Hardware implementation of auto-mutual information function for condition monitoring

This study is aimed at showing applicability of mutual information, namely auto-mutual information function for condition monitoring in electrical motors, through age detection in accelerated motor aging. Vibration data collected in artificial induction motor experiment is used for verification of both the original auto-mutual information function algorithm and its hardware implementation in Verilog, produced from an initial version made with Matlab HDL (Hardware Description Language) Coder. A conceptual model for industry and education based on a field programmable logic array development board is developed and demonstrated on the auto-mutual information function example, while suggesting other applications as well. It has also been shown that attractor reconstruction for the vibration data cannot be straightforward.

💡 Research Summary

The paper presents a comprehensive framework for condition monitoring of induction motors by leveraging the auto‑mutual information function (AMIF) and implementing it in hardware on an FPGA development board. The authors begin by reviewing the theoretical foundations of AMIF, a measure of statistical dependence between two time‑series that is traditionally used to determine optimal delay times for phase‑space reconstruction in nonlinear dynamics analysis. While previous work has employed AMIF to estimate delay and embedding dimensions for Lyapunov exponent calculation, the present study demonstrates that, for vibration data sampled at 12 kHz from artificially aged motors, full attractor reconstruction is impractical due to insufficient data length. Instead, the first minimum of the AMIF curve is directly used as a binary indicator of motor health, distinguishing “healthy” from “aged” states.

To translate this algorithm into a real‑time monitoring solution, the authors employ MATLAB HDL Coder to automatically generate Verilog code from an existing MATLAB implementation of AMIF. The generated code is then manually optimized for deployment on the Altera DE2i‑150 platform, which combines a Cyclone IV FPGA with an Intel Atom processor running Yocto Linux. The hardware architecture updates histograms for the current and delayed samples on each new data point, maintaining separate two‑dimensional histograms for each lag value. By incrementally adjusting histogram counts rather than recomputing them from scratch, the design limits memory accesses to a constant small number per sample, enabling a fully pipelined, real‑time operation. With 128 quantization levels, the design consumes roughly 3 k logic elements, well within the 150 k available on the board, and can comfortably handle input frequencies up to 3 MHz—far exceeding the 12 kHz sampling rate of the vibration sensor.

Experimental validation uses an artificial aging protocol applied to an induction motor, producing eight distinct health states (0 = new, 7 = severely aged). For each state, 15 windows of 512 samples are processed with 32 quantization levels. The AMIF curves reveal a clear separation: the first minimum is 4 for the healthy state and drops to 1 for the most aged state, providing a sharp binary threshold rather than a monotonic degradation metric. Hardware tests reproduce these results, with processing latency measured in microseconds, confirming that the FPGA implementation meets real‑time requirements.

The authors acknowledge several limitations. The memory required for the two‑dimensional histograms grows with the square of the quantization level, potentially constraining scalability. The paper does not detail the analog‑to‑digital front‑end for direct sensor integration, focusing instead on a software‑driven emulator feeding data to the FPGA. Moreover, while AMIF effectively distinguishes between two broad categories, it does not differentiate among multiple fault types or quantify gradual wear. Future work is suggested to explore compressed histogram representations, parallel processing of a larger set of lag values, and the integration of complementary nonlinear measures such as cross‑entropy or permutation entropy to enrich the diagnostic capability.

In summary, the study demonstrates that AMIF can serve as a robust, low‑complexity feature for motor condition monitoring and that its computation can be efficiently realized on modest FPGA hardware, offering a viable path toward embedded, real‑time health‑assessment systems for industrial rotating machinery.