# Fault detection and isolation

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Fault detection and isolation is a subfield of control engineering which concerns itself with monitoring a system, identifying when a fault has occurred, and pinpointing the type of fault and its location. Two approaches can be distinguished: A direct pattern recognition of sensor readings that indicate a fault and an analysis of the discrepancy between the sensor readings and expected values, derived from some model. In the latter case, it is typical that a fault is said to be detected if the discrepancy or residual goes above a certain threshold. It is then the task of fault isolation to categorize the type of fault and its location in the machinery. Fault detection and isolation (FDI) techniques can be broadly classified into two categories. These include Model-based FDI and Signal processing based FDI.

## Model-based

Example of model-based FDI logic for an actuator in an aircraft elevator control system[1]

In model-based FDI techniques some model of the system is used to decide about the occurrence of fault. The system model may be mathematical or knowledge based. Some of the model-based FDI techniques include [2] observer-based approach, parity-space approach, and parameter identification based methods.

The example shown in the figure on the right illustrates a model-based FDI technique for an aircraft elevator reactive controller through the use of a truth table and a state chart. The truth table defines how the controller reacts to detected faults, and the state chart defines how the controller switches between the different modes of operation (passive, active, standby, off, and isolated) of each actuator. For example, if a fault is detected in hydraulic system 1, then the truth table sends an event to the state chart that the left inner actuator should be turned off. One of the benefits of this model-based FDI technique is that this reactive controller can also be connected to a continuous-time model of the actuator hydraulics, allowing the study of switching transients.[3]

## Signal processing based FDI

In signal processing based FDI, some mathematical or statistical operations are performed on the measurements, or some neural network is trained using measurements to extract the information about the fault.[4]

A good example of signal processing based FDI is Time Domain Reflectometry where a signal is sent down a cable or electrical line and the reflected signal is compared mathematically to original signal to identify faults. Spread Spectrum Time Domain Reflectometry, for instance, involves sending down a spread spectrum signal down a wire line to detect wire faults.[5] Several clustering methods have also been proposed to identify the novel fault and segment a given signal into normal and faulty segments.[6]

## Machine fault diagnosis

Machine fault diagnosis is a field of Mechanical Engineering concerned with finding faults arising in machines. A particularly well developed part of it applies specifically to rotating machinery, one of the most common types encountered. To identify the most probable faults leading to failure, many methods are used for data collection, including vibration monitoring, thermal imaging, oil particle analysis, etc. Then these data are processed utilizing methods like spectral analysis, wavelet analysis, wavelet transform, short term Fourier transform, Gabor Expansion, Wigner-Ville distribution (WVD), cepstrum, bispectrum, correlation method, high resolution spectral analysis, waveform analysis (in the time domain, because spectral analysis usually concerns only frequency distribution and not phase information) and others. The results of this analysis are used in a root cause failure analysis in order to determine the original cause of the fault. For example, if a bearing fault is diagnosed, then it is likely that the bearing was not itself damaged at installation, but rather as the consequence of another installation error (e.g., misalignment) which then led to bearing damage. Diagnosing the bearing's damaged state is not enough for precision maintenance purposes. The root cause needs to be identified and remedied. If this is not done, the replacement bearing will soon wear out for the same reason and the machine will suffer more damage, remaining dangerous. Of course, the cause may also be visible as a result of the spectral analysis undertaken at the data-collection stage, but this may not always be the case.

The most common technique of detecting fault is the time-frequency analysis technique. For a rotating machine, the rotational speed of the machine (often known as the RPM), is not a constant, especially not during the start-up and shutdown stages of the machine. Even if the machine is running in the steady state the rotational speed would vary around a steady-state mean value, and such a variation depends on load and other factors. Since the sound and vibration signals are directly obtained from a rotating machine which is strongly related to its rotational speed or RPM, it can be said that they are time-variant signals in nature. These time-variant features carry the machine fault signatures. Consequently, how these features are extracted and interpreted is important to research and industrial applications.

The most common signal analysis used method would be the FFT, The Fourier Transform and its inverse counterpart offer two perspectives to study a signal which is the time domain or frequency domain. The FFT based spectrum of a time signal tells us the existence of its frequency contents. By studying them and their magnitude or phase relations we can obtain a lot of information such as the harmonics, sidebands, beat frequency, bearing fault frequency and so on. However, FFT is only suitable for signals whose frequency contents do not change over time but as mentioned above these frequency contents of the sound and vibration signals obtained from a rotating machine are very much time dependent. In Conclusion, FFT based spectrum is unable to detect how the frequency contents develop over time. To be more specific if the RPM of a machine is increasing or decreasing during start up or shut down period its bandwidth in the FFT spectrum becomes much wider than its supposed to be. Hence, in such a case the harmonics are not so distinguishable in the spectrum.

The time frequency approach for machine fault diagnosis is explained by diving them into two broad categories, the linear methods and the quadratic methods. The difference is the linear transform can be inverted to construct the time signal thus it is more suitable for signal processing, such as noise reduction and time-varying filtering. Although the quadratic method describes the energy distribution of a signal in the joint time frequency domain, which is although useful to analyze, classify and detect features of the signal the phase information is lost in the quadratic time-frequency representation also the time histories cannot be reconstructed.

In the linear time-frequency methods the short-term Fourier Transform (STFT) and the Gabor Transform are two algorithms. Considering linear time-frequency analysis as the evolution of conventional FFT, the quadratic time frequency analysis is the counterpart of the power spectrum. Quadratic algorithms include the Gabor spectrogram, Cohen's class and the adaptive spectrogram. The main advantage of time frequency analysis is discovering the patterns of frequency changes, which usually represent the nature of the signal. As long as this pattern is identified the machine fault associated with this pattern can be identified. Another important use of the time frequency analysis is the ability to filter out a particular frequency component using a time varying filter.

Methods used to collect data include vibration measurement, thermal imaging, oil particle analysis and others.

## Schemes of applying diagnostics

Fault diagnostics in usual industrial practice need to be applied according to guidelines. This need arises from the fact that diagnostics on their own may be capable of saving a single machine if monitoring is adequate, but it is impossible to apply them to all the equipment. The investment needed to either install continuous condition monitoring sensors on all the machinery in a factory or to check enough samples from all machinery on a regular basis would be forbidding.

As a result, using fault diagnostics to meet industrial needs in a cost-effective way, and to reduce maintenance costs without requiring more investments than the cost of what is to be avoided in the first place, requires an effective scheme of applying them. This is the subject of maintenance, repair and operations; the different strategies include:

## References

1. ^ Jason R. Ghidella and Pieter J. Mosterman, "Requirements-Based Testing in Aircraft Control Design," Paper ID AIAA 2005-5886 in AIAA Modeling and Simulations Technologies Conference and Exhibit 2005, August 15-18, San Francisco, California, 2005.
2. ^ Ding, S.X., Model-based fault diagnosis techniques, Springer 2008
3. ^ Pieter J. Mosterman and Jason Ghidella, "Model Reuse for the Training of Fault Scenarios in Aerospace," in Proceedings of the AIAA Modeling and Simulation Technologies Conference, CD-ROM, paper 2004-4931, August 16 - 19, Rhode Island Convention Center, Providence, RI, 2004.
4. ^ Liu, Jie (2012). "Shannon wavelet spectrum analysis on truncated vibration signals for machine incipient fault detection". Measurement Science and Technology 23 (5): 1–11. doi:10.1088/0957-0233/23/5/055604.
5. ^ Furse,Cynthia; Smith, Paul; Lo, Chet. "Spread Spectrum Sensors for Critical Fault Location on Live Wire Networks" Structural Control and Health Monitoring June 6, 2005.
6. ^ Bahrampour,Soheil; Moshiri, Behzad; Salahshour, Karim. "Weighted and constrained possibilistic C-means clustering for online fault detection and isolation [1]" Applied Intelligence, Vol 35, pp. 269-284, 2011 June 6th, 2005.