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High-resolution azimuth estimation algorithm based on data fusion method for the vector hydrophone vertical array 被引量:3
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作者 CHEN Yu MENG Zhou +1 位作者 MA Shuqing BAO Changchun 《Chinese Journal of Acoustics》 CSCD 2015年第3期312-324,共13页
To aim at the problem that the horizontal directivity index of the vector hy- drophone vertical array is not higher than that of a vector hydrophone, the high-resolution azimuth estimation algorithm based on the data ... To aim at the problem that the horizontal directivity index of the vector hy- drophone vertical array is not higher than that of a vector hydrophone, the high-resolution azimuth estimation algorithm based on the data fusion method was presented. The proposed algorithnl first employs MUSIC algorithm to estimate the azimuth of each divided sub-band signal, and then the estimated azimuths of multiple hydrophones are processed by using the data fusion technique. The high-resolution estimated result is achieved finally by adopting the weighted histogram statistics method. The results of the simulation and sea trials indicated that the proposed algorithm has better azimuth estimation performance than MUSIC algorithm of a single vector hydrophone and the data fusion technique based on the acoustic energy flux method. The better performance is reflected in the aspects of the estimation precision, the probability of correct estimation, the capability to distinguish multi-objects and the inhibition of the noise sub-bands. 展开更多
关键词 MUSIC High-resolution azimuth estimation algorithm based on data fusion method for the vector hydrophone vertical array DATA
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Combinations of Estimation of Distribution Algorithms and Other Techniques 被引量:2
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作者 Qingfu Zhang Jianyong Sun Edward Tsang 《International Journal of Automation and computing》 EI 2007年第3期273-280,共8页
This paper summaries our recent work on combining estimation of distribution algorithms (EDA) and other techniques for solving hard search and optimization problems: a) guided mutation, an offspring generator in w... This paper summaries our recent work on combining estimation of distribution algorithms (EDA) and other techniques for solving hard search and optimization problems: a) guided mutation, an offspring generator in which the ideas from EDAs and genetic algorithms are combined together, we have shown that an evolutionary algorithm with guided mutation outperforms the best GA for the maximum clique problem, b) evolutionary algorithms refining a heuristic, we advocate a strategy for solving a hard optimization problem with complicated data structure, and c) combination of two different local search techniques and EDA for numerical global optimization problems, its basic idea is that not all the new generated points are needed to be improved by an expensive local search. 展开更多
关键词 estimation distribution algorithm guided mutation memetic algorithms global optimization.
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An improved estimation of distribution algorithm for multi-compartment electric vehicle routing problem 被引量:4
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作者 SHEN Yindong PENG Liwen LI Jingpeng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2021年第2期365-379,共15页
The multi-compartment electric vehicle routing problem(EVRP)with soft time window and multiple charging types(MCEVRP-STW&MCT)is studied,in which electric multi-compartment vehicles that are environmentally friendl... The multi-compartment electric vehicle routing problem(EVRP)with soft time window and multiple charging types(MCEVRP-STW&MCT)is studied,in which electric multi-compartment vehicles that are environmentally friendly but need to be recharged in course of transport process,are employed.A mathematical model for this optimization problem is established with the objective of minimizing the function composed of vehicle cost,distribution cost,time window penalty cost and charging service cost.To solve the problem,an estimation of the distribution algorithm based on Lévy flight(EDA-LF)is proposed to perform a local search at each iteration to prevent the algorithm from falling into local optimum.Experimental results demonstrate that the EDA-LF algorithm can find better solutions and has stronger robustness than the basic EDA algorithm.In addition,when comparing with existing algorithms,the result shows that the EDA-LF can often get better solutions in a relatively short time when solving medium and large-scale instances.Further experiments show that using electric multi-compartment vehicles to deliver incompatible products can produce better results than using traditional fuel vehicles. 展开更多
关键词 multi-compartment vehicle routing problem electric vehicle routing problem(EVRP) soft time window multiple charging type estimation of distribution algorithm(EDA) Lévy flight
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Archimedean copula estimation of distribution algorithm based on artificial bee colony algorithm 被引量:8
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作者 Haidong Xu Mingyan Jiang Kun Xu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2015年第2期388-396,共9页
The artificial bee colony (ABC) algorithm is a com- petitive stochastic population-based optimization algorithm. How- ever, the ABC algorithm does not use the social information and lacks the knowledge of the proble... The artificial bee colony (ABC) algorithm is a com- petitive stochastic population-based optimization algorithm. How- ever, the ABC algorithm does not use the social information and lacks the knowledge of the problem structure, which leads to in- sufficiency in both convergent speed and searching precision. Archimedean copula estimation of distribution algorithm (ACEDA) is a relatively simple, time-economic and multivariate correlated EDA. This paper proposes a novel hybrid algorithm based on the ABC algorithm and ACEDA called Archimedean copula estima- tion of distribution based on the artificial bee colony (ACABC) algorithm. The hybrid algorithm utilizes ACEDA to estimate the distribution model and then uses the information to help artificial bees to search more efficiently in the search space. Six bench- mark functions are introduced to assess the performance of the ACABC algorithm on numerical function optimization. Experimen- tal results show that the ACABC algorithm converges much faster with greater precision compared with the ABC algorithm, ACEDA and the global best (gbest)-guided ABC (GABC) algorithm in most of the experiments. 展开更多
关键词 artificial bee colony(ABC) algorithm Archimedean copula estimation of distribution algorithm(ACEDA) ACEDA based on artificial be
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Improved Estimation of Distribution Algorithm for Solving Unrelated Parallel Machine Scheduling Problem
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作者 孙泽文 顾幸生 《Journal of Donghua University(English Edition)》 EI CAS 2016年第5期797-802,共6页
Scheduling problem is a well-known combinatorial optimization problem.An effective improved estimation of distribution algorithm(IEDA) was proposed for minimizing the makespan of the unrelated parallel machine schedul... Scheduling problem is a well-known combinatorial optimization problem.An effective improved estimation of distribution algorithm(IEDA) was proposed for minimizing the makespan of the unrelated parallel machine scheduling problem(UPMSP).Mathematical description was given for the UPMSP.The IEDA which was combined with variable neighborhood search(IEDA_VNS) was proposed to solve the UPMSP in order to improve local search ability.A new encoding method was designed for representing the feasible solutions of the UPMSP.More knowledge of the UPMSP were taken consideration in IEDA_ VNS for probability matrix which was based the processing time matrix.The simulation results show that the proposed IEDA_VNS can solve the problem effectively. 展开更多
关键词 estimation of distribution algorithm(EDA) unrelated parallel machine scheduling problem(UPMSP)
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Feature Extraction of Localized Scattering Centers Using the Modified TLS-Prony Algorithm and Its Applications 被引量:5
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作者 Wang Jun Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900, P.R.China 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2002年第3期31-39,共9页
This paper presents an all-parametric model of radar target in optic region, in which the localized scattering center's frequency and aspect angle dependent scattering level, distance and azimuth locations are mod... This paper presents an all-parametric model of radar target in optic region, in which the localized scattering center's frequency and aspect angle dependent scattering level, distance and azimuth locations are modeled as the feature vectors. And the traditional TLS-Prony algorithm is modified to extract these feature vectors. The analysis of Cramer-Rao bound shows that the modified algorithm not only improves the restriction of high signal-to-noise ratio(SNR)threshold of traditional TLS-Prony algorithm, but also is suitable to the extraction of big damped coefficients and high-resolution estimation of near separation poles. Finally, an illustrative example is presented to verify its practicability in the applications. The experimental results show that the method developed can not only recognize two airplane-like targets with similar shape at low SNR, but also compress the original radar data with high fidelity. 展开更多
关键词 Localized scattering centers estimation algorithm Low SNR High resolution.
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Motion Estimation Based on Global and Local Compensability Analysis
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作者 Fan Jinping(Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, 201800, P. R. China)Zhang Liming(Department of Electronic Engineering, Fudan University, Shanghai 200433, P. R. China) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1997年第2期19-23,共5页
This paper reports our study of a novel motion estimation algorithm based on global and local compensability analysis. The spatial correlation of motion field is used to reduce the burden of estimation computation and... This paper reports our study of a novel motion estimation algorithm based on global and local compensability analysis. The spatial correlation of motion field is used to reduce the burden of estimation computation and extra bit rate for motion vectors. Experimental results show that this algorithm is more efficient than the conventional methods, especially for temporal activity regions. 展开更多
关键词 Motion estimation algorithm Frame difference contrast Local variance contrast.
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Relative efficiency appraisal of discrete choice modeling algorithms using small-scale maximum likelihood estimator through empirically tailored computing environment
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作者 Hyuk-Jae Roh Prasanta K. Sahu +1 位作者 Ata M. Khan Satish Sharma 《Journal of Modern Transportation》 2015年第1期67-79,共13页
Discrete choice models are widely used in multiple sectors such as transportation, health, energy, and marketing, etc., where the model estimation is usually carried out by using commercial software. Nonetheless, tail... Discrete choice models are widely used in multiple sectors such as transportation, health, energy, and marketing, etc., where the model estimation is usually carried out by using commercial software. Nonetheless, tailored computer codes offer modellers greater flexibility and control of unique modelling situation. Aligned with empirically tailored computing environment, this research discusses the relative performance of six different algorithms of a discrete choice model using three key performance measures: convergence time, number of iterations, and iteration time. The computer codes are developed by using Visual Basic Application (VBA). Maximum likelihood function (MLF) is formulated and the mathematical relationships of gradient and Hessian matrix are analytically derived to carry out the estimation process. The estimated parameter values clearly suggest that convergence criterion and initial guessing of parameters are the two critical factors in determining the overall estimation performance of a custom-built discrete choice model. 展开更多
关键词 estimation algorithms - Visual basicapplication Convergence criterion Binary logitMaximum likelihood
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Optimization by Estimation of Distribution with DEUM Framework Based on Markov Random Fields 被引量:5
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作者 Siddhartha Shakya John McCall 《International Journal of Automation and computing》 EI 2007年第3期262-272,共11页
This paper presents a Markov random field (MRP) approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general he... This paper presents a Markov random field (MRP) approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields (DEUM). DEUM is a subclass of estimation of distribution algorithms (EDAs) where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are: 1) use of MRF models, 2) fitness modeling approach to estimating the parameter of the model and 3) Monte Carlo approach to sampling from the model. 展开更多
关键词 estimation of distribution algorithms evolutionary algorithms fitness modeling Markov random fields Gibbs distri-bution.
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Improvement of Channel Estimation with 16QAM Modulation over Fading Channel for DS-CDMA
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作者 杨宇 匡镜明 《Journal of Beijing Institute of Technology》 EI CAS 2004年第S1期12-16,共5页
The application of low complexity and low order robust regression algorithm in channel estimation with 16QAM over fading channel for DS-CDMA is presented in this paper After initial channel estimation with classical m... The application of low complexity and low order robust regression algorithm in channel estimation with 16QAM over fading channel for DS-CDMA is presented in this paper After initial channel estimation with classical methods, channel gains estimated are filtered by linear or conic regression algorithm within a given regression length Simulation results show that this method offers up to 0,3 dB gain in a DS-CDMA system. The length and order of regression algorithm are two key parameters, which affect the system performance significantly and the optimal values of which depend on the speed of mobile station. It is demonstrated that this improved method can track fading channel accurately and outperforms over classical methods substantially by selecting appropriate parameters of regression algorithm under a certain channel environment. 展开更多
关键词 regression algorithm. 16QAM. channel estimation
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Failure analysis on China power grid based on power law 被引量:1
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作者 Xiaofeng WENG Yiguang HONG +1 位作者 Ancheng XUE Shengwei MEI 《控制理论与应用(英文版)》 EI 2006年第3期235-238,共4页
This paper is concerned with the mechanism of blackouts in China power system from the viewpoint of self-organized criticality. By using two estimation algorithms of scaled window variance (SWV) and rescaled rangest... This paper is concerned with the mechanism of blackouts in China power system from the viewpoint of self-organized criticality. By using two estimation algorithms of scaled window variance (SWV) and rescaled rangestatistics (R/S), this paper studies the blackout data in China power system during 1988-1997. The result of analysis shows that the blackout data of 1994-1997 coincides well with the autocorrelation. Furthermore, it is found that the function of blackout probability vs. blackout size exhibits power law distribution. 展开更多
关键词 Power system BLACKOUT Power law estimation algorithm
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Histogram-Based Estimation of Distribution Algorithm:A Competent Method for Continuous Optimization 被引量:6
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作者 丁楠 周树德 孙增圻 《Journal of Computer Science & Technology》 SCIE EI CSCD 2008年第1期35-43,共9页
Designing efficient estimation of distribution algorithms for optimizing complex continuous problems is still a challenging task. This paper utilizes histogram probabilistic model to describe the distribution of popul... Designing efficient estimation of distribution algorithms for optimizing complex continuous problems is still a challenging task. This paper utilizes histogram probabilistic model to describe the distribution of population and to generate promising solutions. The advantage of histogram model, its intrinsic multimodality, makes it proper to describe the solution distribution of complex and multimodal continuous problems. To make histogram model more efficiently explore and exploit the search space, several strategies are brought into the algorithms: the surrounding effect reduces the population size in estimating the model with a certain number of the bins and the shrinking strategy guarantees the accuracy of optimal solutions. Furthermore, this paper shows that histogram-based EDA (Estimation of distribution algorithm) can give comparable or even much better performance than those predominant EDAs based on Gaussian models. 展开更多
关键词 evolutionary algorithm estimation of distribution algorithm histogram probabilistic model surrounding effect shrinking strategy
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Joint Analysis Method for Major Genes Controlling Multiple Correlated Quantitative Traits 被引量:5
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作者 XIAO Jing WANG Xue-feng HU Zhi-qiu TANG Zai-xiang SUI Jiong-ming LI Xin XU Chen-wu 《Agricultural Sciences in China》 CAS CSCD 2006年第3期179-187,共9页
Based on the major gene and polygene mixed inheritance model for multiple correlated quantitative traits, the authors proposed a new joint segregation analysis method of major gene controlling multiple correlated quan... Based on the major gene and polygene mixed inheritance model for multiple correlated quantitative traits, the authors proposed a new joint segregation analysis method of major gene controlling multiple correlated quantitative traits, which include major gene detection and its effect and variation estimation. The effect and variation of major gene are estimated by the maximum likelihood method implemented via expectation-maximization (EM) algorithm. Major gene is tested with the likelihood ratio (LR) test statistic. Extensive simulation studies showed that joint analysis not only increases the statistical power of major gene detection but also improves the precision and accuracy of major gene effect estimates. An example of the plant height and the number of tiller of F2 population in rice cross Duonieai x Zhonghua 11 was used in the illustration. The results indicated that the genetic difference of these two traits in this cross refers to only one pleiotropic major gene. The additive effect and dominance effect of the major gene are estimated as -21.3 and 40.6 cm on plant height, and 22.7 and -25.3 on number of tiller, respectively. The major gene shows overdominance for plant height and close to complete dominance for number of tillers. 展开更多
关键词 multiple correlated quantitative traits major gene joint segregation analysis maximum likelihood estimation EM algorithm
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Intelligent Scheduling Controller Design for Networked Control Systems Based on Estimation of Distribution Algorithm 被引量:2
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作者 李洪波 孙增圻 +1 位作者 陈霸东 刘华平 《Tsinghua Science and Technology》 SCIE EI CAS 2008年第1期71-77,共7页
The use of communication networks in control loops has gained increasing attention in recent years due to its advantages and flexible applications. The network quality-of-service (QoS) in those socalled networked co... The use of communication networks in control loops has gained increasing attention in recent years due to its advantages and flexible applications. The network quality-of-service (QoS) in those socalled networked control systems always fluctuates due to changes of the traffic load and available network resources, This paper presents an intelligent scheduling controller design approach for a class of NCSs to handle network QoS variations, The sampling period and control parameters in the controller are simultaneously scheduled to compensate for the network QoS variations. The estimation of distribution algorithm is used to optimize the sampling period and control parameters for better performance. Compared with existing networked control methods, the controller has better ability to compensate for the network QoS variations and to balance network loads. Simulation results show that the plant setting time with the intelligent scheduling controller is reduced by about 64.0% for the medium network load and 49.1% for high network load and demonstrate the effectiveness of the proposed approaches. 展开更多
关键词 networked control systems (NCSs) estimation of distribution algorithm (EDA) network-induced delay packet dropout network quality-of-service (QoS) variation
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Estimation of distribution algorithm enhanced particle swarm optimization for water distribution network optimization 被引量:1
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作者 Xuewei QI Ke LI Walter D. POTTER 《Frontiers of Environmental Science & Engineering》 SCIE EI CAS CSCD 2016年第2期341-351,共11页
The optimization of a water distribution network (WDN) is a highly nonlinear, multi-modal, and constrained combinatorial problem. Particle swarm opti- mization (PSO) has been shown to be a fast converging algorith... The optimization of a water distribution network (WDN) is a highly nonlinear, multi-modal, and constrained combinatorial problem. Particle swarm opti- mization (PSO) has been shown to be a fast converging algorithm for WDN optimization. An improved estimation of distribution algorithm (EDA) using historic best positions to construct a sample space is hybridized with PSO both in sequential and in parallel to improve population diversity control and avoid premature conver- gence. Two water distribution network benchmark exam- ples from the literature are adopted to evaluate the performance of the proposed hybrid algorithms. The experimental results indicate that the proposed algorithms achieved the literature record minimum (6.081 MS) for the small size Hanoi network. For the large size Balerma network, the parallel hybrid achieved a slightly lower minimum (1.921M) than the current literature reported best minimum (1.923MC). The average number of evaluations needed to achieve the minimum is one order smaller than most existing algorithms. With a fixed, small number of evaluations, the sequential hybrid outperforms the parallel hybrid showing its capability for fast convergence. The fitness and diversity of the populations were tracked for the proposed algorithms. The track record suggests that constructing an EDA sample space with historic best positions can improve diversity control significantly. Parallel hybridization also helps to improve diversity control yet its effect is relatively less significant. 展开更多
关键词 particle swarm optimization (PSO) diversitycontrol estimation of distribution algorithm (EDA) waterdistribution network (WDN) premature convergence hybrid strategy
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Synthetic aperture sonar movement compensation algorithm based on time-delay and phase estimation 被引量:4
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作者 JIANG Nan SUN Dajun TIAN Tan(Harbin Engineering University Harbin 150001) 《Chinese Journal of Acoustics》 2003年第3期261-267,共7页
The effects of movement errors on imaging results of synthetic aperture sonar and the necessity of movement compensation are discussed. Based on analyzing so-called displaced phase center algorithm, an improved algori... The effects of movement errors on imaging results of synthetic aperture sonar and the necessity of movement compensation are discussed. Based on analyzing so-called displaced phase center algorithm, an improved algorithm is proposed. In this method, the time delay is estimated firstly, then the phase is estimated for the residual error, so that the range of movement error suited to the algorithm is extended to some extent. Some simulation results on computer and experimental results in the test tank using the proposed algorithm are given as well. 展开更多
关键词 TIME as for is Synthetic aperture sonar movement compensation algorithm based on time-delay and phase estimation been SAS that of into PING
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Large-Scale Estimation of Distribution Algorithms with Adaptive Heavy Tailed Random Pro jection Ensembles
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作者 Momodou L.Sanyang Ata Kabán 《Journal of Computer Science & Technology》 SCIE EI CSCD 2019年第6期1241-1257,共17页
We present new variants of Estimation of Distribution Algorithms (EDA) for large-scale continuous optimisation that extend and enhance a recently proposed random projection (RP) ensemble based approach. The main novel... We present new variants of Estimation of Distribution Algorithms (EDA) for large-scale continuous optimisation that extend and enhance a recently proposed random projection (RP) ensemble based approach. The main novelty here is to depart from the theory of RPs that require (sub-)Gaussian random matrices for norm-preservation, and instead for the purposes of high-dimensional search we propose to employ random matrices with independent and identically distributed entries drawn from a t-distribution. We analytically show that the implicitly resulting high-dimensional covariance of the search distribution is enlarged as a result. Moreover, the extent of this enlargement is controlled by a single parameter, the degree of freedom. For this reason, in the context of optimisation, such heavy tailed random matrices turn out to be preferable over the previously employed (sub-)Gaussians. Based on this observation, we then propose novel covariance adaptation schemes that are able to adapt the degree of freedom parameter during the search, and give rise to a flexible approach to balance exploration versus exploitation. We perform a thorough experimental study on high-dimensional benchmark functions, and provide statistical analyses that demonstrate the state-of-the-art performance of our approach when compared with existing alternatives in problems with 1000 search variables. 展开更多
关键词 covariance adaptation estimation of distribution algorithm random projection ensemble T-DISTRIBUTION
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Using Markov Chain Based Estimation of Distribution Algorithm for Model-Based Safety Analysis of Graph Transformation
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作者 Einollah Pira 《Journal of Computer Science & Technology》 SCIE EI CSCD 2021年第4期839-855,共17页
The ability to assess the reliability of safety-critical systems is one of the most crucial requirements in the design of modern safety-critical systems where even a minor failure can result in loss of life or irrepar... The ability to assess the reliability of safety-critical systems is one of the most crucial requirements in the design of modern safety-critical systems where even a minor failure can result in loss of life or irreparable damage to the environment.Model checking is an automatic technique that verifies or refutes system properties by exploring all reachable states(state space)of a model.In large and complex systems,it is probable that the state space explosion problem occurs.In exploring the state space of systems modeled by graph transformations,the rule applied on the current state specifies the rule that can perform on the next state.In other words,the allowed rule on the current state depends only on the applied rule on the previous state,not the ones on earlier states.This fact motivates us to use a Markov chain(MC)to capture this type of dependencies and applies the Estimation of Distribution Algorithm(EDA)to improve the quality of the MC.EDA is an evolutionary algorithm directing the search for the optimal solution by learning and sampling probabilistic models through the best individuals of a population at each generation.To show the effectiveness of the proposed approach,we implement it in GROOVE,an open source toolset for designing and model checking graph transformation systems.Experimental results confirm that the proposed approach has a high speed and accuracy in comparison with the existing meta-heuristic and evolutionary techniques in safety analysis of systems specified formally through graph transformations. 展开更多
关键词 safety analysis model checking Markov chain estimation of distribution algorithm graph transformation system
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Trabecular spacing estimation based on quadratic transformation algorithm
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作者 XU Yiwen HOU Li +4 位作者 SHU Xiao WU Guangli LIU Chengcheng XU Kailiang TA De'an 《Chinese Journal of Acoustics》 CSCD 2015年第2期177-185,共9页
The quadratic transformation method is proposed to estimate the trabecular spac- ing (Tb.Sp), an important index for osteoporosis diagnosis. The performance of this algorithm was investigated by scatter model, two-d... The quadratic transformation method is proposed to estimate the trabecular spac- ing (Tb.Sp), an important index for osteoporosis diagnosis. The performance of this algorithm was investigated by scatter model, two-dimension finite difference time domain (2D-FDTD) simulation and in vitro experiments of bovine cancellous bone specimens. Comparing with the other four methods autoregressive cepstrum (AR), adaptive filter- autoregressive cepstral (AFAR), inverse filter-autoregressive eepstrum (InvAR), and simplified inverse filter tracking (SIFT), quadratic transformation is much more stable and accurate. The results demonstrated that quadratic transformation is a great algorithm for Tb.SD estimation. 展开更多
关键词 FDTD SIFT Trabecular spacing estimation based on quadratic transformation algorithm
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High accuracy eigensolution and its extrapolation for potential equations
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作者 程攀 黄晋 曾光 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第12期1527-1536,共10页
From the potential theorem, the fundamental boundary eigenproblems can be converted into boundary integral equations (BIEs) with the logarithmic singularity. In this paper, mechanical quadrature methods (MQMs) are... From the potential theorem, the fundamental boundary eigenproblems can be converted into boundary integral equations (BIEs) with the logarithmic singularity. In this paper, mechanical quadrature methods (MQMs) are presented to obtain the eigensolutions that are used to solve Laplace's equations. The MQMs possess high accuracy and low computation complexity. The convergence and the stability are proved based on Anselone's collective and asymptotical compact theory. An asymptotic expansion with odd powers of the errors is presented. By the h3-Richardson extrapolation algorithm (EA), the accuracy order of the approximation can be greatly improved, and an a posteriori error estimate can be obtained as the self-adaptive algorithms. The efficiency of the algorithm is illustrated by examples. 展开更多
关键词 potential equation mechanical quadrature method Richardson extrapolation algorithm a posteriori error estimate
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