FPA on the General Pump System

In Section 4.2.1 it is argued that logical models of the components forming the system can be described as defined in Definition 4.2.1. Using this definition the component model of the centrifugal pump, presented in Section 4.3.1, is given in Table 4.4.

Table 4.4: The component description of the centrifugal pump. The structure of each of the logical matrices is given in Appendix A.

Comp. Faults Effects Transformations c1 fem eem A^em_f ,A^em_dy

c2 0 edy A^dy_em,A^dy_mm,A^dy_sh,A^dy_mp,A^dy_i c3 fmm emm A^mm_f ,A^mm_dy c4 fsh esh A^sh_f ,A^sh_dy c5 fi ei Aⁱ_f,Aⁱ_sh,Aⁱ_ip c6 fmp emp A^mp_f ,A^mp_sh,A^mp_i

c7 fip eip A^ip_f

c8 fop eop A^op_f ,A^op_mp c9 0 edh A^dh_i ,A^dh_op,A^dh_ip

Having a model on this form Algorithm 4.2.1 and Theorem 4.2.1 can be used to de-rived the connection from the faults and disturbing events, to any effect vectorein the system. Therefore, by identifing all measureable effects of interest it is possible to estab-lish a connection between faults and disturbing events, and a subset of the measurable effects. This connection can then be used to evaluate the usability of the given sensor configuration, when the design of signal-based fault detection schemes is considered.

In the previous section a list of sensors used on centrifugal pumps is presented.

Moreover, it is argued that some of these sensors are only used in special applications.

The most frequently used sensors are the electrical sensors and the pressure difference

sensor. Therefore these should attend special attention when developing intelligent FDI algorithms. The electrical and pressure sensors are often used for control purposes in hydraulic applications, and are therefore often available for other purposes too. This means that the cost of implementing a supervision system is reduced considerably by using only these sensors as input to the FDI algorithms.

Beside the sensors just mentioned, the flow sensor is considered. Flow sensors are normally expensive, but by using the newest micro technology it is possible to reduce the cost considerably. This means that this sensor will become interesting in even small centrifugal pump applications. Also a sensor measuring the impeller eye pressure is considered. The flow sensor and the impeller eye pressure sensor are considered to be additional sensors and are therefore increasing the cost of implementing the supervision system.

To summarize; the effects seen in the following sensors are analysed using the FPA,

• Current sensors.

• Voltage sensors.

• pressure difference sensor (between outlet and inlet).

• Flow sensor.

• Impeller eye pressure sensor.

The results of the FPA using these sensors are presented in the following, where each of the logical matrices are obtained by using Algorithm 4.2.1.

Effects on the electrical part of the motor

The effects measurable using the current and voltage sensors are all found in component c1Electrical Part of the Motor. The measurable effects on this component are,

eem,i1 ∼ Increased current.

eem,i2 ∼ Decreased current.

eem,i3 ∼ Oscillations in the length of the pack transform current.

eem,i4 ∼ Unbalanced stator current.

eem,v1 ∼ Zero voltage in one or more of the phases.

eem,v2 ∼ Oscillations in the length of the pack transform voltage.

The connection between these effects and the faults and disturbing events in the system is given by the following logical equation,









 eem,i1

eem,i2

eem,i3

eem,i4

e_em,v1 eem,v2











←











1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0









 µf

d

¶

(4.18) wheref is the fault vector anddis disturbing event vector, both defined in (4.17).

Effects on the pressure difference generated by the pump

The effects measuable using the pressure difference sensor are all found in component c9Pressure Difference. The measurable effects on this component are,

eop,h1 ∼ Increased pressure difference across the pump.

eop,h2 ∼ Decreased pressure difference across the pump.

eop,h3 ∼ Zero pressure difference across the pump.

eop,h4 ∼ Harmonic oscillations in the pressure difference signal.

eop,h5 ∼ High frequence oscillations in the pressure difference signal.

eop,h6 ∼ Pressure difference across the pump is not defined.

The connection between these effects and the faults and disturbing events in the system is given by the following logical equation,









 edh1

edh2

edh3

edh4

edh5

e_dh6











←











0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0









 µf

d

¶

(4.19) wheref is the fault vector anddis disturbing event vector, both defined in (4.17).

Effects on the flow measurement

Using a flow sensor it is possible to measure effects on the flow input, meaning that the effects of the input faults and disturbing events, which are associated with the flow, are measurable with this sensor. The measurable effects on this component are,

eq1 ∼ Increased flow eq2 ∼ Decreased flow eq3 ∼ Not defined

The connection between these effects, and the faults and disturbing events in the system is given by the following logical equation,



 eq1

eq2

eq3



←



 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0



 µf

d

¶

(4.20) wheref is the fault vector anddis disturbing event vector, both defined in (4.17).

Effects on the impeller eye pressure measurement

It is well known that the inlet pressure has large impact on the pump performance, as cavitation will occur if this pressure becomes too low. If cavitation does occure it will destroy the pump over time. Therefore, by measuring the pressure at the impeller eye it might be possible to detect decreases in this pressure and thereby detect the possibilities for cavitation. Moreover measuring the pressure at the impeller eye pressure noise due to cavitation might be measurable. The effects in the impeller eye pressure are found in componentc7Inlet of the Pump andc5Hydraulic part of the centrifugal pump, where the mean pressure is coming fromc7and the pressure noise due to cavitation is coming fromc5. The measurable effects are,

eeh1 ∼ Noise like pressure oscillations eeh2 ∼ Impeller eye pressure not defined eeh3 ∼ Impeller eye pressure too low

The connection between these effects and the faults and disturbing events in the system is given by the following logical equation,



 eeh1

e_eh2 eeh3



←



 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0



 µf

d

¶

(4.21)

In document Aalborg Universitet Fault Detection and Isolation in Centrifugal Pumps Kallesøe, Carsten (Sider 90-93)