Search results for "lcsh:Mathematics"
showing 10 items of 384 documents
On the application of the generalized means to construct multiresolution schemes satisfying certain inequalities proving stability
2021
Multiresolution representations of data are known to be powerful tools in data analysis and processing, and they are particularly interesting for data compression. In order to obtain a proper definition of the edges, a good option is to use nonlinear reconstructions. These nonlinear reconstruction are the heart of the prediction processes which appear in the definition of the nonlinear subdivision and multiresolution schemes. We define and study some nonlinear reconstructions based on the use of nonlinear means, more in concrete the so-called Generalized means. These means have two interesting properties that will allow us to get associated reconstruction operators adapted to the presence o…
Study on Support Vector Machine-Based Fault Detection in Tennessee Eastman Process
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/836895 Open Access This paper investigates the proficiency of support vector machine (SVM) using datasets generated by Tennessee Eastman process simulation for fault detection. Due to its excellent performance in generalization, the classification performance of SVM is satisfactory. SVM algorithm combined with kernel function has the nonlinear attribute and can better handle the case where samples and attributes are massive. In addition, with forehand optimizing the parameters using the cross-validation technique, SVM can produce high accuracy i…
A mahalanobis hyperellipsoidal learning machine class incremental learning algorithm
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/894246 Open Access A Mahalanobis hyperellipsoidal learning machine class incremental learning algorithm is proposed. To each class sample, the hyperellipsoidal that encloses as many as possible and pushes the outlier samples away is trained in the feature space. In the process of incremental learning, only one subclassifier is trained with the new class samples. The old models of the classifier are not influenced and can be reused. In the process of classification, considering the information of sample's distribution in the feature space, the Ma…
Research on Vocabulary Sizes and Codebook Universality
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/697245 Open Access Codebook is an effective image representation method. By clustering in local image descriptors, a codebook is shown to be a distinctive image feature and widely applied in object classification. In almost all existing works on codebooks, the building of the visual vocabulary follows a basic routine, that is, extracting local image descriptors and clustering with a user-designated number of clusters. The problem with this routine lies in that building a codebook for each single dataset is not efficient. In order to deal with th…
The Finding and Dynamic Detection of Opinion Leaders in Social Network
2014
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2014/328407 It is valuable for the real world to find the opinion leaders. Because different data sources usually have different characteristics, there does not exist a standard algorithm to find and detect the opinion leaders in different data sources. Every data source has its own structural characteristics, and also has its own detection algorithm to find the opinion leaders. Experimental results show the opinion leaders and theirs characteristics can be found among the comments from the Weibo social network of China, which is like Facebook…
Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness
2020
Non-local time evolution of material stress/strain is often referred to as material hereditariness. In this paper, the widely used non-linear approach to single integral time non-local mechanics named quasi-linear approach is proposed in the context of fractional differential calculus. The non-linear model of the springpot is defined in terms of a single integral with separable kernel endowed with a non-linear transform of the state variable that allows for the use of Boltzmann superposition. The model represents a self-similar hierarchy that allows for a time-invariance as the result of the application of the conservation laws at any resolution scale. It is shown that the non-linear spring…
An Adaptive Metamodel-Based Optimization Approach for Vehicle Suspension System Design
2014
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2014/965157 The performance index of a suspension system is a function of the maximum and minimum values over the parameter interval. Thus metamodel-based techniques can be used for designing suspension system hardpoints locations. In this study, an adaptive metamodel-based optimization approach is used to find the proper locations of the hardpoints, with the objectives considering the kinematic performance of the suspension. The adaptive optimization method helps to find the optimum locations of the hardpoints efficiently as it may be unachie…
Quantized State-Feedback Stabilization for Delayed Markovian Jump Linear Systems with Generally Incomplete Transition Rates
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/961925 open Access This paper is concerned with the robust quantized state-feedback controller design problem for a class of continuous-time Markovian jump linear uncertain systems with general uncertain transition rates and input quantization. The uncertainties under consideration emerge in both system parameters and mode transition rates. This new uncertain model is more general than the existing ones and can be applicable to more practical situations because each transition rate can be completely unknown or only its estimate value is known. B…
Observer-Based Robust Control for Switched Stochastic Systems with Time-Varying Delay
2013
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/320703 Open Access This paper investigates the problem of observer-based robust H ∞ control for a class of switched stochastic systems with time-varying delay. Based on the average dwell time method, an exponential stability criterion for switched stochastic delay systems is proposed. Then, H ∞ performance analysis and observer-based robust H ∞ controller design for the underlying systems are developed. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.
Stabilization and controller design of 2D discrete switched systems with state delays under asynchronous switching
2013
Published version of a paper from the journal: Abstract and Applied Analysis. Also available from Hindawi:http://dx.doi.org/10.1155/2013/961870. Open Access This paper is concerned with the problem of robust stabilization for a class of uncertain two-dimensional (2D) discrete switched systems with state delays under asynchronous switching. The asynchronous switching here means that the switching instants of the controller experience delays with respect to those of the system. The parameter uncertainties are assumed to be norm-bounded. A state feedback controller is proposed to guarantee the exponential stability. The dwell time approach is utilized for the stability analysis and controller …