Aliyu Isa Aliyu, Jibrin Sale Yusuf, Malik Muhammad Nauman, Dilber Uzun Ozsahin, Baba Galadima Agaie, Juliana Haji Zaini, Huzaifa Umar
In this study, we investigate the symmetry analysis and explicit solutions for the Estevez–Mansfield–Clarkson (EMC) equation. Our main objectives are to identify the Lie point symmetries of the EMC equation, construct an optimal system of one-dimensional subalgebras, and reduce the EMC equation to a set of ordinary differential equations (ODEs). We employ the Riccati–Bernoulli sub-ODE method (RBSODE) to solve these reduced ODEs and obtain explicit solutions for the EMC model. The obtained solutions are validated using numerical analyses, and corresponding figures are presented to illustrate the physical implications of the derived solutions.
{"title":"Lie Symmetry Analysis and Explicit Solutions to the Estevez–Mansfield–Clarkson Equation","authors":"Aliyu Isa Aliyu, Jibrin Sale Yusuf, Malik Muhammad Nauman, Dilber Uzun Ozsahin, Baba Galadima Agaie, Juliana Haji Zaini, Huzaifa Umar","doi":"10.3390/sym16091194","DOIUrl":"https://doi.org/10.3390/sym16091194","url":null,"abstract":"In this study, we investigate the symmetry analysis and explicit solutions for the Estevez–Mansfield–Clarkson (EMC) equation. Our main objectives are to identify the Lie point symmetries of the EMC equation, construct an optimal system of one-dimensional subalgebras, and reduce the EMC equation to a set of ordinary differential equations (ODEs). We employ the Riccati–Bernoulli sub-ODE method (RBSODE) to solve these reduced ODEs and obtain explicit solutions for the EMC model. The obtained solutions are validated using numerical analyses, and corresponding figures are presented to illustrate the physical implications of the derived solutions.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, the concept of symmetry is employed to implement an intelligent fuzzy traffic signal control system for complex intersections. This approach suggests that the implementation of reduced fuzzy rules through the reduction method, without compromising the performance of the original fuzzy rule base, constitutes a symmetrical approach. In recent decades, urban and city traffic congestion has become a significant issue because of the time lost as a result of heavy traffic, which negatively affects economic productivity and efficiency and leads to energy loss, and also because of the heavy environmental pollution effect. In addition, traffic congestion prevents an immediate response by the ambulance, police, and fire brigades to urgent events. To mitigate these problems, a three-stage intelligent and flexible fuzzy traffic control system for complex intersections, using a novel hybrid reduction approach was proposed. The three-stage fuzzy traffic control system performs four primary functions. The first stage prioritizes emergency car(s) and identifies the degree of urgency of the traffic conditions in the red-light phase. The second stage guarantees a fair distribution of green-light durations even for periods of extremely unbalanced traffic with long vehicle queues in certain directions and, especially, when heavy traffic is loaded for an extended period in one direction and the short vehicle queues in the conflicting directions require passing in a reasonable time. The third stage adjusts the green-light time to the traffic conditions, to the appearance of one or more emergency car(s), and to the overall waiting times of the other vehicles by using a fuzzy inference engine. The original complete fuzzy rule base set up by listing all possible input combinations was reduced using a novel hybrid reduction algorithm for fuzzy rule bases, which resulted in a significant reduction of the original base, namely, by 72.1%. The proposed novel approach, including the model and the hybrid reduction algorithm, were implemented and simulated using Python 3.9 and SUMO (version 1.14.1). Subsequently, the obtained fuzzy rule system was compared in terms of running time and efficiency with a traffic control system using the original fuzzy rules. The results showed that the reduced fuzzy rule base had better results in terms of the average waiting time, calculated fuel consumption, and CO2 emission. Furthermore, the fuzzy traffic control system with reduced fuzzy rules performed better as it required less execution time and thus lower computational costs. Summarizing the above results, it may be stated that this new approach to intersection traffic light control is a practical solution for managing complex traffic conditions at lower computational costs.
{"title":"Intelligent Fuzzy Traffic Signal Control System for Complex Intersections Using Fuzzy Rule Base Reduction","authors":"Tamrat D. Chala, László T. Kóczy","doi":"10.3390/sym16091177","DOIUrl":"https://doi.org/10.3390/sym16091177","url":null,"abstract":"In this study, the concept of symmetry is employed to implement an intelligent fuzzy traffic signal control system for complex intersections. This approach suggests that the implementation of reduced fuzzy rules through the reduction method, without compromising the performance of the original fuzzy rule base, constitutes a symmetrical approach. In recent decades, urban and city traffic congestion has become a significant issue because of the time lost as a result of heavy traffic, which negatively affects economic productivity and efficiency and leads to energy loss, and also because of the heavy environmental pollution effect. In addition, traffic congestion prevents an immediate response by the ambulance, police, and fire brigades to urgent events. To mitigate these problems, a three-stage intelligent and flexible fuzzy traffic control system for complex intersections, using a novel hybrid reduction approach was proposed. The three-stage fuzzy traffic control system performs four primary functions. The first stage prioritizes emergency car(s) and identifies the degree of urgency of the traffic conditions in the red-light phase. The second stage guarantees a fair distribution of green-light durations even for periods of extremely unbalanced traffic with long vehicle queues in certain directions and, especially, when heavy traffic is loaded for an extended period in one direction and the short vehicle queues in the conflicting directions require passing in a reasonable time. The third stage adjusts the green-light time to the traffic conditions, to the appearance of one or more emergency car(s), and to the overall waiting times of the other vehicles by using a fuzzy inference engine. The original complete fuzzy rule base set up by listing all possible input combinations was reduced using a novel hybrid reduction algorithm for fuzzy rule bases, which resulted in a significant reduction of the original base, namely, by 72.1%. The proposed novel approach, including the model and the hybrid reduction algorithm, were implemented and simulated using Python 3.9 and SUMO (version 1.14.1). Subsequently, the obtained fuzzy rule system was compared in terms of running time and efficiency with a traffic control system using the original fuzzy rules. The results showed that the reduced fuzzy rule base had better results in terms of the average waiting time, calculated fuel consumption, and CO2 emission. Furthermore, the fuzzy traffic control system with reduced fuzzy rules performed better as it required less execution time and thus lower computational costs. Summarizing the above results, it may be stated that this new approach to intersection traffic light control is a practical solution for managing complex traffic conditions at lower computational costs.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce the random high-local performance client selection strategy, termed Fed-RHLP. This approach allows opportunities for higher-performance clients to contribute more significantly by updating and sharing their local models for global aggregation. Nevertheless, it also enables lower-performance clients to participate collaboratively based on their proportional representation determined by the probability of their local performance on the roulette wheel (RW). Improving symmetry in federated learning involves IID Data: symmetry is naturally present, making model updates easier to aggregate and Non-IID Data: asymmetries can impact performance and fairness. Solutions include data balancing, adaptive algorithms, and robust aggregation methods. Fed-RHLP enhances federated learning by allowing lower-performance clients to contribute based on their proportional representation, which is determined by their local performance. This fosters inclusivity and collaboration in both IID and Non-IID scenarios. In this work, through experiments, we demonstrate that Fed-RHLP offers accelerated convergence speed and improved accuracy in aggregating the final global model, effectively mitigating challenges posed by both IID and Non-IID Data distribution scenarios.
{"title":"Fed-RHLP: Enhancing Federated Learning with Random High-Local Performance Client Selection for Improved Convergence and Accuracy","authors":"Pramote Sittijuk, Kreangsak Tamee","doi":"10.3390/sym16091181","DOIUrl":"https://doi.org/10.3390/sym16091181","url":null,"abstract":"We introduce the random high-local performance client selection strategy, termed Fed-RHLP. This approach allows opportunities for higher-performance clients to contribute more significantly by updating and sharing their local models for global aggregation. Nevertheless, it also enables lower-performance clients to participate collaboratively based on their proportional representation determined by the probability of their local performance on the roulette wheel (RW). Improving symmetry in federated learning involves IID Data: symmetry is naturally present, making model updates easier to aggregate and Non-IID Data: asymmetries can impact performance and fairness. Solutions include data balancing, adaptive algorithms, and robust aggregation methods. Fed-RHLP enhances federated learning by allowing lower-performance clients to contribute based on their proportional representation, which is determined by their local performance. This fosters inclusivity and collaboration in both IID and Non-IID scenarios. In this work, through experiments, we demonstrate that Fed-RHLP offers accelerated convergence speed and improved accuracy in aggregating the final global model, effectively mitigating challenges posed by both IID and Non-IID Data distribution scenarios.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many problems in scientific research are reduced to a nonlinear equation by mathematical means of modeling. The solutions of such equations are found mostly iteratively. Then, the convergence order is routinely shown using Taylor formulas, which in turn make sufficient assumptions about derivatives which are not present in the iterative method at hand. This technique restricts the usage of the method which may converge even if these assumptions, which are not also necessary, hold. The utilization of these methods can be extended under less restrictive conditions. This new paper contributes in this direction, since the convergence is established by assumptions restricted exclusively on the functions present on the method. Although the technique is demonstrated on a two-step Traub-type method with usually symmetric parameters and weight functions, due to its generality it can be extended to other methods defined on the real line or more abstract spaces. Numerical experimentation complement and further validate the theory.
{"title":"Convergence of a Family of Methods with Symmetric, Antisymmetric Parameters and Weight Functions","authors":"Ramandeep Behl, Ioannis K. Argyros","doi":"10.3390/sym16091179","DOIUrl":"https://doi.org/10.3390/sym16091179","url":null,"abstract":"Many problems in scientific research are reduced to a nonlinear equation by mathematical means of modeling. The solutions of such equations are found mostly iteratively. Then, the convergence order is routinely shown using Taylor formulas, which in turn make sufficient assumptions about derivatives which are not present in the iterative method at hand. This technique restricts the usage of the method which may converge even if these assumptions, which are not also necessary, hold. The utilization of these methods can be extended under less restrictive conditions. This new paper contributes in this direction, since the convergence is established by assumptions restricted exclusively on the functions present on the method. Although the technique is demonstrated on a two-step Traub-type method with usually symmetric parameters and weight functions, due to its generality it can be extended to other methods defined on the real line or more abstract spaces. Numerical experimentation complement and further validate the theory.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ahmet Mehmet Karadeniz, Áron Ballagi, László T. Kóczy
This research introduces an innovative approach for End-to-End steering angle prediction and its control in electric power steering (EPS) systems. The methodology integrates transfer learning-based computer vision techniques for prediction and control with fuzzy signatures-enhanced fuzzy systems. Fuzzy signatures are unique multidimensional data structures that represent data symbolically. This enhancement enables the fuzzy systems to effectively manage the inherent imprecision and uncertainty in various driving scenarios. The ultimate goal of this work is to assess the efficiency and performance of this combined approach by highlighting the pivotal role of steering angle prediction and control in the field of autonomous driving systems. Specifically, within EPS systems, the control of the motor directly influences the vehicle’s path and maneuverability. A significant breakthrough of this study is the successful application of transfer learning-based computer vision techniques to extract respective visual data without the need for large datasets. This represents an advancement in reducing the extensive data collection and computational load typically required. The findings of this research reveal the potential of this approach within EPS systems, with an MSE score of 0.0386 against 0.0476, by outperforming the existing NVIDIA model. This result provides a 22.63% better Mean Squared Error (MSE) score than NVIDIA’s model. The proposed model also showed better performance compared with all other three references found in the literature. Furthermore, we identify potential areas for refinement, such as decreasing model loss and simplifying the complex decision model of fuzzy systems, which can represent the symmetry and asymmetry of human decision-making systems. This study, therefore, contributes significantly to the ongoing evolution of autonomous driving systems.
{"title":"Transfer Learning-Based Steering Angle Prediction and Control with Fuzzy Signatures-Enhanced Fuzzy Systems for Autonomous Vehicles","authors":"Ahmet Mehmet Karadeniz, Áron Ballagi, László T. Kóczy","doi":"10.3390/sym16091180","DOIUrl":"https://doi.org/10.3390/sym16091180","url":null,"abstract":"This research introduces an innovative approach for End-to-End steering angle prediction and its control in electric power steering (EPS) systems. The methodology integrates transfer learning-based computer vision techniques for prediction and control with fuzzy signatures-enhanced fuzzy systems. Fuzzy signatures are unique multidimensional data structures that represent data symbolically. This enhancement enables the fuzzy systems to effectively manage the inherent imprecision and uncertainty in various driving scenarios. The ultimate goal of this work is to assess the efficiency and performance of this combined approach by highlighting the pivotal role of steering angle prediction and control in the field of autonomous driving systems. Specifically, within EPS systems, the control of the motor directly influences the vehicle’s path and maneuverability. A significant breakthrough of this study is the successful application of transfer learning-based computer vision techniques to extract respective visual data without the need for large datasets. This represents an advancement in reducing the extensive data collection and computational load typically required. The findings of this research reveal the potential of this approach within EPS systems, with an MSE score of 0.0386 against 0.0476, by outperforming the existing NVIDIA model. This result provides a 22.63% better Mean Squared Error (MSE) score than NVIDIA’s model. The proposed model also showed better performance compared with all other three references found in the literature. Furthermore, we identify potential areas for refinement, such as decreasing model loss and simplifying the complex decision model of fuzzy systems, which can represent the symmetry and asymmetry of human decision-making systems. This study, therefore, contributes significantly to the ongoing evolution of autonomous driving systems.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the field of statistics, uncertain regression analysis occupies an important position. It can thoroughly analyze data sets contained in complex uncertainties, aiming to quantify and reveal the intricate relationships between variables. It is worth noting that the traditional least squares method only takes into account the reduction in the deviations between predictions and observations, and fails to fully consider the inherent characteristics of the correlation uncertainty distributions under the uncertain regression framework. In light of this, this paper constructs a statistical invariant with symmetric uncertainty distribution based on the observations and the disturbance term. It also proposes the least squares estimation of unknown parameters and disturbance term in the uncertain regression model based on the least squares principle and, combined with the mathematical properties of the normal uncertainty distribution, gives a numerical algorithm for solving specific estimates. Finally, in order to verify the effectiveness of the least squares estimation method proposed in this paper, we also design two numerical examples and an empirical study of forecasting of electrical power output.
{"title":"Estimating Unknown Parameters and Disturbance Term in Uncertain Regression Models by the Principle of Least Squares","authors":"Han Wang, Yang Liu, Haiyan Shi","doi":"10.3390/sym16091182","DOIUrl":"https://doi.org/10.3390/sym16091182","url":null,"abstract":"In the field of statistics, uncertain regression analysis occupies an important position. It can thoroughly analyze data sets contained in complex uncertainties, aiming to quantify and reveal the intricate relationships between variables. It is worth noting that the traditional least squares method only takes into account the reduction in the deviations between predictions and observations, and fails to fully consider the inherent characteristics of the correlation uncertainty distributions under the uncertain regression framework. In light of this, this paper constructs a statistical invariant with symmetric uncertainty distribution based on the observations and the disturbance term. It also proposes the least squares estimation of unknown parameters and disturbance term in the uncertain regression model based on the least squares principle and, combined with the mathematical properties of the normal uncertainty distribution, gives a numerical algorithm for solving specific estimates. Finally, in order to verify the effectiveness of the least squares estimation method proposed in this paper, we also design two numerical examples and an empirical study of forecasting of electrical power output.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The original Choi–Davis–Jensen’s inequality, known for its extensive applications in various scientific and engineering fields, has inspired researchers to pursue its generalizations. In this study, we extend the Choi–Davis–Jensen’s inequality by introducing a nonlinear map instead of a normalized linear map and generalize the concept of operator convex functions to include any continuous function defined within a compact region. Notably, operators can be matrices with structural symmetry, enhancing the scope and applicability of our results. The Stone–Weierstrass theorem and the Kantorovich function play crucial roles in the formulation and proof of these generalized Choi–Davis–Jensen’s inequalities. Furthermore, we demonstrate an application of this generalized inequality in the context of statistical physics.
{"title":"Generalized Choi–Davis–Jensen’s Operator Inequalities and Their Applications","authors":"Shih Yu Chang, Yimin Wei","doi":"10.3390/sym16091176","DOIUrl":"https://doi.org/10.3390/sym16091176","url":null,"abstract":"The original Choi–Davis–Jensen’s inequality, known for its extensive applications in various scientific and engineering fields, has inspired researchers to pursue its generalizations. In this study, we extend the Choi–Davis–Jensen’s inequality by introducing a nonlinear map instead of a normalized linear map and generalize the concept of operator convex functions to include any continuous function defined within a compact region. Notably, operators can be matrices with structural symmetry, enhancing the scope and applicability of our results. The Stone–Weierstrass theorem and the Kantorovich function play crucial roles in the formulation and proof of these generalized Choi–Davis–Jensen’s inequalities. Furthermore, we demonstrate an application of this generalized inequality in the context of statistical physics.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The diagnosis of bearing faults is a crucial aspect of ensuring the optimal functioning of mechanical equipment. However, in practice, the use of small samples and variable operating conditions may result in suboptimal generalization performance, reduced accuracy, and overfitting for these methods. To address this challenge, this study proposes a bearing fault diagnosis method based on a symmetric two-stream convolutional neural network (CNN). The method employs hybrid signal processing techniques to address the issue of limited data. The method employs a symmetric parallel convolutional neural network (CNN) for the analysis of bearing data. Initially, the data are transformed into time–frequency maps through the utilization of the short-time Fourier transform (STFT) and the simultaneous compressed wavelet transform (SCWT). Subsequently, two sets of one-dimensional vectors are generated by reconstructing the high-resolution features of the faulty samples using a symmetric parallel convolutional neural network (CNN). Feature splicing and fusion are then performed to generate bearing fault diagnosis information and assist fault classification. The experimental results demonstrate that the proposed mixed-signal processing method is effective on small-sample datasets, and verify the feasibility and generality of the symmetric parallel CNN-support vector machine (SVM) model for bearing fault diagnosis under small-sample conditions.
{"title":"Research on Small Sample Rolling Bearing Fault Diagnosis Method Based on Mixed Signal Processing Technology","authors":"Peibo Yu, Jianjie Zhang, Baobao Zhang, Jianhui Cao, Yihang Peng","doi":"10.3390/sym16091178","DOIUrl":"https://doi.org/10.3390/sym16091178","url":null,"abstract":"The diagnosis of bearing faults is a crucial aspect of ensuring the optimal functioning of mechanical equipment. However, in practice, the use of small samples and variable operating conditions may result in suboptimal generalization performance, reduced accuracy, and overfitting for these methods. To address this challenge, this study proposes a bearing fault diagnosis method based on a symmetric two-stream convolutional neural network (CNN). The method employs hybrid signal processing techniques to address the issue of limited data. The method employs a symmetric parallel convolutional neural network (CNN) for the analysis of bearing data. Initially, the data are transformed into time–frequency maps through the utilization of the short-time Fourier transform (STFT) and the simultaneous compressed wavelet transform (SCWT). Subsequently, two sets of one-dimensional vectors are generated by reconstructing the high-resolution features of the faulty samples using a symmetric parallel convolutional neural network (CNN). Feature splicing and fusion are then performed to generate bearing fault diagnosis information and assist fault classification. The experimental results demonstrate that the proposed mixed-signal processing method is effective on small-sample datasets, and verify the feasibility and generality of the symmetric parallel CNN-support vector machine (SVM) model for bearing fault diagnosis under small-sample conditions.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sergio Elaskar, Pascal Bruel, Luis Gutiérrez Marcantoni
Many physical processes feature random telegraph signals, e.g., a time signal c(t) that randomly switches between two values over time. The present study focuses on the class of telegraphic processes for which the transition rates are formulated by using fractal-like expressions. By considering various restrictive hypotheses regarding the statistics of the waiting times, the present analysis provides the corresponding expressions of the unconditional and conditional probabilities, the mean waiting times, the mean phase duration, the autocorrelation function and the associated integral time scale, the spectral density, and the mean switching frequency. To assess the relevance of the various hypotheses, synthetically generated signals were constructed and used as references to evaluate the predictive quality of the theoretically derived expressions. The best predictions were obtained by considering that the waiting times probability density functions were Dirac peaks centered on the corresponding mean values.
{"title":"Random Telegraphic Signals with Fractal-like Probability Transition Rates","authors":"Sergio Elaskar, Pascal Bruel, Luis Gutiérrez Marcantoni","doi":"10.3390/sym16091175","DOIUrl":"https://doi.org/10.3390/sym16091175","url":null,"abstract":"Many physical processes feature random telegraph signals, e.g., a time signal c(t) that randomly switches between two values over time. The present study focuses on the class of telegraphic processes for which the transition rates are formulated by using fractal-like expressions. By considering various restrictive hypotheses regarding the statistics of the waiting times, the present analysis provides the corresponding expressions of the unconditional and conditional probabilities, the mean waiting times, the mean phase duration, the autocorrelation function and the associated integral time scale, the spectral density, and the mean switching frequency. To assess the relevance of the various hypotheses, synthetically generated signals were constructed and used as references to evaluate the predictive quality of the theoretically derived expressions. The best predictions were obtained by considering that the waiting times probability density functions were Dirac peaks centered on the corresponding mean values.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article presents the results of research on a new combined process involving multi-cycle wire-drawing and subsequent cryogenic cooling after each deformation stage. For theoretical research, modeling in the Deform software was performed. The analysis of temperature fields and the martensitic component in all models showed that for both considered thicknesses, the most effective option is a low deformation velocity and the conduct of a process without heating. The least effective option is to use an increased thickness of the workpiece at an increased deformation velocity and the conduct of a process without of heating to ambient temperature, which acts as a local cooling of the axial zone of the workpiece with an increase in the workpiece thickness. An analysis of laboratory studies on this combined process revealed that in the absence of intermediate heating of a wire between deformation cycles, 100% martensite is formed in the structure. However, if intermediate heating to 20 °C between deformation cycles is carried out, a gradient distribution of martensite can be obtained. And, since the wire has a circular cross-section, in all cases, martensite is distributed symmetrically about the center of the workpiece.
{"title":"Symmetrical Martensite Distribution in Wire Using Cryogenic Cooling","authors":"Irina Volokitina, Andrey Volokitin, Evgeniy Panin, Bolat Makhmutov","doi":"10.3390/sym16091174","DOIUrl":"https://doi.org/10.3390/sym16091174","url":null,"abstract":"This article presents the results of research on a new combined process involving multi-cycle wire-drawing and subsequent cryogenic cooling after each deformation stage. For theoretical research, modeling in the Deform software was performed. The analysis of temperature fields and the martensitic component in all models showed that for both considered thicknesses, the most effective option is a low deformation velocity and the conduct of a process without heating. The least effective option is to use an increased thickness of the workpiece at an increased deformation velocity and the conduct of a process without of heating to ambient temperature, which acts as a local cooling of the axial zone of the workpiece with an increase in the workpiece thickness. An analysis of laboratory studies on this combined process revealed that in the absence of intermediate heating of a wire between deformation cycles, 100% martensite is formed in the structure. However, if intermediate heating to 20 °C between deformation cycles is carried out, a gradient distribution of martensite can be obtained. And, since the wire has a circular cross-section, in all cases, martensite is distributed symmetrically about the center of the workpiece.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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