Sigmoid Function Research Articles

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.

Extreme learning machine approach on heart abnormalities identification in ECG images

Heart abnormalities are atypical heart conditions that can lead to chronic heart disease. Heart abnormalities can be severe if not treated directly due to the crucial function of the heart as the blood circulation center. Heart abnormalities cannot be seen with the naked eye so it requires the recording of a heartbeat wave or electrocardiogram (EKG) for the disease to be detected. Therefore, a strategy that uses image processing and artificial neural networks to detect anomalies in the heart is strongly advocated. The proposed methods for feature extraction and identification are Invariant Moments and Extreme Learning Machine respectively. The testing procedure for this research employed a total of 386 ECG images as training data. and 44 ECG images for test data, and the heart condition was classified into 4 classes, namely Atrial Fibrillation, T-Wave, ST-Segment, and normal heart conditions. The test was carried out using 3 choices of extreme learning machine activation functions, namely sigmoidal, sine and hard-lim. The test also applied the parameter of hidden neurons in which amounting to 10, 30, 50, 100 and 500. The system accuracy in identifying heart abnormalities achieved 95.45% by the application of the sigmoid function with the total number of hidden neurons equal to 500.

Two‐dimensional adaptive Whittaker–Shannon Sinc‐based zooming

AbstractIn this work, we introduce a novel image zooming methodology that transitions from a nonadaptive Sin‐based approach to an adaptive Sinc‐based zooming technique. The two techniques base their theoretical foundation on the Whittaker–Shannon interpolation formula and the Nyquist theorem. The evolution into adaptive Sinc‐based zoom is accomplished through the use of two novel concepts: (1) the pixel‐local scaled k‐space and (2) the k‐space filtering sigmoidal function. The pixel‐local scaled k‐space is the standardized and scaled k‐space magnitude of the image to zoom. The k‐space filtering sigmoidal function scales the pixel‐local scaled k‐space values into the numerical interval [0, 1]. Using these two novel concepts, the Whittaker–Shannon interpolation formula is elaborated and used to zoom images. Zooming is determined by the shape of the Sinc functions in the Whittaker–Shannon interpolation formula, which, in turn, depends on the combined effect of the pixel‐local scaled k‐space, the sampling rate, and the k‐space filtering sigmoidal function. The primary outcome of this research demonstrates that the Whittaker–Shannon interpolation formula can achieve successful zooms for values of the sampling rate significantly greater than the bandwidth. Conversely, when the sampling rate is much greater than the bandwidth, the nonadaptive technique fails to perform the zoom correctly. The conclusion is that the k‐space filtering sigmoidal function is identified as the crucial parameter in the adaptive Sinc‐based zoom technique. The implications of this research extend to Sinc‐based image zooming applications.

Linearly-coupled sigmoid bistable stochastic resonance for weak signal detection

Abstract The paper focuses on developing a stochastic resonance (SR) system designed for the detection of weak signals under alpha-stable-distributed noises. Initially, in view of the strong impulsive characteristics of noises, a linearly-coupled sigmoid bistable stochastic resonance (LSBSR) system is proposed, which is constructed by potential function and sigmoid function. Through formula derivation, it is theoretically proved that the output signal-to-noise ratio (SNR) of the LSBSR system is superior to that of the classical bistable SR system. Then, a new signal processing strategy based on the LSBSR system is introduced. Simulation experiments have demonstrated that under the input SNR = −20 dB, the detection probability of the LSBSR system exceeds 95% for the alpha-stable-distributed noise with α= 1.5. When α is reduced to 0.1, the detection probability approaches 80%, significantly outperforming other detection methods. Finally, the LSBSR system is applied to detect sea-trial signals with an SNR improvement of 22.5 dB, which further validates the practicability of the proposed system.

Modelling pH Dynamics, SCOBY Biomass Formation, and Acetic Acid Production of Kombucha Fermentation Using Black, Green, and Oolong Teas

Kombucha is a traditional, fermented beverage made with an essential biomaterial known as SCOBY (symbiotic culture of bacteria and yeast). Three different tea types, namely black, green, and oolong, were compared in kombucha fermentation in terms of pH dynamics, the formation of SCOBY biomass, and the production of acetic acid. The rational, exponential, and polynomial models described pH dynamics with good fit, R2 > 0.98. The formation of SCOBY biomass and the production of acetic acid were modelled using sigmoidal functions, with three-parameter logistic and Gompertz models and four-parameter Boltzmann and Richards models. The F-test indicated that the three-parameter models were statistically adequate; thus, the Gompertz model was modified to present the biological meaning of the parameters. The SCOBY biomass formation rates ranged from 7.323 to 9.980 g/L-day, and the acetic acid production rates ranged from 0.047 to 0.049% acid (wt/vol)/day, with the highest values from the non-conventional substrate, oolong tea. The correlations between pH and SCOBY biomass or acetic acid using polynomial models enable the prediction of product formation in kombucha processing.

Prediction of case depth for deep carburising heat treatments based on the spatial gradient feature of the grain size profile

ABSTRACT Precise evaluation of carburising heat treatment is necessary to avoid failure and degradation of high-performance industrial mechanical components. In this work, a novel non-destructive detection method is proposed for the deep carburised case depth (>2 mm) combining spatial ultrasonic backscatter technique and linear regression model. To create various carburised case depths, three groups of cylindrical 20CrMnMo steel samples were heat-treated in various cycles (Carburising, diffusing, quenching at 850–870°C (holding in range of 2.5–3 h) and tempering). The carburising heat treatment results in a gradient microstructure within the surface region caused by changes in grain size. We employed a transverse-to-transverse scattering model to provide the gradient feature of the grain size profile in the depth direction. The extracted gradient profiles of different carburised case depths exhibit two overlapped growth rates with high- and low-slope factors, respectively. With the increase of the carburised case depth, the positions of the centre points increase and the slope factors decrease. Based on these observations, a modified double sigmoidal function was utilised to parametrise the gradient profile curve. The relationship among the selected gradient feature parameters and various carburised case depths has been established. The predicted results were compared to hardness measurements with good agreement.

Comparative Analysis of Recurrent Neural Network Models Performance in Predicting Bitcoin Prices

The recurring neural network is a deep learning algorithm that is commonly used to develop prediction systems. There are many variants of RNN such as RNN itself, long-short-term memory (LSTM), and gated recurring unit, so it is frequently debatable which algorithm from the RNN family has the most optimal efficiency and computation time. When developing a prediction system, sequential or time series data is required so that an accurate prediction can be made. Sequential or time series data involve data arranged in a time sequence, such as weather data, financial data, carbon emission data, and traffic data recorded over time. This research will be carried out by predicting the three RNN models against historical Bitcoin value data. The research method used is Experimental Design by comparing the performance between the three models on bitcoin value time series data, testing is done by involving hyperparameters such as Tanh, Sigmoid, and ReLU activation functions, batch size, and epochs. The aim of this research is to find out which RNN model can produce the most optimal performance and find out what performance measures can be used to evaluate and compare the performance between the three models. The results of the study show that LSTM is the most effective model with RMSE 0.012441 and MSE 0.000155 but inefficient because it takes 3 minutes 24 seconds to run the computation; in the meantime, the Tanh activation function gives the most optimal prediction than Sigmoid and RelU and therefore should be the main candidate to be used with RNN models when predicting Bitcoin prices.

Modeling the anisotropy evolution in sheet metals with heterogeneous properties

The adoption of local heat treatments to effectively modify the material behavior is an interesting solution for improving the formability limits of sheet metals during complex forming processes. Being the Finite Element approach the most effective way to design the material modification, in this study we develop a comprehensive constitutive framework to describe the spectrum of plastic responses associated with different levels of annealing, while considering the effect of the anisotropy.Both changes of the flow stress and the anisotropy with the level of annealing are modeled using sigmoidal functions and introduced in a metal plasticity anisotropic model (Hill48). This approach provides a constitutive framework that, relying on a limited number of experimental characterization tests, allows to predict the evolution of the yield locus according to the level of annealing experienced by the material during the heat treatment. The proposed approach revealed to be an effective tool for modeling the spectrum of heterogeneous mechanical responses, particularly valuable, for instance, in the context of local heat treatments, such as laser-based methods or welding processes. It allows to capture the material behavior in terms of R-values distribution, not only in the region irradiated by the laser spot but also in the transitional region. The detailed hybrid numerical/experimental methodology allows to plug-in any anisotropic plasticity model, making the constitutive framework extremely versatile and needing a very limited number of tests. The calibration of the model from experiments and the accuracy of the predictions are thoroughly discussed.

Normalised similarity assessment to inform grouping of advanced multi-component nanomaterials by means of an Asymmetric Sigmoid function

This manuscript presents a procedure for similarity assessment as a basis for grouping of multi component nanomaterials (MCNMs). This methodology is an adaptation of the approach by Zabeo et al. (2022), which includes an impactful change: the calculated similarities are normalised in the [0,1] domain by means of asymmetric Logistic scaling to simplify comparisons among properties' distances. This novel approach allows for grouping of nanomaterials that is not affected by the dataset, so that group membership will not change when new candidates are included in the set of assessed materials. It can be applied to assess groups of MCNMs as well as mixed groups of multi and single component nanomaterials as well as chemicals. To facilitate the application of the proposed methodology, a software script was developed by using the Python programming language, which is currently undergoing migration to a user-friendly web-based tool. The presented approach was tested against a real industrial case study provided by the Andalusian Innovation Centre for Sustainable Solution (CIAC): SiO2-ZnO hybrid nanocomposite used in building coatings, which is designed to facilitate photocatalytic removal of NOx gases from the atmosphere. The results of applying the methodology in the case study demonstrated that ZnO is dissimilar from the other candidates mainly due to its different dissolution profiles.

Investigation of Dynamic Viscoelastic Characteristics of Permeable Asphalt

In order to provide a basis for the structural analysis, design and maintenance of permeable asphalt pavements, and to promote their engineering promotion and application, this study investigated the dynamic viscoelastic properties of permeable asphalt mixtures (PAC-13) under complex stress states. A Simple Performance Tester (SPT) system was used to measure the dynamic modulus of the mix under complex stress states. The displacement factor and principal dynamic modulus curves were formed by fitting Sigmoidal functions and using 1stOpt (first optimization) software, the phase angle principal curves were further determined, and the dynamic modulus was predicted for the ambient phase (15–25 °C) using the Hirsch model. The results showed that the dynamic modulus of the mixtures decreases with an increasing temperature, and the maximum decrease in the dynamic modulus is 93% when the confining pressure is 100 kPa and the loading frequency is 10 Hz. The dynamic modulus increases with an increasing confining pressure and loading frequency, the maximum increase with an increasing confining pressure is 26.1% when the temperature is 25 °C and the loading frequency is 10 Hz, and the maximum increase with an increasing loading frequency is 411% when the temperature is 25 °C and the confining pressure is 100 Hz. The dynamic modulus has a strong frequency dependence at low temperatures, while it is stress-dependent at high temperatures. Meanwhile, based on the Hirsch model, a new modified prediction model was developed, which can well predict the dynamic modulus of permeable asphalt mixtures at room temperature.

Phase field modeling of ductile fracture with isotropic hardening and radius return method

Phase field model has been investigated for brittle fracture in many static and dynamic scenarios, but its applications to ductile fracture is not as common as brittle fracture, especially implementing in software LS-DYNA with explicit scheme. In this study, an efficient LS-DYNA implementation of the phase field modeling of ductile fracture is presented and both with and without the split of elastic strain energy have been considered for the damage evolution. In more detail, plasticity formulation of ductile material with isotropic hardening is briefly presented first and then the governing equations of the classical phase field model are derived, which gives the displacement-phase coupled problem. For with the split of elastic strain energy, the shear component of elastic strain energy is considered for the damage evolution. The influence of degradation function on stress–strain curve is also investigated by using three kinds of function (polynomial function, algebraic fraction function and sigmoid function), which leads to linear and nonlinear finite element method (FEM) formulation of the phase field model and Newton–Raphson method is used to solve the nonlinear FEM formulation of the phase field model. A tensile bar test shows the influence of critical energy release rate and degradation function on stress–strain curve. Mode Ⅰ failure of three-point bending test, Mode Ⅱ failure of single-edge notched plate and mixed-mode failure of asymmetrical double-notched plate verify the proposed model in this study. From these simulations, with the split of elastic strain energy shows improvements on plastic deformation than without the split of elastic strain energy.

Developing an Innovative Imperfect Debugging Software Reliability Growth Model with Enhanced Testing Coverage Strategies

In this paper, we introduce an innovative Software Reliability Growth Model (SRGM) designed to tackle the pivotal challenges associated with software reliability in the contemporary digital landscape, where the prevalence of online systems is ubiquitous. This SRGM integrates Imperfect Debugging (ID), Testing Coverage (TC), Testing Effort (TE), and error generation into a cohesive framework. Employing a sigmoid function to encapsulate TE, it incorporates three distinct TC functions: Delayed S-shaped, Exponential, and Logistic. This model relies on foundational assumptions, including the proportionality of fault detection rates to remaining faults, the introduction of new faults during debugging, and the intricate connection between fault detection and code coverage. The Mean Value Function (MVF) is computed through these differential equations, and the resultant MVFs are systematically tabulated for all models. An examination of the sigmoid TE function and the Weibull TE function across diverse datasets, utilizing a range of goodness-of-fit criteria including Mean Square Error (MSE), Pham’s Criterion (PC), Predictive Risk Ratio (PRR), Bayesian Information Criterion (BIC), and Akaike’s Information Criterion (AIC), reveals the superior performance of the sigmoid TE function over the Weibull counterpart across various datasets and evaluation criteria. In conclusion, this paper introduces a groundbreaking SRGM that seamlessly integrates ID, TC, and TE, offering valuable insights for assessing software reliability in the dynamic landscape of modern digital systems.

A topological description of loss surfaces based on Betti Numbers

In the context of deep learning models, attention has recently been paid to studying the surface of the loss function in order to better understand training with methods based on gradient descent. This search for an appropriate description, both analytical and topological, has led to numerous efforts in identifying spurious minima and characterize gradient dynamics. Our work aims to contribute to this field by providing a topological measure for evaluating loss complexity in the case of multilayer neural networks. We compare deep and shallow architectures with common sigmoidal activation functions by deriving upper and lower bounds for the complexity of their respective loss functions and revealing how that complexity is influenced by the number of hidden units, training models, and the activation function used. Additionally, we found that certain variations in the loss function or model architecture, such as adding an ℓ2 regularization term or implementing skip connections in a feedforward network, do not affect loss topology in specific cases.