Padé Approximant Neural Networks for Enhanced Electric Motor Fault Diagnosis Using Vibration and Acoustic Data

TL;DR

The paper addresses fault diagnosis in induction motors from vibration and acoustic data by introducing 1D PadéNets built on Padé Approximant Neurons with learnable rational activations. It systematically compares 1D PadéNets against 1D CNNs and 1D Self-ONNs on the University of Ottawa constant-speed motor dataset, demonstrating near-perfect accuracies on accelerometer data (up to 99.96%) and high performance on acoustic inputs (up to 98.33%). The study analyzes the impact of Padé order (P,Q) and activation choices, showing that incorporating a denominator branch (Q>0) and using moderate orders yields the best results while maintaining training stability. It also evaluates robustness to additive Gaussian noise and demonstrates feasible edge deployment with modest model sizes and real-time inference on embedded hardware. Overall, the PadéNet approach offers a powerful, efficient, and generalizable solution for real-time motor condition monitoring across multiple sensing modalities.

Abstract

Purpose: The primary aim of this study is to enhance fault diagnosis in induction machines by leveraging the Padé Approximant Neuron (PAON) model. While accelerometers and microphones are standard in motor condition monitoring, deep learning models with nonlinear neuron architectures offer promising improvements in diagnostic performance. This research investigates whether Padé Approximant Neural Networks (PadéNets) can outperform conventional Convolutional Neural Networks (CNNs) and Self-Organized Operational Neural Networks (Self-ONNs) in the diagnosis of electrical and mechanical faults from vibration and acoustic data. Methods: We evaluate and compare the diagnostic capabilities of three deep learning architectures: one-dimensional CNNs, Self-ONNs, and PadéNets. These models are tested on the University of Ottawa's publicly available constant-speed induction motor datasets, which include both vibration and acoustic sensor data. The PadéNet model is designed to introduce enhanced nonlinearity and is compatible with unbounded activation functions such as LeakyReLU. Results and Conclusion: PadéNets consistently outperformed the baseline models, achieving diagnostic accuracies of 99.96%, 98.26%, 97.61%, and 98.33% for accelerometers 1, 2, 3, and the acoustic sensor, respectively. The enhanced nonlinearity of PadéNets, together with their compatibility with unbounded activation functions, significantly improves fault diagnosis performance in induction motor condition monitoring.

Figures (10)

• Figure 1: The proposed 1D PadéNet-based framework and the diagram of a Padé neuron with $P = 2, Q = 1$, where $w_{0}$ represents the bias term in the numerator, $(\cdot)^{n}$ denotes element-wise exponentiation of the input to the $n^{\text{th}}$ power, $\mathbf{\ast}$ indicates convolution, and $\frac{\cdot}{\cdot}$ implements Equation \ref{['eq9']}.
• Figure 2: An illustrative overview of the operations involved in a convolutional, generative, and Padé neuron.
• Figure 3: The experimental setup sehri2024university.
• Figure 4: Examples of segmented and normalized waveforms for 45 Hz input frequency: (a) Accelerometer-1, (b) microphone.
• Figure 5: Aggregated confusion matrices over 5 runs for the 1D CNN ($P=1, Q=0$), Self-ONN ($P=2, Q=0$), and PadéNet ($P=2, Q=1$) models with the first accelerometer data as input. The 1D Self-ONN and PadéNet models use the $\tanh$ activation function, while the 1D CNN utilizes $\mathrm{LeakyReLU}$ with negative slope of 0.01.