Journal Description
Mathematics
Mathematics
is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), RePEc, and other databases.
- Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.9 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Sections: published in 13 topical sections.
- Companion journals for Mathematics include: Foundations, AppliedMath, Analytics, International Journal of Topology, Geometry and Logics.
Impact Factor:
2.4 (2022);
5-Year Impact Factor:
2.3 (2022)
Latest Articles
A Novel Method for Predicting the Behavior of a Sucker Rod Pumping Unit Based on the Polished Rod Velocity
Mathematics 2024, 12(9), 1318; https://doi.org/10.3390/math12091318 (registering DOI) - 25 Apr 2024
Abstract
Fault dynamometer cards are the basis of the diagnosis technique for sucker rod pumping systems. Predicting fault cards with a pumping condition model is an economical and effective method. The usual model is described by a mixed function of the pump displacement and
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Fault dynamometer cards are the basis of the diagnosis technique for sucker rod pumping systems. Predicting fault cards with a pumping condition model is an economical and effective method. The usual model is described by a mixed function of the pump displacement and pump load, and it is difficult to use in the prediction method based on the analytical solution of the sucker rod string wave equation. In this paper, a normal pumping condition model described by a function of polished rod velocity is proposed. For the analytical solution of the sucker rod wave equation, an iterative prediction algorithm with pumping condition models is proposed, its convergence is analyzed, and then it is validated by classical finite difference method simulated cards and measured surface dynamometer cards. The results show that the proposed algorithm is accurate. The algorithm has a maximum relative error of 0.10% for the classical method simulated card area and 1.45% for the measured card area. The research of this paper provides an effective scheme for the design, prediction, and fault diagnosis of a sucker rod pumping system with an analytical solution.
Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd Edition)
Open AccessArticle
The Blow-Up of the Local Energy Solution to the Wave Equation with a Nontrivial Boundary Condition
by
Yulong Liu
Mathematics 2024, 12(9), 1317; https://doi.org/10.3390/math12091317 (registering DOI) - 25 Apr 2024
Abstract
In this study, we examine the wave equation with a nontrivial boundary condition. The main target of this study is to prove the local-in-time existence and the blow-up in finite time of the energy solution. Through the construction of an auxiliary function and
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In this study, we examine the wave equation with a nontrivial boundary condition. The main target of this study is to prove the local-in-time existence and the blow-up in finite time of the energy solution. Through the construction of an auxiliary function and the imposition of appropriate conditions on the initial data, we establish the both lower and upper bounds for the blow-up time of the solution. Meanwhile, based on these estimates, we obtain the result of the local-in-time existence and the blow-up of the energy solution. This approach enhances our understanding of the dynamics leading to blow-up in the considered condition.
Full article
(This article belongs to the Special Issue Advances in Differential and Difference Equations and Their Applications)
Open AccessArticle
Meshless Generalized Finite Difference Method Based on Nonlocal Differential Operators for Numerical Simulation of Elastostatics
by
Yeying Zhou, Chunguang Li, Xinshan Zhuang and Zhifen Wang
Mathematics 2024, 12(9), 1316; https://doi.org/10.3390/math12091316 (registering DOI) - 25 Apr 2024
Abstract
This study proposes an innovative meshless approach that merges the peridynamic differential operator (PDDO) with the generalized finite difference method (GFDM). Based on the PDDO theory, this method introduces a new nonlocal differential operator that aims to reduce the pre-assumption required for the
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This study proposes an innovative meshless approach that merges the peridynamic differential operator (PDDO) with the generalized finite difference method (GFDM). Based on the PDDO theory, this method introduces a new nonlocal differential operator that aims to reduce the pre-assumption required for the PDDO method and simplify the calculation process. By discretizing through the particle approximation method, this technique proficiently preserves the PDDO’s nonlocal features, enhancing the numerical simulation’s flexibility and usability. Through the numerical simulation of classical elastic static problems, this article focuses on the evaluation of the calculation accuracy, calculation efficiency, robustness, and convergence of the method. This method is significantly stronger than the finite element method in many performance indicators. In fact, this study demonstrates the practicability and superiority of the proposed method in the field of elastic statics and provides a new approach to more complex problems.
Full article
(This article belongs to the Special Issue Recent Advances in Numerical Methods for Scientific and Engineering Applications, 2nd Edition)
Open AccessArticle
Efficient Large-Scale IoT Botnet Detection through GraphSAINT-Based Subgraph Sampling and Graph Isomorphism Network
by
Lihua Yin, Weizhe Chen, Xi Luo and Hongyu Yang
Mathematics 2024, 12(9), 1315; https://doi.org/10.3390/math12091315 (registering DOI) - 25 Apr 2024
Abstract
In recent years, with the rapid development of the Internet of Things, large-scale botnet attacks have occurred frequently and have become an important challenge to network security. As artificial intelligence technology continues to evolve, intelligent detection solutions for botnets are constantly emerging. Although
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In recent years, with the rapid development of the Internet of Things, large-scale botnet attacks have occurred frequently and have become an important challenge to network security. As artificial intelligence technology continues to evolve, intelligent detection solutions for botnets are constantly emerging. Although graph neural networks are widely used for botnet detection, directly handling large-scale botnet data becomes inefficient and challenging as the number of infected hosts increases and the network scale expands. Especially in the process of node level learning and inference, a large number of nodes and edges need to be processed, leading to a significant increase in computational complexity and posing new challenges to network security. This paper presents a novel approach that can accurately identify diverse intricate botnet architectures in extensive IoT networks based on the aforementioned circumstance. By utilizing GraphSAINT to process large-scale IoT botnet graph data, efficient and unbiased subgraph sampling has been achieved. In addition, a solution with enhanced information representation capability has been developed based on the Graph Isomorphism Network (GIN) for botnet detection. Compared with the five currently popular graph neural network (GNN) models, our approach has been tested on C2, P2P, and Chord datasets, and higher accuracy has been achieved.
Full article
(This article belongs to the Special Issue Advanced Research on Information System Security and Privacy)
Open AccessArticle
A Privacy Protection Scheme of Certificateless Aggregate Ring Signcryption Based on SM2 Algorithm in Smart Grid
by
Hongna Song, Zhentao Liu, Teng Wang, Ling Zhao, Haonan Guo and Shuanggen Liu
Mathematics 2024, 12(9), 1314; https://doi.org/10.3390/math12091314 (registering DOI) - 25 Apr 2024
Abstract
With the rapid increase in smart grid users and the increasing cost of user data transmission, proposing an encryption method that does not increase the construction cost while increasing the user ceiling has become the focus of many scholars. At the same time,
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With the rapid increase in smart grid users and the increasing cost of user data transmission, proposing an encryption method that does not increase the construction cost while increasing the user ceiling has become the focus of many scholars. At the same time, the increase in users will also lead to more security problems, and it is also necessary to solve the privacy protection for users during information transmission. In order to solve the above problems, this paper proposes an aggregated ring encryption scheme based on the SM2 algorithm with special features, referred to as SM2-CLARSC, based on the certificateless ring signcryption mechanism and combining with the aggregate signcryption. SM2-CLARSC is designed to satisfy the basic needs of the smart grid, and it can be resistant to replay attacks, forward security and backward security, etc. It has better security and higher efficiency than existing solutions. Comparing SM2-CLARSC with existing typical solutions through simulation, the result proves that this solution has more comprehensive functions, higher security, and significant computational efficiency improvement.
Full article
(This article belongs to the Topic Recent Advances in Security, Privacy, and Trust)
Open AccessArticle
Enhancing Surveillance Vision with Multi-Layer Deep Learning Representation
by
Dong-Min Son and Sung-Hak Lee
Mathematics 2024, 12(9), 1313; https://doi.org/10.3390/math12091313 (registering DOI) - 25 Apr 2024
Abstract
This paper aimed to develop a method for generating sand–dust removal and dehazed images utilizing CycleGAN, facilitating object identification on roads under adverse weather conditions such as heavy dust or haze, which severely impair visibility. Initially, the study addressed the scarcity of paired
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This paper aimed to develop a method for generating sand–dust removal and dehazed images utilizing CycleGAN, facilitating object identification on roads under adverse weather conditions such as heavy dust or haze, which severely impair visibility. Initially, the study addressed the scarcity of paired image sets for training by employing unpaired CycleGAN training. The CycleGAN training module incorporates hierarchical single-scale Retinex (SSR) images with varying sigma sizes, facilitating multiple-scaled trainings. Refining the training data into detailed hierarchical layers for virtual paired training enhances the performance of CycleGAN training. Conventional sand–dust removal or dehazing algorithms, alongside deep learning methods, encounter challenges in simultaneously addressing sand–dust removal and dehazing with a singular algorithm. Such algorithms often necessitate resetting hyperparameters to process images from both scenarios. To overcome this limitation, we proposed a unified approach for removing sand–dust and haze phenomena using a single model, leveraging images processed hierarchically with SSR. The image quality and image sharpness metrics of the proposed method were BRIQUE, PIQE, CEIQ, MCMA, LPC-SI, and S3. In sand–dust environments, the proposed method achieved the highest scores, with an average of 21.52 in BRISQUE, 0.724 in MCMA, and 0.968 in LPC-SI compared to conventional methods. For haze images, the proposed method outperformed conventional methods with an average of 3.458 in CEIQ, 0.967 in LPC-SI, and 0.243 in S3. The images generated via this proposed method demonstrated superior performance in image quality and sharpness evaluation compared to conventional algorithms. The outcomes of this study hold particular relevance for camera images utilized in automobiles, especially in the context of self-driving cars or CCTV surveillance systems.
Full article
(This article belongs to the Special Issue New Advances and Applications in Image Processing and Computer Vision)
Open AccessArticle
Deep Learning Based Fall Recognition and Forecasting for Reconfigurable Stair-Accessing Service Robots
by
Jun Hua Ong, Abdullah Aamir Hayat, Braulio Felix Gomez, Mohan Rajesh Elara and Kristin Lee Wood
Mathematics 2024, 12(9), 1312; https://doi.org/10.3390/math12091312 (registering DOI) - 25 Apr 2024
Abstract
This paper presents a comprehensive study on fall recognition and forecasting for reconfigurable stair-accessing robots by leveraging deep learning techniques. The proposed framework integrates machine learning algorithms and recurrent neural networks (RNNs), specifically Long Short-Term Memory (LSTM) and Bidirectional LSTM (BiLSTM), for fall
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This paper presents a comprehensive study on fall recognition and forecasting for reconfigurable stair-accessing robots by leveraging deep learning techniques. The proposed framework integrates machine learning algorithms and recurrent neural networks (RNNs), specifically Long Short-Term Memory (LSTM) and Bidirectional LSTM (BiLSTM), for fall detection of service robots on staircases. The reconfigurable stair-accessing robot sTetro serves as the platform, and the fall data required for training models are generated in a simulation environment. The two machine learning algorithms are compared and their effectiveness on the fall recognition task is reported. The results indicate that the BiLSTM model effectively classifies falls with a median categorical accuracy of 94.10% in simulation and 90.02% with limited experiments. Additionally, the BiLSTM model can be used for forecasting, which is practically valuable for making decisions well before the onset of a free fall. This study contributes insights into the design and implementation of fall detection systems for service robots used to navigate staircases through deep learning approaches. Our experimental and simulation data, along with the simulation steps, are available for reference and analysis via the shared link.
Full article
Open AccessArticle
A Few Similarity Measures on the Class of Trapezoidal-Valued Intuitionistic Fuzzy Numbers and Their Applications in Decision Analysis
by
Jeevaraj Selvaraj and Melfi Alrasheedi
Mathematics 2024, 12(9), 1311; https://doi.org/10.3390/math12091311 (registering DOI) - 25 Apr 2024
Abstract
Similarity measures on trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) are functions that measure the closeness between two TrVIFNs, which has a lot of applications in the area of pattern recognition, clustering, decision-making, etc. Researchers around the world are proposing various similarity measures on the
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Similarity measures on trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) are functions that measure the closeness between two TrVIFNs, which has a lot of applications in the area of pattern recognition, clustering, decision-making, etc. Researchers around the world are proposing various similarity measures on the generalizations of fuzzy sets. However, many such measures do not satisfy the condition that “the similarity between two fuzzy numbers is equal to 1 implies that both the fuzzy numbers are equal” and this gives a pathway for the researchers to introduce different similarity measures on various classes of fuzzy sets. Also, all of them try to find out the similarity by using a single function, and in the present study, we try to propose a combined similarity measure principle by using four functions (four similarity measures). Thus, the main aim of this work is to introduce a few sets of similarity measures on the class of TrVIFNs and propose a combined similarity measure principle on TrVIFNs based on the proposed similarity measures. To do this, in this paper, firstly, we propose four distance-based similarity measures on TrVIFNs using score functions on TrVIFNs and study their mathematical properties by establishing various propositions, theorems, and illustrations, which is achieved by using numerical examples. Secondly, we propose the idea of a combined similarity measure principle by using the four proposed similarity measures sequentially, which is a first in the literature. Thirdly, we compare our combined similarity measure principle with a few important similarity measures introduced on various classes of fuzzy numbers, which shows the need for and efficacy of the proposed similarity measures over the existing methods. Fourthly, we discuss the trapezoidal-valued intuitionistic fuzzy TOPSIS (TrVIF-TOPSIS) method, which uses the proposed combined similarity measure principle for solving a multi-criteria decision-making (MCDM) problem. Then, we discuss the applicability of the proposed modified TrVIF-TOPSIS method by solving a model problem. Finally, we discuss the sensitivity analysis of the proposed approaches by using various cases.
Full article
(This article belongs to the Special Issue Various Generalizations of Fuzzy Sets and Their Applications in Engineering and Management)
Open AccessArticle
Robust Bias Compensation Method for Sparse Normalized Quasi-Newton Least-Mean with Variable Mixing-Norm Adaptive Filtering
by
Ying-Ren Chien, Han-En Hsieh and Guobing Qian
Mathematics 2024, 12(9), 1310; https://doi.org/10.3390/math12091310 (registering DOI) - 25 Apr 2024
Abstract
Input noise causes inescapable bias to the weight vectors of the adaptive filters during the adaptation processes. Moreover, the impulse noise at the output of the unknown systems can prevent bias compensation from converging. This paper presents a robust bias compensation method for
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Input noise causes inescapable bias to the weight vectors of the adaptive filters during the adaptation processes. Moreover, the impulse noise at the output of the unknown systems can prevent bias compensation from converging. This paper presents a robust bias compensation method for a sparse normalized quasi-Newton least-mean (BC-SNQNLM) adaptive filtering algorithm to address these issues. We have mathematically derived the biased-compensation terms in an impulse noisy environment. Inspired by the convex combination of adaptive filters’ step sizes, we propose a novel variable mixing-norm method, BC-SNQNLM-VMN, to accelerate the convergence of our BC-SNQNLM algorithm. Simulation results confirm that the proposed method significantly outperforms other comparative works regarding normalized mean-squared deviation (NMSD) in the steady state.
Full article
(This article belongs to the Special Issue Advanced Research in Data-Centric AI)
Open AccessArticle
Study of Random Walk Invariants for Spiro-Ring Network Based on Laplacian Matrices
by
Yasir Ahmad, Umar Ali, Daniele Ettore Otera and Xiang-Feng Pan
Mathematics 2024, 12(9), 1309; https://doi.org/10.3390/math12091309 (registering DOI) - 25 Apr 2024
Abstract
The use of the global mean first-passage time (GMFPT) in random walks on networks has been widely explored in the field of statistical physics, both in theory and practical applications. The GMFPT is the estimated interval of time needed to reach a state
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The use of the global mean first-passage time (GMFPT) in random walks on networks has been widely explored in the field of statistical physics, both in theory and practical applications. The GMFPT is the estimated interval of time needed to reach a state j in a system from a starting state i. In contrast, there exists an intrinsic measure for a stochastic process, known as Kemeny’s constant, which is independent of the initial state. In the literature, it has been used as a measure of network efficiency. This article deals with a graph-spectrum-based method for finding both the GMFPT and Kemeny’s constant of random walks on spiro-ring networks (that are organic compounds with a particular graph structure). Furthermore, we calculate the Laplacian matrix for some specific spiro-ring networks using the decomposition theorem of Laplacian polynomials. Moreover, using the coefficients and roots of the resulting matrices, we establish some formulae for both GMFPT and Kemeny’s constant in these spiro-ring networks.
Full article
(This article belongs to the Special Issue Geometry and Topology with Applications)
Open AccessArticle
Semi-Analytical Closed-Form Solutions for Dynamical Ro¨ssler-Type System
by
Remus-Daniel Ene and Nicolina Pop
Mathematics 2024, 12(9), 1308; https://doi.org/10.3390/math12091308 (registering DOI) - 25 Apr 2024
Abstract
Mathematical models and numerical simulations are necessary to understand the functions of biological rhythms, to comprehend the transition from simple to complex behavior and to delineate the conditions under which they arise. The aim of this work is to investigate the R
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Mathematical models and numerical simulations are necessary to understand the functions of biological rhythms, to comprehend the transition from simple to complex behavior and to delineate the conditions under which they arise. The aim of this work is to investigate the R ssler-type system. This system could be proposed as a theoretical model for biological rhythms, generalizing this formula for chaotic behavior. It is assumed that the R ssler-type system has a Hamilton–Poisson realization. To semi-analytically solve this system, a Bratu-type equation was explored. The approximate closed-form solutions are obtained using the Optimal Parametric Iteration Method (OPIM) using only one iteration. The advantages of this analytical procedure are reflected through a comparison between the analytical and corresponding numerical results. The obtained results are in a good agreement with the numerical results, and they highlight that our procedure is effective, accurate and usefully for implementation in applicationssuch as an oscillator with cubic and harmonic restoring forces, the Thomas–Fermi equation and the Lotka–Voltera model with three species.
Full article
(This article belongs to the Special Issue Analytical Approaches to Nonlinear Dynamical Systems and Applications II)
Open AccessArticle
Monitoring the Wear Trends in Wind Turbines by Tracking Fourier Vibration Spectra and Density Based Support Vector Machines
by
Claudiu Bisu, Adrian Olaru, Serban Olaru, Adrian Alexei, Niculae Mihai and Haleema Ushaq
Mathematics 2024, 12(9), 1307; https://doi.org/10.3390/math12091307 (registering DOI) - 25 Apr 2024
Abstract
To make wind power more competitive, it is necessary to reduce turbine downtime and reduce costs associated with wind turbine operation and maintenance (O&M). Incorporating machine learning in the development of condition-based predictive maintenance methodologies for wind turbines can enhance their efficiency and
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To make wind power more competitive, it is necessary to reduce turbine downtime and reduce costs associated with wind turbine operation and maintenance (O&M). Incorporating machine learning in the development of condition-based predictive maintenance methodologies for wind turbines can enhance their efficiency and reliability. This paper presents a monitoring method that utilizes Density Based Support Vector Machines (DBSVM) and the evolutionary Fourier spectra of vibrations. This method allows for the smart monitoring of the function evolution of the turbine. A complex optimal function (FO) for 5-degree order has been developed that will be the boundary function of the DBSVM to be timely determined from the Fourier spectrum through the magnitude–frequency and place of the failure occurring in the wind turbine drivetrains. The trend of the failure was constructed with the maximal values of the optimal frequency function for both yesthe cases of the upwind and downwind parts of the gearbox.
Full article
(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 2nd Edition)
Open AccessArticle
A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers
by
Haizhao Liang, Yunhao Luo, Haohui Che, Jingxian Zhu and Jianying Wang
Mathematics 2024, 12(9), 1306; https://doi.org/10.3390/math12091306 (registering DOI) - 25 Apr 2024
Abstract
The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve
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The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.
Full article
(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application, 2nd Edition)
Open AccessArticle
On α-Pseudo Spiralike Functions Associated with Exponential Pareto Distribution (EPD) and Libera Integral Operator
by
Hamzat Jamiu Olusegun, Oluwayemi Matthew Olanrewaju, Oladipo Abiodun Tinuoye and Alb Lupas Alina
Mathematics 2024, 12(9), 1305; https://doi.org/10.3390/math12091305 - 25 Apr 2024
Abstract
The present study aims at investigating some characterizations of a new subclass and obtaining the bounds on the first two Taylor–Maclaurin coefficients for functions belonging to the newly introduced subclass. In order to achieve this, a
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The present study aims at investigating some characterizations of a new subclass and obtaining the bounds on the first two Taylor–Maclaurin coefficients for functions belonging to the newly introduced subclass. In order to achieve this, a compound function is derived from the convolution of the analytic function and a modified exponential Pareto distribution in conjunction with the famous Libera integral operator . With the aid of the derived function, the aforementioned subclass is introduced, while some properties of functions belonging to this subclass are considered in the open unit disk.
Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Research, 2nd Edition)
Open AccessArticle
Sparsity-Constrained Vector Autoregressive Moving Average Models for Anomaly Detection of Complex Systems with Multisensory Signals
by
Meng Ma, Zhongyi Zhang, Zhi Zhai and Zhirong Zhong
Mathematics 2024, 12(9), 1304; https://doi.org/10.3390/math12091304 - 25 Apr 2024
Abstract
Detecting anomalies in large, complex systems is a critical and challenging task, and this is especially true for high-dimensional anomaly detection due to the underlying dependency structures among sensors. To incorporate the interrelationships among various sensors, a novel sparsity-constrained vector autoregressive moving average
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Detecting anomalies in large, complex systems is a critical and challenging task, and this is especially true for high-dimensional anomaly detection due to the underlying dependency structures among sensors. To incorporate the interrelationships among various sensors, a novel sparsity-constrained vector autoregressive moving average (scVARMA) model is proposed for anomaly detection in complex systems with multisensory signals. This model aims to leverage the inherent relationships and dynamics among various sensor readings, providing a more comprehensive and accurate analysis suitable for complex systems’ complex behavior. This research uses convex optimization to search for a parameterization that is sparse based on the principal of parsimony. This sparse model will not only contribute to meeting the real-time requirements of online monitoring strategies but also keeps the correlations among different sensory signals. The performance of the proposed scVARMA model is validated using real-world data from complex systems. The results affirm the superiority of the proposed scheme, demonstrating its enhanced performance and potential in practical applications.
Full article
(This article belongs to the Special Issue Functional Statistics: Outliers Detection and Quality Control, 2nd Edition)
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Open AccessArticle
TPTM-HANN-GA: A Novel Hyperparameter Optimization Framework Integrating the Taguchi Method, an Artificial Neural Network, and a Genetic Algorithm for the Precise Prediction of Cardiovascular Disease Risk
by
Chia-Ming Lin and Yu-Shiang Lin
Mathematics 2024, 12(9), 1303; https://doi.org/10.3390/math12091303 - 25 Apr 2024
Abstract
The timely and precise prediction of cardiovascular disease (CVD) risk is essential for effective prevention and intervention. This study proposes a novel framework that integrates the two-phase Taguchi method (TPTM), the hyperparameter artificial neural network (HANN), and a genetic algorithm (GA) called TPTM-HANN-GA.
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The timely and precise prediction of cardiovascular disease (CVD) risk is essential for effective prevention and intervention. This study proposes a novel framework that integrates the two-phase Taguchi method (TPTM), the hyperparameter artificial neural network (HANN), and a genetic algorithm (GA) called TPTM-HANN-GA. This framework efficiently optimizes hyperparameters for an artificial neural network (ANN) model during the training stage, significantly enhancing prediction accuracy for cardiovascular disease (CVD) risk. The proposed TPTM-HANN-GA framework requires far fewer experiments than a traditional grid search, making it highly suitable for application in resource-constrained, low-power computers, and edge artificial intelligence (edge AI) devices. Furthermore, the proposed TPTM-HANN-GA framework successfully identified the optimal configurations for the ANN model’s hyperparameters, resulting in a hidden layer of 4 nodes, a tan h activation function, an SGD optimizer, a learning rate of 0.23425849, a momentum rate of 0.75462782, and seven hidden nodes. This optimized ANN model achieves 74.25% accuracy in predicting the risk of cardiovascular disease, which exceeds the existing state-of-the-art GA-ANN and TSTO-ANN models. The proposed TPTM-HANN-GA framework enables personalized CVD prediction to be efficiently conducted on low-power computers and edge-AI devices, achieving the goal of point-of-care testing (POCT) and empowering individuals to manage their heart health effectively.
Full article
Open AccessArticle
Single and Multi-Valued Ordered-Theoretic Perov Fixed-Point Results for θ-Contraction with Application to Nonlinear System of Matrix Equations
by
Fahim Ud Din, Salha Alshaikey, Umar Ishtiaq, Muhammad Din and Salvatore Sessa
Mathematics 2024, 12(9), 1302; https://doi.org/10.3390/math12091302 (registering DOI) - 25 Apr 2024
Abstract
This paper combines the concept of an arbitrary binary connection with the widely recognized principle of -contraction to investigate the innovative features of vector-valued metric spaces. This methodology demonstrates the existence of fixed points for both single- and multi-valued mappings within complete
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This paper combines the concept of an arbitrary binary connection with the widely recognized principle of -contraction to investigate the innovative features of vector-valued metric spaces. This methodology demonstrates the existence of fixed points for both single- and multi-valued mappings within complete vector-valued metric spaces. Through the utilization of binary relations and -contraction, this study advances and refines the Perov-type fixed-point results in the literature. Furthermore, this article furnishes examples to substantiate the validity of the presented results. Additionally, we establish an application for finding the existence of solutions to a system of matrix equations.
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Open AccessArticle
Synergising an Advanced Optimisation Technique with Deep Learning: A Novel Method in Fault Warning Systems
by
Jia Tian, Xingqin Zhang, Shuangqing Zheng, Zhiyong Liu and Changshu Zhan
Mathematics 2024, 12(9), 1301; https://doi.org/10.3390/math12091301 - 25 Apr 2024
Abstract
In the realm of automated industry and smart production, the deployment of fault warning systems is crucial for ensuring equipment reliability and enhancing operational efficiency. Although there are a multitude of existing methodologies for fault warning, the proficiency of these systems in processing
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In the realm of automated industry and smart production, the deployment of fault warning systems is crucial for ensuring equipment reliability and enhancing operational efficiency. Although there are a multitude of existing methodologies for fault warning, the proficiency of these systems in processing and analysing data is increasingly challenged by the progression of industrial apparatus and the escalating magnitude and intricacy of the data involved. To address these challenges, this research outlines an innovative fault warning methodology that combines a bi-directional long short-term memory (Bi-LSTM) network with an enhanced hunter–prey optimisation (EHPO) algorithm. The Bi-LSTM network is strategically utilised to outline complex temporal patterns in machinery operational data, while the EHPO algorithm is employed to meticulously fine-tune the hyperparameters of the Bi-LSTM, aiming to enhance the accuracy and generalisability of fault warning. The EHPO algorithm, building upon the foundational hunter–prey optimisation (HPO) framework, introduces an advanced population initialisation process, integrates a range of strategic exploration methodologies, and strengthens its search paradigms through the incorporation of the differential evolution (DE) algorithm. This comprehensive enhancement aims to boost the global search efficiency and accelerate the convergence speed of the algorithm. Empirical analyses, conducted using datasets from real-world industrial scenarios, have validated the improved warning performance of this proposed methodology against some benchmark techniques, as evidenced by superior metrics such as root mean square error (RMSE) and mean absolute error (MAE), albeit with a slight increase in computational resource requirements. This study not only proposes a novel paradigm for fault warning within complex industrial frameworks but also contributes to the discourse on hyperparameter optimisation within the field of machine learning algorithms.
Full article
(This article belongs to the Special Issue Computational Intelligence and Machine Learning with Applications)
Open AccessArticle
Estimating the Complier Average Causal Effect with Non-Ignorable Missing Outcomes Using Likelihood Analysis
by
Jierui Du, Gao Wen and Xin Liang
Mathematics 2024, 12(9), 1300; https://doi.org/10.3390/math12091300 - 25 Apr 2024
Abstract
Missing data problems arise in randomized trials, which complicates the inference of causal effects if the missing mechanism is non-ignorable. We tackle the challenge of identifying and estimating the complier average causal effect parameters under non-ignorable missingness by increasing the covariates to mitigate
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Missing data problems arise in randomized trials, which complicates the inference of causal effects if the missing mechanism is non-ignorable. We tackle the challenge of identifying and estimating the complier average causal effect parameters under non-ignorable missingness by increasing the covariates to mitigate the sensitivity to the violation of specific identification assumptions. The missing data mechanism is assumed to follow a logistic model, wherein the absence of the outcome is explained by the outcome itself, the treatment received, and the covariates. We establish the identifiability of the models under mild conditions by assuming that the outcome follows a normal distribution. We develop a computational method to estimate model parameters through a two-step likelihood estimation approach, employing subgroup analysis. The bootstrap method is employed for variance estimation, and the effectiveness of our approach is confirmed through simulation. We applied the proposed method to analyze the household income dataset from the Chinese Household Income Project Survey 2013.
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(This article belongs to the Special Issue Advances in Statistical AI and Casual Inference)
Open AccessArticle
Robust Design Optimization of Electric Machines with Isogeometric Analysis
by
Theodor Komann, Michael Wiesheu, Stefan Ulbrich and Sebastian Schöps
Mathematics 2024, 12(9), 1299; https://doi.org/10.3390/math12091299 - 25 Apr 2024
Abstract
In electric machine design, efficient methods for the optimization of the geometry and associated parameters are essential. Nowadays, it is necessary to address the uncertainty caused by manufacturing or material tolerances. This work presents a robust optimization strategy to address uncertainty in the
[...] Read more.
In electric machine design, efficient methods for the optimization of the geometry and associated parameters are essential. Nowadays, it is necessary to address the uncertainty caused by manufacturing or material tolerances. This work presents a robust optimization strategy to address uncertainty in the design of a three-phase, six-pole permanent magnet synchronous motor (PMSM). The geometry is constructed in a two-dimensional framework within MATLAB®, employing isogeometric analysis (IGA) to enable flexible shape optimization. The main contributions of this research are twofold. First, we integrate shape optimization with parameter optimization to enhance the performance of PMSM designs. Second, we use robust optimization, which creates a min–max problem, to ensure that the motor maintains its performance when facing uncertainties. To solve this bilevel problem, we work with the maximal value functions of the lower-level maximization problems and apply a version of Danskin’s theorem for the computation of generalized derivatives. Additionally, the adjoint method is employed to efficiently solve the lower-level problems with gradient-based optimization. The paper concludes by presenting numerical results showcasing the efficacy of the proposed robust optimization framework. The results indicate that the optimized PMSM designs not only perform competitively compared to their non-robust counterparts but also show resilience to operational and manufacturing uncertainties, making them attractive for industrial applications.
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(This article belongs to the Special Issue Numerical Optimization for Electromagnetic Problems)
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