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15 December 2022, Volume 39 Issue 6 Previous Issue    Next Issue

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Review on the Virtual Element Method of Eigenvalue Problems MENG Jian, MEI Liquan 2022, 39 (6):  851-861.  doi: 10.3969/j.issn.1005-3085.2022.06.001 Abstract ( 198 )   PDF (348KB) ( 542 )   Save With the introduction of the virtual element method, the numerical methods of eigenvalue problems have made further progress. This paper systematically summarizes the main achievements of the virtual element method for eigenvalue problems and claims the characteristics of various virtual element methods of eigenvalue problems. Based on the existing theory and numerical analysis, the problems which are needed to be solved on the virtual element method of eigenvalue problems are summarized. Related Articles | Metrics

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Study on Storage Layout Optimization of Modern Warehouse Center ZHU Lingyao, ZHOU Li 2022, 39 (6):  862-874.  doi: 10.3969/j.issn.1005-3085.2022.06.002 Abstract ( 165 )   PDF (579KB) ( 180 )   Save The layout of shelves in the storage center is one of the important factors affecting the efficiency of picking operation. In order to study the impact of layout of shelves on the effective storage area, the Fishbone layout is chosen as the research object, an estimation model of the proportion of effective storage area is constructed and verified by simulation. The results show that when the angle of the main picking channel is fixed, the larger the ratio of the picking channel width to the shelf width, the smaller the utilization of the effective storage area, when the ratio of the picking channel width to the shelf width is fixed, the more the angle of the main picking channel approaches 0 degree or 90 degrees, the greater the utilization of the effective storage area. Therefore, the improved storage layout such as the Fishbone layout provides a new way for decision-making in picking operation, and also proves the feasibility of the practical application of the improved storage warehouse layout. Related Articles | Metrics

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Research on Double Compound Poisson-Geometric Processes Insurance Risk Model with Stochastic Portfolios XU Hao, WEI Zhiya, PENG Xuhui 2022, 39 (6):  875-885.  doi: 10.3969/j.issn.1005-3085.2022.06.003 Abstract ( 87 )   PDF (196KB) ( 155 )   Save A double compound Poisson-Geometric processes insurance risk model is investigated, in which the arrivals of premiums and claims are compound Poisson-Geometric processes. Through the martingale method and stopping time technique, we get the Lundberg inequality, adjustment coefficient equation and formula about the ruin probability. Also obtained are the integral differential equations for survival probabilities of infinite intervals and finite intervals, respectively, which can be regarded as indices to measure the payment ability. Related Articles | Metrics

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Fuzzy Adaptive Event-triggered Fault-tolerant Control for a Class of Nonlinear Systems with Unknown Control Directions YAN Yan, WU Libing, ZHAO Nannan, ZHANG Ruiyan 2022, 39 (6):  886-898.  doi: 10.3969/j.issn.1005-3085.2022.06.004 Abstract ( 108 )   PDF (604KB) ( 450 )   Save The problem of fuzzy adaptive event-triggered fault-tolerant control is developed for uncertain nonlinear systems with unknown control directions, unknown nonlinear functions and actuator faults. Firstly, the adaptive event-triggered fault-tolerant controller and the adaptive laws are constructed by combining the backstepping method and theoretical knowledge about fuzzy logic system, which can effectively compensate the influence of actuator faults on the system. Secondly, the Nussbaum function is introduced into the design of the adaptive event-triggered fault-tolerant controller. Finally, the control scheme is designed to ensure that the closed-loop signal is uniformly and ultimately bounded within a given compact set, and the effectiveness of the proposed control scheme is verified through simulation results. Related Articles | Metrics

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Asynchronous Control of Switched Systems with Nonlinear Perturbation: a Mode-dependent Average Dwell Time Approach GAO Juan, LI Tongbin 2022, 39 (6):  899-909.  doi: 10.3969/j.issn.1005-3085.2022.06.005 Abstract ( 85 )   PDF (219KB) ( 150 )   Save This paper studies the asynchronous control problem for a class of switched systems with nonlinear perturbation. Asynchrony means that the switching of the controllers experien-ces a time delay with respect to that of the subsystems. The analytical solution to the state equation of the asynchronously switched systems is utilized to study the dynamics of systems directly without constructing any Lyapunov function. Sufficient conditions that ensure the exponential stability of the closed-loop system under the mode-dependent average dwell time (MDADT) scheme are proposed. MDADT means that each subsystem has its own average dwell time (ADT), which is more general than ADT. Moreover, asynchronously switched controllers are designed in terms of a set of solvable linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method. Related Articles | Metrics

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A Comparison Theorem and the Uncertainty Distribution of Solutions for Fractional Difference Equations with Nonsingular Kernel CHEN Yuting, LI Xiaoyan, WANG Xueqin 2022, 39 (6):  910-924.  doi: 10.3969/j.issn.1005-3085.2022.06.006 Abstract ( 118 )   PDF (185KB) ( 523 )   Save Comparison theorems play an essential role in studying the properties of the fractional equations. Firstly, a comparison theorem for ABR type fractional difference equations is proved. Next, based on the proven comparison theorem, the connections between the solution for an uncertainty fractional difference equation and its $\alpha$-path are established. Then, the uncertainty distribution of solutions for ABR type uncertainty fractional difference equations is also derived. Finally, examples are given to verify the correctness of main results. Related Articles | Metrics

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Existence of Positive Solutions for Boundary Value Problems of Nonlinear Fractional Integro-differential Equations YANG Xiaoying, JIA Mei, LIU Xiping 2022, 39 (6):  925-940.  doi: 10.3969/j.issn.1005-3085.2022.06.007 Abstract ( 118 )   PDF (190KB) ( 145 )   Save The integral boundary value problem for a class of nonlinear fractional integro-differential equations with two fractional derivative terms is studied. Firstly, the original problem is transformed into an equivalent form with only one derivative term. The existence and uniqueness theorems of positive solutions of the original problem are established by defining the upper and lower solutions of the equivalent problem and using the monotone iterative technique. The iterative schemes and error estimates for finding the unique solutions are obtained. Finally, an example is presented to illustrate the effectiveness and potential applications of our main results. Related Articles | Metrics

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Numerical Analysis of BDF2 Modular Grad-div Stabilization Method for the Navier-Stokes/Darcy Equations YANG Cuiping, WANG Jiangshan, JIA Hongen 2022, 39 (6):  941-956.  doi: 10.3969/j.issn.1005-3085.2022.06.008 Abstract ( 119 )   PDF (227KB) ( 193 )   Save Navier Stokes/Darcy equation can be used to simulate the pollution of pollutants in rivers to groundwater, and the penetration of blood in blood vessels and organs. Due to its wide applications in practice, the research on the numerical method for Navier Stokes/Darcy equations has attracted extensive attention. A BDF2 modular gradient divergence stablized numerical scheme for solving Navier Stokes/Darcy equations is proposed. This scheme improves the validity and accuracy of the solution by adding a stabilization term. While retaining the advantages of the gradient divergence stable scheme, it can effectively avoid bad effects caused by large stabilization parameters. The stability and error analysis of the scheme are given. Finally, the correctness of the theoretical analysis is verified by numerical examples. Related Articles | Metrics

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Pathfinder Grey Wolf Algorithm for Solving Multiple-roots Nonlinear Equations LU Miao, QU Liangdong, HE Dengxu 2022, 39 (6):  957-968.  doi: 10.3969/j.issn.1005-3085.2022.06.009 Abstract ( 129 )   PDF (204KB) ( 170 )   Save In order to overcome the shortcomings of traditional algorithms such as depending on the selection of initial value, the non-complete number of solutions and the poor solution accuracy, a gray wolf optimization algorithm combined with pathfinder algorithm (PGWO) is proposed. Due to the slow convergence speed of the gray wolf optimization algorithm, this paper combines the pathfinder algorithm to modify the position of an individual gray wolf according to the update mechanism of the follower in the pathfinder algorithm, so as to balance the global search and local search abilities of the algorithm. Finally, the simulation results of nine groups of multi-roots nonlinear equations are compared with other swarm intelligent algorithms. The experimental results show that the PGWO method improves the solution accuracy of multi-roots nonlinear equations, and the number of solutions is significantly improved, which further proves the effectiveness of the proposed algorithm. Related Articles | Metrics

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Sharp Wirtinger Inequalities and Optimal Hermite Interpolation Nodes YU Xiaochen, XU Guiqiao 2022, 39 (6):  969-978.  doi: 10.3969/j.issn.1005-3085.2022.06.010 Abstract ( 99 )   PDF (179KB) ( 116 )   Save In the worst case setting, by using the remainder estimate of the Hermite interpolation, the optimal Hermite interpolation nodes for the approximation problem of the Sobolev spaces in maximal and mean norms, respectively, are determined. The method for calculating the best constants in the Wirtinger's inequality is given for functions whose Hermite data is vanished at Hermite interpolation nodes. First, a remainder estimate of the Hermite interpolation approximation error is given by using the method of constructing auxiliary function. After that, the calculation of the best constants in the Wirtinger's inequality is turned into an explicit integral expression, and two examples are used to illustrate the results. At the same time, in the worst case setting, the approximation error values of the Sobolev spaces by using Hermite interpolation are given, and the optimal Hermite interpolation nodes are found when the number of Hermite interpolation nodes is fixed. For some special cases, the explicit expression for the optimal interpolation nodes is given. For the general case, the calculation of the optimal interpolation nodes is reduced to finding the minimum point of some specific functions. Using Mathematical, the values of some optimal coefficients in the Wirtinger's inequality are obtained. Related Articles | Metrics

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Subdirect Sum of Dashnic-Zusmanovich Type Matrices DAI Pingfan, PAN Pan 2022, 39 (6):  979-996.  doi: 10.3969/j.issn.1005-3085.2022.06.011 Abstract ( 82 )   PDF (178KB) ( 226 )   Save The subdirect sum of two square matrices has important applications in the matrix completion problem, the overlapping subdomains of domain decomposition methods, and the global stiffness matrices in finite elements. Applying classification ideas and inequality scaling techniques to the Dashnic-Zusmanovich type matrices, we derive some easily checkable sufficient conditions for determining that the subdirect sum of the Dashnic-Zusmanovich type matrices remains such class of matrices. Numerical examples show that the given conditions are true and valid. Related Articles | Metrics

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Hybrid Flower Pollination Algorithm for Job Shop Scheduling Problem TANG Lijun, PENG Shiyan 2022, 39 (6):  997-1004.  doi: 10.3969/j.issn.1005-3085.2022.06.012 Abstract ( 79 )   PDF (517KB) ( 254 )   Save The job shop scheduling problem with the shortest maximum completion time is studied, and the current research status for the solution of the job shop scheduling problem is reviewed. A hybrid algorithm combining flower pollination algorithm with genetic algorithm is proposed. Based on the flower pollination algorithm, the iterative formula of global search and local search are redefined, and the selection, priority crossover and mutation operations of genetic algorithm are integrated into the assimilation operation, so as to further enhance the exploration ability of the proposed algorithm. Numerical testing on the 26 classic benchmark scheduling problems and comparison with other algorithms in recent 5 years show the proposed algorithm's advantages in solving job-shop scheduling problems. Related Articles | Metrics

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The General Formula of Composite Translation and Rotation Transformations of Inertial Tensor and Its Application LI Xu, CHEN Qianghong, ZHEN Wenqiang, WANG Shuo 2022, 39 (6):  1005-1011.  doi: 10.3969/j.issn.1005-3085.2022.06.013 Abstract ( 110 )   PDF (234KB) ( 407 )   Save In the fields of automobile and other industries, there are many complex subsystems, which need to synthesize the inertia of different subsystems. The physical-measurement-based method has strict requirements for measuring equipment, long cycle and high cost. The CAD-measurement-based method has high requirements for model integrity and poor real-time performance. The theoretical-transformation-based methods are difficult to solve the composite transformation. Therefore, starting from the coordinate transformation of the position vector, the general form of the composite transformation of the translation and rotation of the inertial tensor component matrix is derived by using the matrix transformation, which further improves the theoretical transformation method. At the same time, the coordinate transformation problem of the inertial moment and inertial product is solved, the physical meaning of each item in the transformation relationship is given, and the theoretical results under different simplified conditions are discussed. The results of the typical example show that the theoretical method is consistent with the measurement results of CAD software, which verifies the effectiveness of the derived theoretical method. The relevant results can realize the rapid synthesis of inertia of multi component complex systems in engineering. Thus, the proposed method has certain theoretical significance and engineering application value. Related Articles | Metrics

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Numerical Algorithm for Two-dimensional Volterra-Fredholm Integral Equations and Its Convergence Analysis XIE Jiaquan, LIU Xiaoqi, ZHANG Jiale 2022, 39 (6):  1012-1020.  doi: 10.3969/j.issn.1005-3085.2022.06.014 Abstract ( 138 )   PDF (1311KB) ( 596 )   Save A two-dimensional nonlinear Volterra-Fredholm Hammerstein integral equation is numerically solved by using the two-dimensional block pulse function as the basis function. Firstly, the definition of the block pulse function and the vector representation of the basis function are introduced. Secondly, according to the disjointness and orthogonality of two-dimensional block pulse functions, the integral operator matrix and product operator matrix of the basis vector are derived. Thirdly, the operator matrix is used to transform the problem to be solved into the product form of a series of vectors, and the unknown variables are discretized by the collocation method to obtain the numerical solution of the original problem, Finally, the feasibility and convergence of the proposed algorithm are verified by two numerical examples. Related Articles | Metrics