Hidden Markov models are piecewise-stationary models which have been used successfully in many classification applications, including a long history in speech recognition. In HMMs, the hidden states are observed through noisy measurements which are assumed to be conditionally independent given the current discrete state. For the work proposed here, these ``noisy measurements'' would be the features provided by auditory processing and/or the feature transformation techniques to be explored in Thrust area II(A). However, it is likely that other models will be better suited to take advantage of these features than standard discrete-state HMMs which do not capture the continuity of acoustic dynamics that is observed in many applications (e.g. speech recognition). Moreover, the discrete hidden state in an HMM may not be appropriate for characterizing continuous variations in operating conditions (e.g. load on a helicopter gear box, changes in background noise). Extensions of HMMs that use a continuous or mixed continuous and discrete hidden state, as surveyed in [. Ostendorf Digalakis 1996 .], are better suited to such problems and will be explored here. In particular, we propose to extend our past work in Gauss-Markov state sequence model described in [. Digalakis Ostendorf 1993 .] to capture the temporal dynamics of these features and to better represent continuously varying operating conditions. An alternative approach is to use mean trajectory adaptation techniques as described in [.Kannan 1997.].
Modeling variations in background noise: Another reason for using dynamic models is to account for variations in the background noise. This background noise is often produced by other parts of the mechanical system, and thus can be correlated with the acoustic signatures of the fault conditions, particularly in cases where multiple faults occur. However, it is unlikely that changes in acoustic signatures due to fault conditions will be synchronous with changes in background conditions. This poses two interesting problems: detecting the presence of faults in nonstationary environments with correlated noise, and detecting and classifying the presence of multiple correlated faults in noisy, nontransient environments. In speech processing using discrete-state HMMs, nonstationary noise sources are handled well using a product space of noise and signal states (assuming independence of the noise and signal) in a technique referred to as parallel model combination [.Gales 1993.]. We plan in the proposed work to extend this technique to continuous-state models, and investigate the use of the adaptation techniques described above for detection in correlated noise. For detection in the presence of multiple, correlated faults, we propose to exploit our research on binaural auditory models in Thrust area I to provide pre-processing algorithms for signature isolation from multiple faults, and to use the resulting outputs as the basis for detection and classification algorithms.
Stochastic resonant circuits: Another direction which will be investigated is the enhancement of weak signals in heavy noise using nonlinear stochastic resonant circuits, motivated by the peripheral auditory models discussed in Thrust area I. Stochastic resonant circuits are bistable devices which, when driven by weak sinusoids, produce outputs which significantly enhance the signal-to-noise ratio. These circuits were used successfully in [.Asdi 1995, Asdi 1997.] to detect weak sinusoidal signals; the signal-to-noise ratio was enhanced by an order of magnitude, thereby improving significantly the detection performance. Unfortunately, the signatures of faults in rotating mechanical systems is significantly more complex than simple sinusoids. We propose to extend the analysis of [. Asdi 1995, Asdi 1997.] to design weak signature detectors using resonant circuits for complex, multi-tone signals, and to develop adaptive strategies which can be used to tune the parameters of the stochastic resonant system to nonstationary conditions.
Statistical characterization of auditory signals and dynamic systems: One of the consequences of integrating complex, nonlinear auditory preprocessing with dynamical detection and classification processing is that simple analytical representations of preprocessing outputs are difficult to develop. Developing appropriate dynamical HMM models to represent the nonstationary behavior of the system/environment is also a difficult task. Thus, our research must also address the issue of statistical characterization of these signals and models, based on sample data collected from actual applications. Initially, we will focus on the problem of distinguishing fault vs. no-fault cases where the fault is constantly present (if present) but the loading conditions may vary with time. Acoustical data for typical applications with these conditions should be readily available from Navy sources [.Lopez heli1 1996.].
Once good performance has been achieved on the fault/no-fault classification task, the effort will move to the problem of detecting transitions from a no-fault to a fault state, where the transition may occur under variable loading conditions. For the second phase, we hope to work with the Navy to obtain realistic data samples of no-fault/fault transitions for training and evaluating our models. In order to detect such transitions, it will be important to represent the connection between these two states when under the same loading condition. We propose to investigate either a mixed mode hidden state sequence to capture the coupling and/or a non-linear mapping (parameter tying function) between the continuous hidden states associated with these two discrete states. It may also be useful to augment the state space with transient (rather than stationary) models and/or to include transient detection as a preprocessing step for identifying candidate state change points, building on the results of the asymptotic local approach for change detection described in the previous section. The particular approach taken in this second phase of the fault detection research will depend in part on the characteristics of the new data and the developments in feature processing in other efforts of this project.