application of condition monitoring to an electromechanical actuator: a parameter estimation based...

Application of condition monitoring to an electromechanical actuator a parameter estimation based approach by R. Dixon and A.W. Pike

As part of a recent R&D programme, a model-based monitoring technique for an electromechanical actuator has been the developed and validated on laboratory scale plant. Estimates of the key physical parameters of the electromechanical positioning system are calculated from a transfer function model of the system, which is obtained using system identification techniques. The estimates are then assessed against baseline parameters and trended historically for monitoring purposes. In addition, a fuzzy-logic based significant change detector and fault classifier is applied to the estimates. The experimental results highlight the considerable potential of the applied techniques for achieving improved condition monitoring of actuation systems.

ilst engineers can strive to produce high reliability systems that require little or no attention over their design life, the w adoption of a monitoring and main-

tenance strategy is generally considered a necessary safegtmd against the vagaries of manufacturing quality, mechanicahaterial integrity, environmental effects, wear and tear etc. This is particularly true in aerospace applications, where safety is of paramount importance.

Improved aircraft maintainability and availability are two of the benefits promised by smart electromechanical actuators. However, the question of what algorithms should be incorporated in smart actuators has not yet been answered, and in many cases there remains some doubt as to their effectiveness and reliability. This article describes research that has been carried out in order to develop and prove the feasibility of a healthicondition monitoring technique for an electromechanical position-

ing system. The research described was carried out by ALSTOM

Power as part of the Reliable Electrical ACTuation Systems (REACTS) programme, which concluded in January 2001. The aim of this multi-company research programme was to demonstrate the potential for re- placing current hydraulidpneumaticieldraulic engine actuation systems on civil aircraft with smart electromechanical equivalents. The focus was on development of a concept demonstrator actuation system to prove the effectiveness for controlling the variable inlet guide vanes and variable stator vanes on an aero engine. More details of this demonstrator and of the overall programme may be found in Reference 2.

Test rig system The prototype actuator consisted of a brushless DC

motor (with two separate three-phase windings) driving

A COMPUTING & CONTROL ENGINEERING JOURNAL APRIL 2002

A TUATOR MONITORING 2 encoder brushless pneumatic ballscrew and position (velocity) DC motor brakes carriage sensor 'i '!,

'J i\

torque gearbox pneumatic load cell transducer actuators

Fig. 1 Test-bed system

into a hall screw via a gearbox. In order to progress algorithm development in parallel with design and manufacture of the prototype system, the experimental test-bed system shown in Fig. 1 was commissioned as a research vehicle. The system was extensively instrumented and linked to a dSPACE digital signal processor (DSP) housed within a PC that provided a facility for test waveform generation, data collection, data transmission to MATLABISMULINK, control loop closure, fault detection and condition monitoring implementation.

Monitoring methodology A built-in-test (BIT) specification was proposed which

would allow for pre or post flight tests (under unloaded conditions) and would permit the historical trending of test measurement dataor analysisresults. In thiscontext, there are many possible monitoring technologies which might he suitable for application to the system (e.g. contaminant monitoringianalysis, acoustic monitoring, vibration monitoringianalysis, performance trend monitoring, model-based monitoring techniques).

On a typical electromechanical system, condition monitoring often comprises the monitoring of

measurable output signals (e.g. current) against pre-determined limit values. However, the potential exists for detecting developing faults earlier and for better identification of the root cause, by using algorithms based on physically representative mathematical process models. The application of such models in either parameter estimation, parity equations or state estimator (observer) based fault detection schemes has been widely discussed in the literature (see, for example, References 1 and 5 and references therein). However, there still appears to he some way to go in terms of the practical applications that are necessary to convince senior managers in indusb-y of the benefits of investing in such techniques.

Of particular interest for the REACTS application were methods that allow the estimation of non-measurable physical process parameters from the measured signals. These are predominantly founded on system identification and parameter estimation theory. Such an approach was appropriate for the REACTS application, with its low duty cycle, hostile environment and restricted access, for two reasons: (i) the availability of a well~undersiood physical model of the plant, and (i3j the desire to have some form of flight history parameter trending in order to detect developing faults. The latter

COMPUTING & CONTROL ENGINEERING JOURNAL APRIL 2002 A

permits the smart actuator to provide an early warning of incipient faults, rather than simply reporting a failure after the event.

Physical parameter estimation The estimation of the physical system parameters

relies on the following five-step procedure:

1 Perturbation of the system with a suitable input signal and recording of the resulting input and output data.

2 Estimation of the parameters of a suitahly identified discrete time linear model of the system.

3 Model assessment to ensure it is sufficiently accurate. 4 Transformation of the discrete model to a continuous

5 Mapping of the continuous time model parameters to time model.

the key physical parameters of the system.

The various elements of this procedure are discussed below.

Physical model It is first necessary to develop a suitable model of the

electromechanical actuator based on physical laws. This task is relatively straightforwxd and results in a single- input two-output linear model of the system. This can either be presented in state-space form or in a transfer function matrix form as in eqn. 1, which is more convenient for the purpose here:

I I I

where s is the Laplace operator, I(s) is the motor winding

current, w(s) is the motor shaft speed, V(s) is the voltage applied to the stator windingsJis the system inertia (as seen at the motor), D IS the systems viscous friction (as seen at the motor), Ke is the motor back-EMF constant, Kt is the motor torque constant, L is the motor winding inductance and R is the winding resistance. Note that, in an ideal motor Ke = Kr. However, in practice due to losses and non-linearity, K, = yKt, where y ij a constant (0.95 for this motor).

It can be seen from eqn. 1 that, io order to describe the physical parameters of interest, two transfer functions are required. It is interesting to note that a model of the relationship between the motor speed and the ball screw carnage position is not required-this is because the values of all the key parameters can be monitored as 'seen' at the motor shaft

Identificution test definition Fig. 2 is a block diagram showing the configuration of

the test-bed positioning actuator. Clearly, the physical model of interest (eqn. 1) does not include the control law, which is fixed and should not change. Therefore the aim is to estimate the two open-loop transfer functions of the system under closed-loop control. This poses a number of problems associated with identifiability (see, for example, Reference 6). In the case of this system, injecting perturbation signals on both the demand input, yd(s), and the input disturbance, ud(s), followed by direct estimation of the transfer functions from voltage to current and speed was found to yield the best parameter estimates.

Therefore the prdpost flight test involves driving the system with these two perturbation signals for a period of four seconds and collecting the inpuuoutput data (with a sampling frequency of 1Wz). From this data the linear discrete-time TF models can be estimated.

' band limited white noise

Fig. 2 Closed-loop system diagram

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A TUATOR MONITORING > reSUIt5: test 1

100 r

-100 I I I I I I 0 0.2 0.4 0 6 0.8 1 -0

model M2: 093095 30 c - testbed

- linear mo 20 10

$ 0 5 0 -10

-20 , , , 1

0 0.2 0 4 0.6 0-8 1 .o

model Ri? 0-98166 200 r , ~ - -

m e 100

1 0 - testbed - linear model

a

L b -100

, I I I I

0 0.2 0.4 0-6 0.8 1 -0

time, s

Fig. 3 Model parameter estimation results for test 1 of friction experiment (i.e. no change from baseline)

Estimation &orithm With a known model structure (based on the physical

laws), the model identification problem is already solved. All that remains is to estimate the parameters of the equivalent discrete time TF model assuming a zero order hold transformation, that is estimate a model of the structure:

There are a profusion of algorithms discussed in the literature for obtaining estimates of model parameters for a system. For example, the well known method of least squares (IS), along with other more complex approaches such as: extended least squares @E), instrumental variables (IV) and refined instrumental variables 0. Detailed information about these and other methods can

he found in the many texts on the subject, see for example References 6 and 7; a useful summary chart of 'unified' recursive estimation algorithms can be found in Reference 3, p. 37. However, the above algorithms rely on assumptions made ahout the noise properties of the system and in practical applications the simplified refined instrumental variable (SRW) method, described in Reference 8, is often found to he more robust in the presence of noise with an unknown structure. Here, the SRIV algorithm was used for estimation of the parameters of the two discrete time transfer function models and was found to give superior results (i.e. to RLS, IV) in this relatively noisy application.

In terms of the practical implementation for the actuator system, the estimation takes place as follows:

1 Estimate parameters of TF from

2 Estimate numerator parameters of V[+) to I(T1).

TF for V(r l ) to ~(1~).

For step 1 the SRN algorithm is used en bloc (for speed) to estimate the parameters. Subsequently, a recursive version of the algorithm is used for step 2, which enables the initial conditions for the individual parameters to he specified, together with their corresponding diagonal value in the parameter error co-variance matrix. In this way, the denominator can he forced

to he the same as that obtained in step 1.

Estimate assessment Occasionally, unmeasured disturbances or unknown

effects can lead to estimation of erroneous model parameters. In order to avoid calculating and trending the erroneous physical parameters, a simple statistical test is applied, which gives a measure of how well the predicted model output represents the actual output.

The Coefficient of Determination is defined as:7

(3)

where 0' is the sampled variance of the model residuals e(& and aJr2 is the sample variance of the measured system outputy(k) about its mean value. This results in a 'goodness of fit' criterion which tends to unity as the fit of the model to the data improves.

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ACTUATOR MONITORI G ..::

800

600

400

200

95

* 90 85

80 1 2 3 4 5 6 7

test number

resistance inductance

400

- % ? :::I,, I , , , I I ;:;I,, , , , - , I

0 4 w 8 z I)

200 2 w

0 1 2 3 4 5 6 7 1 2 3 4 5 6 7

EMF const torque const

-

-

-

-

1 2 3 4 5 6 7 0

1 2 3 4 5 6 7

friction 800 r

1 2 3 4 5 6 7

test number

0 1 2 3 4 5 6 7

test number

Fig. 4 Estimated parameter change over seven tests with increasing Coulomb friction (4

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A TUATOR MONITORING 'p

I

Fig. 5 Estimated resistance parameter change over three tests with 4o increasing resistance (R) 3 1 30

fl 20 ae : I

10

0 1 2

EMF const torque const

inductance

~, :ji*= 10

3 1 2 3

I 20

ae

l o t -nn 0 1 2 3 1 2 3

friction inertia

40 1 3 30 2oh 10 0 1 2 3

r

l o 0 t,ll7_0, 2 3

I test number test number

In order to evaluate both models, R T ~ is calculated in each case, averaged and multiplied by 100. The resulting 'percentage fit' term gives an indication of the overall fidelity of the model and of the resulting physical parameter estimates. In the experimental results presented later a 90% fit is selected as the minimum permissible value.

Parameter transfirmation Having obtained an estimated transfer function model

of the form of eqn. 2, the model is transformed to continuous time assuming a zero-order hold on the input. The continuous model takes the form:

from which the following mappings of the parameters (in eqn. 4) to those in eqn. 1 can be formulated

Ke vbhib, , L = ybzl R = aiL Kt = yKe J = 'eKdk2 D btzLJ

Based on these, calculation of the estimates of physical parameters (from those of the estimated model) is elementary.


ACTUATOR MONITORI G \ resistance

40 c 1 2 3

EMF Const

40

30

z 10

0 1 2 3

triction

40 c 30

z 10

0 1 2 3

test number

inductance Fig. 6 Estimated parameter change

over three tests with increasing inductance (L)

and resistance (R) B 30

0 20 z I

4 0 ~ 10 0 1 2 3

torque const

40 c 0

1 2 3

inenia

40 c io 0 L 1 2 3

lest number

Parameter trending In the experimental results that follow, the parameter

estimates are simply assessed as percentage changes against the set of base-line (fault free) parameters and trended historically for monitoring purposes. Interpretation of these results is traditionally carried out by the human operator. The ultimate goal is fuller automation of the fault diagnosis, and this is considered later in the article.

Initially the parameter estimation scheme was developed and tested on a non-linear simulation model of the system (for a brief description of model development and validation see Reference 2). The algorithms were validated on this simulation and were found to be capable

of detecting changes in the six system parameters with little cross-coupling between the estimated parameters. Having concluded that the estimation algorithm was feasible on the simulated system, the algorithms where then applied to the test rig itself.

In order to generate experimental fault results, the test- bed system was set up to allow changes in three of the key parameters: a braking system was developed to introduce friction changes (0); and inductors and resistors were wired in series with each of the motor phase windings such that they could be switched in and out (hence varying L andR). To demonstrate the efficacy of the developed routine, three experimental investiga- tions are described below. The first two involve

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report maintenanm information

diagnoser

faun report to operator

parameter monitor

t model parameter

estimation

plant

Fig. 7 Model-based condition monitor and fault diagnoser block diagram

individual changes in friction and resistance and the third inductance and resistance changes combined.

Friction increase For this experiment seven tests (of four seconds

duration) were conducted on the test-bed system. In the first test there was no change in the fnction, for the remaining six the friction was increased incrementally (in a linear fashion) by application of the brake. Fig. 3 shows a one second section of the actual data collected and the corresponding model resultsfor test 1 (i.e. fault freecad. As can he seen, the dominant modes are captured by the model, with individual model fits of 931% and 98.2%, indicating an overall fidelity of 95.7%.

The results presented in Fig. 4 show the algorithm output based on the seven tests. In the Figure, the uppermost graph shows the ‘percentage fit’ or model fidelity parameter (described earlier) for each of the seven tests. If any test score was less than 90% the parameter estimates would be ignored-this very rarely occurred in practice.

It can beseen that theestimation algorithm iscorrectly identifying the change in friction. There is also some degree of cross-coupling with the other parameters

(which do not change in practice), though this is at least an order of magnitude less than the friction change. It is clear from inspection that the developing problem is friction related.

Resistance increase Here, known resistances were connected in series with

the phase windings of the motor. The additional values of 0.2Q and 0.4Q represent changes of approximately 20% and 40% over the manufacturers’ quoted winding resistance. The results of the analysis are shown in Fig. 5, with the first case including no additional resistance, the second 0 2 0 and the third 0.4Q. Whilst (for the sake of brevity) the model confidence is not plotted it was well above 90% in each case.

The estimated changes in resistance are consistent with the known physical change. Again there is some cross-coupling (in this case mainly to friction), though the experienced operator could identify that the developing fault was due to resistance change. It should be noted that the permissible friction changes (before the change would be deemed a ‘fault’) are significantly higher than the changes in resistance: e.g. on this rig a 100% change in resistance would cause major problems to the system, whereas friction does not cause concern until it is greater than 500% of base value.

Inductance and resistance increase For the final experiment, hand-wound inductors were

placed in series with the phase windings of the motor. The inductors were designed to generate inductance changes of 0.25mH and 06mH, i.e. 20% and 50%, respectively, over the manufacturers quoted values. (Note that the inductance values have some variability with current due to saturation effects and other core non- linearities.) The measured additional resistances due to the length of coiled wire were 0.13Q and 0.2Q respectively (or ahout 13% and 20% of the base value).

In Fig. 6, the parameter change results from the three tests are shown. In the first case there was no change; in the second the 0.25mH inductance was switched into the line; finally, in test 3 the full 06mH coil was inserted. As in the previous examples, the model confidence was above 90% in each case, indicating that the parameter estimates were reliable.

As before, the algorithm estimates the actual parameter percentage changes reasonably accurately. Furthermore, interpretation of the results would definitely highlight a problem developing with the motor windings (1.e. changed resistance and inductance).

Significant change detection and fault classification

Having obtained some very encouraging experimental results for estimating the parameters and tracking changes, there remains the problem of developing a suitable supervisory system. This is essential in order to


symptom (S) high (H)

Fig. 8 Parameter mnnitnr- fuzzy sets for detecting significant changes

provide the appropriate meaningful diagnostic information to operatorsimaintenance personnel. For example, a flight-worthy actuator might have two communication tasks: firstly, after a preflight test to inform the engine control system either 'go' or 'no-go'; secondly, on interrogation by maintenance personnel to comment on developing faults that are likely to become faultsifailures before the next maintenance. In the literature there are a variety of approaches that are worthy of consideration (see References). Taking Reference 4 as a starting point, steps have been taken toward addressing such issues, and the supervisory scheme that has been developed also acts to minimise the effects of cross-coupling in the parameter estimates.

Fault symptoms (Sym) can be formulated by monitoring the changes to model parameters (Ae) over time. Fig. 7 shows a block diagram of the condition monitoring and fault detection scheme applied in the lab. Some promising algorithms, formulated using fuzzy logic, have been applied in the parameter monitor and fault diagnoser blocks and are described in the following.

Parameter monitor The approach adopted was to develop an algorithm

that was capable of capturing significant changes to the model parameters. This was achieved in the following way:

1 Perform a number of model parameter estimations under normal process operation. Then calculate the sample mean and sample variance of the parameter estimates:

(5)

2 Subsequently, significant changes to the process can be detected by calculating by how much the current parameter estimates deviate from the normal behaviour:

A e = e - ;

A major issue at this point is how to judge what is a significant deviation of a parameter. From a theoretical standpoint, this is a problem because the probability distribution of the model parameter estimates is not generally known in advance for real applications. One solution identified is the use of fuzzy logic, which provides an appropriate framework for reasoning given uncertain information. The approach taken here was based on the work of Isermann? who described a method to classify significant deviations using fuzzy set theory.

In Fig. 8, the high fuzzy set parameters ri and rz are calibrated according to prior process knowledge such that:

r<i-1 process condition is normal ri < r < rz r>rz a process fault exists

a process fault may be developing

where

AQ r%=-=- XIOO e

Similarly a low fuzzy set may be defined. The symptom fuzzy set is centred on Leas"& and has

width koei8. The width is non-zero to reflect the fact that the true A0 may deviate from the measured A B k is usually selected as 1 or 2, depending on the degree of confidence associated with the model parameter deviation estimate.

Max and min operations are applied to the fuzzy sets in order to determine the degree of membership to high (low), denoted as SymH (SymL). This yields a worst-case membership value of high (low), which takes into account the uncertainty relating to the true value of AO. From Fig. 8:


A TUATOR MONITORING > I YES

run test. r"l- COlleCt

I YES

paismeter data in

generate symptoms based upon

model parameter

operator (provide

diagnosis

histanal

NO fault fault

dstsnion and

Fig. 9 Top-level condition monitoring flowchart for test-bed rig

SymH = max(min(ll(S),p(H))) (8

Similarly,

SymL = max(minUS),p&))) (9)

where p(.) denotes the fuzzy set membership function value.

In the case of the test-bed rig, ri and Ts were selected as shown in Table 1. (Note the large fuzzy set breakpoints associated with the friction parameter, indicating that friction changes of up to 300% are of no concern for this particular system.)

With the above settings, the parameter monitor successfully identified significant changes in electrical resistance (see subsection on 'Resistance increase') and in electrical resistance and inductance (see subsection on 'Inductance and resistance increase'). For example, with L increased by 60% and R increased by 40%, the parameter monitor correctly assigns a value of 1 to the SymH(R) and SymH(L) values and zero for all others. However in the case of a significant change in the friction parameter, Table 2 shows typical symptom values obtained.

Again, the correct fault symptom has been highlighted (increasedD), but the bias present in the other parameters Ui,, K f andJ leads to a large partial membership of high, which may lead to a misdiagnosis of the fault. It is believed that the observed parameter biasing is primarily due to model approximation error. Note that the parameter estimation is carried out using a linear model with fixed structure (see eqn. 4). At hest, this can only provide a local approximation to the non- linear process dynamics.

In the case of a slowly developing fault, it may be expected that a significant increase in D (or in general any other parameter or parameter combination) can be detected in a timely fashion, allowing preventive maintenance to take place. In this situation the parameter biasing may remain at an acceptably low level and not seriously degrade the fault diagnoser performance. However, for an abrupt major change in the friction D (or any other parameter or parameter combination), e.g. a 1000% increase, the parameter bias existing on the other parameters may prevent diagnosis of the fault since many parameter deviations will be detected as high or low immediately. Nonetheless a clear indication that a fault exists is given and therefore the unit should


he taken out of service for repair.

Fault dzagnosev In the following a brief outline of the diagnoser fuzzy

inference system is given. The inputs to the fault diagnoser are the array of symptom values Sym = [SymL, SymH] associated with the various model parameters, calculated by the parameter monitor.

Expert knowledge can be coded as fuzzy rules that operate on Sym in order to arrive at a conclusion concerning the operating condition of the plant. For example consider the following generic fuzzy rule applied to the REACTS test-bed

IF (ul is X) & (u2 is u) THEN (FAULT is Z) u l = SymI-6) i.e. the degree of membership to low

relating to the phase winding inductance estimate

u2 = SymL(R) i.e. the degree of membership to low relating to the phase winding resistance estimate

IF (ul is LOW) and (u2 is LOW) THEN (FAULT is SHORTED WINDING)

Note that rules may he added to compensate for known systematic biases in the parameters. For example considering Table 2, it may be sensible to code the following rule:

IF SymH(D) >all other SymH(.), THEN set SymH(Ke), Sym"(Kt1 and SymH(/) to 0

This is based on the physical knowledge that it is extremely unlikely that Ke, Ki or J could increase significantly.

The diagnoser incorporates a number of fuzzy rules as above, on which fuzzy inference and defuzzification methods operate, in order to produce an unambiguous condition status and fault diagnosis.

Conclusion A model-based condition monitor and fault diagnoser

was developed for the test-bed system of Fig. 1. A flowchart showing the complete monitoring and change detection process as implemented on the test rig is shown in Fig. 9.

Experience from the experimental research carried out on this system suggests that there is significant potential for detecting faults on an electromechanical actuator using such an approach. Furthermore, the techniques are applicable to almost any system where a linear model can he related to known physical parameters.

An issue that should not pass without mention is the use here of a discrete time parameter estimation scheme rather than direct estimation of the continuous time parameters. For this application, the discrete time algorithm was found to he more robust (in terms of

/ ACTUATOR MONITORI@G

Table 1 Test-bed system-fuzzy set parameters

r, rp% parameter 1 I 20 50 L I

20 40 20 50 20 50

300 600 20 50

R K, Kt D J

Table 2 Significant change detector s h p t o m values-600% increase in D

SvmL SvmH Darameter I 0 0 L 0 0 R 0 069729 K, 0 069729 Kf 0 1 D 0 0.94354 J

~

. .


numerical stability and convergence) than its continuous counterparts.

Acknowledgments The authors are grateful to ALSTOM Power

Technology Centre for permission to publish this article, to the partner companies within the REACTS project (Rolls-Royce plc, BAE Systems Avionics Ltd., and FR- HiTEMP Ltd.) for their support and to the DTI for providing part funding under the CARAD (Civil Aircraft Research and technology Demonstration) programme.

References 1 PATTON, R. J.. FRANK, P. M. et d: 'Fault diagnosis in dynamic

svstems. thwrv and aoolicatian' lContiol Enxineering Series. Prentice . .. I I . Hall, 1999)

2 DKON, R., GIFFORD, N., SEWELL, C., and SPALTON, M. C.: 'REACTS: Reliable Electrical ALTuation Systems', Proceedings of the IEE Colloquium on Electrical machines and systems far the more electric aircraft'. 991180, London, November 1999

3 ISERMA", R.. LACHMANN. K. H., and MATKO, D.: 'Adaptive control systems' @'rentice Hall Int. (LIK) Ltd., 1992)

4 ISERMA", R.: 'Integration of iault det-tion and diagnosis methods'. PAC Symposium an Fault detection supervision and safety far technical processes, Espao, Finland, 1994

5 ISERMA", R.. and BALLE, P.: 'Trends in the application of model based iault detection and diagnosis of technical proem', Proceedings of the IFAC 13th World Congress, San Franosco, USA, 1WR ""1.12 ----.rr - --

6 LJUNG, L.: 'System identification thwry for the user' (Prentice Hall, Englewwd Clifis, NJ, USA, 1987)

7 YOUNG, P. C.: 'Recursive estimation and time series analysis' (Communication and Control Engineering Senes, Springer-Verlag. %din. 19841 ~ ~~ ~ ~,

8 YOlJhG, P. C.: 'The instrumental variable method a practid approach to identification and system parameter estimation', in BARKER, H. A,, and YOUNG, P. C.: 'Identification and system parameter estimation' @'ergamon Press, Oxford, 1985, volume 1)

0 IEE 2002

The authors are with ALSTOM Power, Technology Centre, Whetstone, Leicester LE8 6LH, UK; Fax: t44 (0) 116 2845461; E-mail: [email protected]

mailto:[email protected]

application of condition monitoring to an electromechanical actuator: a parameter estimation based...

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