Chaos Synchronization: A Lagrange Programming Network Approach

Suykens, Johan A. K.; Vandewalle, Joos

doi:10.1142/s0218127400000566

Cited by 5 publications

(5 citation statements)

References 21 publications

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“…Based on the phase space reconstruction theory, we can obtain the following training samples set:S={(x t , y t )}(x t =[x(t), x(t+1),…,x(t+m-1)]∈R m , y t =[x(t+1)]∈R). In accordance with the LSSVM regression modeling [1] , the online prediction modeling of BFG output is to solve the following model in a high-dimension feature space F composed of m'-dimension ( ) x ϕ mapped by the m-dimension input.…”

Section: Online Prediction Of Bfg Outputmentioning

confidence: 99%

“…In recent years, least squares support vector machine [1] (LSSVM)based on statistical learning theory has emerged as a paradigm for time series forecasting to many practical problems [2][3][4], which characterizes with the rapid small-sample learning process and excellent model generalization performance. Based on the great quantity of production data of BFG output in practice, time series forecasting method is a sort of effective attempt to solve the prediction problem of BFG output.…”

Section: Introductionmentioning

confidence: 99%

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An Online Prediction Model for BFG Output in Steel Industry

Zhang

Zhao

2012

AMR

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The output prediction of blast furnace gas (BFG), influenced by many complex production factors, is a very important and difficult problem concerning the byproduct gas balance in steel industry. A new online least squares support vector machine (LSSVM) prediction model is proposed in this paper, in which the training data is filtered by an improved empirical mode decomposition threshold filtering (IEMDTF). The model is solved and optimized by an online learning algorithm and an online bayesian parameters optimization, respectively. The experimental results using practical BFG output data from BaoSteel Co. Ltd., China show the proposed model is effective and enable to offer reasonable gas balance scheduling for operators.

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Section: Online Prediction Of Bfg Outputmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Online Prediction Model for BFG Output in Steel Industry

Zhang

Zhao

2012

AMR

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“…Additionally, compared with support vector machines (SVM), LS-SVM has overcame the shortcoming of higher computational burden by solving linear equations, and as SVM, the solution of LS-SVM is always unique and globally optimal. With these advantages, LS-SVM has been successfully used in time serials prediction, classification and nonlinear modeling [6,7].…”

Section: Introductionmentioning

confidence: 99%

Sensor Dynamic Modeling Based on LS-SVM and NGA

Wang

Feng

Shida

2008

KEM

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Least squares support vector machine (LS-SVM) combined with niche genetic algorithm (NGA) are proposed for nonlinear sensor dynamic modeling. Compared with neural networks, the LS-SVM can overcome the shortcomings of local minima and over fitting, and has higher generalization performance. The sharing function based niche genetic algorithm is used to select the LS-SVM parameters automatically. The effectiveness and reliability of this method are demonstrated in two examples. The results show that this approach can escape from the blindness of man-made choice of LS-SVM parameters. It is still effective even if the sensor dynamic model is highly nonlinear.

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“…The CLM method is related to Lagrange programming network approaches for chaos synchronization [Suykens & Vandewalle, 2000], where identical or generalized synchronization constraints are imposed on dynamical systems. CLMs also fit within the framework of Cellular Neural Networks (CNN) [Chua & Roska, 1993;Chua et al, 1995;Chua, 1998].…”

Section: Introductionmentioning

confidence: 99%

“…Synchronization theory has been intensively studied within the area of chaotic systems and secure communications [Chen & Dong, 1998;Pecora & Carroll, 1990;Suykens et al, 1996Suykens et al, , 1997Suykens et al, , 1998Wu & Chua, 1994]. The CLM method is related to Lagrange programming network approaches for chaos synchronization [Suykens & Vandewalle, 2000], where identical or generalized synchronization constraints are imposed on dynamical systems. CLMs also fit within the framework of Cellular Neural Networks (CNN) [Chua & Roska, 1993;Chua et al, 1995;Chua, 1998].…”

Section: Introductionmentioning

confidence: 99%

Intelligence and Cooperative Search by Coupled Local Minimizers

Suykens

Vandewalle

Moor

2001

Int. J. Bifurcation Chaos

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We show how coupling of local optimization processes can lead to better solutions than multi-start local optimization consisting of independent runs. This is achieved by minimizing the average energy cost of the ensemble, subject to synchronization constraints between the state vectors of the individual local minimizers. From an augmented Lagrangian which incorporates the synchronization constraints both as soft and hard constraints, a network is derived wherein the local minimizers interact and exchange information through the synchronization constraints. From the viewpoint of neural networks, the array can be considered as a Lagrange programming network for continuous optimization and as a cellular neural network (CNN). The penalty weights associated with the soft state synchronization constraints follow from the solution to a linear program. This expresses that the energy cost of the ensemble should maximally decrease. In this way successful local minimizers can implicitly impose their state to the others through a mechanism of master-slave dynamics resulting into a cooperative search mechanism. Improved information spreading within the ensemble is obtained by applying the concept of small-world networks. We illustrate the new optimization method on two different problems: supervised learning of multilayer perceptrons and optimization of Lennard-Jones clusters. The initial distribution of the local minimizers plays an important role. For the training of multilayer perceptrons this is related to the choice of the prior on the interconnection weights in Bayesian learning methods. Depending on the choice of this initial distribution, coupled local minimizers (CLM) can avoid overfitting and produce good generalization, i.e. reach a state of intelligence. In potential energy surface optimization of Lennard-Jones clusters, this choice is equally important. In this case it can be related to considering a confining potential. This work suggests, in an interdisciplinary context, the importance of information exchange and state synchronization within ensembles, towards issues as evolution, collective behaviour, optimality and intelligence.2

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Chaos Synchronization: A Lagrange Programming Network Approach

Cited by 5 publications

References 21 publications

An Online Prediction Model for BFG Output in Steel Industry

An Online Prediction Model for BFG Output in Steel Industry

Sensor Dynamic Modeling Based on LS-SVM and NGA

Intelligence and Cooperative Search by Coupled Local Minimizers

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