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Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field Research Article

Naveed Ahmed Azam, Umar Hayat, Ikram Ullah,azam@amp.i.kyoto-u.ac.jp,umar.hayat@qau.edu.pk

Frontiers of Information Technology & Electronic Engineering 2019, Volume 20, Issue 10,   Pages 1378-1389 doi: 10.1631/FITEE.1800434

Abstract: We study the balance problem caused by forward leaning of the wearer’s upper body during rehabilitation training with a lower limb rehabilitation exoskeleton. The instantaneous capture point is obtained by modeling the human-exoskeleton system and using the capture point theory. By comparing the stability region with instantaneous capture points of different gait phases, the balancing characteristics of different gait phases and changes to the equilibrium state in the gait process are analyzed. Based on a model of the human-exoskeleton system and the condition of balance of different phases, a trajectory correction strategy is proposed for the instability of the human-exoskeleton system caused by forward leaning of the wearer’s upper body. Finally, the reliability of the trajectory correction strategy is verified by carrying out experiments on the Zhejiang University Lower Extremity Exoskeleton. The proposed trajectory correction strategy can respond to forward leaning of the upper body in a timely manner. Additionally, in the process of the center of gravity transferred from a double-support phase to a single-support phase, the ratio of gait cycle to zero moment point transfer is reduced correspondingly, and the gait stability is improved.

Keywords： 密码置换盒；有限域；莫德尔椭圆曲线；总阶数；计算复杂度    

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Fractional-order global optimal backpropagation machine trained by an improved fractional-order steepest descent method Research Articles

Yi-fei Pu, Jian Wang,puyifei@scu.edu.cn,wangjiannl@upc.edu.cn

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 6,   Pages 809-962 doi: 10.1631/FITEE.1900593

Abstract: We introduce the fractional-order global optimal backpropagation machine, which is trained by an improved (FSDM). This is a fractional-order backpropagation neural network (FBPNN), a state-of-the-art fractional-order branch of the family of backpropagation neural networks (BPNNs), different from the majority of the previous classic first-order BPNNs which are trained by the traditional first-order steepest descent method. The reverse incremental search of the proposed FBPNN is in the negative directions of the approximate fractional-order partial derivatives of the square error. First, the theoretical concept of an FBPNN trained by an improved FSDM is described mathematically. Then, the mathematical proof of fractional-order global optimal convergence, an assumption of the structure, and of the FBPNN are analyzed in detail. Finally, we perform three (types of) experiments to compare the performances of an FBPNN and a classic first-order BPNN, i.e., example function approximation, , and comparison of global search and error fitting abilities with real data. The higher optimal search ability of an FBPNN to determine the global optimal solution is the major advantage that makes the FBPNN superior to a classic first-order BPNN.

Keywords： 分数阶微积分；分数阶反向传播算法；分数阶最速下降法；均方误差；分数阶多尺度全局优化    

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Fractional-order memristive neural synaptic weighting achieved by pulse-based fracmemristor bridge circuit Research Articles

Yifei Pu, Bo Yu, Qiuyan He, Xiao Yuan,heqiuyan789@163.com,yuanxiao@scu.edu.cn

Frontiers of Information Technology & Electronic Engineering 2021, Volume 22, Issue 6,   Pages 862-876 doi: 10.1631/FITEE.2000085

Abstract: We propose a novel circuit for the fractional-order memristive neural synaptic weighting (FMNSW). The introduced circuit is different from the majority of the previous integer-order approaches and offers important advantages. Since the concept of memristor has been generalized from the classic integer-order memristor to the (), a challenging theoretical problem would be whether the can be employed to implement the or not. In this research, characteristics of the FMNSW, realized by a pulse-based bridge circuit, are investigated. First, the circuit configuration of the FMNSW is explained using a pulse-based bridge circuit. Second, the mathematical proof of the fractional-order learning capability of the FMNSW is analyzed. Finally, experimental work and analyses of the electrical characteristics of the FMNSW are presented. Strong ability of the FMNSW in explaining the cellular mechanisms that underlie learning and memory, which is superior to the traditional integer-order memristive neural synaptic weighting, is considered a major advantage for the proposed circuit.

Keywords： 分数阶微积分；分忆抗；分忆抗值；分数阶忆阻；分数阶记忆性突触    

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Mittag-Leffler stability analysis ofmultiple equilibrium points in impulsive fractional-order quaternion-valued neural networks Research Articles

K. UDHAYAKUMAR, R. RAKKIYAPPAN, Jin-de CAO, Xue-gang TAN

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 2,   Pages 234-246 doi: 10.1631/FITEE.1900409

Abstract: In this study, we investigate the problem of multiple Mittag-Leffler stability analysis for fractional-order quaternion-valued neural networks (QVNNs) with impulses. Using the geometrical properties of activation functions and the Lipschitz condition, the existence of the equilibrium points is analyzed. In addition, the global Mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order QVNNs is investigated by employing the Lyapunov direct method. Finally, simulation is performed to illustrate the effectiveness and validity of the main results obtained.

Keywords： Mittag-Leffler stability     Fractional-order     Quaternion-valued neural networks     Impulse    

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Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation Research Articles

Zahra Sadat Aghayan, Alireza Alfi, J. A. Tenreiro Machado,a_alfi@shahroodut.ac.ir

Frontiers of Information Technology & Electronic Engineering 2021, Volume 22, Issue 10,   Pages 1402-1412 doi: 10.1631/FITEE.2000438

Abstract: This study analyzes the problem of of fractional-order delay systems of neutral type under actuator . A Lyapunov–Krasovskii (LK) function is constructed and conditions of the asymptotic of such systems are given, which are formulated by linear matrix inequalities (LMIs), using the Lyapunov direct method. An algorithm is introduced to compute the gain of the state feedback controller for extending the domain of attraction. The theoretical results are validated using some numerical examples.

Keywords： 分数阶系统；稳定性；中立时滞；鲁棒性；饱和性    

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Bifurcation-based fractional-order PI None

Karima RABAH, Samir LADACI, Mohamed LASHAB

Frontiers of Information Technology & Electronic Engineering 2018, Volume 19, Issue 2,   Pages 180-191 doi: 10.1631/FITEE.1601543

Abstract: We propose a novel approach called the robust fractional-order proportional-integral-derivative (FOPID) controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability analysis of the nonlinear chaotic system is made based on the proportional-integral-derivative actions using the bifurcation diagram. We extract an initial set of controller parameters, which are subsequently optimized using a quadratic criterion. The integral and derivative fractional orders are also identified by this quadratic criterion. By applying numerical simulations on two nonlinear systems, namely the multi-scroll Chen system and the Genesio-Tesi system, we show that the fractional PIλDμ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.

Keywords： Fractional order system     Bifurcation diagram     Fractional PIλDμ controller     Multi-scroll Chen chaotic system     Genesio-Tesi chaotic system    

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A novel color image encryption algorithm based on a fractional-order discrete chaotic neural network and DNA sequence operations Research Articles

Li-ping Chen, Hao Yin, Li-guo Yuan, António M. Lopes, J. A. Tenreiro Machado, Ran-chao Wu,lip_chenhut@126.com

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 6,   Pages 809-962 doi: 10.1631/FITEE.1900709

Abstract: A novel algorithm based on dynamic deoxyribonucleic acid (DNA) encoding and chaos is presented. A three-neuron fractional-order discrete Hopfield neural network (FODHNN) is employed as a pseudo-random chaotic sequence generator. Its initial value is obtained with the secret key generated by a five-parameter external key and a hash code of the plain image. The external key includes both the FODHNN discrete step size and order. The hash is computed with the SHA-2 function. This ensures a large secret key space and improves the algorithm sensitivity to the plain image. Furthermore, a new three-dimensional projection confusion method is proposed to scramble the pixels among red, green, and blue color components. DNA encoding and diffusion are used to diffuse the image information. Pseudo-random sequences generated by FODHNN are employed to determine the encoding rules for each pixel and to ensure the diversity of the encoding methods. Finally, confusion II and XOR are used to ensure the security of the encryption. Experimental results and the security analysis show that the proposed algorithm has better performance than those reported in the literature and can resist typical attacks.

Keywords： 分数阶离散系统；神经网络；DNA加密；彩色图像加密    

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In consideration of the LNG sale and purchase in one core for constructing of business structure concerning sale and purchase agreement for liquefied natural gas in offshore and onshore and passing the risk

Wang Jiaxiang,Luo Weizhong,Chen Xiang,Zhao Ruicong,Sun Qian,Mu Qi,Wang Xi

Strategic Study of CAE 2011, Volume 13, Issue 5,   Pages 98-102

Abstract:

Under the form of LNG sale and purchase in one core, by arranging onshore sale and purchase agreement for liquefied natural gas,CNOOC Gas and Power Trading & Marketing Ltd became one party of the offshore and onshore agreement, which not only kept the consistence of offshore and onshore agreement and reduced the risk for the CNOOC Gas and Power Trading & Marketing Ltd in maxima level, but also passed all the risks smoothly.

Keywords： sale and purchase in one core     business structure     risk passing    

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Study on the Optimization of Public Traffic Line Network Based on Grey Fuzzy Numbers and Its Application

Deng Wei,Hu Qizhou

Strategic Study of CAE 2007, Volume 9, Issue 11,   Pages 21-25

Abstract:

On the basis of considering each factor of urban public traffic line network,  the decision-making method for the optimization of urban public traffic line network is set up by grey theory and fuzzy theory.  This paper proposes to use interval numbers of three parameters to present grey fuzzy numbers.  A comprehensive optimization method for urban public traffic line network is given by using theories above.  It was applied to the practical optimization of urban public traffic line network in the city.  Applied results indicate that the method improves the efficiency of urban public traffic line network.

Keywords： public traffic line network     optimization     grey fuzzy numbers    

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Sampling formulas for 2D quaternionic signals associated with various quaternion Fourier and linear canonical transforms Research Articles

Xiaoxiao HU, Dong CHENG, Kit Ian KOU,huxiaoxiao3650@163.com

Frontiers of Information Technology & Electronic Engineering 2022, Volume 23, Issue 3,   Pages 463-478 doi: 10.1631/FITEE.2000499

Abstract: The main purpose of this paper is to study different types of sampling formulas of quaternionic functions, which are bandlimited under various quaternion Fourier and linear canonical transforms. We show that the quaternionic bandlimited functions can be reconstructed from their samples as well as the samples of their derivatives and Hilbert transforms. In addition, the relationships among different types of sampling formulas under various transforms are discussed. First, if the quaternionic function is bandlimited to a rectangle that is symmetric about the origin, then the sampling formulas under various are identical. If this rectangle is not symmetric about the origin, then the sampling formulas under various are different from each other. Second, using the relationship between the two-sided quaternion Fourier transform and the linear canonical transform, we derive sampling formulas under various . Third, of these sampling formulas are estimated. Finally, some simulations are provided to show how the sampling formulas can be used in applications.

Keywords： Quaternion Fourier transforms     Quaternion linear canonical transforms     Sampling theorem     Quaternion partial and total Hilbert transforms     Generalized quaternion partial and total Hilbert transforms     Truncation errors    

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A fractional-order multifunctionaln-step honeycomb RLC circuit network Article

Ling ZHOU, Zhi-zhong TAN, Qing-hua ZHANG

Frontiers of Information Technology & Electronic Engineering 2017, Volume 18, Issue 8,   Pages 1186-1196 doi: 10.1631/FITEE.1601560

Abstract: We investigate a multifunctional -step honeycomb network which has not been studied before. By adjusting the circuit parameters, such a network can be transformed into several different networks with a variety of functions, such as a regular ladder network and a triangular network. We derive two new formulae for equivalent resistance in the resistor network and equivalent impedance in the LC network, which are in the fractional-order domain. First, we simplify the complex network into a simple equivalent model. Second, using Kirchhoff’s laws, we establish a fractional difference equation. Third, we construct an equivalent transformation method to obtain a general solution for the nonlinear differential equation. In practical applications, several interesting special results are obtained. In particular, an step impedance LC network is discussed and many new characteristics of complex impedance have been found.

Keywords： Honeycomb network     Equivalent transformation     Fractional differential equation     Impedance characteristics    

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Dynamics of a neuron exposed to integer- and fractional-order discontinuous externalmagnetic flux Regular Papers

Karthikeyan RAJAGOPAL, Fahimeh NAZARIMEHR, Anitha KARTHIKEYAN, Ahmed ALSAEDI, Tasawar HAYAT, Viet-Thanh PHAM

Frontiers of Information Technology & Electronic Engineering 2019, Volume 20, Issue 4,   Pages 584-590 doi: 10.1631/FITEE.1800389

Abstract:

We propose a modified Fitzhugh-Nagumo neuron (MFNN) model. Based on this model, an integerorder MFNN system (case A) and a fractional-order MFNN system (case B) were investigated. In the presence of electromagnetic induction and radiation, memductance and induction can show a variety of distributions. Fractionalorder magnetic flux can then be considered. Indeed, a fractional-order setting can be acceptable for non-uniform diffusion. In the case of an MFNN system with integer-order discontinuous magnetic flux, the system has chaotic and non-chaotic attractors. Dynamical analysis of the system shows the birth and death of period doubling, which is a sign of antimonotonicity. Such a behavior has not been studied previously in the dynamics of neurons. In an MFNN system with fractional-order discontinuous magnetic flux, different attractors such as chaotic and periodic attractors can be observed. However, there is no sign of antimonotonicity.

Keywords： Fitzhugh-Nagumo     Chaos     Fractional order     Magnetic flux    

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Research on 3D Dynamic Visual Graphic Simulation for Construction Layout of Xiluodu Project

Zhong Denghua,Zhu Huirong,Zheng Jiaxiang

Strategic Study of CAE 2003, Volume 5, Issue 11,   Pages 65-70

Abstract:

Xiluodu hydroelectric plant is the biggest plant to be built on Jinsha River, and also, Xiluodu project is the biggest hydraulic engineering in China except Three George Project. To intuitively and accurately describe the complex and dynamic spatial relationship among all sides interfered in construction layout design of Xi Luodu project, the construction layout system is divided into 6 subsystems： dam construction, diversion and enclosure construction, dynamic water flow, underground structure construction, quarry stacking and redigging, and road and traffic inside construction site, and the research on 3D dynamic visual graphic simulation for construction layout of the designed whole construction process is developed. Flow of the 3D dynamic graphic simulation data is designed. Dynamic graphic simulation data can be divided into graphic data and attribute data, which organized based on GIS, then, 3D dynamic visual digital model for construction layout is built, which itself is an important part of digital hydraulic engineering. 3D dynamic visual graphic simulation demonstration and visual inquiry of dynamic graphic simulation data are realized with this digital model. Practical engineering application shows that a scientific and intuitive visualization analysis way is provided. for construction layout design and decision-making by this research, moreover, hydroelectric design work will be promoted to develop in an intellective and modern way, and the research is worth to be spread.

Keywords： Xiluodu Project     construction layout     graphic simulation     geographic information system     digital hydraulic engineering    

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Design of a fractional PI None

Pritesh SHAH, Sudhir AGASHE, Anand J. KULKARNI

Frontiers of Information Technology & Electronic Engineering 2018, Volume 19, Issue 3,   Pages 437-445 doi: 10.1631/FITEE.1601495

Abstract: The cohort intelligence (CI) method has recently evolved as an optimization method based on artificial intelligence. We use the CI method for the first time to optimize the parameters of the fractional proportionalintegral-derivative (PID) controller. The performance of the CI method in designing the fractional PID controller was validated and compared with those of some other popular algorithms such as particle swarm optimization, the genetic algorithm, and the improved electromagnetic algorithm. The CI method yielded improved solutions in terms of the cost function, computing time, and function evaluations in comparison with the other three algorithms. In addition, the standard deviations of the CI method demonstrated the robustness of the proposed algorithm in solving control problems.

Keywords： Cohort intelligence     Fractional calculus     Fractional PID controller     Tuning    

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TODIM and TOPSIS with Z-numbers None

Renato A. KROHLING, André G. C. PACHECO, Guilherme A. dos SANTOS

Frontiers of Information Technology & Electronic Engineering 2019, Volume 20, Issue 2,   Pages 283-291 doi: 10.1631/FITEE.1700434

Abstract:

In this paper, we present an approach that can handle Z-numbers in the context of multi-criteria decision-making problems. The concept of Z-number as an ordered pair Z=(A, B) of fuzzy numbers A and B is used, where A is a linguistic value of a variable of interest and B is a linguistic value of the probability measure of A. As human beings, we communicate with each other by means of natural language using sentences like “the journey from home to university most likely takes about half an hour.” The Z-numbers are converted to fuzzy numbers. Then the Z-TODIM and Z-TOPSIS are presented as a direct extension of the fuzzy TODIM and fuzzy TOPSIS, respectively. The proposed methods are applied to two case studies and compared with the standard approach using crisp values. The results obtained show the feasibility of the approach.

Keywords： Multi-criteria decision-making     TODIM     TOPSIS     Fuzzy number     Z-number    

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Title Author Date Type Operation

Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field

Naveed Ahmed Azam, Umar Hayat, Ikram Ullah,azam@amp.i.kyoto-u.ac.jp,umar.hayat@qau.edu.pk

Journal Article

Fractional-order global optimal backpropagation machine trained by an improved fractional-order steepest descent method

Yi-fei Pu, Jian Wang,puyifei@scu.edu.cn,wangjiannl@upc.edu.cn

Journal Article

Fractional-order memristive neural synaptic weighting achieved by pulse-based fracmemristor bridge circuit

Yifei Pu, Bo Yu, Qiuyan He, Xiao Yuan,heqiuyan789@163.com,yuanxiao@scu.edu.cn

Journal Article

Mittag-Leffler stability analysis ofmultiple equilibrium points in impulsive fractional-order quaternion-valued neural networks

K. UDHAYAKUMAR, R. RAKKIYAPPAN, Jin-de CAO, Xue-gang TAN

Journal Article

Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation

Zahra Sadat Aghayan, Alireza Alfi, J. A. Tenreiro Machado,a_alfi@shahroodut.ac.ir

Journal Article

Bifurcation-based fractional-order PI

Karima RABAH, Samir LADACI, Mohamed LASHAB

Journal Article

A novel color image encryption algorithm based on a fractional-order discrete chaotic neural network and DNA sequence operations

Li-ping Chen, Hao Yin, Li-guo Yuan, António M. Lopes, J. A. Tenreiro Machado, Ran-chao Wu,lip_chenhut@126.com

Journal Article

In consideration of the LNG sale and purchase in one core for constructing of business structure concerning sale and purchase agreement for liquefied natural gas in offshore and onshore and passing the risk

Wang Jiaxiang,Luo Weizhong,Chen Xiang,Zhao Ruicong,Sun Qian,Mu Qi,Wang Xi

Journal Article

Study on the Optimization of Public Traffic Line Network Based on Grey Fuzzy Numbers and Its Application

Deng Wei,Hu Qizhou

Journal Article

Sampling formulas for 2D quaternionic signals associated with various quaternion Fourier and linear canonical transforms

Xiaoxiao HU, Dong CHENG, Kit Ian KOU,huxiaoxiao3650@163.com

Journal Article

A fractional-order multifunctionaln-step honeycomb RLC circuit network

Ling ZHOU, Zhi-zhong TAN, Qing-hua ZHANG

Journal Article

Dynamics of a neuron exposed to integer- and fractional-order discontinuous externalmagnetic flux

Karthikeyan RAJAGOPAL, Fahimeh NAZARIMEHR, Anitha KARTHIKEYAN, Ahmed ALSAEDI, Tasawar HAYAT, Viet-Thanh PHAM

Journal Article

Research on 3D Dynamic Visual Graphic Simulation for Construction Layout of Xiluodu Project

Zhong Denghua,Zhu Huirong,Zheng Jiaxiang

Journal Article

Design of a fractional PI

Pritesh SHAH, Sudhir AGASHE, Anand J. KULKARNI

Journal Article

TODIM and TOPSIS with Z-numbers

Renato A. KROHLING, André G. C. PACHECO, Guilherme A. dos SANTOS

Journal Article