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Fault analysis

The detection and diagnosis of malfunctions in technical systems. Such systems include production equipment (chemical plants, steel mills, paper mills, and power stations), transportation vehicles (ships, airplanes, automobiles), and household appliances (washing machines, air conditioners). In any of these systems, malfunctions of components may lead to damage of the equipment itself, degradation of its function or product, jeopardy of its mission, and hazard to human life. While the need to detect and diagnose malfunctions is not new, advanced fault detection has been made possible only by the proliferation of the computer. Fault detection and diagnosis actually means a scheme in which a computer monitors the technical equipment to signal any malfunction and determines the components responsible. The detection and diagnosis of the fault may be followed by automatic actions, enabling the fault to be corrected such that the system may operate successfully even under the particular faulty condition.

Diagnostic concepts

Fault detection and diagnosis applies to both the basic technical equipment and the actuators and sensors attached to it. In the case of a chemical plant, the former includes the reactors, distillation columns, heat exchangers, compressors, storage tanks, and piping. Typical faults are leaks, plugs, surface fouling, and broken moving parts. The actuators are mostly valves, together with their driving devices (electric motors and hydraulic or pneumatic drives). The sensors are devices measuring the different physical variables in the plant, such as thermocouples, pressure diaphragms, and flow meters. Actuator and sensor fault detection is very important because these devices are prone to faults.

The on-line or real-time detection and diagnosis of faults means that the equipment is constantly monitored during its regular operation by a permanently connected computer, and any discrepancy is signaled almost immediately. On-line monitoring is very important for the early detection of any component malfunction before it can lead to more substantial equipment failure. In contrast, off-line diagnosis involves monitoring the system by a special, temporarily attached device, under special conditions (for example, car diagnostics at a service station).

The diagnostic activity may be broken down into several logical stages. Fault detection is the indication of something going wrong in the system. Fault isolation is the determination of the fault location (the component which malfunctions), while fault identification is the estimation of its size. On-line systems usually contain the detection and isolation stage; in off-line systems, detection may be superfluous. Fault identification is usually less important than the two other stages.

Fault detection and isolation can never be performed with absolute certainty because of circumstances such as noise, disturbances, and model errors. There is always a trade-off between false alarms and missed detections, with the proper balance depending on the particular application. In professionally supervised large plants, false alarms are better tolerated and missed detections may be more critical, while in consumer equipment (including cars) the situation may be the opposite.

Approaches

A number of different approaches to fault detection and diagnosis may be used individually or in combination.

Limit checking

In this approach, which is the most widely used, system variables are monitored and compared to preset limits. This technique is simple and appealing, but it has several drawbacks. The monitored variables are system outputs that depend on the inputs. To make allowance for the variations of the inputs, the limits often need to be chosen conservatively. Furthermore, a single component fault may cause many variables to exceed their limits, so it may be extremely difficult to determine the source. Monitoring the trends of system variables may be more informative, but it also suffers from the same drawbacks as limit checking.

Special and multiple sensors

Special sensors may be applied to perform the limit-checking function (such as temperature or pressure limit sensors) or to monitor some fault-sensitive variable (such as vibration or sound). Such sensors are used mostly in noncomputerized systems. Multiple sensors may be applied to measure the same system variable, providing physical redundancy. If two sensors disagree, at least one of them is faulty. A third sensor is needed to isolate the faulty component (and select the accepted measurement value) by “majority vote.” Multiple sensors may be expensive, and they provide no information about actuator and plant faults.

Frequency analysis

This procedure, in which the Fourier transforms of system variables are determined, may supply useful information about fault conditions. The healthy plant usually has a characteristic spectrum, which will change when faults are present. Particular faults may have their own typical signature (peaks at specific frequencies) in the spectrum.  See also: Fourier series and transforms

Fault-tree analysis

Fault trees are the graphic representations of the cause-effect relations in the system. On the top of the tree, there is an undesirable or catastrophic system event (top event), with the possible causes underneath (intermediate events), down to component failures or other elementary events (basic events) that are the possible root causes of the top event. Thelogic relationships from bottom up are represented by AND and OR (or more complex) logic gates. Fault trees can be used in system design to evaluate the potential risks associated with various component failures under different design variants (bottom-up analysis). In a fault diagnosis framework, the tree is used top down; once the top event is observed, the potential causes are analyzed by following the logic paths backward.

Parameter estimation

This procedure uses a mathematical model of the monitored system. The parameters of the model are estimated from input and output measurements in a fault-free reference situation. Repeated new estimates are then obtained on-line in the normal course of system operation. Deviations from the reference parameters signify changes in the plant and a potential fault. The faulty component location may be isolated by computing the new physical plant parameters and comparing them with those from the model.  See also: Estimation theory; Model theory

Consistency checking

This is another way of using the mathematical-system model. The idea is to check if the observed plant outputs are consistent with the outputs predicted by the model (Fig. 1). Discrepancies indicate a deviation between the model and the plant (parametric faults) or the presence of unobserved variables (additive faults). This testing concept is also called analytical redundancy since the model equations are used in a similar way as multiple sensors.

Fig. 1  Two stages of model-based fault detection and isolation. (After R. Isermann and B. Freyermuth, eds., Proceedings of the IFAC SAFEPROCESS Symposium, Baden-Baden, Germany, September 10–13, 1991, Pergamon, 1992)

In preparation for fault monitoring by analytical redundancy methods, a mathematical model of the plant needs to be established. This may be done from “first principles,” relying on the theoretical understanding of the plant's operation, or by systems identification using experimental data from a fault-free plant.

The actual implementation of fault monitoring usually consists of two stages (Fig. 1). The first is residual generation, where residuals are mathematical quantities expressing the discrepancy between the actual plant behavior and the one expected based on the model. Residuals are nominally zero and become nonzero by the occurrence of faults. The second stage is residual evaluation and decision making, where the residuals are subjected to threshold tests and logic analysis. Disturbances and model errors may also cause the residuals to become nonzero, leading to false alarms.

Fault isolation requires specially manipulated sets of residuals. In the most frequently used approach, residuals are arranged so that each one is sensitive to a specific subset of faults (structured residuals). Then in response to a particular fault, only a fault-specific subset of residuals triggers its test, leading to binary fault codes.

Principal component analysis (PCA)

In this approach, empirical data (input and output measurements) are collected from the plant. The eigenstructure analysis of the data covariance matrix yields a statistical model of the system in which the eigenvectors point at the “principal directions” of the relationships in the data, while the eigenvalues indicate the data variance in the principal directions. This method is successfully used in the monitoring of large systems. By revealing linear relations among the variables, the dimensionality of the model is significantly reduced. Faults may be detected by relating plant observations to the normal spread of the data, and outliers indicate abnormal system situations. Residuals may also be generated from the principal component model, allowing the use of analytical redundancy methods in this framework.  See also: Eigenfunction

Example of fault-tree analysis

The schematic of a simple electrical circuit in which a light is operated by a pair of three-way switches is shown in Fig. 2. (Such circuits are used in long hallways.) Figure 3 shows the detailed fault tree of the circuit. The tree goes down to subcomponents (contacts of the switches) in order to illustrate more complex logic relations on this simple system. Note that nonfailure events (operating conditions) are also among the basic events because such conditions (the position of each switch) determine whether a particular failure event triggers the top event.

Fig. 2  Simple electrical circuit: a lamp operated by a pair of three-way switches.

Fig. 3  Detailed fault tree of the circuit shown in Fig. 2.

Example of consistency checking

Traditionally, a few fundamental variables, such as coolant temperature, oil pressure, and battery voltage, have been monitored in automobile engines by using limit sensors. With the introduction of onboard microcomputers, the scope and number of variables that can be considered have been extended. Active functional testing may be applied to at least one actuator, typically the exhaust-gas recirculation valve. Model-based schemes to cover the components affecting the vehicle's emission control system are gradually introduced by manufacturers. One approach (Fig. 4) uses analytical redundancy to monitor two groups of actuators (fuel injectors and exhaust gas recirculation) and four sensors (throttle position, manifold pressure, engine speed, and exhaust oxygen). By the appropriate selection of the model relations, the residuals are insensitive to the load torque and the vehicle's mass. The structured residual technique is used to support fault isolation. The critical issue is to find sufficiently general models so that a single scheme may function well across an entire automobile product line and under widely varying operating conditions.  See also: Automotive engine; Microcomputer; Microprocessor

Janos J. Gertler

Fig. 4  Car engine system with onboard fault detection and diagnosis. (After R. Isermann and B. Freyermuth, eds., Proceedings of the IFAC SAFEPROCESS Symposium, Baden-Baden, Germany, September 10–13, 1991, Pergamon, 1992)

Bibliography

• L. H. Chiang, R. D. Braatz, and E. Russel, Fault Detection and Diagnosis in Industrial Systems, Springer, 2001
• P. L. Clemens, Fault Tree Analysis, 4th ed., Jacobs Sverdrup, 2002
• J. Gertler, Fault Detection and Diagnosis in Engineering Systems, 1998
• J. Gertler, Survey of model-based failure detection and isolation in complex plants, IEEE Control Sys. Mag., 8(7):3–11, 1988
• R. Patton, P. Frank, and R. Clark (eds.), Fault Diagnosis in Dynamic Systems, 1989
• Alifazeli=egeology.blogfa.com

Additional Readings

• Fault Tree Analysis
• Alifazeli=egeology.blogfa.com