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.

Condition monitoring of induction machines is crucial to prevent costly interruptions and equipment failure. Mechanical faults such as misalignment and rotor issues are among the most common problems encountered in industrial environments. To effectively monitor and detect these faults, a variety of sensors, including accelerometers, current sensors, temperature sensors, and microphones, are employed in the field. As a non-contact alternative, thermal imaging offers a powerful monitoring solution by capturing temperature variations in machines with thermal cameras. In this study, we propose using 2-dimensional Self-Organized Operational Neural Networks (Self-ONNs) to diagnose misalignment and broken rotor faults from thermal images of squirrel-cage induction motors. We evaluate our approach by benchmarking its performance against widely used Convolutional Neural Networks (CNNs), including ResNet, EfficientNet, PP-LCNet, SEMNASNet, and MixNet, using a Workswell InfraRed Camera (WIC). Our results demonstrate that Self-ONNs, with their non-linear neurons and self-organizing capability, achieve diagnostic performance comparable to more complex CNN models while utilizing a shallower architecture with just three operational layers. Its streamlined architecture ensures high performance and is well-suited for deployment on edge devices, enabling its use also in more complex multi-function and/or multi-device monitoring systems.

Although numerous R-peak detectors have been proposed in the literature, their robustness and performance levels may significantly deteriorate in low-quality and noisy signals acquired from mobile electrocardiogram (ECG) sensors, such as Holter monitors. Recently, this issue has been addressed by deep 1-D convolutional neural networks (CNNs) that have achieved state-of-the-art performance levels in Holter monitors; however, they pose a high complexity level that requires special parallelized hardware setup for real-time processing. On the other hand, their performance deteriorates when a compact network configuration is used instead. This is an expected outcome as recent studies have demonstrated that the learning performance of CNNs is limited due to their strictly homogenous configuration with the sole linear neuron model. In this study, to further boost the peak detection performance along with an elegant computational efficiency, we propose 1-D Self-Organized ONNs (Self-ONNs) with generative neurons. The most crucial advantage of 1-D Self-ONNs over the ONNs is their self-organization capability that voids the need to search for the best operator set per neuron since each generative neuron has the ability to create the optimal operator during training. The experimental results over the China Physiological Signal Challenge-2020 (CPSC) dataset with more than one million ECG beats show that the proposed 1-D Self-ONNs can significantly surpass the state-of-the-art deep CNN with less computational complexity. Results demonstrate that the proposed solution achieves a 99.10% F1-score, 99.79% sensitivity, and 98.42% positive predictivity in the CPSC dataset, which is the best R-peak detection performance ever achieved.

Deep Convolutional Neural Networks (CNNs) have recently reached state-of-the-art Handwritten Text Recognition (HTR) performance. However, recent research has shown that typical CNNs' learning performance is limited since they are homogeneous networks with a simple (linear) neuron model. With their heterogeneous network structure incorporating non-linear neurons, Operational Neural Networks (ONNs) have recently been proposed to address this drawback. Self-ONNs are self-organized variations of ONNs with the generative neuron model that can generate any non-linear function using the Taylor approximation. In this study, in order to improve the state-of-the-art performance level in HTR, the 2D Self-organized ONNs (Self-ONNs) in the core of a novel network model are proposed. Moreover, deformable convolutions, which have recently been demonstrated to tackle variations in the writing styles better, are utilized in this study. The results over the IAM English dataset and HADARA80P Arabic dataset show that the proposed model with the operational layers of Self-ONNs significantly improves Character Error Rate (CER) and Word Error Rate (WER). Compared with its counterpart CNNs, Self-ONNs reduce CER and WER by 1.2% and 3.4 % in the HADARA80P and 0.199% and 1.244% in the IAM dataset. The results over the benchmark IAM demonstrate that the proposed model with the operational layers of Self-ONNs outperforms recent deep CNN models by a significant margin while the use of Self-ONNs with deformable convolutions demonstrates exceptional results.

Preventive maintenance of modern electric rotating machinery (RM) is critical for ensuring reliable operation, preventing unpredicted breakdowns and avoiding costly repairs. Recently many studies investigated machine learning monitoring methods especially based on Deep Learning networks focusing mostly on detecting bearing faults; however, none of them addressed bearing fault severity classification for early fault diagnosis with high enough accuracy. 1D Convolutional Neural Networks (CNNs) have indeed achieved good performance for detecting RM bearing faults from raw vibration and current signals but did not classify fault severity. Furthermore, recent studies have demonstrated the limitation in terms of learning capability of conventional CNNs attributed to the basic underlying linear neuron model. Recently, Operational Neural Networks (ONNs) were proposed to enhance the learning capability of CNN by introducing non-linear neuron models and further heterogeneity in the network configuration. In this study, we propose 1D Self-organized ONNs (Self-ONNs) with generative neurons for bearing fault severity classification and providing continuous condition monitoring. Experimental results over the benchmark NSF/IMS bearing vibration dataset using both x- and y-axis vibration signals for inner race and rolling element faults demonstrate that the proposed 1D Self-ONNs achieve significant performance gap against the state-of-the-art (1D CNNs) with similar computational complexity.

Glaucoma leads to permanent vision disability by damaging the optical nerve that transmits visual images to the brain. The fact that glaucoma does not show any symptoms as it progresses and cannot be stopped at the later stages, makes it critical to be diagnosed in its early stages. Although various deep learning models have been applied for detecting glaucoma from digital fundus images, due to the scarcity of labeled data, their generalization performance was limited along with high computational complexity and special hardware requirements. In this study, compact Self-Organized Operational Neural Networks (Self- ONNs) are proposed for early detection of glaucoma in fundus images and their performance is compared against the conventional (deep) Convolutional Neural Networks (CNNs) over three benchmark datasets: ACRIMA, RIM-ONE, and ESOGU. The experimental results demonstrate that Self-ONNs not only achieve superior detection performance but can also significantly reduce the computational complexity making it a potentially suitable network model for biomedical datasets especially when the data is scarce.

Despite their recent success on image denoising, the need for deep and complex architectures still hinders the practical usage of CNNs. Older but computationally more efficient methods such as BM3D remain a popular choice, especially in resource-constrained scenarios. In this study, we aim to find out whether compact neural networks can learn to produce competitive results as compared to BM3D for AWGN image denoising. To this end, we configure networks with only two hidden layers and employ different neuron models and layer widths for comparing the performance with BM3D across different AWGN noise levels. Our results conclusively show that the recently proposed self-organized variant of operational neural networks based on a generative neuron model (Self-ONNs) is not only a better choice as compared to CNNs, but also provide competitive results as compared to BM3D and even significantly surpass it for high noise levels.

Discriminative learning based on convolutional neural networks (CNNs) aims to perform image restoration by learning from training examples of noisy-clean image pairs. It has become the go-to methodology for tackling image restoration and has outperformed the traditional non-local class of methods. However, the top-performing networks are generally composed of many convolutional layers and hundreds of neurons, with trainable parameters in excess of several millions. We claim that this is due to the inherent linear nature of convolution-based transformation, which is inadequate for handling severe restoration problems. Recently, a non-linear generalization of CNNs, called the operational neural networks (ONN), has been shown to outperform CNN on AWGN denoising. However, its formulation is burdened by a fixed collection of well-known nonlinear operators and an exhaustive search to find the best possible configuration for a given architecture, whose efficacy is further limited by a fixed output layer operator assignment. In this study, we leverage the Taylor series-based function approximation to propose a self-organizing variant of ONNs, Self-ONNs, for image restoration, which synthesizes novel nodal transformations onthe-fly as part of the learning process, thus eliminating the need for redundant training runs for operator search. In addition, it enables a finer level of operator heterogeneity by diversifying individual connections of the receptive fields and weights. We perform a series of extensive ablation experiments across three severe image restoration tasks. Even when a strict equivalence of learnable parameters is imposed, Self-ONNs surpass CNNs by a considerable margin across all problems, improving the generalization performance by up to 3 dB in terms of PSNR.

Operational Neural Networks (ONNs) have recently been proposed to address the well-known limitations and drawbacks of conventional Convolutional Neural Networks (CNNs) such as network homogeneity with the sole linear neuron model. ONNs are heterogenous networks with a generalized neuron model that can encapsulate any set of non-linear operators to boost diversity and to learn highly complex and multi-modal functions or spaces with minimal network complexity and training data. However, Greedy Iterative Search (GIS) method, which is the search method used to find optimal operators in ONNs takes many training sessions to find a single operator set per layer. This is not only computationally demanding, but the network heterogeneity is also limited since the same set of operators will then be used for all neurons in each layer. Moreover, the performance of ONNs directly depends on the operator set library used, which introduces a certain risk of performance degradation especially when the optimal operator set required for a particular task is missing from the library. In order to address these issues and achieve an ultimate heterogeneity level to boost the network diversity along with computational efficiency, in this study we propose Self-organized ONNs (Self-ONNs) with generative neurons that have the ability to adapt (optimize) the nodal operator of each connection during the training process. Therefore, Self-ONNs can have an utmost heterogeneity level required by the learning problem at hand. Moreover, this ability voids the need of having a fixed operator set library and the prior operator search within the library in order to find the best possible set of operators. We further formulate the training method to back-propagate the error through the operational layers of Self-ONNs.