Table of Content

15 April 2022, Volume 39 Issue 2 Previous Issue   

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UAV Track Prediction Model Based on Error-corrected NLSTM Neural Network LIANG Tianyu, GAO Yong, LIU Junmin, HUI Yongchang 2022, 39 (2):  171-182.  doi: 10.3969/j.issn.1005-3085.2022.02.001 Abstract ( 112 )   PDF (829KB) ( 98 )   Save The UAV industry has developed rapidly in recent years, and has broad application prospects in both military and civilian applications. The track record of UAV plays an important role in its navigation process, and the track prediction of the UAV has also become a hot spot in the current world research. The use of neural network for track prediction can develop to its advantages. Firstly, the domestic and foreign scholars' literatures on track prediction are sorted out, and the current aircraft track prediction algorithms are summarized and classified according to the principle of track prediction. The problem of improving prediction accuracy is studied. Then, aiming at the problem that the prediction accuracy of the traditional neural network model is not high enough, an error-corrected nested long short-term memory (ENLSTM) neural network prediction model is proposed. ENLSTM introduces an error correction term based on the nested long short-term memory network model, which makes the prediction accuracy higher. Finally, four neural network models of BP, RNN, LSTM and ENLSTM are used to simulate the real track data and simulated track data of the UAV respectively. It is concluded that RNN has more advantages in the prediction of UAV track than BP neural network. The gradual improvement based on the basic RNN model improves the prediction ability of the model. ENLSTM model has a better effect on the track prediction of UAV. Related Articles | Metrics

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Dynamic Output Feedback Guaranteed Cost Control of Switched Systems under Asynchronous Switching LI Tongbin, GAO Juan 2022, 39 (2):  183-195.  doi: 10.3969/j.issn.1005-3085.2022.02.002 Abstract ( 48 )   PDF (252KB) ( 60 )   Save As an important hybrid system, switching system is composed of several subsystems and a switching signal to coordinate the switching between subsystems. It is widely used in natural science, engineering control and social systems. For the control problem of switched systems, it is generally assumed that the subsystem and controller operate synchronously. However, in practical engineering control, the switching of the controllers experiences a time delay with respect to that of subsystems, which results in the asynchronous switching. It is very necessary to study the switching system under asynchronous switching. The problem of dynamic output feedback guaranteed cost control for a class of switched systems under asynchronous switching is studied. The research status of switched systems and the latest research results of switched systems under asynchronous switching are reported. By using the piecewise Lyapunov function approach and the average dwell time technique, a sufficient condition for the existence of dynamic output feedback controllers is derived, which guarantees the exponential stability of the closed-loop system. Dynamic output feedback guaranteed cost controllers for switched systems under asynchronous switching are designed in terms of linear matrix inequalities. Moreover, an upper bound of the guaranteed cost function is obtained. The optimization problem to minimize the guaranteed cost is solved. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. Related Articles | Metrics

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The Authenticity Identification Method of Calligraphy Based on Image Shape Fidelity JI Jing 2022, 39 (2):  196-208.  doi: 10.3969/j.issn.1005-3085.2022.02.003 Abstract ( 62 )   PDF (2150KB) ( 68 )   Save The traditional authenticity identification of calligraphy is usually applied in the manner of expert appraisal or spectral analysis. A new authenticity identification method of calligraphy which is based on image shape fidelity is proposed in this paper. The invariant moment applying to the field of pattern recognition is used for the authenticity identification of calligraphy. Seven invariant moments are tested for the performance of shape fidelity, including Hu moment, Zernike moment, Pseudo-Zernike moment, Legendre moment, Fourier-Mellin moment, Tchebichef moment and Krawtchouk moment. The concept of shape fidelity is proposed as the assessment index of the authenticity of calligraphy. The reliability of identification is further guaranteed by the high definition, high precision and high fidelity image acquisition and processing of calligraphies. Experimental results show that our method can recognize the differences in calligraphies which are difficult to distinguish with the naked eyes and can improve the efficiency and credibility of the identification of calligraphies with low cost of identification time and better anti-interference. It has a good significance in the authenticity identification of calligraphy. Related Articles | Metrics

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Thermal Stress Analysis for Interface Cracks between Dodecagonal Two-dimensional Symmetric Quasicrystals and Circular Elastic Inclusion ZHAI Ting, ZHAO Xuefen, DING Shenghu 2022, 39 (2):  209-223.  doi: 10.3969/j.issn.1005-3085.2022.02.004 Abstract ( 49 )   PDF (499KB) ( 57 )   Save The problem of circular elastic inclusion with multiple interface cracks in an infinite dodecagonal two-dimensional symmetrical quasicrystal is studied under the action of a point heat source. Based on the holomorphic theory of complex function partition, the residue theorem, the generalized Liouville theorem, the Riemann-Schwarz analytic extension theorem and the singular principal part analysis method of complex stress function, the general complex potential solutions of temperature field, and the phonon field inside and outside the inclusion are obtained when the concentrated heat source acts on any point in the matrix. The closed form solutions of temperature field and phonon field thermal stress with one interface crack and two interface cracks are derived. The results are compared with the existing results, and the validity of the method is verified. Finally, the influence of inclusion radius, the heat source strength and crack angle on thermal stress and thermal stress intensity factor is discussed by numerical examples. The results show that the thermal stress of phonon field at the crack tip increases with the increase of heat source intensity. With the increase of crack angle and the increase of radius, the thermal stress intensity factor of phonon field at the crack tip increases and the change trend of thermal stress intensity factor is more obvious, and the higher the peak value is, that is, the increase of crack angle and inclusion radius promotes the crack propagation. These conclusions provide a scientific basis for the structural design and application of quasicrystal materials. Related Articles | Metrics

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Stability of an Eco-epidemiological Model with Disease in the Predators and Stage-structure for the Prey ZHANG Mei, WANG Lingshu, JIA Meizhi 2022, 39 (2):  224-236.  doi: 10.3969/j.issn.1005-3085.2022.02.005 Abstract ( 73 )   PDF (180KB) ( 238 )   Save An eco-epidemiological model with disease in the predator and stage-structure for the prey is analyzed. The Holling type-II functional response and a time delay due to the gestation of the predator are considered in this model. By analyzing the corresponding characteristic equations, the local stability of the trivial equilibrium, the predator-extinction equilibrium, the disease free equilibrium and the positive equilibrium are discussed, respectively. The existence of Hopf bifurcations at the positive equilibrium is established. By using Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are obtained for the global stability of the trivial equilibrium, the predator-extinction equilibrium, the disease free equilibrium and the positive equilibrium, respectively. Related Articles | Metrics

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Over-relaxed Primal-dual Fixed Point Algorithm with Applications HUANG Wenli, TANG Yuchao, WEN Meng 2022, 39 (2):  237-264.  doi: 10.3969/j.issn.1005-3085.2022.02.006 Abstract ( 43 )   PDF (9923KB) ( 33 )   Save The optimization problem about the sum of two convex functions has been received much attention in recent years, in which one of them is differentiable with Lipschitz continuous gradient, and the other one contains a bounded linear operator. In this paper, an over-relaxed primal-dual fixed point algorithm is proposed to solve such problem. Compared with the original primal-dual fixed point algorithm, the proposed algorithm expands the selection range of relaxation parameters. By defining a suitable norm and using the fixed point theory of nonexpansive operators, we prove the convergence of the proposed iterative algorithm and together with the ergodic convergence rate. Under some strong conditions of the objective function, we prove that the algorithm has a global linear convergence rate. Finally, we apply the proposed algorithm to solve the total variation image restoration model to verify the validity of the proposed algorithm. Numerical results show that the primal-dual fixed point algorithm with the relaxation parameter larger than one (i.e., over-relaxation) converges faster than the relaxation parameter less than one. Related Articles | Metrics

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A Modified PRP Type Spectral Conjugate Gradient Method with Sufficient Descent Property JIAN Jinbao, SONG Dan, JIANG Xianzhen 2022, 39 (2):  265-276.  doi: 10.3969/j.issn.1005-3085.2022.02.007 Abstract ( 56 )   PDF (279KB) ( 85 )   Save A modified PRP type spectral conjugate gradient method with sufficient descent property spectral conjugate gradient method is an important extension of conjugate gradient method. By adjusting the conjugate parameters and spectral parameters, the search direction of the designed algorithm can meet a certain preset condition, such as sufficient descent condition or conjugate condition. The two core tasks of designing spectral parameters and conjugate parameters are spectral conjugate gradient method, which determine the convergence and numerical effect of the method. Based on the PRP method, a modified PRP type conjugate parameter is proposed and a spectral parameter is chosen by sufficient descent conditions, and then a new spectral conjugate gradient method is established. Sufficient descent condition of the new algorithms does not depend on any line search. Under the usual assumptions, using the strong Wolfe line search to generate the step-length, the global convergence of the presented method is proved. By testing 100 numerical experiments, the corresponding performance profiles for the proposed method and other five comparisons are reported, which indicate that the proposed method is effective. Related Articles | Metrics

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Hopf Bifurcation and Turing Instability in a Reversible Biochemical Reaction-diffusion Model Combining Second-order Saturation GUO Gaihui, GUO Feiyan, LIU Xiaohui 2022, 39 (2):  277-291.  doi: 10.3969/j.issn.1005-3085.2022.02.008 Abstract ( 65 )   PDF (1157KB) ( 70 )   Save In this paper, a four-molecule reversible biochemical reaction-diffusion model combining second-order saturation subject to homogeneous Neumann boundary conditions is studied. Taking the reversible reaction rate as a parameter, the existence, direction and stability of Hopf bifurcation for ordinary differential system and the diffusive system are respectively given applying the normal form theory and the central manifold theorem. Moreover, the effect of diffusive coefficient on the stability of the system is studied extensively. The results show that the positive equilibrium point is unstable when the reversible reaction rate is small. When the reversible reaction rate is large, the positive equilibrium point is stable. When the reversible reaction rate is in a certain range, the diffusive coefficient has a great effect on the stability of the system. In this case, if the catalyst's diffusive coefficient is small, then Turing instability occurs. Finally, the parameters satisfying the conditions of the theorem are selected and the theoretical results are verified by numerical simulations. Related Articles | Metrics

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Oscillation of Third-order Nonlinear Emden-Fowler Delay Dynamic Equation with a Sublinear Neutral Term on Time Scales ZHANG Zhiyu, FENG Ruihua 2022, 39 (2):  292-308.  doi: 10.3969/j.issn.1005-3085.2022.02.009 Abstract ( 57 )   PDF (219KB) ( 73 )   Save Judging the oscillation and asymptotic behavior of delay dynamic equations on time scale plays an important role in mathematical physics, automatic control theory and engineering, infectious disease model analysis, bridge design and so on. Thus, the oscillation behavior of third-order nonlinear Emden-Fowler type delay dynamic equation with a sublinear neutral term on time scales are investigated. By using the dynamic calculus on time scales, generalized Riccati transformation and inequality technique, two oscillation theorems to ensure that every solution of the equation oscillates or converges to zero are obtained. These results extend and improve the results established in previous literatures. Finally, the effectiveness of the theoretical results obtained here are illustrated with two examples. Related Articles | Metrics

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On Strong Deviation Theorems for Dependent Random Array YANG Shanshan, HU Ping 2022, 39 (2):  309-318.  doi: 10.3969/j.issn.1005-3085.2022.02.010 Abstract ( 65 )   PDF (179KB) ( 123 )   Save The strong deviation theorem in probability theory is a natural extension of the classical strong law of large numbers. In this paper, we first introduce the concept of the asymptotic generalized logarithmic likelihood ratio as a random measure of deviation between the arbitrarily dependent array of random variables and an array of row-wise independent random variables. Using truncation technique for random variables, we construct likelihood ratio with one parameter and expectation of 1, then by applying of the Borel-Cantelli lemma, we derive almost everywhere convergence of random variables. Under some conditions of Chung type, we obtain the upper and lower bounds on the deviation between the partial sum of arbitrarily dependent array of random variables and the expectations of the random variable of the reference measure. And the upper and lower bounds are presented by the generalized relative entropy functions. It is worth noting that the proof of the theorem does not involve the complex measure theory, but only the simple pure analysis method. The results extend some existing conclusions and the applications of the strong limit theorem. Related Articles | Metrics

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Free Vibration Analysis of Laminated Composite Plates by the Genetic Algorithm and Multiquadrics Radial Basis Function LI Lin, SHI Feng, XIANG Song, ZHAO Weiping, WANG Yanbing 2022, 39 (2):  319-329.  doi: 10.3969/j.issn.1005-3085.2022.02.011 Abstract ( 59 )   PDF (293KB) ( 210 )   Save In order to improve the accuracy of free vibration analysis of laminated composite plate, free vibration of laminated composite plates is analyzed by the meshless radial basis function collocation method. The shape parameter of radial basis function has important effect on the accuracy of calculation. The genetic algorithm is utilized to optimize the shape parameter of multiquadrics radial basis function. Natural frequencies of laminated composite plates are calculated by the multiquadrics radial basis function with optimal shape parameter and compared of the existing literatures. The numerical results are consistent with the results with the results. The genetic algorithm has great potential in shape parameter optimization. The proposed method has higher calculation precision. Related Articles | Metrics

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Darboux Transformation of the Integrable Coupling AKNS Equations and Its Exact Explicit Solutions CHENG Jianling, FENG Yihu 2022, 39 (2):  330-340.  doi: 10.3969/j.issn.1005-3085.2022.02.012 Abstract ( 65 )   PDF (181KB) ( 288 )   Save For many physical phenomena, it is necessary to establish wave models with two or more components to explain different patterns, frequencies and polarization phenomenna. In addition, only multi-component systems can explain the energy exchange of multiple physical fields theoretically and practically. Therefore, for a integrable system, how to construct a non-trivial differential equation system that is integrable and contains the original system as a subsystem is one of the important problems in the study of integrable coupling. In this work, the integrable couplings of the Ablowitz-Kaup-Newell-Segur equation are constructed based on a stationary equation. Then a Darboux transformation in which the elements can be expressed by the quotient of two determinants is obtained, and the production process is proved strictly. By comparing the forms and characteristics of the one-fold Darboux transformation, $N$-fold Darboux transformation formula which can be demonstrated as determinants is derived. Therefore, by means of seed solutions and $N$-fold Darboux transformation, any-order soliton solutions can be derived. As the application of Darboux tarnsformation, we solve the exact explicit one-soliton solutions. Related Articles | Metrics