, in whatever order or simultaneously.
[0077] In the method, a resampling 130 of the measured mechanical
and/or acoustic vibration data to an another domain, e.g.
resampling from a time domain to an angle domain, may be performed.
In one embodiment, such a resampling may be performed by using the
system reference data. Furthermore such system reference data may
be used as a reference point. In other embodiments according to the
present invention, the measured mechanical and/or acoustic
vibration data may be obtained directly in the appropriate domain
for the technique applied, or may already be converted.
[0078] The method further comprises combining the mechanical and/or
acoustic vibration data and the system reference data and applying
a digital FIR filter to at least the mechanical and/or acoustic
vibration data, e.g. to the mechanical and/or acoustic vibration
data or a processed version thereof or to a combination of the
mechanical and/or acoustic vibration data and the system reference
data. In the present example, the latter is obtained by
demodulating the mechanical and/or acoustic vibration data and
applying a digital low-pass FIR filter, as will be described in
more detail in the following steps. Embodiments according to the
present invention nevertheless are not limited thereto.
[0079] The method for tracking orders 100 furthermore comprises
combining 140 the mechanical and/or acoustic vibration data with
the system reference data. Combining the data may for example be
performed by multiplying the mechanical and/or acoustic vibration
data per observation period with the respective order carrier
wave(s). This process is also known as demodulation. The latter
may, for an order X.sub.k(p(.alpha.)), a vibration and/or acoustic
measurement data x(.alpha.) and an order carrier wave
j k .alpha. Q ##EQU00003##
be expressed as
x ( .alpha. ) j k .alpha. Q [ 3 ] ##EQU00004##
with p the reference angular speed or a derived parameter, for
example a multiple or fraction of it.
[0080] After combining the mechanical and/or acoustic vibration
data with the system reference data, the method comprises applying
150 a FIR filter to the combined data. The latter results in
filtered results, providing an estimate for the order {circumflex
over (X)}.sub.k(p(.alpha.)). This can be mathematically expressed,
with B.sub.k.sup..alpha. the angle-domain order bandwidth, as:
X ^ k ( p ( .alpha. ) ) = FIRLowPass ( B k .alpha. , .alpha. ) x (
.alpha. ) j k .alpha. Q [ 4 ] ##EQU00005##
[0081] The latter represents the application of a low-pass FIR
filter of bandwidth B.sub.k.sup..alpha. and with minimum phase
distortion to the combined signal, i.e. the phasor shifted signal,
to extract order information, e.g. the complex order envelope, and
remove all the additional side bands that were introduced. Applying
a FIR filter may be performed in any suitable way. Design of the
FIR filter corresponds with selection of the coefficients in the
filter such that the filter has specific characteristics. The
required characteristics may be based on filter specifications.
Such filter specifications may be a function of the frequency
response of the filter. The filter design may be determined using
different methods, such as for example based on a window design
method, a frequency sampling method, a weighted least squares
design, a minimax design, an equiripple design etc. The actual
design of the FIR filter thereby may be a trade-off between the (i)
amount of data needed to run the filters, (ii) the computation
effort required and (iii) the accuracy of the filter. A FIR filter
that produces a sharp cut-off along with a flat pass-band generally
consists of a large number of taps. Such filter better separates
order components, but is computationally more demanding, since the
computational load is proportional with the product of the number
of filter taps and the sampling frequency. Applying a FIR filter
provides the advantage that an accurate order tracking technique is
obtained.
[0082] After application of the FIR filter to the combined results,
the obtained filtered results represent the order information, thus
allowing to track the order. Comparison of the order information
between subsequent samplings thus may allow tracking of the order,
resulting in a full track of the order during the experiment. Such
an order tracking may comprise tracking the amplitude profile
and/or tracking the phase profile of at least one order in a
mechanical vibration. In order to track the order, the complex
envelope of at least one order component may be extracted over
time, angle, rotational speed or any derived variable.
[0083] By way of illustration, the present invention not being
limited thereto, an example of a run-up order tracking experiment
is shown in FIG. 2, whereby in FIG. 3 the amplitude profile of the
first order is shown.
[0084] The method for order tracking 100 furthermore may comprise
outputting 160 data regarding the at least one tracked order. The
latter may be performed by providing a visualisation of the tracked
order, or it may be performed in electronic way. Outputting may be
performed to generate an input signal for a control system,
controlling the physical system under study, in order to adjust the
control of the physical system, e.g. in an optimisation
procedure.
[0085] It is an advantage of embodiments according to the present
invention that the order tracking method works properly as long as
the angle-domain order bandwidth is smaller than half the order
resolution. The order envelope may vary over the observation
interval.
[0086] It is an advantage of embodiments according to the present
invention that order tracking in the mechanical and/or acoustic
vibrations may be performed in real-time. It also is an advantage
of embodiments according to the present invention that the order
tracking process of embodiments according to the present invention
can better deal with fast varying orders, fast varying system
reference data values and closely spaced orders. The latter allows
that with the methods and systems according to embodiments of the
present invention, physical systems that have a fast ramp-up or a
fast coast-down or fast varying system data or closely spaced
orders (e.g. a closely spaced engine and gearbox order) still can
be studied, analysed, evaluated, etc.
[0087] One, more or preferably all steps of the above described
method may be performed by a computing device. One, more or all of
the steps of the above described method may be performed in an
automated or automatic way. Steps of the order tracking method may
be based on predetermined algorithms and decisions taken in the
algorithm may be based on basic rules, predetermined requirements,
neural network processing, etc.
[0088] In the above illustrated example, the mechanical and/or
acoustic vibration data first is demodulated with the order carrier
wave, for which the order carrier frequency is proportional to the
angular seed or a multiple or fraction thereof. Such a demodulation
is performed in the present example by multiplying the mechanical
and/or acoustic vibration data with the carrier wave in the angle
domain. The latter results in phasor-shifted data, around DC.
Thereafter, an angle-domain low pass FIR filter is applied to the
phasor-shifted mechanical and/or acoustic vibration data. Such a
FIR filter is designed once and does in principle not need to
change during the run-up. It thus may be a fixed FIR filter.
Applying the FIR filter comprises multiplying the phasor-shifted
data with the filter taps of the filter. Nevertheless, in
particular embodiments of the present invention, the order tracking
technique can also be used directly in the time-domain, wherein the
mechanical vibration data may be originally recorded. The latter
thus may allow to avoid resampling of the time domain to the angle
domain and also avoids the error incurred by the resampling. An
adaptive FIR filter is used which is computed once for each desired
system reference parameter value and applied on all system response
points of interest. The filter may be adaptive by adjusting the
filter length, i.e. the number of taps, over a variation in the
system reference, in order to maintain the same angle domain
cut-off (e.g. 1/(2Q)). E.g. in case of a run-up of a rotational
speed experiment, the filter length may be adapted in order to
maintain the same angle-domain cut-off at low RPM's and at high
RPM's. The adoption of an adaptive FIR filter in the time domain is
illustrated in the example below. Since the time domain approach
according to this particular embodiment combines adaptive filtering
and amplitude demodulation in a single computation run, it may be
referred to as adaptive amplitude demodulation order tracking.
[0089] According to a particular embodiment of the present
invention, a method as described above is provided, wherein
furthermore a down-decimation technique is applied resulting in
production of a single order estimate per observation frame. The
latter is achieved by applying the FIR filter only once per
observation frame, requiring only a single multiplication of the
phasor-shifted data segment by the vector of filter taps. This
allows designing a filter which not only produces a sharp cut-off
and flat pass-band, but which is also computationally efficient,
and if desired, applicable in real-time. It is to be noticed that
the down-decimation is not endless. It imposes a restriction on the
filter's cut-off frequency and vice-versa. To avoid aliasing, the
order sampling rate must be larger than the twice the filter
bandwidth.
[0090] It is to be noticed that, for both the angle and time domain
formulations of the order tracking method, a Fourier Transform
based computation scheme can also be adopted, which yields the same
results, but better performance for high channel count/orders. Such
a Fourier Transform based computation scheme may comprise applying
a Fourier Transform of the mechanical vibration data, applying a
Fourier Transform of a band-pass FIR filter and combining the two
Fourier Transform results, e.g. by multiplying the spectral lines,
as also described above. Applying the digital FIR filter then is
performed by combining the two Fourier Transform result. Combining
the mechanical vibration data and the system reference data then is
performed indirectly by using a band-pass FIR filter as this
implies centering a FIR filter around the carrier frequency of the
order for which the system reference data is used in order to find
the carrier frequency and by combining the Fourier Transform of
this band-pass FIR filter with the Fourier Transform of the
mechanical vibration data.
[0091] The methods and systems according to embodiments of the
present invention may be used for example in design departments of
automotive companies. They may be used in a way dedicated to the
design of new engines, new gear boxes, for matching engine and
power train components, etc. In one aspect the present invention
therefore also relates to a method for order tracking, whereby the
obtained output regarding the at least one tracked order is used as
feedback for adjusting a design or construction of a physical
system. Based upon the output, a variation of components and
properties of a physical system may be performed. The latter could
be applied in a trial and error fashion, by varying parameters
within a predetermined range, etc. Such a method may be performed
in an automated and/or automatic way, embodiments of the present
invention not being limited thereto.
[0092] In a second aspect, the present invention relates to a
system for order tracking. Such a system may comprise one, several
or all components having the functionality of performing a method
as described in embodiments of the first aspect of the present
invention. The system for order tracking may be made in hardware as
well as in software, in the latter case being suitable for
operating on a computing device. By way of illustration, the
present invention not being limited thereto, an example order
tracking system according to an embodiment of the present invention
is shown in FIG. 4, indicating standard and optional components of
the system. The system 200 comprises an input means 210 for
receiving one or multiple mechanical and/or acoustic vibration data
of a physical system and for receiving system reference data. The
system reference data thereby relates to a parameter of the
physical system influencing the vibration spectrum, such as for
example a rotation speed of a component present in the physical
system. The input means 210 may comprise a separate input means 212
for the mechanical and/or acoustic vibration data and a separate
input means 214 for the system reference data. The input means 212
for the mechanical and/or acoustic vibration data may comprise a
detection means for detecting the mechanical and/or acoustic
vibration data or may be connected to it to receive data or input
signals from it. Such a detection means thus may be part of or
external to the input means 100. The detection means may be adapted
for converting a mechanical and/or acoustic vibration signal in an
electric vibration signal and mechanical and/or acoustic vibration
data. Similarly, the input means 214 for the system reference data
may comprise a detection means for detecting the system reference
data or may be connected to it to receive data or input signals
from it. Such a detection means thus may be part or external to the
order tracking system. Alternatively or in addition thereto, the
input means also may be connected to a memory where the input data
are stored. The input may be received real-time, i.e. by recording
it directly at the physical system and having it directly as an
input, or it may concern stored data. The order tracking system 100
furthermore comprises a means for combining 224 the mechanical
and/or acoustic vibration data and the system reference data and a
means 226 for applying a FIR filter . The means for combining 224
and means for applying 226 may be performed by a processor with
suitable software running on it or by dedicated hardware processor.
Extracting the orders may thus be achieved by determining a complex
envelope of at least one order component from the filtered data.
Such a processor 220 may further optionally comprise a means for
resampling the data 222 to the appropriate domain in which the
applied FIR filter operates. As in principle the different order
components will be present in the processed data, the system may be
adapted for deriving different order components from the data. The
processor 220 may be any suitable processor such as for example a
microprocessor, a digital signal processing device, a programmable
digital logic device such as a Programmable Array Logic (PAL), a
Programmable Logic Array, a Programmable Gate Array or a Field
Programmable Gate Array (FPGA), etc. The system furthermore may
comprise an output means 240 for outputting the obtained order
component information. Such an output means 240 may be a
visualisation means for visualising the obtained results, or it may
be a data port for providing output to an external component. The
output means 240 may be adapted for outputting control information
for controlling a system in agreement with the obtained results.
More particularly, in some embodiments according to the present
invention, the system furthermore may comprise a feedback
calculating means 230 for determining a feedback and/or adapted
control system for adapting the system operation in view of the
obtained order tracking information. The latter may for example be
based on a predetermined algorithm, comparison with previously
obtained results, e.g. stored locally, based on predetermined
rules, based on neural networking etc. Such feedback may be
provided in an automatic and/or automated way.
[0093] In one embodiment, the present invention not being limited
thereto, part of the system or the complete system may be built in
a handheld device. The latter is especially advantageous if the
detection means for detecting the mechanical and/or acoustic
vibrations is incorporated in the hand held device.
[0094] The output of the order tracking system may be used in a
plurality of applications. As described above, the output of the
order tracking system may be used as feedback for controlling the
physical system. Therefore, the present invention also relates to a
self-regulating physical entity comprising both the physical system
and an order tracking system, such that based on the determined
tracked order information, the system can be automatically or
semi-automatically controlled or adjusted. For example, such an
entity may comprise a physical system generating a mechanical
and/or acoustic vibration by a moving component in the physical
system, an order tracking system as described above and a
controller for controlling the physical system taking into account
the results obtained in the order tracking system. The order
tracking system then may be used as feedback module and the system
may be operated according to predetermined standards. Upon
generation of information in the order tracking system, the
controller may either adjust the system parameters in order to
adjust the operation of the order tracking system, leave the
operation of the physical system as is or shut down the physical
system and optionally provide an error message.
[0095] The output of the order tracking system furthermore may be
used as an input for simulation of a mechanical and/or acoustic
vibration, e.g. in simulation software. The latter may for example
be used for software games, test benches, design systems, etc.
Based on the tracked orders, simulation of the sound may be
performed. It thereby is an advantage that the different orders in
the vibration spectra may be determined for one set of conditions,
whereby the simulation may be performed for another set of
conditions, thus allowing to pro-actively determine the
corresponding mechanical and/or acoustic vibration in conditions
not experimentally tested. Such a simulation thus takes into
account the order tracking information determined with the proposed
order tracking method.
[0096] The above-described method embodiments of the present
invention may be implemented in a processing system 500 such as
shown in FIG. 5. FIG. 5 shows one configuration of processing
system 500 that includes at least one programmable processor 503
coupled to a memory subsystem 505 that includes at least one form
of memory, e.g., RAM, ROM, and so forth. It is to be noted that the
processor 503 or processors may be a general purpose, or a special
purpose processor, and may be for inclusion in a device, e.g., a
chip that has other components that perform other functions. Thus,
one or more aspects of the present invention can be implemented in
digital electronic circuitry, or in computer hardware, firmware,
software, or in combinations of them. The processing system may
include a storage subsystem 507 that has at least one disk drive
and/or CD-ROM drive and/or DVD drive. In some implementations, a
display system, a keyboard, and a pointing device may be included
as part of a user interface subsystem 509 to provide for a user to
manually input information. Ports for inputting and outputting data
also may be included. More elements such as network connections,
interfaces to various devices, and so forth, may be included, but
are not illustrated in FIG. 5. The various elements of the
processing system 500 may be coupled in various ways, including via
a bus subsystem 513 shown in FIG. 5 for simplicity as a single bus,
but will be understood to those in the art to include a system of
at least one bus. The memory of the memory subsystem 505 may at
some time hold part or all (in either case shown as 511) of a set
of instructions that when executed on the processing system 500
implement the steps of the method embodiments described herein.
Thus, while a processing system 500 such as shown in FIG. 5 is
prior art, a system that includes the instructions to implement
aspects of the methods for tracking orders in a mechanical and/or
acoustic vibration spectrum using a FIR filter is not prior art,
and therefore FIG. 5 is not labelled as prior art.
[0097] The present invention also includes a computer program
product which provides the functionality of any of the methods
according to the present invention when executed on a computing
device. Such computer program product can be tangibly embodied in a
carrier medium carrying machine-readable code for execution by a
programmable processor. The present invention thus relates to a
carrier medium carrying a computer program product that, when
executed on computing means, provides instructions for executing
any of the methods as described above. The term "carrier medium"
refers to any medium that participates in providing instructions to
a processor for execution. Such a medium may take many forms,
including but not limited to, non-volatile media, and transmission
media. Non volatile media includes, for example, optical or
magnetic disks, such as a storage device which is part of mass
storage. Common forms of computer readable media include, a CD-ROM,
a DVD, a flexible disk or floppy disk, a tape, a memory chip or
cartridge or any other medium from which a computer can read.
Various forms of computer readable media may be involved in
carrying one or more sequences of one or more instructions to a
processor for execution. The computer program product can also be
transmitted via a carrier wave in a network, such as a LAN, a WAN
or the Internet. Transmission media can take the form of acoustic
or light waves, such as those generated during radio wave and
infrared data communications. Transmission media include coaxial
cables, copper wire and fibre optics, including the wires that
comprise a bus within a computer.
[0098] By way of illustration, the present invention not being
limited thereto, a number of examples are shown, illustrating
features and advantages according to embodiments of the present
invention.
[0099] A first example illustrates the new order tracking method in
comparison to other order tracking methods, indicated in FIG. 6.
The simulations consist of a single order with a constant unity
amplitude but oscillating phase, i.e.
X.sub.k(.rho.(.alpha.))=e.sup.i.omega..alpha.. In order to
investigate the errors, the oscillation frequency .omega. was moved
from 0 to 5 in steps of 0.1. Order tracking was done by employing
time-domain DC-estimation, with uniform and Hanning windows
applied, and by employing a method according to an embodiment of
the present invention. The order resolution 1/Q was always 1. For
all .omega. values smaller than 0.5 (the limit of what belongs to
the order), the order estimate was compared to the input order
X.sub.k. For all .omega. values larger than 0.5, the order estimate
was compared to 0, since an ideal order estimator would find this
data or signal to consist entirely of orders different from
X.sub.k. FIG. 6 illustrates the order estimation errors of both
methods when tracking an order that is not constant over the
observation period, i.e. B.sup..alpha..sub.k larger than 0. This
example illustrates that the order tracking method according to
embodiments of the present invention is better than the
DC-estimation based order tracking method. It can be seen that
cross-talk errors occur in the DC-estimation when the order
bandwidth differs from zero. A typical sinc behaviour of
DC-estimation with a uniform window and an inherent cross-talk
error of 0.5 for .omega.=1 can be seen when using a Hanning window.
The new order tracking method does not suffer from order cross-talk
as long as .omega.<0.5, i.e. B.sup..alpha..sub.k<0.5/Q
[0100] By way of illustration, embodiments of the present invention
not being limited thereto, a more detailed description of an
exemplary method and system for order tracking is described below,
with reference to FIG. 7 and FIG. 8.
[0101] The example is worked out for a rotating system, such as a
combustion engine, with a number of shafts S.sub.i, although the
invention is not limited thereto. For the ease of interpretation,
all excitations in the system are supposed to be caused by the
rotation of the shafts, methods and systems according to
embodiments of the present invention not being limited thereto. In
such system, often there are several independent rotations going on
at once. For the sake of simplicity, we assume for this example
only one rotational cause.
[0102] In the example given, all shafts are tied such that their
rotational speeds are proportional. The ratio of the rotation
angles of a shaft S.sub.i and an arbitrary reference shaft S.sub.0
is a rational number as expressed in equation [5]. The rotation
angles of a shaft S.sub.1 thus is indicated as S.sub.1..alpha..
Equation [5] means that if we know the reference shaft angle
S.sub.0..alpha. (rad), we also know the angles of all the other
shafts.
S i .alpha. S 0 .alpha. = S 1 q S 0 p .di-elect cons. Q ; S i q , S
0 p .di-elect cons. N [ 5 ] ##EQU00006##
[0103] The system excitation x at a certain response point depends
on a plurality of system's state .sigma., e.g. torque, throttle,
rotational speed, temperature, etc., and the shaft angles. Since it
suffices to know one angle to know all others, we can state that x
is a function of the state and the reference shaft rotation
angle:
x(.sigma.,S.sub.0..alpha.) [6]
[0104] Since the state .sigma. a is multidimensional, it would be
hard to do repeatable measurements if all of these parameters were
to vary. Therefore, all but one of these parameters is supposed to
be under environmental control, such as for example on a roller
bench for vehicles. Typically, this reduces the state a to just one
parameter, for example the rotational speed of the reference
shaft.
[0105] If the rotational speed of the reference shaft is expressed
as S.sub.0..rho.(rad/s), then the equation for x becomes:
x(S.sub.0..rho.,S.sub.0..alpha.) [7]
[0106] For reasons of convenience, the S.sub.0 prefix will be
omitted henceforth:
x(.rho.,.alpha.) [8]
[0107] Furthermore, since all angles are proportional, as indicated
in equation [5], a section for constant rotational speed .rho. is
actually a periodic function, with period the smallest common
integer multiple of S.sub.i.q, henceforth called Q. The inverse of
the smallest common integer multiple of S.sub.i.q, i.e. 1/Q, is
also known as the order resolution.
[0108] Because of the periodic nature of x, this function
simplifies in the order-domain. Suppose r is the order number, then
the order-domain function is as follows:
X ( .rho. , r ) = 0 if r is not a multiple of 1 Q = X k ( .rho. )
if r = k Q [ 9 ] ##EQU00007##
[0109] The relation between the angle- and order-domain functions
can be formulated as:
x ( .rho. , .alpha. ) = k = - .infin. .infin. X k ( .rho. ) j k
.alpha. Q [ 10 ] ##EQU00008##
where X.sub.k(.rho.) is a continuous complex function, representing
the order envelope of the k/Q'th order component of x. The
amplitude and phase profile of an order component is varying with
rotational speed. This is illustrated in FIG. 7, which shows the
order 2 envelope for an acoustic response point in the passenger
compartment of a vehicle, in the present example being a 4-cylinder
car. In the present example, the order bandwidth B.sup.92.sub.k is
clearly different from zero. The order bandwidth B.sup..rho..sub.k
depends on the system's transfer function characteristics. Orders
crossing a frequency region with strong modal density typically
have a large order bandwidth. Their amplitude and phase profile
rapidly varies with rotational speed.
[0110] For the above example of a rotating shaft machinery, the
order tracking is further illustrated. The goal of order tracking
is to estimate the order profiles X.sub.k(.rho.) from measurement
data, e.g. acoustical or mechanical vibration data. They are
typically estimated by sweeping the rotational speed .rho. over a
certain range in a run-up or coast-down experiment. Of course, also
other types of tests can be performed. A tacho pulse signal is
typically measured to obtain the rotational speed. It is also used
to resample the time-data x(t) to the angle-domain and serves as a
phase reference.
[0111] By resampling the measured time-data x(t) to the
angle-domain, we obtain:
x ( .alpha. ) = .infin. k = - .infin. X k ( .rho. ( .alpha. ) ) j k
.alpha. Q [ 11 ] ##EQU00009##
where the rotational speed .rho. varies with .alpha.. By way of
illustration, embodiments of the present invention not being
limited to it, FIG. 8 shows an example of the rotational speed
.rho. as a function of the rotation angle .alpha. for a linear
engine run-up from 1000 to 6000 RPM in 30 s. Equation [1]J can be
read as a composite amplitude modulation of the orders
X.sub.k(.rho.(.alpha.)) with
j k .alpha. Q ##EQU00010##
the carrier wave for order k/Q. Suppose that the order
X.sub.k(.rho.(.alpha.)) has an angle-domain bandwidth
B.sup..alpha..sub.k, expressed in 1/rad. If all orders are
amplitude modulated into the measured function x(.alpha.),
demodulation should be sufficient to know the orders. As long as
B.sup..alpha..sub.k<0.5/Q, there will be no interference between
all modulations of all orders and they can be picked up separately
from the data.
[0112] Suppose the order X.sub.k(.rho.(.alpha.)) has a bandwidth
B.sup..alpha..sub.k<0.5/Q. Demodulation is then achieved in two
steps. First, the measurement data x(.alpha.) is multiplied per
observation frame with the order carrier wave, such that the
resultant data signal is now centered about zero. Then, a low-pass
filter of bandwidth B.sup..alpha..sub.k and with minimum phase
distortion is applied to the phasor-shifted data to extract the
complex order envelope and remove all the additional side bands
that have been introduced. This is expressed, mathematically, in
equation [12].
X ^ k ( .rho. ( .alpha. ) ) = LowPass ( B k .alpha. , .alpha. ) x (
.alpha. ) j k .alpha. Q [ 12 ] ##EQU00011##
The ideal low-pass filter is the sinc filter:
X ^ k ( .rho. ( .alpha. 0 ) ) = ( sin c ( .alpha. ) ( x ( .alpha. )
j k .alpha. Q ) ) ( .alpha. 0 ) [ 13 ] ##EQU00012##
However, since the sinc filter is of infinite length, it is
replaced by a FIR filter of finite length.
[0113] In the above example, the principle of order tracking
according to embodiments of the present invention is expressed in
the angle-domain formulation. As discussed above there are
possibilities to avoid the need for resampling of the measurement
data. Next to the angle-domain formulation, embodiments of the
present invention therefore also cover the following time-domain
variant:
X ^ k ( .rho. ( .alpha. 0 ) ) = .intg. - .infin. .infin. sin c (
.alpha. 0 - .alpha. ( t ) ) ( x ( t ) j k .alpha. Q ) .alpha. t t [
14 ] ##EQU00013##
[0114] By tracking the angle .alpha. over time, for any given
rotational speed .rho. during an experiment with varying system
parameter, e.g. during run-up or coast-down experiments with
respect to the rotational speed, the corresponding angle
.alpha..sub.0 can be found. Subsequently, a FIR filter can be
defined for .alpha..sub.0 that is an approximation of the ideal
sinc filter
[0115] This time-domain approach saves you from resampling the time
data to the angle-domain and the error incurred by doing so, and
yields an adaptive FIR filter that can be computed once for each
desired rotational speed, and applied on all system response points
of interest.
[0116] It is to be noticed that, for both (i) the angle domain
method with angle-domain FIR filter (as approximation for the ideal
sinc filter in [13]) and (ii) the time domain variant with adaptive
time domain FIR filter (as approximation for the ideal sinc filter
in [14]), a Fourier Transform based computation scheme can also be
adopted, which yields the same results, but better performance for
high channel count/orders.
[0117] The proposed order tracking method works properly as long as
the order bandwidth in the angle-domain is smaller than half the
order resolution, i.e. B.sup..alpha..sub.k<0.5/Q. If not, there
is inherent order cross-talk and adjacent orders can not longer be
separated. B.sup..alpha..sub.k depends on three parameters: (i) the
order bandwidth B.sup..rho..sub.k, which depends on the system's
transfer function characteristics as mentioned before, (ii) the
instantaneous angular acceleration d.rho./dt and (iii) the
instantaneous rotational speed .rho.. If .alpha.(t) is more or less
parabolic over a run-up, one can prove that:
B k .alpha. .apprxeq. .differential. .rho. t B k .rho. .rho. [ 15 ]
##EQU00014##
This means that, for a certain rotating system, the risks for
inherent order cross-talk will increase with increasing run-up
speed. There is a maximum tolerable run-up speed for which
B.sup..alpha..sub.k=0.5/Q. As long as this speed is not exceeded
during the measurements, the order components can be well
separated, which is not the case with the existing DC-estimation
methods.
[0118] It is to be understood that although preferred embodiments,
specific constructions and configurations, as well as materials,
have been discussed herein for devices according to the present
invention, various changes or modifications in form and detail may
be made without departing from the scope of this invention as
defined by the appended claims. For example, any formulas given
above are merely representative of procedures that may be used.
Functionality may be added or deleted from the block diagrams and
operations may be interchanged among functional blocks. Steps may
be added or deleted to methods described within the scope of the
present invention.
* * * * *