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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A low-power analog sensor front-end is described that reduces the energy required to extract environmental sensing spectral features without using Fast Fouriér Transform (FFT) or wavelet transforms. An Analog Harmonic Transform (AHT) allows selection of only the features needed by the back-end, in contrast to the FFT, where all coefficients must be calculated simultaneously. We also show that the FFT coefficients can be easily calculated from the AHT results by a simple back-substitution. The scheme is tailored for low-power, parallel analog implementation in an integrated circuit (IC). Two different applications are tested with an ideal front-end model and compared to existing studies with the same data sets. Results from the military vehicle classification and identification of machine-bearing fault applications shows that the front-end suits a wide range of harmonic signal sources. Analog-related errors are modeled to evaluate the feasibility of and to set design parameters for an IC implementation to maintain good system-level performance. Design of a preliminary transistor-level integrator circuit in a 0.13

Sensor systems typically operate by transducing some physical quantity (e.g., pressure, velocity, flux) into the electrical domain and applying signal conditioning. They then compute “features” of the sensed signal relevant to its cause and make decisions or perform actions as a result of the extracted information. Because digital computers are best suited for back-end information processing and decision-making tasks, there must be an analog-to-digital conversion (ADC) as part of the system-level operation. Where in the processing chain the dofor digital operations. The magnitude main conversion happens can affect implementation characteristics such as hardware complexity, energy consumption and service lifetime. Our long-term goal is a very low-power, single-chip, multi-modal environmental sensor that contains a micro-processor and flexible analog signal processing blocks.

The majority of signal detection and classification schemes first transform the acquired signal into a representation that can reveal significant characteristics in a relatively condensed feature vector. Fouriér and wavelet transforms have been proven to generate suitable features for many signal detection and classification tasks, including speech recognition [

Compressive Sensing (CS) has been proposed as an efficient alternative to high-rate Nyquist sampling [

Hardware-oriented architectures and designs utilizing CS concepts have recently been proposed in [

While extracting spectral information with the Fast Fouriér Transform (FFT) is a common method, its disadvantages are apparent within an energy-or power-constrained sensor node. As an example, energy usage data for a military vehicle classification application was measured in [

Directly extracting spectral information in the analog domain bypasses the FFT computation and allows selectively converting features as needed.

In this paper, an Analog Harmonic Transform (AHT) is developed, which extracts feature vectors directly from acquired analog signals. These features may then be used for signal classification or other back-end processing, either directly or transformed into equivalent Fouriér series coefficients by a simple back-substitution. This transform replaces the typical ADC/FFT with a multi-channel analog projection to extract a signal's spectral features.

The outline of the paper is as follows. In Section 2, we introduce the AHT and its relationship to the Fouriér series for performing the feature extraction function within an analog front-end, with emphasis on power consumption and overall system performance. Two case studies are presented in Section 3 to validate the approach within a classification system using ideal calculations. Section 4 describes a hardware realization of the AHT, modeling analog-related errors to determine the feasibility of, and set design specifications for, a hardware design. The paper concludes with Section 5.

Comparisons of the power and area required to implement signal-processing operations at a given precision between analog or digital integrated circuitry have been described by [_{2}(SNR) for digital operations. The magnitude and crossover point depends on factors, such as task, technology and the skill level of the designers [

Clearly, from

Sensed harmonic signals originating from rotating machinery may be modeled as a sum of two components: a deterministic harmonic signal model approximating the revolving parts and a non-deterministic component approximating all other components. Selective features extracted from these signals are sufficient for signal/source discrimination, as shown in [_{k}_{k}_{1} is the fundamental frequency (FF),

To estimate the _{k}_{k}_{1} and, then, projected onto a pair of quadrature basis functions with frequency _{1} and integrated over T= 1/_{1} as:

The AHT scheme takes the Fouriér series' sinusoidal basis functions and uses only their signs, as shown in

The harmonic part of the signal in

Substituting

The result of each in-phase and quadrature projection represents the sum of scaled in-phase and quadrature harmonics' amplitudes, respectively. To better illustrate the relationship between the harmonic parameters (_{k}_{k}_{Ik}_{Qk}

The relation may then be written as:

The in-phase and quadrature amplitude vectors may then be calculated by:

Individual harmonic magnitude and phase estimates may be calculated from the rectangular parameters via:

Matrices _{I}_{Q}_{Ik}_{Qk}

To illustrate the digital computation savings,

Unlike the FFT, which produces all coefficients in the signal's bandwidth, it is not necessary to calculate all the AHT coefficients if the back-end application will not use them. For example, if the lower 5% of the coefficients (three harmonics for _{I}_{,} _{Q}

Finally, it has been shown in [

It is first necessary to determine if this transform provides useful information for a back-end classifier before considering its analog implementation. Two case studies are presented to validate the use of the AHT for harmonic signal classification applications. The first is classification of vehicle types from acoustic recordings, while the second is the identification of machine bearing faults from acceleration data. System classification performance for both applications will be shown to be comparable to existing studies using considerably more complex front-end processing techniques on the same data sets.

Monitoring large regions for military vehicle activity for peacekeeping purposes is an application well-suited for wireless sensor modules. The acoustic emissions of such ground vehicles contain a wealth of information for purposes such as classification [

For ground vehicles, the engine-related FF of the acoustic signal typically lies within the range, 8–20 Hz [

The acoustic data of nine different vehicles covering all combinations of wheeled/tracked and heavy/light-weight types (Leopard 1, Leopard 2, Wiesel, Jaguar, M48, Fuchs, Hermelin, Unimog, and Mercedes-Benz 1017) were recorded by the Bochum Verification Project (BVP) during verification experiments in 2000 [

To determine the presence of a vehicle, an adaptive Constant False Alarm Rate (CFAR) detector [

For classification, a three-layer feed-forward neural network (FNN) was utilized with sigmoid neuron transfer functions. Harmonic amplitudes from each window (_{k}_{k})

Harmonic amplitudes were calculated using the AHT of Section 2.2 with three harmonic models, each with an assumed

From

Previously published classification results from this data set include the original research [

Induction motor failures may be classified as bearing, stator, broken rotor bar, end ring or eccentricity-related faults [

Unlike the other fault classes, which have signatures directly related to shaft speed, bearing-related faults are difficult to represent with a single harmonic model. The natural mechanical resonance frequencies of the machine are modulated by the defect frequency, resulting in spectral components that are not harmonics of either the defect frequency or the machine's natural resonance frequencies [

The data set from [

Under normal operation, most energy is concentrated below about 2 kHz, while the presence of faults moves this energy into the 2–4 kHz band. A single harmonic model with

The transform scheme presented in Section 2 has features well-suited to analog-domain implementation. The results of using this approach in Section 3 show that it is competitive in terms of performance with state-of-the-art techniques, while presenting the promise of very low-power analog implementations. This section explores an example system, which exploits these analog-friendly features and extracts relevant hardware specifications that would be required to maintain good system-level performance.

Multiplication of the input signal by the basis function values of ±1 may be viewed as a conditional signal pass-through or inversion. Using a differential signal path, this inversion is simply a re-labeling of the signal branches, as illustrated in

Other projection systems use a similar hardware topology, but employ Compressive Sensing concepts for basis function generation [

Furthermore, featured in this topology are the low bandwidth requirements placed on the active circuitry; only the input buffer amplifier must operate over the entire signal bandwidth. The integrators in the projection blocks only need response on the order of the integration time window,

Errors introduced into the computation of

_{M}_{clk}

_{I}_{,}_{Q}

_{Ik}_{Qk}

Verification of the technique, including estimated analog hardware error sources, was conducted by replacing the explicit computation of _{h}

The low FF of the vehicle classification case study presents very severe hardware requirements (much longer time constant) and correspondingly larger potential errors than those of bearing fault detection in Section 3.2. Hence, for the feasibility study, we will present results for the vehicle classification task. Initialization data for the error modeling was obtained from a system design implemented in a standard 0.13

Neural network training was performed on a system instance whose _{gain} and _{offset} values and noise magnitudes were set to zero—

Achieving acceptable single-event average classification rates of 75% or above at moderate 20 dB SNR requires offset deviations less than about 10 mV, as indicated by the boxed area in

To determine whether these offset values are feasible, we performed Monte Carlo simulations of a transistor-level integrator design, which included offset calibration circuitry.

The integrators utilized for this study dissipated 200 nW each, when tuned for a 5 Hz FF [

On-chip custom FFT circuitry, such as [

In this paper, a transform suited to parallel, low-power analog implementation was presented. The Analog Harmonic Transform allows efficient extraction of only the narrow spectral features needed by the back-end processing without requiring transforming of the entire signal bandwidth at once, like FFT-based approaches. It does, however, provide the data to easily back-resolve the Fouriér coefficients if required by the back-end processing.

The AHT was tested on two monitoring applications using different modalities (acoustic and vibration signals) and a wide range of fundamental frequencies with good discrimination using neural network classifiers. Hardware modeling simulations show that the effect of implementation errors can be small enough with proper design and calibration to allow reliable detection and classification to be feasible with the proposed low-power approach.

The authors would like to thank Jürgen Altmann at Experimentelle Physik III, Technische Universität Dortmund for providing the acoustic signatures of the military vehicles for peace-keeping and verification applications and Kenneth A. Loparo at Case Western Reserve University for providing the bearing fault vibration data.

The authors declare no conflict of interest.

Performing the feature extraction operation in the analog domain moves the system's analog-to-digital conversion (ADC) later.

Analog and digital power requirements for signal processing as a function of signal-to-noise ratio (SNR). Power is in arbitrary units and normalized to signal bandwidth.

Quadrature basis function waveforms for

Structure of matrices _{I}_{,}_{Q}

Time-frequency acoustic response of two ground military vehicles.

Vibration spectra of an electric motor with various drive-end bearing faults at 1,772 RPM and 2HP load.

Analog projection system block diagram.

Differential ±1 multiplier.

Harmonic projection channel block diagram.

Simulation model of hardware error sources.

Average classification rate variation over gain/offset standard deviation and added noise values for the vehicle classification task.

Scatter plot and histogram showing pre- and post-calibration integrator offset error for 100 Monte Carlo simulations. Note the horizontal scale change for the right post-calibration histogram. Adapted from [

Comparison of digital real-valued operations to compute Fouriér series coefficients from the Analog Harmonic Transform (AHT) back-substitution (

| |||||
---|---|---|---|---|---|

1–32 | 74+74 | 148 | 98+420 | 518 | |

3–32 | 52+52 | 104 | 98+420 | 518 | |

| |||||

1–64 | 194+194 | 388 | 258+1,028 | 1,286 | |

4–64 | 82+82 | 164 | 258+1,028 | 1,286 |

Military vehicle single-event detection, false alarm and classification rates, from [

| |||||
---|---|---|---|---|---|

Detection rate (%) | Leopard 1 | TH | 92.87 | 96.20 | 95.83 |

Leopard 2 | TH | 81.25 | 90.91 | 91.85 | |

Jaguar | TH | 80.09 | 90.16 | 88.79 | |

M48 | TH | 88.09 | 95.62 | 95.47 | |

Wiesel | TL | 77.42 | 82.95 | 86.62 | |

Fuchs | WH | 81.89 | 88.79 | 87.66 | |

Hermelin | WH | 53.04 | 66.77 | 64.82 | |

MB1017 | WL | 49.39 | 59.02 | 65.94 | |

Unimog | WL | 56.81 | 64.20 | 63.77 | |

| |||||

False alarm rate (%) | Leopard 1 | TH | 1.33 | 0.89 | 1.09 |

Leopard 2 | TH | 5.15 | 2.48 | 2.69 | |

Jaguar | TH | 3.87 | 2.30 | 2.14 | |

M48 | TH | 2.08 | 0.63 | 0.55 | |

Wiesel | TL | 3.29 | 2.27 | 2.21 | |

Fuchs | WH | 2.49 | 1.98 | 1.64 | |

Hermelin | WH | 1.58 | 1.26 | 0.89 | |

MB1017 | WL | 2.10 | 1.54 | 1.70 | |

Unimog | WL | 1.04 | 0.56 | 0.59 | |

| |||||

Classification rate (%) | 80.00 | 87.73 | 88.14 |

Type key: T = tracked, W = wheeled, H = heavy-weight, L = light-weight.

Bearing fault single-event detection, false alarm and classification rates, from [

| ||||
---|---|---|---|---|

Det. (%) | No fault | 99.68 | 99.83 | 100.00 |

Ball fault | 83.80 | 94.34 | 98.79 | |

Inner race fault | 86.70 | 96.04 | 98.93 | |

Outer race fault | 76.73 | 94.90 | 98.49 | |

| ||||

F.A. (%) | No fault | 0.10 | 0.03 | 0.00 |

Ball fault | 9.28 | 2.16 | 0.45 | |

Inner race fault | 1.22 | 0.85 | 0.33 | |

Outer race fault | 6.23 | 1.66 | 0.39 | |

| ||||

Classification rate (%) | 87.20 | 96.42 | 99.09 |