Conflict of interest

It can be seen from Figure 5 that although noise exists, the developed input reconstruction techniques can provide reconstructed inputs with a good accuracy. At actuator of process fluid, sudden decrease occurs at 60 s which indicates occurrence of a fault, and it takes 4 s to steady at new value. For actuator of utility fluid, the reconstructed value increases from 40 s,

As illustrated in Figure 6, detection residual r<sup>1</sup> indicates a fault in actuator of process fluid at 60 s, it takes 1.2 s to determine the occurrence of the fault. Detection residual r<sup>2</sup> refers to a fault in actuator of utility fluid at 40 s, and it takes 1.5 s to detect it. We can shorten the detection time and detect smaller fault by employing larger gain for the detection observers or adopt a smaller threshold. However, larger gain or larger threshold may fail to detect the fault correctly, since observer with larger gain is too sensitive to noise and smaller threshold may lead to be undistinguished from noise. Therefore, a trade between detectability and sensitivity should be made in order to detect the fault correctly. In summary, a small magnitude fault may not be detected within the existence of the noise. Again, after detection of the faults, we

We can see from Figure 7 that only RCA residual s12 breaks through its threshold and remains beyond it; the rest three RCA residuals are below their thresholds, and then the fault resource f2 of actuator of process fluid is identified. When comes to RCA residuals for actuator of utility fluid in Figure 8, only s23 is beyond its threshold which verifies the occurrence of fault cause f3. From the above simulation results, we can see that the proposed strategy is available to detect and locate a fault correctly, and root cause analysis for each detected fault is achieved with a

good accuracy. Encouraging simulation results are obtained thanks to the robustness.

and is stable after about 3 s. A fault is detected due to the unexpected increase.

have to identify their root causes.

Figure 8. Residuals for identifying fault cause in utility fluid.

146 Actuators

The authors declare that there is no conflict of interest regarding the publication of this paper.
