Sigmoid Function Research Articles

Multi-label feature selection based on nonlinear mapping

Feature selection is one of the important pre-processing methods for dimensionality reduction in multi-label learning tasks, which has attracted extensive attention in recent years. Most of the existing approaches transform feature data into the label space during the feature-label mapping process by assuming linear relationship between the feature and label spaces. However, the linearity assumption does not hold in most cases, especially for high-dimensional spaces. This work proposes a novel dimension reduction model for multi-label data by using nonlinear mapping (NMFS). The model introduces a point-to-point sigmoid function to describe the intrinsic relationship from data space to label space. The proposed method improves the generalization ability of feature selection by limiting the range of data transformation to the interval [0,1] which is consistent with the predicted values of the labels. The feature weight matrix is constrained by the l2,1-norm to ensure its sparsity, which forms the basis of feature selection. The variables in the NMFS model are iteratively updated using the gradient momentum optimization strategy, and a sparse weight-coefficient matrix is obtained for multi-label feature ordering. Experimental results on 14 multi-label data sets verify the effectiveness of the proposed method, and show the proposed method is superior to the most advanced multi-label feature selection methods.

Firing pattern manipulation of neuronal networks by deep unfolding‐based model predictive control

AbstractThe complexity of neuronal networks, characterized by interconnected neurons, presents significant challenges in control due to their nonlinear and intricate behaviour. This paper introduces a novel method designed to generate control inputs for neuronal networks to regulate the firing patterns of modules within the network. This methodology is built upon temporal deep unfolding‐based model predictive control, a technique rooted in the deep unfolding method commonly used in wireless signal processing. To address the unique dynamics of neurons, such as zero gradients in firing times, the method employs approximations of input currents using a sigmoid function during its development. The effectiveness of this approach is validated through extensive numerical simulations. Furthermore, control experiments were conducted by reducing the number of input neurons to identify critical features for control. Various selection techniques were utilized to pinpoint key input neurons. These experiments shed light on the importance of specific input neurons in controlling module firing within neuronal networks. Thus, this study presents a tailored methodology for managing networked neurons, extends temporal deep unfolding‐based model predictive control to nonlinear systems with reset dynamics, and demonstrates its ability to achieve desired firing patterns in neuronal networks.

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.

Smooth Logistic Real and Complex, Ordinary and Fractional Neural Network Approximations over Infinite Domains

In this work, we study the univariate quantitative smooth approximations, including both real and complex and ordinary and fractional approximations, under different functions. The approximators presented here are neural network operators activated by Richard’s curve, a parametrized form of logistic sigmoid function. All domains used are obtained from the whole real line. The neural network operators used here are of the quasi-interpolation type: basic ones, Kantorovich-type ones, and those of the quadrature type. We provide pointwise and uniform approximations with rates. We finish with their applications.

A Pareto-optimality based black widow spider algorithm for energy efficient flexible job shop scheduling problem considering new job insertion

The utilization of flexible job shops is on the rise, driven by the decreasing life cycle of consumer products. In dynamic flexible job shops, the occurrence of disruptive events like machine breakdown, tool wear, and new job arrivals is common, emphasizing the critical need for efficient scheduling to achieve productivity and cost-effectiveness. Additionally with the growing concerns about energy consumption and global warming, the imperative to contemplate workshops with lower energy usage is becoming increasingly significant. Therefore, in this study a multi-objective dynamic flexible job shop scheduling problem (MODFJSP) with insertion of new jobs for optimization objectives: makespan, total energy consumption and schedule instability is addressed. A novel multi-objective black widow spider algorithm (MOBWSA), inspired by the mating behavior of black widow spiders, is proposed. The MOBWSA ensures an optimal balance between minimizing makespan and energy consumption through its superior evolutionary processes of procreation, mutation and cannibalism. Furthermore, a strategic on/off strategy is implemented to enhance energy efficiency. The disruptions in schedule at rescheduling stage are addressed through the proposed sigmoidal weighted instability function. To handle the multi-objective nature of the problem this work incorporates Pareto-optimality approach in combination with novel hybrid crowding distance metric. The optimization is further aided by exploitation of search space through an ensemble of local search operators. Testing and evaluation of the MOBWSA with 30 benchmark problems is conducted, and its performance for multiple metrics is compared with recently published state-of-the-art algorithms. The results establish the effectiveness and efficiency of the proposed algorithm.

Parallel Synapses with Transmission Nonlinearities Enhance Neuronal Classification Capacity.

Cortical neurons often establish multiple synaptic contacts with the same postsynaptic neuron. To avoid functional redundancy of these parallel synapses, it is crucial that each synapse exhibits distinct computational properties. Here we model the current to the soma contributed by each synapse as a sigmoidal transmission function of its presynaptic input, with learnable parameters such as amplitude, slope, and threshold. We evaluate the classification capacity of a neuron equipped with such nonlinear parallel synapses, and show that with a small number of parallel synapses per axon, it substantially exceeds that of the Perceptron. Furthermore, the number of correctly classified data points can increase superlinearly as the number of presynaptic axons grows. When training with an unrestricted number of parallel synapses, our model neuron can effectively implement an arbitrary aggregate transmission function for each axon, constrained only by monotonicity. Nevertheless, successful learning in the model neuron often requires only a small number of parallel synapses. We also apply these parallel synapses in a feedforward neural network trained to classify MNIST images, and show that they can increase the test accuracy. This demonstrates that multiple nonlinear synapses per input axon can substantially enhance a neuron's computational power.

Application of Artificial Intelligence to the Alert of Explosions in Colombian Underground Mines

The use of Artificial Intelligence (AI), particularly of Artificial Neural Networks (ANN), in alerting possible scenarios of methane explosions in Colombian underground mines is illustrated by the analysis of an explosion that killed twelve miners. A combination of geological analysis, a detailed characterization of samples of coal dust and scene evidence, and an analysis with physical modeling tools supported the hypothesis of the existence of an initial methane explosion ignited by an unprotected tool that was followed by a coal dust explosion. The fact that one victim had a portable methane detector at the moment of the methane explosion suggested that the ubiquitous use of these systems in Colombian mines could be used to alert regulatory agencies of a possible methane explosion. This fact was illustrated with the generation of a database of possible readouts of methane concentration based on the recreation of the mine atmosphere before the explosion with Computational Fluid Dynamics (CFD). This database was used to train and test an ANN that included an input layer with two nodes, two hidden layers, each with eight nodes, and an output layer with one node. The inner layers applied a rectified linear unit activation function and the output layer a Sigmoid function. The performance of the ANN algorithm was considered acceptable as it correctly predicted the need for an explosion alert in 971.9 per thousand cases and illustrated how AI can process data that is currently discarded but that can be of importance to alert about methane explosions.

Investigating the effect of using aluminum oxide nanofluid and twisted tapes with different twisted pitches on the heat transfer efficiency and using perceptron artificial neural networks in data prediction

This study investigates the effect of aluminum oxide nanofluid with 1% and 2% volume fractions (VFs) in four different tubes with identical bending and the uniform, low-high-low, low-high, and high-low-high longitudinal states with twist ratios of 0, 2 and 4. These tubes are affected by a constant thermal flux of 10000 W/m2 and Reynolds numbers of 2000-10000. For the numerical solution of these equations, the finite difference method on the basis of the control volume and the SIMPLEC algorithm and the K-ε-RNG method were applied for the turbulent flow modeling. The determined Nusselt number from the numerical methods were evaluated applying the perceptron neural network. The most optimal increase in the Nusselt number was in the twisted tube with twist ratio of 4 in the Reynolds number of 10,000 and VF of 1% and 2% nanofluid with increasing trend of length from low to high. The most optimal increase in Nusselt number compared to base fluid was about 25%. The sum of squared error and the relative error data obtained from the hyperbolic tangent function for the training and test data were 0.080-1.331 and 0.113-0.675, and from the sigmoid function for the training and test data were 0.093-0.392 and 0.097-0.147.

Using Support Vector Machines to Classify Road Surface Conditions to Promote Safe Driving.

Accurate detection of road surface conditions in adverse winter weather is essential for traffic safety. To promote safe driving and efficient road management, this study presents an accurate and generalizable data-driven learning model for the estimation of road surface conditions. The machine model was a support vector machine (SVM), which has been successfully applied in diverse fields, and kernel functions (linear, Gaussian, second-order polynomial) with a soft margin classification technique were also adopted. Two learner designs (one-vs-one, one-vs-all) extended their application to multi-class classification. In addition to this non-probabilistic classifier, this study calculated the posterior probability of belonging to each group by applying the sigmoid function to the classification scores obtained by the trained SVM. The results indicate that the classification errors of all the classifiers, excluding the one-vs-all linear learners, were below 3%, thereby accurately classifying road surface conditions, and that the generalization performance of all the one-vs-one learners was within an error rate of 4%. The results also showed that the posterior probabilities can analyze certain atmospheric and road surface conditions that correspond to a high probability of hazardous road surface conditions. Therefore, this study demonstrates the potential of data-driven learning models in classifying road surface conditions accurately.

Adaptive chaotic dynamic learning-based gazelle optimization algorithm for feature selection problems

Feature Selection (FS) is considered a crucial procedure for eliminating unnecessary features from datasets. FS is considered a challenging problem that is difficult to solve efficiently due to its combinatorial nature. As the problem size increases, so does the computation time. Recently, researchers have been focusing on metaheuristic FS algorithms. Therefore, this paper introduces an adaptive chaotic dynamic gazelle optimization algorithm (ACD-GOA) with enhanced elite Strategy for FS problems. The ACD-GOA is a novel enhanced version of the recently published GOA, incorporating multiple improved strategies to enhance its search capabilities and convergence speed. The initialization phase and iteration initialization adopt the dynamic opposition learning strategy to avoid premature convergence. Additionally, several enhancement strategies are employed to improve the efficiency of the standard GOA. Adaptive inertia weight and sigmoid function are used to enhance search efficiency. Furthermore, enhanced elite and exchanging information strategies are implemented to maintain population diversity and avoid local solutions, respectively. Experimental evaluations are conducted using various functions, including the twelve CEC2022 standard functions and fourteen FS benchmark datasets. The performance of ACD-GOA is compared with several other metaheuristic algorithms. Statistical tests such as Friedman and Wilcoxon signed-rank tests are used to analyze the experimental data. The experimental results highlight the proposed algorithm’s exceptional capacity to overcome problems associated with local minima and expedite the convergence process. The suggested algorithm has been extensively compared to state-of-the-art algorithms, demonstrating significant breakthroughs. The reported accuracy of the proposed algorithm ranges from 0.78 to 1.00 with K-NN classifier.

Single-Frequency Lasers’ Linewidths Elegantly Characterized with Sigmoid Functions of Observation Time

Single-Frequency Lasers’ Linewidths Elegantly Characterized with Sigmoid Functions of Observation Time

A physics-informed machine learning model for the prediction of drop breakup in two-phase flows

Predictive simulations of two-phase flows are highly sought after because of their widespread applications in propulsion, energy, agriculture, and medicine. One crucial goal for many of these simulations is the accurate and efficient prediction of the size distribution and number density of atomized drops. The multi-scale nature of these flows makes it practically impossible to capture all scales within a single simulation. In particular, the breakup processes producing the smallest drops through secondary breakup often necessitate resolutions far below the Kolmogorov scale. Consequently, models must be employed for secondary breakup. Existing physics-based and stochastic breakup models are not universal and fail to account for the local and instantaneous flow field and drop geometry. We present a physics-informed machine learning model for predicting the statistics of daughter drops generated during the breakup of under-resolved drops. By training on high-fidelity simulations, the model can predict breakup outcomes from severely under-resolved input fields. This is made possible by a careful choice of quantities of interest and by taking inspiration from the discrete nature of breakup events to encode the temporal evolution via a mixture of sigmoid functions. We showcase proof-of-concept results from the canonical settings of 3D Taylor–Green vortex flows and homogeneous isotropic turbulence. Compared to results generated by low-resolution simulations (i.e., without a model) and baseline state-of-the-art models, our approach achieves superior accuracy in predicting drop size distribution and critical quantities of interest, such as surface area. This work paves the path towards the development of embedded machine learning models for the prediction of primary and secondary breakup.

Sigmoid function model of parallel-connected DC-DC converters and analysis of their dynamic characteristics.

Because of the manufacturing variations of circuit elements and the effects of parasitic parameters, the switching elements of parallel-connected modules cannot be synchronously switched. Consequently, the characteristics of these converters, which are multi-mode, high-order systems, cannot be comprehensively described using reduced-order models based on the symmetry of circuit topology and parameters. It is also difficult to fully describe the characteristics of these systems using discrete mapping models and averaged models. Therefore, we developed a smooth, sigmoid function-based continuous-time model for systems comprising parallel-connected buck converters with average current-sharing control. The proposed model provides a unified description of the continuous and discontinuous conduction modes of the system. The criteria for ensuring the stability of the system were derived based on the Floquet theory. The nonlinear dynamic behavior of the system and the effects of the key parameters on the stability of the system were investigated. The results showed that the system may undergo period doubling bifurcation, border collision bifurcation, and Neimark-Sacker bifurcation as the system parameters varied. The theoretical analysis and simulation results were verified experimentally. Our results provide a basis for the configuration of controller parameters.

Deep Learning Application as a Method for Classification Equipment Failure on Natural Gas Pipeline

Predicting maintenance and preventing failures in natural gas pipelines is critical for safety and efficiency in the oil and gas industry. This research utilizes machine learning (ML) and deep learning (DL) methods to predict failures in natural gas transmission pipelines. Using a dataset from the U.S. Department of Transportation’s Pipeline and Hazardous Materials Safety Administration (PHMSA), the study examines failure incidents from 2010-2019 and non-failure data from 2020-2023. The research involves comprehensive data preprocessing, addressing missing values and dataset imbalances. Key pipeline attributes such as diameter, wall thickness, age, and operating pressure are used for failure prediction. The ML approach employs logistic regression, optimized for binary classification tasks, to establish the probability of pipeline failures. For the DL approach, an Artificial Neural Network (ANN) with Feed Forward and Back Propagation algorithms is developed. Key parameters, including activation functions and hyperparameters, are finely tuned to enhance predictive performance. ReLU activation functions are used in input and hidden layers, while the sigmoid function is applied to the output layer. Performance evaluation of both ML and DL models is based on accuracy, F1 Score, and Area Under Curve (AUC). In summary, ML showed better performance than DL, with value of accuracy is 0.74, F1 Score is 0.85, and AUC is 0.55 while the value of accuracy, F1 score, AUC from DL is 0.61, 0.003, and 0.58 respectively. DL offers superior performance in handling complex and huge amounts of data. In the other hand, ML offers more robust models and simpler adjustable models than DL. Because of the amount of computed data in this research, it is better to have ML as a predictive algorithm.

Effect of Micromechanical Models on Mechanical Behavior of Functionally Graded Plates Based on a Quasi-3D Hyperbolic Shear Deformation Theory

Five alternative micromechanical models (Voigt, Reuss, Tamura, LRVE, Hashin) are used to predict the valid material properties of a simply-supported functionally graded materials (FGM) plate. The free vibration and static behavior are studied based on a quasi-3D hyperbolic shear deformation theory considering the stretching effect. The profile of an FGM plate is assumed by the power-law, Sigmoid and exponential functions. The numerical results of an FGM plate behavior reveal via Navier-type solution. The temperature effects of the micromechanical models on the fundamental frequency and transverse displacement for an FGM plate are also discussed. By analyzing the influence of different micro-models on the mechanical behavior of an FGM plate, researchers can objectively understand the establishment and differences of structural micromechanical models. And considering the actual high temperature situation, the deformation prediction ability of the structure is predicted. This study provides theoretical guidance for the analysis and modeling of FGM structures for the purpose of engineering practice.

Deconvolution of Cyclic Voltammograms in the Hydrogen Region of the Platinum-Black Electrodes with the Asymmetric Double Sigmoid Function

Deconvolution of Cyclic Voltammograms in the Hydrogen Region of the Platinum-Black Electrodes with the Asymmetric Double Sigmoid Function

Advanced Innovations in Electronic Control Units: Enhancing Performance and Reliability with AI

This paper proposes a methodology for the design of electronic control unit (ECU) hardware units with increased performance and reliability. Today's vehicles are equipped with dozens of ECUs that significantly influence the system's efficiency, reliability, performance, and safety. With the increased complexity of control algorithms and the environmental constraints that automotive systems operate, the robustness and efficiency of the ECUs are of utmost importance. In this work, an approach is proposed based on combining hardware redundancy, commercial field programmable gate arrays (FPGAs), and artificial intelligence strategies to provide increased redundancy checks and robust control. An additional redundancy is added to the hardware architecture of the ECU to include a parallel hardware unit. The two controlling units operate in parallel. The output of each of them is compared, allowing redundancy checks in the computation of the output variable (oV) of the system. The mathematical model of the ECU depicts the governing equations of the ECU in the form of differential equations, which results in a corresponding state-space configuration. These mathematical models are encoded into the field programmable gate array (FPGA) and processed in hardware, leading to an equivalent software-based implementation. To analyze the performance of both models within the ECU, an artificial neural network (ANN)-based strategy is proposed. The ANN depicts the governing equations of the ECU in the form of differential equations encoded in the form of sigmoidal functions. To analyze the reliability of the control action in the ECU, the temperature of the system is increased, which leads to a random variation of the system parameters. The variability of the ECU parameters leads to a deviation in the computation of the oV and the corresponding control action. The robustness of the control is determined in such conditions. A control law is determined to guarantee proper control action under variations in the governing equations of the system. This control law is represented by a simple algebraic equation, which can then be cast in various control strategies, such as look-up tables or fuzzy logic controllers. Several cases are simulated to assess the performance of the proposed control law for the hardware redundancy scheme, for the ANN-based equivalent software implementation approach, and for the additional fuzzy logic controller. The simulation results are analyzed concerning the requested oV and give insight into the performance and reliability of the proposed dedicated ECU design.

Interface capturing schemes based on sigmoid functions

The non-polynomial THINC (tangent of hyperbola for interface capturing) scheme has been reported to show both numerical simplicity and high fidelity for resolving contact interfaces. In this paper, two types of smooth sigmoid functions are employed to construct the non-polynomial reconstructions for capturing interfaces (similarly, called SFINC schemes, sigmoid functions for interface capturing). One type is that the exact jump location (a parameter introduced in the reconstruction) can be analytically calculated, and another type cannot. The algebraic function and the Gudermannian function belong to the first and the second types, respectively, and are investigated in this paper. An approximate method for calculating the jump location of the Gudermannian function is proposed. The method avoids the iteration process of determining the jump location, and hence is efficient and practical in applications. The numerical validations and comparisons of SFINC schemes are presented to show their performance for simulating complex compressible flow fields.

Three-way decision based on three-way preference measures and three-level dominance relations in interval-valued systems

Interval-valued systems facilitate data decision, and their preference measures and dominance relations become pivotal for three-way decision (3WD). However, the recent D-type preference measure and partial-overall dominance relation between intervals respectively exhibit the weak representation and incomplete hierarchy, so corresponding results need further development. Aiming at interval-valued systems, an S-type measure is proposed to constitute three-way preference measures, and three-level dominance relations are established, so criss-cross knowledge granulations motivate systematic 3WD models and applications. First, the S-type preference measure is proposed from the sigmoid function, it exhibits good learning semantics and mathematical properties, and its supplementation and improvement induce three-way preference measures. Then, by three-level constructions, three-way preference measures are applied for sorting and classification, and the S-type measure exhibits decision effectiveness and recognition superiority. Furthermore, hierarchical three-way preference measures induce three-level dominance relations, and vertical-horizontal condition granulations generate multiple 3WD models on preference decision classes. Finally, all 3WD strategies from criss-cross dominance relations are comprehensively compared and selected via classification error rates; by data experiments, the S-type measure and its hierarchical relations become effective and optimal for 3WD, and the corresponding 3WD approaches outperform the existing methods from the D-type measure and partial-overall relation.

Research on a Machine Vision-based Blade Measurement Method

A high-precision visual measurement method for the geometric dimensions of oil pump blades is proposed, utilizing an auxiliary measurement mechanism to assist in sub-pixel edge positioning. Based on images of calibration boards, the camera distortion is corrected by partitioning the image into regions and establishing a mapping index between pixel coordinates and real-world coordinates. Under fixed object and image distances, images of the oil pump blades and the contact between the blades and the pump are separately captured. The Canny operator and Sigmoid function are employed to fit the edges, extracting sub-pixel coordinates, which are then mapped to real-world coordinates. Finally, a least squares edge fitting is conducted to compute the dimensional parameters. Experimental results indicate that the use of auxiliary measurement mechanisms effectively enhances the precision of blade measurements, as compared to measurements solely based on oil pump blade images and images of the blade in contact with the pump.