Activation Function Research Articles

Improved research on coral bleaching detection model based on FCOS model

Coral bleaching detection is vital for assessing coral reef health. This paper introduces FCOS_EfficientNET, an improved model that enhances accuracy, recall, and real-time performance in coral bleaching detection. Utilizing EfficientNet as the backbone, the model optimizes parameter throughput. We adopt the ReLU activation function and utilize cosine similarity and softmax to assign weights to datasets, modifying the attention structure to reduce memory consumption. The model also integrates BiFPN for better feature extraction and employs an improved training method to enhance detection accuracy. To cater to different scenarios, we have developed four variants: FCOS_EfficientNETb0, FCOS_EfficientNETb1, FCOS_EfficientNETb2, and FCOS_EfficientNETb3. Experimental results on the MS COCO dataset show that FCOS_EfficientNETb3 achieves a mean average precision (mAP) of 48.5%, while FCOS_EfficientNETb0 reaches a frame rate of 167.17 fps, highlighting the superior performance of the series. On a custom coral bleaching detection dataset, FCOS_EfficientNETb3 achieves 81.5% accuracy and a 59.3% recall rate, demonstrating the effectiveness of the model. FCOS_EfficientNETb1 and FCOS_EfficientNETb2 offer a balance between operations per second, frame rate, and mAP, making them suitable for mobile and edge computing. These models effectively track movement or changes in marine traffic around coral reefs with moderate fps and recall rates.

A liver immune rheostat regulates CD8 T cell immunity in chronic HBV infection

Chronic hepatitis B virus (HBV) infection affects 300 million patients worldwide1,2, in whom virus-specific CD8 T cells by still ill-defined mechanisms lose their function and cannot eliminate HBV-infected hepatocytes3–7. Here we demonstrate that a liver immune rheostat renders virus-specific CD8 T cells refractory to activation and leads to their loss of effector functions. In preclinical models of persistent infection with hepatotropic viruses such as HBV, dysfunctional virus-specific CXCR6+ CD8 T cells accumulated in the liver and, as a characteristic hallmark, showed enhanced transcriptional activity of cAMP-responsive element modulator (CREM) distinct from T cell exhaustion. In patients with chronic hepatitis B, circulating and intrahepatic HBV-specific CXCR6+ CD8 T cells with enhanced CREM expression and transcriptional activity were detected at a frequency of 12–22% of HBV-specific CD8 T cells. Knocking out the inhibitory CREM/ICER isoform in T cells, however, failed to rescue T cell immunity. This indicates that CREM activity was a consequence, rather than the cause, of loss in T cell function, further supported by the observation of enhanced phosphorylation of protein kinase A (PKA) which is upstream of CREM. Indeed, we found that enhanced cAMP–PKA-signalling from increased T cell adenylyl cyclase activity augmented CREM activity and curbed T cell activation and effector function in persistent hepatic infection. Mechanistically, CD8 T cells recognizing their antigen on hepatocytes established close and extensive contact with liver sinusoidal endothelial cells, thereby enhancing adenylyl cyclase–cAMP–PKA signalling in T cells. In these hepatic CD8 T cells, which recognize their antigen on hepatocytes, phosphorylation of key signalling kinases of the T cell receptor signalling pathway was impaired, which rendered them refractory to activation. Thus, close contact with liver sinusoidal endothelial cells curbs the activation and effector function of HBV-specific CD8 T cells that target hepatocytes expressing viral antigens by means of the adenylyl cyclase–cAMP–PKA axis in an immune rheostat-like fashion.

DAILY DANUBE RIVER WATER LEVEL PREDICTION USING EXTREME LEARNING MACHINE APPROACH

Anticipating water levels in vast riverbeds is crucial for preventing and mitigating floods or droughts, assessing power plant capacity, and facilitating navigation management. This study introduces an innovative water level prediction model utilizing an Extreme Learning Machine developed to solve the issues of low performance of existing forecasting methods. Development of such a system is of extreme importance when talking about the largest European river – the Danube River. Experimental findings reveal the model's satisfactory performance across various accuracy metrics, complexity considerations, and calculation speed. The prediction with the highest error rate based on MAPE criteria was for Prahovo water level prediction over a 365-day period at 2.02%, whilst the most accurate predictions were for Novi Sad and Banatska Palanka over 30 days and 180 days horizons, respectively, at 0.0550%. The highest coefficient of determination (R2) was achieved with the Novi Sad data at 0.9968, whilst the lowest was observed with the Prahovo data at 0.7353. The ELM model achieved high precision by adjusting the activation functions of the hidden layer neurons, which involved using different combinations of sigmoid and radial-basis activation functions.

Detection of breast cancer by deep belief network with improved activation function

SummaryBreast cancer is the most prevalent kind of tumor to occur in females and the primary cause of death for women. Early detection is perhaps the most successful strategy to minimize breast cancer mortality. Early diagnosis necessitates a consistent and efficient diagnostics method that allows doctors to differentiate benign from malignant breast cancers without a surgical sample. The goal of this endeavor is to develop a sophisticated breast cancer diagnosis method. The primary goal of the paper is to reduce the death rate among women by promoting early detection of breast cancer. First, pre‐processing techniques such as median filtering and contrast limiting adaptive histogram equalization are used to the obtained raw images. By doing this, the machine‐learning model's computational complexity is decreased and the image quality is enhanced. K‐means clustering is used to segregate the pre‐processed image. Additionally, features including the enhanced local vector pattern, grey‐level co‐occurrence matrix and local vector patterns are produced in the course of the feature extraction stage. Finally, an optimized deep belief network (DBN) is carrying out the classification process. To boosts the classification accuracy, activation function of DBN (tanh, softmax, ReLu) as well as its weight function is optimized by the proposed grey wolf updated whale optimization algorithm The accuracy of the greywolf updated whale optimization algorithm+DBN is above 93% for datasets 1 and 2 when compared to extant models. Finally, calculation of the performance validates the proposed model's performance.

Estimation of the interaction parameters between carbon dioxide and an organic solvent by the Peng–Robinson equation of state via an artificial neural network

The equation of state (EoS) is a tool for estimating the thermodynamic and physical properties of compounds, including mixtures, across a range of temperatures and pressures. When dealing with mixtures, a mixing rule is required to calculate the mixture parameters. Mixing rules may involve interaction parameters, such as kij and lij, that correct for differences between components. However, obtaining this data requires specialized equipment and techniques and significant measurement time, resulting in limited reported EoS parameters. In this study, we introduce an artificial neural network (ANN) to predict interaction parameters in the van der Waals one-fluid mixing rule. These parameters are used to calculate the physical properties of mixtures using the Peng–Robinson (PR) EoS. The interaction parameters are used in two cases, namely the one-parameter and two-parameter mixing rules (OP and TP, respectively), in which only kij and both kij and lij are employed, respectively. The vapor–liquid equilibrium (VLE) data of CO2/organic solvent binary systems are collected and correlated by the PR EoS to construct a database of 1286 and 1292 parameters for the OP and TP, respectively. The molecular weight, critical temperature and pressure, acentric factor of the organic solvent, and temperature are used as input parameters for the ANN. In addition, we optimize the structure of the ANN by changing the activation function, number of neurons, and number of hidden layers. The optimized ANN uses a tanh activation function. Hidden layers are used for both the OP and TP, along with 40 and 50 neurons, respectively. The results confirm that the model can determine the interaction parameters of the PR EoS, which can be used to estimate the VLE. These results are useful for incorporation into process simulators for chemical process design.

Quantitative Uniform Approximation by Activated Singular Operators

In this article, we study the approximation properties of activated singular integral operators over the real line. We establish their convergence to the unit operator with rates. The kernels here derive from neural network activation functions and their corresponding density functions. The estimates are mostly sharp, and they are pointwise and uniform. The derived inequalities involve the higher order modulus of smoothness.

Gastrointestinal tract disease detection via deep learning based structural and statistical features optimized hexa-classification model.

Gastrointestinal tract (GIT) diseases impact the entire digestive system, spanning from the mouth to the anus. Wireless Capsule Endoscopy (WCE) stands out as an effective analytic instrument for Gastrointestinal tract diseases. Nevertheless, accurately identifying various lesion features, such as irregular sizes, shapes, colors, and textures, remains challenging in this field. Several computer vision algorithms have been introduced to tackle these challenges, but many relied on handcrafted features, resulting in inaccuracies in various instances. In this work, a novel Deep SS-Hexa model is proposed which is a combination two different deep learning structures for extracting two different features from the WCE images to detect various GIT ailment. The gathered images are denoised by weighted median filter to remove the noisy distortions and augment the images for enhancing the training data. The structural and statistical (SS) feature extraction process is sectioned into two phases for the analysis of distinct regions of gastrointestinal. In the first stage, statistical features of the image are retrieved using MobileNet with the support of SiLU activation function to retrieve the relevant features. In the second phase, the segmented intestine images are transformed into structural features to learn the local information. These SS features are parallelly fused for selecting the best relevant features with walrus optimization algorithm. Finally, Deep belief network (DBN) is used classified the GIT diseases into hexa classes namely normal, ulcer, pylorus, cecum, esophagitis and polyps on the basis of the selected features. The proposed Deep SS-Hexa model attains an overall average accuracy of 99.16% in GIT disease detection based on KVASIR and KID datasets. The proposed Deep SS-Hexa model achieves high level of accuracy with minimal computational cost in the recognition of GIT illness. The proposed Deep SS-Hexa Model progresses the overall accuracy range of 0.04%, 0.80% better than GastroVision, Genetic algorithm based on KVASIR dataset and 0.60%, 1.21% better than Modified U-Net, WCENet based on KID dataset respectively.

Predicting the Influence of Ammonium Toxicity Levels in Water Using Fuzzy Logic and ANN Models

The study aimed to address the complex and critical issue of surface water quality monitoring by proposing a diversified approach that incorporates a range of chemical indicators. (1) Background: the purpose of the study was to address the problem of surface water quality monitoring in relation to the toxic effects of ammonium on aquatic ecosystems by developing predictive models using fuzzy logic and artificial neural networks. (2) Water samples from the Styr River, influenced by the Rivne Nuclear Power Plant, were analyzed using certified standard methods and measured parameters, while fuzzy logic and artificial neural network models, including Mamdani’s algorithm and various configurations of activation functions and optimization algorithms, were employed to assess water quality and predict ammonium toxicity. (3) A fuzzy logic system was developed to classify water quality based on ammonia content and other parameters, and six Artificial Neural Network (ANN) models were tested, with the ANN#2 model (using ReLU activation and ADAM optimizer) showing the best performance. (4) This study emphasizes the critical need for precise monitoring and modeling of total ammonium in surface water, considering its variable toxicity and interactions with environmental factors, to effectively protect aquatic ecosystems, namely ichthyofauna.

Neural network-based algorithm for door handle recognition using RGBD cameras

The ability to recognize and interact with a variety of doorknob designs is an important component on the path to true robot adaptability, allowing robotic systems to effectively interact with a variety of environments and objects The problem addressed in this paper is to develop and implement a method for recognizing the position of a door handle by a robot using data from an RGBD camera. To achieve this goal, we propose a revolutionary approach designed for autonomous robots that allows them to identify and manipulate door handles in different environments using data obtained from RGBD cameras. This was achieved by creating and annotating a complete dataset consisting of 5000 images of door handles from different angles, with the coordinates of the vertices of the bounding rectangles labeled. The architectural basis of the proposed approach is based on MobileNetV2, combined with a special decoder that optimally increases the resolution to 448 pixels. A new activation function specially designed for this neural network is implemented to ensure increased accuracy and efficiency of raw data processing. The most important achievement of this study is the model's ability to work in real-time, processing up to 16 images per second. This research paves the way for new advancements in the fields of robotics and computer vision, making a substantial contribution to the practical deployment of autonomous robots in a myriad of life's spheres.

Night target detection algorithm based on improved YOLOv7

Aiming at the problems of error detection and missing detection in night target detection, this paper proposes a night target detection algorithm based on YOLOv7(You Only Look Once v7). The algorithm proposed in this paper preprocesses images by means of square equalization and Gamma transform. The GSConv(Group Separable Convolution) module is introduced to reduce the number of parameters and the amount of calculation to improve the detection effect. ShuffleNetv2_×1.5 is introduced as the feature extraction Network to reduce the number of Network parameters while maintaining high tracking accuracy. The hard-swish activation function is adopted to greatly reduce the delay cost. At last, Scylla Intersection over Union function is used instead of Efficient Intersection over Union function to optimize the loss function and improve the robustness. Experimental results demonstrate that the average detection accuracy of the proposed improved YOLOv7 model is 88.1%. It can effectively improve the detection accuracy and accuracy of night target detection.

Fully nonlinear neuromorphic computing with linear wave scattering

The increasing size of neural networks for deep learning applications and their energy consumption create a need for alternative neuromorphic approaches, for example, using optics. Current proposals and implementations rely on physical nonlinearities or optoelectronic conversion to realize the required nonlinear activation function. However, there are considerable challenges with these approaches related to power levels, control, energy efficiency and delays. Here we present a scheme for a neuromorphic system that relies on linear wave scattering and yet achieves nonlinear processing with high expressivity. The key idea is to encode the input in physical parameters that affect the scattering processes. Moreover, we show that gradients needed for training can be directly measured in scattering experiments. We propose an implementation using integrated photonics based on racetrack resonators, which achieves high connectivity with a minimal number of waveguide crossings. Our work introduces an easily implementable approach to neuromorphic computing that can be widely applied in existing state-of-the-art scalable platforms, such as optics, microwave and electrical circuits.

Establishment of a novel DNNSS-MOVES prediction model for carbon emissions of trucks driving on dirt roads

This study proposes a novel prediction model to accurately quantify the carbon emissions of the trucks driving on dirt roads based on the deep learning neural network for small sample (DNNSS) and the motor vehicle emission simulator (MOVES). The application range of the MOVES model was extended to the transportation of asphalt mixtures on the temporary road. The model correction method was also established based on the rolling resistance coefficient (CR) and the correction coefficient (μ). By comparing the measured fuel consumption of the truck with the carbon emissions calculated by the MOVES model, the values of CR × μ can be back-calculated. DNNSS was constructed for estimating the CR × μ. The Adaptive Moment Estimation (Adam) algorithm was used to dynamically adjust the learning rate and accelerate the convergence of the network; the Dropout function was used to alleviate overfitting; and the Rectified Linear Unit (ReLU) function was used as the activation function to solve the gradient vanishing problem. The test results showed that the vehicle speed and load greatly influence the CR × μ. The DNNSS algorithm was better at predicting the CR × μ. The proposed DNNSS-MOVES model was more accurate than the conventional methods.

Multi-physics information-integrated neural network for fatigue life prediction of additively manufactured Hastelloy X superalloy

ABSTRACT The inherent ‘black-box’ characteristic of neural networks renders the physical interpretability of fatigue life prediction challenging, resulting in physically inconsistent prediction results. In response to this challenge, a multi-physics information-integrated neural network framework is proposed for fatigue life prediction. Rooted in the continuous damage mechanics with embedded additive manufacturing process parameters (AM-CDM), coupled with activation functions and loss functions that amalgamate physical information, a multi-tiered and multi-physical information source network framework emerges. The framework incorporates the outcomes of the AM-CDM model as input features for domain knowledge enhancement, embeds the fatigue limit within the activation function, and establishes a loss function integrating the physical model. Through the integration of multiple physical information, the model can be restricted by different physical constraints during training, thereby improving its prediction accuracy and physical consistency. Validation of the proposed framework is conducted using laser powder bed fusion (LPBF)-fabricated Hastelloy X subjected to varying orientations, post-treatments and test temperatures. The findings demonstrate that the prediction accuracy of an integrating-physics-informed neural network (IPINN) is improved by 27.51%, and its life prediction results are capped at the fatigue limit life, yielding a better physical consistency. The IPINN framework provides a novel perspective for fatigue life prediction.

Airborne transient electromagnetic imaging method based on wavelet neural network

The airborne transient electromagnetic method is a crucial technique for near-surface exploration in rugged terrains. In this study, we introduce a multi-input, single-output double-hidden wavelet neural network design for airborne transient electromagnetic pseudo-resistivity imaging. We construct uniform half-space, stratified stratum, and three-dimensional geoelectric models. By evaluating various performance indicators of neural networks that employ different wavelet basis functions as activation functions, we identify the most suitable wavelet basis functions. The quasi-resistivity is computed using both the wavelet neural network and the backpropagation neural network and then juxtaposed with traditional apparent resistivity. Our findings indicate that the wavelet neural network's quasi-resistivity aligns more closely with the resistivity of the real model. It is also more responsive to low resistivity anomalies than the conventional apparent resistivity translation algorithm. The wavelet approach moderates the undershoot or overshoot occurrences during abrupt stratum changes, offering a more accurate representation of subterranean electrical properties. When compared to the backpropagation neural network, the wavelet neural network provides a superior fit for the model, rendering a smoother quasi-resistivity depth curve. Therefore, it stands out as an improved method for pseudo-resistivity imaging. By processing survey data via the trained wavelet neural network, we find that the all-time apparent resistivity and quasi-resistivity align well with real-world situations. The wavelet neural network prominently showcases the low-resistance calculation results, offering a broader resistivity range. This clarity enhances anomaly detection, confirming the wavelet neural network's applicability and practicality for airborne transient electromagnetic imaging.

MC-ShuffleNetV2: A lightweight model for maize disease recognition

Maize has a long history of cultivation and is renowned for its high yield, superior quality, and adaptability. Currently, maize holds a significant position in grain cultivation and occupies a significant place in the agricultural structure. However, maize is susceptible to various diseases during its growth process, which can have a significant impact on the quality and yield. Traditional machine learning is heavily reliant on feature extraction, whereas deep learning has demonstrated notable success in image recognition for computer vision.The use of bloated models and the resulting wastage of computational resources represent significant challenges. The paper proposes a lightweight model, MC-ShuffleNetV2 (Mish + Convolutional Block Attention Module + ShuffleNetV2), to meet the practical needs of convolutional neural networks in maize disease image recognition. The model has designed with a focus on network lightweighting and accurate feature extraction. The model was constructed upon the foundation of the high-performance ShuffleNetV2 1 × network. The Convolutional Block Attention Module was integrated into the network architecture to enhance the model’s adaptive expressiveness. The depthwise separable convolution kernel of the depth-separable module was modified from a 3 × 3 kernel to a 5 × 5 kernel. This modification was implemented with the objective of expanding the image receptive field and extracting more detailed features of the image. It was necessary to modify the activation function in each stage for Mish. The model was compressed through the application of pruning operations. In the maize disease dataset test, the accuracy of the test set recognition accuracy of the network model constructed in this paper reaches 99.86 %, the model parameters are only 873,936, and the FLOPs (Floating-point Operations) are only 1,751,286. Compared with LeNet, AlexNet, MobileNetV2, and EfficientNetV2 models, the MC-ShufflenetV2 model’s recognition ability and size have obvious advantages, and it is more conducive to the actual deployment of the agricultural mobile terminal.

Investigating and Engineering an 1,2-Propanediol-Responsive Transcription Factor-Based Biosensor.

Transcription factor (TF)-based biosensors have arisen as powerful tools in the advancement of metabolic engineering. However, with the emergence of numerous bioproduction targets, the variety of applicable TF-based biosensors remains severely limited. In this study, we investigated and engineered an 1,2-propanediol (1,2-PD)-responsive transcription activator, PocR, from Salmonella typhimurium to enrich the current biosensor repertoire. Heterologous characterization of PocR in E. coli revealed a significantly limited operational range and dynamic range, primarily attributed to the leaky binding between PocR and its corresponding promoters in the absence of the 1,2-PD inducer. Promiscuity characterization uncovered the minor responsiveness of PocR toward glycerol and 1,2-butanediol (1,2-BD). Using AlphaFold-predicted structure and protein mutagenesis, we preliminarily explored the underlying mechanism of PocR. Based on the investigated mechanism, we engineered a PcoR-F46R/G105D variant with an altered inducer specificity to glycerol, as well as a PocR-ARE (Q107A/S192R/A203E) variant with nearly a 4-fold higher dynamic range (6.7-fold activation) and a 20-fold wider operational range (0-20 mM 1,2-PD). Finally, we successfully converted PocR to a repressor through promoter engineering. Integrating the activation and repression functions established a versatile 1,2-PD-induced bifunctional regulation system based on PocR-ARE. Our work showcases the exploration and exploitation of an underexplored type of transcriptional activator capable of recruiting RNA polymerase. It also expands the biosensor toolbox by providing a 1,2-PD-responsive bifunctional regulator and glycerol-responsive activator.

Effects of virtual reality-based robot therapy combined with task-oriented therapy on upper limb function and cerebral cortex activation in patients with stroke.

This study aimed to investigate the effects of virtual reality (VR)-based robot therapy combined with task-oriented therapy on cerebral cortex activation and upper limb function in patients with stroke. This study included 46 patients with hemiplegia within 1 year of stroke onset. Patients were divided into an experimental group (n = 23) and a control group (n = 23) using a computer randomization program. The experimental group received VR-based robot and task-oriented therapies, whereas the control group received only task-oriented therapy. All participants received interventions for 40 minutes per session, 5 times a week, for 8 weeks. For the pre- and post-evaluation of all participants, the Fugl-Meyer Assessment for the upper extremity, manual function test, motor activity log, and Jebsen-Taylor Hand Function Test were used to evaluate changes in upper limb function and motor-evoked potential amplitudes were measured to compare cerebral cortex activation. In comparison to the control group, experimental group demonstrated an improvement in the function of the upper limb (P < .01) and activation of the cerebral cortex (P < .01). The combined intervention of VR-based robot and task-oriented therapies is valuable for improving upper limb function and cerebral cortex activation in patients with stroke.

The R-mAtrIx Net

We provide a novel neural network architecture that can: i) output R-matrix for a given quantum integrable spin chain, ii) search for an integrable Hamiltonian and the corresponding R-matrix under assumptions of certain symmetries or other restrictions, iii) explore the space of Hamiltonians around already learned models and reconstruct the family of integrable spin chains which they belong to. The neural network training is done by minimizing loss functions encoding Yang–Baxter equation, regularity and other model-specific restrictions such as hermiticity. Holomorphy is implemented via the choice of activation functions. We demonstrate the work of our neural network on the spin chains of difference form with two-dimensional local space. In particular, we reconstruct the R-matrices for all 14 classes. We also demonstrate its utility as an Explorer, scanning a certain subspace of Hamiltonians and identifying integrable classes after clusterisation. The last strategy can be used in future to carve out the map of integrable spin chains with higher dimensional local space and in more general settings where no analytical methods are available.

Efficient Error-Rate Estimation for Optical Transmission Systems Using Artificial Neural Networks

ABSTRACT With the advancement in modulation formats, optical transmission systems are becoming more adaptable and dynamic. Predicting bit errors of higher-order modulation formats is a challenging problem for the optimum design of communication systems. The existing simulation methods have persisted by employing iterative procedures that frequently incur high computing expenses and time consumption. On the other hand, deep learning (DL) algorithms have demonstrated remarkable efficacy as practical computing tools, presenting a viable approach to accelerate modulation simulations. In this paper, an artificial neural network (ANN) based bit error rate (BER) estimation scheme is proposed for the popular modulation forms including 56 Gbps 16-quadrature amplitude modulation (16QAM), 100 Gbps 32QAM, and 120 Gbps 64QAM optical system. Based on constellation diagrams (CDs) acquired with different launch power, laser linewidth, transmission distance, and OSNR, amplitude histograms (AHs) are generated via a manual preprocessing method. The properly trained ANN architecture exhibits a computational speed that surpasses traditional simulation methods by a factor exceeding 347. Moreover, the design considerations including the number of layers, nodes, activation functions, learning rate, optimizers, and evolution epochs are also investigated in detail. This research paves the way for optical transmission systems to use fast DL-based optimization strategies.

A Novel Error-Based Adaptive Feedback Zeroing Neural Network for Solving Time-Varying Quadratic Programming Problems

This paper introduces a novel error-based adaptive feedback zeroing neural network (EAF-ZNN) to solve the time-varying quadratic programming (TVQP) problem. Compared to existing variable gain ZNNs, the EAF-ZNN dynamically adjusts the parameter to adaptively accelerate without increasing to very large values over time. Unlike adaptive fuzzy ZNN, which only considers the current convergence error, EAF-ZNN ensures regulation by introducing a feedback regulation mechanism between the current convergence error, the historical cumulative convergence error, the change rate of the convergence error, and the model gain parameter. This regulation mechanism promotes effective neural dynamic evolution, which results in high convergence rate and accuracy. This paper provides a detailed analysis of the convergence of the model, utilizing four distinct activation functions. Furthermore, the effect of changes in the proportional, integral, and derivative factors in the EAF-ZNN model on the rate of convergence is explored. To assess the superiority of EAF-ZNN in solving TVQP problems, a comparative evaluation with three existing ZNN models is performed. Simulation experiments demonstrate that the EAF-ZNN model exhibits a superior convergence rate. Finally, the EAF-ZNN model is compared with the other three models through the redundant robotic arms example, which achieves smaller position error.