With the explosive growth of information resources in the age of big data, mankind has gradually fallen into a serious “information overload” situation. In the face of massive data, collaborative filtering algorithm plays an important role in information filtering and information refinement. However, the recommendation quality and efficiency of collaborative filtering recommendation algorithms are low. The research combines the improved artificial bee colony algorithm with K-means algorithm and applies them to the recommendation system to form a collaborative filtering recommendation algorithm. The experimental results show that the MAE value of the new fitness function is 0.767 on average, which has good separation and compactness in clustering effect. It shows high search accuracy and speed. Compared with the original collaborative filtering algorithm, the average absolute error value of this algorithm is low, and the running time is only 50 s. It improves the recommendation quality and ensures the recommendation efficiency, providing a new research path for the improvement of collaborative filtering recommendation algorithm.
{"title":"Application of Improved K-Means Algorithm in Collaborative Recommendation System","authors":"Hui Jing","doi":"10.1155/2022/2213173","DOIUrl":"https://doi.org/10.1155/2022/2213173","url":null,"abstract":"With the explosive growth of information resources in the age of big data, mankind has gradually fallen into a serious “information overload” situation. In the face of massive data, collaborative filtering algorithm plays an important role in information filtering and information refinement. However, the recommendation quality and efficiency of collaborative filtering recommendation algorithms are low. The research combines the improved artificial bee colony algorithm with K-means algorithm and applies them to the recommendation system to form a collaborative filtering recommendation algorithm. The experimental results show that the MAE value of the new fitness function is 0.767 on average, which has good separation and compactness in clustering effect. It shows high search accuracy and speed. Compared with the original collaborative filtering algorithm, the average absolute error value of this algorithm is low, and the running time is only 50 s. It improves the recommendation quality and ensures the recommendation efficiency, providing a new research path for the improvement of collaborative filtering recommendation algorithm.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"114 1","pages":"2213173:1-2213173:10"},"PeriodicalIF":0.0,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77656712","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}
With the continuous development of voice coil motors, it has also been widely used in today’s sports competitions. For example, the Hawk-Eye system in tennis matches uses voice coil motors to focus on the camera to capture the trajectory of the tennis ball. Therefore, in order to better solve the problem of dynamic parameter uncertainty, external load disturbance, and tracking control of the voice coil motor servo system in motion, this paper proposes for the first time the strategy of using L1 adaptive control algorithm to control the voice coil motor servo system. First, it briefly analyzes the working principle and control method of the voice coil motor, and then constructs the uncertain parameter model according to the mathematical model of the voice coil motor. The closed-loop system of voice coil motor is simulated and analyzed by L1 adaptive controller. The results show that the L1 adaptive control method effectively suppresses the high-frequency interference caused by the voice coil motor in operation, can control the tracking error to gradually converge and so the tracking effect is better, and has strong robustness to the perturbation of system parameters. It can be applied to voice coil motor servo control.
{"title":"Research on a New Control System Based on L1 Adaptive Control Scheme for the Voice Coil Motor","authors":"Huaiguo Jing, Ying Li, Bo Li, Shuo Huang, Ruidian Zhan, Hao Li, Xuexi Zhang","doi":"10.1155/2022/3340331","DOIUrl":"https://doi.org/10.1155/2022/3340331","url":null,"abstract":"With the continuous development of voice coil motors, it has also been widely used in today’s sports competitions. For example, the Hawk-Eye system in tennis matches uses voice coil motors to focus on the camera to capture the trajectory of the tennis ball. Therefore, in order to better solve the problem of dynamic parameter uncertainty, external load disturbance, and tracking control of the voice coil motor servo system in motion, this paper proposes for the first time the strategy of using L1 adaptive control algorithm to control the voice coil motor servo system. First, it briefly analyzes the working principle and control method of the voice coil motor, and then constructs the uncertain parameter model according to the mathematical model of the voice coil motor. The closed-loop system of voice coil motor is simulated and analyzed by L1 adaptive controller. The results show that the L1 adaptive control method effectively suppresses the high-frequency interference caused by the voice coil motor in operation, can control the tracking error to gradually converge and so the tracking effect is better, and has strong robustness to the perturbation of system parameters. It can be applied to voice coil motor servo control.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"22 1","pages":"3340331:1-3340331:12"},"PeriodicalIF":0.0,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90540301","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}
A new method is presented to study the interaction of multiple cracks, especially for the areas near crack tips by using the extended finite element method. In order to track the cracks, a new geometric tracking technique is proposed to track enriched elements and nodes along the crack instead of using the narrow band level set method. This allows to accurately determine enriched elements and nodes and calculate enrichment values. A method is proposed for constructing a multicrack matrix, which involves numbering enriched nodes of multiple cracks and solving the global stiffness matrix. In this approach, the stress fields around multiple cracks can be studied. The interaction integral method is employed to study the crack propagation and its direction by calculating the stress intensify factor. The developed model has been coded in MATLAB environment and validated against analytical solutions. The application of the model in the crack interaction study is demonstrated through a number of examples. The results illustrate the influence of the interaction of multiple cracks as they approach each other.
{"title":"Analysis of Interaction of Multiple Cracks Based on Tip Stress Field Using Extended Finite Element Method","authors":"Yuxiao Wang, A. Javadi, C. Fidelibus","doi":"10.1155/2022/1010174","DOIUrl":"https://doi.org/10.1155/2022/1010174","url":null,"abstract":"A new method is presented to study the interaction of multiple cracks, especially for the areas near crack tips by using the extended finite element method. In order to track the cracks, a new geometric tracking technique is proposed to track enriched elements and nodes along the crack instead of using the narrow band level set method. This allows to accurately determine enriched elements and nodes and calculate enrichment values. A method is proposed for constructing a multicrack matrix, which involves numbering enriched nodes of multiple cracks and solving the global stiffness matrix. In this approach, the stress fields around multiple cracks can be studied. The interaction integral method is employed to study the crack propagation and its direction by calculating the stress intensify factor. The developed model has been coded in MATLAB environment and validated against analytical solutions. The application of the model in the crack interaction study is demonstrated through a number of examples. The results illustrate the influence of the interaction of multiple cracks as they approach each other.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"1 1","pages":"1010174:1-1010174:15"},"PeriodicalIF":0.0,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90910352","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}
With the continuous application and development of big data and algorithm technology, intelligent recommendation algorithms are gradually affecting all aspects of people’s daily life. The impact of smart recommendation algorithm has both advantages and disadvantages; it can facilitate people’s life, but also exists at the same time the invasion of privacy, information cocoon, and other problems. How to optimize intelligent recommendation algorithms to serve the society more safely and efficiently becomes a problem that needs to be solved nowadays. We propose an intelligent recommendation algorithm combining recurrent neural network (RNN) and knowledge graph (KG) and analyze and demonstrate its performance by building models and experiments. The results show that among the five different recommendation models, the intelligent recommendation algorithm model combining RNN and knowledge graph has the highest AUC and ACC values in the Book-Crossing and MovieLens-1M. At the same time, the algorithm’s rating prediction error values are small (less than 2%) in extracting different users’ ratings for different books. In addition, the intelligent recommendation algorithm combining RNN and knowledge graph has the lowest RMSE and MAE values in the comparison of three different recommendation algorithms, indicating that it has better performance and stability, which is important for the improvement of user recommendation effect.
{"title":"Intelligent Recommendation Algorithm Combining RNN and Knowledge Graph","authors":"Fengsheng Zeng, Qin Wang","doi":"10.1155/2022/7323560","DOIUrl":"https://doi.org/10.1155/2022/7323560","url":null,"abstract":"With the continuous application and development of big data and algorithm technology, intelligent recommendation algorithms are gradually affecting all aspects of people’s daily life. The impact of smart recommendation algorithm has both advantages and disadvantages; it can facilitate people’s life, but also exists at the same time the invasion of privacy, information cocoon, and other problems. How to optimize intelligent recommendation algorithms to serve the society more safely and efficiently becomes a problem that needs to be solved nowadays. We propose an intelligent recommendation algorithm combining recurrent neural network (RNN) and knowledge graph (KG) and analyze and demonstrate its performance by building models and experiments. The results show that among the five different recommendation models, the intelligent recommendation algorithm model combining RNN and knowledge graph has the highest AUC and ACC values in the Book-Crossing and MovieLens-1M. At the same time, the algorithm’s rating prediction error values are small (less than 2%) in extracting different users’ ratings for different books. In addition, the intelligent recommendation algorithm combining RNN and knowledge graph has the lowest RMSE and MAE values in the comparison of three different recommendation algorithms, indicating that it has better performance and stability, which is important for the improvement of user recommendation effect.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"28 1","pages":"7323560:1-7323560:11"},"PeriodicalIF":0.0,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84621155","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 continuous monitoring and real-time feedback on the uniformity of the mixture after paving and compaction is important to guide the construction and improve the life of the asphalt pavement. Thus, in this study, the latest digital image technology was used to collect images of asphalt pavement after paving and compaction according to the set parameters. The images collected were preprocessed in steps such as binary grayscale, filtering, histogram, and small particle filtering, which established the method for calculating the construction depth H P of the digital images of pavement. Moreover, a method was proposed to evaluate the uniformity of asphalt pavement using the construction depth coefficient of variation. The coefficients of variation were computed based on 100 images of the dependent project and compared with the actual images. The results indicated that the construction depth coefficient of variation of the digital images obtained by the developed calculation procedure was in agreement with the actual situation and combined the correlation degree of the calculation results. Small areas of 42 are recommended as the division of the asphalt pavement compaction uniformity evaluation method based on construction depth variation, and the use of C v 4 ≥ 8.0 as the evaluation standard for the segregation of asphalt pavement is recommended. The method proposed is a new and rapid test to evaluate and detect the asphalt pavement uniformity.
{"title":"Evaluation of Compaction Uniformity of Asphalt Pavement Based on Construction Depth Variation","authors":"Xiaodong Jia","doi":"10.1155/2022/5732050","DOIUrl":"https://doi.org/10.1155/2022/5732050","url":null,"abstract":"The continuous monitoring and real-time feedback on the uniformity of the mixture after paving and compaction is important to guide the construction and improve the life of the asphalt pavement. Thus, in this study, the latest digital image technology was used to collect images of asphalt pavement after paving and compaction according to the set parameters. The images collected were preprocessed in steps such as binary grayscale, filtering, histogram, and small particle filtering, which established the method for calculating the construction depth \u0000 \u0000 \u0000 \u0000 H\u0000 \u0000 \u0000 P\u0000 \u0000 \u0000 \u0000 of the digital images of pavement. Moreover, a method was proposed to evaluate the uniformity of asphalt pavement using the construction depth coefficient of variation. The coefficients of variation were computed based on 100 images of the dependent project and compared with the actual images. The results indicated that the construction depth coefficient of variation of the digital images obtained by the developed calculation procedure was in agreement with the actual situation and combined the correlation degree of the calculation results. Small areas of 42 are recommended as the division of the asphalt pavement compaction uniformity evaluation method based on construction depth variation, and the use of \u0000 \u0000 \u0000 \u0000 C\u0000 \u0000 \u0000 v\u0000 4\u0000 \u0000 \u0000 ≥\u0000 8.0\u0000 \u0000 as the evaluation standard for the segregation of asphalt pavement is recommended. The method proposed is a new and rapid test to evaluate and detect the asphalt pavement uniformity.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"12 1","pages":"5732050:1-5732050:9"},"PeriodicalIF":0.0,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77738086","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}
Francis Oketch Ochieng, M. Kinyanjui, J. Abonyo, P. R. Kiogora
The formation of solid wax crystals, which interlock and form a gel-like layer on the inner wall of the crude oil pipeline, influences the transportation of waxy crude oil. The deposited layer grows continuously and hardens during the oil transportation, reducing the effective inside diameter of the crude oil pipeline and the flow rate. In extreme cases, the deposited layer may block the crude oil pipeline leading to a loss of production and capital investment. In this paper, wax deposition from multiphase flow in field-scale oil pipeline transport systems has been studied. The novelty of this work is to develop a mathematical model that incorporates water-in-oil emulsions, wax precipitation kinetics, molecular diffusion, and shear dispersion to enable accurate predictions of both the wax deposit growth rate and aging of the deposit. The coupled nonlinear partial differential equations governing the flow are discretized in time by a second-order semi-implicit time discretization scheme based on the Adams-Bashforth and Crank-Nicolson methods, which completely decouples the computation of the governing equations. The resulting temporal schemes are discretized in space by the bivariate spectral collocation method based on Chebyshev-Gauss-Lobatto grid points and simulated in MATLAB software to obtain the profiles of the flow variables. The simulation results are presented in graphical and in tabular forms and discussed. This study found that the deposit thickness is directly proportional to the Reynolds number and inversely proportional to the mass Grashof number, Schmidt number, and Weber number. Deposit aging is rampant during the early stages of wax deposition, after which it stabilizes at a specific value as time elapses. A deposition model to predict the wax deposit thickness and aging is proposed in this study. The findings of this study will help in making informed decisions on the planning of pigging operations, thermal insulation, and other remediation techniques to be applied in controlling wax deposition in field-scale crude oil pipeline systems.
{"title":"Mathematical Modeling of Wax Deposition in Field-Scale Crude Oil Pipeline Systems","authors":"Francis Oketch Ochieng, M. Kinyanjui, J. Abonyo, P. R. Kiogora","doi":"10.1155/2022/2845221","DOIUrl":"https://doi.org/10.1155/2022/2845221","url":null,"abstract":"The formation of solid wax crystals, which interlock and form a gel-like layer on the inner wall of the crude oil pipeline, influences the transportation of waxy crude oil. The deposited layer grows continuously and hardens during the oil transportation, reducing the effective inside diameter of the crude oil pipeline and the flow rate. In extreme cases, the deposited layer may block the crude oil pipeline leading to a loss of production and capital investment. In this paper, wax deposition from multiphase flow in field-scale oil pipeline transport systems has been studied. The novelty of this work is to develop a mathematical model that incorporates water-in-oil emulsions, wax precipitation kinetics, molecular diffusion, and shear dispersion to enable accurate predictions of both the wax deposit growth rate and aging of the deposit. The coupled nonlinear partial differential equations governing the flow are discretized in time by a second-order semi-implicit time discretization scheme based on the Adams-Bashforth and Crank-Nicolson methods, which completely decouples the computation of the governing equations. The resulting temporal schemes are discretized in space by the bivariate spectral collocation method based on Chebyshev-Gauss-Lobatto grid points and simulated in MATLAB software to obtain the profiles of the flow variables. The simulation results are presented in graphical and in tabular forms and discussed. This study found that the deposit thickness is directly proportional to the Reynolds number and inversely proportional to the mass Grashof number, Schmidt number, and Weber number. Deposit aging is rampant during the early stages of wax deposition, after which it stabilizes at a specific value as time elapses. A deposition model to predict the wax deposit thickness and aging is proposed in this study. The findings of this study will help in making informed decisions on the planning of pigging operations, thermal insulation, and other remediation techniques to be applied in controlling wax deposition in field-scale crude oil pipeline systems.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"69 1","pages":"2845221:1-2845221:13"},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85869283","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 authors proposed a nonlinear deterministic model and stability analysis for the transmission dynamics of chewing khat. The model’s solution is proved to be positive and bounded, and the basic reproduction number ( R 0 ) is calculated using the next-generation matrix method. Following that, the authors have looked at the local and global stability of the model’s khat-free and endemic equilibrium points. When R 0 < 1 , the chewing khat-free equilibrium point is locally and globally asymptotically stable, whereas when R 0 > 1 , the endemic equilibrium point is locally and globally asymptotically stable. The simulation results demonstrate the analytical results.
{"title":"Chewing Khat Transmission Dynamics: A Mathematical Model and Stability Analysis","authors":"Abayneh Kebede Fantaye, Z. Birhanu","doi":"10.1155/2022/3844885","DOIUrl":"https://doi.org/10.1155/2022/3844885","url":null,"abstract":"In this study, the authors proposed a nonlinear deterministic model and stability analysis for the transmission dynamics of chewing khat. The model’s solution is proved to be positive and bounded, and the basic reproduction number (\u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 \u0000 ) is calculated using the next-generation matrix method. Following that, the authors have looked at the local and global stability of the model’s khat-free and endemic equilibrium points. When \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 <\u0000 1\u0000 \u0000 , the chewing khat-free equilibrium point is locally and globally asymptotically stable, whereas when \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 >\u0000 1\u0000 \u0000 , the endemic equilibrium point is locally and globally asymptotically stable. The simulation results demonstrate the analytical results.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"83 1","pages":"3844885:1-3844885:11"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83761514","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 present study, a hydromagnetic non-Newtonian (dilatant) fluid flow in a convergent conduit, in the presence of a variable transverse magnetic field, has been investigated. The governing nonlinear partial differential equations are reduced to system of ordinary differential equations. These equations are solved numerically by the collocation method and implemented in MATLAB. The study determines the flow profiles and the impact of the flow parameters on the flow variables. Joule heating, variable viscosity, viscous dissipation, skin friction, the rate of heat transfer, and the induced magnetic field are taken into account. The obtained results are presented graphically and the impact of varying flow parameters on the skin friction coefficient and the Nusselt number is presented in tabular form. These results indicate that an increase in the Reynolds number, Eckert’s number, and the Joule heating parameter increases the fluid’s velocity, while an increase in the Hartmann number and the unsteadiness parameter decreases the convective heat transfer and the fluid’s velocity. Further, the skin friction coefficient decreases with increase in the Reynolds number, the Hartmann number, and the Joule heating parameter. Therefore, a less viscous fluid is appropriate to facilitate the fluid’s motion, but the presence of high magnetic field reduces the fluid’s motion.
{"title":"Hydromagnetic Non-Newtonian Fluid Flow in a Convergent Conduit","authors":"Njue Caroline Wawira, M. Kinyanjui, K. Giterere","doi":"10.1155/2022/8131528","DOIUrl":"https://doi.org/10.1155/2022/8131528","url":null,"abstract":"In the present study, a hydromagnetic non-Newtonian (dilatant) fluid flow in a convergent conduit, in the presence of a variable transverse magnetic field, has been investigated. The governing nonlinear partial differential equations are reduced to system of ordinary differential equations. These equations are solved numerically by the collocation method and implemented in MATLAB. The study determines the flow profiles and the impact of the flow parameters on the flow variables. Joule heating, variable viscosity, viscous dissipation, skin friction, the rate of heat transfer, and the induced magnetic field are taken into account. The obtained results are presented graphically and the impact of varying flow parameters on the skin friction coefficient and the Nusselt number is presented in tabular form. These results indicate that an increase in the Reynolds number, Eckert’s number, and the Joule heating parameter increases the fluid’s velocity, while an increase in the Hartmann number and the unsteadiness parameter decreases the convective heat transfer and the fluid’s velocity. Further, the skin friction coefficient decreases with increase in the Reynolds number, the Hartmann number, and the Joule heating parameter. Therefore, a less viscous fluid is appropriate to facilitate the fluid’s motion, but the presence of high magnetic field reduces the fluid’s motion.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"32 1","pages":"8131528:1-8131528:13"},"PeriodicalIF":0.0,"publicationDate":"2022-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79981823","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 manuscript, we have established relation-theoretic version of some common fixed point results in metric space for generalized β − ϕ − Z -contractive pair of mappings furnished with an arbitrary binary relation R . Recently, the concept of binary relation is well known leading trend in fixed point theory. Our results extend and unify several fixed point theorems present in the literature. An illustrative example is given to support our main theorem. Finally, we exploit our main result for proving existence and uniqueness results to established the solution of a fractional differential equation of Caputo type.
{"title":"Common Fixed Point Theorems for Generalized Contractive Pair of Mappings in a Metric Space and Their Application to Fractional Calculus","authors":"Priyanka Goel., M. Kumar, D. Singh, Kamal Kumar","doi":"10.1155/2022/6760602","DOIUrl":"https://doi.org/10.1155/2022/6760602","url":null,"abstract":"In this manuscript, we have established relation-theoretic version of some common fixed point results in metric space for generalized \u0000 \u0000 β\u0000 −\u0000 ϕ\u0000 −\u0000 Z\u0000 \u0000 -contractive pair of mappings furnished with an arbitrary binary relation \u0000 \u0000 R\u0000 \u0000 . Recently, the concept of binary relation is well known leading trend in fixed point theory. Our results extend and unify several fixed point theorems present in the literature. An illustrative example is given to support our main theorem. Finally, we exploit our main result for proving existence and uniqueness results to established the solution of a fractional differential equation of Caputo type.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"4 1","pages":"6760602:1-6760602:12"},"PeriodicalIF":0.0,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78906564","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}
While the process of intelligent industrial production is accelerating, the application scope of welding robots is also expanding. For the purpose of reducing the work efficiency and time consumption of the welding robot, the ACO is used for the shortest distance and the GA is used for the shortest time fixed-point path trajectory optimization. The application of parameter optimization and random disturbance factor in the ACO increases the global search performance of the algorithm. In the shortest time trajectory optimization, the B-spline curve interpolation method and the GA are combined to carry out the segmental optimization processing. Simulation experiments show that the optimization strategy of ACO can increase the iterative calculation efficiency and path optimization performance of the algorithm. At the same time, the robot with optimized genetic algorithm has smaller fluctuations in joint angle and angular velocity in the simulated welding task, and the optimization algorithm takes 17.6 s less than the traditional particle swarm algorithm and 11 s less than the single A ∗ algorithm. The experiments confirmed the performance of the ACO-GA for the path optimization of the welding robot, and research can provide a scientific path optimization reference for the welding task of the industrial production line.
{"title":"Path Optimization of Welding Robot Based on Ant Colony and Genetic Algorithm","authors":"Yan Gao, Yiwan Zhang","doi":"10.1155/2022/3608899","DOIUrl":"https://doi.org/10.1155/2022/3608899","url":null,"abstract":"While the process of intelligent industrial production is accelerating, the application scope of welding robots is also expanding. For the purpose of reducing the work efficiency and time consumption of the welding robot, the ACO is used for the shortest distance and the GA is used for the shortest time fixed-point path trajectory optimization. The application of parameter optimization and random disturbance factor in the ACO increases the global search performance of the algorithm. In the shortest time trajectory optimization, the B-spline curve interpolation method and the GA are combined to carry out the segmental optimization processing. Simulation experiments show that the optimization strategy of ACO can increase the iterative calculation efficiency and path optimization performance of the algorithm. At the same time, the robot with optimized genetic algorithm has smaller fluctuations in joint angle and angular velocity in the simulated welding task, and the optimization algorithm takes 17.6 s less than the traditional particle swarm algorithm and 11 s less than the single \u0000 \u0000 \u0000 \u0000 A\u0000 \u0000 \u0000 ∗\u0000 \u0000 \u0000 \u0000 algorithm. The experiments confirmed the performance of the ACO-GA for the path optimization of the welding robot, and research can provide a scientific path optimization reference for the welding task of the industrial production line.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"1 1","pages":"3608899:1-3608899:11"},"PeriodicalIF":0.0,"publicationDate":"2022-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83335683","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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