The topic of this chapter is fault detection in a centrifugal pump based on steady state measurements only. Here the steady state measurements are Root Mean Square (RMS) measurement of the voltage and current, the voltage frequency, the electrical angle be-tween the voltage and current, and the pressure and volume flow of the pump. Three residuals are derived form the steady state model of the pump, using Structural Analy-sis and Analytical Redundant Relations (ARR’s). The faults under consideration in this chapter are only affecting the second subsystem. Hence the ARR’s are only developed for this part. The connecting variables between the two subsystems are calculated using a steady state model of the motor.
Structural analysis has been used to analyse the system. As a result of this analysis the system is divided into two cascade-connected subsystems simplifying the derivation of the Analytical Redundancy Relation (ARR) considerably. The first subsystem con-sists of the induction motor model, and the mechanical and hydraulic parts of the pump
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time [sec]
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(a) Detection of the faultKfclogging.
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(b) Detection of the faultKlleakage flow.
Figure 7.5: Test results. The top figures show the residual boundaries for each of the three residual setsR1,R2andR3. The bottom figures show the decision signalsD1, D2, andD3.
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(a) Detection of the fault∆Brub impact.
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(b) Detection of the faultfccavitation.
Figure 7.6: Test results. The top figures show the residual boundaries for each of the three residual setsR1,R2andR3. The bottom figures show the decision signalsD1, D2, andD3.
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Figure 7.7: Test results showing detection of the faultfddry running. The top figures show the residual boundaries for each of the three residual setsR1,R2andR3. The bottom figures show the decision signalsD1,D2, andD3.
form the second subsystem. The approach of dividing the system into two cascade-connected subsystems was also utilized in Chapter 6. Parameter variations are only considered for the second subsystem, with the drawback that the algorithm can handle only parameter variations in the hydraulic part of the pump. However, the possibility of handling parameter variations in the hydraulic part can be used to obtain a simple and logical way of setting alarm levels for a user of the system, as these can be defined directly on pump curves, as those shown in Section 3.3.5.
The residuals obtained from the ARR’s are made robust with respect to parame-ter variations in the centrifugal pump model by using the set-valued approach. It is shown that linearization of the parameter function can be used to calculate relatively tight boundaries of the residual in the centrifugal pump case. Using the set-valued ap-proach the set of possible residual values are changed as a function of the operating point of the pump. This could be compared to a residual with an adaptive threshold. The presented method has the advantage of connecting the physics of the pump and the set of residuals in a straightforward manner.
Conclusion and Recommendations
In this thesis different aspects of Fault Detection and Identification (FDI) in centrifugal pumps were considered. Special focus was put on the robustness of the FDI algorithms.
In this connection an analysis method for analysing robustness in signal-based fault detection schemes was proposed. In most model-based fault detection schemes, robust-ness considerations are a part of the design. Therefore, the possibilities of using these approaches on the centrifugal pump were investigated too, ending up with three new FDI algorithms. Here, a small example of connecting these algorithms into one FDI scheme is given. This example is followed by a conclusion and a number of recommendations for further research.
8.1 Algorithm Example
In the thesis four different FDI algorithms were considered. One of these was based on the signal-based approach, and the remaining three on the model-based approach. In the design of the three model-based algorithms, a subset of the following 6 faults were considered.
1. Inter-turn short circuit in the stator of the induction motor.
2. Clogging inside the pump.
3. Increased friction due to either rub impact or bearing faults.
4. Increased leakage flow.
5. Performance degradation due to cavitation.
6. Dry running.
In chapter 5 the detection and identification of the inter-turn short circuit were consid-ered, and in Chapters 6 and 7 the remaining five faults were handled. The difference between the two algorithms in Chapters 6 and 7 lies in their ability to handle transient behaviour in the system. The algorithm derived in Chapter 6 was based on a dynamic description of the pump and was therefore able to handle transient behaviour. The al-gorithm derived in Chapter 7 was on the other hand based on a steady state model and therefore had inherent problems during transient phases.
Composing the algorithm derived in Chapter 5 with the FDI part of the algorithm derived in Chapter 6, the final FDI scheme is obtained. This FDI scheme is capable of detecting and identifying the 6 different faults in the centrifugal pump. The composition of the two algorithms is shown in Fig. 8.1.
Motor ω Pump
Tl
Vs Is Q,H
ω Software
algorithm Real world
Te Residual
observers
D1 D2 D3 fp1
fp2 fp3 Adaptive
observers
Stator faults.
Mech. and hyd. faults.
Figure 8.1: The composition of the adaptive observer, designed for inter-turn short cir-cuit detection, and residual observers, designed for fault detection and identification in the mechanical and hydraulic part of the centrifugal pump.
In Fig. 8.1 the block denoted adaptive observer, contains the observer used for de-tecting stator faults. The output from this observer is the estimates of the electrical states, the speed, and the inter-turn short circuit. The estimates of the electrical states are used for calculating the torque, meaning that the adaptive observer is capable of estimating both the speed, the torque, and the inter-turn short circuit fault.
The inputs to the block, denoted residual observers in Fig. 8.1, are the measured pressure, the measured volume flow, and the estimates of the speed and torque. The output of the residual observer block is the three decision signals described in Chapter 6, meaning that the information of the mechanical and hydraulic faults are available.
In Chapter 7 residual generators, designed using the steady state model of the me-chanical and hydraulic parts of the centrifugal pump, are described. These residual gen-erators could also be used for residual generation in the block, denoted residual observer
in Fig. 8.1. However, by using these residual generators, problems will arise during transient phases.