Sensor Validation Using Nonlinear Minor-Component Analysis

Linearity is not assumed and the physical plant is not modeled.

Aconcept of sensor validation using nonlinear minor-component analysis (NLMCA) has been proposed as a theoretical basis of a sensor fault-detection-and isolation (FDI) module in a fault-tolerant control system of an aircraft jet engine or other complex physical plant. As used here, "sensor validation" signifies, loosely, analysis of the readouts of all the sensors in such a system for the purpose of identifying which (if any) sensors are faulty and, if possible, the magnitudes of the faults. Once a fault in a sensor or any other component was detected and isolated, the fault-tolerant control system would automatically reconfigure itself to compensate for the effect of that and any other faults so as to maintain acceptable (or as nearly acceptable as possible) control performance of the plant even in the presence of the faults. In the case of a faulty sensor, the system would utilize any available analytical redundancy among all sensor signals to estimate the value of the physical quantity desired to be measured by that sensor, and that value would then be used for feedback control.

Figure 1. An NLMCA Structure can be represented as an assembly of concatenated NLPCA structures.
The present sensor-validation concept can be characterized as a data-driven (in contradistinction to a model-driven) FDI concept: the concept involves the use of sensor output data only, and a model of the physical behavior of the physical plant is not needed or used. Moreover, unlike in some prior sensorvalidation concepts, training data in the form of output data from faulty sensors is not needed or used: instead, only training data acquired during normal operation are used.

NLMCA is an extension of nonlinear principal-component analysis (NLPCA), in which a neural network or other suitable nonlinear signal-data-processing structure is used to extract the principal components, defined as the components corresponding to the largest eigenvalues of an input vector, X. The first residual (e1 C the residue left after extraction of the first principal component, PC1) is fed as input into the same NLPCA structure to obtain the second principal component (PC2), the second residual (e2) is fed into the same NLPCA structure to obtain the third principal component, and so forth. In NLPCA (see Figure 1), the process as described thus far is truncated once the principal components have been obtained. In NLMCA, the process is not so truncated and, instead, is continued to obtain the minor components (MC1...MCk), defined as those corresponding to the smallest eigenvalues.

Figure 2 depicts the FDI process according to the present concept. Under normal operating conditions with properly functioning sensors, the minor components are usually close to zero. The amounts by which the minor components differ from zero are summarized by means of a square weighted residual (SWR), which is calculated from a combination of training data and the residuals of the minor components. It has been proven that in comparison with a prior FDI measure calculated from non-weighted residuals, this SWR is more sensitive to faults and more robust to noise. This SWR in normal operation has a chisquare distribution that can easily be used to determine the threshold SWR value for a given confidence level. A fault is deemed to be detected when this SWR exceeds the threshold.

Figure 2. Readings From m Sensors are processed by m+1 NLMCA structures to determine which (if any) sensor is faulty.
Once a fault has been thus detected, a fault-isolation estimator is activated. This estimator contains a bank of NLMCA structures, each of which monitors only one sensor and uses training data from all the other sensors. The sensor monitored by the NLMCA structure that produces the smallest SWR is most likely the one that is faulty and is so labeled by fault-isolation logic.

Once a fault has been thus isolated, a reverse scan method is used to estimate the reading that the faulty sensor would generate if it were not faulty. The faulty-sensor reading is replaced by a substitute reading and the SWR is calculated for the substitute reading. The faulty-sensor reading is then replaced with another substitute reading and a new SWR calculated. This procedure is repeated a number of times to obtain a series of substitute-reading/SWR combinations spanning a range of values of the physical quantity desired to be measured by the faulty sensor. The substitute reading associated with the smallest SWR is taken to be the estimate of the reading that the sensor would generate if it were not faulty.

This work was done by Kenneth Semega of the Air Force Research Laboratory; Roger Xu, Guangfan Zhang, Leonard Haynes, and Chiman Kwan of Intelligent Automation, Inc.; and Xiaodong Zhang of GM R & D and Planning. AFRL-0035

This Brief includes a Technical Support Package (TSP).
Sensor Validation Using Nonlinear Minor-Component Analysis

(reference AFRL-0035) is currently available for download from the TSP library.

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