21

CHAPTER-2:

System Identification & Qualitative Fault Isolation of Hydrostatic Transmission

System.

2.1. Introduction

Hydrostatic transmission (HST) system [Watton,1989] consists of hydrostatic

pump, hydraulic motor and control mechanism; all combined in single housing, and are

operated together in a circuit made of solid pipes or flexible hoses. The output of the

transmission pump can be reversed, and both the direction and speed of motor rotation

can be controlled by direction control valve. Because of the fact that the hydraulic

power is easily started, stopped and controlled, hydrostatic drive can substitute clutch,

gear and shaft in power train, and also can produce infinite speed and torque changes

from full forward to full reverse.

This chapter is focussed on an open circuit hydrostatic transmission (HST)

system, for which a bond graph model is developed for system identification and also

for qualititave fault detection and isolation [Blanke et al. 2003, Simani et al. 2003]. For

the fault analysis, single fault is hypothesised; i.e. a single independent parameter of the

system may be faulty at a time.

Although there have been extensive research on modeling and simulation

[Manring & Luecke, 1998] and failure monitoring [Chinniah et al. 2006] of hydrostatic

transmission systems, to the knowledge of the authors there are little works on the

model-based qualitative fault diagnosis of hydrostatic systems using fault tree and

temporal causal graph (TCG) [Hogan et al. 1996, Hogan et al. 1992]. An analogous

type of system was modelled [Dasgupta et al. 2006] in which dynamic behaviour was

studied through simulation and then it was experimentally validated. But in that

literature neither system identification problem nor FDI analysis was described, which

is addressed in this work.

2.2. Hydrostatic Transmission System:

2.2.1. System Description:

The setup is a typical hydrostatic transmission system with pump loading. It

comprises of a hydraulic power pack, a hydraulic motor with a control valve, a pump

22

with loading circuit and a PLC operated Control Panel. The pictographic view of the

hydraulic transmission system is shown in Fig. 2.1. The circuit diagram of this system

is shown in Fig. 2.2 and bill of materials is given in Table 2.1.

(a) (b)

Fig.2.1: Pictographic view of the set-up installed in ISM,as viewed from different angle.

Fig.2.2: Circuit diagram for the system

23

Table 2.1

Bill of Material

31 Electrical control panel STD SHPL 01

30 Hose 3/8” BSP MARKWELL 06

29 Ball valve 3/8” BSP HYDAC 01

28 Pressure relief valve DPRH 06 T 100 POLYHYDRON 01

27 Pressure relief valve DPRH 06 S 315 POLYHYDRON 01

26 Direction control valve 4DE 06D DSA 220-01-3 POLYHYDRON 01

25 Check valve C 06 S1 03 POLYHYDRON 04

24 Pressure transmitter S10-250, 4-20 ma, 0~200 BAR WIKA 01

23 Hydraulic pump 1 RC 7C (8.6 LPM) POLYHYDRON 01

22 Coupling HYDAX 19 HYDAX 01

21 Hydraulic motor 8 CC M+S 01

20 Pressure transmitter S10-250, 4-20 ma, 0~200 BAR WIKA 01

19 Pressure transmitter S10-250, 4-20 ma, 0~200 BAR WIKA 01

18 Throttle cum check

valve

TCT-10 HYLOC 01

17 Throttle cum check

valve

TCT-10 HYLOC 01

16 D.C. valve 4WE 6E/6X G24V DC REXROTH 01

15 Pressure gauge 0~280 BAR ‘G’ Filled, 1/4”

BSP, 4” Dial

WIKA 03

14 Needle valve ¼”BSP STD 01

13 Pressure reducing

valve

DPMS-06 S A 200 POLYHYDRON 01

12 Pressure relief valve DPRH 06 S 315 POLYHYDRON 01

11B Coupling HYDRAX 19 HYDRAX 01

11A Bell housing SH4284-01-52-3 HYDAXA SHPL 01

10 Electrical motor 0.75KW (1 HP),1450

RPM,420V

LHP 01

09 Hydraulic pump (Gear) 7 LPM (5 cc/rev) DOWTY 01

08B Coupling HYDAX 38 HYDAX 01

08A Bell housing SH4284-01-53-3 SHPL 01

07 Electrical motor 5KW (7.5 HP),1450 RPM, 420

V

LHP 01

06 Hydraulic pump 15 LPM (12 cc/rev) HAWE 01

05 Suction strainer SC3-007 HRDROLINE 01

04 Suction strainer SC3-010 HRDROLINE 01

03 Filler breather FSB 25 HRDROLINE 01

02 Oil level indicator LG2-10 HRDROLINE 01

01 Oil reservoir 100 Lts SHPL 01

Tag Description Specifications/Model code Make Qty

24

A solenoid operated Direction Control valve (DCV) is used to control the flow

direction, while flow control valves (FCV) are used to control the flow quantity. The

load on the system can be varied with a Pressure Relief Valve (PRV). The fluid

pressures at the inlet and outlet side of the motor (motor is item No. 21 in Fig. 2.2) and

outlet side of the pump (item No. 23 in Fig. 2.2) are measured by pressure transducers

(Pmi, Pmo and Ppp represent those measured signals respectively) and speed of the motor

(ωm) is also measured by speed sensor and finally the data are transmitted to PC for

further analysis and signal processing through DAS mounted inside the control panel.

2.2.2. Modeling of the system:

The bond graph model of the system is shown in Fig. 2.3. In the formulation of the

model the following assumption were made:

Fluid inertia is neglected

The fluid has Newtonian characteristics.

Lumped Resistive and capacitive effects are used wherever appropriate.

In Fig. 2.3, the source of effort, Se1 is the pressure source Psupl (N/m2) from the

hydraulic power pack. Likewise, Se14 represents the outlet pressure Ps (which is the

atmospheric pressure in this case). In this study, square-root type nonlinearity is

imposed to model all the Direction Control valves (DCV) and Pressure Relief Valves

(PRV) as given in equation 2.1 in its general form.

. 2( )

( ) (2.1)

d

PQ C A sign P

k P sign P

Where, .

Q is the volume flow rate of oil in m3/sec. Cd is the coefficient of

discharge assumed to be unchanged. A is the port area (in m2) which is perturbed for

fault introduction. ρ is the density of oil, in Kg/m3.ΔP is the pressure differential

between upstream and downstream in N/m2. Sign ΔP is the sign function returns +1

when ΔP is positive and -1 when ΔP is negative.

25

Fig. 2.3: Bond Graph Model of System

The flows through DCV inlet and outlet are modeled as given in Equation 2.2

and 2.3 respectively.

milmilfi PPsignPPkSf supsup2 (2.2)

smosmofo PPsignPPkSf 15 (2.3)

Where kfi and kfo are the parameters related to coefficient of discharge at the inlet and

outlet of the DC valve, respectively.

The next zero junctions linked with 3,4,5,6,7,11 and 12,16,17,18,19,20 represent

the hydraulic motor inlet and outlet ports respectively. R13 shows the resistance cross-

port leakage while R6 and R17 stand for the resistances due to absolute leakage at the

inlet and outlet ports. The C elements, i.e C4, C18, are related to the compressibility of

the fluid with their values representing the bulk stiffness of the fluid. The transformer

accounts for the conversion of the fluid flow into mechanical rotation of the motor with

its transference value equal to the displacement of the motor Dm. The resistances R9 and

R22 show the friction due to the flow control valves that are installed in the fluid

26

pipeline. The elements R25 and I24 represent the frictional resistance to the shaft and the

total moment of inertia of all the rotating devices respectively.

Proceeding further to the secondary (loading) circuit, the two transformers

represent the displacement of the pump while C31 accounts for the bulk modulus of the

fluid just like C4 and C18. The flow through the PRV (item No. 27 in Fig. 2.2) is written

as:

bpppbpppp PPsignPPkSf 33 , (2.4)

Where, Pbp is the pressure maintained by the booster pump in the secondary (loading)

circuit.

The state equations obtained from the bond graph model (Fig. 2.3) are given in

equations 2.5-2.8:

01

supsup

pm

mi

ipl

momi

lkg

mi

mmmilmilfiK

P

R

PP

R

PDPPsignPPk

(2.5)

02

pm

mo

ipl

momi

smosmofo

lkg

mo

mmK

P

R

PPPPsignPPk

R

PD

(2.6)

0pp

pp

bpppbppppmpK

PPPsignPPkD

(2.7)

0121 mbppppfblblmmomim JPPDRRRPPD (2.8)

For estimation of unknown parameters nonlinear regression analysis was done

with steady state consideration and following assumptions.

The bulk modulus of the fluid remains same at all the pressures due to

Newtonian behaviour, i.e. pmpppmopmi KKCKCKC 31184

27

The effect ofR9 and R22 is cumulative and hence their sum i.e. R9+R22 is

important mathematically. Therefore it is chosen

that blblbl RRRRR 22219

The fluid comes out of the motor with the same flow rate as it has entered.

Hence mD 21 . Similarly, pD 43

The parameter related to coefficient of discharge of orifice in the DC valve

inlet and outlets are same, i.e. ffofi kkk .

Leakage resistances at suction and delivery side of the hydraulic motor are

same, i.e. lkglkglkg RRR 21 .

2.3. System Identification:

2.3.1. Nonlinear Regression Analysis:

The following activities were done during experimental study and data acquisition:

The values of mppmomi PPP ,,, (refer Fig. 2.3) were recorded for different loads

on the system.

The load on the system was altered by changing the set point of the pressure

relief valve.

The supply pressure from the power pack was maintained at constant value of 35

bar by adjusting the Pressure Reducing Valve.

Data were recorded only after allowing the system to reach a steady state for

every value of load.

The unknown parameters were found by nonlinear regression analysis [Huang et

al. 2010, Argyrous, 2010]. The estimated parameters were used to identify the kp value

corresponding to each position of the pressure relief valve. The assumption underlying

nonlinear regression is that the model can be approximated by a linear function, given in

Eq. (2.9).

28

j

jiji Jfxf 0, , (2.9)

Where, the function f (..) is defined by each of the Eq. (2.5)-(2.8), 0f the initial

guess, xi the measured states,

j

iij

d

xdfJ

, , and is the unknown set of parameters.

It follows from this that the least squares estimators are given by

yJJJ TT 1 . (2.10)

SPSS non-linear regression package [Argyrous, 2010] was used for this

estimation. All the estimated unknown parameters, and known parameters (provided by

manual) are listed in Table 2.2.

TABLE 2.2

LIST OF PARAMETERS

Parameter Value

Displacement rate of motor, Dm 7.96×10-6

m3/rad

Displacement rate of pump, Dp 1.00745×10-6

m3/rad

Supply pressure, Psupl 3.5×106 Pa

Booster pump pressure, bpP 1.00×106 Pa

Resistance to leakage, Rlkg 6.4779×1016

N.s.m-5

Resistance to cross port leakage, Ripl 16.97088×1018

N.s.m-5

Frictional Resistance to rotation of shaft Rf 1.59154×10-3

N.s.m/rad

Frictional Resistance to the fluid, Rbl 4.758732×10-2

N.s.m/rad

Parameter related to coefficient of discharge

of orifice in the DC valve, kf

0.3226×10-5

kg-0.5

.m3.5

Aggregate moment of inertia of motor pump

combination, J1

1×10-3

kg.m2

Bulk modulus of fluid, Kpm 1×1014

Pa

Parameter related to coefficient of discharge

of orifice in the PRV, kp

4.41x10-8

kg-0.5

.m3.5

29

The values of the parameters, Dm, Dp, and Kpm were obtained from the manual,

and Psupl, Pbp were set at the value given in the Table 2.2. The value of J1 was chosen

suitably as the actual value could not be estimated by steady state analysis of the

system. This assumption would have an effect to the transient characteristics of the

model. However, the behaviour of the system would remain the same at steady state.

Rest of the parameter values were obtained through regression analysis [Draper &

Smith, 1998, Seber & Wild, 1989] using SPSS software [Argyrous 2010].

2.3.2. Validation of System Identification:

The readings from the three pressure sensors Pmi, Pmo, and Ppp and one speed

sensor (ωm or RPM) were recorded at steady state from numerous run of the physical

system at different pump loading, by modulating the set point of PRV in loading circuit.

To compare the system’s response with that from the model, the bond graph model

(Fig.2.3) was transformed to block diagram, as given in Fig. 2.4, and simulated in

MATLAB-Simulink. In the block model (Fig. 2.4), a step function was added inside the

shaded oval (Fig. 2.4) to vary kp (similar to PRV set point modulation in real system),

and then the mean fluid pressures at three tapping points were observed from simulation

at different RPM, when steady state condition reached. Both the data from the real

system experimentation and model simulation are plotted in common scale and shown

in Fig. 2.5-2.7. The figures show that the simulation results are closely matching with

the experimental results. But the experimental data are discreet; because those were

recorded for finite number of run of the system.

The average error and Root Mean Square (RMS) error were calculated as given

in tabular form in Table 2.3. A negative error shows that the simulated value is less than

the experimental value while a positive error indicates that the experimental value is

less than the simulated value. The error percentage is less than 5% for all the four states,

which measures the accuracy of the system identification.

The identified model thus obtained is now the replica for the original system. So

this model has been used for FDI analysis. In this chapter, special importance is given

on qualitative FDI analysis for different hypothesized faults imposed in the real system.

Bond graph model is used for some prediction viz-a-viz fault detection, which has been

validated through model simulation and experimentation.

30

Fig.2.4: The Plant Model

Fig.2.5: Comparison of Experimental

& simulation values of Ppp

Fig. 2.6: Comparison of Experimental

&Simulation values of Pmo

Fig. 2.7: Comparison of Experimental

& Simulation values of Pmi

31

TABLE: 2.3

COMPARISON OF EXPERIMENTAL AND SIMULATION DATA

Variable Average Error RMS Error

Pmi -0.123 % 0.172%

Pmo 2.99% 3.71%

Ppp -2.21% 2.83%

RPM 1.52% 1.82%

2.4. Qualitative FDI Using Fault Tree:

A Fault tree is a logic tree that propagates events, like a qualitative change in

value. For creating a fault tree one starts off with an effect level event. One then

logically proceeds through the fault tree connecting the events. The tree is extended in a

manner till one reaches a cause event which need not be further explored. In order to

construct a fault tree firstly a list is prepared with the effecting (antecedents) and the

affected (consequences) parameters or the power variables at each junction of bond

graph. The variables corresponding to a strong bond becomes the affected one while the

variables and parameters corresponding to all the other weak bonds become effecting

ones or the antecedents. This list is then used to construct a fault tree by searching for

all the antecedents corresponding to a given consequence. The antecedents and

consequences for the concerned hydrostatic system are obtained from the system bond

graph model (refer Fig. 2.3), and are given in Table 2.4.

The tree diagram is now constructed by searching for all the probable antecedents

for an observed consequence. Since, the antecedents obtained from Table 2.4 are the

consequence of some other antecedents from the same table; the diagram continues to

expand like a branch of a tree. A negative sign in the antecedent indicates that it bears

an inverse relationship with the consequence. In each of the fault trees the sign in the

superscript denotes the direction of change in the parameter value. The tree then

proceeds logically to other elements. Fault Tree diagrams for the causes for change in

Pmi, Pmo, Ppp and ωm are shown in Fig. 2.8, Fig. 2.9, Fig. 2.10 and Fig. 2.11 respectively.

The fault tree of Pmi has shown in complete, whereas the fault trees of Pmo, Ppp and ωm

are expanded up to the parameter kp (highlighted in shade), the discharge coefficient of

PRV (item No. 27 in Fig. 2.2), for the sake of brevity.

32

TABLE 2.4: THE ANTECEDENT-CONSEQUENCE CHART FOR THE HST SYSTEM

No Antecedents

Consequences Parameter Power variables

1 Psupl e1

2

e2 f2

3 f2 f1,f3

4 e1,-e3 e2

5 e4 e3,Pmi,e6,e7,e11

6 Kpm f4 e4

7 f3,-f7,-f6, -f11 f4

8 Rlkg-1

e6 f6

9 e11,-e12 e13

10 Ripl-1

e13 f13

11 Kpm f18 e18

12 Rbl2 f22 e22

13

e8,-e9 e10

14 e21,-e22 e23

15

e10,-e23,-e25,-e26, e27 e24

16 J1-1

e24 f24

17 f24 f10, f23, f25, f26, f27

18 Rf f25 e25

19 Dp e29,f26 e26,f29

20 e35,f27 e27,f35

21 f12,-f16,- f17,f20 f18

22 e18 Pmo,e16,e17,e20,e12

23 Ps -e14

24 e14, e16 e15

25

e15 f15

26 f15 f14, f16

27 Dm f21,e20 f20, e21

28 Dm f8,e7 f7,e8

29 Rbl1 f9 e9

30 f10 f8,f9

31 f23 f21,f22

32

f29 ,-f32 f31

33

Fig. 2.8: Fault tree for Pmi

34

Fig. 2.9: Fault tree for Pmo

Fig. 2.10: Fault tree

for Ppp

Fig.2.11: Fault tree

for ωn

From the tree diagrams (Fig. 2.8-2.11), it can be inferred that any decrease (-ve)

in kp with all the other parameters kept unaltered, increases Pmi (+ve), decreases Pmo

(–ve), increases Ppp(+ve) and decreases ωm(–ve). Actually when Pmo is +ve, kp is +ve

(refer Fig. 2.9); conversely when kp goes –ve, Pmo decreases (-ve).

This has been validated though experimentation by switching off the bypass line

DCV (item No. 26 in Fig. 2.2) at a time of 80 s, thereby forcing the flow to pass through

the pressure relief valve (item no.27 in Fig. 2.2) with higher restriction or lower the

parameter related to coefficient of discharge (kp : –ve). The data archived through the

DAS to PC are plotted in Fig. 2.12, which shows the variation of the measured states as

per the prediction made by using Fault Tree.

The time responses of the measured states i.e. Pmi, Pmo, and Ppp and m , obtained from

simulation of block model (Fig.2.4) are given in Fig.2.13. In that simulation, the value

of kp is modulated by halving the step output from initial value to final value at step

time 80 s so that 50 % blockage in PRV is introduced at that time. The simulation result

35

is found in good agreement with the experimental observation both during healthy

condition and after blockage in PRV (item No. 27 in Fig. 2.2) in loading circuit was

introduced.

Fig.2.12: Variation of measured states Pmi, Pmo, Pppandωn both in

normal and faulty condition (Experimental).

Fig.2.13: Variation of measured states Pmi, Pmo, Ppp and ωn both in

normal and faulty condition (Simulation).

36

2.5. Qualitative FDI Using Temporal Causal Graphs:

Fig. 2.14: Linearized bond graph model of the system

Causal graphs are a type of linear graphs, which represent the model structure by

linking various nodes representing variables in the model. The directed edges in the

graph are used to represent constraints corresponding to various passive elements in a

bond graph model (I, C, R and also TF and GY); whereas additive constraints are

represented at the nodes. Temporal causal graph (TCG) [Mostermann and Biswas,

1999] is a special class of causal graphs, in which temporal evolution of variables are

represented qualitatively by accounting for the storage elements encountered in the

causal path. Since TCG is not applicable to nonlinear system model so the BG model

given in Fig.2.3 is linearised by replacing square root type nonlinear representation of

all the valves with linear resistances. The linearized BG model is shown in Fig.2.14.The

linear resistances can be found out by the following way.

37

For same flow rate in DCV

in

mil

milfR

PPPPk

i

sup

sup )(

(2.11)

In Eq. (2.11), estimated value ofif

k is used to find out inR which is equal to

1.386 x 108m

4s

-1N

-1/2.In the same manner the value of outR and plR are found out as

1.386 x 108m

4s

-1N

-1/2 and 5.99 x 10

10 m

4s

-1N

-1/2 respectively.

Temporal causal graphs have a strong similarity to signal flow graphs and thus

they are easily constructed from bond graph models using the method for creating signal

flow graphs. The '1/s' terms in frequency domain representing Laplace transform of

integration with respect to independent variable t (time) are represented as integrals in

temporal causal graphs. The integration with respect to time corresponding to integrally

causalled storage elements introduces delay[Ghiaus 1999; Mosterman and Biswas 1999]

in the system’s response. This delay is depicted as 'dt' in temporal causal graph.

Similarly, 1/dt term is used to represent differentiation in edges corresponding to

storage elements in derivative causality.

The temporal causal graph can be traversed in both forward and backward

direction from an observed or hypothesized fault (in a signal or a parameter). The

backward propagation is used to construct the list of fault candidates, whereas the

forward propagation derives predictions for posteriori behaviour (time evolution)

corresponding to each of the hypothesized faults.

The temporal causal graph for the hydrostatic transmission system is shown in

Fig. 2.15. Let us now consider a fault scenario, whereby the measured pressure in

loading pump (i.e. Ppp) is found to be above its nominal value, i.e. in qualitative terms

e31+.

38

Fig. 2.15: Temporal Causal Graph for the Hydrostatic Transmission System

2.5.1. Hypothesis Generation:

Backward propagation, i.e. chasing the path opposite to the signal flow

direction, is used to produce the fault hypothesis, i.e. a list of fault candidates.

Backward propagation starts from the measurement node whose qualitative state is

available and terminates at parameters or conflicting nodes.

39

Fig. 2.16: Backward Propagation

When traverse back from, e31+ there is a single edge with gain kpp dt to the node

f31. Since e31 is qualitatively higher, it results that bulk modulus of fluid at outlet side of

pump is higher (kpp+) and/or f31 is higher (f31

+). When a parameter is encountered, the

propagation is completed for that branch. Then the back propagation continues for

remaining nodes, i.e. from f31+. The tree representing the back propagation is given in

Fig. 2.16. During back propagation, instantaneous edges are given precedence. This

means that if there are two backward edges from a node with two different orders of

delays and then those two branches meet somewhere else, i.e. they are parallel, and then

the branch with least order of delays is propagated first.

The generated fault hypothesis contains the list of fault candidates and their

likely qualitative state. Under single fault hypothesis, it is assumed that only one

parameter from the set (Kpp+, Rpl

+, Dp

+, J1

-, Rf

-, Dm

+, Rbl1

-, Rbl2

-, Kpmi

+, Kpmo

-, Rin

-, Rlkg1

+,

Rlkg2-, Ripl

+, Rout

-) has deviated from its nominal value. Then the objective is to find

which one parameter?

The very first step in isolating the fault candidate is reduction of dimension of

the set of initial fault candidates. This requires qualitative input from other sensors and

follows the principle similar to the fault tree analysis. In the next step, there are some

parameters that can be considered robust or at least robust to drift in a specific direction.

Considering that the observed deviation in measured signal is abrupt fault, and

not progressive fault and making pragmatic assumptions like the leakage or blockage

40

resistances and the pump displacement do not change, so the initial fault set can be

reduced to (Kpp+, Rpl

+, J1

-, Dm

+, Kpmi

+, Kpmo

-, Rlkg1

+, Ripl

+), which corresponds to the set

of parameters belonging to faulty components in the pump and motor.

2.5.2. Hypothesis Validation:

After the hypothesis generation next is its validation. In this analysis, single fault

hypothesis is considered, among the fault candidates, only one is faulty. Next it is

generated the qualitative trend (QT), i.e. magnitude, slope, and so on, of the output after

inception of the fault, considering each fault candidate one by one. The forward

propagation of the temporal causal graph yields predictions for future behaviour for the

set of measurements for a postulated fault. This prediction takes account of temporal

delays encountered during forward propagation.

Let us consider the fault hypothesis that the resistance in pump plenum has

increased (Rpl+). This can be achieved by switching off the bypass line DCV (item No.

26 in Fig. 2.2), thereby forcing the flow to pass through the pressure relief valve (item

no. 27 in Fig. 2.2) with higher restriction. Starting forward propagation (along the

direction of signal only) from the edge containing parameter Rpl leads to 3132 ff . At

this node, temporal edge (dt in forward path) is encountered and therefore effect on

consequent nodes is time delayed (due to integration). This implies derivative of e31 is

affected instead of its magnitude. This is represented as e31↑, where the number of

arrows represents the number of time delays encountered during forward propagation to

that node and the arrow direction represents the qualitative magnitude, i.e. ‘↓’ for ‘–’

and ‘↑’ for ‘+’.

Fig. 2.17: Forward Propagation

41

Normally, forward propagation is completed when predictions are presented for

a sufficiently higher order. The predicted temporal qualitative trend, also called

temporal signatures, corresponding to hypothesized fault Rpl+ is given in Fig. 2.17.

(a) (b)

(c) (d)

Fig. 2.18: Time response of outputs from sensors (Pmi, Pmo, Ppp, ωn) corresponding to 0.1s of

normal fault-free operation and 50% blockage in the PRV (item No. 27 in Fig. 2.2) thereafter

From TCG (Fig. 2.17), it can be predicted that for the blockage fault in PRV

(Rpl+) the steady state value of Ppp should increase (as e31+ ), that of Pmi (e4+ ) should

increase, Pmo (e18-) should decrease and ωm (f24-) should also decrease. Again, first

derivative (i.e. slope) increases for Ppp (e31). In case of Pmi (e4), first derivative

decreases, second derivative increases and then third derivatives decreases.Similarly the

qualitative states attributed to slope changes can also be observed for Pmo and ωm. The

variation of the states e4 (Pmi), e18 (Pmo), e31 (Ppp) and f24 (ωm) are obtained through

simulation as shown in Fig. 2.18, which is closely matching with the prediction made

through TCG in Fig. 2.17.

42

Note that the sampling period of the DAS (Data Acquisition System) for the

experimental setup is 4 secs. So the transient dynamics could not be validated through

experimentation.

2.6. Conclusions:

Experimental and simulation study in the context of system identification and

model based qualitative FDI were carried out on a hydrostatic transmission system. The

unknown system parameters are estimated offline though nonlinear regression analysis

and then assigned in the system model for simulation study and compared with the state

response of the real system. It is found that the response of the model with the estimated

parameters tracks that from the physical system with sufficient accuracy. Also, the time

response trend of states due to a blockage fault introduced in a PRV (item 27 in Fig.

2.2) in the physical system was observed matching with the responses from the model

simulation. Then this model was used for qualitative FDI through fault tree and TCG.

The prediction from fault tree analysis was validated through model simulation and

experimentation, while that of TCG could be validated through model simulation only.

In TCG, back propagation is used for hypothesis generation, which examines the

qualitative changes of different component parameters (+ or -) for qualitative change (+

or -) of measured state. Next, hypothesis validation is done using forward propagation,

whereby qualitative trend, i.e. magnitude (+ or -), slope ( or ) and temporal delays

due to integration of the states are predicted and matched with the measurement. Now,

assigned nominal parameter value is based on some measurement which contains some

inherent uncertainty. But, the qualitative changes of the states (+ or -) are not measured

quantitatively, thus the uncertainty component is ignored. So, it is difficult to fix a

threshold for the measurements within which the deviation is due to uncertainty and

beyond which the deviation is due to fault. Hence, the fixation of threshold is done

using quantitative FDI and LFT method, addressed in chapter 4 onwards.