METHOD AND SYSTEM FOR EVALUATING A FLOW RATE OF A FLUID
FIELD OF THE INVENTION
The present description relates to a method of
5 evaluating a fluid flow rate coming from a tank, and more
particularly it relates to making such a method reliable.
The description also relates to a system enabling the
method to be performed.
10 TECHNOLOGICAL BACKGROUND
A known evaluation method for evaluating a flow rate
of a fluid coming from a tank comprises measuring a level
of the fluid in the tank. In simple circumstances, e.g.
assuming that the level measurement is continuously
15 available, that the tank is cylindrical in shape, and
that fluid does not accumulate anywhere between the
outlet from the tank and the point at which the flow rate
is evaluated, then the fluid flow rate can be evaluated
with certainty merely by using an affine function.
2 0 Nevertheless, in practice, the measurement of the
fluid level is rarely continuously available, which means
that it is necessary to make use of interpolations or of
estimators during periods when the level measurement is
unavailable. However, uncertainties and biases can exist
25 in association with level measurements and/or with the
estimators used. Furthermore, the tank may be of noncylindrical
shape, thereby introducing nonlinearity into
the evaluation function. There therefore exists a need
for a novel type of method of evaluating a flow rate.
30
SUMMARY OF THE INVENTION
The present description relates to an evaluation
method for evaluating a flow rate of a fluid coming from
a tank, the method comprising measuring a level of the
35 fluid in the tank and being characterized in that it
comprises an estimation step for estimating the flow rate
of the fluid by using an unscented Kalman filter, said
estimation step comprising an obtaining step for
obtaining the raw fluid flow rate and, when a level
5 measurement is available, a correcting step during which
the obtained raw flow rate is corrected as a function of
the level measurement.
A Kalman filter is a method of calculation that can
be performed by a computer and that makes it possible to
10 estimate the states of a dynamic system from an input
data series that is incomplete or noisy. A Kalman filter
is modelled by a state equation (I), which represents
variation of the dynamic system, and by a measurement
equation (2), which represents the relationship between
15 measured observable magnitudes and the intrinsic state of
the system. These equations are of the following type:
20 where k is the current instant, k+l is the following
instant, x is the (intrinsic) state of the system, u is
the input data, y is the (observed) measured magnitude, f
is the state function, h is the measurement function, and
v and w are noise (respectively measurement noise and
25 state noise). The variables x, y, u, v, and w, may all be
vectors having one or more components. In order to
implement a Kalman filter in a method of the invention,
the state x comprises the fluid flow rate that is
observed from the measurement y, which by way of example
30 comprises the level of fluid in the tank. By way of
example, the input data u comprises parameters of the
system, such as the speed of a pump and/or the pressure
of the fluid at one or more positions in the fluid
circuit. The input data u may be estimated from
35 measurements other than y, or it may be operating data of
the system.
The Kalman filter comprises an obtaining step for
obtaining a value of the state (k+l) following the
current state (k) on the basis of input data u,, and a
correction step for correcting the value obtained from
5 the measurement y,<. These steps are widely described in
the literature and they are not explained again herein
for the general situation.
An unscented Kalman filter (UKF), as described in "A
new extension of the Kalman filter to nonlinear systems"
10 (Julier and Uhlmann, in the llth international symposium
on Aerospace/Defence sensing, simulation and controls,
Vol. multi sensor fusion, tracking and resource
management 11, Orlando, Florida, 1997), is a variant of
the Kalman filter that is particularly adapted to
15 nonlinear systems as may apply to the flow rate of a
fluid as a function of the level in the tank from which
the fluid comes. In addition to the steps of a Kalman
filter, and unscented Kalman filter includes a step
referred to as the "unscented transformation", which
20 consists in approximating the current state x, by a
Gaussian random variable represented by a set of suitably
chosen points referred to as sigma-points. This set of
points accurately reproduces the mean and the covariance
of the Gaussian random variable. During the obtaining
25 step, the state equation (1) is applied to each of the
sigma-points in order to obtain the following state.
This gives rise to a set of sigma-points at the instant
k+l, which points reproduce the mean and the covariance
of the following state x,,, with accuracy that reaches the
30 second order (in terms of a Taylor series analysis). In
contrast, an extended Kalman filter, which is another
variant of a Kalman filter used with nonlinear systems,
achieves accuracy of the first order only. Furthermore,
unlike an extended Kalman filter, a UKF does not require
35 any costly explicit linearizing calculation (calculating
Hessian or Jacobj an matrices) .
The obtaining step consists in an optionally
provisional initial determination of the flow rate that
it is desired to evaluate. It may be performed by
measurement, by calculation (in particular by using the
5 state equation (1) of the UKF), or by a combination of
both. In other words, the state x of the UKF comprises
the flow rate that it is desired to evaluate. The raw
flow rate obtained by the obtaining step is then
subjected to the correction step.
10 As mentioned above, the correction step makes use of
the results of the measurement step. The measurement
step does not assume that the level measurement is
available continuously: it consists in verifying whether
a measurement is available, and if so in taking it. If
15 the measurement is not available at some instant, then
the measurement step does not return any data to the
correction step, and consequently the flow rate that is
obtained at that instant is not corrected.
The evaluation method may be used to evaluate an
20 instantaneous flow rate, an accumulated flow rate, or any
other magnitude that is calculated on the basis of the
flow rate.
The evaluation method thus provides an evaluation of
the flow rate of the fluid that is accurate, consistent
25 with the measurements of level in the tank, and that
intrinsically corrects for the biases and errors of the
obtaining step, as a result of using a UKF. Furthermore,
the method is compatible with a tank of any shape, and in
particular with tanks that are not cylindrical. Also, by
30 using the UKF state equation, the obtaining step makes it
possible to evaluate the flow rate of the fluid in a
manner that is accurate, even when level measurements are
not available. Finally, the method adapts well to
variations in flow rate and to variations in the
35 operating point of the system in which the flow rate is
being measured.
In certain embodiments, the raw flow rate value is
measured by at least one sensor, in particular a
flowmeter. In these embodiments, the obtaining step is
essentially performed by the flowmeter and the correction
5 step serves to correct the flowmeter on the basis of the
measured level values. When a flowmeter is present, the
evaluation method thus makes it possible to make it
reliable, to reset it, and/or to recalibrate it.
In certain embodiments, the raw flow rate value is
10 calculated by mathematical estimation with iteratively
evaluated coefficients, in particular by using an
artificial neural network. The term "mathematical
estimation with iteratively evaluated coefficients" is
used to exclude physical measurements and mathematical
15 expressions in which the coefficients are constants and
known explicitly a priori. The coefficients that are
evaluated iteratively may be evaluated in particular by
successively adapting a model to a set of data, as is
done by an artificial neural network, or by an equation
20 that is solved numerically having a solution that
converges.
An artificial neural network (ANN) is a calculation
model comprising one or more neurons, each neuron being
provided with a transfer function. An AAN thus possesses
25 an overall 'ransfer function suitable for calcn:l.ating at
least one output as a function of at least one input.
The transfer functions of each neuron or the relative
weights of the neurons in thenetwork may be weighted by
biases and by coefficients referred to as synaptic
30 weights (or more simply as weights). The weights may be
modulated as a function of training the AAN. Training
consists in providing the AAN with a set of situations in
which the inputs and the outputs are known. During
training, the AANadapts the biases and the synaptic
35 weights so that they comply with the training situations,
possibly with a certain amount of tolerance. AANs are
thus mathematical expressions having coefficients that
are adapted iterative1.y as a function of training. The
biases and the weights, once they have been determined at
the end of the stage of training, may optionally remain
constant during the subsequent stage of operation.
5 An M N is thus capable of intelligently modelling a
system by learning from the real behavior of said system,
without it being necessary to know the theoretical laws
that govern it. An AAN also possesses the capacity to
generalize (also known as "inference"), i.e. it is
10 capable of determining the output values for a situation
for which it has been given the input values, even if it
has not been trained to that situation during the
training stage, provided that the inputs are contained
within a validity domain (in other words, it is ensured
15 that the input values for the situation that is to be
calculated lie between, or close to, the extreme input
values that have been used for training). This is
particularly useful for systems that present a wide range
of operating points and for which, in an industrial
20 situation, it is inconceivable to envisage setting the
parameters explicitly for all possible situations. For
better accuracy, it is necessary to verify that the
training situations constitute a suitably fine mesh
covering the operating domain. Finally, an AAN is a
25 system that is easy to adapt. These advantages are also
valid for other types of mathematical expression having
coefficients that are evaluated iteratively.
Furthermore, in such implementations, the obtaining
step is thus performed by a mathematical estimation,
30 which makes it possible to omit the flowmeter and achieve
savings in cost, in weight, and in bulk.
Unlike certain systems known elsewhere, in which an
unscented Kalman filter is used to determine the synaptic
weights of an AAN, the present method makes use o f a
35 mathematical expression having coefficients that are
evaluated iteratively (in particul.ar an M N ) by
incorporating it in the obtaining step of the UKF. Its
operation and purpose are thus entirely different.
In certain embodiments, the mass of fluid in the
tank is a non-linear function of the level of fluid in
5 the tank. In certain embodiments, the tank is not
cylindrical. In certain other embodiments, the tank is a
cylinder having generator lines that are not
perpendicular to the mean level of the fluid in the tank.
It should be recalled that a cylinder is a surface
10 defined by sweeping a straight line of fixed direction,
referred to as a generator line, around a closed plane
curve. The term "cylinder" is also used to designate a
truncated cylinder, i.e. the solid that is defined by a
cylinder and by two parallel planes, the planes not being
15 parallel to the generator lines of the cylinder.
The above characteristics apply to the shape of most
tanks, and in particular tanks having spherical end
walls. When the tank is not cylindrical, the speed at
which the tank empties (i.e. the derivative of the level
20 as a function of time) is not an affine function of the
outlet flow rate from the tank. As mentioned above, this
nonlinearity is taken into account particularly well by a
UKF .
In certain embodiments, a state of the unscented
25 Kalman filter includes a bias of the raw flow rate value.
In certain embodiments, it is assumed that the flow rate
is equal to the sum of the raw flow rate obtained in the
obtaining step plus a bias (which may be positive or
negative). More generally, in other implementations, it
30 is assumed that the flow rate is an affine function of
the raw flow rate that is obtained, the bias then being a
vector constituted by the coefficients of the affine
function. The fact that the state of the Kalman filter
includes the bias as such makes it possible to.extract
35 and use the value of the bias subsequently, e.g. in order
to detect an anomaly when the value of the bias exceeds a
certain threshold.
In certai.n embodiments, a state of the unscented
Kalman filter incl-udes the raw value of the flow rate and
a bias of this value.
In certain ernbodi.ments, the evaluation method
5 further includes a step of filtering fluctuations in the
fluid level. Fluid level fluctuations are transient
variations in the fluid level for a constant volume of
fluid in the tank, as contrasted to changes in level
resulting from the fluid flow rate. Fluctuations in
10 fluid may be due to the fluid sloshing in the tank or to
wideband noise in the signal (white noise associated
essentially with interactions between the tank and its
mechanical and hydraulic environment). By way of
example, this filtering step may be performed with a
15 lowpass filter or by the UKF including rejection of the
resonant mode of the sloshing. For example, it is
possible to write the fluid level in a form comprising a
fluctuation function and to determine the coefficients of
this fluctuation function (e.g. the amplitudes,
20 frequencies, and phases of the main terms of its Fourier
series analysis) by including these coefficients in the
state vector of the UKF.
Such a filtering step, serves to attenuate noise in
the level measurements and to make the evaluation method
25 even more reliable.
The present description also relates to a method of
evaluating two flow rates of fluids coming respectively
from a first tank and from a second tank, wherein the
flow rates of the fluids are evaluated by separately
30 implementing: a first evaluation method comprising a step
A
of estimating the flow rates of the fluids ( d , ) using an
unscented Kalman filter, in which no level measurement is
taken into account in a step of correcting the unscented
Kalman filter; a second method of the above proposed
35 type, wherein only a level measurement of the first tank
is taken into account; a third method of the above
proposed type, wherein only a level measurement of the
second tank is taken into account; and a fourth method of
the above proposed type, wherein both level measurements
are taken into account; and wherein the flow rates that
are returned are the flow rates as evaluated by that one
5 of the four methods that takes account exactly of the
measurements that are available.
In the present method, it is desired to evaluate two
flow rates of values that are corrected on the basis of
two level measurements. Both level measurements may be
10 available simultaneously, both measurements may be
unavailable simultaneously, or only one or the other of
the two measurements may be available. There are thus
four level measurement availability situations.
The idea of such a method is to evaluate the two
15 flow rates using four variants of the above-described
method, and then to select the variant that is the most
appropriate for the level measurements that are
available. The four methods differ in that they take
account of some, all, or none of the level measurements
20 that are returned by the measurement step. Each of the
four methods can thus be optimized as a function of the
measurements that it is suitable for taking into account.
Among the four methods used, the method retained is
the method that takes account exactly of the measurements
25 that are available, i.e. the method that, at the instant
under consideration, takes account of the measurements
being returned by the measurement step and does not take
account of the measurements that are not being returned
by the measurement step. This selection thus consists in
30 selecting the method that is the best adapted to the
situation under consideration. Selection from among the
four methods may be performed before, after, or during
application of the methods. Also, this method can be
generalized to a greater number of flow rates and/or of
35 measurement availability situations.
The present description also provides an evaluation
system for evaluating a flow rate of a fluid coming from
a tank, the system comprising measurement means suitable
for measuring a fluid level in the tank and being
characterized in that it includes estimation means for
estimating the flow rate of the fluid using an unscented
5 Kalman filter, said estimation means comprising obtaining
means for obtaining the raw fluid flow rate and
correction means connected to the obtaining means and to
the measurement means and configured to correct the raw
flow rate as obtained by the obtaining means as a
10 function of the level measured by the measurement means.
Such a system is particularly suitable for performing the
above-descri.bed method.
The present description also provides a propulsion
system, in particular for a space launcher, the system
15 comprising two tanks, each containing a propellant, a
combustion chamber into which the two propellants are
injected, and an evaluation system as described above for
evaluating the flow rate of at least one of the
propellants. For a propulsion system, it is particularly
20 important to estimate propellant flow rates correctly.
Also, a lightening of mass and an increase in compactness
due to omitting flowmeters likewise constitute looked-for
savings.
If such a propulsion system has a system for
25 evaluating two flow rates, or a system for evaluating
each of the flow rates, it is possible to calculate the
mixture ratio of the propellants, i.e. the ratio of the
propellant flow rates at the inlet to the combustion
chamber. The mixture ratio of two propellants is an
30 important parameter for controlling the propulsion
system.
The present description also relates to a program
including instructions for executing steps of the
, evaluation method according to any.of the above described
35 implementations when said program is executed by a
computer.
In a particular implementation, the various steps of
the evaluation method are determined by computer program
instructions.
The program may use any programming language, and
5 may be in the form of source code, object code, or code
intermediate between source code and object code, such as
in a partially compiled form, or in any other desirable
form.
The present description also provides a computer-
10 readable data medium storing a computer program including
instructions for executing steps of the evaluation method
according to any of the above described implementations.
The data medium may be any entity or device capable
of storing the program. For example, the medium may
15 comprise storage means, such as a read only memory (ROM),
for example a compact disk (CD) ROM or a microelectronic
circuit ROM, or indeed magnetic recording means, for
example a floppy disk or a hard disk.
Furthermore, the data medium may be a transmissible
20 medium such as an electrical or optical signal that can
be conveyed via an electrical or optical cable, by radio,
or by other means. The program of the invention may in
particular be downloaded from a network of the Internet
type.
25
BRIEF DESCRIPTION OF THE DRAWINGS
The invention and its advantages can be better
understood on reading the following detailed description
of implementations of the invention given as non-limiting
30 examples. The description refers to the accompanying
drawings, in which:
Figure 1 shows a propulsion systems fitted with a
first embodiment of a flow rate evaluation system;
Figure 2 plots the mass.of propellant contained in
35 the tanks of the Figure 1 propulsion system as a funcLion
of level;
Figures 3A and 3B show the availability of
measurements from the level probes in the tanks as a
function of time;
Figures 4A to 4C show the application of the
5 Figure 1 flow rate evaluation system;
Figure 5 shows a propulsion system fitted with a
second embodiment of a flow rate evaluation system; and
Figure 6 shows a fluid circuit fitted with a third
embodiment of a flow rate evaluation system.
10
DETAILED DESCRIPTION OF THE INVENTION
Figure 1 shows a propulsion system 50, in particular
for a space launcher, comprising two tanks 20 and 21,
each containing a propellant (e.g. respectively liquid
15 hydrogen and liquid oxygen), a combustion chamber 30 into
which the two propellants are injected, and a system 10
for evaluating the flow rate, of the propellants at the
inlet to the combustion chamber 30. The combustion gas
develops thrust on being ejected via a nozzle 32
20 downstream from the combustion chamber 30.
Specifically, the propulsion system 50 is an
integrated flow system in which the heated propellant
(e.g. hydrogen) drives turbopumps 24 and 25 prior to
being reinjected into the combustion chamber 30. Two
25 regulation valves V1 and V2 serve to modulate t11e flow
rate of heated propellant entering the turbines of the
turbopumps 24 and 25 so as to control the flow rate of
liquid propellants pumped by these turbopumps 24 and 25.
As can be seen in Figure 1, the tanks 20 and 21 are
30 non-cylindrical tanks. More particularly, in the example
shown, they are tanks with spherical ends. As a result,
the relationship between the level of propellant in each
tank and the mass of propellant in said tank is not
linear. Specifically, an example of such a relationship
35 is given in Figure 2. Curve G20 (or curve G21 as the
case may be) plots the mass m - of propellant in the tank
20 (or in the tank 21) as a function of the level -n of
propellant in the same tank. Each of these curves G20
and G21 includes a substantially linear central portion
(corresponding to a substantially cylindrical central
portion of the tank). For the highest levels or the
5 lowest levels, the curves are flattened, which means that
the tanks are narrower compared with their central
portions. This appearance of the curves is
characteristic of the ends of the tanks having a shape
that is hemispherical or the like. In the present
10 example, the non-linearity of the relationship between
propellant flow rate at the inlet to the combustion
chamber 30 and the level of propellant in the tanks 20,
21 comes not only from the shape of the tanks
(geometrical non-linearity) as explained above, but also
15 from a second non-linearity associated with flow rate
being expressed as a function of the operating parameters
of the propulsion system (mechanical and thermodynamic
non-linearities) .
As shown in Figure 1, the tanks 20 and 21 have
20 respective level probes 22 and 23 for measuring the level
in each tank. The size and the shape of the tanks and
the configuration of the level probes 22 and 23 may vary
from one tank to another. Each level probe 22, 23
consists of a set of sensors. These sensors return a
25 signal that can be taken into account only while they are
being uncovered, i.e. while they are at least partially
above the free surface of the propellant contained in the
tank. For example, curves showing the availability of
the level probes 22 and 23 as a functionof time -t during
30 operation of the propulsion system 50 are plotted
respectively in Figures 3A and 3B. Since the tanks 20
and 21 empty at different speeds, the availability curves
for the level probes 22 and 23 are generally different.
Availability has value 1 when the level probe is in the
35 process of being uncovered and is capable of sending a
measurement; otherwise availability has the value 0.
As shown in Figure 3A, the level probe 22 is made up
of a plurality of segments and it is in the process of
being uncovered between t1=10 seconds (s) and t2=40s and
also between t5=120s and t7=150s. During the remainder
5 of the time, its availability is zero, i.e. the level
probe 22 does not return any measurement: the level of
propellant lies between two consecutive sensors.
In analogous manner, as shown in Figure 3B, the
level probe 23 is in the process of being uncovered
10 firstly between t3=60s and t4=90s and secondly between
t6=130s and t8=160s. During the remainder of the time,
the level probe 23 is not available.
It can be seen from Figures 3A and 3B that the level
probes 22 and 23 provide measurements intermittently.
15 Furthermore, the periods of availability of the level
probes 22 and 23 do not necessarily coincide. The first
period during which the level probe 22 is in the process
of being uncovered, from tl to t2, is completely separate
from the first period during which the level probe 23 is
20 in the process of being uncovered, from t3 to t4, whereas
the second period during which the level probe 22 is in
the process of being uncovered, from t5 to t7, overlaps
the second period during which the level probe 23 is in
the process of being uncovered, from t6 to t8, for a
25 period of ten seconds from t6 to t7. It is thus possible
that the measurements supplied by the level probes 22 and
23 are not available simultaneously.
The level probes 22 and 23 are connected to a flow
rate evaluation system 10, as shown in Figure 1. As
30 mentioned above, the evaluation system 10 has measurement
means 17 suitable for measuring the level of fluid in the
tank. The measurement means 17 comprise the level probes
22 and 23 and an acquisition card 19 to which they are
connected.
3 5 The evaluation system 10 has means for estimating
the flow rate of each propellant by using an unscented
Kalman filter. These are calculation means comprising in
particu1.ar a computer 11 that of which the acquisition
card 19 is part. Specifically, the estimation means
comprise an initi-alization device 12, a transformation
device 14, an obtaining device 16, and a correction
5 device 18. In addition to the level measurements
collected by the measurement means 17, the evaluation
system 10 makes use as input data of data about the
operation of the propulsion system 50. For example,
there can be seen an acquisition device 15 connected to
10 the turbopumps 24 and 25 so as to receive data about the
speeds of rotation of the turbopumps and the pressures of
the propellants at the outlets from the turbopumps.
Other data may also be collected. Furthermore, the
acquisition device 15 may be connected to other
15 components or locations of the propulsion system 50 in
order to acquire other data. For example, it may also be
connected to the combustion chamber 30 to measure the
pressure of the gas in the combustion chamber 30.
An unscented Kalman filter is an iterative filter,
20 each new estimate being calculated on the basis of the
preceding estimate and of current data. The values
returned by the correction device 18 serve both as input
values to the transformation system 14, thus providing
the iterative operation of the evaluation system 10, and
25 also as ove:call output values. These output val.ues may
be used for various purposes, e.g. for monitoring the
operation of the engine or for regulating the engine, in
particular for adjusting the opening of the bypass valves
V1 and V2 as a function of the evaluated flow rates.
30 In Figure 1, where k is the current instant (or the
current iteration), the following notation ,. is used:
xk the current state, xk an estimate of its mean
value, and Pk its covariance matrix;
Qk and Rk the covariance matrices respectively of
35 the state noise wk and of the measurement noise vk of the
Kalman filter (cf. above-described equations (1) and
(2)), that are assumed to be known -a -pr-io ri, knowing that
the measurement noise can be measured;
,Sik the it'' sigma point at instant k;
uk the input data;
A
5 ~ ( ~ + ~ tl h~ e, raw value of the state x obtained at
instant ktl, knowing the same value as instant k;
P(k+iltkh,e raw covariance matrix of the state x at
the instant kt1 knowing the covariance matrix Pk;
y, the measured values from the measurement means
10 17; and
A
xki1 the value of the state x at instant k+l
corrected as a function of the level measurements
measured by the measurement means 17, and Pkili ts
covariance matrix.
15 The state x,< of the unscented Kalman filter selected
in the present embodiment comprises the fuel level n,,, the
flow rate qk estimated by the ANN, and the bias E, of the
flow rate. This gives:
xk = [nkr q k r E k l T
20 The state of the UKF may have as many levels, flow rates,
and biases as the number of flow rates that it is desired
to evaluate using the UKF. In the example of Figure 1,
the magnitudes n, q, and E are vectors, each having two
components, one of which refers to the propellant of the
25 tank 20 and the other to the propellant of the Lank 21.
For reasons of clarity, and unless mentioned to the
contrary, the description below relates to only one flow
rate, however the elements described are equally valid
when there is more than one flow rate.
3 0 The initialization device 12 is configured to supply
A
the transformation device 14 with an initial state x,,
Po, which is a function of the characteristics of the
propulsion system 50.
The transformation device 14 is configured to
35 perform the unscented transformation of the UKF at each
instant k, i.e. to create a set of sigma points S,k from
a
the value xk and the covariance matrix Pi, approximating
the current state xi,.
The obtaining device 16 is configured to perform the
obtaining step of the evaluation method. In the present
5 implementation, the obtaining step is implemented by an
artificial neural network. This ANN provides the raw
propellant flow rates at the inlets of the corresponding
turbopumps 24 and 25 taking as its inputs the pressures
of said propellants at the outlet from the pumps, the gas
10 pressure in the combustion chamber 30, and/or the speed
of rotation of said turbopumps. Other things being
equal, the greater the amount of input data (giving a
corresponding number of situation-discriminating
criteria), the more accurate the estimate supplied by the
15 ANN. In particular, the ANN may be of the multi-layer
perceptron type, in particular having a single hidden
layer for the various sets of inputs, being established
on the basis of a database corresponding to a map
obtained from experimental data or from physical models.
2 0 Empirically, it is found that the flow rate supplied
at the output of the ANN is noisy. In this
implementation, a lowpass filter is applied thereto,
specifically a first order filter. By writing qk for the
flow rate obtained by the obtaining device 16 at instant
25 k, AN& for the function applied by the ANN to the input
data ukr At for the time step between k and k+l, and T for
the time constant of the filter (of the order of one
second in this example), an example of such a filter is
an expression of the following type:
It is also assumed that the flow rate d is the sum
of the raw flow rate q returned by the ANN plus an
35 unknown bias E, which may be positive or negative,
representing the effects of errors in modeling the flow
rate. In other words, for each propellant, the following
relationship applies:
4 =q,+E, (4)
In other implementations, equation (4) may be
generalized in the following form:
d, = Ekq, + E;
in which the bias E is a vector and is applied to the
flow rate in the form of an affined function. In
particular, the coefficient E; makes it possible to take
account of a multiplicative bias, while the coefficient
E; serves to take account of an additive bias. In the
above first example of equation (4),
E:=1 and E: =Eh.
For the obtaining device 16, it is assumed that the
bias E is constant; this does not prevent the bias E from
being corrected subsequently by the correction device 18.
This assumption can be expressed by the following
relationship:
Ek+l = Ek (5)
Other types of relationship for variation in the
bias Ek are possible for the obtaining device 16, for
example bias that is proportional to the thrust of the
propulsion system 50, or indeed bias that increases as a
function of the square of the distance from the nominal
operating point at which it can be assumed that the bias
is at its smallest (since the system at that point is
best known by definition). Thus, equations (3), (4), and
(5) define equations for variation in the flow rate
relying on the ANN implemented in the obtaining device
16.
Furthermore, the obtaining device 16 also has a
model for variation in the fuel levels nk in the tanks.
By writing that the mass of fuel nz,< decreases at each
time step At by a quantity Alxdk and that the mass is
associated with level by the functions G20 and G21 (cf.
Figure 2; these functions are referred to below
generically by the letter G), then the following
relationship is obtained for each propellant:
nk+, = G (G-I (M, ) - at x (qk + E~ ))
where G-I is the inverse of the function G.
5 The operation of the evaluation device 10 is
described below in detail. The initialization device 12
initializes the initial state x,, e.g. taking the initial
filling level of the tanks, a flow rate of zero, and a
bias of zero. The initialization device 12 supplies the
*
10 transformation device 14 with the values x,, Po
corresponding to the initial state. For this
calculation, the state x is assumed to be a random
Gaussian variable of means 2 and of covariance P.
At each iteration k, the transformation device 14
15 calculates an enlarged state vector
x, = [x, Vk w, IT
Its covariance matrix PXk is the block diagonal matrix
formed by the respective covariance matrices Pkr Qk, and
Rk. The covariance matrices Qk, R,, are obtained
20 empirically and stored in a memory 13. Alternatively, or
in addition, the measurement covariances Rk may be
calculated automatically by estimating the variances of
measurement noise vk over a moving time window.
The transformation device 14 generates a set of
25 sigma points corresponding to the Gaussian random
variable xkr Pn that approximate the current state Xk.
The sigma points S,k are generated using the conventional
unscented Kalman filter technique, which is not described
in detail herein. Each sigma point SIkr which has the same
30 structure as the vector xk, is supplied to the obtaining
device 16.
The role of the obtaining device 16 is to obtain an
initial estimate (raw value) of the state vector at
, instant k+l, knowing an estimate for that vector at
35 instant k, and data about the propulsion system 50
(specifically the input data uk) AS mentioned above,
this obtaining is performed using equations (3), (4),
(5), arid (6) which make use of an ANN. Insofar as the
ANN is a predictive model, the obtaining step may be
referred to herein more particularly as a prediction
step. The variations in noise vk and wk are determined
using the conventional methods that are employed when
using an unscented Kalman filter. For the state noise,
in the specific situation when use is being made of a
model that has been constructed (such as an ANN), it is
possible to compare the results of the model with known
situations in order to obtain a map showing the accuracy
of the ANN in its domain of validity.
The values of the sigma points S,,, at instant k+l,
supplied by the ANN are then used to determine at the
output of the obtaining device 16 a (predicted) obtained .
value ~ ( ~ + ~ fl o~r ) t he state x at the instant k+l, knowing
the value xk at the instant k, and the covariance matrix
P(k+llko,f the state x that the instant k+l, knowing the
covariance matrix Pk. As shown in Figure 1, these values
are then supplied to the correction device 18.
The correction device 18 then corrects the values
obtained by the obtaining device 16 when measurements are
available. For each propellant, if the level measurement
is available (i.e. if the corresponding level probe is
being uncovered), the state value x ~ +is~ c orrected as a
function of the difference between the measured level yk
and the predicted level (the level that has been
A
obtained) y k . The state value is corrected in particular
by a va'lue proportional to said difference, the
proportionality factor being referred to as the "Kalman
gain". The Kalman gain is calculated in conventional
manner from sigma points and from the level measurement.
Otherwise, if the level measurement is not available, it
is the state value x, as determined using equation (6) by
the obtaining device 16 that is retained, e.g. by setting
the Kalman gain to zero. Depending on whether no, one,
or two level measurements are available (four possible
situations), the correction device 18 corrects the flow
rates obtained by the obtaining device 16 accordingly.
The correction device 18 thus has an incorporated
selection function that adapts to the measurements that
are available.
5 A variant is shown in Figure 5, in which
distinguishing between measurement-availability
situations is performed by arranging four calculation
functions lla, llb, llc, and lld in parallel in the
evaluation system 110, which functions are incorporated
10 in a calculation unit 111 and each of which is set to
cover one of the four above-mentioned measurementavailability
situations. In Figure 5, unchanged portions
of the propulsion system 50 (in particular the propulsion
chamber 30 and the inputs to the calculation unit) are
15 not shown. In addition, each calculation function lla,
lb, llc, and lld has an architecture that is similar to
that incorporated in the computer 11.
The calculation function lla evaluates the fluid
flow rates coming from the tanks 20 and 21 without taking
20 account of level measurements. The correction device 18
provided within the calculation unit lla is thus not
used. The calculation function llb evaluates the flow
rates of fluid from the tanks 20 and 21 while taking
account only of measurements returned by the level probe
25 22, when such measurements are available. In similar
manner, the calculation function lld evaluates the fluid
flows from the tanks 20 and 21 while taking account only
of the measurements returned by the level probe 23, when
they are available. Finally, the calculation function
30 ilc evaluates the flow rates of fluid from the tanks 20
and 21 by taking account of measurements returned by both
of the level probes 22 and 23, when available.
The flow rate values evaluated by the calculation
functions lla, llb, llc, and lld are transmitted to a
35 selection device 118. The selection device 118 is also
connected to the level probes 22 and 23 in order to know
when they are available. The selection device 118 thus
makes a selection from among the four sets of flow rates
it has received, as a function of the availabi1j.t~ of
measurements returned by the level probes 22 and 23. At
its output, the selection device 118 returns the set of
5 flow rates supplied by the calculation unit that takes
account exactly those measurements that are available.
For example, if only the measurement returned by the
level probe 22 is available, then the correction device
118 forwards the set of flow rates received from the
10 calculation unit llb.
In a variant, the selection device 118 may be
upstream from or even at the same level as the
calculation functions lla, llb, llc, and lld.
Under all circumstances, the evaluation system 10,
15 110 thus serves to reset the value obtained by the
obtaining device 16 on the basis of measurements that are
discontinuous and asynchronous.
The method performed by the evaluation system 10
enables flow rates to be evaluated instant by instant.
20 As can be seen in Figure 1, in order to evaluate
successive flow rates, a recurrence loop makes it
possible to pass to the following instant and to
reiterate the above-described steps. At each step, the
evaluated propellant flow rate, i.e. the obtained and
25 then corrected flow rate is:
in which relationship the estimated raw flow rate qk is
determined essentially by the ANN and the estimated bias
I Ek is determined essentially by the UKF.
3 0 An application example is described below with
reference to Figures 3A-3B and 4A-4C. Figures 4A-4C show
I the operation of the propulsion system 50 during two
1 stages (two operating points) each lasting one hundred
, , seconds. Figure 4A shows variation in the propellant
35 flow rate coming from the tank 20 and entering the
combustion chamber 30, as estimated by the ANN alone
(curve Q20a) and by the evaluation devicc 10 (curve
Q20b). By way of comparison, the real value of the flow
rate is also plotted (curve Q20c). As can be seen in
Figure 4A, during the initial seconds, the flow rate
estimated by the ANN alone (curve Q20a) is closer to the
5 real flow rate (curve Q20c) than is the flow rate
estimated by the evaluation device (curve Q20b). This is
due to the arbitrary nature of the values supplied by the
initialization device 12. After a few seconds, this
difference is absorbed.
10 At instant t=tl (lOs), as shown in Figure 3A, the
level probe 22 is being uncovered and the measurement
means 17 acquire level measurements. On the basis of
these measurements, the correction device 18 can thus
correct the values supplied by the obtaining device 16.
15 This leads to a transient regime in the curve Q20b,
followed by the evaluated flow rate stabilizing at a
level that is close to the real flow rate (curve Q20c).
The level probe 22 continues to be uncovered until t=t3
(40s) after which it is once more unavailable. Between
20 t3 and t5, the evaluated flow rate as represented by
curve Q20b is evaluated solely by using the obtaining
device 16, since the correction device 18 does not
perform any action. It can be seen that, as from the
first resetting on the basis of measurements, and in
25 particular on either side of the change in operat-ing
point (t=100s), the flow rate evaluated by the evaluation
device 10 follows the real flow rate (curve Q20c) with
great accuracy, while the flow rate evaluated by an ANN
alone (curve Q20a) continues to maintain a bias or offset
30 that is more or less constant relative to the real flow
rate.
Figure 4B is analogous to Figure 4A and shows
variation in the flow rate of propellant coming from the
tank 21 and entering the combustion chamber 30. The
35 curve Q21a shows the flow rate estimated by an ANN alone,
the curve Q21b shows the flow rate evaluated by the
evaluation device 10, and the curve Q21c shows the real^
flow rate. It can he seen that the curve Q21b follows
the curve Q21a so long as the correction device is not
effective (cf. Figure 3B: up to t=t3, 60s, the level
probe 23 does not return any measurement). Thereafter,
5 the curve Q21b comes substantially closer to the curve
Q21c. The right-hand enlargement in Figure 4B reveals a
similar effect taking place during the second uncovering
of the level probe 23, i.e. between t6 (130s) and t8
(160s). The use of an unscented Kalman filter thus
10 significantly improves the results that can be provided
by an estimator alone, in particular an ANN type
estimator.
Figure 4C shows the variation in the mixing ratio as
a function of time. The mixing ratio is defined as the
15 ratio between the flow rates of the two propellants.
Each curve MRz is obtained by taking the ratio Q21z/Q20z,
where - z is equal to -a, b-, or c. The mixing ratio is a
magnitude that is often used for regulating the operating
point of a propulsion system such as the propulsion
20 system50.
The variation in the curve MRb showing the mixing
ratio calculated from the flow rates evaluated by the
evaluation device 10 clearly shows the respective
resetting of each of the flow rates at instants tl and t3
25 and then at instants t5 and t6. The evaluation device 10
thus provides an accurate estimate of the mixing ratio by
virtue of the successive resetting operations made
possible by the unscented Kalman filter.
Figure 6 shows another embodiment of a device 210
30 for evaluating fluid flow rate. In this figure, elements
that correspond to or are identical with elements of the
first embodiment are given the same reference signs, with
a different hundreds digit, and they are not described
again.
35 The evaluation device 210 of Figure 6 is
incorporated within a fluid circuit 250 having a tank 220
from which a fluid flows. Downstream from the tank, a
flow meter 215a measures the flow rate of the fluid.
Nevertheless, the flow meter 215a may be inaccurate or
biased. The role of the device 210 is to correct the
value of the flow rate returned by the flow meter 215a on
5 the basis of measurements of the level of fluid in the
tank 220.
The evaluation device 210 operates by like the
evaluation device 10 except that it makes use of the
measurements returned by the flow meter 215a instead of
10 relying on a predictive mathematical estimator such as an
ANN. In other words, in above equation ( 3 ) , the term
ANNk(uk) is replaced by the current. value measured by the
flow meter 215a and acquired by the acquisition device
215. The flow rate value obtained by the obtaining
15 device 216 is then supplied to the correction device 18
which corrects it as a function of measurement yk received
from the acquisition card 19. As shown in Figure 6, the
corrected evaluated flow rate is returned to the flow
meter 215a by the evaluation device 210 so as to modify
20 the calibration of the flow meter in order to reduce its
measurement bias.
Although the present invention is described with
reference to specific embodiments, modifications may be
adopted to these embodiments without going beyond the
25 general ambit of the invention as defined by the claims.
In particular, individual characteristics of the various
embodiments shown and/or mentioned may be combined in
additional embodiments. Consequently, the description
and the drawings should be considered in a sense that is
30 illustrative rather than restrictive.
CLAIMS
1. An evaluation method for evaluating a flow rate of a
fluid coming from a tank ( 2 0 , 2 1 ) , the method comprising
measuring a level of the fluid ( y , ) in the tank and being
5 characterized in that it comprises an estimation step for
estimating the flow rate of the fluid ( d , ) by using an
unscented Kalman filter, said estimation step comprising
an obtaining step for obtaining the raw fluid flow rate (
4 k ) and, when a level measurement ( y k ) is available, a
10 correcting step during which the obtained raw flow rate
is corrected as a function of the level measurement.
2 . An evaluation method according to claim 1, wherein the
raw flow rate value (4,) is measured by at least one
15 sensor ( 2 1 5 a ) , in particular a flowmeter.
3. An evaluation method according to claim 1, wherein the
raw flow rate value ( 4 , ) is calculated by mathematical
estimation with iteratively evaluated coefficients, in
20 particular by using an artificial neural network.
4. An evaluation method according to any one of claims 1
to 3, wherein the mass of fluid (m,) in the tank ( 2 0 , 2 1 )
is a non-linear function of the level of fluid ( n , ) in
25 the tank.
5. An evaluation method according to any one of claims 1
to 4, wherein a state of the unscented Kalman filter
includes a bias ( E ) of the raw flow rate value ( 4 , ) .
30
6. An evaluation method according to any one of claims 1
to 5, further comprising, before the correction step, a
filtering step of filtering fluctuations in the level
measurement ( yk ) .
35
7. A method of evaluating two flow rates of fluids coming
respectively from a flrst tank and from a second tank,
wherein the flow rates of the fluids are evaluated by
separately implementing:
a first evaluation method comprising a step of
n
estimating the flow rates of the fluids ( d , ) using an
5 unscented Kalman filter, in whichno level measurement is
taken into account in a step of correcting the unscented
Kalman filter;
a second method according to any one of claims 1
to 6, wherein only a level measurement of the first tank
10 is taken into account;
a third method according to any one of claims 1 to
6, wherein only a level measurement of the second tank is
taken into account; and
a fourth method according to any oneof claims 1
15 to 6, wherein both level measurements are taken into
account; and
returning the flow rates as evaluated by that one of
the four methods that takes account exactly of the
measurements that are available.
2 0
8. An evaluation system (10, 110, 210) for evaluating a
flow rate of a fluid coming from a tank (20, 21, 220),
the system comprising measurement means (17, 22, 23)
suitable for measuring a fluid level ( y , ) in the tank
25 (20, 21, 220) and being characterized in that it includes
"
estimation means for estimating the flow rate ( d , ) of the
fluid using an unscented Kalman filter, said estimation
means comprising obtaining means (16, 216) for obtaining
the raw fluid flow rate and correction means (18)
30 connected to the obtaining means and to the measurement
means and configured to correct the raw flow rate ) as
obtained by the obtaining means (16, 216) as a function
of the level ( y , ) measured by the measurement means.
35 9. A propulsion system (50), in particular for a space
launcher, the system comprising two tanks (20, 21), each
containing a propellant, a combustion chamber (30) into
which the two propellants are injected, and an evaluation
system (10) for evaluating the flow ra-te of at least one
of the propellants according to claim 8.
5 10. A system for resetting a flowmeter (215a), the system
comprising an evaluation system (220) according to claim
8 in order to evaluate the flow rate passing through the
flowmeter.
10 11. A program including instructions for executing steps
of the evaluation method according to any one of claims 1
to 7, when said program is executed by a computer (11).
12. A computer-readable data medium storing a computer
15 program including instructions for executing steps of the
evaluation method according to any one of claims 1 to 7.