A method of automated diagnosis of helicopter gearboxes involves processing of selected features of digitized outputs of vibration sensors via structure-based connectionist networks (SBCNs), which are mathematical constructs that incorporate elements from the disciplines of dynamical modeling, fuzzy systems, and neural networks. Like vibration-analysis gear-diagnostic methods that have been reported previously in NASA Tech Briefs, the SBCN method offers a partial solution to the basic problem of using pattern-classification techniques to extract indications of specific faulty gearbox components from the outputs of accelerometers mounted at several locations on a gearbox.
In the traditional approach to diagnosis by analysis of vibrations, one relies on a combination of (1) human expertise regarding abnormal features of vibration signals and (2) information on the proximity of each vibration sensor to each component that could be faulty. The traditional approach entails difficulty in processing large numbers of both normal and abnormal signal features and in identifying abnormal features in signals contaminated with noise. The SBCN approach offers greater potential capability for coping with noise and multiple features.
In its graphical representation (see figure), an SBCN is reminiscent of a simple artificial neural network. Vibration signals to be processed in the SBCN are preprocessed via the Single Category-Based Classifier (SCBC) algorithm, which classifies signal features by comparing their values with corresponding values recorded during normal operation in the absence of faults. Some features are flagged on the basis of their degrees of abnormality. The flagged features are fed as inputs to the SBCN.
The flagged features propagate through the SBCN similarly to the way in which they would propagate through a corresponding neural network. The responses of the SBCN are given by
where pk(t) is a measure of the time-dependent index that the kth gearbox component is faulty, fi(t) is a value representative of the time-dependent flagged vibration-signal features from the ith accelerometer, and wik is a connection weight. As they would in a neural network, the connection weights embody the ranges of flagged feature values associated with various specific faults.
Unlike in a neural network, the connection weights are not established by supervised training on comprehensive sets of measurement data associated with known faults. Instead, each wik is based on the lower and upper bounds of fuzzy influences between the ith accelerometer and the kth component. The "structure-based" aspect of the SBCN arises as follows: The need for supervised training is eliminated by using knowledge of the dynamics of the gearbox structure to account for the effects of the proximity of the components and the accelerometers on the features of the vibration signals. In principle, this would involve the use of the dynamics to predict the effects of propagation of vibrations through the structure and the resulting attenuation of the flagged signal features at every frequency of interest. In practice, exact mathematical modeling of the dynamics is impossible; instead, one uses a simplified lumped-mass mathematical model to approximate root-mean-square (rms) attenuation values that are used as average attenuation levels applicable to all frequencies. The rms values are used to assign structural influences, which are then represented by fuzzy variables.
The structural-influence fuzzy variables embody knowledge of the structure only. It is necessary to also assign featural-influence fuzzy variables, which embody knowledge of the effects of component failures on flagged signal features. Inasmuch as vibration-signal features are usually obtained at frequencies related to rotational frequencies of individual components, the effects of component faults on the features can be determined readily and used to calculate the featural-influence fuzzy variables. The structural- and featural-influence fuzzy variables are then incorporated as connection weights in the SBCN.
This work was done by Vinay B. Jammu and Kourosh Danai of The University of Massachusetts and David G. Lewicki of the Propulsion Directorate of the U.S. Army Research Laboratory for Lewis Research Center. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com under the Mathematics and Information Sciences category, or circle no. 129 on the TSP Order Card in this issue to receive a copy by mail ($5 charge).
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