The acoustic emissions of a ground vehicle contain a wealth of information, which can be used for vehicle classification, e.g. in the battlefield. However, features that are extracted from the acoustic measurements are time-varying and contain a lot of uncertainties, especially when the acoustic measurements are obtained from multiple terrains, which makes the classification challenging. In this paper we present our study on the multi-category classification of ground vehicles based on the acoustic data of four environmental conditions. The goal is to design one classifier that can operate in all four terrains without a priori knowledge of a specific terrain. We first perform the data pre-processing (including elimination of redundant records, processing of data distortion and generation of prototypes), feature extraction, and uncertainty analysis. We then develop the Bayesian classifier, and type-1 (T1) and interval type-2 (T2) fuzzy logic rule-based classifiers (FLRBC). These classifiers have similar architectures, consist of four sub-systems each for one terrain, and have one probability model (Bayesian classifier) or one fuzzy logic rule (T1 and interval T2 FLRBCs) for each kind of vehicle on each terrain. They differ in the way that this common architecture is implemented.
We also present the results of the experiments to evaluate the performance of all classifiers. Experimental results reveal that (1) both the T1 and interval T2 FLRBCs have better performance than the Bayesian classifier, and the interval T2 FLRBC has better performance than the T1 FLRBC; (2) each classifier has a smaller average but a slightly larger standard deviation of classification error rates when the majority voting-based temporal decision fusion is applied; and (3) when the majority voting-based temporal decision fusion is applied, both the T1 and interval T2 FLRBCs have better performance than the Bayesian classifier, and the interval T2 FLRBC has better performance than the T1 FLRBC.
The acoustic emissions of a ground vehicle contain a wealth of information which can be used for vehicle classification, e.g. in the battlefield. However, features that are extracted from the acoustic measurements are time-varying and contain a lot of uncertainties, which makes the classification challenging. Since it is impossible to establish precise mathematical models to describe these variations and uncertainties contained in the features, we have applied fuzzy set and fuzzy logic theories to model and manage them, and have proposed three fuzzy logic rule-based classifier (FL-RBC) architectures -- non-hierarchical, hierarchical in parallel and hierarchical in series -- for the multi-category classification of ground vehicles. These FL-RBC architectures have been implemented based on both type-1 and type-2 fuzzy logic theories. We have also conducted experiments on our proposed FL-RBC architectures as well as on a Bayesian classifier to evaluate their performances. The experiments have shown that for this multi-category classification problem, (1) all FL-RBC architectures perform much better than the Bayesian classifier, (2) the type-2 FL-RBC architectures perform better than their competing type-1 implementations, (3) the type-2 non-hierarchical and hierarchical in series FL-RBC architectures perform the best, and (4) the performance of a classifier can be improved by incorporating decision fusion.
In array signal processing, it is well known that the effective aperture of a physical array can be increased by means of combined spatial and temporal processing of measurements. In the same spirit, the combined decision of an array of experts can be made more accurate by means of spatio-temporal fusion. We propose three approaches to implement spatio-temporal decision fusion based on the majority voting technique, namely overall, space-time and time-space. We compare these three approaches in terms of their implementation costs, and the probability of the fully-combined decision being correct, and conclude that both the overall and the time-space approaches are better choices than the space-time approach.
Our goal for this study is to construct classifiers with minimum
classification error rates for three binary classification problems based on their acoustic emissions, namely tracked versus wheeled vehicles, heavy-tracked versus light-tracked vehicles, and heavy-wheeled versus light-wheeled vehicles. Because the acoustic measurements of a run correspond to tens or hundreds of seconds, and are time-varying, we segment them into one-second data blocks, and use the data blocks (which we call prototypes) for classification. The magnitudes of the second through 12th harmonics of each prototype are used as the features. We find, by analyzing the features within each run and across runs, that the run-means and run-standard-deviations of the features vary from run to run for all kinds of vehicles. We therefore use type-2 fuzzy sets to model the uncertainties contained in these features, and then construct type-2 fuzzy logic rule-based classifiers (FL-RBC) for these three binary
classification problems. To evaluate the performance of the type-2
FL-RBCs in a fair way, we also construct the Bayesian classifiers
and type-1 FL-RBCs, and compare their performance through leave-one-out experiments. Our experiments show that both the type-1 and type-2 FL-RBCs have significantly better performance than the Bayesian classifier, and the type-2 FL-RBC has better performance than the type-1 FL-RBC for all three classification problems. So we conclude that the type-2 FL-RBCs are the desired classifiers for these three binary classification problems.
There are lots of uncertainties with ground vehicle classification when such a classification is based only on acoustic emissions. To handle such uncertainties, we apply type-2 fuzzy system theoreies to the designs of FL rule-based vehicle classifiers, using amplitudes of the 2nd through 12th harmonics as the features. Statistical analysis of these features for both tracked and wheeled vehicles demonstrates that their standard deviations vary as much as their means; hence, the membership functions for the antecedents of the type-2 FL rule-based classifier were chosen to be Gaussian primary memberships with uncertain means of standard deviations. We constructed three classifiers for tracked/wheeled vehicle classification, namely Bayesian, type-1 and type-2 FL rule-based, and used the leave-one-out scheme to evaluate these classifiers. Our experiments demonstrated that the average false alarm rates of the type-1 and type-2 FL rule-based classifiers are much smaller than that of the Bayesian classifier; and the average false alarm rate of teh type-2 FL rule-based classifier is smaller than that of the type-1 FL rule-based classifier.
KEYWORDS: Signal processing, Acoustics, Interference (communication), Statistical analysis, Systems modeling, Process modeling, Signal detection, Fourier transforms, Automatic control, Signal analyzers
Most real-world signals are non-Gaussian. If they were Gaussian then they could be completely characterized by their first- and second-order statistics, because the probability density function (p.d.f.) for a Gaussian signal is completely described by these statistics. Because most real-world signals are not Gaussian, we need to use more than just first- and second-order statistics, i.e., we need to use "higher-order statistics." We could use higher-order moments, e.g., triplecorrelations, quadruple-correlations, etc., or we could use cumulants. Cumulants are related to higher-order moments, but do not necessarily always equal these moments. Reasons for preferring cumulants over moments are explained below.
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