In this study,a dynamic model for an inverted pendulum system(IPS)attached to a car is created,and two different control methods are applied to control the system.The designed control algorithms aim to stabilize the p...In this study,a dynamic model for an inverted pendulum system(IPS)attached to a car is created,and two different control methods are applied to control the system.The designed control algorithms aim to stabilize the pendulum arms in the upright position and the car to reach the equilibrium position.Grey Wolf Optimization-based Linear Quadratic Regulator(GWO-LQR)and GWO-based Fuzzy LQR(FLQR)control algorithms are used in the control process.To improve the performance of the LQR and FLQR methods,the optimum values of the coefficients corresponding to the foot points of the membership functions are determined by the GWO algorithm.Both a graphic and a numerical analysis of the outcomes are provided.In the comparative analysis,it is observed that the GWO-based FLQR method reduces the settling time by 22.58% and the maximum peak value by 18.2% when evaluated in terms of the angular response of the pendulum arm.Furthermore,this approach outperformed comparable research in the literature with a settling time of 2.4 s.These findings demonstrate that the suggested GWO-based FLQR controlmethod outperforms existing literature in terms of the time required for the pendulum arm to reach equilibrium.展开更多
The main purpose of this paper is to use the Chelyshkov-collocation spectral method for solving nonlinear Quadratic integral equations of Volterra type.The method is based on the approximate solutions in terms of Chel...The main purpose of this paper is to use the Chelyshkov-collocation spectral method for solving nonlinear Quadratic integral equations of Volterra type.The method is based on the approximate solutions in terms of Chelyshkov polynomials with unknown coefficients.The Chelyshkov polynomials and their properties are employed to derive the operational matrices of integral and product.The application of these operational matrices for solving the mentioned problem is explained.The error analysis of the proposed method is investigated.Finally,some numerical examples are provided to demonstrate the efficiency of the method.展开更多
The cross-modal person re-identification task aims to match visible and infrared images of the same individual.The main challenges in this field arise from significant modality differences between individuals and the ...The cross-modal person re-identification task aims to match visible and infrared images of the same individual.The main challenges in this field arise from significant modality differences between individuals and the lack of high-quality cross-modal correspondence methods.Existing approaches often attempt to establish modality correspondence by extracting shared features across different modalities.However,these methods tend to focus on local information extraction and fail to fully leverage the global identity information in the cross-modal features,resulting in limited correspondence accuracy and suboptimal matching performance.To address this issue,we propose a quadratic graph matching method designed to overcome the challenges posed by modality differences through precise cross-modal relationship alignment.This method transforms the cross-modal correspondence problem into a graph matching task and minimizes the matching cost using a center search mechanism.Building on this approach,we further design a block reasoning module to uncover latent relationships between person identities and optimize the modality correspondence results.The block strategy not only improves the efficiency of updating gallery images but also enhances matching accuracy while reducing computational load.Experimental results demonstrate that our proposed method outperforms the state-of-the-art methods on the SYSU-MM01,RegDB,and RGBNT201 datasets,achieving excellent matching accuracy and robustness,thereby validating its effectiveness in cross-modal person re-identification.展开更多
The work comparing the Yamada-Ota and Xue models for nanoparticle flow across a stretching surface has benefits in nanotechnology,medicinal treatments,environmental engineering,renewable energy,and heat exchangers.Mos...The work comparing the Yamada-Ota and Xue models for nanoparticle flow across a stretching surface has benefits in nanotechnology,medicinal treatments,environmental engineering,renewable energy,and heat exchangers.Most published nanofluid flow models assumed constant thermal conductivity and viscosity.With such great physiognomies in mind,the novelty of this work focuses on comparing the performance of the nanofluid models,Xue,and Yamada-Ota models on a stretched sheet with variable thickness under the influence of a magnetic field and quadratic thermal radiation.The altered boundary layer equations for momentum and temperature,subject to adequate boundary conditions,are numerically solved using an optimized,efficient,and extensive bvp-4c approach.The effects of non-dimensional constraints such as magnetic field,power index of velocity,wall thickness parameter,and quadratic radiation parameter on momentum and temperature profile in the boundary layer area are analyzed thoroughly and outcomes were illustrated graphically.Additionally,the consequences of certain distinctive parameters over engineering factors are also examined and results were presented in tabular form.From the outcomes,it is seen that fluid velocity slows down in the presence of a magnetic field but the opposite nature is observed in the case of temperature profile.With a higher index of velocity,the velocity profile decreases and the temperature field elevates.It has been found that the presence of quadratic convection improves the temperature field.The outcomes of the two models are compared.The Yamada-Ota model performed far better than the Xue model in the heat transfer analysis.展开更多
The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the ...The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.展开更多
This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis...This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.展开更多
This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises,multiple missing measurements as well as the dynamic event-triggered transmission scheme.The...This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises,multiple missing measurements as well as the dynamic event-triggered transmission scheme.The multiple missing measurements are characterized through random variables that obey some given probability distributions,and thresholds of the dynamic event-triggered scheme can be adjusted dynamically via an auxiliary variable.Our attention is concentrated on designing a dynamic event-triggered quadratic nonfragile filter in the well-known minimum-variance sense.To this end,the original system is first augmented by stacking its state/measurement vectors together with second-order Kronecker powers,thus the original design issue is reformulated as that of the augmented system.Subsequently,we analyze statistical properties of augmented noises as well as high-order moments of certain random parameters.With the aid of two well-defined matrix difference equations,we not only obtain upper bounds on filtering error covariances,but also minimize those bounds via carefully designing gain parameters.Finally,an example is presented to explain the effectiveness of this newly established quadratic filtering algorithm.展开更多
The third-harmonic generation(THG)coefficient for a spherical quantum dot system with inversely quadratic Hellmann plus inversely quadratic potential is investigated theoretically,considering the regulation of quantum...The third-harmonic generation(THG)coefficient for a spherical quantum dot system with inversely quadratic Hellmann plus inversely quadratic potential is investigated theoretically,considering the regulation of quantum size,confinement potential depth and the external environment.The numerical simulation results indicate that the THG coefficient can reach the order of 10~(-12)m~2V~(-2),which strongly relies on the tunable factor,with its resonant peak experiencing a redshift or blueshift.Interestingly,the effect of temperature on the THG coefficient in terms of peak location and size is consistent with the quantum dot radius but contrasts with the hydrostatic pressure.Thus,it is crucial to focus on the influence of internal and external parameters on nonlinear optical effects,and to implement the theory in practical experiments and the manufacture of optoelectronic devices.展开更多
Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equa...Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.展开更多
This paper discusses the data-driven design of linear quadratic regulators,i.e.,to obtain the regulators directly from experimental data without using the models of plants.In particular,we aim to improve an existing d...This paper discusses the data-driven design of linear quadratic regulators,i.e.,to obtain the regulators directly from experimental data without using the models of plants.In particular,we aim to improve an existing design method by reducing the amount of the required experimental data.Reducing the data amount leads to the cost reduction of experiments and computation for the data-driven design.We present a simplified version of the existing method,where parameters yielding the gain of the regulator are estimated from only part of the data required in the existing method.We then show that the data amount required in the presented method is less than half of that in the existing method under certain conditions.In addition,assuming the presence of measurement noise,we analyze the relations between the expectations and variances of the estimated parameters and the noise.As a result,it is shown that using a larger amount of the experimental data might mitigate the effects of the noise on the estimated parameters.These results are verified by numerical examples.展开更多
Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of...Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.展开更多
This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By i...This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.展开更多
Energy is the driving force behind all economic and industrial development. Africa is the least advanced continent in terms of energy consumption and production. Paradoxically, it is the sunniest continent, which is w...Energy is the driving force behind all economic and industrial development. Africa is the least advanced continent in terms of energy consumption and production. Paradoxically, it is the sunniest continent, which is why our objective is to exploit this energy potential in order to produce and use sufficient energy. To achieve this, we are carrying out a series of studies aimed at developing a device capable of converting solar photovoltaic energy into electrical energy. This device is a two-stage converter, the first of which is a quadratic boost and the second a full bridge. Initially, this paper is devoted to studying the performance of the quadratic boost.展开更多
The quadratic boost is studied under its real model. The equations, of the continuous conduction mode, descriptive of this model are established. From these equations, the expressions of the voltage gain and the effic...The quadratic boost is studied under its real model. The equations, of the continuous conduction mode, descriptive of this model are established. From these equations, the expressions of the voltage gain and the efficiency are extracted. These two quantities are plotted as a function of the duty cycle in order to appreciate them in different operating points of the transistor. The values of the different components have also been extracted for the fabrication of a prototype of the converter. Thanks to a set of experimental measurements at the input as well as at the output of the prototype converter, the voltage gain and the efficiency could also be observed. These were also plotted for different loads to observe converter behavior. The theoretical curves were compared with the experimental curves which allowed to validate the proposed mathematical models on a large range of duty cycles.展开更多
The development of defect prediction plays a significant role in improving software quality. Such predictions are used to identify defective modules before the testing and to minimize the time and cost. The software w...The development of defect prediction plays a significant role in improving software quality. Such predictions are used to identify defective modules before the testing and to minimize the time and cost. The software with defects negatively impacts operational costs and finally affects customer satisfaction. Numerous approaches exist to predict software defects. However, the timely and accurate software bugs are the major challenging issues. To improve the timely and accurate software defect prediction, a novel technique called Nonparametric Statistical feature scaled QuAdratic regressive convolution Deep nEural Network (SQADEN) is introduced. The proposed SQADEN technique mainly includes two major processes namely metric or feature selection and classification. First, the SQADEN uses the nonparametric statistical Torgerson–Gower scaling technique for identifying the relevant software metrics by measuring the similarity using the dice coefficient. The feature selection process is used to minimize the time complexity of software fault prediction. With the selected metrics, software fault perdition with the help of the Quadratic Censored regressive convolution deep neural network-based classification. The deep learning classifier analyzes the training and testing samples using the contingency correlation coefficient. The softstep activation function is used to provide the final fault prediction results. To minimize the error, the Nelder–Mead method is applied to solve non-linear least-squares problems. Finally, accurate classification results with a minimum error are obtained at the output layer. Experimental evaluation is carried out with different quantitative metrics such as accuracy, precision, recall, F-measure, and time complexity. The analyzed results demonstrate the superior performance of our proposed SQADEN technique with maximum accuracy, sensitivity and specificity by 3%, 3%, 2% and 3% and minimum time and space by 13% and 15% when compared with the two state-of-the-art methods.展开更多
In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality o...In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.展开更多
In this paper, an EOQ inventory model is developed for deteriorating items with variable rates of deterioration and conditions of grace periods when demand is a quadratic function of time. The deterioration rate consi...In this paper, an EOQ inventory model is developed for deteriorating items with variable rates of deterioration and conditions of grace periods when demand is a quadratic function of time. The deterioration rate considered here is a special type of Weibull distribution deterioration rate, i.e., a one-parameter Weibull distribution deterioration rate and it increases with respect to time. The quadratic demand precisely depicts of the demand of seasonal items, fashion apparels, cosmetics, and newly launched essential commodities like android mobiles, laptops, automobiles etc., coming to the market. The model is divided into three policies according to the occurrence of the grace periods. Shortages, backlogging and complete backlogging cases are not allowed to occur in the model. The proposed model is well-explained with the help of a simple solution procedure. The three numerical examples are taken to illustrate the effectiveness of the EOQ inventory model along with sensitivity analysis.展开更多
This study investigates the efficacy of the Mathematics Independent Learning Activity Practice and Play Unite Scheme(MILAPlus)as an instructional strategy to improve the proficiency levels of Grade 9 students in quadr...This study investigates the efficacy of the Mathematics Independent Learning Activity Practice and Play Unite Scheme(MILAPlus)as an instructional strategy to improve the proficiency levels of Grade 9 students in quadratic equations and functions through a study carried out at Quezon National High School.The research involved 116 Grade 9 students and utilized a quantitative approach,incorporating both pre-assessment and post-assessment measures.The research utilizes a quasi-experimental design,examining the academic performance of students before and after the introduction of MILAPlus.The pre-assessment establishes a baseline,and the subsequent post-assessment measures the impact of the instructional strategy.Statistical analyses,including t-tests,assess the significance of differences in mean scores and mean percentage scores,providing quantitative insights into the effectiveness of MILAPlus.Findings from the study revealed a statistically significant improvement in both mean scores and mean percentage scores after the utilization of MILAPlus,indicating enhanced proficiency in quadratic equations and functions.The Mean Proficiency Scores(MPS)also showed a substantial increase,demonstrating a marked improvement in overall proficiency levels among Grade 9 students.In light of the results,recommendations were given including the continued utilization of MILAPlus as an instructional strategy and aligning its development with prescribed learning competencies.Emphasizing the consistent adherence to policies and guidelines for MILAPlus implementation is suggested for sustaining positive effects on students’long-term performance in mathematics.This research contributes valuable insights into the practical application and effectiveness of MILAPlus within the context of Grade 9 mathematics education at Quezon National High School.展开更多
Drought risk assessment plays a crucial role in effective drought management.However,it is often challenging due to the intricate relationships among various indicators and the lack of practical guidance.This study pr...Drought risk assessment plays a crucial role in effective drought management.However,it is often challenging due to the intricate relationships among various indicators and the lack of practical guidance.This study presents a drought risk assessment model developed using the Semi-partial Quadratic Subtraction Set Pair Potential(SQSSPP)method,which is derived from the theory of set pair analysis.The indicator system comprises 21 indicators divided into four subsystems.The SQSSPP method utilizes uncertainty information in the overall development trend of regional drought risk states by extracting connection numbers from the Sub-traction Set Pair Potential(SSPP),improving the reliability of evaluation results.The SQSSPP method is validated through a case study of Suzhou City,China,from 2007 to 2017.Three grades are used to evaluate comprehensive drought risk.The result shows an overall decreasing trend over time,with a level III risk in 2010 and consistently at level II from 2011 to 2017.Indicators in the hazard and resilience subsystems are the primary factors influencing drought risk in the Suzhou City.Specific indicators requiring emphasis for improvement are identified,including arable land rate,agricultural population ratio,reservoir regulation rate,current water supply capacity,and irrigation index.The SQSSPP method not only provides targeted drought risk assessment but also provides valuable guidance for future water resource management.While the study focuses on Suzhou City,the proposed approach is applicable to broader-scale risk management evaluations and practices.展开更多
文摘In this study,a dynamic model for an inverted pendulum system(IPS)attached to a car is created,and two different control methods are applied to control the system.The designed control algorithms aim to stabilize the pendulum arms in the upright position and the car to reach the equilibrium position.Grey Wolf Optimization-based Linear Quadratic Regulator(GWO-LQR)and GWO-based Fuzzy LQR(FLQR)control algorithms are used in the control process.To improve the performance of the LQR and FLQR methods,the optimum values of the coefficients corresponding to the foot points of the membership functions are determined by the GWO algorithm.Both a graphic and a numerical analysis of the outcomes are provided.In the comparative analysis,it is observed that the GWO-based FLQR method reduces the settling time by 22.58% and the maximum peak value by 18.2% when evaluated in terms of the angular response of the pendulum arm.Furthermore,this approach outperformed comparable research in the literature with a settling time of 2.4 s.These findings demonstrate that the suggested GWO-based FLQR controlmethod outperforms existing literature in terms of the time required for the pendulum arm to reach equilibrium.
文摘The main purpose of this paper is to use the Chelyshkov-collocation spectral method for solving nonlinear Quadratic integral equations of Volterra type.The method is based on the approximate solutions in terms of Chelyshkov polynomials with unknown coefficients.The Chelyshkov polynomials and their properties are employed to derive the operational matrices of integral and product.The application of these operational matrices for solving the mentioned problem is explained.The error analysis of the proposed method is investigated.Finally,some numerical examples are provided to demonstrate the efficiency of the method.
文摘The cross-modal person re-identification task aims to match visible and infrared images of the same individual.The main challenges in this field arise from significant modality differences between individuals and the lack of high-quality cross-modal correspondence methods.Existing approaches often attempt to establish modality correspondence by extracting shared features across different modalities.However,these methods tend to focus on local information extraction and fail to fully leverage the global identity information in the cross-modal features,resulting in limited correspondence accuracy and suboptimal matching performance.To address this issue,we propose a quadratic graph matching method designed to overcome the challenges posed by modality differences through precise cross-modal relationship alignment.This method transforms the cross-modal correspondence problem into a graph matching task and minimizes the matching cost using a center search mechanism.Building on this approach,we further design a block reasoning module to uncover latent relationships between person identities and optimize the modality correspondence results.The block strategy not only improves the efficiency of updating gallery images but also enhances matching accuracy while reducing computational load.Experimental results demonstrate that our proposed method outperforms the state-of-the-art methods on the SYSU-MM01,RegDB,and RGBNT201 datasets,achieving excellent matching accuracy and robustness,thereby validating its effectiveness in cross-modal person re-identification.
基金supported by the National Research Foundation,Korea(Grant No.NRF2022-R1A2C2002799)support provided by the German Jordanian University,Amman,Jordan,is greatly acknowledged by the authors.Ulavathi Shettar Mahabaleshwar wishes to thank Sang Woo Joo,School of Mechanical Engineering,Yeungnam University,Gyeongsan,Korea,for his hospitality.
文摘The work comparing the Yamada-Ota and Xue models for nanoparticle flow across a stretching surface has benefits in nanotechnology,medicinal treatments,environmental engineering,renewable energy,and heat exchangers.Most published nanofluid flow models assumed constant thermal conductivity and viscosity.With such great physiognomies in mind,the novelty of this work focuses on comparing the performance of the nanofluid models,Xue,and Yamada-Ota models on a stretched sheet with variable thickness under the influence of a magnetic field and quadratic thermal radiation.The altered boundary layer equations for momentum and temperature,subject to adequate boundary conditions,are numerically solved using an optimized,efficient,and extensive bvp-4c approach.The effects of non-dimensional constraints such as magnetic field,power index of velocity,wall thickness parameter,and quadratic radiation parameter on momentum and temperature profile in the boundary layer area are analyzed thoroughly and outcomes were illustrated graphically.Additionally,the consequences of certain distinctive parameters over engineering factors are also examined and results were presented in tabular form.From the outcomes,it is seen that fluid velocity slows down in the presence of a magnetic field but the opposite nature is observed in the case of temperature profile.With a higher index of velocity,the velocity profile decreases and the temperature field elevates.It has been found that the presence of quadratic convection improves the temperature field.The outcomes of the two models are compared.The Yamada-Ota model performed far better than the Xue model in the heat transfer analysis.
基金supported by the National Natural Science Foundation of China under Grant No.12072090.
文摘The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.
文摘This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.
基金supported in part by the National Natural Science Foundation of China(61933007,U21A2019,U22A2044,61973102,62073180)the Natural Science Foundation of Shandong Province of China(ZR2021MF088)+1 种基金the Hainan Province Science and Technology Special Fund of China(ZDYF2022SHFZ105)the Royal Society of the UK,and the Alexander vonHumboldt Foundation of Germany。
文摘This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises,multiple missing measurements as well as the dynamic event-triggered transmission scheme.The multiple missing measurements are characterized through random variables that obey some given probability distributions,and thresholds of the dynamic event-triggered scheme can be adjusted dynamically via an auxiliary variable.Our attention is concentrated on designing a dynamic event-triggered quadratic nonfragile filter in the well-known minimum-variance sense.To this end,the original system is first augmented by stacking its state/measurement vectors together with second-order Kronecker powers,thus the original design issue is reformulated as that of the augmented system.Subsequently,we analyze statistical properties of augmented noises as well as high-order moments of certain random parameters.With the aid of two well-defined matrix difference equations,we not only obtain upper bounds on filtering error covariances,but also minimize those bounds via carefully designing gain parameters.Finally,an example is presented to explain the effectiveness of this newly established quadratic filtering algorithm.
基金National Natural Science Foundation of China(Grant Nos.11674312,52174161,51702003,12174161 and 61775087)Anhui University of Science and Technology(Grant No.2023CX2141)。
文摘The third-harmonic generation(THG)coefficient for a spherical quantum dot system with inversely quadratic Hellmann plus inversely quadratic potential is investigated theoretically,considering the regulation of quantum size,confinement potential depth and the external environment.The numerical simulation results indicate that the THG coefficient can reach the order of 10~(-12)m~2V~(-2),which strongly relies on the tunable factor,with its resonant peak experiencing a redshift or blueshift.Interestingly,the effect of temperature on the THG coefficient in terms of peak location and size is consistent with the quantum dot radius but contrasts with the hydrostatic pressure.Thus,it is crucial to focus on the influence of internal and external parameters on nonlinear optical effects,and to implement the theory in practical experiments and the manufacture of optoelectronic devices.
文摘Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.
文摘This paper discusses the data-driven design of linear quadratic regulators,i.e.,to obtain the regulators directly from experimental data without using the models of plants.In particular,we aim to improve an existing design method by reducing the amount of the required experimental data.Reducing the data amount leads to the cost reduction of experiments and computation for the data-driven design.We present a simplified version of the existing method,where parameters yielding the gain of the regulator are estimated from only part of the data required in the existing method.We then show that the data amount required in the presented method is less than half of that in the existing method under certain conditions.In addition,assuming the presence of measurement noise,we analyze the relations between the expectations and variances of the estimated parameters and the noise.As a result,it is shown that using a larger amount of the experimental data might mitigate the effects of the noise on the estimated parameters.These results are verified by numerical examples.
基金Supported by the National Natural Science Foundation of China(12001395)the special fund for Science and Technology Innovation Teams of Shanxi Province(202204051002018)+1 种基金Research Project Supported by Shanxi Scholarship Council of China(2022-169)Graduate Education Innovation Project of Taiyuan Normal University(SYYJSYC-2314)。
文摘Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.
基金the National Natural Science Foundation of China(62273058,U22A2045)the Key Science and Technology Projects of Jilin Province(20200401075GX)the Youth Science and Technology Innovation and Entrepreneurship Outstanding Talents Project of Jilin Province(20230508043RC)。
文摘This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.
文摘Energy is the driving force behind all economic and industrial development. Africa is the least advanced continent in terms of energy consumption and production. Paradoxically, it is the sunniest continent, which is why our objective is to exploit this energy potential in order to produce and use sufficient energy. To achieve this, we are carrying out a series of studies aimed at developing a device capable of converting solar photovoltaic energy into electrical energy. This device is a two-stage converter, the first of which is a quadratic boost and the second a full bridge. Initially, this paper is devoted to studying the performance of the quadratic boost.
文摘The quadratic boost is studied under its real model. The equations, of the continuous conduction mode, descriptive of this model are established. From these equations, the expressions of the voltage gain and the efficiency are extracted. These two quantities are plotted as a function of the duty cycle in order to appreciate them in different operating points of the transistor. The values of the different components have also been extracted for the fabrication of a prototype of the converter. Thanks to a set of experimental measurements at the input as well as at the output of the prototype converter, the voltage gain and the efficiency could also be observed. These were also plotted for different loads to observe converter behavior. The theoretical curves were compared with the experimental curves which allowed to validate the proposed mathematical models on a large range of duty cycles.
文摘The development of defect prediction plays a significant role in improving software quality. Such predictions are used to identify defective modules before the testing and to minimize the time and cost. The software with defects negatively impacts operational costs and finally affects customer satisfaction. Numerous approaches exist to predict software defects. However, the timely and accurate software bugs are the major challenging issues. To improve the timely and accurate software defect prediction, a novel technique called Nonparametric Statistical feature scaled QuAdratic regressive convolution Deep nEural Network (SQADEN) is introduced. The proposed SQADEN technique mainly includes two major processes namely metric or feature selection and classification. First, the SQADEN uses the nonparametric statistical Torgerson–Gower scaling technique for identifying the relevant software metrics by measuring the similarity using the dice coefficient. The feature selection process is used to minimize the time complexity of software fault prediction. With the selected metrics, software fault perdition with the help of the Quadratic Censored regressive convolution deep neural network-based classification. The deep learning classifier analyzes the training and testing samples using the contingency correlation coefficient. The softstep activation function is used to provide the final fault prediction results. To minimize the error, the Nelder–Mead method is applied to solve non-linear least-squares problems. Finally, accurate classification results with a minimum error are obtained at the output layer. Experimental evaluation is carried out with different quantitative metrics such as accuracy, precision, recall, F-measure, and time complexity. The analyzed results demonstrate the superior performance of our proposed SQADEN technique with maximum accuracy, sensitivity and specificity by 3%, 3%, 2% and 3% and minimum time and space by 13% and 15% when compared with the two state-of-the-art methods.
文摘In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.
文摘In this paper, an EOQ inventory model is developed for deteriorating items with variable rates of deterioration and conditions of grace periods when demand is a quadratic function of time. The deterioration rate considered here is a special type of Weibull distribution deterioration rate, i.e., a one-parameter Weibull distribution deterioration rate and it increases with respect to time. The quadratic demand precisely depicts of the demand of seasonal items, fashion apparels, cosmetics, and newly launched essential commodities like android mobiles, laptops, automobiles etc., coming to the market. The model is divided into three policies according to the occurrence of the grace periods. Shortages, backlogging and complete backlogging cases are not allowed to occur in the model. The proposed model is well-explained with the help of a simple solution procedure. The three numerical examples are taken to illustrate the effectiveness of the EOQ inventory model along with sensitivity analysis.
文摘This study investigates the efficacy of the Mathematics Independent Learning Activity Practice and Play Unite Scheme(MILAPlus)as an instructional strategy to improve the proficiency levels of Grade 9 students in quadratic equations and functions through a study carried out at Quezon National High School.The research involved 116 Grade 9 students and utilized a quantitative approach,incorporating both pre-assessment and post-assessment measures.The research utilizes a quasi-experimental design,examining the academic performance of students before and after the introduction of MILAPlus.The pre-assessment establishes a baseline,and the subsequent post-assessment measures the impact of the instructional strategy.Statistical analyses,including t-tests,assess the significance of differences in mean scores and mean percentage scores,providing quantitative insights into the effectiveness of MILAPlus.Findings from the study revealed a statistically significant improvement in both mean scores and mean percentage scores after the utilization of MILAPlus,indicating enhanced proficiency in quadratic equations and functions.The Mean Proficiency Scores(MPS)also showed a substantial increase,demonstrating a marked improvement in overall proficiency levels among Grade 9 students.In light of the results,recommendations were given including the continued utilization of MILAPlus as an instructional strategy and aligning its development with prescribed learning competencies.Emphasizing the consistent adherence to policies and guidelines for MILAPlus implementation is suggested for sustaining positive effects on students’long-term performance in mathematics.This research contributes valuable insights into the practical application and effectiveness of MILAPlus within the context of Grade 9 mathematics education at Quezon National High School.
基金Natural Science Foundation of Anhui Province,Grant/Award Numbers:2308085US13,2208085US03National Natural Science Foundation of China,Grant/Award Number:U2243228+1 种基金the Belt and Road Special Foundation of the National Key Laboratory of Water Disaster Prevention,Grant/Award Number:2022nkms04The Ministry of Education of Humanities and Social Science Project,Grant/Award Number:23YJCZH332。
文摘Drought risk assessment plays a crucial role in effective drought management.However,it is often challenging due to the intricate relationships among various indicators and the lack of practical guidance.This study presents a drought risk assessment model developed using the Semi-partial Quadratic Subtraction Set Pair Potential(SQSSPP)method,which is derived from the theory of set pair analysis.The indicator system comprises 21 indicators divided into four subsystems.The SQSSPP method utilizes uncertainty information in the overall development trend of regional drought risk states by extracting connection numbers from the Sub-traction Set Pair Potential(SSPP),improving the reliability of evaluation results.The SQSSPP method is validated through a case study of Suzhou City,China,from 2007 to 2017.Three grades are used to evaluate comprehensive drought risk.The result shows an overall decreasing trend over time,with a level III risk in 2010 and consistently at level II from 2011 to 2017.Indicators in the hazard and resilience subsystems are the primary factors influencing drought risk in the Suzhou City.Specific indicators requiring emphasis for improvement are identified,including arable land rate,agricultural population ratio,reservoir regulation rate,current water supply capacity,and irrigation index.The SQSSPP method not only provides targeted drought risk assessment but also provides valuable guidance for future water resource management.While the study focuses on Suzhou City,the proposed approach is applicable to broader-scale risk management evaluations and practices.
