On the Complexity of Optimization over the Standard Simplex

We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard simplex.This extends an earlier result by De Klerk, Laurent and Parrilo [A PTAS for the minimization of polynomials of fixed degree over the simplex, Theoretical Computer Science, to appear.]global optimization;standard simplex;PTAS;multivariate Bernstein approximation;semidefinite programming

On the Complexity of Optimization over the Standard Simplex

We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard simplex.This extends an earlier result by De Klerk, Laurent and Parrilo [A PTAS for the minimization of polynomials of fixed degree over the simplex, Theoretical Computer Science, to appear.]

Artificial Neural Networks (ANNs) as a Novel Modeling Technique in Tribology

In the present paper, artificial neural networks (ANNs) are considered from a mathematical modeling point of view. A short introduction to feedforward neural networks is outlined, including multilayer perceptrons (MLPs) and radial basis function (RBF) networks. Examples of their applications in tribological studies are given, and important features of the data-driven modeling paradigm are discussed

Variable selection for wind turbine condition monitoring and fault detection system

With the fast growth in wind energy, the performance and reliability of the wind power generation system has become a major issue in order to achieve cost-effective generation. Integration of condition monitoring system (CMS) in the wind turbine has been considered as the most viable solution, which enhances maintenance scheduling and achieving a more reliable system. However, for an effective CMS, large number of sensors and high sampling frequency are required, resulting in a large amount of data to be generated. This has become a burden for the CMS and the fault detection system. This thesis focuses on the development of variable selection algorithm, such that the dimensionality of the monitoring data can be reduced, while useful information in relation to the later fault diagnosis and prognosis is preserved. The research started with a background and review of the current status of CMS in wind energy. Then, simulation of the wind turbine systems is carried out in order to generate useful monitoring data, including both healthy and faulty conditions. Variable selection algorithms based on multivariate principal component analysis are proposed at the system level. The proposed method is then further extended by introducing additional criterion during the selection process, where the retained variables are targeted to a specific fault. Further analyses of the retained variables are carried out, and it has shown that fault features are present in the dataset with reduced dimensionality. Two detection algorithms are then proposed utilising the datasets obtained from the selection algorithm. The algorithms allow accurate detection, identification and severity estimation of anomalies from simulation data and supervisory control and data acquisition data from an operational wind farm. Finally an experimental wind turbine test rig is designed and constructed. Experimental monitoring data under healthy and faulty conditions is obtained to further validate the proposed detection algorithms

Global optimisation of neural networks using a deterministic hybrid approach

Selection of the topology of a neural network and correct parameters for the learning algorithm is a tedious task for designing an optimal artificial neural network, which is smaller, faster and with a better generalization performance. In this paper we introduce a recently developed cutting angle method (a deterministic technique) for global optimization of connection weights. Neural networks are initially trained using the cutting angle method and later the learning is fine-tuned (meta-learning) using conventional gradient descent or other optimization techniques. Experiments were carried out on three time series benchmarks and a comparison was done using evolutionary neural networks. Our preliminary experimentation results show that the proposed deterministic approach could provide near optimal results much faster than the evolutionary approach.<br /